
    [No. S044870.
    May 11, 1998.]
    THE PEOPLE, Plaintiff and Respondent, v. SERGIO VENEGAS, Defendant and Appellant.
    
      Counsel
    Fern M. Laethem, State Public Defender, under appointment by the Supreme Court, Valerie Hriciga, Deputy State Public Defender, and Donnalee H. Huffman for Defendant and Appellant.
    Linda Robertson, Alan Crivaro and John W. Lawrence as Amici Curiae on behalf of Defendant and Appellant.
    Daniel E. Lungren, Attorney General, George Williamson, Chief Assistant Attorney General, Robert R. Anderson, Assistant Attorney General, Doris A. Calandra, Frederick R. Millar, Jr., and Jo Graves, Deputy Attorneys General, for Plaintiff and Respondent.
    Thomas J. Orloff, District Attorney (Alameda), Rockne P. Harmon, Deputy District Attorney, Kent S. Scheidegger, Charles L. Hobson, Lepper, Schaefer & Harrington, Gary M. Lepper, Keith E. Petersen Inman and Matthew P. Harrington as Amici Curiae on behalf of Plaintiff and Respondent.
   Opinion

BAXTER, J.

I. Introduction

Defendant was convicted of rape by a jury that heard incriminating evidence based on forensic analysis of deoxyribonucleic acid (DNA). The prosecution’s evidence indicated (1) that defendant’s DNA profile matched the DNA profile of semen recovered from the victim’s body and from bedding at the crime scene, and (2) that the probability of a match between those DNA profiles and the profile of a person chosen at random from the general population was 1 in 65,000.

The Court of Appeal reversed the conviction for prejudicial error in the admission of the DNA evidence, basing that error on two grounds: (1) failure to prove general scientific acceptance of the methodology used by the Federal Bureau of Investigation (FBI) in performing its DNA analysis, and (2) lack of compliance by the FBI with procedures recommended in 1992 by the National Research Council (NRC) for determining the statistical probability of a random match. We conclude reversal of the conviction is required on the second, but not on the first, of those two grounds, and that, accordingly, the judgment of the Court of Appeal should be affirmed.

The first ground for reversal stated by the Court of Appeal was based on the correct premise that the admissibility of evidence produced by a new scientific technique requires a preliminary showing of the technique’s general acceptance in the relevant scientific community. (People v. Kelly (1976) 17 Cal.3d 24, 30 [130 Cal.Rptr. 144, 549 P.2d 1240] (Kelly); People v. Leahy (1994) 8 Cal.4th 587, 593-604 [34 Cal.Rptr.2d 663, 882 P.2d 321]; Frye v. United States (D.C. Cir. 1923) 293 F. 1013 [54 App.D.C. 46, 34 A.L.R. 145] (Frye).) An important corollary of that rule, however, is that if a published appellate decision in a prior case has already upheld the admission of evidence based on such a showing, that decision becomes precedent for subsequent trials in the absence of evidence that the prevailing scientific opinion has materially changed. (Kelly, supra, 17 Cal.3d at p. 32.) Prior to the present trial, two California appellate decisions—People v. Axell (1991) 235 Cal.App.3d 836 [1 Cal.Rptr.2d 411] (Axell), and People v. Barney (1992) 8 Cal.App.4th 798 [10 Cal.Rptr.2d 731] (Barney)—had confirmed the general scientific acceptance of restriction fragment length polymorphism (RFLP) analysis, the technique used by the FBI to generate and compare the DNA profiles in this case. Nonetheless, the Court of Appeal held the prosecution should have been required to prove anew that the relevant scientific community either accepts the reliability of the FBI’s particular RFLP methodology as such, or considers it essentially the same as the RFLP methodology utilized by Cellmark Diagnostics (Cellmark) and upheld in Axell.

We disagree with the Court of Appeal’s first stated ground for reversal. Apart from procedures for determining the statistical probability of a random match, the methodology used here, as described in testimony of the FBI agent in charge, appears indistinguishable from the RFLP methodology described and upheld, in Axell, supra, 235 Cal.App.3d 836, and Barney, supra, 8 Cal.App.4th 798. In the absence of proof of any material scientific distinction between the two methodologies, therefore, the trial court could properly rely on Axell as establishing general scientific acceptance of the FBI’s RFLP methodology used in this case to elicit and compare the DNA profiles of the evidentiary samples.

In contrast, we conclude the Court of Appeal properly upheld the trial court’s finding of a scientific consensus that the NRC’s “modified ceiling” approach or method—used to calculate the statistical probabilities of a match between the evidentiary samples and the DNA of an unrelated person chosen at random from the general population—is forensically reliable, in that from the scientifically based range of probabilities it selects the figures that most favor the accused, and therefore cannot furnish a basis on which to invalidate the admissibility of such evidence on motion of the accused. The Court of Appeal also held, however, that the FBI had failed in one material respect to follow correct scientific procedures in implementing the NRC’s methodology. As will be explained, we agree that the FBI’s implementation was defective, but in a somewhat different respect from that with which the Court of Appeal took issue. We further agree with the Court of Appeal’s conclusion that the FBI’s failure to use correct procedures in this case required exclusion of the DNA evidence, and that the erroneous admission of such evidence prejudiced defendant, requiring that the trial court’s judgment be reversed.

II. Facts and Procedural Background

Defendant was convicted and sentenced to 65 years of imprisonment on multiple counts of rape and related offenses, committed during the early afternoon of November 2, 1989, at the Red Lion Inn in Bakersfield. The victim, a hotel guest, had worked that morning as a stenographic reporter for the initial session of a conference being held in one of the hotel’s meeting rooms. When the session ended, she packed up her briefcase and stenography machine and, at approximately 11:45 a.m., took the five-minute walk along corridors, through the lobby, across the pool area, and through double glass doors down a long hallway to her room.

The double doors were opened for her by a Hispanic man, almost six feet tall, wearing a light T-shirt and light denim pants. Reaching her room, she set the stenography machine down in the hallway, unlocked the door, and put her briefcase inside. Just as she turned back to bring in the machine, the man entered the room and pushed her to the floor. He said he had a knife and ordered her to keep silent and to not look at him. He remained in the room for about two hours, committing the charged sexual offenses, cutting her with the knife, hitting her with his hand, ransacking her belongings, and binding her tightly with bedding and electrical cord. A hotel housekeeper discovered her plight about 2 p.m. The victim was unable to see the man’s face during her ordeal. Thereafter, at a live lineup, she was unable to positively identify defendant or any other particular individual as her assailant.

Earlier that morning, at approximately 10:45 a.m., defendant had appeared at the hotel’s human resources department, located upstairs from the meeting rooms, to apply for employment. The administrative assistant gave him a written application and invited him to sit and fill it out at a table outside her office. She said she would see him again after she completed a scheduled orientation tour of the premises for a group of new employees. When she left her office about 11:00 a.m., he was seated at the table, but during the tour she was surprised to see him in a different part of the hotel, descending an outdoor stairway located near the hallway leading to the victim’s room. When the tour was over, at approximately 11:30 a.m., he was again seated outside her office. He handed her the filled-in application form (which is in evidence); she interviewed him for 15 or 20 minutes; and he departed. She testified he was dressed in a white T-shirt, gray cotton pants, and white tennis shoes, and that he also wore a nylon jacket and blue baseball cap that he removed for the interview.

The victim was taken from the crime scene to a hospital, where medical personnel examined her, observed her bruises and lacerations, took vaginal swabs and samples of her hair, blood and saliva, and removed a foreign pubic hair from her vagina. She also reported she had engaged in consensual intercourse with a friend, M.M., two days earlier.

Defendant was brought to a police interview room on November 15, where he was asked for samples of his hair, saliva, and blood. He refused at first, but gave the hair and saliva samples the next day. A sample of his blood was taken on February 1, 1990, pursuant to a search warrant. At the crime scene police could find no fingerprints other than those of the victim. They collected some, bedding and other evidentiary items for stain (blood, semen, saliva) analysis. They also obtained a blood sample from the victim’s friend, M.M.

A county criminalist testified the victim could not have been the source of the pubic hair found in her vagina; that the hair was similar to, but not exactly the same as, defendant’s hair samples; and that the dissimilarities were insufficient to exclude it as originating from defendant. Another criminalist tested the vaginal swabs and some semen stains found on the bedspread for “genetic markers,” seeking to compare them with the markers found in the saliva and blood samples from defendant and the victim. Although no markers could be drawn from the swabs, two of the semen stains yielded markers consistent with defendant’s being their source.

On November 27, 1990, the police sent the vaginal swabs, swatches of the bedspread containing the two semen stains, and blood samples from the victim, defendant, and M.M. (the victim’s friend), to the FBI laboratory in Washington, D.C., for DNA testing. In April 1991, the FBI returned the samples, reporting that defendant’s DNA profile “matched”—i.e., was consistent with—the DNA profiles from the swabs and one of the stains, and that the probability of selecting an unrelated individual at random from the Hispanic population with a profile that also matched the samples was approximately 1 in 31,000.

Defendant was then charged with the crimes described above. He pleaded not guilty and moved for an evidentiary hearing (Evid. Code, § 402 et seq.) to determine what, if any, Kelly/Frye foundational showing would be required for admission of the DNA test results, including the statistical probabilities of a random match, into evidence. The motion was heard, where-after the trial court granted a Kelly/Frye hearing “with regard to the statistical methodology.” At the conclusion of the five-day hearing, the trial court ruled that the prosecution would be allowed to present evidence of random match statistical probabilities under specified restrictions explained below.

On the same day the trial court made its ruling (Oct. 13, 1992), the present Court of Appeal filed its decision in another DNA case—People v. Pizarro (1992) 10 Cal.App.4th 57 [12 Cal.Rptr.2d 436] (Pizarro)—wherein it required the prosecution to demonstrate general scientific acceptance of the FBI’s particular DNA methodology through impartial expert testimony, notwithstanding that Axell, supra, 235 Cal.App.3d 836, had already confirmed the general scientific acceptance of the highly similar Cellmark RFLP methodology. Relying on Pizarro, defendant here petitioned for writ relief from the trial court’s ruling. The Court of Appeal denied the petition on the ground defendant had failed to demonstrate he was without a remedy in the trial court.

In light of that denial order, the trial court granted defendant’s request to reopen the Kelly/Frye hearing for further cross-examination of Audrey Lynch, the FBI agent in charge of the DNA testing, and for testimony of a defense expert, Dr. Randell Libby, on the matter of whether the FBI had followed correct scientific procedures. The reopened hearing did not persuade the court to place any further restrictions on the scope of the DNA evidence admissible before the jury. The trial proceeded to jury verdict, and defendant was convicted on all counts as charged. As noted, the Court of Appeal reversed the judgment of conviction. We granted the Attorney General’s petition for review.

III. Overview of RFLP Analysis

“DNA analysis ... is a process by which characteristics of a suspect’s genetic structure are identified, are compared with samples taken from a crime scene, and, if there is a match, are subjected to statistical analysis to determine the frequency with which they occur in the general population.” (Barney, supra, 8 Cal.App.4th at p. 805.) The DNA profiles in this case were created through a method known as RFLP (restriction fragment length polymorphism), one of the two systems now widely used for forensic DNA typing. To clarify our discussion, we begin with a brief overview of DNA theory and RFLP methodology.

A. DNA Theory and RFLP Analysis

Virtually each one of the trillions of cells in the human body, with the exception of red blood cells, has a nucleus containing the DNA that underlies the person’s entire genetic makeup. The DNA is organized into 23 pairs of homologous chromosomes, 1 chromosome in each pair being inherited from the mother and the other from the father. (1996 NRC Rep., supra, pp. 60-61.) A chromosome is a long DNA molecule in the shape of a spiral staircase. (1992 NRC Rep., supra, p. 33.) “It consists of two parallel spiral sides (i.e., a double helix) composed of repeated sequences of phosphate and sugar. The two sides are connected by a series of rungs, which constitute the steps in the staircase. Each rung consists of a pair of chemical components called bases. There are four types of bases—adenine (A), cytosine (C), guanine (G), and thymine (T). A will pair only with T, and C will pair only with G.” (Barney, supra, 8 Cal.App.4th at p. 805.) There are over 3 billion base pairs in the 46 chromosomes of a single human cell. When a cell reproduces, the parallel sides, or strands, of its DNA separate, and the bases of each strand pair off with the complementary bases of a new strand. (1996 NRC Rep., supra, p. 63.)

“A person’s individual genetic traits are determined by the sequence of base pairs in his or her DNA molecules. That sequence is the same in each molecule regardless of its source (e.g., hair, skin, blood, or semen) and is unique to the individual. Except for identical twins, no two human beings have identical sequences of all base pairs. [^] In most portions of DNA, the sequence of base pairs is the same for everyone. Those portions are responsible for shared traits such as arms and legs. In certain regions, however, the sequence of base pairs varies from person to person, resulting in individual traits. A region—or locus—that is variable is said to be polymorphic.” (Barney, supra, 8 Cal.App.4th at pp. 805-806.)

The DNA sequences that determine a person’s genetic traits are contained in the 50,000 to 100,000 genes making up his or her genetic code. (See 1992 NRC Rep., supra, p. 33.) Human DNA also includes other sequences that are noncoding, i.e., they serve no known genetic function. Compared to the genes, the noncoding sequences are more likely to be polymorphic since their individual variation is less constrained by forces of selection. (Id. at p. 34; 1996 NRC Rep., supra, p. 63.)

