Journal of Heredity 2004:95(3):209-210
© 2004 The American Genetic Association
Male-biased Mutation Rates and the Overestimation of Extrapair Paternity: Problem, Solution, and Illustration Using Thick-Billed Murres (Uria lomvia, Alcidae)
From the Department of Biology, Queen's University, Kingston, Ontario K7L 3N6, Canada (Ibarguchi, Gissing, Boag, and Friesen), and National Wildlife Research Centre, Canadian Wildlife Service, 1125 Colonel By Drive, Ottawa, Ontario K1A 0H3, Canada (Gaston).
Address correspondence to G. Ibarguchi at the address above, or e-mail: ibarguch{at}biology.queensu.ca.
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Abstract |
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The widespread utility of hypervariable loci in genetic studies derives from the high mutation rate, and thus the high polymorphism, of these loci. Recent evidence suggests that mutation rates can be extremely high and may be male biased (occurring in the male germ-line). These two factors combined may result in erroneous overestimates of extrapair paternity, since legitimate offspring with novel alleles will have more mismatches with respect to the biological father than the biological mother. As mutations are male driven, increasing the number of hypervariable loci screened may simply increase the number of mismatches between fathers and their legitimate offspring. Here we describe a simple statistic, the probability of resemblance (PR), to distinguish between mismatches due to parental misassignment versus mutation in either sex or null alleles. We apply this method to parentage data on thick-billed murres (Uria lomvia), and demonstrate that, without considering either mutations or male-biased mutation rates, cases of extrapair paternity (7% in this study) would be grossly overestimated (14.5%–22%). The probability of resemblance can be utilized in parentage studies of any sexually reproducing species when allele or haplotype frequency data are available for putative parents and offspring. We suggest calculating this probability to correctly categorize legitimate offspring when mutations and null alleles may cause mismatches.
The versatility and high resolution of hypervariable molecular markers for investigations of parentage, kinship, and population affinities (e.g. Lifjeld et al. 1993; MacDougall-Shackleton and MacDougall-Shackleton 2001; Möller et al. 2001; Primmer et al. 1995) arise principally from the high mutation rate and resulting polymorphism of these loci. Despite their widespread use, the mutational properties of these markers are still not fully understood (Di Renzo et al. 1994). Recent evidence suggests that mutation rates can be extremely high [e.g., 4.5 x 10–2 to 5.1 x 10–6 per locus for microsatellites (Udupa and Baum 2001; Vázquez et al. 2000); 1.1 x 10–2 to 6 x 10–3 per fragment for minisatellites (Lubjuhn et al. 1999; Westneat 1990)]. Moreover, new evidence suggests that mutation rates in many regions throughout the genome may be male biased (arising in the male germ-line; Table 1). This bias in mutation rate arises primarily from the high number of germ-cell divisions involved in sperm versus egg production (e.g., Miyata et al. 1987; Roosen-Runge 1977), and, to a lesser extent, from the presence of more methylated sites (where mutations may occur often) in male germ-lines (Huttley et al. 2000). The combined effect of high rates of mutation and male-driven mutations has potentially serious implications in parentage studies since genetic mismatches between fathers and offspring are usually attributed to extrapair paternity (EPP). Offspring with novel alleles (mutations) will have more mismatches with respect to the biological father than to the biological mother, even when legitimate. Here we consider the effects of high rates of mutation at hypervariable loci and the male bias in mutation rates, and we show a simple method to distinguish between mismatches due to parental misassignment versus mutation in either sex or null alleles. To illustrate this method, we apply it to paternity data from thick-billed murres (Uria lomvia).
