Full opinion text
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 whet