Estimating effective paternity number in social insects and the effective number of alleles in a population

Estimating paternity and genetic relatedness is central to many empirical and theoretical studies of social insects. The two important measures of a queen's mating number are her actual number of mates and her effective number of mates. Estimating the effective number of mates is mathematically identical to the problem of estimating the effective number of alleles in population genetics, a common measure of genetic variability introduced by Kimura & Crow (1964). We derive a new bias-corrected estimator of effective number of types (mates or alleles) and compare this new method to previous methods for estimating true and effective numbers of types using Monte Carlo simulations. Our simulation results suggest that the examined estimators of the true number of types have very similar statistical properties, whereas the estimators of effective number of types have quite different statistical properties. Moreover, our new proposed estimator of effective number of types is approximately unbiased, and has considerably lower variance than the original estimator. Our new method will help researchers more accurately estimate intracolony genetic relatedness of social insects, which is an important measure in understanding their ecology and social behaviour. It should also be of use in population genetic studies in which the effective number of alleles is of interest.     

Impact of a chromosome X STR Decaplex in deficiency paternity cases

Deficiency paternity cases, characterized by the absence of the alleged father, are a challenge for forensic genetics. Here we present four cases with a female child and a deceased alleged father in which the analysis of a set of 21 or 22 autosomal STRs (AS STRs) produced results within a range of doubt when genotyping relatives of the alleged father. Aiming to increase the Paternity Index (PI) and obtain more reliable results, a set of 10 X-linked STR markers, developed by the Spanish and Portuguese Group of the International Society for Forensic Genetics (ISFG), was then added. Statistical analysis substantially shifted the results towards the alleged fatherhood in all four cases, with more dramatic changes when the supposed half-sister and respective mother were the relatives tested.     

Population genetical study of Japanese macaques,Macaca fuscata,in the shimokita A1 troop,with special reference to genetic variability and relationships to Japanese macaques in other troops

The genetic variations of 35 individuals of the Shimokita A1 troop of mainland Japanese macaques,Macaca fuscata fuscata, which live at the northern end of the habitat of the species, were investigated using 33 electrophoretically detectable blood protein loci. Among the loci examined, six were polymorphic. The average heterozygosity per individual was calculated as 0.0442. This was the highest value among all troops of Japanese macaques so far investigated. The mainland macaques of the Shimokita A1 troop were more differentiated genetically from other mainland macaque troops than were Yaku macaques, the subspeciesM. f. yakui.     

Multiple paternity: determining the minimum number of sires of a large brood

We describe an efficient algorithm for determining exactly the minimum number of sires consistent with the multi-locus genotypes of a mother and her progeny. We consider cases where a simple exhaustive search through all possible sets of sires is impossible in practice because it would take too long to complete. Our algorithm for solving this combinatorial optimization problem avoids visiting large parts of search space that would not result in a solution with fewer sires. This improvement is of particular importance when the number of allelic types in the progeny array is large and when the minimum number of sires is expected to be large. Precisely in such cases, it is important to know the minimum number of sires: this number gives an exact bound on the most likely number of sires estimated by a random search algorithm in a parameter region where it may be difficult to determine whether it has converged. We apply our algorithm to data from the marine snail, Littorina saxatilis.     

Effectiveness of human microsatellite loci for assessing paternity in a captive colony of vervets (Chlorocebus aethiops sabaeus)

Microsatellite polymorphisms are playing an increasingly vital role in primatological research, and are particularly useful for paternity exclusion in both wild and captive populations. Although vervet monkeys (Chlorocebus aethiops) are commonly studied in both settings, few previous studies have utilized microsatellite markers for assessing genetic variation in this species. In a pilot project to assess paternity in the UCLA-VA Vervet Monkey Research Colony (VMRC), we screened 55 commercially available human microsatellite markers chosen from a panel of 370 that have been shown to be polymorphic in baboons (Papio hamadryas). Using a standard PCR protocol, 43 (78%) loci produced amplifiable product. Of these, 14 were polymorphic and 11 were genotyped in 51 individuals, including 19 offspring and 14 potential sires. The average heterozygosity across the 11 loci was.719. In all 19 paternity cases all but one male was excluded as the true sire at two or more loci. This includes successfully distinguishing between two maternal half-sib brothers who were potential sires in most of the paternity cases. Given that the colony is descended from 54 wild-caught founders trapped between 1975 and 1987 from an introduced population on St. Kitts, West Indies, these values imply high microsatellite variability in natural vervet populations. Our results provide a panel of markers derived from the human genome that is suitable for assessing genetic variation and paternity in vervets.     

