Judge PHILLIPS dissenting.

The main issue in this case is whether defendant is the father of Jonathan Derrick Cole.

Plaintiff and defendant were married on 19 April 1970. They bore one child on 19 August 1971 and another on 29 September 1975. Defendant had a bilateral vasectomy on 20 February 1976. On 20 May 1976, the physician who performed the vasectomy made a sperm count on a specimen brought by defendant, and it was negative. Also, a pathology test was performed on the sections of the vasa deferentia removed from defendant, and the tests confirmed that the vasectomy had been successful.

On 10 September 1982 the plaintiff gave birth to a son, Jonathan Derrick Cole. The defendant acknowledged that he was the child's father on the child's birth certificate. In the Spring of 1983 the parties' marriage deteriorated. They separated on 9 July 1983. On 18 August 1983 the plaintiff filed a complaint requesting alimony, temporary alimony, custody of the children, child support and attorney's fees. The defendant filed an answer denying he was the father of Jonathan Derrick Cole.

On 15 September 1983, Dr. John Grimes performed a semen analysis on defendant and determined that he was sterile. Dr. Grimes found no evidence of any vasectomy performed on defendant except for the one of 20 February 1976. Dr. Grimes testified that he believed defendant was sterile during the years 1981-82 and that the likelihood of defendant becoming fertile after his vasectomy was "one in a million and probably less than that now."

A blood test was performed on defendant, on the child Jonathan Cole, and on plaintiff. The test indicated that the probability of defendant being Jonathan's father was 95.98%, assuming that defendant "was a fertile male at the time of presumed conception, [sic] Undisputed evidence to the contrary would drop the probability of paternity to 0%."

The district judge ruled that the defendant is the biological father of Jonathan Derrick Cole.

Defendant appeals this judgment.

ARNOLD, Judge.

The issue which determines this appeal is whether the district judge's findings of fact support his conclusion of law that the defendant is the biological father of Jonathan Derrick Cole. See Moore v. Deal, 239 N.C. 224, 228, 79 S.E.2d 507, 510 (1954). We hold that they do not.

The findings of fact read, in pertinent part:

4. Jonathan Derrick Cole was born to Dorothy Lesniak Cole [plaintiff] on September 10, 1982; present age approx. 1 1/2 yrs. old.

. . . .

7. The parties were married on April 19, 1970.

. . . .

12. Husband noticed, with at first annoyance and later with strong objection, that sometimes when he was away from home the wife had a male visitor. The children were present, and there was no reason for him to believe that the relationship between his wife and this male visitor, Mr. X, was anything more than friends. But it began to worry him, burrowing within. But he said nothing.

13. Sometime in November or December, 1981, the wife became pregnant.

38. On February 20, 1976, the husband had a vasectomy.

39. On May 20, 1976, a sperm count was taken on the husband to check and seek [sic] if the vasectomy was working. It was. The sperm count was zero, meaning in the opinion of the doctor, no sperm was getting through.

40. On Sept. 15, 1983, a sperm count was again taken of the husband. A fresh semen specimen was obtained, 30 to 40 specimens of which were examined under the microscope. No sperm were found. The opinion of the medical expert was that the husband is nonfertile at the present time.

41. As to the possibility of the husband becoming fertile during the period of November-December, 1981, the medical expert appeared to be certain and confident that the husband was not fertile. He expressed the odds against the father having been fertile as a million to one.

42. On or about October 13, 1983 a blood testing for paternity was done. It showed that the probability of paternity of the father was 95.98%.

43. The above test also stated: "This probability of paternity assumes that (husband) was a fertile male at time of conception. Undisputed evidence to the contrary would drop the possibility to 0%."

44. The husband has had no other vasectomy.

. . . .

50. When asked by the judge if she saw any similarity of movement or expression as between the baby Derrick and the husband, she said yes, that sometimes when he looked at her they had a similar characteristic.

51. When asked the same question by the judge, the husband said no. (That is, no similarity). However the husband has not had a lot of opportunity to observe him, because, once he became convinced that Derreck [sic] was not his son, he stopped seeing him.

