Adrian Paul Martinez was convicted by a jury in the United States District Court for the District of South Dakota 1 of aggravated sexual abuse and sexual abuse of a minor in violation of 18 U.S.C. §§ 1153, 2241(a)(1) and 2243. Martinez appeals, challenging three aspects of the court’s ruling admitting DNA profiling evidence, the most important of which is the admission of evidence concerning DNA profiling analysis while excluding statistical probability analysis and data. Martinez also challenges the admission of the DNA profiling analysis under criteria previously estаblished by this court and the court’s ruling that adequate discovery materials were provided. We affirm the judgment of the district court.
I.
Martinez’ conviction arises out of the rape of a fourteen-year-old girl in Little Eagle, *1193 South Dakota. Martinez, an Indian security guard, lured the girl away from a pow-wow which she was attending and raped her. The girl immediately reported the incident, was examined at the local hospital, and stated that she knew whom the individual was who had attacked her. At trial, the girl positively identified Martinez. Martinez presented the alibi defense that he was sleeping on the hood of a nearby car at the time of the rape. Evidence gathered at the hospital shortly after the occurrence included vaginal swabbing, pants, panties, and blood. These samples were tested by the Federal Bureau of Investigation (FBI) laboratory and semen stains were found on two vaginal swabs, the pants, and the panties. Using the scientific technique DNA (deoxyribonucleic acid) profiling, with the procedure RFLP (restriction fragment length polymorphism), to isolate and analyze the semen, the FBI concluded that only 1 in 2600 American Indians would be expected to produce the identical genetic characteristics as Martinez. The tests conducted on the remaining samples were inconclusive. Further serology tests disclosed blood grouping data consistent with a rapist with blood type “0” and who is an “0” secretor. Martinez, along with 56% of the American Indian population, is type “0” and an “O” secretor.
Speciаl Agent Dwight Adams, of the FBI DNA Analysis Unit, testified at a pretrial hearing, held to determine the admissibility of the DNA evidence. Dr. Adams testified that his qualifications include a Ph.D. in biology from the University of Oklahoma, specialized training and research in the field of DNA profiling, publication on the subject, and membership in the American Academy of Forensic Scientists and the International Electrophoresis Society. Dr. Adams discussed the DNA principle and technology and described the RFLP testing procedure in detail. He further explained thе FBI protocol and its attendant quality controls. Last, he discussed the probability statistics and the analysis used in characterizing the instant DNA “match” in mathematical terms.
The district court determined that (1) DNA typing is generally accepted by the scientific community; (2) the testing procedures used in this case are generally accepted as reliable; (3) the FBI protocol was properly followed in this case; and (4) the evidence was not more prejudicial than probative in this case. However, the court also decided that the statistics used to determine the probability of any other individual having the same genetic characteristics as Martinez were more prejudicial than probative under Rule 403 of the Federal Rules of Evidence. For this reason the court admitted the DNA profiling analysis evidence and the results of the testing in this case, but declined to allow the jury to hear the evidence of statistical probability with regard to Martinez. 2
The principal issue in this appeal is Martinez’ contention that, upon its decision to withhold the evidence of statistical probability from the jury, the court should have ruled that all of the DNA evidence was inadmissible. There is no question that a DNA “match” (a term of art used in the scientific community to describe positive testing results) means that the DNA testing has shown the person tested to be a potential contributor, but not necessarily the contributor of, in this instance, the semen. It is for this reason that the government argued to the jury that Martinez “fits the profile of the DNA.” (Tr.Vol. II at 267.) Martinez insists, however, that the jury could only have been left with the impression that Martinez was the sole person who could have been the source of the semen. Martinez contends that this kind of “fingerprinting” rendered the DNA evidence, in total, more prejudicial than probative.
II.
While the facts of this case are not complicated, the issue of DNA profiling is unsettled and complex. To resolve this issue, we must determine whether and to what extent DNA *1194 profiling evidence should be admissible in criminal cases, and what evidentiary standard the trial court should use in assessing the evidence. This issue is one of first impression in this circuit 3 and only the second case to be considered by the federal appellate courts. 4
A. DNA Profiling
Before examining the standard of admissibility, we shall outline the process of DNA identification profiling. 5 The process of DNA profiling identification involves, broadly speaking, two steps. First, the scientist compares DNA from a known sample with DNA from an unknown source. The DNA is compared at several different points, to see if the DNA pattern in the unknown sample at eaсh specific point matches the DNA pattern in the known sample at each specific point. The scientist will declare a “match” only if all DNA segments compared on the two samples are identical, i.e., show the same pattern, within a certain range of error.
Finding a match is not, however, the end of the procedure. A DNA match merely tells the scientist that the person who contributed the known sample is a potential contributor of the unknown sample. The second step of the DNA idеntification process then involves a determination of the probability that someone other than the contributor of the known sample could have contributed the unknown sample.