Primary pollinator exclusion has divergent consequences for pollen dispersal and mating in different populations of a bird‐pollinated tree

Pollination by nectarivorous birds is predicted to result in different patterns of pollen dispersal and plant mating compared to pollination by insects. We tested the prediction that paternal genetic diversity, outcrossing rate and realized pollen dispersal will be reduced when the primary pollinator group is excluded from bird‐pollinated plants. Pollinator exclusion experiments in conjunction with paternity analysis of progeny were applied to Eucalyptus caesia Benth. (Myrtaceae), a predominantly honeyeater‐pollinated tree that is visited by native insects and the introduced Apis mellifera (Apidae). Microsatellite genotyping at 14 loci of all adult E. caesia at two populations (n = 580 and 315), followed by paternity analysis of 705 progeny, revealed contrasting results between populations. Honeyeater exclusion did not significantly impact pollen dispersal or plant mating at Mount Caroline. In contrast, at the Chiddarcooping site, the exclusion of honeyeaters led to lower outcrossing rates, a threefold reduction in the average number of sires per fruit, a decrease in intermediate‐distance mating and an increase in near‐neighbour mating. The results from Chiddarcooping suggest that bird pollination may increase paternal genetic diversity, potentially leading to higher fitness of progeny and favouring the evolution of this strategy. However, further experimentation involving additional trees and study sites is required to test this hypothesis. Alternatively, insects may be effective pollinators in some populations of bird‐adapted plants, but ineffective in others.     

The effect of male tenure and female mate choice on paternity in free-ranging Japanese macaques

In this study, the paternity of all the infants born in 2002 and 2003 in a free-ranging Japanese macaque (Macaca fuscata) group at Arashiyama in Kyoto, Japan, was analyzed in relation to males' age, dominance rank, and tenure and females' mate choice. The fathers of 20 out of 23 infants were determined by DNA analyses. Central adult (high-ranking) males sired two infants, whereas peripheral adult (low-ranking) males sired 14 infants. Young males sired only one infant. Among adult males, tenure was the most dominant factor that negatively affected male reproductive success. The mating behavior of females who gave birth was also analyzed. The number of male copulations in the peri-fertilization period was positively correlated with the number of infants that they sired. Females copulated with central males with a long tenure only when fertilization was unlikely or impossible. The females probably avoided insemination by males with a long tenure and selected males with a shorter tenure as their mating partners during the ovulation period.     

Male dominance rank and offspring-initiated affiliative behaviors were not predictors of paternity in a captive group of pigtail macaques (Macaca nemestrina)

Paternity of 16 pigtail macaque offspring was determined using a DNA profile analysis and was based on two independent assays of the genome of each individual using multilocus DNA probes. The offspring were members of a group of 59 pigtail macaques, including 5 adult males, 1 subadult male, and 37 adult and subadult females. Rank was unrelated to paternity as the first ranking male sired 0, the second ranking male sired 3; the third ranking male sired 0, the fourth ranking male sired 8, and the fifth ranking male sired 2 offspring. The subadult male sired 0 offspring. The DNA analysis was effective in excluding possible sires of 3 offspring whose mothers had become pregnant by another male before being introduced to the study males. Subsequent semen evaluation revealed an absence of sperm in the semen of the alpha male, but revealed a sperm count within normal limits in the third ranking male, who also sired no offspring. Behavioral data focusing on male-offspring interactions found that offspring did not preferentially affiliate with their sire and that males did not affiliate with their offspring frequently enough for analysis. Thus, this study of one captive pigtail macaque group demonstrates that: (1) rank was not a predictor of reproductive success; and (2) there was no preferential attraction for one's own offspring by males or one's own sire by offspring.     

