Statistical approaches to paternity analysis in natural populations and applications to the North Atlantic humpback whale

Patterns of paternity: insights into mating competition and gene flow in a recovering population of humpback whales

Variation in reproductive success is a fundamental prerequisite for sexual selection to act upon a trait. Assessing such variation is crucial in understanding a species' mating system and offers insights into population growth. Parentage analyses in cetaceans are rare, and the underlying forces of sexual selection acting on their mating behaviours remain poorly understood. Here, we combined 25 years of photo-identification and genetic data to assess patterns of male reproductive success and reproductive autonomy of the New Caledonian (Oceania, South Pacific) humpback whale breeding population. Paternity analysis of 177 mother-offspring pairs and 936 males revealed low variation in male reproductive success (average 1.17 offspring per father) relative to other polygynous species. The observed skew in success was higher than expected under random mating and skewed overall towards males (93%) without evidence of paternity over the study period. Finally, an updated male gametic mark-recapture abundance estimate of 2084 (95% confidence interval = 1761-2407, 1995-2019) fell between previous census estimates of the New Caledonian population and the wider Oceanian metapopulation. Our results provide critical insights into the mating competition of male humpback whales and population dynamics across Oceanian populations, two important factors affecting the slow recovery from whaling across the South Pacific region.

Advances in wildlife abundance estimation using pedigree reconstruction

The conservation and management of wildlife populations, particularly for threatened and endangered species are greatly aided with abundance, growth rate, and density measures. Traditional methods of estimating abundance and related metrics represent trade-offs in effort and precision of estimates. Pedigree reconstruction is an emerging, attractive alternate approach because its use of one-time, noninvasive sampling of individuals to infer the existence of unsampled individuals. However, advances in pedigree reconstruction could improve its utility, including forming a measure of precision for the method, establishing required spatial sampling effort for accurate estimates, ascertaining the spatial extent of abundance estimates derived from pedigree reconstruction, and assessing how population density affects the estimator's performance. Using established relationships for a stochastic, spatially explicit simulated moose (Alces americanus) population, pedigree reconstruction provided accurate estimates of the adult moose population size and trend. Novel bootstrapped confidence intervals performed as expected with intensive sampling but underperformed with moderate sampling efforts that could produce abundance estimates with low bias. Adult population estimates more closely reflected the total number of adults in the extant population, rather than number of adults inhabiting the area where sampling occurred. Increasing sampling effort, measured as the proportion of individuals sampled and as the proportion of a hypothetical study area, yielded similar asymptotic patterns over time. Simulations indicated a positive relationship between animal density and sampling effort required for unbiased estimates. These results indicate that pedigree reconstruction can produce accurate abundance estimates and may be particularly valuable for surveying smaller areas and low-density populations.

Wild pedigrees inform mutation rates and historic abundance in baleen whales

Phylogeny-based estimates suggesting a low germline mutation rate (μ) in baleen whales have influenced research ranging from assessments of whaling impacts to evolutionary cancer biology. We estimated μ directly from pedigrees in four baleen whale species for both the mitochondrial control region and nuclear genome. The results suggest values higher than those obtained through phylogeny-based estimates and similar to pedigree-based values for primates and toothed whales. Applying our estimate of μ reduces previous genetic-based estimates of preexploitation whale abundance by 86% and suggests that μ cannot explain low cancer rates in gigantic mammals. Our study shows that it is feasible to estimate μ directly from pedigrees in natural populations, with wide-ranging implications for ecological and evolutionary research.

Evaluating the suitability of close-kin mark-recapture as a demographic modelling tool for a critically endangered elasmobranch population