Because there is no practical way to sequence all three billion base pairs in a person’s DNA, forensic scientists seek to identify individuals through variations in their base-pair sequences at polymorphic DNA locations (loci). Each variation in sequence is called an “allele.” The greatest variations are found at noncoding loci containing “variable number tandem repeats” (VNTR’s) in which the same sequence of base pairs is repeated successively for numbers of times that differ from person to person. “This variance is what makes DNA analysis possible. In effect, the lengths of sets of multiple (usually eight) polymorphic fragments (or VNTR alleles) obtained from a suspect’s DNA and from crime scene samples are compared to see if any sets match . . . (Barney, supra, 8 Cal.App.4th at p. 806.) In the absence of a nonmatch that conclusively eliminates the suspect as the source of the crime scene sample, each match between alleles from the suspect and from the crime scene may be accorded statistical significance.

“There are three discrete steps in [RFLP] analysis as performed by the FBI . . . and by Cellmark . . . : (1) processing of DNA from the suspect and the crime scene to produce X-ray films [autorads] which indicate the lengths of the polymorphic fragments; (2) examination of the [autorads] to determine whether any sets of fragments match; and (3) if there is a match, determination of the match’s statistical significance.” (Barney, supra, 8 Cal.App.4th at p. 806, original italics.)

B. Processing DNA Samples and Generating Autorads

DNA processing through application of RFLP methodology to a DNA sample involves seven distinct substeps: extraction, restriction, electrophoresis, denaturing, “Southern transfer,” hybridization, and autoradiography. These component procedures were succinctly described in Barney, supra, 8 Cal.App.4th at pages 806-808.

First, “DNA is extracted from bodily material such as hair, skin, blood, or semen by application of chemical enzymes.” (Barney, supra, 8 Cal.App.4th at p. 806.)

Second, “The extracted DNA is ‘cut’ into thousands of fragments at specific points by application of restriction enzymes. The restriction enzymes act as ‘chemical scissors’ in that they sever the DNA at targeted base-pair sites. This substep gives its name to the overall DNA analytical process: restrictive fragment length polymorphism (RFLP) analysis.” {Barney, supra, 8 Cal.App.4th at p. 806.) The enzyme used by the FBI in this case was Hae III, which “cuts” the DNA at the restriction site GGCC, thereby producing millions of DNA fragments of widely varying lengths. (See 1996 NRC Rep., supra, p. 66.)

Third, “The DNA fragments are separated by size through a process called electrophoresis. The various sample fragments being tested are placed in separate lanes on one end of a gel slab and an electrical current is applied, causing the fragments to move across the gel. Shorter fragments move farther than longer fragments. Thus, at the completion of electrophoresis, the sample fragments are arrayed across the gel according to size, [ft In addition .to the sample fragments, other fragments called size markers, which have known base-pair lengths, are placed in separate lanes on the gel in order to facilitate measurement of the sample fragments. The array of size markers [or ‘sizing ladders’] across the gel provides points of comparison, which permit assessment of the base-pair lengths of the sample fragments.” {Barney, supra, 8 Cal.App.4th at pp. 806-807.) One or more lanes of a previously measured human DNA sample is also customarily included as a control for accuracy.

Fourth, “each DNA fragment is separated at its bases into two parts—i.e., is ‘unzipped’ into two single strands—through a chemical process called denaturing” {Barney, supra, 8 Cal.App.4th at p. 807; see also 1996 NRC Rep., supra, p. 67; 1992 NRC Rep., supra, p. 37.)

Fifth, “To facilitate handling of the DNA fragments, a nylon membrane is placed on the gel, and by wicking action the fragments are transferred to the membrane, becoming permanently fixed in their respective positions. This process is called Southern transfer (named for the scientist who developed it).” {Barney, supra, 8 Cal.App.4th at p. 807.)

Sixth and seventh, “The last two substeps [hybridization and autoradiography] enable visualization of the lengths of the sample DNA fragments by producing X-ray films [autoradiographs or autorads] which show the distance the fragments traveled as a result of electrophoresis.” {Barney, supra, 8 Cal.App.4th at p. 807.) As will be explained, the combination of those two substeps is performed four times.

In the hybridization substep, single-strand DNA fragments called “single-locus probes” (because they have known base-pair sequences that occur at only one location on DNA) are applied in a liquid solution to the nylon membrane. Each probe has been radioactively treated to make it susceptible to X-ray photography, and contains bits of single-strand DNA that seek out and bind themselves to all the unzipped fragments on the membrane containing a complementary base-pair sequence. The fragments can thereby be identified as belonging to a particular locus on a particular pair of chromosomes.

The membrane is then washed of all unbound probe and exposed to X-ray film, producing an autoradiograph (hereafter autorad) on which the bound probe shows up as one or two short dark bands in each lane, perpendicular to the DNA’s direction of movement through the gel. After completion of the first autorad, the probe is stripped from the membrane, which is then exposed to a second probe that seeks out DNA fragments at a different locus, usually on a different chromosome. A second autorad is produced; the second probe is stripped; and in the same manner, third and fourth probes are successively applied, leading to third and fourth autorads. The purpose of each autorad is to depict bands that reflect the size of the DNA fragments at the locus specific to the probe from which the autorad was produced. Normally there are two such bands for each sample, each band representing the fragment contributed by one of the parents. If the parents have contributed identical fragments at the locus in question, only one band will appear. In the former situation, the individual is said to be heterozygous as to that locus. In the latter case, the individual is said to be homozygous. (See 1996 NRC Rep., supra, p. 63.)

“The location of a band on the X-ray film indicates the distance a fragment traveled as a result of electrophoresis, and hence the length of the fragment. The size-marker fragments also appear on the films, enabling measurement of the base-pair lengths of the sample fragments. fi[] The end result of the processing substeps is a picture of a person’s DNA pattern . . . consisting] of a series of bands (usually eight) representative of a few selected bits of DNA . . . .” (Barney, supra, 8 Cal.App.4th at p. 808.)

C. Interpreting Autorads Through Application of “Match Criteria”

“The second step of DNA analysis is to compare the DNA patterns produced by the processing step in order to determine whether the suspect’s DNA pattern matches the DNA pattern of bodily material found at the crime scene. [^] First, the patterns are visually evaluated ... to determine whether there is a likely match. Most exclusions will be obvious, since the patterns will be noticeably different.” (Barney, supra, 8 Cal.App.4th at p. 808.)

If an exclusion is obvious on any of the autorads, there is a conclusive nonmatch of the samples. Otherwise, “the bands in the patterns are subjected to computer-assisted analysis to determine the length of the represented DNA fragments as measured in base-pair units. The measurements are taken by comparing the bands for the sample fragments with the bands for the size-marker fragments of known base-pair lengths.” (Barney, supra, 8 Cal.App.4th at p. 808.)

Because of. inherent limitations in the DNA processing system, it is not possible to obtain exact base-pair measurements of the sample DNA fragments. For that reason, forensic laboratories have developed DNA match criteria based on the variations they have experienced in repeated measurements of DNA from the same source. Those criteria determine the “match window”—or range of sizes—constructed around each band for purposes of declaring a “match.” For example, under the FBI’s match criterion of plus or minus 2.5 percent, the window around a band that measures 1,000 base pairs is from 975 to 1,025 base pairs. If the window of either band, or a single band, on one sample fails to overlap the window of the corresponding band on another sample, there is an exclusion of any match between the samples. If the windows of both bands, or of the single bands, of each sample overlap, there is a match at the locus disclosed by that probe.

Some conditions adverse to reliability of measurement may call for a determination that a match at that locus is inconclusive. That determination, however, does not invalidate matches at the other loci. There can be a match at multiple loci only if (1) the match criteria are met for all the bands at those loci, and (2) there is no locus at which a match of any band was excluded.

D. Use of Population Databases to Assess Significance of Match

Once a match at multiple loci has been declared, the next step is to determine its statistical significance. (Barney, supra, 8 Cal.App.4th at p. 809.) Unless a nonmatch between any band of the suspect’s DNA and the corresponding band of the questioned sample conclusively eliminates the suspect as the source of that sample, a match of one or more of the suspect’s bands with those of the sample places the suspect within a class of persons from whom the sample could have originated. The fact finder’s determination of guilt may then turn on the degree of probability that the suspect was indeed the source of the sample. That probability, however, will usually depend, not on the DNA findings alone, but on a combination of those findings together with other, non-DNA incriminating evidence. (See State v. Bloom (Minn. 1994) 516 N.W.2d 159, 162-163.)

The question properly addressed by the DNA analysis is therefore this: Given that the suspect’s known sample has satisfied the “match criteria,” what is the probability that a person chosen at random from the relevant population would likewise have a DNA profile matching that of the evidentiary sample? That probability is usually expressed as a fraction—i.e., the probability that one out of a stated number of persons in the population (e.g., 1 out of 100,000) would match the DNA profile of the evidentiary sample in question. A greater probability, that is to say, a fraction with a smaller denominator (e.g., 1 out of 10,000), would tend to favor the suspect by increasing the probability that one or more other persons has a DNA profile matching the evidentiary sample.

To assess the probability in question, “the FBI and Cellmark calculate how frequently each pair of bands produced by one probe is found in a target population.” (Barney, supra, 8 Cal.App.4th at p. 809.) For this purpose, those and other forensic laboratories use one or more population databases containing measurements of the DNA fragments of several hundred persons at each of the loci reached by the probes. The samples from which those measurements are derived come, from such varied sources as blood banks, hospitals, clinics, genetics laboratories, and law enforcement personnel. (See 1996 NRC Rep., supra, p. 126.)

E. Comparing Individual Band Size With Population Database

Bands— “Binning ”

Like the base-pair measurements of the evidentiary bands, the measurements of bands in a comparative database are, by their nature, inexact. For comparison purposes, therefore, the database bands are sorted into ranges of size called “bins.” There are two kind's: “floating bins” and “fixed bins.”

A floating bin, constructed for each forensic comparison, is a range of sizes at least as large as the match window, centered on the measured size of the evidentiary band in question. The evidentiary band’s frequency, i.e., the probability of its appearing in the DNA profile of a randomly selected member of the population underlying the database, is calculated from the ratio of the number of bands in the bin to the total number of bands in the database for that locus.

Fixed bins, on the other hand, compartmentalize the entire spectrum of VNTR base-pair sizes likely to appear as bands on an autorad. The spacing of the fixed-bin boundaries is somewhat uneven because, like the bands in the autorad’s sizing-ladder lanes, they are derived from viral DNA that has been exactly measured. A separate fixed-bin table is compiled for each locus in each database. Each database band is entered within the bin that encompasses its base-pair size. To protect a suspect against unduly small frequencies, any bin with four or fewer bands is combined with its neighbor until each bin contains a minimum of five bands. The fixed-bin table shows not only each bin’s range of sizes and number of bands, but also each bin’s frequency, which is calculated from the ratio of the number of bands in the bin to the total number of bands in the table. (See 1996 NRC Rep., supra, pp. 97, 143; Budowle et al., Fixed-Bin Analysis for Statistical Evaluation of Continuous Distributions of Allelic Data from VNTR Loci, for Use in Forensic Comparisons (1991) 48 Am. J. Hum. Genetics 841, 846 [citing an example in which a table of 31 bins, ranging from 0 to over 12,000 base pairs, was collapsed into a table of 23 bins].)

In fixed-bin analysis, the frequency of an evidentiary band is determined by assigning it the frequency of the fixed bin into which its base-pair size falls. Special rules may apply when a window around the evidentiary band overlaps multiple bins.

F. Probability of a Random Profile Match—The “Product Rule”

The final task is to calculate the statistical probability that the DNA profile of any one person, selected at random from the relevant population, would contain all the alleles represented by the measured bands of the evidentiary sample. The most straightforward means of making this calculation is through application of the “product rule.” There has been significant scientific controversy over whether constraints should be imposed on the use of this rule in light of certain population genetics theories. We shall first describe the product rule and examine its application in its unmodified form as a frame of reference for highlighting the controversy.

The essence of the product rule is the multiplication of individual band probabilities to arrive at an overall probability statistic expressed as a simple fraction, such as 1 in 100,000. The rule is applied in two stages: first, for determining the allelic frequency at each locus, and then, for determining the alleles’ combined frequency at all loci. When the evidentiary sample has two bands at a locus, making the donor heterozygous, the frequencies of those bands are multiplied by each other and the result multiplied by two to reflect the fact that each band could have originated from either parent. If there is only one band at the locus, either the donor is homozygous or there is a second allele that for some reason did not appear on the autorad. In order to take both those possibilities into account while avoiding prejudice to the suspect, the frequency of the first band is simply multiplied by two. (See 1992 NRC Rep., supra, p. 78; 1996 NRC Rep., supra, pp. 105-106.)

Finally, under the product rule, the frequencies found at each locus are multiplied together to generate a probability statistic reflecting the overall frequency of the complete multi-locus profile. The resulting statistic will oftentimes be very small.

G. Effects of Population Substructure—the “Ceiling Principles”

The foregoing application of the product rule to calculate the frequency of a multi-locus profile will produce an accurate result only to the extent that each multiplied frequency is statistically independent from all the others. (See People v. Collins (1968) 68 Cal.2d 319, 328-329 [66 Cal.Rptr. 497, 438 P.2d 33, 36 A.L.R.3d 1176].)

