All right. Mrs. Robertson, witness.
Bruce Weir, (402) called as a witness by the People, pursuant to Evidence Code section 402, was sworn and testified as follows:
Please raise your right hand. You do solemnly swear that the testimony you may give in the cause now pending before this court, shall be the truth, the whole truth and nothing but the truth, so help you God.
Please have a seat on the witness stand and state and spell your first and last names for the record.
I'm currently a professor of statistics and genetics at a North Carolina State University.
I first went there as a graduate student in 1965. I've been on the faculty since 1976.
Your Honor, I have what can be described as I believe a CV of Dr. Weir that I would ask be marked as--does the Court wish us to continue with the exhibit numbers?
Dr. Weir, showing you what will be marked as an exhibit shortly, can you describe what that is?
All right. Could you tell us then and describe for the Court, if you would initially, your educational background?
I have a bachelor's degree in mathematics from the University of Canterbury in New Zealand, a Ph.D. in statistics with a minor in genetics from North Carolina State University and I spent time as a postgraduate research geneticist at the University of California at Davis.
In particular you described your Ph.D. being in the area of statistics. What did that encompass, if you can briefly summarize that?
Well, it was fairly detailed examination of the methods in statistics, both the theory of statistics, the mathematical theory, and the appropriate means of analyzing data.
All right. With the Court's permission it would be my request that the Court actually have the exhibit before the Court and then I have a copy that the witness can utilize as well.
When I completed my postdoctoral period I returned to New Zealand as a senior lecturer in mathematics at Massey University. I remained there for almost six years and then returned to this country in 1976 as an associate professor of statistics and genetics and I have remained in that department, the department of statistics.
During the time--and I believe you said that was a six-year period at the--in the department of mathematics at Massey University in New Zealand?
I did then what I do now. I teach statistics and statistical genetics. I conduct research in the appropriate ways of analyzing genetic data.
I do teach. I have taught general statistics courses. In recent years I have taught courses based on my book on genetic data analysis.
Now, you have used this term "Genetic data" and you have also used the term "Statistics" as well?
Well, we use statistical methods--statistics, as you know, can be applied to many different fields. My specialty is in applying statistical methods to data concerned with genetic entities. What we will be talking about today is the specific DNA markers used in forensic science. Those are of course just one of many types of possible genetic data.
On your CV, and in particular on page 1, there is also a category listed as "Honors"; is that right?
Well, I think I'm most proud of two. I had a Guggenheim fellowship in 1983 of which I am proud, and then in 1992 I was given a named professorship at my university.
Now, the Guggenheim fellowship, did that involve your conducting any research or other activities at another university other than your own?
Well, the fellowship enabled--it enabled me to take a year sabbatical and I went to the University of Edinburgh for a year and essentially brought myself up to speed on the current DNA methodologies.
While you were at the University of Edinburgh did your activity--and you have described getting yourself up to speed; is that right?
Well, prior to that period, although I should stress that my statistical methods have not changed since--have not changed direction fundamentally, but prior to 1983 I was concerned mainly with genetic data on protein polymorphisms. Since that time I've dealt more with DNA sequences and the molecular markers. It is just a change of emphasis. It is not that the methods of statistics have changed, but the language needed to describe the data have changed and I needed to be sure I understood all the terminology being used by the molecular biologists.
When you described this transition, you are referring to this transition from the use of electrophoresis to type proteins into DNA typing itself?
And I believe you also mentioned, as far as the other Honor of note, your current professorship; is that right?
Turning to page 2, there are a number of professional societies listed of which you are a member?
I think the most relevant ones here were the American Statistical Association, the American Society for Human Genetics and the Genetic Society of America.
Yes, I do. I am one of the senior editors for our theoretical population biology. I'm responsible for the genetics paper in that journal. For a long time I have been on the editorial board for the journal of genetics and for the last two or three years I'm on the editorial board for the American Journal of Human Genetics.
Again referring you to page 2 of your CV, you list a number of other publications of which you are either editor or associate editor?
There have been other journals. I believe I'm still on the editorial board for the journal of heredity and some other journals that are rotated off those boards.
I would like to shift your attention, if I can, to scientific presentations. Are you involved in giving scientific presentations?
Yes, I am. It is a very important part of our work to disseminate our findings, both through publications, which of course is the most important, but a more immediate dissemination is at scientific meetings. And in the last--I guess since 1990 I have been very heavily involved in the statistics associated with the forensic uses of DNA and on the basis of my published work I am now being--I am now receiving several presentations to present at international meetings. I will be going to Spain in the fall for the International Forensic Human Genetics Conference and in the summer of next year to Edinburgh to the International Conference on Forensic Statistics.
Prior to today have you actually been invited and lectured in conferences involving statistics in DNA?
Yes. There was a meeting in phoenix, I believe two years ago, and at the FBI academy there was an international symposium on the forensic aspects of DNA analysis.