Estimating the demographic parameters of contemporary populations is essential to the success of elasmobranch conservation programmes, and to understanding their recent evolutionary history. For benthic elasmobranchs such as skates, traditional fisheries-independent approaches are often unsuitable as the data may be subject to various sources of bias, whilst low recapture rates can render mark-recapture programmes ineffectual. Close-kin mark-recapture (CKMR), a novel demographic modelling approach based on the genetic identification of close relatives within a sample, represents a promising alternative approach as it does not require physical recaptures. We evaluated the suitability of CKMR as a demographic modelling tool for the critically endangered blue skate (Dipturus batis) in the Celtic Sea using samples collected during fisheries-dependent trammel-net surveys that ran from 2011 to 2017. We identified three full-sibling and 16 half-sibling pairs among 662 skates, which were genotyped across 6291 genome-wide single nucleotide polymorphisms, 15 of which were cross-cohort half-sibling pairs that were included in a CKMR model. Despite limitations owing to a lack of validated life-history trait parameters for the species, we produced the first estimates of adult breeding abundance, population growth rate, and annual adult survival rate for D. batis in the Celtic Sea. The results were compared to estimates of genetic diversity, effective population size (N e ), and to catch per unit effort estimates from the trammel-net survey. Although each method was characterized by wide uncertainty bounds, together they suggested a stable population size across the time-series. Recommendations for the implementation of CKMR as a conservation tool for data-limited elasmobranchs are discussed. In addition, the spatio-temporal distribution of the 19 sibling pairs revealed a pattern of site fidelity in D. batis, and supported field observations suggesting an area of critical habitat that could qualify for protection might occur near the Isles of Scilly.

Estimating contemporary migration numbers of adults based on kinship relationships in iteroparous species

This paper describes the development of estimators for the contemporary migration number and rate of adults between two populations in iteroparous species. The proposed estimators are based on known half-sibling (HS) and/or parent-offspring (PO) relationships observed between populations across breeding seasons. The rationale is that HS and PO pairs exhibit information about the occurrence frequency of parental movements during the breeding interval. The proposed method allows for variance in the average number of offspring per parent within and between populations. In addition, coupled with the PO pairs found within the population, the estimators can be obtained using only genetic data. Generally, a sample size representing the square root of the population size is required to obtain meaningful migration information. We describe a detailed evaluation of the performance of the proposed estimators by running an individual-based model, and the results provide guidance regarding sample sizes to ensure the required accuracy and precision. In addition, given that there are few effective methods to estimate adult movement (especially when populations cannot be genetically distinct), we discuss the usefulness of the proposed kinship assignment method in terms of conservation biology and wildlife management.

Pedigree simulations reveal that maternity assignment is reliable in populations with conspecific brood parasitism, incomplete parental sampling and kin structure

Modern genetic parentage methods reveal that alternative reproductive strategies are common in both males and females. Under ideal conditions, genetic methods accurately connect the parents to offspring produced by extra-pair matings or conspecific brood parasitism. However, some breeding systems and sampling scenarios present significant complications for accurate parentage assignment. We used simulated genetic pedigrees to assess the reliability of parentage assignment for a series of challenging sampling regimes that reflect realistic conditions for many brood-parasitic birds: absence of genetic samples from sires, absence of samples from brood parasites and female kin-structured populations. Using 18 microsatellite markers and empirical allele frequencies from two populations of a conspecific brood parasite, the wood duck (Aix sponsa), we simulated brood parasitism and determined maternity using two widely used programs, cervus and colony. Errors in assignment were generally modest for most sampling scenarios but differed by program: cervus suffered from false assignment of parasitic offspring, whereas colony sometimes failed to assign offspring to their known mothers. Notably, colony was able to accurately infer unsampled parents. Reducing the number of markers (nine loci rather than 18) caused the assignment error to slightly worsen with colony but balloon with cervus. One potential error with important biological implications was rare in all cases-few nesting females were incorrectly excluded as the mother of their own offspring, an error that could falsely indicate brood parasitism. We consider the implications of our findings for both a retrospective assessment of previous studies and suggestions for best practices for future studies.

Mating frequency of Apis mellifera jemenitica under desert conditions of Saudi Arabia

Queen mating frequency is an important reproductive trait of the western honeybee Apis mellifera. Yet, it demands more attention when investigated under extreme or confined ecosystems. Queen mating frequency of the Yemeni Honeybee A. m. jemenetica was estimated under Saudi Arabia desert conditions, Riyadh (24°71'36″N, 46°67'53″E). Mating of queens took place after 8-13 days from emergence. Duration of mating flight ranged between 26 and 39 min. Subsequently, six microsatellite loci were used to genotype queen's progeny (n = 30 workers/queen). The average number of drone alleles using workers genotypes ranged between 5.83 ± 0.31 and 6.33 ± 1.09. However, effective paternal allele number was extremely low and ranged between 3.35 ± 0.34 and 3.60 ± 0.40. This relatively low mating frequency of the Yemeni honeybee, A. m. jemenetica, might have striking effect on the overall colony survival. Providentially, this relatively low mating frequency does not impact colonial heterozygosity, shown in this study (0.66 ± 0.07-70 ± 0.04), adversely. These results may affect hive survivability and entails distinctive management practices under such conditions.