Population genetics theory teaches that pairs of alleles at the same locus are statistically independent from each other if they are in “Hardy-Weinberg equilibrium.” Hardy-Weinberg equilibrium has been defined as “the condition, for a particular genetic locus and a particular population, with the following properties: allele frequencies at the locus are constant in the population over time and there is no statistical correlation between the two alleles possessed by individuals in the population; such a condition is approached in large randomly mating populations in the absence of selection, migration, and mutation.” (1992 NRC Rep., supra, p. 169 [Glossary], italics added; see id. at p. 78; 1996 NRC Rep., supra, pp. 90-92.)

Alleles at different loci are said to be independent if they are in “linkage equilibrium.” Alleles are not in linkage equilibrium if “a specific allele at one locus is non-randomly associated with an allele at another locus.” (1992 NRC Rep., supra, p. 170 [Glossary]; see id. at p. 78; 1996 NRC Rep., supra, p. 106.)

Generally, the presence of both kinds of equilibrium in a given population depends on the extent to which mating within that population has been at random. If both kinds of equilibrium are not present, application of the product rule in theory may prejudice the suspect by understating the frequency of a profile within particular segments of the population.

Major laboratories that do RFLP analysis, including the FBI and Cell-mark, have developed their own separate population databases for each of several broad racial or ethnic categories such as Caucasian, Black, and Hispanic (see Barney, supra, 8 Cal.App.4th at p. 809), the assumption being that mating among members of any one of those categories of the United States population is sufficiently random to justify using them in conjunction with the product rule to calculate the frequency of a DNA profile. (See 1996 NRC Rep., supra, p. 156.)

A number of scientists have criticized this laboratory approach on the ground that the broad racial categories may include genetically distinct subpopulations, and that the existence of such population substructures precludes the Hardy-Weinberg equilibrium and linkage equilibrium necessary to justify use of the product rule. Other scientists disagree. (See, e.g., Barney, supra, 8 Cal.App.4th at pp. 814-816.) The 1992 NRC Report acknowledged the dispute, but rather than undertaking to resolve it, proposed circumvention of any alleged population substructure problem through application of a “ceiling principle” formula that would retain the product rule calculation but modify the data to which it is applied. Random samples would be drawn from 100 persons in each of 15 to 20 homogeneous U.S. subpopulations, and the allele frequency used for each locus would be either the highest frequency found in any subpopulation or 5 percent, whichever is higher. (1992 NRC Rep., supra, pp. 82-85.)

This ceiling principle was ultimately never applied because the population studies required to implement it were never conducted. (See 1996 NRC Rep., supra, pp. 156-157.) However, the 1992 NRC Report also recommended use of a “modified ceiling principle” (also known as the “interim ceiling principle”) for use pending completion of those studies. The modified ceiling principle has since been used in many cases. It calls for the calculation of frequencies from at least three major racial categories (e.g., Caucasian, Black, Hispanic). The product rule is applied after assigning to each band either the highest frequency found in any of those groups (slightly increased to reflect a 95 percent upper confidence limit), or 10 percent, whichever is higher. (1992 NRC Rep., supra, pp. 91-93.) The modified ceiling calculation is specifically intended and designed to avoid any possible prejudice to a suspect from the understatement of any frequencies on account of ethnicity.

IV. The Kelly/Frye Hearing Below

A. Audrey Lynch

Although the Kelly/Frye hearing was initially limited in scope to the admissibility of statistical data, the prosecution began with an overview of RFLP analysis presented through Audrey Lynch, the FBI special agent in charge of the DNA testing in this case. Lynch has a master’s degree in cell biology. She worked from 1985 to 1989 as an examiner in the serology unit of the FBI laboratory in Washington D.C., then transferred to the DNA analysis unit where she was trained in laboratory techniques, molecular biology, and statistical calculations. As one of the FBI laboratory’s 10 qualified DNA examiners, she was assisted by a laboratory technician in her own casework and from time to time was called upon to review other examiners’ findings of a match. The trial court ruled Lynch was qualified to testify as an expert on how the FBI performs RFLP analysis, but not on the broader issue of whether there is general scientific acceptance of the statistical databases here in question. Lynch, it should be added, did not claim expert qualification in either population genetics or statistics.

Lynch reviewed the nature of human DNA and systematically described the FBI’s methodology of RFLP analysis, both as a general matter and as applied in this case. The FBI laboratory used a probe for each of four loci, e.g., D2S44. She explained that because stripping a probe to make way for another probe consumes DNA, the number of probes usable seriatim on the same sample is limited by the amount of DNA contained in the sample. The autorads for each probe are first visually examined to determine the presence of an obvious match between the suspect’s known sample and the evidentiary sample. If visual inspection indicates a possible match, a computer-assisted program makes a more exact determination, using the markers in the sizing ladder and applying the FBI’s match criterion of plus or minus 2.5 percent. That criterion was determined from studies of variations in the results of the laboratory’s repetitive analyses of the same DNA samples. Windows of plus or minus 2.5 percent are constructed around both the known band and the questioned band, and a match is declared if the windows overlap.

Lynch explained that the FBI has developed fixed bins, for each probe, from databases of approximately 500 Hispanics, 750 Caucasians, 500 Blacks, and 200 American Indians. The Hispanic database is a composite of databases from the Southwest (Texas) and the Southeast (Florida). Because of their pronounced frequency differences, the Texas and Florida databases are combined into the composite Hispanic database, bin by bin for each locus, the higher frequency (i.e., the one more conservative in that it favors the suspect) being selected for each bin.

In the present case, Lynch found matches at three loci between defendant’s known DNA sample and two questioned evidentiary samples. The match determination at locus D1S7 was deemed inconclusive because one of defendant’s bands at that locus exceeded 10,000 base pairs and therefore, under the FBI laboratory’s policy, was deemed too large for accurate measurement.

In comparing the matched bands with the fixed bins, Lynch constructed windows of 5 percent (i.e., plus or minus 2.5 percent) around the bands produced by defendant’s DNA sample and both questioned evidentiary samples, so that if any of those windows overlapped a bin boundary, the bin with the higher frequency (again, that favoring the suspect) would be selected. Thus, at locus D17S79 in the Hispanic database, a bin with a higher frequency was used solely because of the overlap of a window around one of the questioned samples.

Lynch’s initial FBI report to the police in this case was based on a profile made in March 1991 from the Hispanic database alone, as it was at that time the FBI’s practice to report only the frequency for the racial group to which the suspect belonged. That report stated, that the frequency of the samples’ profile in the Hispanic population was about 1 out of 31,000. Later, the FBI started routinely reporting Hispanic, Black, and Caucasian frequencies in every case. Thus, profiles in this case, dated August 12, 1992, showed approximate frequencies of 1 out of 31,000 from an updated Hispanic database, 1 out of 225,000 from a Black database, and 1 out of 53,000 from a Caucasian database.

At the prosecutor’s request, Lynch also calculated the frequencies of the DNA profiles in this case under the FBI’s version of the modified ceiling method recommended by the 1992 NRC Report. A calculation was made for each of the two questioned evidentiary samples. At each locus, the measured size of each allele in defendant’s sample was added to the measured size of the allele in the questioned sample, and the sum was divided by two to arrive at a mean. Lynch then constmcted a floating bin of plus or minus 2.5 percent around that mean, on the ground that plus or minus 2.5 percent is the FBI’s window criterion for declaring a match. The computer searched the Caucasian, Black, Southeast Hispanic, and Southwest Hispanic databases for the number of bands within each floating bin and thereby calculated an “observed” frequency in each database for that bin. In conformance with the modified ceiling calculation recommended in the 1992 NRC Report, the observed frequency in each database was then adjusted upward (i.e., in defendant’s favor) to reflect the 95 percent confidence level. The frequency of the evidentiary allele (i.e., the mean of defendant’s and the questioned alleles) at that locus was fixed at either the highest of the six adjusted observed frequencies or at 0.10 (10 percent), whichever was higher.

The product rule was then applied to arrive at an overall frequency for the combined alleles of each evidentiary sample. The calculated overall frequency based on one of the questioned samples was 1 out of 65,000; the frequency based on the other questioned sample was 1 out of 67,000.

B. Martin Tracey

The second prosecution witness—Dr. Martin Tracey, a professor at Florida International University in Miami—qualified as an expert in molecular biology and population genetics. Tracey reviewed the FBI’s autorads and laboratory notes in this case and found no errors in its analysis under the fixed-bin method. He was familiar with the FBI’s Hispanic database and considered it adequate in that it exceeded the minimum number of 150 subjects that the genetics community deems necessary for RFLP studies.

Tracey opined that the FBI’s fixed-bin method is “a very good method” for estimating the rarity of a DNA pattern, but that in view of the caliber of those criticizing it, he could not say it was generally accepted by population geneticists. The modified ceiling principle, on the other hand, though “not accurate” in his opinion (in the sense that it is not intended or designed to reflect scientifically accurate measurement), does have general scientific acceptance. Moreover, Tracey prefers it for courtroom purposes because it gives the best estimate without assumptions about racial or ethnic background.

C. Ranajit Chakraborty

The prosecution’s last witness at the initial phase of the Kelly/Frye hearing was Dr. Ranajit Chakraborty, a professor at the University of Texas Graduate School of Biomedical Sciences in Houston. Chakraborty has been conducting research in human population genetics since 1966 and has written many published articles and book chapters in that field.

Chakraborty was very familiar with the FBI’s fixed-bin methodology and views it as a scientifically valid means of arriving at frequencies in a criminal case, even though he considers it conservative in the sense that it generates larger statistical frequencies (thus favoring the accused) than would be the case if objectively accurate measurement were feasible. He strongly disagreed with the concerns expressed by Professors Lewontin and Hartl that results obtained through application of the product rule may be distorted by the effects of population substructuring. Although recognizing that substructuring exists, he asserted that it has no practical effect on the reliability of the FBI’s test results. He said the fixed bins are conservative because they range in size from plus or minus 3 percent to plus or minus 9 percent even though the match criterion is only plus or minus 2.5 percent. When asked whether “the fixed bin approach” has general scientific acceptance, he said it is accepted by “those of us who are working with the DNA and doing it,” but not by Lewontin and Hartl.

Chakraborty was asked whether the modified ceiling principle recommended by the 1992 NRC Report is generally accepted in the pertinent scientific community. He replied that “even the critics agree with the conservativeness of the ceiling principle,” but that as a population geneticist, he sees no scientific justification for it. Although use of the modified ceiling method, with floating bins, was ostensibly supposed to produce more conservative results than the FBI’s databases with fixed bins, the latter approach produced more conservative results in this and two other cases on which Chakraborty made computations. His explanation for that apparent anomaly was the inclusion, in the FBI’s fixed-bin approach, of conservative cushions such as the large size of the fixed bins (3 to 9 percent)' and the collapsing of small bins.

D. Lawrence Mueller

The defense called Lawrence Mueller, associate professor of ecology and evolutionary biology at the University of California, Irvine. He was found qualified as an expert in population genetics.

Mueller criticized the FBI calculations in which Lynch used a floating bin together with the modified ceiling database recommended by the 1992 NRC Report. Both of the frequencies Lynch reported from those calculations—1 out of 65,000 as to one questioned sample, and 1 out of 67,000 as to the other questioned sample—were less conservative than the 1 in 31,000 calculated with fixed bins from the FBI’s Hispanic database.

Mueller testified that the NRC’s modified ceiling method—which he viewed as essentially a formula for a composite multi-ethnic database—did not call for changes in the basic methodology for allele frequency estimation. (See 1992 NRC Rep., supra, p. 86 [floating-bin and fixed-bin approaches both acceptable].) He acknowledged that if the method of estimating individual allele frequencies is kept constant, the modified ceiling approach will always produce the more conservative result. Here, in Mueller’s opinion, the FBI’s modified ceiling calculation reached the less conservative result not because it used the modified ceiling database, but because it replaced the fixed bins with floating bins that were too narrow. Mueller attributed this improper narrowing to two shortcomings in the FBI’s analysis.

First, the floating bin should be as wide as the window used to declare a match. (See 1992 NRC Rep., supra, pp. 85-86; 1996 NRC Rep., supra, p. 143.) Here, the FBI constructed a floating bin of plus or minus 2.5 percent on the ground that such was its match criterion. In determining a match, however, the FBI placed plus or minus 2.5 percent windows around the bands of both the known sample and the questioned sample, and declared a match if the windows overlapped. That overlap could thus occur between windows of bands of the known and questioned samples that were within 5 percent of one other. Stated differently, one band could match another within a distance of 5 percent in either direction. For that reason, said Mueller, the width of the floating bin should have been doubled, from plus or minus 2.5 percent to plus or minus 5 percent.