In your role at North Carolina State do you also supervise Ph.D. candidates in this area?
That's right. One student in particular, Paul Maiste, completed a thesis under my direction in 1993 and we conducted a fairly extensive examination of the means for testing for independence and mark the various components of a DNA profile. His thesis was completed and it has been on the record since 1993. The first paper from the thesis appeared in print last week in the Journal of Genetica.
I would like to turn your attention to what appears to be page 4 of your CV and beginning on that page are there publications listed of which you have either been sole author or co-author?
Well, starting on page 4 and then running some pages it lists my complete publication list, yes.
Well, yes and no. They are all involved in statistical analyses of genetica. Some of them are purely theoretical. Some of them are applications of these methods to specific data sets, human, drosophilia, maize, mice. It doesn't really matter as far as my work is concerned what the organism is, whenever genetic data are collected, then I'm happy to be involved in their analysis.
Have your publications included a substantial number dealing with human genetic characteristics?
Yes, in two different directions. What I'm primarily interested in is looking for associations of genetic markers with human diseases. I think that is very important and very exciting work and I've had several papers in that field. And as I said earlier, I have also been involved in the forensic arena recently, so I have had several papers targeted specifically to the kind of data used by forensic scientists.
I would like to call your attention, if I could, to two publications in particular, the first on page 5 that I believe is labeled no. 29 titled, "Inferences about linkage disequilibrium."
Yes. That is a paper published in `79 talking about the methods to detect associations or lack of independence between elements at different genetic loci. It is--it is one of my--I think one of my important papers. It is just a foundation for a lot of our subsequent work.
All right. When you use the term "Independence among loci," can you tell us a little bit more about what you mean?
Well, it goes back to Mendel's second law of course. What we are interested in knowing is if the information transmitted from parents to offspring at one locus, one region of the genome, is transmitted independently of information at different loci, different regions. For loci on different chromosomes we would expect to find such independence, although as I showed in my thesis in 1968, even loci on different chromosomes may have some slight dependence on their frequencies imposed by the size of the population and the mating structure. I'm digressing. The point is that we laid out in that paper some of the methods appropriate for detecting associations, regardless of the biological cause. And I think we need to stress that today. We are not interested in the biological mechanisms as much as in the consequences. What do the data look like? Do they exhibit independence and therefore may we proceed to use product rules? Or do they not show consistency with independence in which case we need to do something else?
In other words, basically you are looking at whether or not different regions of DNA may be linked in some fashion?
Yes. I would prefer to use the word "Associated." Linked has the technical term and we are not talking about linkage. We are talking about associations.
Turning your attention, if I can, to page 9 of your CV, in particular a publication numbered 89 entitled, "Effects of inbreeding on forensic calculations," was that another paper that you personally authored?
Yes, it is one of my more recent and we always think our most recent papers are our best, but this was an invited paper for the annual review of genetics. The invitation came some time ago and then when it came time to actually put pen to paper, I chose to write on this current area of the forensic applications. The paper was invited, but it still was subject to a peer review, and although it has a somewhat narrow focus, I really took the opportunity to summarize a great deal of my thinking in the appropriate ways of analyzing the data. And I think I should say here that--that this, I believe, lays out the appropriate way to account for population structuring and thereby diffuse some of the problems people have felt faced by these data.
Turning to the next page, page 10, there is also a category labeled "Commentaries and correspondence."
That appears to have thirteen different items it in. Can you just tell us in summary fashion what commentaries and correspondence are?
Well, I would like to remove from my publication those things which are not scientific papers in the sense of being through a peer review process and present novel scientific information. Some of these are reviews. The 1992 paper and the proceedings of the national academy of science was a review of the population genetic issues. I was invited by the editor of the journal to write a review, which I was pleased to do, but it did not go through a review process, a formal review. I solicited comments from several colleagues, so that is a review, then there are several letters which are felt are sufficiently annoyed with papers and journals that I would write a response, particularly to science and nature who have published once again non-peer reviewed--I don't want to say articles because they are not article--pieces of writing, they have published items often critical of the forensic uses of DNA. I think they have given a very one-sided view of the debate and occasion I have managed to get a rebuttal letter published.
When you are referring to science and nature you are referring to science magazine and nature magazine?
Turning to page 11, in particular a category labeled "Books," have you published books in the area of population genetics and their relationship with statistical data?
Yes. In 1990 I published a book genetic data analysis which is meant to be a very broad reference work, if would you like, of all the methods likely to be encountered by people generating genetic data of the kind we will be talking about and some other kinds. In press currently there is a book to be published by a kluwer entitled human identification. For that volume I acted as editor. I solicited articles from a variety of people who have made substantial contributions to this field and I was pleased with. They agreed to write papers. The articles all went through a review process. The collection of papers has appeared already as a special issue of a Journal Genetica and will appear as a hard cover book later this year.