52. In making this decision, this judge is taking into consideration the fact that the husband failed to clearly state his doubt that he was the father until this suit was instituted; and then never became convinced in his own mind until he found out the results of the Sept. 1983 sperm test. The fact that he was not willing to attend counseling (e.g. state plainly to a counselor his worry that the child might not be his — and deal honestly with the issue) weighs against his position. If he wanted to protect the reputation of his wife, yet communicate this to her, then counseling would have been the ideal way. He could have stated in the presence of the counselor: "I have some doubts that I am the father of Derrick, but I do not want to say this to my wife because it might make her more upset, and I do not want to ruin her reputation — but this doubt is worrying me to death." And then the counselor would have seen this vital factor affecting the marriage, and dealt with it. Also, the father did not clearly state when he left that one of the reasons he was leaving was that he had doubts as to parentage. After having specifically on one occasion told his wife he had no doubts, indicating repeatedly in public that he had no doubts, appearing from his fatherly reactions to accept parentage, and allowing his name to be put on the birth certificate, he had the duty of revelation prior to separation, because each day that passed made the consequences of a possible question of paternity more damaging to the children. After a vasectomy, each sexual act would give a very small possibility of impregnation. But with a couple with an active sex life, each act of sexual intercourse makes the impossible a little more possible. I find find [sic] that in November or December, 1981 that little Derrick was conceived by the union of Dorothy and Donald Cole.

The district judge thus found that the defendant had a vasectomy in 1976. Several months after the vasectomy, his semen was analyzed, yielding a sperm count of zero. In 1982, Jonathan Cole was born to plaintiff. In 1983, defendant's sperm count again was found to be zero. The judge found that a medical expert was "certain and confident" that defendant was not fertile at the time Jonathan Cole was conceived, the odds against this being a million to one.

The district judge also found that in 1983 a blood test was done which showed that the probability of defendant's paternity of Jonathan Cole was 95.98%. The district judge found that the test results had the following condition: "This probability of paternity assumes that (husband) was a fertile male at time of conception. Undisputed evidence to the contrary would drop the possibility to 0%."

Evidence that the defendant was not a fertile male at the time of conception was presented at trial and, as noted above, was adopted by the district judge in his findings of facts. This evidence was not contradicted at trial, and the judge gave no indication that he doubted the accuracy of the sperm counts or the credibility of the expert testimony.

It cannot be assumed, then, that defendant was a fertile male at the time of conception. Without this assumption, the probability that defendant fathered Jonathan Cole. calculated on the basis of the blood test, is therefore very small, or nil. Taken together, the judge's findings as to the medical evidence suggest that defendant has been sterile since 1976 and could not have fathered Jonathan Cole.

In this case, we are presented with what appears to be a sharp contrast in the medical evidence, between the results of fertility tests done on defendant, and blood tests done on defendant, plaintiff and Jonathan Cole. Because the results of the blood test appear to suggest such a high probability of paternity, we believe it is necessary to discuss how that probability is calculated, and why it should be discounted in cases where there is strong evidence of the father's infertility.

While much progress has been made in the blood tests used in cases of disputed paternity, by expanding the number of antigens examined, the test's greatest value still lies primarily in excluding falsely accused fathers. A "probability of paternity" can now be calculated for alleged fathers not excluded, and this is admissible on the issue of paternity, but it is not conclusive.

Serious questions have been raised about the validity of the method used to calculate the probability. I. Ellman and D. Kaye, Probabilities and Proof: Can HLA and Blood Group Testing Prove Paternity? 54 N.Y.U. L.Rev. 1131 (1979); Jaffee, Comment on the Judicial Use of HLA Paternity Test Results and Other Statistical Evidence: A Response to Terasaki, 17 J. Fam. L. 457 (1978-79). Critics of the probability of paternity calculation have focused on the assumptions made in the calculations, which greatly limit the usefulness of the probability in certain cases. For example, the calculation generally assumes that all possible fathers are unrelated. If the alleged father and the true father are related, then their HLA and red blood cell antigen profiles are likely to be very similar. Even the strongest proponent of the probability of paternity calculation admits it cannot be used in the case where potential fathers are related. P. Terasaki, Resolution by HLA Testing of 1000 Paternity Cases Not Excluded by ABO Testing, 16 J. Fam. L. 543, 549 (1977-78).