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Parental exclusion is unambiguous when multiple loci contain mismatches between putative parents and offspring (Lifjeld et al. 1993). However, ambiguities arise when one or a few loci contain mismatches, but the presence of shared rare alleles or behavioral data suggest true parentage. A threshold (e.g., less than 30% of the mismatched loci or fragments) is often chosen, sometimes arbitrarily, above which the offspring are presumed to be extrapair (Jones and Ardren 2003; Lifjeld et al. 1993; Lubjuhn et al. 1999; Primmer et al. 1995). Mutations or null alleles [nonamplifying alleles due to mutations at polymerase chain reaction (PCR) priming sites] are sometimes invoked to explain mismatches, but the true frequencies of mutations and null alleles are generally unknown for the loci being employed, as their direct quantification is best accomplished by conducting controlled pedigree studies. In field studies, however, these frequencies are sometimes determined from the same data that are being used in the parentage analysis (inferring the meioses that must have occurred to result in the inheritance patterns observed in the offspring), making the analyses circular (unless parentage was unambiguous). One approach used to discriminate between cases of mutation and nonpaternity involves comparing the frequency of mismatches in offspring against a Poisson distribution of rare events (Westneat 1990). This approach has been useful in studies that utilize minisatellites, particularly when there are clear nonoverlapping distributions of offspring with few novel bands (mutations) versus offspring with large numbers of novel bands (nonlegitimate). However, with the increasing popularity of hypervariable loci, ambiguities occur due to increasing overlap between the distributions of offspring with "few" (presumed mutations) and "many" mismatches (presumed nonpaternity). This overlap occurs due to the overall faster rate of evolution of these markers, and to the general scoring of fewer loci compared with minisatellites.
To circumvent this problem, we developed a simple statistical method to determine the probability that parentage was correctly assigned but that mismatches are due to some other factor, such as mutations or null alleles, when the genotypes of both the parent and offspring are known. This method has the additional advantage that information contained in the allele frequencies from codominant markers can be used. We define the probability of resemblance (PR) as the probability that two specific individuals (e.g., from the same nest or breeding site) share at least one allele at a given locus by chance, so that they misleadingly appear to be related. The probability of sharing alleles is dependent on the frequency of those alleles in the population; thus the probability of resemblance is high when sharing common alleles. The probability that a diploid individual has at least one copy of a specific allele a is Pa1 + Pa2 – Pa(1 and 2), the general addition rule for the union of two events, where Pa1 and Pa2 are the probabilities of sampling allele a at the first and second allelic positions of a locus, respectively, and Pa(1 and 2) is the probability of sampling a at both positions simultaneously. For a given allele frequency pa in the population, we simplify the above as 2pa – 
. This equation is analogous to the probability of "false inclusion," the probability that an individual carries the same band (e.g., minisatellite) as an unrelated offspring (Jeffreys et al. 1992). However, when allele frequencies can be calculated directly from the data (e.g., when codominant markers are used), and when comparing two specific individuals (e.g., a social parent and its offspring), use of the probability of resemblance (PRa, below) improves resolution power. If one just wishes to calculate the probability of finding all the individuals in a population that may carry alleles so that they may be considered in the pool of putative parents, one can use the probability of false inclusion. Thus for the specific case, the probability that two particular diploid individuals share at least one specific allele a at a locus by chance (PRa) is
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For the general case, using the same rule for the union of two or more events (as above), the probability that two individuals share at least one allele (any allele) at a locus by chance (PR) is simply the probability of resemblance for the locus:
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In the case of haploid individuals or haploid loci (such as mitochondrial DNA), the above equations can be simplified. The probability that two particular individuals share a specific haplotype a is related to its frequency in the population:
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We wish to emphasize that, to apply the probability of resemblance, an association between an offspring and a putative parent needs to exist (e.g., observed behavioral interactions between them or presence at the same nest or breeding site); we are testing the probability that the offspring has certain specific alleles (event 1) that match those of the putative parent (event 2) and that these events occur simultaneously [in space and/or time (event 3), hence the squared Equation 1). This critical distinction from the probability of false inclusion (above) enables one to apply the greater discriminatory power of the probability of resemblance for the identification of mutations or null alleles.
In this article we used computer randomizations and data from a wild population of thick-billed murres to test the utility of these equations for discriminating between mutations, null alleles, and parental misassignments. Thick-billed murres are arctic seabirds that breed at high densities on cliff ledges, where they lay a single egg without constructing a nest. They exhibit natal philopatry and social monogamy, and individuals often retain their mates for many years. However, extrapair copulations have been observed in murres, and recent genetic studies have estimated EPP in common murres (Uria aalge) to be approximately 7–7.8% (Birkhead et al. 2001; Walsh C, Memorial University of Newfoundland, unpublished); however, no genetic paternity data exist for thick-billed murres. In addition, egg stealing (Gaston et al. 1993) and alloparenting behavior (feeding, brooding, or adoption of chicks) have been documented in murres (Birkhead and Nettleship 1984; Gaston et al. 1995), possibly increasing the proportion of extrapair offspring in this species. Variation in five microsatellite loci and the mitochondrial cytochrome b gene were analyzed to identify EPP and illegitimate offspring in thick-billed murres.