The other ground on which Mueller considered the floating bin too narrow was that it failed to take into account the fact that measurement of base-pair sizes on different gels generally varies more widely than measurements of sizes on the same gels. (See 1992 NRC Rep., supra, p. 86 [“inter-gel comparisons ... are typically less precise than intra-gel comparisons”].) The criteria for matching the sizes of bands from known and questioned samples on the same gel may therefore not suffice for matching those bands with the database of band sizes derived from many different samples on many different gels. Mueller studied a series of dual DNA profiles, each measuring the sizes of alleles from the same person, which had been erroneously furnished to the FBI for its database as if each profile were of a different individual. Some of the dual measurements were intra-gel, i.e., from the same gel; others were inter-gel, i.e., from different gels. Mueller found that the range of variation in the inter-gel measurements was almost twice that of the variation in intra-gel measurements. From that finding, he reasoned that the size of the floating bin should not only be increased from plus or minus 2.5 percent to plus or minus 5 percent to account for the intra-gel matching criterion, but also should be further increased to plus or minus 9 percent to account for a wider range of inter-gel variation between the evidentiary bands and the bands in the database.

Mueller also criticized the FBI’s floating-bin, modified ceiling calculation for failing to use more than its three databases, Hispanic, Caucasian, and Black. He thought the use of additional databases to be implicit in the NRC’s recommendation that data from “at least three” major ethnic groups be examined. (1992 NRC Rep., supra, p. 91). He testified further that he had recomputed the floating-bin, modified ceiling results reported by the FBI, enlarging the bin to'plus or minus 9 percent and adding the FBI’s American Indian database as well as Hispanic and American Indian databases from other laboratories. On that basis, he said he arrived at a frequency of 1 out of 378 as compared with the 1 out of 65,000 frequency reported by the FBI.

E. The Trial Court’s Initial Kelly/Frye Ruling

After the initial phase of the Kelly/Frye hearing, on October 13, 1992, the trial court made its oral ruling. The court stated it had considered not only the expert testimony but also all the written materials presented as exhibits or by way of judicial notice. The court then ruled substantially as follows: There is unanimous scientific approval of the biochemical methods of extracting and isolating DNA and declaring a match. Opinions differ, however, when it comes to the statistical significance of a match. Notwithstanding the prosecutor’s objection to the contrary, DNA methodology and statistical analysis are subject to the Kelly/Frye rule under the holding in Barney, supra, 8 Cal.App.4th at pages 817-818. Thus, the prosecution must establish that a new technique of DNA statistical analysis has gained general acceptance in its scientific field. The modified ceiling approach recommended in the 1992 NRC Report has achieved such general scientific acceptance; therefore, the prosecution may present results obtained through that method. Questions raised by the defense expert, Dr. Mueller, on the correctness of the FBI’s utilization of that method simply go to the weight of the evidence, not its admissibility, and hence can be determined by the jury. The FBI’s traditional fixed-bin approach (which applies the unmodified product rule) is still controversial, as shown by the testimony of Dr. Tracey, and therefore statistical probabilities arrived at through use of that methodology may not be introduced by the prosecution. However, should the defense bring up methodologies outside the modified ceiling approach, either on cross-examination or in its own case, the door will be open to the jury’s hearing evidence based on all the statistical methodologies.

F. The Reopened Kelly/Frye Proceedings in the Trial Court

On the same day the trial court made its initial Kelly/Frye ruling, the present Court of Appeal filed its decision in Pizarro, supra, 10 Cal.App.4th 57 (see ante, p. 57), requiring the prosecution to demonstrate general scientific acceptance of the FBI’s particular DNA methodology. Relying on Pizarro, defendant petitioned for writ relief from the trial court’s ruling. The Court of Appeal denied the petition on the ground defendant had failed to demonstrate he was without a remedy in the trial court. In light of that denial order, the trial court granted defendant’s request to reopen the Kelly/Frye hearing.

A jury trial commenced. The additional Kelly/Frye testimony was taken outside the presence of the jury during two recesses. Implicit in this arrangement was the understanding that if the court were to conclude the DNA evidence was inadmissible, it would declare a mistrial. (See ante, fn. 4.) During the first recess, FBI Agent Lynch, under examination by the defense, described the FBI’s procedures in great detail, from extraction of the DNA through production of the autorads.

The jury returned, whereupon Lynch gave them a detailed explanation of DNA theory and of the RFLP analysis she had performed for the FBI in this case, up through the matching of the autorad bands from defendant’s blood sample with those from the two questioned samples taken from the victim’s vaginal swab and the bedspread (see ante, fn. 25). At the conclusion of her direct testimony, Lynch said the probability of another person having the DNA profile found in defendant’s blood sample was 1 in 65,000.

On cross-examination Lynch testified as follows: The frequency of 1 in 65.000 was calculated with the modified ceiling method recommended by the 1992 NRC Report. For her original report on this case, in 1991, she had used the FBI’s fixed-bin approach to calculate a frequency of 1 in 31,000 in the Hispanic population. Later she used the same approach to calculate additional frequencies of 1 in 53,000 for the Caucasian population and 1 in 225.000 for the Black population.

For the modified ceiling calculation, Lynch used floating bins instead of fixed bins. Although it would be possible to make that calculation with fixed bins, the FBI would consider it unreasonable to do so. Lynch opined that because the fixed-bin approach is itself designed to be conservative, combining it with modified ceilings would be “absurdly conservative.” Floating bins, she said, are measured by the match criterion of plus or minus 2.5 percent, which is based on both intra-gel and inter-gel experiments (see ante, fn. 28).

During the second recess, outside of the jury’s presence, defendant called Dr. Randell Libby, a molecular biologist from the University of Washington who asserted that the FBI protocol for RFLP analysis lacks sufficient quality controls. For example, he said he found deficiencies in the prescribed measures for detecting incomplete “digestion” (“cutting”) by the restriction enzyme (Hae III) and abnormal migration of bands along the gel (“band shifting”). He further believed the FBI protocol failed to follow certain NRC recommendations on the use of ethidium bromide (a dye used to help visualize DNA), on externally administered blind proficiency testing, and on the use of monomorphic probes to detect band shifting. Libby’s testimony failed to persuade the court to strike or exclude the DNA evidence. In declining to give weight to his testimony, the court characterized Libby as an advocate, observing that his testimony did not touch upon the key issue of whether there is scientific consensus concerning the FBI’s RFLP methodology and protocol.

After that second recess, the jury heard testimony from both of defendant’s Kelly/Frye witnesses, Mueller and Libby.

V. Admissibility of FBI’s RFLP Methodology

A. General Scientific Acceptance—Kelly’s First Prong

Defendant contends the prosecution’s DNA evidence should have been excluded for failure to prove general scientific acceptance of the FBI’s RFLP methodology. In Kelly, supra, 17 Cal.3d at page 30, we held that admissibility of expert testimony based on “a new scientific technique” requires proof of its reliability—i.e., that the technique is “ ‘sufficiently established to have gained general acceptance in the particular field to which it belongs’ ” (quoting Frye, supra, 293 F. at p. 1014, italics omitted). Moreover, a witness testifying to such reliability “must be properly qualified as an expert to give an opinion on the subject.” (Kelly, supra, 17 Cal.3d at p. 30, italics omitted.)

Kelly also holds, however, that “once a trial court has admitted evidence based upon a new scientific technique, and that decision is affirmed on appeal by a published appellate decision, the precedent so established may control subsequent trials, at least until new evidence is presented reflecting a change in the attitude of the scientific community.” (17 Cal.3d at p. 32.) Thus, the prosecution refrained from filing the present charges against defendant until after Axell, supra, 235 Cal.App.3d 836, was filed in October 1991, anticipating that Axell, as California’s first published decision on the subject, would assure the admissibility of the DNA evidence generated by the FBI laboratory six months earlier for this case.

In Axell, the trial court had ruled, based on extensive testimony by qualified experts, that there was general scientific acceptance of the RFLP methodology used by Cellmark to extract DNA from evidentiary samples, generate autorad displays of bands indicating sizes of DNA fragments, compare those bands with one another and declare a match, and make statistical calculations of the frequencies of the matched bands in a population database. The Court of Appeal in Axell reviewed and upheld the underpinnings of that ruling. {Axell, supra, 235 Cal.App.3d at pp. 853-863.)

In August 1992, a second DNA decision, Barney, supra, 8 Cal.App.4th 798, reviewed convictions of two separately tried defendants, one of whom (Barney) had been the subject of RFLP analysis by Cellmark, the other (Howard) having been the subject of RFLP analysis by the FBI. Although concluding that a post-Axell “change in the attitude of the scientific community” {Kelly, supra, 17 Cal.3d at p. 32) had undermined the Kelly/Frye foundation for statistical calculations of frequencies, Barney rejected both defendants’ Kelly/Frye challenges to basic RFLP methodology, relying primarily upon the record and rationale of the decision in Axell. {Barney, supra, 8 Cal.App.4th at pp. 811-814.) Significantly, no distinction was drawn by the Barney court between Axell’s effect on scientific acceptance of Cell-mark’s RFLP analysis in defendant Barney’s case, and that of the FBI’s RFLP analysis in defendant Howard’s companion case.

Relying on the Barney decision as precedent, the trial court in this case limited the first phase of the Kelly/Frye hearing conducted below to the question of scientific acceptance of statistical calculations of probability frequencies. In light of that ruling, the prosecution did not attempt to prove general scientific acceptance of the FBI’s RFLP methodology for generating the autorads and determining matches between the DNA profiles of defendant and of the questioned samples. FBI Agent Lynch, though vigorously defending the merits of the FBI’s RFLP analytical procedures she had followed in this case, did not purport to be qualified, as a molecular biologist or otherwise, to testify on questions of general scientific acceptance of the validity of those procedures. Nor was the testimony of the prosecution’s qualified experts, Tracey and Chakraborty, concerning statistical calculations of probability frequencies, directed to the matter of general scientific acceptance of the FBI’s RFLP methodology; their testimony appears to have assumed the validity and reliability of the autorads and matching data generated by that methodology.

As already explained, the reopened or second phase of the Kelly/Frye hearing below was prompted by the intervening filing, by the present Court of Appeal, of its decision in Pizarro, supra, 10 Cal.App.4th 57. As here, defendant Pizarro challenged the admissibility of the RFLP analysis performed by the FBI laboratory. The Pizarro court found the testimony of the FBI agent in charge of the lab work in that case insufficient to establish general acceptance of the analysis as a “new scientific technique.” (Pizarro, supra, 10 Cal.App.4th at pp. 79-80, quoting Kelly, supra, 17 Cal.3d at p. 30.) The prosecution’s contention that general acceptance had been established by Axell was rejected on the ground that Axell had approved only the RFLP procedures of Cellmark, not those of the FBI. In the present case, the Court of Appeal reiterated its holding in Pizarro as a ground for reversal of the judgment below.

Pizzaro concludes that approval of Cellmark’s RFLP procedures in Axell did not establish scientific acceptance of the FBI’s RFLP procedures, primarily because of the differences between the protocols, restriction enzymes, probes, matching criteria, and databases used by Cellmark and the FBI, and the absence of affirmative evidence that their respective RFLP protocols are the same. “[Ojn this record we are unable to evaluate whether or not the purported differences between [Cellmark’s and the FBI’s methods] have any scientific consequence at all with respect to . . . reliability . . . .” (Pizarro, supra, 10 Cal.App.4th at p. 78.)

The Pizarro opinion, however, overlooks the distinction properly drawn by the court in Axell between the first and third prongs of the long-standing Kelly test for the admissibility of scientific evidence. .The first prong of the Kelly test requires that the “reliability” of a new scientific technique be established by showing that the technique has “ ‘gained general acceptance in the particular field to which it belongs.’ ” (Kelly, supra, 17 Cal.3d at p. 30, quoting Frye, supra, 293 Fed., at p. 1014, italics omitted). The second prong requires that any witness testifying on general acceptance be properly qualified as an expert on the subject. (Kelly, supra, 17 Cal.3d at p. 30.) The third prong of the test was separately set forth in Kelly as follows: “Additionally, the proponent of the evidence must demonstrate that correct scientific procedures were used in the particular case. [Citations.]” (Ibid.)

The Kelly test’s third prong does not apply the Frye requirement of general scientific acceptance—it assumes the methodology and technique in question has already met that requirement. Instead, it inquires into the matter of whether the procedures actually utilized in the case were in compliance with that methodology and technique, as generally accepted by the scientific community. (See Barney, supra, 8 Cal.App.4th at p. 824.) The third-prong inquiry is thus case specific; “it cannot be satisfied by relying on a published appellate decision.” (People v. Morganti, supra, 43 Cal.App.4th at p. 661.)

The Axell opinion, after extensive discussion and analysis, upheld “the trial court’s determination that forensic use of RFLP analysis is generally accepted in the relevant scientific community” {Axell, supra, 235 Cal.App.3d at p. 860). Following that conclusion, the Axell court shifted its focus to separate consideration of the third prong of the Kelly test, under the heading, “Procedures Used by Cellmark.” {Ibid.) Axell rejected the Attorney General’s contention “that any issue pertaining to whether the procedures were applied correctly in a given test is relevant not to admissibility but only to the weight and is, therefore, for the trier of fact to determine.” {Axell, supra, 235 Cal.App.3d at p. 861.) “Due to the complexity of the DNA multisystem identification tests and the powerful impact that this evidence may have on a jury, satisfying Frye [i.e., satisfying Kelly’s first prong] alone is insufficient to place this type of evidence before a jury without a preliminary critical examination of the actual testing procedures performed. ...[<[[] We hold that the procedures used in this case were the ones generally accepted as reliable in the scientific community.” {Id. at p. 862.)

