144 Wis.2d 638 (1988)
425 N.W.2d 404
IN RE the PATERNITY OF M.J.B.: T.A.T., Petitioner-Respondent,
v.
R.E.B., Appellant.
No. 86-1134.
Supreme Court of Wisconsin.
Argued March 2, 1988.
Decided June 24, 1988.
For the appellant there were briefs by Robert E. Krambs, Viroqua and oral argument by Robert E. Krambs.
For the petitioner-respondent there was a brief by David L. Jenkins, Vernon County Child Support Agency, Viroqua and oral argument by David L. Jenkins.
STEINMETZ, J.
This is a review of a decision of the court of appeals[1] which reversed the judgment of the circuit court for Vernon county, Honorable Walter S. Block, judge, in a paternity action declaring R.E.B. to be the father of the child in question and which remanded the cause for a new trial. Petitioner T.A.T. challenges the court of appeals ruling that the circuit court improperly limited appellant's argument in closing argument.
The primary issue in the case is whether a defendant in a paternity action may challenge the validity of a genetic blood test report for the first time in closing argument. The court of appeals answered this issue in the affirmative. This case also raises the issue of whether a jury may consider the report of a genetic blood test in determining whether sexual intercourse took place between the mother and the alleged father at a time when the child could have been conceived. Though the parties did not raise or discuss this issue, the court of appeals held that the blood test report could not be used as evidence of sexual intercourse during the conceptive period.
Finally, this case presents the question of whether a jury must make a separate finding by clear, satisfactory and convincing evidence that sexual intercourse took place between the mother and putative father before the jury may consider the blood test report. Although the parties did not raise or discuss this issue, the court of appeals held that an independent finding of sexual intercourse was required before the jury could consider the statistical chance of paternity as evidence of paternity.
In this paternity action, R.E.B. was adjudged the father of M.J.B. The child's mother, T.A.T., gave birth to M.J.B. on December 19, 1984, and subsequently filed this paternity action pursuant to sec. 767.45(1), Stats.[2]
Because the child weighed more than five and one-half pounds at birth, pursuant to sec. 891.395, Stats.,[3] the circuit court took judicial notice that the child was conceived between February 21, 1984, and April 22, 1984. T.A.T. testified that she had sexual intercourse exclusively with R.E.B. during the statutory conception period and that she had sexual intercourse with him between March 17, 1984 and March 24, 1984.
R.E.B. admitted that he had sexual intercourse with T.A.T. but stated that this intercourse did not occur during the statutory conception period. Specifically, R.E.B. testified that he only dated T.A.T. until February 14, 1984, approximately one week prior to the earliest date of the statutory conception period. On February 17, 1984, R.E.B. began courting another woman who testified that both R.E.B. and T.A.T. had communicated separately to her that R.E.B. had not dated or seen T.A.T. after February 17, 1984.
Pursuant to sec. 767.48(1), Stats.,[4] T.A.T. introduced an HLA (Human Leukocyte Antigen) blood test report from the American Red Cross histocompatibility laboratory without accompanying expert testimony. The report, based upon raw data obtained from blood samples of the mother, the child and the alleged father, stated the following:
"[R.E.B.] cannot be excluded as the father of [M.J.B.] The cumulative paternity index (genetic odds in favor of paternity) is 218. The relative chance of paternity, assuming a 50% prior chance, is 99.54%. Paternity is extremely likely.
"98.99% of falsely accused men would be excluded as the father."
In the report, the testing agency did not explain how it computed the relative chance of paternity, did not indicate that it had any factual basis for the assumption of a "50% prior chance" and did not explain the meaning of a "50% prior chance."
R.E.B. offered no evidence or expert testimony to rebut the HLA blood test report or its presumption of a fifty percent prior chance of sexual intercourse. Prior to closing argument, the parties stipulated to allowing R.E.B. to argue that there was no basis in the record or within the blood test report to support the fifty percent prior chance assumption. Notwithstanding the stipulation, the circuit court barred R.E.B. from referring to the assumption as erroneous, from attacking the assumption in any way, or from pointing out to the jury that the HLA report does not state a basis for the fifty percent prior chance assumption. The circuit court ruled that because R.E.B. had failed to introduce any evidence assailing the reliability of the assumption, he had no basis in the trial record to attack the assumption in closing argument.
On February 24, a jury found R.E.B. to be the father of M.J.B. After the circuit court denied R.E.B.'s post-verdict motions for a new trial and a judgment notwithstanding the verdict, R.E.B. appealed the judgment to the court of appeals.