This is of very little consequence, I think. I publish reviews of other people's books.
Then lastly, on what appearing to be the remaining two pages, there is a listing of published abstracts by you?
All right. Your Honor, for purposes of this hearing I would ask that this particular exhibit, People's exhibit 407, be admitted.
Dr. Weir, I would like to turn your attention to any activity you may have in terms of consulting forensic DNA cases.
Well, on cases in particular I'm approached by both Defense and Prosecution attorneys to give them assistance. I've al declined Defense requests because I don't believe I can argue against the forensic uses of DNA, so when an attorney contacts me for the Prosecution, I ask to see a copy of all reports provided them by the forensic scientists, and I focus on the statistical aspects of those reports. I then obtain the necessary databases used by that particular forensic scientist, conduct tests of such things as association. Essentially duplicate the statistical aspects of the report and then, if necessary, I give testimony at both admissibility hearings and the subsequent trial.
Now, when you say you review the data, do you review the data in terms of not only the results of DNA testing in a forensic case, but also ultimately what are the frequencies reported to describe any matches?
And as far as looking at that type of data and your analysis, what are you looking for?
I'm looking for confirmation of my prior beliefs that the DNA markers used in forensic science associated freely, there is no evidence for dependence within loci.
Yes, I'm sorry. Once we have demonstrated consistency with independence, then we may proceed to use the product rule. As I think I said earlier, if I find evidence for dependence, then we have to modify the production of profile frequencies.
When you use the term "Dependence," would that then be the same as referring to association, if you find it?
And in those instances have you been allowed to testify as an expert in this area of genetic data and population frequencies?
Now, as far as your own experience, and if you could describe to the Court, please, how is it that in terms of these DNA type techniques and genetic marker results that are obtained using them, that you became involved and experienced in examining the data obtained as a result of these testings? Is that question clear?
I didn't think so. What I'm really asking you, Dr. Weir, is, as far as these DNA typing techniques and then ultimately obtaining results from them, how did you gain your experience to be able to look at these results and then determine from these tests whether or not there is, for instance, any of this association?
Well, my experience really points to my entire career since my--the early publications I have been involved in setting up methods, not all of them of course directly relevant, but we talked about a 1979 paper. And at that time we were setting up statistical methods to analyze genetic data. This was, remember, a long time before DNA markers were in vogue. The methods we developed at that point have--have come to be seen as appropriate for the data we are currently involved with. So I think I'm qualified and have been requested to work on these issues on the basis of my publications, which as I said, date back a long way.
And they deal with, for example, RFLP typing results and data generated as a result of that?
Have you in fact developed methods, that is, personally developed methods to evaluate this type of information?
Well, I can't publish a paper unless I have something new, so my papers I think invariably describe new tests or new approaches to old tests or evaluations of tests, so I think it is fair to say that the methods I use are either so standard that they don't need to be justified or they are ones that we have worked on provided the justification.
You described around I believe it was 1983 during your sabbatical and I think that was the Guggenheim fellowship period?
That obviously--or first of all, let me ask it as a question. Was that around the time that DNA typing techniques were being developed?
As it turns out probably while I was sitting in Edinburgh Professor Jeffries was down the road at Lester working on the method which subsequently came to be called DNA fingerprints.
As far as these methods that you utilized or have developed to evaluate genetic marker data, did you develop some of those methods even before DNA typing was available?
Yes. One of the--one of the interesting aspects of the forensic uses, apart from the obvious applications, the interest to me is that the data are so discriminating, the RFLPs in particular have so many types, which is the reason they are used, that they presented some novel challenges for such issues as testing for independence, so we had to do a little development and extension of our previous works and then of course our methods must be tailored to the way that the data are generated. I'm sure you've heard described Cellmark's floating bands method or the FBI's fixed band method. These are different ways of generating data. Those different ways must be reflected in the method of analysis, so I've had to accommodate those methods in the subsequent analyses.
That was actually going to be the next question I asked and perhaps I can ask it in a somewhat summary fashion: In your evaluation of DNA typing data, do you use methods that were involved either by yourself or others even before DNA typing was available?
And do you also then use methods developed either by yourself or others to evaluate DNA typing data that were involved as DNA typing was available?
Certainly, yes. I think it is necessary to perform appropriate statistical validation studies on the forensic databases--
Is it correct to say then that many of these techniques that are even used today to evaluate DNA data have been in existence for many, many years?
Now I would like to turn your attention, Dr. Weir, to experience that you've previously had with Cellmark diagnostics.
Yes. We have a contractual arrangement. I think it is effectively called a memorandum of understanding whereby my university undertakes to perform analyses for Cellmark.
I'm currently--the immediate reason for the contract was to evaluate their new databases. As you probably know, they have data collected from their paternity testing business, and they have culled data from their paternity records to serve as a forensic database and Cellmark wished these new databases to be evaluated for independence.