As previously explained, Barney, supra, 8 Cal.App.4th 798, was a consolidated appeal in which the appellate court reviewed the RFLP analysis performed by Cellmark in one defendant’s case and by the FBI in the other. Relying primarily on Axell, the Barney court approved a finding in both cases of the general scientific acceptance of the preparatory phases of RFLP methodology—from the extraction of DNA out of the known and questioned evidentiary samples, through production of the autorads and the basic procedures applied to compare and match bands depicted on the autorads. {Barney, supra, 8 Cal.App.4th at pp. 811-814.) The courts that tried defendants Barney and Howard were held to have erred, however, by failing to incorporate into their Kelly/Frye deliberations on admissibility any hearings pursuant to Kelly’s third prong—i.e., whether the generally accepted scientific procedures (including specific match criteria) had actually been utilized in those cases. (8 Cal.App.4th at pp. 814, 822-825.)

We conclude that for purposes of the trial of this case, the Axell and Barney opinions clearly established the general scientific acceptance, under Kelly’s first prong, of the basic RFLP methodology utilized by the FBI in (1) producing autorads with bands reflecting the base-pair sizes of forensic samples at particular DNA locations, and (2) comparing the bands in order to determine whether the samples matched at those locations. Whether specific steps in the FBI’s RFLP analysis, including the match criteria which that laboratory applied, were in compliance with that long-standing and accepted methodology, presents questions of correct scientific procedures properly considered under the third prong of the Kelly rule.

B. Following Correct Scientific Procedures—Kelly’s Third Prong

The Attorney General contends this court has in effect nullified the third prong of the Kelly test as a requirement for determining the admissibility, as distinct from the weight, of scientific evidence. He relies for that contention on the following statement made by this court in People v. Farmer (1989) 47 Cal.3d 888, at page 913 [254 Cal.Rptr. 508, 765 P.2d 940] (Farmer), and thereafter quoted as follows in People v. Cooper (1991) 53 Cal.3d 111, at page 814 [281 Cal.Rptr. 90, 809 P.2d 865] (Cooper): “ ‘[T]he Kelly-Frye rule tests the fundamental validity of a new scientific methodology, not the degree of professionalism with which it is applied. [Citation.] Careless testing affects the weight of the evidence and not its admissibility, and must be attacked on cross-examination or by other expert testimony.’ ”

The rule referred to by this court in the above-quoted statement is the first prong of the Kelly test, a fact plainly demonstrated by our recognition of the continued vitality of the test’s third prong in the following three cases, all decided within a year before or after Cooper: People v. Morris, supra, 53 Cal.3d 152, at pages 206-208; People v. Ashmus (1991) 54 Cal.3d 932, 970-972 [2 Cal.Rptr.2d 112, 820 P.2d 214]; and People v. Fierro (1991) 1 Cal.4th 173 [3 Cal.Rptr.2d 426, 821 P.2d 1302], at pages 214-215. In each of those cases, we analyzed the evidence and data under all three prongs of the Kelly test, determining that their requirements had been complied with.

Our reference to “careless testing affect[ing] the weight of the evidence and not its admissibility” in Farmer, supra, 47 Cal.3d at page 913, and Cooper, supra, 53 Cal.3d at page 814, was intended to characterize shortcomings other than the failure to use correct, scientifically accepted procedures such as would preclude admissibility under the third prong of the Kelly test (Kelly, supra, 17 Cal.3d at p. 30). The Kelly test is intended to forestall the jury’s uncritical acceptance of scientific evidence or technology that is so foreign to everyday experience as to be unusually difficult for laypersons to evaluate. (Id. at pp. 31-32.) In most other instances, the jurors are permitted to rely on their own common sense and good judgment in evaluating the weight of the evidence presented to them. (See, e.g., People v. Webb (1993) 6 Cal.4th 494, 524 [24 Cal.Rptr.2d 779, 862 P.2d 779] [laser procedure for visualizing latent fingerprints not subject to Kelly test because the familiar image of the fingerprint makes reliability of the process readily apparent]; People v. Clark (1993) 5 Cal.4th 950, 1017-1019 [22 Cal.Rptr.2d 689, 857 P.2d 1099] [“blood-spatter” tests not subject to Kelly requirements because it is common knowledge that inferences can be drawn from spatter patterns of blood expelled from the human body]; People v. Stoll (1989) 49 Cal.3d 1136, 1157 [265 Cal.Rptr. Ill, 783 P.2d 698] [“absent some special feature which effectively blindsides the jury, expert opinion testimony is not subject to Kelly/Frye”]; Farmer, supra, 47 Cal.3d at pp. 912-913 [where expert conclusively identified one of several photographed footprints, no Kelly/Frye foundation necessary to establish whether better photographs could have been taken].)

DNA evidence is different. Unlike fingerprint, shoe track, bite mark, or ballistic comparisons, which jurors essentially can see for themselves, questions concerning whether a laboratory has adopted correct, scientifically accepted procedures for generating autorads or determining a match depend almost entirely on the technical interpretations of experts. (See State v. Bogan (1995) 183 Ariz. 506, 516 [905 P.2d 515, 525] (cone. opn. of Weisberg, J.), review den. as improvidently granted, 186 Ariz. 198 [920 P.2d 320].) Consideration and affirmative resolution of those questions constitutes a prerequisite to admissibility under the third prong of Kelly.

The Kelly test’s third prong does not, of course, cover all derelictions in following the prescribed scientific procedures. Shortcomings such as mislabeling, mixing the wrong ingredients, or failing to follow routine precautions against contamination may well be amenable to evaluation by jurors without the assistance of expert testimony. Such readily apparent missteps involve “the degree of professionalism” with which otherwise scientifically accepted methodologies are applied in a given case, and so amount only to “[cjareless testing affect[ing] the weight of the evidence and not its admissibility” (Farmer, supra, 47 Cal.3d at p. 913; Cooper, supra, 53 Cal.3d at p. 814).

The Kelly third-prong inquiry involves further scrutiny of a methodology or technique that has already passed muster under the central first prong of the Kelly test, in that general acceptance of its validity by the relevant scientific community has been established. The issue of the inquiry is whether the procedures utilized in the case at hand complied with that technique. Proof of that compliance does not necessitate expert testimony anew from a member of the relevant scientific community directed at evaluating the technique’s validity or acceptance in that community. It does, however, require that the testifying expert understand the technique and its underlying theory, and be thoroughly familiar with the procedures that were in fact used in the case at bar to implement the technique. (People v. Smith (1989) 215 Cal.App.3d 19, 27 [263 Cal.Rptr. 678]; People v. Reilly (1987) 196 Cal.App.3d 1127, 1153-1155 [242 Cal.Rptr. 496].)

FBI Agent Audrey Lynch, who took charge of the RFLP analysis in the present case, clearly had the latter qualifications and was properly permitted to testify as to the correctness of the scientific procedures followed by the FBI in conducting that analysis. Her testimony at the initial phase of the Kelly!Frye hearing satisfied the prosecution’s threshold burden of producing evidence that correct scientific procedures were used. At the reopened Kelly!Frye hearing, the trial court properly allowed defendant to cross-examine Lynch on those procedures, and to present the testimony of his own expert, Randell Libby, on the subject. Libby’s testimony was critical of the FBI’s alleged failure to apply numerous precautions and controls (many of which were recommended in the 1992 NRC Report) to assure quality and guard against error. But there is little evidence in the record before us to support an inference that any of those alleged derelictions affected the reported DNA test results adversely to defendant. Having reviewed the record of the Kelly/Frye hearing conducted below, we conclude it supports the trial court’s determination that the FBI used correct scientific procedures in conducting its RFLP analysis up through the matching of defendant’s known DNA samples with the questioned DNA samples.

VI. Admissibility of Statistical Probability Calculations

A. Applicability of Kelly/Frye

A determination that the DNA profile of an evidentiary sample matches the profile of a suspect establishes that the two profiles are consistent, but the determination would be of little significance if the evidentiary profile also matched that of many or most other human beings. The evidentiary weight of the match with the suspect is therefore inversely dependent upon the statistical probability of a similar match with the profile of a person drawn at random from the relevant population. As explained earlier, the assessment of that probability is ordinarily deemed to require the assembling of hundreds of DNA profiles from one or more population databases, the organization of such data through use of a binning procedure to accommodate imprecision in the measurements of individual allele frequencies, and the combining of those frequencies into an overall probability statistic through calculations that include an application of the product rule.

The Attorney General contends that, unlike the procedures for translating VNTR segments of DNA into bands on an autorad and for ascertaining the existence of any matches between those bands, the procedures for determining the statistical significance of a match are immune from the requirements of Kelly/Frye. He argues that estimating the probability of a random match of such DNA bands requires no more than well-established mathematical formulae such as those used to calculate the frequency of blood-group markers (see People v. Fierro, supra, 1 Cal.4th at p. 215 [upholding admission of expert testimony that “based on population frequency statistics, only one-half of 1 percent of California’s general population had the victim’s blood type”]). We disagree.

Frequencies of bodily fluid characteristics such as blood markers are readily “tested by simple empirical counting” (1992 NRC Rep., supra, p. 77) because they are far higher than the DNA frequencies typically generated by forensic RFLP analysis. (See, e.g., People v. Coleman (1988) 46 Cal.3d 749, 760 [251 Cal.Rptr. 83, 759 P.2d 1260] [expert testified that one body fluid characteristic occurred in 20 percent of the general population, a second characteristic in 40 percent, and a combination of the two in 8 percent; and that “these are established statistical frequencies, not projected possibilities”].) Not only the frequencies of those individual characteristics but also their independence for purposes of applying the product rule has been established. (Ibid.) Accordingly, calculations of the frequencies of these non-DNA traits within the general population are readily understandable by laypersons and need not be screened under Kelly/Frye before being admitted into evidence.

In contrast, calculating the statistical probability of a random DNA/VNTR match is much more complicated. Procedures designed to address imprecision of measurement—such as selection of the size of the match window— affect not only the matches between the suspect’s alleles and those of the evidentiary sample, but also the measurements of the samples in the population database. The bins, or ranges of base-pair lengths in the database, must be at least as large as the windows used to match the alleles of the suspect with those of the evidentiary sample. Even more complex is the determination of statistical independence of individual frequencies for purposes of applying the product rule. Various precautions may be deemed necessary to protect the defendant from prejudice caused by the lack of such independence. Some of these precautions may pertain to selection of the persons to be included in the database. Others—such as utilization of the ceiling principles recommended by the 1992 NRC Report—may impose upper or lower frequency limits in the application of the product rule. Moreover, the necessity or desirability of such precautions has been the subject of intense scientific debate. (See Barney, supra, 8 Cal.App.4th at pp. 814-817.)

It is the very complexity of the issues surrounding the propriety of the various recognized methods of computing RFLP probability frequencies that draws them under the Kelly/Frye umbrella. “To . . . leave it to jurors to assess the current scientific debate on statistical calculation as a matter of weight rather than admissibility, would stand Kelly-Frye on its head. We would be asking jurors to do what judges carefully avoid—decide the substantive merits of competing scientific opinion as to the reliability of a novel method of scientific proof. . . . The result would be predictable. The jury would simply skip to the bottom line—the only aspect of the process that is readily understood—and look at the ultimate expression of match probability, without competently assessing the reliability of the process by which the laboratory got to the bottom line. This is an instance in which the method of scientific proof is so impenetrable that it would ‘ . . assume a posture of mystic infallibility in the eyes of a jury . . . [Citation.]’ (People v. Kelly, supra, 17 Cal.3d at p. 32, quoting United States v. Addison (D.C. Cir. 1974) 498 F.2d 741, 744 [162 App.D.C. 199].)” {Barney, supra, 8 Cal.App.4th at pp. 817-818.) The statistical calculation phase of RFLP analysis therefore requires Kelly/Frye screening of evidence on statistical probabilities of random matches at VNTR loci to assure that (1) the methodology used is generally accepted in the scientific community, and (2) the calculations in the particular case followed correct scientific procedures.

B. FBFs Floating-bin/Modified Ceiling Calculations

1. General Scientific Acceptance of the NRC’s Modified Ceiling Approach

Following the initial phase of the Kelly/Frye hearing, the trial court below ruled that the modified ceiling approach, recommended in the 1992 NRC Report, had achieved general scientific acceptance, and that accordingly, the prosecution could present statistical probability figures obtained by that means. The trial court further ruled, however, that the FBFs preferred method of calculating statistical probabilities—through application of the product rule to fixed-bin frequencies derived from its Hispanic, Caucasian and Black databases—lacked general scientific acceptance, and that therefore the figures generated by that method were inadmissible. Accordingly, FBI Agent Lynch testified in the prosecution’s case-in-chief that application of the FBI’s version of the NRC’s modified ceiling approach (using floating bins) established a 1 in 65,000 probability that the DNA profiles of the evidentiary samples would match the profile of a person selected at random from the general population.

The Court of Appeal agreed that probability figures based on the NRC’s modified ceiling approach are admissible, declaring that notwithstanding the prosecution experts’ concerns over that approach’s “unnecessarily conservative results,” the relevant scientific community has come to regard it as “forensically reliable” in that it resolves any imprecision in the statistical calculations in a way that preserves the constitutional presumption of the suspect’s innocence. Nonetheless, defendant urges us to conclude.otherwise and find that the modified ceiling approach lacks general scientific acceptance. We have independently reviewed the lower court’s Kelly/Frye first-prong determination that the modified ceiling approach has gained general acceptance in the relevant scientific community. (See People v. Ashmus, supra, 54 Cal.3d at p. 971.) We perceive no basis for rejecting the Court of Appeal’s affirmance of the trial court’s ruling in this regard.