The court of appeals reversed the circuit court judgment concluding that it was an abuse of discretion to limit R.E.B. from commenting in closing argument on the reliability of the fifty percent prior chance assumption. Moreover, because a statistic contained in the HLA blood test report assumed that R.E.B. had had sexual intercourse with T.A.T. during the statutory conceptive period, the court of appeals found this evidence inappropriate for jury consideration of paternity. The court of appeals held that before the probability of paternity statistic could be considered as evidence of paternity, the jury must first independently determine whether the mother and putative father had sexual intercourse during the conceptive period.
The court of appeals also found that the jury instructions should provide that if the evidence does not prove to a reasonable certainty by clear, satisfactory and convincing evidence that the mother and alleged father had sexual intercourse at a time when the child could have been conceived, then the jury should find nonpaternity regardless of the probability of paternity results in the report.
We note at the outset that R.E.B. did not base his challenge in this case on an erroneous admission of the HLA blood test results into evidence. Nor does he attack the validity of the paternity statute itself. In fact, R.E.B. specifically conceded that "[t]here is no question that pursuant to Section 767.48, T.A.T. has the right to submit such a document into evidence without expert testimony ...."
Rather, R.E.B. argues only that the trial court committed reversible error in limiting his closing argument. Specifically, R.E.B. claims that the trial court erroneously precluded him from arguing that the probability of paternity statistic was based on an unsupported fifty percent prior assumption of sexual intercourse. He argues that the fifty percent prior chance assumption and its effects on the resulting statistical conclusion is a matter that the jury could not be expected to understand without explanation. He concludes that had the trial court permitted the argument, the jury "might probably have returned a verdict in favor of R.E.B."
[1]
Whether a circuit court may limit counsel's closing argument is a matter within the circuit court's discretion which will be upheld absent an abuse of discretion. Johnson v. Johnson, 78 Wis. 2d 137, 143-44, 254 N.W.2d 198, 202 (1977). The consideration of the HLA blood test report as evidence of sexual intercourse is a question of law. Accordingly, this court owes no deference to the decisions of the trial court or court of appeals when deciding this matter. Lambert v. Wrensch, 135 Wis. 2d 105, 115, 399 N.W.2d 369 (1987). Similarly, this court may independently decide whether sexual intercourse during the conceptive period must be found separately by a trier of fact in order to sustain a finding of paternity.
Section 767.48(1), Stats., states the blood test report, which addresses blood test results and the statistical probability of paternity, is admissible as evidence without expert testimony. However, the statute is silent as to whether the test can be used to prove that sexual intercourse occurred between the alleged father and the mother during the conceptive period or whether the jury must independently determine that sexual intercourse occurred during the relevant time period before the blood test results can be considered.
Paternity testing is based on the presence of genetic markers which are inherited from one's parents. These markers are identified by an application of Mendelian rules of inheritance to the data obtained from a blood cell or tissue sample. Traditionally, blood cell tests in paternity actions were used for the purpose of excluding a named defendant as the father. That is, where the child at issue lacked a genetic marker that a child of the putative father must have, nonpaternity was established. Likewise, if a dominant genetic marker was present in the child that was absent in both the mother and alleged father, paternity could be conclusively excluded. Lee, Current Status of Paternity Testing, 9 Fam. L. Q. 615, 616-17, 621 (1975).
While courts have not always accepted blood test results excluding a putative father as conclusive evidence of nonpaternity, in recent years such test results have enjoyed universal recognition and a wide acceptance in both the scientific and legal communities. See, e.g., Little v. Streater, 452 U.S. 1, 6-7 (1981); S. Schatkin, Disputed Paternity Proceedings, sec. 9.13 (4th rev. ed. 1987).
More problematic is the question of the admissibility and weight to be afforded paternity inclusion test results. That is, where an individual cannot be conclusively excluded as the father of a child, the question becomes how likely it is that the defendant fathered the child at issue, compared to another randomly selected man in the relevant population. This likelihood statistic, called the probability of paternity or chance of paternity, has generated much debate in the legal and scientific communities. See, e.g., McCormick on Evidence, sec. 211 (3d ed. 1984 & 1987 Supp.); Peterson, A Few Things You Should Know About Paternity Tests (But Were Afraid to Ask), 22 Santa Clara L. Rev. 667 (1982); Ellman & Kaye, Probabilities and Proof: Can HLA and Blood Group Testing Prove Paternity? 54 N.Y.U. L. Rev. 1131 (1979); Annot., 37 A.L.R.4th 167, Admissibility, Weight and Sufficiency of Human Leukocyte Antigen (HLA) Tissue Typing Tests in Paternity Cases (1985).