Certainty of paternity and paternal effort in the collared flycatcher

Models of optimal parental investment predict that variationin certainty of paternity can affect the optimal level of paternalinvestment when a male's expected paternity in different nestingattempts is not fixed throughout his lifetime. Several attemptsto test this prediction experimentally in monogamous birds havefailed to induce a reduction in care by males. This may be becausethe method used, detaining males, is a poor model for what happenswhen a male's certainly of paternity is naturally reduced. Wecaught and detained female collared flycatchers Ficedula albicollisfor 1 h immediately after laying on one or two occasions inan attempt to induce variation in certainty of paternity forthe males they were mated to. By capturing females immediatelyafter laying we hoped to exploit the existence of an "inseminationwindow" since males should be very sensitive to female absenceduring this period. The general effect of the experimental manipulationwas consistent with reduced certainty of paternity: males respondedby reducing their level of paternal care to nestlings, and malesmated to females that had been caught on one morning fed nestlingssignificantly less often and made a smaller share of feedingvisits than males mated to control females. The effects of theexperiment were generally weak, however, and we argue that certaintyof paternity may be fixed well before egg laying, in which caseexperimental manipulations are unlikely to have large effects.It is difficult to predict die effects of natural variationin certainty of paternity on levels of male paternal care becausedifferential allocation by females mated to attractive malesmay act in the opposite direction     

Estimations of the efficacy and reliability of paternity assignments from DNA microsatellite analysis of multiple-sire matings

It is important for bovine DNA testing laboratories to provide the cattle industry with accurate estimates of the efficacy and reliability of DNA tests offered so that end users of this technology can adequately assess the cost-benefits of testing. To address these issues for bovine paternity testing, paternity exclusion probability estimates were obtained from breed panel data and were predictive of the efficacy of the DNA tests used in 39 multiple-sire mating groups, involving 5960 calves and 505 bulls. Paternity testing of these mating groups has demonstrated that the majority involve a variable proportion of unknown sires and this impacts on the reliability of sire allocation. Mathematical models based on binomial or beta-binomial probability distributions were used to estimate the reliability of single-sire allocations from multiple-sire matings involving unknown sires. Reliability of 98-99% is achieved when the exclusion probability is 0.99 or greater, after allowing for up to 20% unknown sires. When the exclusion probability drops below 0.90 and there are 20% unknown sires, the reliability is poor, bringing into question the benefits of testing. This highlights the need for DNA testing laboratories to offer paternity tests with an exclusion power of at least 99%.     

Assessing probability of paternity and the product rule in DNA systems

The genetic resolution of paternity disputes begins with an intricate detection of inherited traits and finishes with a statistical inference (the probability of paternity,W). Notwithstanding some initial fanfare, statistical inference is a necessary component of DNA-based paternity tests because band patterns may be rare but not yet unique, and even rare events in a vacuum are meaningless. The genetic match must be combined with other evidence for relevancy, thus a Bayesian approach is preferred when computingW. This paper reviews the standard model used to computeW and discusses the model's various properties and assumptions. The standard model is extended to include DNA systems in which alleles are operationally continuous due to measurement error. This extension avoids problems associated with matched/non-matched binned decisions. After outlining the model assumptions for a single DNA system, particular attention is given to the product rule-the procedure of multiplying intermediate probabilities across genetic loci to form a combinedW. An empirical alternative to the product rule is also assessed and correlated with standard procedures.Editor's commentsThe authors present a carefully reasoned account of Bayesian inference in the paternity context. Their presentation of an alternative to the product rule for Paternity Index values offers a means of avoiding objections to the rule.     

The morphology and wear of the lingual notch in macaques and langurs

Although interspecific differences in the relative development of molar occlusal features have been documented for most primate species, wear-related changes in these features are only beginning to be understood. In the present study, the notch between the metaconid and entoconid of M₂ was examined in a skeletal sample of Macaca fascicularis, Presbytis cristatus, and Presbytis rubicunda from the Museum of Comparative Zoology at Harvard University. Photogrammetric analyses yielded X, Y, and Z coordinates that were used to compute three angular measurements and two length measurements at the lingual notch. Statistical analyses of measurements from unworn dentitions indicated that the mesial slope of the entoconid is steeper than the distal slope of the metaconid in all three species. In addition, interspecific comparisons demonstrated that P. cristatus has the steepest lingual notch bordered by the largest molar shearing crests, while P. rubicunda and M. fascicularis have molar shearing crests of similar size, with P. rubicunda merely having higher cusps that are closer together than those of M. fascicularis. Fanally, P. cristatus shows a smaller decrease in lingual cusp relief with wear than M. fascicularis, while P. cristatus and P. rubicunda probably show similar decreases in lingual cusp relief with wear. The differences in wear-related changes in lingual cusp relief between M. fascicularis and P. cristatus may well be related to the frugivorous/folivorous dietary differences between these species.     