As already explained, in reviewing the scientific acceptance of the modified ceiling approach de novo under Kelly, we are not required to decide whether such methodology is “reliable as a matter.of ‘scientific fact,’ but simply whether it is generally accepted as reliable by the relevant scientific community.” (People v. Shirley (1982) 31 Cal.3d 18, 55 [181 Cal.Rptr. 243, 723 P.2d 1354].) “ ‘General acceptance’ under Kelly means a consensus drawn from a typical cross-section of the relevant, qualified scientific community.” (People v. Leahy, supra, 8 Cal.4th at p. 612.) The Kelly test does not demand “absolute unanimity of views in the scientific community .... Rather, the test is met if use of the technique is supported by a clear majority of the members of that community.” (People v. Guerra (1984) 37 Cal.3d 385, 418 [208 Cal.Rptr. 162, 690 P.2d 635].) In determining the question of general acceptance, courts “must consider the quality, as well as quantity, of the evidence supporting or opposing a new scientific technique. Mere numerical majority support or opposition by persons minimally qualified to state an authoritative opinion is of little value . . . .” {People v. Leahy, supra, 8 Cal.4th at p. 612.)

It is undisputed that a figure for the statistical probability of a DNA profile derived from multiplying the probabilities of its individual allele frequencies is accurate only insofar as the multiplied frequencies are statistically independent from each other. (See People v. Collins, supra, 68 Cal.2d at pp. 328-329.) The 1992 NRC Report notes the concern of some population geneticists that the necessary statistical independence may be materially compromised by differences in allele frequency patterns among members of population subgroups who tend not to mate across interethnic lines. (1992 NRC Rep., supra, pp. 11-12, 79-80, citing Lewontin & Hartl, Population Genetics in Forensic DNA Typing, supra, 254 Science 1745.) “Other population geneticists, while recognizing the possibility or likelihood of population substructure, conclude that the evidence to date suggests that the effect on estimates of genotype frequencies are minimal [citing Chakraborty & Kidd, The Utility of DNA Typing in Forensic Work, supra, 254 Science 1735] . ... HD Although mindful of the controversy, the committee has chosen to assume for the sake of discussion that population substructure may exist and provide a method for estimating population frequencies in a manner that adequately accounts for it.” (1992 NRC Rep., supra, p. 80.)

Consequently, the 1992 NRC Report proposed “a method of statistical calculation which accounts for the possibility of population substructuring, eliminates ethnicity as a factor in the calculation process, and permits the use of the product rule while ensuring that probability estimates are appropriately conservative. ... HI] ... Using a modified ceiling approach, each allele should be assigned a frequency of either the 95 percent ‘upper confidence limit’ for its frequency in existing data bases (wherein the true frequency has only a 5 percent chance of variance), or 10 percent, whichever is larger, and a statistical calculation should then be made using the product rule. [Citation.]” (Barney, supra, 8 Cal.App.4th at pp. 821-822, italics added; see ante, pp. 66-67.)

The 1992 NRC Report further explained: “Use of the ceiling principle yields the same frequency of a given genotype, regardless of the suspect’s ethnic background, because the reported frequency represents a maximum for any possible ethnic heritage. Accordingly, the ethnic background of the individual suspect should be ignored in estimating the likelihood of a random match. The calculation is fair to suspects, because the estimated probabilities are likely to be conservative in their incriminating power.” (1992 NRC Rep., supra, p. 13.)

Annotating its introduction to the ceiling principle, the 1992 NRC Report, at pages 82, 95, endnote 9, cites a published letter by Professor Eric Lander. (Lander, letter (1991) 49 Am. J. Hum. Genetics 899.) Professor Lander, who served on the authoring committee of the 1992 NRC Report, coauthored an article two and one-half years later that described the ceiling principle as “unabashedly conservative. It gave the benefit of every conceivable doubt to the defendant, so that it could withstand attacks from the most stubborn and creative attorneys. Some of the statistical power was sacrificed to neutralize all possible worries about population substructure.” (Lander & Budowle, DNA Fingerprinting Dispute Laid to Rest (Oct. 27, 1994) 371 Nature 735.)

We recognize that various scientists, including Aldhous, Chakraborty (see ante, pp. 71-72), Devlin et al., Morton, and Weir, have criticized the NRC’s proposed ceiling and modified ceiling approaches as being arbitrary or lacking in scientific foundation. For example, Morton’s article {ante, fn. 35) asserts that those methodologies violate statistical theories for calculating probabilities. Similarly, the article by Devlin et al. {ante, fn. 34), at page 748, describes the NRC’s figures for the modified ceiling approach as arbitrary, finds “little scientific basis” for that “method of forensic inference,” and concludes the scientific basis for adopting a ceiling principle is flawed. The 1996 NRC Report itself acknowledges that the debate has continued after the release of the 1992 NRC Report, and notes that both the ceiling principle and the modified ceiling approach recommended in the report have become the subject of considerable criticism. (1996 NRC Rep., supra, pp. 1, 35, 157-158.)

Critically, however, virtually all of the scientists who have criticized the ceiling approach and modified ceiling approach as arbitrary or lacking in scientific justification do so on the basis that those statistical methodologies produce figures that are far too conservative and unduly favorable to the suspect. (But see Slimowitz & Cohen, Violations of the Ceiling Principle: Exact Conditions and Statistical Evidence (1993) 53 Am. J. Hum. Genetics 314 [criticized by Lander & Budowle in DNA Fingerprinting Dispute Laid to Rest, supra, 371 Nature 735, 737, endnote 15, as raising theoretical but not practical concerns].) Indeed, it appears that most of the critics of the ceiling approaches would in actuality favor application of the unmodified product rule—a methodology highly likely to result in a smaller statistical probability of a random match, to the defendant’s disadvantage. As the Court of Appeal observed below, although the prosecution’s own expert witnesses in this case suggested the 1992 NRC Report’s ceiling methodologies were not scientifically defensible, they reached that conclusion on the basis that such methodologies “produced unnecessarily conservative results that present a particular [DNA] profile as far, far more frequent in the population than the profile is in reality.” We agree with the Court of Appeal’s further conclusion that “the evidence [is] also clear that the scientific community regards the NRC statistical methodology as forensically reliable”—i.e., as selecting figures that most favor the accused from the scientifically based range of probabilities.

Published California appellate decisions likewise support our conclusion that the trial court below properly found the 1992 NRC Report’s modified ceiling approach generally accepted by the relevant scientific community as a forensically sound approach for calculating statistical probabilities of random matches of DNA profiles.

The court in Barney, supra, 8 Cal.App.4th 798, addressed the issue of whether the unmodified product rule—used in some cases in the statistical calculation step of RFLP analysis—is generally accepted by the scientific community within the meaning of the Kelly test. (Id. at p. 809.) In concluding such statistical methodology was not generally accepted at the time Barney was decided, the court cited the competing articles in the December 1991 issue of Science magazine regarding the possible effect of population substructuring on calculation of probability estimates under the unmodified product rule. (8 Cal.App.4th at pp. 802, 814-822; accord, People v. Wallace (1993) 14 Cal.App.4th 651, 657-660 [17 Cal.Rptr.2d 721] [authored by the Barney court].) However, the Barney court indicated the “ceiling frequency” or “modified ceiling” approaches proposed by the 1992 NRC Report “appears to point the way to” a “sufficiently conservative method of determining statistical significance” generally acceptable to the scientific community. (Barney, supra, 8 Cal.App.4th at pp. 821-822.)

The court in People v. Taylor (1995) 33 Cal.App.4th 262 [40 Cal.Rptr.2d 132], likewise addressed the precise question of whether the modified ceiling approach has gained general acceptance in the relevant scientific community, thereby passing muster under the first prong of the Kelly test. (Id. at p. 268.) Taylor notes that the modified ceiling approach assumes “the existence of population subgroups and allow[s] for that possibility by assuming a minimum frequency of DNA patterns unless the actual data gave a higher frequency figure.” (Id. at p. 267.) The Taylor court further observed that the modified ceiling approach “is considered to be conservative in that it presumably overstates the actual frequency of DNA pattern matches in the general population, and therefore benefits the defendant by suggesting that matches made with defendant’s DNA are more common than the actual data would suggest.” (Ibid.)

Published appellate decisions of out-of-state jurisdictions also support the conclusion that the 1992 NRC Report’s modified ceiling approach for the statistical calculation step of RFLP analysis has gained general acceptance in the scientific community nationwide. The appellate courts of Washington (State v. Jones (1996) 130 Wn.2d 302 [922 P.2d 806]); Arizona (State v. Johnson (1996) 186 Ariz. 329 [922 P.2d 294]); Alaska (Harmon v. State (Alaska Ct.App. 1995) 908 P.2d 434); New Hampshire (State v. Vandebogart (1994) 139 N.H. 145 [652 A.2d 671]); Massachusetts (Com, v. Lanigan (1994) 419 Mass. 15 [641 N.E.2d 1342]); and Minnesota (State v. Bloom, supra, 516 N.W.2d 159) have each approved use of the ceiling and interim ceiling principles as generally accepted within the scientific community. Additionally, the high courts of Vermont and New Mexico have approved those principles as scientifically reliable under the Daubert standard (Daubert v. Merrell Dow Pharmaceuticals, Inc., supra, 509 U.S. 579; see ante, fn. 30). (State v. Streich (1995) 163 Vt. 331 [658 A.2d 38]; State v. Anderson, supra, 881 P.2d 29, 47.)

Indeed, “courts have recognized that ‘the [NRC] is a distinguished cross section of the scientific community. . . . Thus, that committee’s conclusion regarding the reliability of forensic DNA typing, specifically RFLP analysis, and the proffer of a conservative method for calculating probability estimates can easily be equated with general acceptance of those methodologies in the relevant scientific community.’ United States v. Porter, 618 A.2d 629, 643 n. 26 (D.C.App.1992) [citations].” (State v. Johnson, supra, 922 P.2d at p. 299.)

Based on our review of the NRC reports, legal commentaries, scientific literature, and consideration and acceptance of the modified ceiling method in the published decisions of several California appellate courts as well as courts of many other jurisdictions, we conclude such methodology has been generally accepted in the relevant scientific community, and that statistical probability calculations of random matches of DNA profiles computed under that methodology are admissible under the Kelly test. “[T]he overwhelming view is that while the interim [modified] ceiling principle is artificially conservative, it has been accepted for what it is, i.e., a method for calculating probabilities which was biased in favor of defendants in order to compensate for any possible effect due to substructuring in human populations.” (State v. Jones, supra, 922 P.2d at p. 810.)

The record of the Kelly hearing and finding of general acceptance under the Kelly test made by the trial court in this case are fully consistent with the foregoing survey of relevant authorities and case law on the issue of general acceptance of the NRC’s modified ceiling methodology. The prosecution’s expert, Martin Tracey, testified that virtually all population geneticists are willing to adopt the ceiling principle as a means for calculating RFLP random-match probabilities. Any dispute, he explained, centers around the FBI’s fixed-bin methodology (used in conjunction with the unmodified product rule). Moreover, Tracey personally prefers the ceiling approach because it gives the best estimate devoid of assumptions about an individual’s ethnicity. The prosecution’s other expert, Ranajit Chakraborty, though expressing a strong preference for use of the FBI’s fixed-bin methodology in conjunction with the unmodified product rule and criticizing the ceiling principle as without scientific justification, testified that even the critics of the ceiling principle “agree with [its] conservativeness.” He explained that, by its very nature, the ceiling principle results in a higher frequency for the defendant’s profile. In the present case, he said, the result of the FBI’s application of the modified ceiling principle with floating bins was less conservative than the outcome from using the unmodified product rule with fixed bins because of the FBI’s fixed bins’ inherent “levels of conservativeness.” Even the defense expert, Lawrence Mueller, conceded on cross-examination that the NRC’s modified ceiling approach may be an appropriate means of presenting random-match probability statistics to the jury. A probability statistic calculated under that methodology could therefore have properly been admitted into evidence in this case if the calculation had not been flawed by a technical error in the scientific procedures actually employed by the FBI, as we next explain.

2. Failure of FBI to Comport Its Floating-bin Technique With Correct Scientific Procedures

As previously explained, the trial court allowed the prosecution to report, through the testimony of FBI Agent Lynch, the FBI’s conclusion that under the NRC’s modified ceiling approach there was a probability of approximately 1 in 65,000 that the evidentiary profiles would match the profile of a randomly selected member of the populations underlying the FBI’s Hispanic, Caucasian and Black databases. On the other hand, the FBI’s calculations under the straight product rule (which the trial court ruled inadmissible and excluded from the prosecution’s case-in-chief) reflected a higher probability—1 in 31,000—of a random match in the Hispanic database alone. The contrast between the two results appears anomalous in light of the general perception that the modified ceiling approach is “unabashedly conservative” (Lander & Budowle, DNA Fingerprinting Dispute Laid to Rest, supra, 371 Nature at p. 736).