A blood grouping test in a paternity action is actually a tissue typing test know as the HLA test. The HLA test gathers raw data from the samples of the mother, child and alleged father and expresses that data in the form of a probability of exclusion, a paternity index, and a probability of paternity.
The first calculation, the probability of exclusion, measures the ability of a paternity test to exclude men falsely accused of paternity. Plemel v. Walter, 303 Or. 262, 735 P.2d 1209, 1213 (1987). This statistic does not rely on the challenged fifty percent prior chance assumption. However, the probability of exclusion "does nothing to distinguish the true father from the perhaps millions of men who fall into this group." Peterson, A Few Things You Should Know, supra, at 680. In the present case, the probability of exclusion was 98.99 percent. That is, 98.99 percent of falsely accused men would be excluded as the father of the T.A.T.'s child.
The second statistic generated by the paternity test is the cumulative paternity index, or likelihood ratio, which describes the genetic odds in favor of paternity. This statistic, expressed as a ratio, compares the relative likelihood of the putative father producing a child with these particular genetic markers than that of a randomly selected man. Plemel, 735 P.2d at 1214. However, this statistic does not describe the likelihood of producing the child in question, but rather, it describes the relative likelihood of producing a child with the same genetic markers. Id. Even though all of the men not excluded in that statistic described above (the probability of exclusion), are capable of fathering such a child, they will have different paternity indexes, i.e., different relative likelihoods of fathering the child. In this case, R.E.B.'s paternity index was 218. This means that he was 218 times more likely to have fathered a child with the same genetic markers as T.A.T.'s child than a randomly selected man. This statistic does not use the challenged fifty percent prior chance assumption.
The third statistic, the probability of paternity, then takes the paternity index and using Bayes' Theorem converts the paternity index or likelihood ratio into a probability of paternity, i.e., the actual likelihood that the putative father is the actual father of this child. Id. at 1215. In this case, the probability of paternity was 99.54 percent.
This statistic, while the most probative of the three, likewise poses the greatest danger of misuse. This figure is calculated by multiplying the prior odds of paternity by the paternity index. Typically, the prior odds of paternity are calculated as one-to-one, or a 50/50 chance (i.e., it assumes a fifty percent likelihood that defendant is the father and fifty percent likelihood that another, randomly selected man, is the father).
While the HLA's probability of paternity calculation expressed as a percentage is considered the most accurate means of communicating the significance of the blood test data to the jury, Commonwealth v. Beausoleil, 397 Mass. 206, 490 N.W.2d 788, 795-96 (1986); Ellman and Kaye, Probabilities and Proof, 54 N.Y.U. L. Rev. at 1146, the probability of paternity calculation nevertheless has been criticized as it is typically computed.[5] Specifically, critics have noted that the use of the fifty percent prior chance assumption in the probability of paternity calculation has no basis in the individual facts of the case. Moreover, the fifty percent prior chance assumption is not sensitive to varying individual fact situations. Finally, even the probability of paternity calculations cannot indicate conclusively which person is the actual father.
As the court of appeals correctly noted, the fifty percent prior chance assumption has no factual basis, but is employed precisely because nothing is known about whether intercourse actually took place between the parties at a time when conception could have occurred. Because the assumption is not based on empirical facts but, rather, is employed to make the paternity formula work, the reliability of the probability of paternity results may be diminished in cases where the occurrence of intercourse and the likelihood of conception at a given time are disputed.
[2]
The assumption underlying the probability of paternity statistic is that the mother and putative father have engaged in sexual intercourse at least once during the period of possible conception. See Peterson, A Few Things You Should Know, supra at 685. We interpret this assumption to mean that the probability of paternity statistic is conditionally relevant evidence; only after competent evidence is offered to show that sexual intercourse between the mother and alleged father occurred during the conceptive period may evidence of the probability of paternity be received.