Are you familiar with the methods used in Cellmark or at Cellmark diagnostics as far as reporting population frequency data based on DNA matches?
I think it must have been late 1990. I had discussions with them and they provided me with copies of their then current databases and were very generous in both sharing the data and explaining in some detail how the data were collected, how they were used, explained their banding strategies and so forth. And with their cooperation I was able to perform analyses and subsequently publish those, I think it was 1990 in the paper in the American Journal of Human Genetics.
In fact in your CV do you list a specific reference, and perhaps if you are able to point us in the direction of what publication number that publication is in which you published your own results of evaluating data at Cellmark?
As far as your familiarity with frequency calculations and frequency data as Cellmark, does that include RFLP data?
Yes. This--this paper we are talking about here was RFLP. As part of our contract we've also examined their current PCR database.
When you use the term "Polymarker" are you referring to five individual genetic markers that are collectively referred to as polymarker or PM?
I would like to turn your attention, Dr. Weir, to the California Department of Justice.
To your knowledge--well, first of all, are you aware of what types of data are used at the California Department of Justice in the area of frequency data?
Yes. Over the last few months I have held--I had several conversations with a Gary Sims who explained to me that Cellmark--excuse me--the DOJ uses data collected by the FBI.
Could you describe for the Court, please, how and if you are familiar with FBI data in the area of DNA typing?
Yes. I first met Dr. Budowle from the FBI I think in December of 1989 and he asked for some assistance in collaboration on interpreting and analyzing their databases and subsequently provided me with their current and subsequent versions of their various databases. As a result of that initial contact I did some work on their RFLPs and published an analysis of that also in 1992, item no. 72, a paper published in the journal of genetics. Since this time I've kept close contact with the FBI and we have no financial contractual arrangements at all with the FBI. I've kept close contact with them and they have added more probes. I have kept up, if you like, with their analysis, and the most recent data I obtained from them was in this year, RFLP, and I've also got a copy of their--a set of their PCR-based loci and performed analyses on those.
So you are familiar with the FBI's databases as used by the Department of Justice in this case both in the "A" markers as well as the PCR markers used at the Department of Justice?
To your knowledge does that include DQ-Alpha and D1S80, and I'm referring to the Department of Justice?
Yes. There is a compilation of seven loci; DQ-Alpha, D1S80 and the five collectively known as the polymarker.
The publication you described, that publication involved your analysis of FBI data; is that right, in particular, RFLP frequencies?
Item no. 72 and then a more recent paper, the one, no. 96, also an RFLP data from the FBI.
As far as your own personal analysis of data, has that been limited to Cellmark and the FBI or has it included other forensic laboratories?
No. I've been kept quite busy in the private sector. I've looked at data from lifecodes, genetic design and a Roche Biomedical. In the government agencies, apart from the FBI, the State Bureau of Investigation in North Carolina and the corresponding agencies in South Carolina, Dade County and Broward County in Florida, Minnesota, Oregon, Toronto, New Zealand, Australia and United Kingdom.
Now, in these analyses that you undertake with regard to these labs, can you briefly tell us what that entails? What are you looking for?
Well, we are looking primarily for any evidence of associations between the various types and we are also looking for measures to the degree to which different populations differ; the amount of difference and frequencies between, say, Caucasians and Hispanics.
Have you, first of all, with reference to this particular case before the Court involving Mr. Simpson, have you undertaken a review of frequency data generated by both Cellmark and the California Department of Justice?
Your Honor, at this time I would ask to have marked as--perhaps the best method would be exhibit 408--
--and 408-A, and I will describe them. Exhibit 408-A appears to be a report by Dr. Weir dated June 21st, 1995, consisting of what appear to be one cover sheet plus pages 1 through 48. And I would ask that 408-B, a similar report dated also June 21st, but with the additional notations "Addendum" which appears to consist of four pages plus a cover sheet.
Which have been provided to the Defense at more than one time period in different forms.
Dr. Weir, showing first what will be exhibit 408, the lengthier document, is that the report that you have prepared in this case?
Referring specifically--well, let me go a little further with exhibit 408. First of all, that has some stamped number in the upper right-hand corner; is that right?
With regard to this particular document--and it is dated yesterday; is that right, June 21st?
Did you, since yesterday, produce what can be categorized as two replacement pages with some changes in data on two of the pages?
Yes, I did, and I should apologize, although I don't think I am completely to blame, in doing PCR--in doing RFLP calculations for the DOJ report, I had included all the bands they reported in their profiles, forgetting or not knowing that they do not report frequencies on the high molecular weight bands, so that I apologize for that. I removed those bands yesterday and essentially replaced those two pages.
Could you just tell us what your page numbers are for those two pages so that the record will be clear?
It is pages 21--excuse me. Page 22 and the corrections are on table 18, and I see this copy is annotated, replaces, and then on page--I believe it is page 43.