Nearly unbiased estimator of contemporary Ne /N based on kinship relationships

This study develops a nearly unbiased estimator of the ratio of the contemporary effective mother size to the census size in a population, as a proxy of the ratio of contemporary effective size (or effective breeding size) to census size (N_e /N or N_b /N). The proposed estimator is based on both known mother-offspring (MO) and maternal-sibling (MS) relationships observed within the same cohort, in which sampled individuals in the cohort probably share MO relationships with sampled mothers. The rationale is that the frequency of MO and MS pairs contains information regarding the contemporary effective mother size and the (mature) census size, respectively. Therefore, the estimator can be obtained only from genetic data. We also evaluate the performance of the estimator by running an individual-based model. The results of this study provide the following: (a) parameter range for satisfying the unbiasedness, and (b) guidance for sample sizes to ensure the required accuracy and precision, especially when the order of the ratio is available. Furthermore, the results demonstrate the usefulness of a sibship assignment method for genetic monitoring, providing insights for interpreting environmental and/or anthropological factors fluctuating N_e /N (or N_b /N), especially in the context of conservation biology and wildlife management.

Mining whole genome sequence data to efficiently attribute individuals to source populations

Whole genome sequence (WGS) data could transform our ability to attribute individuals to source populations. However, methods that efficiently mine these data are yet to be developed. We present a minimal multilocus distance (MMD) method which rapidly deals with these large data sets as well as methods for optimally selecting loci. This was applied on WGS data to determine the source of human campylobacteriosis, the geographical origin of diverse biological species including humans and proteomic data to classify breast cancer tumours. The MMD method provides a highly accurate attribution which is computationally efficient for extended genotypes. These methods are generic, easy to implement for WGS and proteomic data and have wide application.

The future of parentage analysis: From microsatellites to SNPs and beyond

Parentage analysis is a cornerstone of molecular ecology that has delivered fundamental insights into behaviour, ecology and evolution. Microsatellite markers have long been the king of parentage, their hypervariable nature conferring sufficient power to correctly assign offspring to parents. However, microsatellite markers have seen a sharp decline in use with the rise of next-generation sequencing technologies, especially in the study of population genetics and local adaptation. The time is ripe to review the current state of parentage analysis and see how it stands to be affected by the emergence of next-generation sequencing approaches. We find that single nucleotide polymorphisms (SNPs), the typical next-generation sequencing marker, remain underutilized in parentage analysis but are gaining momentum, with 58 SNP-based parentage analyses published thus far. Many of these papers, particularly the earlier ones, compare the power of SNPs and microsatellites in a parentage context. In virtually every case, SNPs are at least as powerful as microsatellite markers. As few as 100-500 SNPs are sufficient to resolve parentage completely in most situations. We also provide an overview of the analytical programs that are commonly used and compatible with SNP data. As the next-generation parentage enterprise grows, a reliance on likelihood and Bayesian approaches, as opposed to strict exclusion, will become increasingly important. We discuss some of the caveats surrounding the use of next-generation sequencing data for parentage analysis and conclude that the future is bright for this important realm of molecular ecology.

Efficient inference of paternity and sibship inference given known maternity via hierarchical clustering

Pedigree and sibship reconstruction are important methods in quantifying relationships and fitness of individuals in natural populations. Current methods employ a Markov chain-based algorithm to explore plausible possible pedigrees iteratively. This provides accurate results, but is time-consuming. Here, we develop a method to infer sibship and paternity relationships from half-sibling arrays of known maternity using hierarchical clustering. Given 50 or more unlinked SNP markers and empirically derived error rates, the method performs as well as the widely used package Colony, but is faster by two orders of magnitude. Using simulations, we show that the method performs well across contrasting mating scenarios, even when samples are large. We then apply the method to open-pollinated arrays of the snapdragon Antirrhinum majus and find evidence for a high degree of multiple mating. Although we focus on diploid SNP data, the method does not depend on marker type and as such has broad applications in nonmodel systems.