This foundational evidence may be supplied by the mother herself, of course, which is likely to happen in the typical paternity case. However, we note that this threshold evidence is not limited to direct testimony by the mother that she engaged in sexual intercourse with the alleged father. Evidence that the defendant had access to the mother during the conceptive period may be offered by any individual knowledgeable of the facts of their association. By "access," we mean that the mother and putative father were together at a time, under circumstances and in a location which would lead a reasonable person to believe that the sexual intercourse took place between them. In this regard, there must be evidence to sustain a reasonable belief by a factfinder that sexual intercourse took place between the mother and the putative father. Once there is competent evidence on the record of sexual intercourse during the conceptive period, the results of the blood tests, including the probability of paternity statistic, may be introduced in a civil paternity proceeding.
[3]
We disagree with the court of appeals that an independent determination of sexual intercourse must be made by the jury before it can consider the statistical probability of paternity as evidence of paternity. Section 767.50 provides that "the main issue shall be whether the alleged ... father is or is not the father of the mother's child." It is true that one of the elements in a paternity suit is sexual intercourse between the mother and alleged father occurring during the conceptive period. However, the occurrence of sexual intercourse during the time of possible conception is not an issue separate from the main issue. It does not require an independent determination by the jury; it is an element of the case.[6] If the petitioner fails to introduce sufficient evidence of sexual intercourse to establish a prima facie case of paternity, the defendant can simply move for a dismissal of the case. Likewise, the petitioner is precluded from introducing the blood test results until evidence of sexual intercourse is received.
We have carefully reviewed much of the literature with respect to probability statistics and its role in paternity testing, and we recognize the problems inherent in the probability of paternity measurement as it is currently typically calculated. Nevertheless, we believe that the legislature, which also was presumably aware of the disadvantages as well as the advantages of admitting this statistic, decided to resolve this question in favor of liberally admitting paternity evidence. An earlier version of the statute relating to blood test evidence in paternity proceedings, sec. 52.36(3), Stats.,[7] formerly limited the introduction of blood test results to those definitely excluding the paternity of an individual tested. Thus, under the old law, the probability of paternity would not have been admissible under any circumstances in a civil proceeding seeking to establish paternity. However, under the current statute, sec. 767.48, not only are inclusion statistics admissible into evidence, but the statute expressly admits the introduction of evidence on the probability of a defendant's paternity.
[4]
The blood test report completed by a certified expert is presumed reliable, because the legislature has provided that it is admissible as evidence in paternity proceedings. This court has consistently recognized a prima facie presumption of accuracy of tests expressly authorized by statute. State v. Disch, 119 Wis. 2d 461, 476-77, 351 N.W.2d 492 (1984). As we have oftentimes stated in the past, "[a]ny contentions that the test result is unreliable or inaccurate goes only to the weight of the evidence as a matter of defense, not to its admissibility." If the blood test report is unreliable or inaccurate, defense counsel has the obligation to attack the credibility of the blood test and, therefore, to rebut the prima facie presumption of reliability. The jury will decide the ultimate weight to be given to the blood test report.
It would be better to have an expert witness present the blood test and results to the court and jury; however, the statute does not require it. Both the petitioner and the defendant have the right to call an expert witness to testify as to the assumption upon which the blood test is based and to the meaning and limitations of the various tests. This presents the defendant with the opportunity, if necessary, to challenge the prior odds assumption of the probability of paternity formula in a meaningful and understandable way. For example, methods of introducing the probability of paternity statistic which do not rely on the fifty percent prior odds assumption are currently being introduced in other jurisdictions to overcome the recognized shortcomings of the formula. See, e.g., Plemel, 735 P.2d at 1219; Ellman and Kay, Probabilities and Proof, supra. It should be noted that while we recognize that other jurisdictions are employing various means of introducing paternity evidence, we do not comment at this time on the reliability or the validity of these alternative methods. We also note that where the use of these other methods of introducing paternity evidence or challenging the prior odds assumption implies that the mother engaged in multiple sexual relationships, any evidence offered which relies on such an inference must conform to the standards as provided in sec. 767.47, Stats.
If an expert is not called, then a treatise under sec. 908.03(18), Stats.,[8] may be introduced into evidence. If either of those two events take place, the defense attorney may then challenge the underlying assumption of the test.
[5]
In this case, R.E.B. did not attempt either to call an expert witness to explain or attack the tests or to introduce a treatise. Consequently, the court was correct in not allowing the defense attorney to argue the invalidity or unreliability of the test to the jury because there was no basis in the record upon which to attack the blood test. Without some kind of explanatory evidence, the test should not be explained to the jury through the attorney's subjective and argumentative closing remarks.
By the Court.The decision of the court of appeals is reversed.