The modified ceiling approach, however, can be used on allele frequencies that have been calculated using either fixed or floating bins. (See 1992 NRC Rep., supra, pp. 85-86, 92.) In its modified ceiling calculations, the FBI used floating bins of plus or minus 2.5 percent, whereas in applying the straight product rule, it used larger fixed bins. The scientists called by the prosecution, Tracey and Chakraborty, both testified the FBI’s fixed bins, being wider than its floating bins, tended to produce higher probabilities, and thus more conservative results. In the FBI’s modified ceiling/floating-bin calculations, therefore, the conservative effects of the modified ceiling approach tended to be offset by the use of the narrower floating bins.

Defendant’s expert witness, Lawrence Mueller, testified at the Kelly hearing that the FBI’s floating bins of plus or minus 2.5 percent, used in its modified ceiling calculations, were overly narrow for two reasons: (1) the bins were narrower than the scope of the FBI’s matching criterion, which placed windows of plus or minus 2.5 percent around the respective bands of both the evidentiary sample and defendant’s known sample and declared a match if the two windows overlapped, and (2) the bins should have been widened to account for the fact that repeated measurements of a particular band on different gels vary more widely than repeated measurements of the band on the same gel. For the latter reason, the Court of Appeal concluded the FBI had failed to use “correct scientific procedures” (Kelly, supra, 17 Cal.3d at p. 30) in its modified ceiling approach calculations. We agree with that conclusion, but only for the former of the two reasons given by Mueller.

Unlike the independent appellate review of a determination of general scientific acceptance under Kelly’s first prong, review of a third-prong determination on the use of correct scientific procedures in the particular case requires deference to the determinations of the trial court. (Cf. People v. Reilly, supra, 196 Cal.App.3d at p. 1155.) Here, the trial court ruled that all of Mueller’s testimony criticizing the FBI’s utilization of the modified ceiling principle raised only factual questions that went to the weight of the evidence and were for the jury to evaluate. In reviewing that ruling, the Court of Appeal was required to accept the trial court’s resolutions of credibility, choices of reasonable inferences, and factual determinations from conflicting substantial evidence. (In re Marriage of Mix (1975) 14 Cal.3d 604, 614 [122 Cal.Rptr. 79, 536 P.2d 479].)

Therefore, the Court of Appeal should have upheld the trial court’s implied conclusion that Mueller’s second reason for deeming the floating bin too narrow—the wider variability of measurements made on bands of different gels than of those made on the same gel—posed only a question for the jury, which could properly have rejected Mueller’s theory in light of the testimony of FBI Agent Lynch. The premise of Mueller’s theory was that because the FBI’s match criterion needed only to reflect intragel variability of measurement in order to test matches of known and questioned samples on the same gel, the criterion failed to accommodate for intergel variability applicable to comparisons between evidentiary samples and the bands in the database. To the contrary, Lynch’s testimony provided substantial evidence that the FBI’s match window was based in significant part on repeated measurements of the same data on multiple gels. (See ante, fn. 28.)

We conclude, however, that the trial court erred in ruling that the FBI’s failure to follow correct scientific procedures by using the unduly narrow floating bins was a matter affecting only the weight of the evidence for the jury’s consideration. (See ante, at p. 74.) The Court of Appeal should have recognized the trial court’s error in that regard, and held instead that the FBI’s use of improperly sized floating bins was a failure to follow correct scientific procedures within the meaning of Kelly s third prong.

Not only was that failure explained by defense expert Mueller, it was further demonstrated by the uncontradicted testimony of FBI Agent Lynch herself. Lynch testified at the Kelly hearing that in implementing the FBI’s ceiling approach, she first established frequencies at each locus by constructing a floating bin of plus or minus 2.5 percent around the evidentiary band, and then used the computer to count the number of database bands falling within that bin. She testified the reason for fixing the floating bin at that size was that “the National Research Council said that your [floating bin] should be, or include, all the bands in the population data base that could be considered a match with that band, and plus or minus 2.5 percent is our match criterifon].”

The FBI’s floating bin of plus or minus 2.5 percent was too narrow because, as Mueller pointed out, it failed to include all the band sizes within the FBI’s actual match criterion. As described by Lynch, that criterion requires not one but two match windows of plus or minus 2.5 percent, one around the band from the known (defendant’s) sample and the other around the questioned evidentiary sample. A match is declared if the windows overlap. If the windows barely overlap, the distance between matched bands may be almost twice 2.5 percent, or 5 percent. Thus, the floating bin should have been plus or minus 5 percent. (Accord, 1996 NRC Rep., supra, pp. 141 [fig. 5.2], 142-143.)

Accordingly, the trial court erred in failing to recognize and rule, based on the testimony presented at the Kelly hearing below, that in using a floating bin of only plus or minus 2.5 percent, the FBI did not follow correct scientific procedures when it calculated a random-match probability of 1 in 65,000 under the modified ceiling approach. There was no substantial evidence upon which to base a contrary conclusion, and therefore the trial court abused its discretion in not excluding the flawed statistical evidence. (People v. Reilly, supra, 196 Cal.App.3d at p. 1155; see generally, People v. Williams (1997) 16 Cal.4th 153, 197 [66 Cal.Rptr.2d 123, 940 P.2d 710]; People v. Rodrigues (1994) 8 Cal.4th 1060, 1167 [36 Cal.Rptr.2d 235, 885 P.2d 1]; People v. Clair (1992) 2 Cal.4th 629, 676 [7 Cal.Rptr.2d 564, 828 P.2d 705].)

C. Prejudice From Improper Admission of Prosecution’s DNA Evidence

Erroneous admission of the results of the FBI’s DNA analysis using the modified ceiling approach with floating bins that were too narrow requires reversal only if it is reasonably probable the verdict would have been more favorable to defendant in the absence of the error. {People v. Watson (1956) 46 Cal.2d 818, 836 [299 P.2d 243].)

The first question relevant to the prejudice inquiry is whether, notwithstanding the error, there would have remained validly admissible DNA probability evidence available for presentation to the jury in this case. As previously explained, FBI Agent Lynch testified on direct examination, in accordance with the trial court’s ruling, that her analysis under the FBI’s modified ceiling, floating-bin approach showed the probability of a random match to be 1 in 65,000. On cross-examination, the defense elicited the results of the analysis in which she used the FBI’s fixed bins together with the straight product rule. Those results were more favorable to defendant in that they showed the probability of a random match in the Hispanic population to be 1 in 31,000. The Attorney General. contends those fixed-bin results were themselves admissible without proof of general scientific acceptance of the underlying methodology because the defense chose to introduce them.

At the Kelly hearing, however, defendant repeatedly objected to the admission of any DNA evidence. The objection was overruled only as to results obtained under the NRC’s modified ceiling methodology. In the face of that ruling, defendant was entitled to elicit the more favorable product-rule/fixed-bin results on cross-examination in order to mitigate the effect of the erroneously admitted evidence. “An attempt to attack the merits of damaging testimony to which a party has unsuccessfully objected has long been recognized as a necessary and proper trial tactic, and it may not be deemed a waiver of a continuing objection.” (People v. Sam (1969) 71 Cal.2d 194, 207 [77 Cal.Rptr. 804, 454 P.2d 700]; 9 Witkin, Cal. Procedure (4th ed. 1997) Appeal, § 393, p. 443.)

The Attorney General, however, urges us to rule as a matter of law that the FBI’s probability calculations using the unmodified product rule, brought before the jury by defendant on cross-examination, have by now themselves achieved general scientific acceptance, and that therefore defendant’s objection to their admission should have been overruled. That proposition, however, was explicitly rejected by the trial court, and implicitly rejected in the opinion of the Court of Appeal. We deem it inappropriate to undertake our own study of the scientific literature as a basis for considering such a ruling in the absence of more guidance than is afforded by the present record. (See People v. Brown, supra, 40 Cal.3d at pp. 533-535.) The separate issue of the propriety of use of the unmodified product rule is pending before us in other cases. (See, e.g., People v. Soto, review granted Mar. 16, 1995 (S044043).)

The second matter relevant to the prejudice inquiry, one dispositive in our view, is the prosecutor’s candid concession below that without the DNA evidence there was insufficient evidence to convict defendant of the charged offenses beyond a reasonable doubt. The Attorney General has not argued to the contrary on appeal. There was, of course, clear evidence of defendant’s presence in the hotel just before commission of the crime, and the victim’s description of her assailant was consistent with his appearance. She was, however, unable tó identify him at a lineup, and there were no fingerprints or other incriminating forensic evidence other than a serologist’s testimony that one of the semen samples and defendant’s blood were of a type (ABO secretor) shared by approximately half the population. On this record, and in light of the prosecution’s concession below, we are compelled to agree with the Court of Appeal that it was reasonably probable defendant would have had a more favorable verdict had the trial court not erroneously admitted the DNA evidence, and that “[r]etrial of this case is not precluded, since the erroneously admitted evidence was sufficient to permit a finding of guilt beyond a reasonable doubt. (Lockhart v. Nelson (1988) 488 U.S. 33, 40 [109 S.Ct. 285, 102 L.Ed.2d 265]; . . . People v. Mattson (1990) 50 Cal.3d 826, 853, fn. 16 [268 Cal.Rptr. 802, 789 P.2d 983].)”

In the event of a retrial, the prosecution will be free to introduce one or more recomputed analyses of the relevant DNA data in this case after demonstrating that such statistical results were generated by either of the following means: (1) recalculation of statistical probabilities under the NRC’s modified ceiling approach, arrived at through use of correct scientific procedures consistent with the views expressed herein, or (2) recalculation made by using correct scientific procedures under any other statistical methodology that is otherwise demonstrated to have gained general acceptance in the relevant scientific community, within the purview of the Kelly test, since the first trial.

VII. Conclusion

The judgment of the Court of Appeal is affirmed, and the cause is remanded for further proceedings consistent with this opinion.

George, C. J., Mosk, J., Kennard, J., Werdegar, J., Chin, J., and Brown, J., concurred. 
      
      All section references are to the Penal Code unless otherwise indicated. Defendant was sentenced to the upper term of eight years each on one count of forcible rape (§ 264, subd. (a); former § 261, subd. (2)); one count of forcible oral copulation (§ 288a, subd. (c)), and two counts of sexual penetration with a foreign object, i.e., his fingers (§ 289, subd. (a)). Three-year enhancements for use of a deadly weapon (§ 12022.3) were imposed on all four counts, and five-year enhancements for infliction of great bodily harm (§ 12022.8) were imposed on the counts of rape and oral copulation and one count of sexual penetration. Defendant was additionally sentenced to the upper term of six years for first degree robbery (§ 212.5, subd. (a), former § 213, subd. (a)(1)). Sentences on a conviction of assault with a deadly weapon (§ 245, subd. (a)(1)) and on enhancements for a prior prison term (§ 667.5, subd. (b)) and for infliction of great bodily harm in committing the robbery (former § 12022.7) were stayed under former section 654.
     
      
      For a discussion of electrophoretic typing of human bodily fluids for genetic markers, see People v. Brown (1985) 40 Cal.3d 512, 528-535 [220 Cal.Rptr. 637, 709 P.2d 440], and People v. Morris (1991) 53 Cal.3d 152, 206-208 [279 Cal.Rptr. 720, 807 P.2d 949] (resolving admissibility question left open in Brown).
      
     
      
      A “Kelly/Frye foundational showing [is] foundational evidence disclosing general acceptance of the [tests or calculations] within the relevant scientific community (see People v. Kelly (1976) 17 Cal.3d 24 ... ; Frye v. United States (D.C. Cir. 1923) 293 F. 1013, 1014 ...)....” (People v. Leahy, supra, 8 Cal.4th at p. 591.)
     
      
      The reopened hearing was held after trial testimony had commenced, during recesses outside the presence of the jury. Counsel apparently agreed to this procedure in light of the prosecutor’s earlier representations that “without the DNA evidence . . . , there is no case” and “we would have to dismiss.” At the hearing on the motion to reopen, the prosecutor suggested that if the court were to rule for defendant, it could grant a mistrial.
     
      
      Forensic DNA analysis need not always involve scrutiny of the suspect’s known DNA profile. In other fact situations, for example, the victim’s known DNA profile might be compared for identification purposes with blood or other bodily fluid stains found on the suspect’s clothing or premises.
     
      
      The other system is known as “polymerase chain reaction” (PCR), “whereby small pieces of DNA are copied or amplified. The technique is employed when the DNA sample available is too small and/or degraded to perform a more common type of DNA analysis known as RFLP.” (People v. Morganti (1996) 43 Cal.App.4th 643, 662 [50 Cal.Rptr.2d 837].) One source suggests that “[t]he technique is faster than RFLP but less discriminating and therefore somewhat less powerful as an identification tool.” (McKenna et al., Reference Guide on Forensic DNA Evidence, in Reference Manual on Scientific Evidence (Fed. Jud. Center 1995) p. 288 (hereafter Reference Guide).) The PCR methodology is not at issue in this case.
     
      
      DNA theory and RFLP methodology are summarized for the nonscientific reader in numerous texts and judicial opinions. (See, e.g., Barney, supra, 8 Cal.App.4th at pp. 805-810; Axell, supra, 235 Cal.App.3d at pp. 844-848; U.S. v. Yee (N.D.Ohio 1991) 134 F.R.D. 161, 169-173, affd. sub nom. U.S. v. Bonds (6th Cir. 1993) 12 F.3d 540; State v. Anderson (1994) 118 N.M. 284 [881 P.2d 29, 32-35]; Reference Guide, supra, pp. 273-329; U.S. Cong., Off. Technology Assessment, Genetic Witness: Forensic Uses of DNA Tests (1990).) Authoritative explanations prepared by committees consisting predominantly of scientists appear in the NRC’s two reports on the subject: DNA Technology in Forensic Science (1992) (hereafter 1992 NRC Report) and The Evaluation of Forensic DNA Evidence (1996) (hereafter 1996 NRC Report). For an in-depth discussion, see Thompson, Evaluating the Admissibility of New Genetic Identification Tests: Lessons from the “DNA War" (1993) 84 J. Crim. L. & Criminology 22.
     
