COANCESTRY: a program for simulating, estimating and analysing relatedness and inbreeding coefficients

The software package COANCESTRY implements seven relatedness estimators and three inbreeding estimators to estimate relatedness and inbreeding coefficients from multilocus genotype data. Two likelihood estimators that allow for inbred individuals and account for genotyping errors are for the first time included in this user-friendly program for PCs running Windows operating system. A simulation module is built in the program to simulate multilocus genotype data of individuals with a predefined relationship, and to compare the estimators and the simulated relatedness values to facilitate the selection of the best estimator in a particular situation. Bootstrapping and permutations are used to obtain the 95% confidence intervals of each relatedness or inbreeding estimate, and to test the difference in averages between groups.     

The use and abuse of genetic marker‐based estimates of relatedness and inbreeding

Genetic marker‐based estimators remain a popular tool for measuring relatedness (r_xy) and inbreeding (F) coefficients at both the population and individual level. The performance of these estimators fluctuates with the number and variability of markers available, and the relatedness composition and demographic history of a population. Several methods are available to evaluate the reliability of the estimates of r_xy and F, some of which are implemented in the program COANCESTRY. I used the simulation module in COANCESTRY since assess the performance of marker‐based estimators of r_xy and F in a species with very low genetic diversity, New Zealand's little spotted kiwi (Apteryx owenii). I also conducted a review of published papers that have used COANCESTRY as its release to assess whether and how the reliability of the estimates of r_xy and F produced by genetic markers are being measured and reported in published studies. My simulation results show that even when the correlation between true (simulated) and estimated r_xy or F is relatively high (Pearson's r = 0.66–0.72 and 0.81–0.85, respectively) the imprecision of the estimates renders them highly unreliable on an individual basis. The literature review demonstrates that the majority of studies do not report the reliability of marker‐based estimates of r_xy and F. There is currently no standard practice for selecting the best estimator for a given data set or reporting an estimator's performance. This could lead to experimental results being interpreted out of context and render the robustness of conclusions based on measures of r_xy and F debatable.     

Distribution of individual inbreeding coefficients, relatedness and influence of stocking on native anadromous brown trout (Salmo trutta) population structure

We examined polymorphism at seven microsatellite loci in 4023 brown trout (Salmo trutta) collected from 32 tributaries to the Limfjord, Denmark (approximately 200 km) and from two hatcheries used for stocking. Populations differ in their estimated sizes and stocking histories. Mean individual inbreeding coefficients do not differ among locations within rivers. Relatedness varies between sites within rivers indicating varied local dynamics at a very small geographical scale. Relatedness is sometimes lower than expected among an equal number of simulated individuals with randomized genotypes, suggesting structure within locations. Five per cent of the genetic variance is distributed among rivers (F(ST) = 0.049), but in the western, less heavily stocked, area of the Limfjord a higher proportion of the genetic variance is distributed among rivers than among locations within rivers. The reverse is true of the eastern, more heavily stocked, area of the Limfjord. Here, a higher proportion of the genetic variance is distributed among locations within rivers than among rivers. Assignment tests reveal that the majority of trout (mean 77% of all fish) are more probably of local origin than hatchery origin but this proportion varies regionally, with rivers in the western area of the Limfjord showing a relatively high (mean 88%) and those in the eastern area showing a relatively low (mean 72%) proportion of locally assigned trout. These results can be interpreted as reflecting stocking impact. Also, the proportion of locally assigned trout correlates with the populations' stocking histories, with rivers presently subjected to stocking (hatchery trout) showing low (mean approximately 0.73), and rivers where stocking was discontinued showing high (mean approximately 0.84) proportions of local fish, probably reflecting lower survival of hatchery than of wild trout. There is evidence for isolation by distance at a large geographical scale when individual river populations are pooled into nine geographical regions but not at a small geographical scale when populations are considered individually. We reject the null hypothesis that stocking has had no impact on population structure but the relatively high proportion of locally assigned trout in populations where stocking with domestic fish no longer takes place suggests limited long-term success of stocking.     

Estimates of relatedness and inbreeding in goose strains from DNA fingerprints

The purpose of this study was to determine if DNA fingerprints (DFPs) could be used to estimate relatedness and inbreeding of strains of geese and to compare three methods of calculating relatedness indices. Strains included a control and selected strain from each of the Chinese and Synthetic (Chinese, Hungarian and Pilgrim) breeds. DFP patterns for each strain were based on individual DNA samples from six females, or on pooled DNA from 15 females different from those used for individual samples. Three relatedness indices were used, namely, genetic distance, modified Rogers distance and band sharing. All relatedness indices showed a closer relationship of strains within than between breeds. Correlation coefficients among relatedness indices were higher based on pooled DNA (r ≥|0·97|) than those based on individual DNA (r ≥|0·741). Inbreeding estimates were higher for selected compared with control strains. It appears that the use of DFPs to estimate relatedness, regardless of index used, and inbreeding can be valuable for studying geese where there is a limited breeding history.     

A model‐based approach to characterize individual inbreeding at both global and local genomic scales

Inbreeding results from the mating of related individuals and may be associated with reduced fitness because it brings together deleterious variants in one individual. In general, inbreeding is estimated with respect to an arbitrary base population consisting of ancestors that are assumed unrelated. We herein propose a model‐based approach to estimate and characterize individual inbreeding at both global and local genomic scales by assuming the individual genome is a mosaic of homozygous‐by‐descent (HBD) and non‐HBD segments. The HBD segments may originate from ancestors tracing back to different periods in the past defining distinct age‐related classes. The lengths of the HBD segments are exponentially distributed with class‐specific parameters reflecting that inbreeding of older origin generates on average shorter stretches of observed homozygous markers. The model is implemented in a hidden Markov model framework that uses marker allele frequencies, genetic distances, genotyping error rates and the sequences of observed genotypes. Note that genotyping errors, low‐fold sequencing or genotype‐by‐sequencing data are easily accommodated under this framework. Based on simulations under the inference model, we show that the genomewide inbreeding coefficients and the parameters of the model are accurately estimated. In addition, when several inbreeding classes are simulated, the model captures them if their ages are sufficiently different. Complementary analyses, either on data sets simulated under more realistic models or on human, dog and sheep real data, illustrate the range of applications of the approach and how it can reveal recent demographic histories among populations (e.g., very recent bottlenecks or founder effects). The method also allows to clearly identify individuals resulting from extreme consanguineous matings.     

Estimating relatedness and inbreeding using molecular markers and pedigrees: the effect of demographic history

Estimates of inbreeding and relatedness are commonly calculated using molecular markers, although the accuracy of such estimates has been questioned. As a further complication, in many situations, such estimates are required in populations with reduced genetic diversity, which is likely to affect their accuracy. We investigated the correlation between microsatellite‐ and pedigree‐based coefficients of inbreeding and relatedness in laboratory populations of Drosophila melanogaster that had passed through bottlenecks to manipulate their genetic diversity. We also used simulations to predict expected correlations between marker‐ and pedigree‐based estimates and to investigate the influence of linkage between loci and null alleles. Our empirical data showed lower correlations between marker‐ and pedigree‐based estimates in our control (nonbottleneck) population than were predicted by our simulations or those found in similar studies. Correlations were weaker in bottleneck populations, confirming that extreme reductions in diversity can compromise the ability of molecular estimates to detect recent inbreeding events. However, this result was highly dependent on the strength of the bottleneck and we did not observe or predict any reduction in correlations in our population that went through a relatively severe bottleneck of N = 10 for one generation. Our results are therefore encouraging, as molecular estimates appeared robust to quite severe reductions in genetic diversity. It should also be remembered that pedigree‐based estimates may not capture realized identity‐by‐decent and that marker‐based estimates may actually be more useful in certain situations.     

Evolution of precopulatory and post‐copulatory strategies of inbreeding avoidance and associated polyandry

Inbreeding depression is widely hypothesized to drive adaptive evolution of precopulatory and post‐copulatory mechanisms of inbreeding avoidance, which in turn are hypothesized to affect evolution of polyandry (i.e. female multiple mating). However, surprisingly little theory or modelling critically examines selection for precopulatory or post‐copulatory inbreeding avoidance, or both strategies, given evolutionary constraints and direct costs, or examines how evolution of inbreeding avoidance strategies might feed back to affect evolution of polyandry. Selection for post‐copulatory inbreeding avoidance, but not for precopulatory inbreeding avoidance, requires polyandry, whereas interactions between precopulatory and post‐copulatory inbreeding avoidance might cause functional redundancy (i.e. ‘degeneracy’) potentially generating complex evolutionary dynamics among inbreeding strategies and polyandry. We used individual‐based modelling to quantify evolution of interacting precopulatory and post‐copulatory inbreeding avoidance and associated polyandry given strong inbreeding depression and different evolutionary constraints and direct costs. We found that evolution of post‐copulatory inbreeding avoidance increased selection for initially rare polyandry and that evolution of a costly inbreeding avoidance strategy became negligible over time given a lower‐cost alternative strategy. Further, fixed precopulatory inbreeding avoidance often completely precluded evolution of polyandry and hence post‐copulatory inbreeding avoidance, but fixed post‐copulatory inbreeding avoidance did not preclude evolution of precopulatory inbreeding avoidance. Evolution of inbreeding avoidance phenotypes and associated polyandry is therefore affected by evolutionary feedbacks and degeneracy. All else being equal, evolution of precopulatory inbreeding avoidance and resulting low polyandry is more likely when post‐copulatory inbreeding avoidance is precluded or costly, and evolution of post‐copulatory inbreeding avoidance greatly facilitates evolution of costly polyandry.     

Estimating the inbreeding level and genetic relatedness in an isolated population of critically endangered Sichuan taimen (Hucho Bleekeri) using genome‐wide SNP markers

Sichuan taimen (Hucho bleekeri) is critically endangered fish listed in The Red List of Threatened Species compiled by the International Union for Conservation of Nature (IUCN). Specific locus amplified fragment sequencing (SLAF‐seq)‐based genotyping was performed for Sichuan taimen with 43 yearling individuals from three locations in Taibai River (a tributary of Yangtze River) that has been sequestered from its access to the ocean for more than 30 years since late 1980s. Applying the inbreeding level and genetic relatedness estimation using 15,396 genome‐wide SNP markers, we found that the inbreeding level of this whole isolated population was at a low level (2.6 × 10^?3 ± 0.079), and the means of coancestry coefficients within and between the three sampling locations were all very low (close to 0), too. Genomic differentiation was negatively correlated with the geographical distances between the sampling locations (p < .001), and the 43 individuals could be considered as genetically independent two groups. The low levels of genomic inbreeding and relatedness indicated a relatively large number of sexually mature individuals were involved in reproduction in Taibai River. This study suggested a genomic‐relatedness‐guided breeding and conservation strategy for wild fish species without pedigree information records.     

Heterozygosity-fitness correlations in zebra finches: microsatellite markers can be better than their reputation

Numerous studies have reported associations between heterozygosity in microsatellite markers and fitness-related traits (heterozygosity-fitness correlations, HFCs). However, it has often been questioned whether HFCs reflect general inbreeding depression, because a small panel of microsatellite markers does not reflect very well an individual's inbreeding coefficient (F) as calculated from a pedigree. Here, we challenge this prevailing view. Because of chance events during Mendelian segregation, an individual's realized proportion of the genome that is identical by descent (IBD) may substantially deviate from the pedigree-based expectation (i.e. F). This Mendelian noise may result in a weak correlation between F and multi-locus heterozygosity, but this does not imply that multi-locus heterozygosity is a bad estimator of realized IBD. We examined correlations between 11 fitness-related traits measured in up to 1192 captive zebra finches and three measures of inbreeding: (i) heterozygosity across 11 microsatellite markers, (ii) heterozygosity across 1359 single-nucleotide polymorphism (SNP) markers and (iii) F, based on a 5th-generation pedigree. All 11 phenotypic traits showed positive relationships with measures of heterozygosity, especially traits that are most closely related to fitness. Remarkably, the small panel of microsatellite markers produced equally strong HFCs as the large panel of SNP markers. Both marker-based approaches produced stronger correlations with phenotypes than the pedigree-based F, and this did not seem to result from the shortness of our pedigree. We argue that a small panel of microsatellites with high allelic richness may better reflect an individual's realized IBD than previously appreciated, especially in species like the zebra finch, where much of the genome is inherited in large blocks that rarely experience cross-over during meiosis.     

Molecular and pedigree measures of relatedness provide similar estimates of inbreeding depression in a bottlenecked population

Individual‐based estimates of the degree of inbreeding or parental relatedness from pedigrees provide a critical starting point for studies of inbreeding depression, but in practice wild pedigrees are difficult to obtain. Because inbreeding increases the proportion of genomewide loci that are identical by descent, inbreeding variation within populations has the potential to generate observable correlations between heterozygosity measured using molecular markers and a variety of fitness related traits. Termed heterozygosity‐fitness correlations (HFCs), these correlations have been observed in a wide variety of taxa. The difficulty of obtaining wild pedigree data, however, means that empirical investigations of how pedigree inbreeding influences HFCs are rare. Here, we assess evidence for inbreeding depression in three life‐history traits (hatching and fledging success and juvenile survival) in an isolated population of Stewart Island robins using both pedigree‐ and molecular‐derived measures of relatedness. We found results from the two measures were highly correlated and supported evidence for significant but weak inbreeding depression. However, standardized effect sizes for inbreeding depression based on the pedigree‐based kin coefficients (k) were greater and had smaller standard errors than those based on molecular genetic measures of relatedness (RI), particularly for hatching and fledging success. Nevertheless, the results presented here support the use of molecular‐based measures of relatedness in bottlenecked populations when information regarding inbreeding depression is desired but pedigree data on relatedness are unavailable.     

Phenotype‐associated inbreeding biases estimates of inbreeding depression in a wild bird population

Inbreeding depression is usually quantified by regressing individual phenotypic values on inbreeding coefficients, implicitly assuming there is no correlation between an individual's phenotype and the kinship coefficient to its mate. If such an association between parental phenotype and parental kinship exists, and if the trait of interest is heritable, estimates of inbreeding depression can be biased. Here we first derive the expected bias as a function of the covariance between mean parental breeding value and parental kinship. Subsequently, we use simulated data to confirm the existence of this bias, and show that it can be accounted for in a quantitative genetic animal model. Finally, we use long‐term individual‐based data for white‐throated dippers (Cinclus cinclus), a bird species in which inbreeding is relatively common, to obtain an empirical estimate of this bias. We show that during part of the study period, parents of inbred birds had shorter wings than those of outbred birds, and as wing length is heritable, inbred individuals were smaller, independent of any inbreeding effects. This resulted in the overestimation of inbreeding effects. Similarly, during a period when parents of inbred birds had longer wings, we found that inbreeding effects were underestimated. We discuss how such associations may have arisen in this system, and why they are likely to occur in others, too. Overall, we demonstrate how less biased estimates of inbreeding depression can be obtained within a quantitative genetic framework, and suggest that inbreeding and additive genetic effects should be accounted for simultaneously whenever possible.     

利用高密度SNP标记分析中国荷斯坦牛基因组近交

畜禽育种中传统上利用系谱信息评估群体近交程度?近年来随着高通量单核苷酸多态(single nucleotide polymorphism, SNP)检测成本降低,使利用基因组信息分析真实的基因组近交程度成为可能?本研究利用牛54 K SNP 芯片数据统计了北京地区2107头荷斯坦牛基因组上的长纯合片段(runs of homozygosity, ROH)的频率和分布,计算了2种基因组近交系数,即染色体上ROH的长度占基因组总长度的比例(Froh)及个体所有标记基因型中纯合子所占比例,即基因组纯合度(Fhom),进而分析了两种基因组近交系数之间的相关性以及基因组近交与系谱近交系数之间的相关性?结果表明,共检测到44 676个ROH片段,其长度主要分布在1~10 Mb之间?不同长度的ROH散布于个体基因组内,短ROH较长ROH更为常见?ROH在染色体上并非均匀分布,ROH频率最高的区域为10号染色体中部?两种基因组近交系数之间相关性很高(91%以上),但基因组近交与系谱近交之间的相关性较低(低于50%)?系谱完整性是影响基因组近交与系谱近交结果一致的重要因素,基因组近交系数能够反映个体真实的近交,本研究为评估群体近交水平提供了有力工具?     

Gene flow and inbreeding depression inferred from fine-scale genetic structure in an endangered heterostylous perennial, Primula sieboldii

We estimated the gene dispersal distance and the magnitude of inbreeding depression from the fine-scale genetic structure in the endangered heterostylous perennial Primula sieboldii. We indirectly estimated the neighbourhood size (Nb) and the standard deviation of gene dispersal distance (sigma(g)) from the detected genetic structure by using 10 microsatellite markers. We also estimated the fitness reduction in mating among neighbouring individuals caused by biparental inbreeding according to the genetic structure. We found clear fine-scale genetic structure (a significantly positive kinship coefficient within 42.3 m), and the indirect estimates of sigma(g) and Nb were 15.7 m and 50.9, respectively. These indirect estimates were similar to the direct estimates (18.4 m and 44.0). The slightly larger indirect estimate of Nb may reflect that inbreeding depression and genetic structure or rare long-distance dispersal that were overlooked in the direct estimate have elongated the long-term average of gene dispersal distance. P. sieboldii is also likely to suffer about 19% fitness reduction in progenies from mating among individuals 5 m apart. Our results suggest that biparental inbreeding and genetic structure can affect the range of gene dispersal and seed reproductive success in P. sieboldii.     

Re‐mating across years and intralineage polygyny are associated with greater than expected levels of inbreeding in wild red deer

The interaction between philopatry and nonrandom mating has important consequences for the genetic structure of populations, influencing co‐ancestry within social groups but also inbreeding. Here, using genetic paternity data, we describe mating patterns in a wild population of red deer (Cervus elaphus) which are associated with marked consequences for co‐ancestry and inbreeding in the population. Around a fifth of females mate with a male with whom they have mated previously, and further, females frequently mate with a male with whom a female relative has also mated (intralineage polygyny). Both of these phenomena occur more than expected under random mating. Using simulations, we demonstrate that temporal and spatial factors, as well as skew in male breeding success, are important in promoting both re‐mating behaviours and intralineage polygyny. However, the information modelled was not sufficient to explain the extent to which these behaviours occurred. We show that re‐mating and intralineage polygyny are associated with increased pairwise relatedness in the population and a rise in average inbreeding coefficients. In particular, the latter resulted from a correlation between male relatedness and rutting location, with related males being more likely to rut in proximity to one another. These patterns, alongside their consequences for the genetic structure of the population, have rarely been documented in wild polygynous mammals, yet they have important implications for our understanding of genetic structure, inbreeding avoidance and dispersal in such systems.     

Female‐biased dispersal alone can reduce the occurrence of inbreeding in black grouse (Tetrao tetrix)

Although inbreeding depression and mechanisms for kin recognition have been described in natural bird populations, inbreeding avoidance through mate choice has rarely been reported suggesting that sex‐biased dispersal is the main mechanism reducing the risks of inbreeding. However, a full understanding of the effect of dispersal on the occurrence of inbred matings requires estimating the inbreeding risks prior to dispersal. Combining pairwise relatedness measures and kinship assignments, we investigated in black grouse whether the observed occurrence of inbred matings was explained by active kin discrimination or by female‐biased dispersal. In this large continuous population, copulations between close relatives were rare. As female mate choice was random for relatedness, females with more relatives in the local flock tended to mate with genetically more similar males. To quantify the initial risks of inbreeding, we measured the relatedness to the males of females captured in their parental flock and virtually translocated female hatchlings in their parental and to more distant flocks. These tests indicated that dispersal decreased the likelihood of mating with relatives and that philopatric females had higher inbreeding risks than the actual breeding females. As females do not discriminate against relatives, the few inbred matings were probably due to the variance in female dispersal propensity and dispersal distance. Our results support the view that kin discrimination mate choice is of little value if dispersal effectively reduces the risks of inbreeding.     

Dcifer: an IBD-based method to calculate genetic distance between polyclonal infections

An essential step toward reconstructing pathogen transmission and answering epidemiologically relevant questions from genomic data is obtaining pairwise genetic distance between infections. For recombining organisms such as malaria parasites, relatedness measures quantifying recent shared ancestry would provide a meaningful distance, suggesting methods based on identity by descent (IBD). While the concept of relatedness and consequently an IBD approach is fairly straightforward for individual parasites, the distance between polyclonal infections, which are prevalent in malaria, presents specific challenges, and awaits a general solution that could be applied to infections of any clonality and accommodate multiallelic (e.g. microsatellite or microhaplotype) and biallelic [single nucleotide polymorphism (SNP)] data. Filling this methodological gap, we present Dcifer (Distance for complex infections: fast estimation of relatedness), a method for calculating genetic distance between polyclonal infections, which is designed for unphased data, explicitly accounts for population allele frequencies and complexity of infection, and provides reliable inference. Dcifer’s IBD-based framework allows us to define model parameters that represent interhost relatedness and to propose corresponding estimators with attractive statistical properties. By using combinatorics to account for unobserved phased haplotypes, Dcifer is able to quickly process large datasets and estimate pairwise relatedness along with measures of uncertainty. We show that Dcifer delivers accurate and interpretable results and detects related infections with statistical power that is 2–4 times greater than that of approaches based on identity by state. Applications to real data indicate that relatedness structure aligns with geographic locations. Dcifer is implemented in a comprehensive publicly available software package.     

A comparison of pedigree‐ and DNA‐based measures for identifying inbreeding depression in the critically endangered Attwater's Prairie‐chicken

The primary goal of captive breeding programmes for endangered species is to prevent extinction, a component of which includes the preservation of genetic diversity and avoidance of inbreeding. This is typically accomplished by minimizing mean kinship in the population, thereby maintaining equal representation of the genetic founders used to initiate the captive population. If errors in the pedigree do exist, such an approach becomes less effective for minimizing inbreeding depression. In this study, both pedigree‐ and DNA‐based methods were used to assess whether inbreeding depression existed in the captive population of the critically endangered Attwater's Prairie‐chicken (Tympanuchus cupido attwateri), a subspecies of prairie grouse that has experienced a significant decline in abundance and concurrent reduction in neutral genetic diversity. When examining the captive population for signs of inbreeding, variation in pedigree‐based inbreeding coefficients (f_pedigree) was less than that obtained from DNA‐based methods (f_DNA). Mortality of chicks and adults in captivity were also positively correlated with parental relatedness (r_DNA) and f_DNA, respectively, while no correlation was observed with pedigree‐based measures when controlling for additional variables such as age, breeding facility, gender and captive/release status. Further, individual homozygosity by loci (HL) and parental r_DNA values were positively correlated with adult mortality in captivity and the occurrence of a lethal congenital defect in chicks, respectively, suggesting that inbreeding may be a contributing factor increasing the frequency of this condition among Attwater's Prairie‐chickens. This study highlights the importance of using DNA‐based methods to better inform management decisions when pedigrees are incomplete or errors may exist due to uncertainty in pairings.     

The decline in fitness with inbreeding: evidence for negative dominance‐by‐dominance epistasis in Drosophila melanogaster

Genetic interactions can play an important role in the evolution of reproductive strategies. In particular, negative dominance‐by‐dominance epistasis for fitness can theoretically favour sex and recombination. This form of epistasis can be detected statistically because it generates nonlinearity in the relationship between fitness and inbreeding coefficient. Measures of fitness in progressively inbred lines tend to show limited evidence for epistasis. However, tests of this kind can be biased against detecting an accelerating decline due to line losses at higher inbreeding levels. We tested for dominance‐by‐dominance epistasis in Drosophila melanogaster by examining viability at five inbreeding levels that were generated simultaneously, avoiding the bias against detecting nonlinearity that has affected previous studies. We find an accelerating rate of fitness decline with inbreeding, indicating that dominance‐by‐dominance epistasis is negative on average, which should favour sex and recombination.     

Individual identification from genetic marker data: developments and accuracy comparisons of methods

Genetic marker‐based identification of distinct individuals and recognition of duplicated individuals has important applications in many research areas in ecology, evolutionary biology, conservation biology and forensics. The widely applied genotype mismatch (MM) method, however, is inaccurate because it relies on a fixed and suboptimal threshold number (T_M) of mismatches, and often yields self‐inconsistent pairwise inferences. In this study, I improved MM method by calculating an optimal T_M to accommodate the number, mistyping rates, missing data and allele frequencies of the markers. I also developed a pairwise likelihood relationship (LR) method and a likelihood clustering (LC) method for individual identification, using poor‐quality data that may have high and variable rates of allelic dropouts and false alleles at genotyped loci. The 3 methods together with the relatedness (RL) method were then compared in accuracy by analysing an empirical frog data set and many simulated data sets generated under different parameter combinations. The analysis results showed that LC is generally one or two orders more accurate for individual identification than the other methods. Its accuracy is especially superior when the sampled multilocus genotypes have poor quality (i.e. teemed with genotyping errors and missing data) and highly replicated, a situation typical of noninvasive sampling used in estimating population size. Importantly, LC is the only method that guarantees to produce self‐consistent results by partitioning the entire set of multilocus genotypes into distinct clusters, each cluster containing one or more genotypes that all represent the same individual. The LC and LR methods were implemented in a computer program COLONY for free download from the Internet.