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Methods |
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TopAbstractMethodsResults and DiscussionReferences |
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Randomizations
To test the general equation for the probability of resemblance (Equation 2), genotypes of 1000 hypothetical birds were constructed by randomly assigning alleles to individuals for one locus, increasing the number of alleles from 1 to 10 in successive runs. For each randomization, pairs of birds were sampled with subsequent replacement, and the alleles they shared were determined (using a simple Visual Basic script; Ibarguchi G and Gissing GJ, unpublished). To simulate more complex datasets, genotypes for three loci were generated for 1000 hypothetical birds. In the first of three sets, all three loci had five equally frequent alleles; in the second, loci had fewer alleles with equal frequencies (two, three, and four alleles); in the third set, loci had more alleles (five, six, and seven, respectively). For randomizations based on real data and on loci with alleles of unequal frequencies, 318 adult murres were randomly sampled 1000 times to determine how many alleles two individuals shared at each of three microsatellite loci (ulo12a12, ulo14b29, and uaa1-23; see below). (Ten runs, each consisting of 100 randomizations, were conducted and an average was obtained from these 10 runs.) All results from randomizations were compared to PR values obtained from Equation 2. Allele frequencies and PR values were calculated using spreadsheets.
Sampling
DNA was obtained from blood and feathers collected from chicks and one or both behavioral parents (n = 27 families, 70 birds) during the 1996 and 1997 breeding seasons at a colony on Coats Island (Nunavut, Canada). The west subcolony, consisting of approximately 15,000 breeding pairs (Gaston et al. 1994), was sampled. All sampled individuals were banded and their breeding sites were mapped. Chicks that were too small to band were identified by unique toenail clipping. Behavioral observations were only possible for 13 of the families from which DNA was obtained. Before these breeding ledges were disturbed, parents were observed providing care to the same chick that was later banded. In three of these cases, marked chicks were monitored from hatching. The other 10 families were part of a study of alloparenting (Ibarguchi G, unpublished) and their breeding site was separated from adjacent sites with cloth sandbags (1–3 bags, 22 cm x 38 cm). All other families were monitored at irregular intervals, without detailed observations. In two families the chicks were not marked before banding, although both sets of parents were known breeders (banded previously and maintaining their breeding site and partner during at least 2 consecutive years), and both families were monitored daily from egg laying.
Laboratory Methods
DNA was extracted from tissue samples by standard protease K digestion and phenol/chloroform protocols (Kocher et al. 1989), precipitated with 0.25 M sodium acetate and 50% cold isopropanol, and resuspended in ddH2O. Since murres are sexually monomorphic, sex was determined using PCR primers that amplify an intron within the chromo-helicase DNA-binding locus in the sex chromosomes of birds (Griffiths et al. 1998). Parentage was assessed by screening family samples for Mendelian inheritance at five unlinked microsatellite loci using primers designed for the genus Uria (Ibarguchi et al. 2000) (ulo12a12, ulo12a22, ulo14b29, uaa1-23, and uaa5-8; Table 2). A 306 bp segment of the mitochondrial cytochrome b gene that exhibits high levels of variation in murres [gene diversity (Nei 1987) h = 0.6198] was also screened using primers L14841 and H15149 (Kocher et al. 1989) with analyses of single-strand conformational polymorphisms and direct sequencing of haplotypes (Friesen et al. 1996b). Although this maternally inherited marker provided only limited information on parentage, some rare haplotypes helped support or reject possible relationships among chicks and their mothers. Genetic data were available for cytochrome b and for microsatellites ulo12a12, ulo14b29, and uaa1-23 (but not for uaa1-23 or uaa5-8) for an additional 258 murres (as part of a separate population study; Ibarguchi G, unpublished); these data were included to provide more accurate estimates of population allele frequencies. As only three loci were available for all 354 birds, randomizations were based on these three loci for this larger sample.
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Several preliminary observations suggested that mutations (five in total) had occurred at one or more microsatellite loci: (1) the most variable loci also exhibited the most mismatches between parents and offspring (Table 2); (2) mismatches often involved small changes (e.g., changes of one repeat unit in three cases, of one base pair in one case, and of two to five repeats in two cases); and (3) some changes were from a rare allele in the parent to a unique allele in the chick (two cases). Allele frequencies were used to calculate cumulative probabilities of resemblance for specific parent-offspring cases where ambiguous mismatches occurred, based on microsatellite loci (excluding the mismatched locus or loci), and including cytochrome b where possible.