Paternity exclusion by DNA fingerprinting,and mate guarding in the hooded seal Cystophora cristata

Hooded seal Cystophora cristata trios consist of an adult female, her pup, and an attending adult male. Using DNA fingerprinting, we excluded the possibility that the attending males within hooded seal trios were the fathers of the pups, proving that these hooded seals did not remain paired from one breeding season to the next. Behavioural observations of the trios after capture and release revealed that male hooded seals displace one another in attending nursing females. Mate guarding appears to be the preferred mating strategy available to male hooded seals given intense competition for females, a very brief nursing period, and oestrus occuring soon after weaning, but its effectiveness remains unclear.     

Isolation and characterization of polymorphic microsatellite loci for the study of paternity and population structure in the little penguin Eudyptula minor

We isolated and characterized eight novel microsatellite loci in the little penguin Eudyptula minor, using nonradioactive polymerase chain reaction‐based techniques to screen GA and GAAA repeats from enriched genomic DNA libraries. All eight loci were polymorphic and seven were variable in our main study population (mean H_E = 0.613, mean N_A = 7.14). Cross‐amplification using a microsatellite primer developed in Spheniscus demersus (African penguin) yielded one additional polymorphic locus. This locus combined with six of the little penguin loci is suitable for paternity assignment in little penguins (exclusion probability for seven unlinked loci = 0.993).     

Ten polymorphic microsatellite DNA loci for paternity and population genetics analysis in the fen raft spider (Dolomedes plantarius)

Ten polymorphic di‐ and trinucleotide microsatellite loci were developed in the fen raft spider Dolomedes plantarius from a partial phagemid genomic library enriched for microsatellite inserts. The expected heterozygosity at these loci ranges from 0.62 to 0.9, with the observed allele numbers varying from four to 15 in the 22 individuals tested. Average paternity exclusion probabilities ranged between 0.290 and 0.686. In combination, the 10 polymorphic loci elicit an exclusion probability of 0.999. The high level of polymorphism of these microsatellite loci makes them ideal genetic markers for paternity and population genetics analysis in this endangered species.     

Complete exclusion of nonsires in an analysis of paternity in a natural plant population using amplified fragment length polymorphism (AFLP)

The utility of the new polymerase chain reaction (PCR)-based multilocus DNA fingerprinting technique amplified fragment length polymorphism (AFLP) for paternity analysis in natural plant populations was assessed. In a natural population of 25 plants of Persoonia mollis (Proteaceae), three AFLP primer pairs generated 147 dominant loci. Of these, 125 (85%) were polymorphic, with a mean recessive allele frequency of 0.735. The theoretical expected percentage of offspring for which all males except the true father can be excluded ( P _ET) was 99.9% for this population. The estimates of P _ET drop marginally to 99.6% and 97.6% for larger populations of 100 and 1000 individuals, respectively. A preliminary investigation confirmed the power of AFLP for paternity analysis by assigning paternity, or excluding all known potential sires, for 242 of 252 (96.0%) naturally pollinated seeds. Ambiguous paternity for the remaining 10 seeds was quickly resolved by utilizing two further AFLP primer pairs, ultimately generating over 200 polymorphic loci and resulting in the exclusion of all nonsires for all 252 (100%) seeds. This study highlights the utility of AFLP for paternity analysis because: (i) it generates sufficiently large numbers of highly reproducible polymorphic loci, that are (ii) quickly and accurately scored using an automated DNA sequencer and dedicated software, and (iii) unlike microsatellites, requires no sequence knowledge so it is more easily applied to new study species.     

Does paternity or paternal investment determine the level of paternal care and does female choice explain egg stealing in the fifteen-spined stickleback?

An earlier field study on the fifteen-spined stickleback (Spinachia spinachia) showed that frequent male—male interactionsresult in high frequencies of sneaking and egg stealing. Moreover,sneaking behavior was performed not only by males adoptingalternative mating strategies, but also by males with theirown nests. The advantage of sneaking is easily understood, but it is more difficult to explain the evolutionary benefitof stealing eggs from other males. I investigated whether malessuffering from sneaking adjust their paternal effort in relationto their degree of paternity. I also examined whether femalesprefer males that have more eggs in their nests, as this couldexplain egg stealing. There was no relationship between thedegree of paternity and fanning activity, hatching success,or nest defense. However, the older the eggs become, the morethe males increase their attack rate toward potential egg predators(goldsinny wrasse and shore crabs). Thus, males adjusted theirlevel of defense to the amount of energy and time already investedin the clutch. Females did not prefer males with more eggs intheir nests. On the contrary, females preferred males withreduced clutches over males with enlarged clutches. Therefore,female choice is unlikely to be a driving force behind eggstealing in this species.     