Further, the calculation assumes that all possible fathers are fertile. In a case like the present, where there is strong evidence that the defendant is not fertile, the calculation, if it does not take into account this information, is likely to overestimate substantially the probability of paternity.

The source of much controversy is the statistical formula generally used to calculate the probability of paternity: the Bayes Theorem. Terasaki, supra at 544. Briefly, the Bayes Theorem shows how new statistical information alters a previously established probability. Ellman and Kaye, supra at 1147-48. When a laboratory uses the Bayes Theorem to calculate a probability of paternity it must first calculate a "prior probability of paternity," i.e., a probability that the alleged father is the true father, based on information other than that gotten from the blood test. This prior probability usually has no connection to the case at hand. Sometimes it reflects the previous success of the laboratory at excluding falsely accused fathers. Traditionally, laboratories use the figure 50%, which may or may not be appropriate in a given case. E. G. Reisner and T. A. Bolk, A Layman's Guide to the Use of Blood Group Analysis in Paternity Testing, 20 J. Fam. L. 657, 673-74 (1981-82).

Critics suggest that this prior probability should take into account the circumstances of the particular case. Ellman and Kaye, supra at 1151. For example, if the woman has accused three men of fathering her child, or if there are reasons to doubt her credibility, or if there is evidence that the husband is infertile, as in the present case, then the prior probability should be reduced to less than 50%. Most laboratories, however, do not do this.

The importance of the prior probability to the final probability cannot be overemphasized. The Bayes Theorem calculates a final probability only by applying new statistical information to the prior probability. In paternity cases, where the defendant has not been previously excluded as the father, and where 50% is used as the prior probability, the Bayes Theorem ensures that every alleged father is "probably" the father, i.e., the blood test results only improve upon the 50% prior probability of paternity.

Thus, the probability of paternity is generally probative, at best, where it is 90%, or as some have suggested 95%. See Joint AMA — ABA Guidelines: Present Status of Serologic Testing in Problems of Disputed Parentage, 10 Fam. L.Q. 247, 262 (table IV) (1976-77). And this assumes, of course, that potential fathers are not related, and that there is no evidence that the alleged father is infertile. In the present case, then, what appears to be a very high probability of paternity based on blood tests actually indicates that it is "likely" to "very likely" that defendant fathered Jonathan Cole. Moreover, if the overwhelming evidence of defendant's infertility is factored in, this apparently high probability drops dramatically. This is why the laboratory test result sheet in the present case contained the proviso that "undisputed evidence [of infertility] would drop the possibility to 0%." If the district judge relied on the probability of paternity, despite the evidence of defendant's successful vasectomy, then he erred.

We now deal with the other findings of fact that might have supported the district judge's conclusion that defendant fathered Jonathan Cole. In finding of fact 52, the district judge states that he took into consideration defendant's failure to state his doubt that the child was his until this suit was commenced and defendant's failure to undergo counseling. These considerations are not relevant to the issue of whether defendant was actually the biological father of Jonathan Cole.

Finally, we deal with the district court judge's finding that after a vasectomy, "each sexual act would give a very small possibility of impregnation." Even if this were true, it is apparently based on a statistical generalization about all couples in which the husband has had a vasectomy, and not about the much smaller group of couples in which the husband has had a vasectomy and has had subsequent sperm counts and a pathology test showing complete sterility. Given that the judge has made much more specific findings about the success of defendant's vasectomy, his general finding that "each sexual act would give a very small possibility of impregnation" is not pertinent to the circumstances of this case and does not support the conclusion that defendant fathered Jonathan Cole.

Thus in light of the district judge's findings that scientific evidence demonstrated that defendant was sterile at the time Jonathan Cole was conceived, and that if defendant was sterile, the blood grouping probability of paternity was reduced to 0%, his conclusion that defendant fathered Jonathan Cole is erroneous. Rather, the judge's findings compel the conclusion that defendant did not father Jonathan Cole.

We see no need to reach defendant's other contentions.

Reversed.

Judge COZORT concurs.

Judge PHILLIPS dissents.