Excuse me. Table 41, table 32. Those are both tables, refers to the DOJ's RFLP calculations now reflecting the fact that the high molecular weight bands do not have frequencies assigned to them.
Incidentally, do those corrections in those two replacement pages have anything to do with DNA mixtures in this case?
Now, if I can turn your attention to the shorter document, 408-A, can you simply tell us briefly what this document is.
Yes. The--my full report contains information on mixtures, except for the RFLP mixtures on the glove reported by DOJ. I received that information later, so this addendum is simply to present really a table of frequencies for the three items from the glove on which there were RFLP mixtures.
As far as this case, can you describe for us the material that you reviewed to conduct your analysis?
Well, I've reviewed the various reports provided by both Cellmark and DOJ and of course as always in any such case I review the appropriate databases from either the FBI or from Cellmark. Maybe this is the appropriate place to say that all my calculations rely on three sets of data; the Cellmark, RFLP databases, both their original and any new information. That is one set. The FBI's RFLP data, seven RFLP loci and then the FBI's PCR database, the whole seven PCR loci.
As far as this review, you utilized material provided to you by both laboratories?
Well, I--yes, both their reports, which I obtained through the Prosecution and numerous telephone conversations.
That was actually going to be my next question. Did there come instances or did there arise instances in which you had questions that you needed answers from the testing laboratories?
Yes. And in particular on the mixtures. I needed to be absolutely sure what the--what the labs had found in their mixture studies and I believe I now understand that and they greatly simplified the analysis to have a complete understanding.
Did there come a time when you were asked to--you were requested to examine pictures in this case as far as frequency data was concerned?
Well, I'm not sure. As soon as I obtained the reports, I proceeded to do an analysis and then I think Miss Kahn asked me, or maybe it was you, who asked me a little while ago to do a complete analysis.
Perhaps we can provide a little bit of a history. Did you produce an initial report earlier this year?
Well, yes. In December I wrote a report and began on the analysis of mixtures and didn't proceed very far at that point, merely to point out that there were mixtures available, these needed to be interpreted, but I don't believe I did any calculations at that point.
Now, carrying forward to later in 1995 were you at some point asked to look at mixtures in terms of calculating frequencies?
Dr. Weir, as far as mixtures, what I'm going to ask you to do is describe for the Court, please, about the area of attaching frequencies to mixtures. What can you tell us about that?
To set the language to talk about single stains first because it is not different. When there is a single stain found to match a person of interest, to attach some numerical weight to that evidence of a match, the first step is to calculate the frequency with which random people would produce the profile found in the stain. So we loosely say we calculate the frequency of the--of the evidentiary profile. In essence we add up all the possible people who could have contributed. Now, the addition is kind of trivial because there is only one type, this is a single genotype, and we add up that single genotype frequency. And that number is what we've seen reported in this case. Typically these are given as 1 in some number, 1 in a thousand, 1 in a million. Remember that those are frequencies. Frequencies of the stain. It is best to interpret that number by flipping it upside down and saying the evidence is a thousand times more likely to have arisen if it was given by this person versus if it was given by an unknown person. It is the unknown person for whom we've calculated the frequency. Now let's turn to a mixture and if we look at the--all the typing, and there are more than two alleles at any locus--
That's correct. Any of the loci examined, if they have more than two alleles, we have evidence that there was more than one contributor to the stain. If we look at all the loci and found two, three or four alleles at every locus, we have evidence that there were two contributors. If we found more than four alleles at any locus, we would have evidence of at least three contributors, and so forth. To keep things in focus here, let's suppose that the evidence and all the loci typed has four or fewer alleles. The evidence points to their being two contributors. We want to attach a frequency. The question--and it is not possible to avoid the proper framework. The framework is how do we interpret the evidence. We believe either that the evidence, the stain, was contributed by these two particular people or three particular people or it was not. The "Or it was not" can be interpreted as this stain was contributed by two unknown people or by three unknown people. What is the frequency with which two unknown people would contribute this stain? So we add up all the frequencies of two people, pairs of people, who between them would have this mixed stain. So if there was a single locus and there were four bands, four alleles, 1, 2, 3 and 4, we have to add up all the possibilities. How likely is it that two people, two unknown people between them would have these four bands? The people might be--the first person might have bands 1 and 2 and the second person have bands 3 or 4 or it might be that the first person has bands 1 and 3, second person 2 and 4.
There are a whole host of situations. It is essential to interpret the data correctly. The evidence suggests there is a mixture. To form an analysis which ignores the evidence of there being a mixture is wrong, it is completing misleading. We must add up the frequencies under the situation suggested by the evidence. The evidence suggests two contributors. We must add up the frequencies with which two contributors between them have this mixed profile.
Your Honor, at this point I was going to turn to the use of the elmo so that the witness could demonstrate something, however, we apparently need, if we could have, a brief recess to be able to do that.
Just the overhead projector, the elmo system turned on, because the document is not complicated--using the document is not complicated.
Dr. Weir, what I'm going to ask you to look at is a particular result in this case. First of all--
Mr. Clarke, why don't you go ahead and spin that around, so both the doctor and I can see it, since we don't have to worry about whether the jury can see it. Thank you.
First of all, Dr. Weir, have you seen a smaller or eight-and-a-half-by-eleven version of this particular board?
What I'm going to ask you to do--and first of all, in your analysis of the results in this case, did you look at what is labeled on this board as item no. 29, steering wheel?
Would that be an example that you could use, that is, the actual results with regard to that item, to talk about frequencies in mixtures?
That particular item contained results, and let's look, if we can, at simply the DQ-Alpha marker. Is that acceptable?
The particular results on item no. 29 at the DQ-Alpha marker showed the appearance of three different alleles; is that right?
That's right. And just reading from the board here would be 1.1, 1.2 and 4, and I should say now that I am taking no notice of descriptors such as weaker or possible trace. I am assuming that if the allele is mentioned, it is present.
So when you perform your own analyses, when a particular allele is described as present, you are not paying attention, for frequency purposes, of a description such as weaker, trace, et cetera?
Now, with regard to that particular item at the DQ-Alpha marker, does that indicate a mixture?
Yes. There are three alleles and that must obviously--implies more than one contributor. One person would only have two alleles.
As far as your review of this particular case and the specific results, and in particular with regard to that item, were you asked to calculate an approximate frequency to describe that mixture and how often one might encounter that mixture?
Yes, I was, and to calculate the frequency with which two contributors or three contributors would have between them those three alleles.
All right. Your Honor, if I may, I would like to have marked then as exhibit 409 a one-page document that is labeled at the top "Percentage of population included in LAPD no. 29."
As a foundation, with what will be marked exhibit 409, the one-page document, have you had an opportunity to look at that document?
And does that page relate to item no. 29 and the particular alleles that were revealed by testing by both Cellmark and the Department of Justice?
Yes. It just lays out, without the--all the details, it lays out the method I used to calculate the frequency of two contributors to a mixture.
Actually let me also hand a copy--first of all, Dr. Weir, there have been copies made.
Showing you this one-page document that will be exhibit 409, is that the document that you had an opportunity to look at?
Yes. This is just as I said, it is to lay out the possibilities with which two people would contribute to the DQ-Alpha mixed stain. As we've said, the mixed stain has three alleles, and we know therefore it is a mixture. I should say there is no evidence at any of the loci typed on item 29 of there being three contributors; however, for this demonstration we have two--we have--we are working under the assumption there where two contributors and I must stress we must work under the assumption of it being a mixture. By definition there is more than one contributor. So we need to examine the possibilities, how likely is it that two people would have between them these three alleles, so we've listed--you have listed out looks like a dozen or so possibilities. The first person, for example, the first row here, the first person could be a 1.1 homozygote, the second person a 1.2 and 4 heterozygote.
In other words, let me stop you for a moment. That is one possibility when there are two contributors to a mixture, to produce the results that were obtained by these laboratories?
That's right. If--if those three people were the contributors to the stain, the stain would look like as it does. The stain would have those three alleles, no more and no less, if those three people were the contributors.
Now, is the remainder of that left-hand column or the two left-hand columns, "First person" and "Second person," simply the remaining possibilities for a two-person mixtures producing those results?
Yes. I think there are all the possibilities, all the ways in which two people between them could have those three alleles.
Should that one point under the listing of first person simply be deleted so that it would read 1.2, 4?
Now, in the upper portion, and this is referring simply to the first listing of first person, 1.1, 1.1, and second person, 1.2 and then 4, there are listed two categories of racial groups; is that right?
Is this simply one listing of what--and if the chart were complete there would be many more listings?
That's right. And in all our calculations, single or mixed stains, when we compute frequencies for unknown people we must recognize that these are really unknown. We know nothing about their ethnicity. We don't know which frequencies to attach, so we go through all the possibilities we have. For example, these two people, the first one may have been African American and the second Caucasian, or vice versa, or the first one may have been African American and the second Hispanic or vice versa, and we could go on. And what I have done in this case is to assume that either of the two people were not of four different ethnicities but have frequencies I've taken from four different databases.
Incidentally, this chart, as is shown now on the overhead projector, is it taken simply from your report?
And in your report have you described all of these combinations under the first person and second person, as well as all of the major racial category combinations for both a two-person and a three-person mixture?
Can you describe for the Court, please, and I'm referring now to again simply the first possible combination listed at the top, how a calculation is made by you or was made by you with regard to this mixture?
Yes. We'll I'm invoking the product rule. I'm calculating the frequency of a combination of alleles by multiplying together their separate frequencies.
So if you could, just describe for us what those numbers--what are they describing that are listed under the two racial categories and then ultimately the frequency at the end.
All right. So the first line of the table is where the first person was a 1.1 homozygote, this unknown person, and this unknown person has frequencies which could be described by the African American database. Now, I've reported those frequencies in my report, but I will just tell you the frequency in the FBI's PCR database for allele 1.1 in the African Americans is .117, so we square that frequency, multiply it by itself because we have two copies of that allele for that unknown homozygous person.
Let me stop you for a moment. When you square it or multiply it by itself, is that the same process that is used for describing stains from one donor in this case?
In other words, those are frequencies that have already, to your knowledge, been reported in Court in this case?
So that we have accounted--now, we have attached a number to the chance of the first person being of 1.1 homozygous genotype and frequency from African American. The second person we have assumed for this calculation are Caucasian. We don't know, we have assumed it for this calculation here, that person is a 1.2, 4 heterozygote, so we multiply together the frequencies of the 1.2 allele. That number is .176 and the 4 allele, that number is .328 and of course we have to double that product from the--we don't know which way round the alleles came to the person, what their parental origins are, so we now have a frequency to--if this is the 2 PQ frequency for that genotype from a Caucasian database.
And again, is that the same step, that is, of multiplying the frequencies of the two different alleles and then multiplying it by two, that is used in the reporting of single-stain DNA results?
Yes, it certainly is. Now, because what--now, the only novel feature of this analysis is to recognize there were two contributors and these people, we are assuming, are independent and we multiply their frequencies together, so--and that is the right-hand column, that .00158, which is about .15 percent. That is the frequency with which two people at random have those two specific genotypes, one person being African American and the other being Caucasian.
Now, do you then undertake that same analysis with regard to--and let's just stay with, for the moment, the first possible combination of 1.1, 1.1 and 1.2, 4, do you calculate that for each of the racial combinations that are possible?
Yes. As I said, I'm using the FBI's four databases, so there are a total of ten possible pairs of databases.
Do you also then, and did you, in terms of your analysis in this case, perform the same calculation for the remaining eleven combinations of DQ-Alpha types amongst two people?
And do you, for each one of those, produce ultimately a frequency for each combination that would on this chart, if it were totally complete, then go under the category or column of "Frequency"?
Add up those--sum those frequencies, sum the frequencies of the unknown contributors.
In other words, sum in this instance what would be .15 percent, sum the next calculation for the second combination of markers and on down to the bottom with all twelve?
That's right. We sum the frequencies of all the possible genotypes for the pairs of people that could have contributed, yes.
And in terms of your analysis in this case, as well as your report, did you report those totals for each racial category combination?
We then need to repeat the calculations for the other loci in the mixture. In this case--well, I guess it is only DQ-Alpha here, so excuse me, so then we are complete. The sum of those twelve numbers as reported here is 1 in 71.
That is when either of the contributors was African American and the other was Caucasian.
Incidentally, with regard to item 29--and let's clarify that. Assuming that were indeed--well, first of all, were you informed and provided material that there were also polymarker results on the steering wheel?
Yes, and I just misled you. The 1 in 71 is in fact the number from using all the loci, so that would be the Cellmark determination. DQ-Alpha plus polymarker I have used all the six loci, done a calculation like we see on this chart, multiplied those results from each locus together, multiplied the sum for each locus.
Now, when you have used the example of 1 out of 71, that was just one of the combinations possible? That is one African American and one Caucasian, correct?
And you also performed this summing technique for each of the combinations of African American, causation, southwest Hispanic and southeast Hispanic?
And you in fact produced tables showing what the frequencies would be using this calculation method for each of these combinations?
This method that you have described, in your opinion, is that an appropriate one to describe a frequency?
What is there about there--well, let me rephrase that question. Did you conduct this same analysis in this same method with regard to the remaining mixtures in this case?
--a document previously provided to the Prosecution by the Defense some weeks ago entitled "Percentage of population included in stain no. 29 Bronco steering wheel." That has a different appearance than the previous chart.
Does this document refer to the same results, and I'm referring to just the DQ-Alpha results on the same evidence item, no. 29, the steering wheel stain?
It describes--it adds up--it describes the single-person genotypes who could have been contributors to the stain. Let me restate. It lays out all the genotypes of individual people who could be amongst the contributors to the mixed stain.
How does this compare--and I'm only referring to the listing of possible genotypes. What differences, if any, are there between this chart and your own?
Well, they are the same for each--for an individual. That chart and yours both list all the possible genotypes.
There were twelve combinations listed on your chart and there appear to be simply six listings under the term "Matching genotypes" on this second chart exhibit 410; is that right?
Well, the one we are looking at on display now is for single people. It has no relevance, of course, because we know this is a mixture. This is a mixture of at least two people. So to add up the frequencies of single individuals I would say at best is misleading.
Well, let's go into a little bit more detail about this chart. What does it list off to the right of the column matching genotypes?