To illustrate how the probability of resemblance was applied, an example is given. The chick at a site FGT4 had genotype 108/104, 156/130, 180/166, 147/143, 110/108 at five microsatellite loci, respectively; its father had genotype 114/104, 136/130, 178/164, 151/143, 110/108 (where the underlined alleles are those that are shared). Since the chick matched its mother, the genotype that would be expected through Mendelian inheritance was "subtracted" from the chick and compared to that of the father (for the fifth locus, both parents were heterozygotes for the same alleles and so either parent could have contributed either allele to the chick). All alleles matched except at locus three, where the father had allele 178 and the chick had allele 180. To determine whether this was a misassignment or a possible mutation at this locus, we excluded the locus in question (locus 3) and obtained population allele frequencies: locus 1 (allele 104), locus 2 (allele 130), locus 4 (allele 143), and locus 5 (first allele 110, then 108). We calculated PRa (Equation 1) for each of these alleles using their frequencies, then multiplied them (PRaCum; Equation 3) to obtain 9.0 x 10–5 (when allele 110 was used for locus 5) and 2.16 x 10–5 (when allele 108 was used). The probability of randomly sampling from the same breeding site a chick and a male that appear by chance to be related was calculated as 1 in 216,000 or less.
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Results and Discussion |
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TopAbstractMethodsResults and DiscussionReferences |
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Randomizations
A smaller PR translates into more power to detect true relationships in tests of parentage. Results from Equation 2 for PR versus 100,000 randomizations closely overlap, as expected, and indicate that the probability of sharing alleles by chance decreases with an increase in the number of alleles at the locus. Results from more realistic sets of randomizations, each with three loci (with varying allele frequencies; see Methods), consistently agreed with predicted values for PR. Equation 2 and averages from 10,000 randomizations differed by 0.004 or less (0.206 versus 0.202 ± 0.012 (SD); 0.457 versus 0.457 ± 0.008; and 0.137 versus 0.138 ± 0.01, respectively). Finally, estimates of PR agreed with estimates based on real genotypic data from 318 thick-billed murres and three microsatellite loci with unequal allele frequencies (0.047 from Equation 2 versus 0.040 ± 0.007 from 1000 randomizations). When two more microsatellite loci were included (ulo12a22 and uaa5-8, based on a smaller sample of birds; Table 2), PR decreased from 0.047 to 0.021, illustrating that discrimination power improves when more loci are used. However, this effect will largely depend on the variability of the loci selected (see below).
Thick-Billed Murres
Two-thirds (18) of all 27 murre families had legitimate chicks (Table 3). Among the nine remaining families, two had a misassigned father. (Family 1: the "father" was actually another female, alloparenting; the social father was not trapped and the possible true father was located breeding less than 1 m away on the same ledge, a possible EPP case. Family 2: another possible case of EPP, as the social father shared only one of five alleles with the chick. Both breeding partners occupied this same site the previous year.) Two families had both parents misassigned (Table 3; possible misidentification or adoption). (Family 3: the female shared no alleles and had a different cytochrome b haplotype than the chick, and the male shared two of five alleles; this case was conservatively classified as "misassigned," as this family was not monitored regularly, and was not considered in EPP/mutation estimates. Family 4: the female shared two of five alleles but had a different cytochrome b haplotype than the chick, and the male shared one of five alleles.) The remaining five of nine families involved ambiguous cases in which mutation, null alleles, or misassignment could explain the observed differences between parents and chicks. Two chicks had differences with respect to both parents, with a total of five ambiguities for these two cases (Table 3; Case 1—two differences with respect to the mother, one with respect to the father. Case 2—one difference with respect to the mother and one with respect to the father). An additional three cases of single mismatches (Table 3) resulted in a total of eight ambiguities in this study. Cumulative probabilities of resemblance were calculated for these eight cases, excluding loci with the mismatched alleles. In seven of the eight cases, probabilities of sharing alleles by chance were so low (7.7 x 10–4 to 3.26 x 10–9) that mutations or null alleles were more probable reasons for the mismatches. In one of these cases, using four microsatellite loci alone gave a probability of 0.0036; however, the mother and the chick shared a rare cytochrome b haplotype (case 2, Table 3), and combining this information with the nuclear data gave a much lower probability (2.31 x 10–5), suggesting this also was a case of mutation. In the last case, the probability of sharing alleles was higher (0.0012) due to the male and the chick sharing common alleles.
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Due to the presence of kin groups on breeding ledges in murres (Friesen et al. 1996a), nonrandom associations of alleles may occur (Ibarguchi G, unpublished). Note that when estimating PR, the allele frequencies which are representative of the group of individuals being analyzed should be used (Lewontin and Hartl 1991). Thus allele frequencies specific to populations on ledges also were used to recalculate PR to control for the increased local frequencies of some alleles. We chose this approach to provide a conservative criterion to discriminate between mutation and misassignment. Due to genetic similarity (kinship), and partly due to smaller sample sizes (fewer loci and alleles sampled per locus), PR's calculated using allele frequencies from individual ledges were approximately one order of magnitude higher than those based on colony-wide frequencies (data not shown). However, these estimates remained so low (probabilities ranged from 2.8 x 10–3 to 7.3 x 10–7) that mismatches were still best explained by mutations and null alleles, except the male in case 2 (Table 3), which was 1.2 x 10–2. To interpret cases of mutation in a conservative manner, case 2 was considered to remain "unresolved" using ledge-wide allele frequencies for the available loci (Table 3). As the remaining probabilities of resemblance were very low, offspring could be reassigned with confidence as legitimate (Table 3, except for case 2).
Ambiguities Due to Null Alleles
Based on PR values, two ambiguities between homozygous mothers and their homozygous offspring (Table 3) were assigned as null alleles at two different loci (ulo12a12 and ulo14b29; Tables 2 and 4). A simple method employed for the detection of null alleles is to test for population-wide deviations from Hardy-Weinberg expectations for each locus, as null alleles result in scoring an excess of "homozygotes." As other explanations exist for deviations from expectations (e.g., the presence of kin groups), this test lacks robustness, but can be used as a guide for detecting high numbers of infrequent null alleles or single null alleles at high frequencies. No significant population-wide deviations were detected for these loci, although both ulo12a12 and ulo14b29 showed slight, nonsignificant departures from expectations in 5 and 2 breeding ledges out of 10, respectively (Ibarguchi G, unpublished). Heterozygosity fell below expected values at locus ulo12a12 (but not at the other loci) in common murres (U. aalge; Ibarguchi et al. 2000), possibly due to null alleles. The frequencies of null alleles were estimated to be very low for these two loci [less than 0.02, with observed heterozygosities lower than expected from the method of Marshall et al. (1998)]. The assignment of "null alleles" to the two mismatches between mothers and offspring based on PR is compatible with the above data.
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Paternity Analyses: Implications of Mutations in Males
Extrapair paternity in thick-billed murres, after applying PR, was estimated as 7.0% (Table 4); the proportion would have been 14.5% if only two mutations had been acknowledged (those involving changes from a rare allele in the father to a unique allele in the chick) and 22% if no mismatches between chicks and fathers had been considered to be mutations. Although this is the first EPP estimate for this species, a published estimate from common murres based on minisatellites is similar (7.8%; Birkhead et al. 2001).
Out of five suspected cases of mutation, four involved fathers (and possibly a fifth, case 2; Table 3), while one involved a mother. We do not attempt to quantify mutation rates or sex-based biases formally in the present study, as our sample sizes are small; we simply wish to illustrate how mutations in males may cause overestimates of extrapair paternity when not considered. However, male-biased mutation rates have been confirmed in multiple regions in the genomes of several taxa (including microsatellites in birds; Table 1). We strongly encourage researchers to consider this mutation bias in studies of paternity and to apply the probability of resemblance when ambiguous mismatches arise, especially when hypervariable markers are employed. Aside from vertebrates, male-driven mutation has been uncovered in some gymnosperms (Whittle and Johnston 2002) and in mussels (Liu et al. 1996); the generality of this bias remains unexplored in other taxa. A further consideration in paternity studies is that germ-line mutations may accumulate or increase with age, so that older males may appear to have more illegitimate offspring (due to more mismatches) than younger males; this age effect is currently under investigation (e.g., Ellegren 2000b; Hansen and Price 1999, Walter et al. 1998).
Inclusion of additional loci may assist in clarifying some ambiguous cases in family studies, especially if the loci are moderately variable (e.g., this study: ulo12a22 and uaa5-8; Table 1). However, the addition of new, highly variable loci (with high mutation rates) will likely introduce additional mismatches. Conversely the incorporation of new, less variable loci (with lower mutation rates) may help, but only when numerous additional loci are included. Thus the probability of resemblance can be a useful tool, and may be utilized whenever codominant markers enable direct estimation of allele frequencies (e.g., microsatellites, sequence data from coding genes or introns) or when haplotype frequencies can be estimated directly from screening haploid genomes. When minisatellites are utilized, the method by Westneat (1990) or the probability of false inclusion (Jeffreys et al. 1992) can be used to evaluate possible mutations (but not with the same power as PR due to the lack of known alleles and their frequencies). Male-driven mutations should also be considered when using these markers.
Available Tools in Parentage Testing
Tools currently exist to find candidate parents in a sampled population or to determine the most likely parent from a subset [reviewed in Jones and Ardren (2003)]. Caution should be exercised because such candidate parents are expected to match offspring. However, mutations observed in offspring may lead to the erroneous exclusion of the legitimate parent from this candidate pool. One useful tool in parentage analysis is the Cervus package (Marshall et al. 1998), which enables the selection of the most likely candidate parent based on likelihood probabilities from a pool of candidates. A beneficial feature of this program is that a conservative error rate (typing errors, mutations, and null alleles) can be incorporated to enable consideration of putative parents with mismatches in the pool of candidates. It also assigns statistical confidence to particular parent-offspring pairs using a simulation approach. However, it assumes a single, experiment-wide mutation rate. When large numbers of offspring genotypes are available, but the parent genotypes are lacking, or when a pool of candidates is absent, the Gerud program (Jones 2001) can be used to reconstruct the genotype of parents that were not sampled. Kinship (Goodnight and Queller 1999) enables testing specific hypothesized levels of relationship between pairs of individuals based on likelihood probabilities, but does not allow for mutations.
These packages can complement each other with respect to the focus of the study. For example, in the absence of behavioral data, or when genetic data for one or both parents are lacking, finding the most likely parents from a pool may be desirable. This is particularly useful for species without parental care or when care is provided by one sex only. In studies of altruistic behavior, one may wish to test genetic relatedness among helpers (including putative parents and offspring). However, use of the probability of resemblance can further complement analyses of paternity when mutations or null alleles are suspected in specific parent-offspring pairs based on additional behavioral observations or spatial information (greatly increasing discrimination power due to this additional interaction). When this additional information is lacking, a putative pool of candidates may then be searched using one of the above packages.
As the degree of genetic variation uncovered in family studies depends partly on the number and type of genetic markers utilized, some measure of the resolution of the markers is desirable. Equations 2 and 4 for PR will be useful in determining the discrimination power that the screened loci will have in detecting true parentage, similar to the use of the probability of exclusion, PE (Jamieson 1994, Jamieson and Taylor 1997), and the probability of identity, PId (Bruford et al. 1992; Hanotte et al. 1991; Table 2) in some studies. The probability of resemblance differs from the probability of identity in that PR considers only half of the alleles at the screened loci: those inherited from the putative parent. The probability of identity is generally much smaller, as it includes all the alleles at the screened loci (i.e., the probability of finding an identical genotype by chance). Once the level of resolution of the chosen genetic markers has been tested (Equations 2 and 4), Equations 1 and 3 for PR will be most useful in the evaluation of specific putative parent-offspring cases involving mutation and null alleles. This approach also enables the consideration of male-driven mutation rates directly, without precise empirical quantification for the loci or species under study, to obtain more accurate estimates of extrapair paternity in many taxa.
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Acknowledgments |
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We thank D. Michaud, C. Crossman, R. Lanctot, and R. Kristensen for laboratory protocols and assistance, and C. Kelly, J. Nakoolak, C. James, K. Woo, and D. Martin for field assistance. C. Walsh and K. Warheit provided unpublished data on paternity in murres. We thank P. Taylor for comments on equations for the probability of resemblance. R. Fleischer and three anonymous referees provided insightful comments on the manuscript. Funding was provided by the Northern Studies Training Program, the Continental Shelf Project (Energy, Mines and Resources Canada), the National Wildlife Research Centre (Canadian Wildlife Service), NSERC (Operating Grant held by V.L.F. and Collaborative Projects Program Grant held by P.T.B.), and Queen's University, Canada.
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Footnotes |
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Corresponding Editor: Robert C. Fleischer
Received November 23, 2002
Accepted December 28, 2003
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References |
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