To do this probability analysis, the scientist compares the tested samples against information about the general population. The FBI and other laboratories have done experiments to determine the frequency with which certain DNA patterns appear in different racial and ethnic populаtions. By reference to these studies, the scientist determines the frequency with which each DNA pattern appearing on the known sample exists in the population from which the known sample comes. After determining this probability for each of the DNA segments tested, the scientist multiplies the probabilities of each of the segments tested to determine the probability that someone in that population would have identical patterns on all the DNA segments tested. For example, if 50% of the poрulation had the pattern the known sample showed at test site A, 50% had the pattern the known sample showed at test site B, 50% had the pattern the known sample showed at test site C, and 50% had the pattern the known sample showed at test site D, the probability that any one member of that population would have all four of those patterns would be .5 x .5 x .5 x .5, or 6.25%. Expert testimony in DNA profiling cases is generally expressed in these terms. For example, the expert will testify that probability studies demonstrate 1 in 2600 American Indians would be expected to produce a matching sample.
DNA profiling is still relatively new as a forensic tool and has been the subject of heated controversy in both the legal and scientific communities. However, it is generally conceded that the principle of DNA profiling is recognized as reliable and that the procedures are not so new or novel as to warrant disagreement.
People v. Castro,
*1195 There is nothing controversial аbout the theory underlying DNA typing. Indeed, this theory is so well accepted that its accuracy is unlikely even to be raised as an issue in hearings on the admissibility of the new tests.
Thompson & Ford, DNA Typing: Acceptance and Weight of the New Genetic Identification Tests, 75 Va.L.Rev. 45, 60 (1989). See also U.S. Congress, Office of Technology Assessment, Genetic Witness: Forensic Uses of DNA Tests 7-8, OTA-BA-438 (Washington, D.C.: U.S. Government Printing Office, July 1990) (stating that DNA profiling is valid and reliable in forensics where procedures are properly performed and analyzed). Nevertheless, beyond the theoretical level, concerns persist over possible error and ambiguity. “The problems arise at two levels: controlling the experimental conditions of the analysis and interpreting the results.” McCormick on Evidence § 203 at 900-01 (4th ed. 1992). 6 Clearly, the procedures are extraordinarily complex and the rigors of forensic probability calculations cannot be trivialized. Super-impose on these concerns the effect of the evidence in a criminal trial, and the dilemma posed is clear. One commentator has suggested:
[w]henever novel scientific evidence is offered in court, the legal system faces competing concerns. One [sic] one hand, there is a danger that excessive caution will prevent valuable evidence from being admitted in a timely manner. On the other hand, there is a danger that evidence accepted quickly and uncritically will later prove less reliable than promised.
Thompson & Ford, DNA Typing, Trial at 64 (Sept.1988). There is no consensus among the state courts which have considered the admissibility of DNA evidence. However, with notable exceptions, the tide seems to be turning in favor of general admissibility. 7
B. The Standard for Admissibility
For many years, the admissibility of novel scientific evidence has been tested under the standard first announced in
Frye v. United States,
Just when a scientific principle or discovery crosses the line between the experimental and demonstrable stages is difficult to define. Somewhere in this twilight zone the evidential force of the principle must be recognized, and while courts will go a long way in admitting expert testimony deduced from a well-recognized scientific principle or discovery, the thing from which the deduction is made must be sufficiently established to have gained general acceptance in the particular field in which it belongs.
Frye,
In
Daubert v. Merrell Dow Pharmaceuticals, Inc.,
— U.S. -,
That the Frye test was displaced by the Rules of Evidence does not mean, however, that the Rules themselves place no limits on the admissibility of purportedly scientific evidence. Nor is the triаl judge disabled from screening such evidence. To the contrary, under the Rules the trial judge must ensure that any and all scientific testimony or evidence admitted is not only relevant, but reliable.
Id.
at -,
Thus, according to the Court, Rule 702 mandates that the district court -act as “gatekeeper” for the admission of novel scientific evidence. Before admitting scientific expert testimony, the court must conclude, pursuant to Federal Rule of Evidence 104(a)
10
that the proposed testimony constitutes (1) scientific knowledge that (2) will assist the trier of fact to understand or determine a fact in issue.
Id.
at -,
The Court first considered the requirement that the expert testify concerning scientific knowledge. According to the Court, the subject of scientific testimony does not have to be known to a certainty; however, “in order to qualify as ‘scientific knowledge,’ an inference or assertion must be derived by the scientific method. Proposed testimony must be supported by appropriate validation — i.e. ‘good grounds,’ based on what is known.”