      
      Though missing from red blood cells, DNA abounds in white blood cells. (See 1996 NRC Rep., supra, p. 66, fn. 4.)
     
      
      Individual sperm and egg cells have only 23 chromosomes that upon conception are paired with 23 chromosomes from the mate. A man’s semen sample, however, normally contains a large quantity of sperm cells that collectively include all 46 chromosomes.
     
      
      In genetics, “allele” usually means an alternate form of gene on one of a pair of chromosomes at a particular locus. In forensic analysis, the term is expanded to include an alternate form of any base-pair sequence. (1996 NRC Rep., supra, p. 214.)
     
      
      ii“vNTR regions are not genes, and our interest in them is solely related to their use for identifying individuals.” (1996 NRC Rep., supra, p. 65.) “[S]ome VNTRs might have disease associations [citation], [but] [t]hese are not used in forensics . . . .” {Id. at p. 71.)
     
      
      The Barney opinion combines the “Southern transfer” and “denaturing” substeps for discussion purposes, apparently because those two procedures are performed at about the same time in the processing sequence. It should be noted, however, that each of the two procedures serves a distinct function.
     
      
      Cf. United States v. Lowe (D.Mass. 1996) 954 F.Supp. 401, 402, 408, 411-416 (discussing a new detection system that visualizes the probes on the X-ray film by means of “chemiluminescence”).
     
      
      For example, a probe with the sequence AGCT would bind with all fragments containing the sequence TCGA.
     
      
      Thus, in the present case, the FBI conservatively reported an inconclusive match at one of the four loci under its policy of refraining from measuring bands of more than ten thousand base pairs because it has concluded the reliability of measurements above that size is open to question.
     
      
      The evidentiary sample targeted for comparison with the population can be a suspect’s sample, a questioned sample, or a combination of both. The FBI in this case used a combination of defendant’s known sample and questioned samples for comparison. (See post, fn. 40.) Barney appears to equate the “statistical significance of a match” with “how unlikely it is that the crime scene samples came from a third party who had the same DNA pattern as the suspect.” (8 Cal.App.4th at p. 809, italics added.) On the other hand, the 1996 NRC Report (supra, pp. 142-144) recommends use of the DNA profile of the questioned sample to calculate the probability of a random match in the pertinent population. It should be kept in mind, however, that at that point in the analysis, the questioned and known suspect samples will themselves already have been declared a “match,” and therefore the fragment sizes used in the calculation cannot vary beyond the bounds of the match criterion.
     
      
      Thus, the measurements are necessarily made on autorads prepared with the same restrictive enzyme and the same probes that are used for testing the evidentiary samples.
     
      
      The rules typically relate to (1) how to determine what bin or bins are overlapped by the appropriate match window, and (2) the consequences of an overlap of multiple bins. The FBI determines an overlap by using a match window that the 1996 NRC Report {supra, pp. 143-145) suggests may be too narrow. When there is an overlap, the FBI selects the overlapped bin containing the highest number of bands. The 1992 NRC Report recommended that the bands in the overlapped bins be added together {supra, p. 86), but the 1996 NRC Report rejects that recommendation as “excessively cautious” {supra, p. 144).
     
      
      The “frequency” of one or more alleles is the statistical probability that it or they will be found in the DNA of a randomly selected member of the population from which the database is derived.
     
      
      Reasons for this nonappearance may be, for example, that the size of the second allele is unusually small or large or is so close to that of the first allele that their two bands are indistinguishable. (See 1996 NRC Rep., supra, p. 69.)
     
      
      For example, if the evidentiary sample were to have two alleles at each of four loci, each allele having a frequency of 1 out of 10 (0.1), application of the product rule would produce a frequency of 1 out of 6.25 million (.00000016),
     
      
      Conversely, the laboratories do not use a single interracial United States database, presumably because the incidence of random mating between members of the different racial categories is deemed low enough to preclude use of the product rule to calculate an overall frequency statistic for the United States population as a whole.
     
      
      “The [1992 NRC] report proposes a method of statistical calculation which accounts for the possibility of population substructuring, eliminates ethnicity as a factor in the calculation process, and permits the use of the product rule while ensuring that probability estimates are appropriately conservative.” (Barney, supra, 8 Cal.App.4th at pp. 821-822.)
     
      
      Lynch used D2S44 as an example to explain the locus numbering system. “D” stands for DNA; “2” for the second pair of chromosomes; and “S” for single copy, meaning that the base-pair sequence selected by the probe appears only at this locus. The number “44” denotes the 44th locus to be scientifically identified on chromosome pair number 2. Later, before the jury, Lynch explained that the other three probes used by the FBI (in addition to D2S44) are D1S7, D4S139, and D17S79.
     
      
      In her trial testimony, Lynch identified the two questioned samples as coming from the vaginal swab and from semen-stained cloth cut out of the bedspread. A third questioned sample, also from the bedspread, was declared a nonmatch.
     
      
      Those concerns and opposing views are fully aired in two articles juxtaposed in the December 20, 1991, issue of Science magazine (vol. 254): Lewontin and Hartl, Population Genetics in Forensic DNA Typing, at page 1745, and Chakraborty and Kidd, The Utility of DNA Typing in Forensic Work, at page 1735. The controversy is analyzed in Barney, supra, 8 Cal.App.4th at pages 814-821.
     
      
      Narrowing a floating bin tends to reduce the number of database bands it contains, thereby reducing the frequency attributed to the evidentiary band that matches the bin, to the disadvantage of the suspect.
     
      
      Mueller appears to have assumed that the FBI measured only intra-gel variations in establishing its match criteria. Lynch, however, had testified that the development of the FBI’s plus or minus 2.5 percent match criterion is described in a paper written by the scientist in charge of the FBI’s DNA research: Budowle, Data for Forensic Matching Criteria for VNTR Profiles, in Proceedings for The International Symposium on Human Identification (1989) at page 103. The paper says that to collect some of the data used to develop the plus or minus 2.5 percent tolerance window, “human DNA derived from whole blood stains was run on several gels." {Id. at p. 104, italics added.)
     
      
      Fifteen scientific articles had been introduced into evidence and approximately fifteen more submitted along with requests to take judicial notice.
     
      
      In Daubert v. Merrell Dow Pharmaceuticals, Inc. (1993) 509 U.S. 579 [113 S.Ct. 2786, 125 L.Ed.2d 469], the United States Supreme Court held that Frye, supra, 293 F. 1013, was abrogated by rule 702 of the Federal Rules of Evidence (28 U.S.C.). In People v. Leahy, supra, 8 Cal.4th 587, at page 591, this court adhered to the Kelly/Frye requirements, concluding that “the Kelly/Frye formulation (or now, more accurately, the Kelly formulation) should remain a prerequisite to the admission of expert testimony regarding new scientific methodology in this state.” We further reiterated that the Kelly/Frye rule was not abrogated by the adoption in 1982 of the “Truth-in-Evidence” provision of article I, section 28, subdivision (d) of the California Constitution. (8 Cal.4th at p. 598.)
     
      
      The courts trying defendants Barney and Howard (whose case was consolidated with Barney’s on appeal) had both admitted the record of the Kelly/Frye hearing conducted in Axell, supra, 235 Cal.App.3d 836. (Barney, supra, 8 Cal.App.4th at pp. 803-804.)
     
      
      Professor Lander may well have originated the term “ceiling principle.” In the cited letter he suggests that “[t]o determine whether VNTR allele frequencies vary significantly among ethnic groups, it should be sufficient to collect perhaps a dozen or so well-separated ethnic population samples. . . . HQ To account for population substructure by using such data, one could then employ a method called the ceiling principle: regardless of a defendant’s ethnic background, each allele frequency used in the calculation would be the maximum observed in the various ethnic samples (the ceiling frequency). Although a defendant’s own ethnic group might not have been among those sampled, the approach should compensate for the extent of possible variability at the locus.” (49 Am. J. Hum. Genetics, supra, at p. 902.)
     
      
      Aldhous, Geneticists Attack NRC Report as Scientifically Flawed (Feb. 5, 1993) 259 Science 755.
     
      
      Devlin et al., Statistical Evaluation of DNA Fingerprinting: A Critique of the N.R.C.’s Report (Feb. 5, 1993) 259 Science 748.
     
      
      Morton, Genetic Structure of Forensic Populations (Apr. 1992) 89 Proc. Nat. Acad. Sci. USA 2556.
     
      
      Weir, letter to the editor, re: Forensic Population Genetics and the National Research Council (NRC) (1992) 52 Am. J. Hum. Genetics 437.
     
      
      Chakraborty testified the FBI’s purpose in doing floating-bin computations was to show that the fixed-bin numbers were truly conservative. He said that the basic 31 fixed bins vary from plus or minus 3 percent to plus or minus 9 percent. The fixed bins become even wider when combined, or collapsed, to satisfy the FBI’s standard minimum of five database alleles in each bin.
     
      
      “For forensic purposes, the frequency of an allele in a laboratory’s databank should be calculated by counting the number of alleles that would be regarded as a match with the laboratory’s forensic matching rule, which should be based on the empirical reproducibility of the system. This matching rule must account for both the quantitative reproducibility of forensic measurements in the testing laboratory and the quantitative reproducibility of the population measurements in the laboratory that generated the databank. In addition, the matching rule should reflect that one is making inter-gel comparisons, which are typically less precise than intra-gel comparisons.” (1992 NRC Rep., supra, pp. 85-86, italics added.)
     
      
      The evidentiary band used for this purpose by the FBI consisted of the mean, or average, of the respective bands of defendant’s known blood sample and the questioned sample. Mueller testified that because the ultimate goal is to determine whether the suspect or some other person was the source of the questioned sample, the floating bin should be centered on that sample alone, whereas the FBI’s use of a mean erroneously presupposes a degree of identity between the questioned sample and the suspect’s sample. (Cf. 1996 NRC Rep., supra, pp. 141-145 [indicating floating bins should be centered on band of questioned sample].)
      The FBI’s fixed bins, in contrast, were not confined to a single center. Instead, the FBI drew windows around the bands of defendant’s sample and of both the questioned samples, and used any fixed bin that encompassed all three windows. If the combined windows overlapped a bin boundary, the bin with the higher frequency was used. Thus, in the bins for the Hispanic and Caucasian databases at locus D17S79, the windows for defendant’s sample and one of the two questioned samples were wholly within bin 4. The window of the other questioned sample, however, overlapped bins 4 and 5, resulting in the use of bin 5’s frequency because it was higher than the frequency in bin 4.
      According to the prosecution’s expert, Tracey, this selection of the higher of the overlapped bins caused the FBI’s product-rule/fixed-bin result to be more conservative than its modified ceiling/floating-bin results.
     
      
      “To determine the probability that a matching allele was found by chance, one counts the number of matching alleles in an appropriately chosen reference population. For the calculation to be valid, the same match criterion must be applied in screening the population databank and in comparing the forensic samples.” (1992 NRC Rep., supra, p. 62; id., pp. 78, 85.)
     
      
      “The size of the floating window should be twice the laboratory’s quantitative match criterion. For example, for a match criterion of ±2.5%, the floating window for ceiling principle allele frequencies will be ±5.0%, which is a total width of 10%.” {The Technical Working Group on DNA Analysis Methods (TWGDAM) Consensus Approach for Applying the “Ceiling Principle” to Derive Conservative Estimates of DNA Profile Frequencies (1994) 39 J. Forensic Sci. 899, 901 [letter to the editor signed by 33 TWGDAM members, including 3 who identified themselves as affiliated with the FBI].)
     
      
      Defendant urged two additional contentions in his brief and in oral argument: (1) that the DNA evidence should have been excluded because it was not accompanied by evidence of the probability of false matches caused by laboratory error; and (2) that a prosecution criminalist should not have been allowed to testify, over objection, that the statistical probability of a random match can properly be cut in half (e.g., from 1 out of 65,000 to 1 out of 130,000) through multiplication of the probability of defendant’s DNA profile, generated by RFLP analysis, by the probability of defendant’s ABO blood type (1 out of 2).
      We decline to reach these contentions for three reasons: (1) The contentions are not fairly included in the issues framed in the Attorney General’s petition for review, and there was no answer to that petition. (Cal. Rules of Court, rules 28(e)(2), 29.3(c); People v. Estrada (1995) 11 Cal.4th 568, 580 [46 Cal.Rptr.2d 586, 904 P.2d 1197]; In re Marriage ofHeikes (1995) 10 Cal.4th 1211, 1215, fn. 5 [44 Cal.Rptr.2d 155, 899 P.2d 1349].) (2) Since we affirm the Court of Appeal’s reversal of the trial court’s judgment, it is unnecessary for us to consider additional grounds for such reversal. (3) The present record pertaining to these issues does not provide a sufficient basis for deciding them.
     