NOTES
[1] In re Paternity of M.J.B., 137 Wis. 2d 157, 404 N.W.2d 64 (Ct. App. 1987).
[2] Sec. 767.45(1), Stats., provides as follows:
"767.45 Determination of paternity. (1) The following persons may bring an action for the purpose of determining the paternity of a child or for the purpose of rebutting the presumption of paternity under s. 891.41:
"(a) The child.
"(b) The child's natural mother.
"(c) A man presumed to be the child's father under s. 891.41.
"(d) A man alleged or alleging himself to be the father of the child.
"(e) The personal representative of a person specified under pars. (a) to (d) if that person has died.
"(f) The legal or physical custodian of the child.
"(g) This state whenever assignment is made under s. 49.19(4)(h)1 or 49.45(19), including the delegates of the state as specified in sub. (6)."
[3] Sec. 891.395, Stats., provides as follows:
"891.395 Presumption as to time of conception. In any paternity proceeding, in the absence of a valid birth certificate indicating the birth weight, the mother shall be competent to testify as to the birth weight of the child whose paternity is at issue, and where the child whose paternity is at issue weighed 5½ pounds or more at the time of its birth, the testimony of the mother as to the weight shall be presumptive evidence that the child was a full term child, unless competent evidence to the contrary is presented to the court. The conception of the child shall be presumed to have occurred within a span of time extending from 240 days to 300 days before the date of its birth, unless competent evidence to the contrary is presented to the court."
[4] Sec. 767.48(1), Stats., provides as follows:
"767.48 Blood tests in paternity actions. (1) The court or family court commissioner may, and upon request of a party shall, require the child, mother, alleged father, or any male witness who testifies or will testify about his sexual relations with the mother at a possible time of conception to submit to blood tests. The tests shall be performed by an expert qualified as an examiner of genetic markers present on blood cells and components, appointed by the court. A report completed and certified by the courtappointed expert stating blood test results and the statistical probability of the alleged father's paternity based upon the blood tests is admissible as evidence without expert testimony and may be entered into the record at the trial or pretrial hearing if, at least 10 days before the trial or pretrial hearing, the party offering the report files it with the court and notifies all other parties of that filing."
[5] Laboratories typically employ the Essen-Moller method in computing the probability of paternity. This method uses the problematic fifty percent prior odds probability. See e.g., American Association of Blood Banks, Inclusion Probabilities in Parentage Testing, 163-66 (1983). This source states of the fifty percent prior odds assumption:
"Although the Essen-Moller equation is flawed for legal purposes, the Bayesian has no difficulty correcting it. The appropriate likelihood ratio should be reported, and the judge or jury should use equation (10) to produce posterior odds. Leaving the choice of the prior odds to the legal decision-maker is preferable to presenting or using an unarticulated prior probability, but many objections have been raised to the suggestion that a judge or jury explicitly try to follow the Bayesian scheme. A variant that avoids most of these objections is to supply the factfinder with a table of prior and posterior odds, not to induce him to state his prior odds and to settle on the corresponding posterior odds, but rather to facilitate his mixing and weighing all the evidence by displaying the impact that the serologic evidence has across a wide range of prior odds. This more flexible approach seems preferable to the Essen-Moller procedure, and some laboratories now provide such calculations." Id. at 166.
[6] The court of appeals referred to the quantum of proof as "clear, satisfactory and convincing." However, the proper standard is provided at sec. 767.47(8), Stats., as a "clear and satisfactory preponderance of the evidence."
[7] Sec. 52.36(3), Stats., provided as follows:
"52.36 Evidence; blood tests. ...
"(3) Whenever the results of said tests exclude the defendant as the father of the child the same shall be conclusive evidence of such fact and the court shall dismiss said action. Whenever the results of said tests exclude any male witness the same shall be conclusive evidence of such fact. Such tests shall be receivable in evidence only in cases where definite exclusion of any person is established. If any party refuses to submit to such test such fact shall be disclosed upon trial."
This statute was repealed effective July 1, 1981, by ch. 352, Laws of 1979.
[8] Sec. 908.03(18), Stats., provides in pertinent part:
"(18) LEARNED TREATISES. A published treatise, periodical or pamphlet on a subject of history, science or art is admissible as tending to prove the truth of a matter stated therein if the judge takes judicial notice, or a witness expert in the subject testifies, that the writer of the statement in the treatise, periodical or pamphlet is recognized in his profession or calling as an expert in the subject."