Sperm competition mechanisms,confidence of paternity,and the evolution of paternal care in the golden egg bug (Phyllomorpha laciniata)

Theoretical models predict how paternal effort should vary depending on confidence of paternity and on the trade-offs between present and future reproduction. In this study we examine patterns of sperm precedence in Phyllomorpha laciniata and how confidence of paternity influences the willingness of males to carry eggs. Female golden egg bugs show a flexible pattern of oviposition behavior, which results in some eggs being carried by adults (mainly males) and some being laid on plants, where mortality rates are very high. Adults are more vulnerable to predators when carrying eggs; thus, it has been suggested that males should only accept eggs if there are chances that at least some of the eggs will be their true genetic offspring. We determined the confidence of paternity for naturally occurring individuals and its variation with the time. Paternity of eggs fertilized by the last males to mate with females previously mated in the field has been determined using amplified fragment length polymorphisms (AFLPs). The exclusion probability was 98%, showing that AFLP markers are suitable for paternity assignment. Sperm mixing seems the most likely mechanism of sperm competition, because the last male to copulate with field females sires an average of 43% of the eggs laid during the next five days. More importantly, the proportion of eggs sired does not change significantly during that period. We argue that intermediate levels of paternity can select for paternal care in this system because: (1) benefits of care in terms of offspring survival are very high; (2) males have nothing to gain from decreasing their parental effort in a given reproductive event because sperm mixing makes it difficult for males to reach high paternity levels and males are left with no cues to assess paternity; (3) males cannot chose to care for their offspring exclusively because they can neither discriminate their own eggs, nor can they predict when their own eggs will be produced; and (4) males suffer no loss of further matings with other females when they carry eggs. Thus, our findings do not support the traditional view that paternal investment is expected to arise only in species where confidence of paternity is high. The results suggest that females maximize the chances that several males will accept eggs at different times by promoting a mechanism of sperm mixing that ensures that all males that have copulated with a female have some chance of fathering offspring, that this probability remains constant with time, and that males have no cues as to when their own offspring will be produced.     

Identifying the minimum number of microsatellite loci needed to assess population genetic structure: A case study in fly culturing

Small, isolated populations are constantly threatened by loss of genetic diversity due to drift. Such situations are found, for instance, in laboratory culturing. In guarding against diversity loss, monitoring of potential changes in population structure is paramount; this monitoring is most often achieved using microsatellite markers, which can be costly in terms of time and money when many loci are scored in large numbers of individuals. Here, we present a case study reducing the number of microsatellites to the minimum necessary to correctly detect the population structure of two Drosophila nigrosparsa populations. The number of loci was gradually reduced from 11 to 1, using the Allelic Richness (AR) and Private Allelic Richness (PAR) as criteria for locus removal. The effect of each reduction step was evaluated by the number of genetic clusters detectable from the data and by the allocation of individuals to the clusters; in the latter, excluding ambiguous individuals was tested to reduce the rate of incorrect assignments. We demonstrate that more than 95% of the individuals can still be correctly assigned when using eight loci and that the major population structure is still visible when using two highly polymorphic loci. The differences between sorting the loci by AR and PAR were negligible. The method presented here will most efficiently reduce genotyping costs when small sets of loci (“core sets”) for long-time use in large-scale population screenings are compiled.     

Why babies look like their daddies: paternity uncertainty and the evolution of self-deception in evaluating family resemblance

It has been suggested that in a socially monogamous system where fathers invest in their mate's offspring but paternity is far from certain, it will be adaptive on the part of infants to conceal their father's identity; but the opposite claim has also been made that this is against the genetic interests of the fathers, and a high frequency of adulterine births will select instead for paternal resemblance. In this article, I present a simple theoretical model that suggests that neonatal anonymity benefits fathers, mothers, and children. Once anonymity becomes established, however, all babies start paying the cost of paternity uncertainty, that is, the reduction in paternal care due to fathers not knowing whether they have truly sired their mate's offspring. By diminishing the fitness of babies, such a cost bounces back as lowered fitness for parents as well. We should then expect the evolution of maternal strategies directed to decrease paternity uncertainty, in the form of instinctive and unsolicited comments on babies' resemblance to their putative fathers. In contradiction to the widespread belief that it would be in fathers' interest to be skeptical of these allegations, the model suggests that, under conditions of infant anonymity, fathers will actually promote their own fitness by believing their spouses. Received in revised form: 5 September 2001 Electronic Publication