Appellant Jeanette Luke (Luke), on behalf of her minor son, Scott E. Luke, appeals the order of the district court1 granting summary judgment in favor of the Sec*975retary of Health and Human Services and affirming the Secretary’s denial of Luke’s application for surviving child’s insurance benefits under Title II of the Social Security Act, 42 U.S.C. § 402(d)(1). 666 F.Supp. 1340. The issue before this court is whether the Secretary’s decision to deny benefits is supported by substantial evidence. Finding that it is, we affirm.
I.
On July 2,1985, Luke filed an application for surviving child’s insurance benefits on behalf of her minor son, Scott E. Luke (Scott), on the earnings record of Gary J. Groth, the deceased wage earner and alleged biological father of Scott. On September 2, 1985, the claim was denied, and that decision was upheld upon reconsideration. Luke then requested and obtained a hearing before an Administrative Law Judge (AU) on May 20, 1986. On July 22, 1986, the AU rendered his decision finding that Scott was not eligible for benefits because Luke had failed to establish that Groth, the deceased wage earner, was Scott’s biological father. The AU based his decision on evidence introduced at the hearing, which is summarized as follows:
Jeanette Luke lived with Gary Groth from July 1980 until she separated from him in May 1984. They were never married. Luke testified that she did not have sexual relations with anyone other than Groth during the period that she lived with him. She further testified that she did not use any birth control during that period because Groth had told her he had had a vasectomy. However, in December of 1980, Luke discovered that she was pregnant, and on August 29, 1981, she gave birth to her son, Scott, who is the claimant in this action.
Luke testified that after she became pregnant, she and Groth consulted with Dr. Irvin Kaufman to determine how, since Groth had had a vasectomy, she could have become pregnant. On January 31, 1981, Dr. Kaufman advised them that not all vasectomies are 100% effective. But when Dr. Kaufman tested Groth’s semen specimen on February 9, 1981, he found no sperm in the specimen.
Notwithstanding the test results on Groth’s semen specimen, Groth referred to Scott as his son and publicly held himself out to be Scott’s father during the period that he (Groth) lived with Luke. Just one and one-half months after Scott’s birth, on October 16, 1981, Groth, who was already receiving social security disability benefits, filed an application for child insurance benefits on behalf of Scott. That application was accompanied by a handwritten, signed statement in which Groth declared that Scott was his natural child.2 Scott was later determined to be eligible to receive child’s insurance benefits, but such benefits apparently were terminated or never initiated upon the Secretary’s finding that Groth’s disability had ceased. Groth reapplied for child’s insurance benefits on December 6, 1982 on behalf of Scott,3 but this claim was later denied on the basis that (1) Groth was not entitled to disability benefits, and (2) Scott failed to meet the relationship requirement of 42 U.S.C. § 402(d) because new evidence, i.e., the medical report of Dr. Irvin Kaufman, indicated that Groth was not capable of fathering Scott due to a prior surgery.
The record reveals that Scott’s birth certificate, filed in the State of South Dakota, does not name a father. Luke reported that she did not list Groth as the father because she and Groth were not married and because Groth was out of town at the time of Scott’s birth. Groth’s name does *976appear on Scott’s hospital record of birth. Luke testified, however, that she placed Groth’s name on that certificate after she returned home from the hospital.
After Luke separated from Groth in 1984, she received Aid for Dependent Children (AFDC). She also received VA pension benefits for Scott under Groth’s name because the Veterans Administration had recognized Scott as Groth’s child. Luke testified, however, that Groth later attempted to terminate Scott’s VA benefits. The record also reflects that Groth indicated that he had no children under 18 years of age when Groth applied for disability insurance benefits on November 1, 1984.
Because Luke was receiving AFDC, the local department of social services initiated a paternity suit against Groth on Luke’s behalf. Luke reported that a hearing in that case was set for June 10th or 11th, 1985, that Groth hired Gary Blue, an attorney, to contest the action, but that Groth did not appear for the hearing. Luke later learned that Groth had died on June 13, 1985. Shortly thereafter, on July 2, 1985, Luke filed the instant application for child’s insurance benefits.
The AU specifically found that:
1. Scott Luke was not entitled to benefits as a legitimate or adopted child of Groth, because Groth never married Jeanette Luke nor adopted Scott under state law.
2. Scott Luke failed to establish that Groth was his biological father; that “there is clear and convincing evidence in the record that [Groth] could not have fathered [Scott] during the relevant time period.”
3. Scott Luke was not entitled to benefits under 42 U.S.C. § 416(h)(2)(A), because under South Dakota Law, S.D. Codified Laws § 29-1-15, he could not inherit as the illegitimate child of Groth. “[T]he status of child [under the state statute] is primarily based on a biological relationship which requires that the individual acknowledging the child have had the capacity or opportunity to father the child.”
4.Scott Luke was not entitled to benefits under 42 U.S.C. § 416(h)(3)(C)(i)(I), because Groth’s written acknowledgment that Scott was his son was insufficient in light of evidence that Scott had no biological relationship to Groth.
Thereafter, on September 29, 1986, the Appeals Council denied Luke’s request for review and the AU’s decision became the final decision of the Secretary. Luke subsequently filed this action for review of the Secretary’s decision in district court pursuant to 42 U.S.C. § 405(g). On cross motions for summary judgment, the district court affirmed the Secretary’s decision to deny benefits. Specifically, the district court found that the AU correctly determined that in order for an illegitimate child to be eligible for benefits under either 42 U.S.C. § 416(h)(2)(A) or § 416(h)(3)(C)(i)(I) he must first establish a biological relationship to the wage earner. The district court also found that substantial evidence supported the conclusion that Groth was not Scott’s biological father, and thus Scott was not eligible for benefits under either 42 U.S.C. § 416(h)(2)(A) or § 416(h)(3)(C)(i)(I). This appeal followed.
II.
Luke argues that the district court erred by misinterpreting South Dakota intestacy law (S.D. Codified Laws § 29-1-15) and 42 U.S.C. § 416(h)(3)(C)(i)(I), and by finding that the Secretary’s decision was supported by substantial evidence. Specifically, she argues that Scott, though illegitimate, should be deemed legitimate and entitled to receive benefits under 42 U.S.C. § 416(h)(2)(A) or § 416(h)(3)(C)(i)(I).
It is well established that where the Secretary has denied benefits, we must affirm the Secretary’s decision if it is supported by substantial evidence on the record as a whole. See Sherrill for Sherrill v. Bowen, 835 F.2d 166, 168 (8th Cir.1987); Gavin v. Heckler, 811 F.2d 1195, 1199 (8th Cir.1987). “This deferential standard of review applies only to findings of fact, however, and ‘no similar presumption of validity attaches to the Secretary’s conclusions of law * * *.’ ” Smith v. Heckler, *977707 F.2d 1284, 1285 (11th Cir.1983) (quoting Wiggins v. Schweiker, 679 F.2d 1387, 1389 (11th Cir.1982)) (referring to the Secretary’s interpretation of state law). A federal district court’s interpretation of state law, however, is given special weight and deferential review on appeal, and will not be reversed unless the appellate court is convinced that the district court has incorrectly ascertained or applied local law. Hazen v. Pasley, 768 F.2d 226, 228 (8th Cir.1985) (citations omitted).
The general criteria for entitlement to child’s insurance benefits are found under 42 U.S.C. § 402(d)(1). Section 402(d)(1) provides that every “child” of an individual who dies fully or currently insured under the Act is entitled to child’s insurance benefits if the child has applied for such benefits, is unmarried, under the age of 18, and was dependent upon the insured individual at the time of the insured’s death. Id.
A child is deemed dependent if he was (1) living with or supported by the wage earner at the time of his death, or (2) is the legitimate child of the wage earner. 42 U.S.C. § 402(d)(3). If a child is illegitimate, he may nonetheless be deemed legitimate for purposes of the Act (and hence deemed dependent and thus entitled to benefits) if he can [establish]:
1) That the [child] would be entitled to inherit personal property from the deceased wage earner under the law that would be applied in determining the devolution of intestate personal property by the courts of the wage earner’s state of domicile at death [under 42 U.S.C. § 416(h)(2)(A)] [or]
* # # * * *
3) That the deceased wage earner had a) acknowledged the [child] claimant in writing as his or her son or daughter * * * [under 42 U.S.C. § 416(h)(3)(C)(i)(I) ].
Allen v. Califano, 452 F.Supp. 205, 208 (D.Md.1978) (emphasis original) (footnotes omitted).
A. Interpretation of South Dakota Law
Under section 416(h)(2)(A),4 Scott would be entitled to benefits if he would inherit from Groth under the intestate laws of the state in which Groth was domiciled at his death. Although Groth apparently died in a Minnesota hospital, the AU found that Groth was domiciled in the State of South Dakota at the time of his death. Therefore, the relevant statute is S.D. Codified Laws § 29-1-15, which provides: “Every illegitimate child is an heir of the person who, in writing, signed in the presence of a competent witness, acknowledges himself to be the father of such child * *
The AU opined that:
[Section 29-1-15] * * * requires that the illegitimate first be the child of the father. One does not obtain the status of child merely by being acknowledged as such in writing. Rather, the status of child is primarily based on a biological relationship which requires that the individual acknowledging the child have had the capacity or opportunity to father the child.
The district court agreed with the AU’s interpretation, citing Application of G.K., 248 N.W.2d 380, 385 (S.D.1976) (Zastrow, J., dissenting) and In re Oakley’s Estate, 149 Neb. 556, 31 N.W.2d 557 (1948), as support.
Luke asserts that the AU’s and district court’s interpretation of section 29-1-15 is erroneous, because the statute explicitly uses the terms “person,” not “natural father” or “father,” and “child,” not “natural child” or “biological child.” She also notes that under South Dakota law, S.D. Codified Laws § 25-8-49, an admission or acknowledgment by an alleged father of paternity of an illegitimate child is prima facie evidence of paternity. She thus argues that because Groth unequivocally acknowledged *978Scott to be his child, Scott would have been entitled to inherit from Groth, and now is entitled to benefits under 42 U.S.C. § 416(h)(2)(A).
While the terms of section 29-1-15 do not make an explicit reference requiring that there be a biological relationship between the child and the person acknowledging paternity, we find that such a requirement is reasonably implied under the statute. Such an interpretation is consistent with Justice Zastrow’s dissenting opinion in Application of G.K., supra, 248 N.W.2d at 385, albeit dicta, in which he made reference to the rights of “natural” parents with respect to their illegitimate children under South Dakota law, e.g., the right of a “natural father” to secure his illegitimate child’s right to inherit upon the father’s written acknowledgment of paternity under S.D. Codified Laws § 29-1-15. The AU’s interpretation is also consistent with S.D. Codified Laws § 25-8-49, which provides that an admission of paternity by an alleged father is prima facie evidence of paternity.5 Acknowledgment of paternity under this statute will suffice, in most cases, to establish an illegitimate child’s right to inherit under section 29-1-15. But where, as here, the alleged father’s acknowledgment of paternity is rebutted by clear and convincing evidence that he was incapable of fathering the child, the father’s acknowledgment alone is insufficient to confer the status of “child” for inheritance purposes. We therefore conclude that the district court and AU did not err in interpreting South Dakota law, section 29-1-15.
B. Interpretation of 42 U.S.C. § 416(h)(3)(C)(i)(I)
Next we address the issue of whether section 416(h)(3)(C)(i)(I) of Title 426 requires the claimant to establish a biological relationship to the wage earner. Both the AU and the district court concluded that it does. The district court based its conclusion on (1) the definition of “child” found within 42 U.S.C. § 416(e), (2) the language of 42 U.S.C. § 416(h)(3)(C)(i)(I) requiring that the applicant be the “son or daughter” of the wage earner, Pray v. Department of Health, Education and Welfare, 1999-81 Unempl. Ins. Rep. (CCH) ¶ 16,665 (S.D.N.Y. Mar. 21, 1979), (3) 20 C.F.R. § 404.355,7 which specifically provides that the claimant must be the insured’s “natural child,” and (4) the legislative history of 42 U.S.C. § 416(h)(3). See Social Security Amendments of 1965, S.Rep. No. 404, 89th Cong., 1st Sess., reprinted in 1965 U.S. Code Cong. & Admin. News 1943, 2049-50; see also Pray, supra, 1999-81 Unempl. Ins. Rep. (CCH) at ¶ 16,666.
We find that the district court correctly determined that 42 U.S.C. § 416(h) (3) (C)(i)(I) requires the claimant to establish that he is the biological child of the wage earner. This court has previously recognized that proof of a biological relationship is a necessary antecedent re*979quirement under § 416(h)(3)(C)(ii). See Sherrill for Sherrill v. Bowen, supra, 835 F.2d at 169; Jones for Carr v. Bowen, 829 F.2d 647 (8th Cir.1987). Accord Imani ex rel. Hayes v. Heckler, 797 F.2d 508, 512 (7th Cir.), cert. denied, 479 U.S. 988, 107 S.Ct. 580, 93 L.Ed.2d 583 (1986); Greer by Greer v. Heckler, 756 F.2d 794, 798 (10th Cir.1985). Section 416(h)(3)(C)(ii) is simply an alternative entitlement provision of § 416(h)(3)(C)(i), at issue in the present case. We agree with the conclusion reached by the Fourth Circuit in McMillian by McMillian v. Heckler, 759 F.2d 1147, 1153 (4th Cir.1985), that:
[I]t is clear that Congress intended that a claimant invoking either of the alternative means of establishing entitlement provided by § 416(h)(3)(C) should be put to proving as one ultimate fact that the insured was his natural parent. * * * [P]arentage of the insured is an ultimate fact to be proven under either subpara-graph (C)(i) or (C)(ii).
C. Review of the Evidence
Having determined that both 42 U.S.C. § 416(h)(3)(C)(i)(I) and § 416(h)(2)(A) (by virtue of the South Dakota intestate statute, § 29-1-15) required the claimant to establish a biological relationship to the insured wage earner, we now consider whether the Secretary’s finding that there was no biological relationship between Scott and Groth is supported by substantial evidence on the record as a whole. This standard of review requires that we take into account evidence which fairly detracts from its weight. Piercy v. Bowen, 835 F.2d 190, 191 (8th Cir.1987).
Luke asserts that the AU erred by giving greater weight to unreliable evidence of non-paternity (i.e., sterilization by vasectomy) than to more reliable evidence of paternity (i.e., Groth’s written and public statements acknowledging Scott as his son, Groth’s attempts to obtain child insurance benefits for Scott, Groth’s tolerance of VA pension payments to Luke for Scott’s benefit after Luke separated from Groth, Scott’s physical resemblance to Groth). She argues that evidence of Groth’s vasectomy should have been given little weight because there was evidence that vasectomies are not always successful in preventing pregnancy, the date of Groth’s vasectomy could not be confirmed,8 there was no evidence verifying the identification or condition of the semen sample tested by Dr. Kaufman, and a second semen sample was never tested to confirm the results of the first semen test.
Having carefully considered the record, we find that the AU did not err by giving greater weight to that evidence tending to prove non-paternity than to the evidence tending to prove paternity. The record indicates that Groth repeatedly admitted having had a vasectomy in 1970 or 1971, that the vasectomy was performed at Crystal Medical Clinics, Crystal, Minnesota, that vasectomies are successful in 399 out of 400 cases (or 99.75 percent of the time), and that Groth’s treating physician, Dr. Kaufman, found no live or dead sperm in Groth’s semen sample just a couple of months after Luke became pregnant. We find this evidence was substantial and clearly outweighed any declarations or belief Groth may have had that he was Scott’s father. We also find that the evidence of Groth’s vasectomy and semen test results was sufficiently reliable to be considered material on the issue of paternity.9
Furthermore, we cannot say that the record supports Luke’s claim that Groth’s acknowledgment of Scott was unequivocal. Six months following Luke’s separation from Groth, Groth indicated on an application for disability benefits that he had no children under the age of 18. The record also indicates that Groth did not make regular child support payments, because the local department of social services had to *980initiate a paternity suit against Groth on Luke’s behalf in order to secure child support. Although Groth did not appear nor file an answer in that proceeding, Luke testified that Groth had hired an attorney, Gary Blue, to contest paternity in that action. Finally we note Luke’s testimony indicating that sometime after she had separated from Groth, Groth attempted to terminate the YA pension benefits which were being paid to Luke on Scott’s behalf. These facts, we believe, substantially support the AU’s conclusion that despite Groth’s written acknowledgment of Scott, he (Groth) also had some misgivings about his biological relationship to Scott. We also agree that it was to Groth’s advantage for him to acknowledge Scott as his child in order to receive additional benefits from both the Secretary and the Veterans Administration at the time he was living with Luke.
Based upon the foregoing considerations, we conclude that there is substantial evidence on the record as a whole to support the Secretary’s decision to deny Luke’s application for surviving child’s insurance benefits. Accordingly, we affirm the district court’s entry of summary judgment in favor of the Secretary.
. The Honorable John B. Jones, United States District Court Judge for the District of South Dakota.
. The record also reveals that on November 21, 1981, Groth filed an additional statement in which he claimed to be the natural father of Scott. This statement was submitted immediately after Groth’s ex-wife, Barbara Groth, had submitted a letter of protest with respect to Groth’s application for benefits for Scott. Scott's entitlement to benefits on the record of Groth would have reduced the amount of benefits already being paid to Barbara Groth for the benefit of James Groth, the youngest of four sons born to Barbara and Groth during their marriage.
. Groth’s December 6, 1982 application also sought benefits for his other minor son, James Groth.
. 42 U.S.C. § 416(h)(2)(A) provides in pertinent part:
In determining whether an applicant is the child * * * [of the insured individual under] this subchapter, the Secretary shall apply such law as would be applied in determining the devolution of intestate personal property by the courts of the State in which such insured individual is domiciled at the time * * * of his death * * *.
. S.D. Codified Laws § 25-8-49, in effect creates a presumption of paternity upon the father's acknowledgment or admission of paternity. The requisite burden of proof for overcoming this presumption, as implicitly recognized by the ALJ, is clear and convincing evidence. See Matter of F.J.F., 312 N.W.2d 718, 721 (S.D.1981)
. 42 U.S.C. § 416(h)(3)(C)(i)(I) provides in relevant part:
An applicant who is the son or daughter of a fully or currently insured individual, but who is not (and is not deemed to be) the child of such insured individual under [state intestacy laws pursuant to § 416(h)(2) ], shall nevertheless be deemed to be the child of such insured individual if:
******
(C) in the case of a deceased individual— (i) such insured individual—
(I) had acknowledged in writing that the applicant is his or her son or daughter
****** and such acknowledgment * * * was made before the death of such insured individual
.20 C.F.R. § 404.355, which interprets 42 U.S.C. § 416(h)(3)(C)(i)(I), provides in relevant part:
You may be eligible for benefits as the insured's natural child if one of the following conditions is met:
******
(c) You are the insured’s natural child and your mother or father has not married the insured, but the insured has either acknowledged in writing that you are his or her child * * *
(Emphasis added.)
. The record indicates that the medical records of Groth’s vasectomy were destroyed in a medical clinic fire.
. In Sherrill for Sherill v. Bowen, 835 F.2d 166, 169 (8th Cir.1987), we recognized that as long as the evidence is material to the issues in question, it may be considered by the AU, although such evidence would otherwise be held inadmissible under the rules of evidence in a court of law.