Id.
at -,
The Court further stated that Rule 702 requires that expert testimony must assist the trier of fact. According to the Court, this condition is primarily one of relevance. In order to satisfy the precondition that the testimony assist, or be “helpful” to the jury, the proponent of the testimony must demonstrate that the evidence bears “a valid scientific connection to the pertinent inquiry.” Id.
In assessing the reliability of novel scientific evidence, courts should consider the following non-exclusive list of factors:
(1) Whether the scientific technique can be (and has been) tested. Id. at -,113 S.Ct. at 2796 .
Preliminary questions concerning the qualification of a person to be a witness, the existence of a privilege, or the admissibility of evidence shall be determined by the court, subject to the provisions of subdivision (b) [pertaining to conditional admissions]. In making its determination the court is not bound by the rules of evidence except those with respect to privileges.
Matters subject to Rule 104(a) should be established by a preponderance of proof. See Bourjaily v. United States,483 U.S. 171 , 175-76,107 S.Ct. 2775 , 2778-79,97 L.Ed.2d 144 (1987).
(2) Whether the technique or theory has been subjected to peer review and publication. While not a sine qua non of admissibility, “[t]he fact of publication (or lack *1197 thereof) in a peer-reviewed journal thus will be a relevant, though not dispositive, consideration in assessing the scientific validity of a particular technique or methodolоgy on which an opinion is premised.” Id.
(3) The known rate of error of the technique and the existence and maintenance of standards controlling the technique’s operation. Id.
(4) Whether the technique is generally accepted. “A ‘reliability assessment does not require, although it does permit, explicit identification of a relevant scientific community and an express determination of a particular degree of acceptance within that community.’ Widespread acceptаnce can be an important factor in ruling particular evidence admissible, and ‘a known technique that has been able to attract only minimal support within the community,’ may properly be viewed with skepticism.” Id. (citations omitted).
The Court noted that other portions of the Rules of Evidence give trial courts the power to control expert testimony. First, the Court noted that Rule 703 requires that if experts rely on otherwise inadmissible hearsay, that expert’s opinion may be admitted only to the extent that the facts or datа “ ‘are of a type reasonably relied upon by experts in the particular field in forming opinions or inferences upon the subject.’ ” Second, the Court also noted that Rule 403 is of special import, because “ ‘[ejxpert evidence can be both powerful and quite misleading because of the difficulty in evaluating it. Because of this risk, the judge in weighing possible prejudice against probative force under Rule 403 of the present rules exercises more control over experts than over lay witnesses.’ ”
Id.
at -,
Finally, the Court stated that “[t]he inquiry envisioned by Rule 702 is, we emphasize, a flexible one. Its overarching subject is the scientific validity — and thus the evidentiary relevance and reliability — of the principles that underlie a proposed submission. The focus, of course, must be solely on principles and methodology, not on the conclusions that they generate.” Id.
We must now consider what effect
Daubert
has on the admissibility of DNA evidence. The Second Circuit recently examined the general theory underlying DNA fingerprinting as well as the specific techniques employed by the FBI, and concluded that in the future courts could take judicial notice of their reliability.
See United States v. Jakobetz,
The fact that we have taken judicial notice of the reliability of the technique of DNA profiling does not mean that expert testimony concerning DNA profiling is automatically admissible under
Daubert.
A number of courts have required that the trial court further inquire into whether the expert properly performed the techniques involved in creating the DNA profiles.
See People v. Castro,
We believe that the reliability inquiry set forth in
Daubert
mandates that there be a preliminary showing that the expert properly performed a reliable methodology in arriving
*1198
at his opinion. The
Daubert
Court stated that “under the Rules, the trial judge must ensure that any and all scientific
testimony
or
evidence
admitted is not only relevant, but reliable.” — U.S. at -,
At the same time, the Court specifically counseled courts to respect the differing functions of judge and jury. It stated that the focus of the foundational inquiry “must be upon the principles and methodology, not on the conclusions that they generate.” — U.S. at -,
Thus, we conclude that the court should make an initial inquiry into the particular expert’s application of the scientific principle or methodology in question. The court should require the testifying expert to provide affidavits attesting that he properly performed the protocols involved in DNA profiling. If the opponent of the evidence challenges the application of the protocols in a particular case, the district court must determine whether the expert erred in applying the protocols, and if so, whether such error so infected the procedure as to make the results unreliable.
We emphasize, however, that this inquiry is of necessity a flexible one. Not every error in the application of a particular methodology should warrant exclusion. An alleged error in the application of a reliable methodology should provide the basis for exclusion of the opinion only if that error negates the basis for the reliability of the principle itself. We agree with the Third Circuit that an allegation of failure to properly apply a scientific principle should provide the basis for exclusion of an expert opinion only if “a reliable methodology was so altered [by a particulаr expert] as to skew the methodology itself_”
In re Paoli R.R. Yard PCB Litig.,
III.