Well, for each of the single genotypes the frequencies are listed from three databases and those frequencies I'm sure are correct, so 1.9 percent of Caucasians are expected to be 1.1 DQ-Alpha homozygote. And it is interesting, 1.9 percent, I imagine, if we--I should say we have slightly different databases, but that 1.9 corresponds to our previous .117 squared. It is the same--purports to be the same frequency. The numbers are different because they are different databases.
Okay. Let me stop you for just a moment. As far as a description of differences in approaches to mixtures, the fact that the databases in this specific example are different, does that impact your ability to describe the different approaches to--
Now, as far as these frequencies then on this chart, exhibit 410, do they reflect then simply frequencies in these three racial groups, major racial groups of these different six genotypes?
You have used the term "This is misleading" referring to this chart; is that right?
And you are referring to it being misleading in the context of the results for item 29 in this case; is that right?
Because it gives the impression that this mixed genotype would occur--it gives the impression--it doesn't say so, but it gives the impression that this mixed stain would occur in 45.4 percent of Caucasians. Now, I know that is not what that chart says, but that is the distinct impression it is giving. The impression is given that this mixed stain would be found almost half the time if the unknown contributor was Caucasian. That is nonsense.
Because we have a mixture of three alleles from two people or more. It is not--it makes no sense at all to say that that mixture could occur nearly fifty percent of the time--
--when I have just demonstrated that the frequency with which two people would give rise to that mixture is 1 in 71 and we can go on to describe the frequency with three people. We cannot and should not present any analyses on mixtures which ignore the fact that it is a mixture.
In your opinion, does this chart, simply summing up the genotypes, ignore the fact that the stain is a mixture?
In your own calculations--and I believe you have already stated you did it for both two possible contributors as well as three possible contributors; is that right?
Does this calculation process, as shown again in the document, exhibit 410, that is on the projector, does it differentiate in any manner between two contributors, three contributors or however many?
This document makes no such distinction. It is only for a single contributor, in fact.
In your opinion, is the method utilized by you in this case a more accurate and reliable means of assigning a frequency to a mixture?
In your view is the method, as demonstrated by this exhibit, 410, can you say the same about it?
Now, for purposes of this hearing only, your Honor, I'm going to ask the witness to refer to a passage that we have previously discussed in the National Research Council report.
And I think I have a Xeroxed copy of that page, if that is acceptable. I don't know if the Court wants it marked as an exhibit or not.
We can refer to it as page 59 of the NRC report, if that is what you are about to do.
Showing you, Dr. Weir, a one-page Xerox--first of all, have you had an opportunity before today to read a document entitled "DNA technology in forensic science" from the National Research Council?
The document before you, that is simply a one-page Xerox, although I believe it has some highlighting on it in yellow of in particular page 59 of that report?
And in particular with respect to that reference, the final sentence in what appears to be the fourth full paragraph contains a statement about an appropriate manner, according to this report, of dealing with mixtures; is that right?
"If a suspect's pattern is found within the mixed pattern, the appropriate frequency to assign such a match is the sum of the frequencies of all genotypes that are contained within. Ie, that are a sub-set of the mixed pattern."
Well, I have trouble answering that question as I would have answering any question on this NRC report, however, because I have little regard for the report's statistics. The report is saying that we should add up the frequencies of all genotypes that is contained. The sentence is ambiguous. It would allow a person to interpret as adding up the genotypes for single people, as we see on the chart--on the board, or to add up the frequencies of genotypes, meaning genotypes of the plural contributors, which is what I've done.
Okay. Let me stop you for just a moment. From your reading of that one-sentence description or recommendation, is it your opinion that it is written in such a fashion that you can't determine from its words whether it is describing the technique that you have used in this case or any other technique?
In your view does it cover the technique as shown by exhibit 410, which is simply adding up genotypes?
In your opinion does it also include the technique utilized by you and previously described this morning in this case?
As far as multiple contributors, and I may have asked this before, you have done it for two or three possible contributors in this case?
That is right. As I said, the evidence contains information of more than one contributor. It contains no information whatever of more than two contributors. I know that there would be interest in there being three contributors to some of the stains. The evidence points to two contributors. I have chosen to do calculations as if there were three contributors in addition.
Your technique allows you the ability to do that for more than two, three, four, et cetera?
Your Honor, I would like to move in these three remaining--actually I think it is four remaining exhibits, again for purposes of this hearing only, and I think that would be 408 as well as 408-A, 409 and 410.
All right. Let's take a ten-minute break and we will start with the cross-examination. All right, doctor. You can step down. Thank you.
To form an analysis which ignores the evidence of there being a mixture is wrong, it is completely misleading. We must add up the frequencies under the situation suggested by the evidence.
I have al declined Defense requests because I don't believe I can argue against the forensic uses of DNA.
I apologize for that. I removed those bands yesterday and essentially replaced those two pages.
I am taking no notice of descriptors such as weaker or possible trace. I am assuming that if the allele is mentioned, it is present.