Absolute abundance of southern bluefin tuna estimated by close-kin mark-recapture

Southern bluefin tuna is a highly valuable, severely depleted species, whose abundance and productivity have been difficult to assess with conventional fishery data. Here we use large-scale genotyping to look for parent-offspring pairs among 14,000 tissue samples of juvenile and adult tuna collected from the fisheries, finding 45 pairs in total. Using a modified mark-recapture framework where 'recaptures' are kin rather than individuals, we can estimate adult abundance and other demographic parameters such as survival, without needing to use contentious fishery catch or effort data. Our abundance estimates are substantially higher and more precise than previously thought, indicating a somewhat less-depleted and more productive stock. More broadly, this technique of 'close-kin mark-recapture' has widespread utility in fisheries and wildlife conservation. It estimates a key parameter for management-the absolute abundance of adults-while avoiding the expense of independent surveys or tag-release programmes, and the interpretational problems of fishery catch rates.

Simple Genetic Distance-Optimized Field Deployments for Clonal Seed Orchards Based on Microsatellite Markers: As a Case of Chinese Pine Seed Orchard

Chinese pine seed orchards are in a period of transition from first-generation to advanced-generations. How to effectively select populations for second-generation seed orchards and significantly increase genetic gain through rational deployment have become major issues. In this study, we examined open- and control-pollinated progeny of the first-generation Chinese pine seed orchards in Zhengning (Gansu Province, China) and Xixian (Shanxi Province, China) to address issues related to phenotypic selection for high volume growth, genetic diversity analysis and genetic distance-based phylogenetic analysis of the selections by simple sequence repeats (SSRs), and phylogenetic relationship-based field deployment for advanced-generation orchards. In total, 40, 28, 20, and 13 superior individuals were selected from the large-scale no-pedigree open-pollinated progeny of Zhengning (ZN-NP), open-pollinated families of Zhengning (ZN-OP), open-pollinated families of Xixian (XX-OP), and control-pollinated families of Xixian, with mean volume dominance ratios of 0.83, 0.15, 0.25, and 0.20, respectively. Phylogenetic relationship analysis of the ZN-NP and XX-OP populations showed that the 40 superior individuals in the ZN-NP selected population belonged to 23 families and could be further divided into five phylogenetic groups, and that families in the same group were closely related. Similarly, 20 families in the XX-OP population were related to varying degrees. Based on these results, we found that second-generation Chinese pine seed orchards in Zhengning and Xixian should adopt a grouped, unbalanced, complete, fixed block design and an unbalanced, incomplete, fixed block design, respectively. This study will provide practical references for applying molecular markers to establishing advanced-generation seed orchards.

Genomic variation among populations of threatened coral: Acropora cervicornis

Background

Acropora cervicornis, a threatened, keystone reef-building coral has undergone severe declines (>90 %) throughout the Caribbean. These declines could reduce genetic variation and thus hamper the species’ ability to adapt. Active restoration strategies are a common conservation approach to mitigate species' declines and require genetic data on surviving populations to efficiently respond to declines while maintaining the genetic diversity needed to adapt to changing conditions. To evaluate active restoration strategies for the staghorn coral, the genetic diversity of A. cervicornis within and among populations was assessed in 77 individuals collected from 68 locations along the Florida Reef Tract (FRT) and in the Dominican Republic.

Results

Genotyping by Sequencing (GBS) identified 4,764 single nucleotide polymorphisms (SNPs). Pairwise nucleotide differences (π) within a population are large (~37 %) and similar to π across all individuals. This high level of genetic diversity along the FRT is similar to the diversity within a small, isolated reef. Much of the genetic diversity (>90 %) exists within a population, yet GBS analysis shows significant variation along the FRT, including 300 SNPs with significant F_ST values and significant divergence relative to distance. There are also significant differences in SNP allele frequencies over small spatial scales, exemplified by the large F_ST values among corals collected within Miami-Dade county.