We arrive, finally, at the specifics of the DNA inquiry in this case.
Martinez contends that the district court erred in admitting the testimony of agent Adams concerning a DNA profile “match” while excluding evidence concerning the statistical probability that another individual could provide matching DNA. Martinez did object to the introduction of the DNA profiling evidence at all, and he renews that objection on appeal. Thus, we must first discuss whether the DNA evidence was admissible at all. Then we must consider whether the district court’s admission of the DNA match testimony without the statistics constitutes reversible error.
We conclude that the district court did not err in admitting the DNA profiling evidence. The district court held a preliminary hearing, inviting the submission of evidence and expert testimony on the subject of DNA profiling. In making its determination to admit the evidence, the court adhered to the elevated test of admissibility announced in People v. Castro, supra. The court thus undertook a broad inquiry, determining that the underlying principle is generally aсcepted by the scientific community, the testing protocol and procedures are also generally accepted as reliable, and the FBI properly followed the protocol, accurately performing the prescribed procedures. The court further balanced the probative value against the prejudicial effect of DNA profiling evidence, and concluded that evidence of a DNA “match” was admissible.
We cannot conclude that the trial court аbused its discretion in admitting this evidence. The Castro test applied by the trial court is at least as stringent as the test mandated in Daubert. It appears that the court carefully considered the testimony concerning a DNA profile match, and found it to be reliable. We have no trouble concluding *1199 that the evidence concerning a DNA match was properly admitted.
The district court barred the expert from testifying about his conclusion that as a matter of probability, one Native American in 2600 could have providеd DNA that matched the samples found on the victim in this case, concluding that such evidence was substantially more prejudicial than probative. Martinez contends that the exclusion of this evidence prejudiced him because the jury would conclude that he was the only possible source of the DNA found on the victim.
We conclude that Martinez is barred from raising this argument on appeal by the doctrine of invited error. After the district court decided to admit the DNA match evidence, the court invited counsel to comment on the propriety of admitting statistical evidence of the likelihood of a match. In response to this invitation, Martinez’ counsel suggested that the court exclude the probability evidence, citing a Georgia ease,
State v. Caldwell,
IV.
Martinez raises one additional, less complicated, issue, claiming that the government failed to provide adequate discovery regarding the DNA evidence. Martinez failed to raise this objection in the district court; we may reverse only for plain error. Finding none, we affirm.
United States v. Krohn,
We conclude that the district court did not abuse its discretion in admitting evidence of DNA typing to the jury, and that Martinez is barred by the invited error doctrine from complaining that the district court erred by excluding statistical probability evidеnce. In addition, we find that there is no merit to Martinez’ claim of inadequate discovery. The judgment of the district court is affirmed.
Notes
. The Honorable Richard H. Battey, United States District Judge for the District of South Dakota.
. Martinez' counsel was unequivocally opposed to the introduction of any DNA profiling evidence. However, upon learning of the court’s ruling, Martinez’ counsel urged the court to exclude the statistical data.
. The Eighth Circuit addressed the DNA issue in a 1990 case which was subsequently rendered moot.
See United States v. Two Bulls,
.
United States v. Jakobetz,
.For a comprehensive yet accessible explanation of the FBI's process of DNA profiling, see
Jako-betz,
For more extensive discussions of DNA profiling in a legal context, see Edward J. Imwinkelried, The Debate in the DNA Cases over the Foundation for the Admission of Scientific Evidence: The Importance of Human Error as a Cause of Forensic Analysis, 69 Wash.U. L.Q. 19 (1991); William C. Thompson & Simon Ford, DNA Typing: Acceptance and Weight of the New Gеnetic Identification Tests, 75 Va.L.Rev. 45 (1989); Paul C. Gianelli & Edward J. Imwinkelried, Scientific Evidence (1986 & 1990 Supp.).
. For further discussion of problems encountered in DNA analysis, see also Gordon, DNA Identification Tests — On the Way Toward Judicial Acceptance, 6 J. Suffolk Acad.L. 1, 12-18 (1989); Thompson & Ford, The Meaning of a Match: Sources of Ambiguity in the Interpretation of DNA Prints in Forensic DNA Technology 93 (Farley & Harrington eds. 1990); Bunk, DNA Fingerprinting: Possibilities and Pitfalls of a New Technique, 29 Jurimetrics J. 455 (1988); Note, The Dark Side of DNA Profiling: Unreliable Scientific Evidence Meets the Criminal Defendant, 42 Stan.L.Rev. 465 (1990).
.
Andrews v. State,
.Gardner v. Meyers,
. In the context of DNA evidence, one court has extended
Frye,
creating an even more strenuous standard, presumably in response to the intimidating complexity of the evidence. In
People v. Castro,
. Rule 104(a) provides: