Basic fallacies in the formulation of the paternity index.

Some basic fallacies in the computation of the paternity index have been pointed out. The general finding that the true fathers' mean paternity index is greater than that of nonfathers is a necessary consequence of an algebraic identity, having nothing to do with paternity or nonpaternity. It has also been shown that the paternity index is not a likelihood ratio as claimed. The fact that a paternity index may frequently take values less than unity leads to absurd conclusions regarding the probability of paternity. A formula relating prior and posterior probabilities of paternity, based solely on genetic marker testing results (exclusion or nonexclusion), is reiterated as a substitute for the current paternity index.     

Some fallacies in the computation of paternity probabilities.

Legal identification of fathers by means of a "paternity probability" has been used in European courts for decades, and has recently been introduced into American courts and accepted by some of them. The voluminous literature on this topic contains virtually no fundamental criticism of the logical basis for the probabilistic computations. Here I suggest that the "paternity probability" suffers from three basic fallacies: (1) contrary to claims, the figure is not, in fact, the probability that the alleged father is the true father, (2) the denominator of the likelihood ratio used in the computation is driven by (sometimes self-contradictory) assumptions and is not based on facts, and (3) post-inclusionary computations are based on speculation about genotypes that does not constitute scientific evidence. It is recommended that pending the resolution of these difficulties "paternity probabilities" should not be computed or introduced as positive evidence of paternity.     

No evidence for extra-pair paternity in the western gull

The genetic mating system of western gulls Larus occidentalis breeding on Southeast Farallon Island, California, was determined using multilocus DNA fingerprints of 33 chicks from 22 broods. No extra-pair paternity (EPP) was found, despite extra-pair copulations (EPCs) occurring. This suggests that paternity guards are effective, and that females gain few genetic benefits from EPCs. The EPP in western gulls concurs with that of other seabirds, reinforcing the idea that seabirds generally have a monogamous genetic mating system.     

Paternity index and attribution of paternity

If blood typing and similar tests do not exclude a putative father in a paternity case, his probability of paternity can be assessed with the formulae of Essen-M?ller[1938]. Gürtler[1956] uses an alternative route, viz. the paternity index, to reach identical end results. Majumder and Nei [1983] claim that the methods are not powerful enough. This opinion can always be defended, but may have been enhanced by their inadequate computer model. They also contend that current methods may more often than not lead to false attributions of paternity. This is outright erroneous.     

No evidence of extra-pair paternity in the little auk Alle alle

Extra-pair paternity is typically rather infrequent in seabirds, as in most other long-lived and socially monogamous birds. Here we report the first paternity study of the little auk Alle alle , a high arctic seabird which raises only a single chick per year. Parentage was determined using three highly polymorphic microsatellite markers. We found that all 26 chicks in our sample were true genetic offspring of their social parents, with an upper 95% confidence limit of 10.88% for the frequency of extra-pair paternity. This level of extra-pair paternity is not significantly different from frequencies reported from the closely related common Uria aalge and Brünnich's guillemots U. lomvia .     

Paternity exclusion and the paternity index for two linked loci

Algebraic expressions for the average exclusion frequency and the paternity index are derived for two linked loci, each with two alleles segregating in a population. The effects of recombination and gametic disequilibrium on these two statistics are discussed. As long as recombination is known to exist, the average exclusion frequency is similar for different recombination fractions. The paternity index, on the other hand, depends very much on both the recombination fraction and gametic disequilibrium. The effects of multiple alleles and dominance on these statistics are also briefly discussed.     

Probability of paternity in paternity testing using the DNA fingerprint procedure

For the purpose of applying DNA fingerprinting to paternity testing, we established a general formula to calculate the probability of paternity and evaluated the ability of DNA fingerprinting to determine paternity.     

No evidence for adjustment of sex allocation in relation to paternal ornamentation and paternity in barn swallows

Sex allocation theory predicts that parents should adjust investment in sons and daughters according to relative fitness of differently sexed offspring. In species with female preference for highly ornamented males, one advantage potentially accruing to parents from investing more in sons of the most ornamented males is that male offspring will inherit characters ensuring sexual attractiveness or high-quality genes, if ornaments honestly reveal male genetic quality. Furthermore, in species where extra-pair fertilizations occur, offspring sired by an extra-pair male are expected to more frequently be male than those of the legitimate male if the latter is of lower quality than the extra-pair male. We investigated adjustment of sex ratio of offspring in relation to ornamentation of the extra-pair and the social mate of females by direct manipulation of tails of male barn swallows Hirundo rustica . Molecular sexing of the offspring was performed using the W chromosome-linked avian chromo-helicase-DNA-binding protein (CHD) gene while paternity assessment was conducted by typing of hypervariable microsatellite loci. Extra-pair offspring sex ratio was not affected by ornamentation of their biological fathers relative to the experimental ornamentation of the parental male. Experimental ornamentation of the parental males did not affect the sex ratio of nestlings in their broods. Female barn swallows might be unable to bias offspring sex ratio at hatching according to the quality of the biological father. Alternatively, fitness benefits in terms of sexual attractiveness of sons might be balanced by the cost of compensating for little parental care provided by highly ornamented parental males, if sons are more costly to rear than daughters, or the advantage of producing more daughters, if males with large ornaments contribute differentially more to the viability of daughters than sons.     

Multiple paternity in the European hedgehog

Previous observations have suggested that European hedgehogs Erinaceus europaeus are promiscuous, although there have been no direct studies of the mating system to confirm this. In this study, the genetic mating system of the European hedgehog was assessed by analysing mother–offspring groups using six polymorphic microsatellite loci. Evidence of multiple paternity was found in two of five litters analysed and therefore demonstrates the occurrence of polyandry in wild populations of hedgehogs.     

Differential paternity in Libya

Libyan census and vital statistics data from 1973 are compared with genealogical records from Utah males born between 1830 and 1834 as representative of populations not using any method of fertility control. The Libyan vital statistics data contained 97% of paternity by age, but only 85% of maternity by age. These missing data were distributed pro rata, and all data were corrected for errors in reporting. Polygamous unions were excluded because polygamy is relatively rare in Libya. The Utah data were from 185,000 genealogies of the Genealogical Society of Utah. The Libyan child-woman ratio (number of children under age 5 per number of women aged 15-49) is 1112.9, compared to 850 in Morocco, suggesting that Libya is experiencing an increase in fertility, in child survival and probably in quality of statistics. The total fertility rates for females were 11.1 for Libya and 11.2 for Utah; the total paternity rates were 14.3 and 13.7, respectively. Male rates are higher because of remarriage after divorce or death of wives. Age-specific paternity rates are tabulated and graphed: The major difference between the 2 populations is the concave shape of the curve for Libyan men under 30. Age at marriage is late, but marriage is virtually universal for Libyan men over 30. Age-specific paternity rates by occupation show apparent lack of fertility regulation in traditional occupations like farming and sales. There is evidence of some parity-related fertility control in professional and administrative workers. Production workers have a high peak in fertility around age 27.5 and 32.5, and a dip occurring at older ages. These figures can be explained by education, since education is required for professional occupations, and older professionals were trained in the West. Production workers took advantage of rapidly expanding education in Libya late in their youth, postponing marriage. Libya's pronatalist policy forbids sale of contraceptives and provides child allowances, free education, health care, subsidized housing and social security. This paper indicates the utility of paternity data where statistics on maternity are unavailable.     

No effect of parental quality or extrapair paternity on brood sex ratio in the blue tit (Parus caeruleus)

Sex allocation theory predicts that parents should manipulatebrood sex ratio in order to maximise the combined reproductivevalue of their progeny. Females mating with high quality malesshould, therefore, be expected to produce brood sex ratiosbiased towards sons, as male offspring would receive a relativelygreater advantage from inheritance of their father's characteristicsthan would their female siblings. Furthermore, it has been suggested that sex allocation in chicks fathered through extrapair fertilizations should also be biased towards sons. Contraryto these predictions, we found no evidence that the distributionof sex ratios in a sample of 1483 chicks from 154 broods ofblue tits (Parus caeruleus) deviated significantly from thatof a binomial distribution around an even sex ratio. In addition,we found no significant effect on brood sex ratio of the individualquality of either parent as indicated by their biometrics, feather mite loads, time of breeding, or parental survival. This suggeststhat females in our population were either unable to manipulateoffspring sex allocation or did not do so because selectionpressures were not strong enough to produce a significant shiftaway from random sex allocation. The paternity of 986 chicks from 103 broods was determined using DNA microsatellite typing.Extrapair males sired 115 chicks (11.7%) from 41 broods (39.8%).There was no significant effect of paternity (within-pair versusextrapair) on the sex of individual offspring. We suggest that,in addition to the weakness of selection pressures, the possiblemechanisms responsible for the allocation of sex may not besufficiently accurate to control offspring sex at the levelof the individual egg.     

Extra-pair paternity in the Skylark Alauda arvensis

We present the first quantitative data on the genetic breeding system of a lark (Alaudidae), the Skylark Alauda arvensis . Using a set of eight microsatellite loci isolated in a variety of passerine species, we genotyped 171 offspring from 52 broods of Skylark and detected 35 extra-pair offspring (20%), in 14 different broods (27%). All offspring matched their putative mother, so there was no evidence of intraspecific brood parasitism. Previous non-genetic studies had suggested that the species was predominantly socially monogamous, with only rare occurrences of social polygyny and polyandry, although some behaviours, such as mate guarding, did suggest the possibility of extra-pair copulations. The relatively high level of extra-pair paternity in this species is likely to affect the variation in male reproductive success because extra-pair paternity was non-randomly distributed amongst males, with those with shorter wings more likely to be cuckolded.     

Battle of the sexes over paternity

Reproductive behaviors have evolved through severe inter-sexual competition. We have recently described a behavior in post-mated female Drosophila melanogaster that controls ejaculate retention and sperm storage, and is a possible mechanism by which females who have mated with several partners can choose which sperm that is stored and used for fertilization. This behavior can also regulate exposure of the female to harmful effects of male SFP that are present in the ejaculate. Our study identified the neural pathway functioning in the female brain that regulates this behavior. [BMB Reports 2015; 48(5): 241-242]