Conclusions

Large standing diversity was found within each population even after recent declines in abundance, including significant, potentially adaptive divergence over short distances. The data here inform conservation and management actions by uncovering population structure and high levels of diversity maintained within coral collections among sites previously shown to have little genetic divergence. More broadly, this approach demonstrates the power of GBS to resolve differences among individuals and identify subtle genetic structure, informing conservation goals with evolutionary implications.

An information theoretic approach to pedigree reconstruction

Network structure is a dominant feature of many biological systems, both at the cellular level and within natural populations. Advances in genotype and gene expression screening made over the last few decades have permitted the reconstruction of these networks. However, resolution to a single model estimate will generally not be possible, leaving open the question of the appropriate method of formal statistical inference. The nonstandard structure of the problem precludes most traditional statistical methodologies. Alternatively, a Bayesian approach provides a natural methodology for formal inference. Construction of a posterior density on the space of network structures allows formal inference regarding features of network structure using specific marginal posterior distributions. An information theoretic approach to this problem will be described, based on the Minimum Description Length principle. This leads to a Bayesian inference model based on the information content of data rather than on more commonly used probabilistic models. The approach is applied to the problem of pedigree reconstruction based on genotypic data. Using this application, it is shown how the MDL approach is able to provide a truly objective control for model complexity. A two-cohort model is used for a simulation study. The MDL approach is compared to COLONY-2, a well known pedigree reconstruction application. The study highlights the problem of genotyping error modeling. COLONY-2 requires prior error rate estimates, and its accuracy proves to be highly sensitive to these estimates. In contrast, the MDL approach does not require prior error rate estimates, and is able to accurately adjust for genotyping error across the range of models considered.

Bayesian pedigree inference with small numbers of single nucleotide polymorphisms via a factor-graph representation

We develop a computational framework for addressing pedigree inference problems using small numbers (80-400) of single nucleotide polymorphisms (SNPs). Our approach relaxes the assumptions, which are commonly made, that sampling is complete with respect to the pedigree and that there is no genotyping error. It relies on representing the inferred pedigree as a factor graph and invoking the Sum-Product algorithm to compute and store quantities that allow the joint probability of the data to be rapidly computed under a large class of rearrangements of the pedigree structure. This allows efficient MCMC sampling over the space of pedigrees, and, hence, Bayesian inference of pedigree structure. In this paper we restrict ourselves to inference of pedigrees without loops using SNPs assumed to be unlinked. We present the methodology in general for multigenerational inference, and we illustrate the method by applying it to the inference of full sibling groups in a large sample (n=1157) of Chinook salmon typed at 95 SNPs. The results show that our method provides a better point estimate and estimate of uncertainty than the currently best-available maximum-likelihood sibling reconstruction method. Extensions of this work to more complex scenarios are briefly discussed.

A trade-off between precopulatory and postcopulatory trait investment in male cetaceans

Mating with multiple partners is common across species, and understanding how individual males secure fertilization in the face of competition remains a fundamental goal of evolutionary biology. Game theory stipulates that males have a fixed budget for reproduction that can lead to a trade-off between investment in precopulatory traits such as body size, armaments, and ornaments, and postcopulatory traits such as testis size and spermatogenic efficiency. Recent theoretical and empirical studies have shown that if males can monopolize access to multiple females, they will invest disproportionately in precopulatory traits and less in postcopulatory traits. Using phylogenetically controlled comparative methods, we demonstrate that across 58 cetacean species with the most prominent sexual dimorphism in size, shape, teeth, tusks, and singing invest significantly less in relative testes mass. In support of theoretical predictions, these species tend to show evidence of male contests, suggesting there is opportunity for winners to monopolize access to multiple females. Our approach provides a robust dataset with which to make predictions about male mating strategies for the many cetacean species for which adequate behavioral observations do not exist.

Stochastic modelling of shifts in allele frequencies reveals a strongly polygynous mating system in the re-introduced Asiatic wild ass

Small populations are prone to loss of genetic variation and hence to a reduction in their evolutionary potential. Therefore, studying the mating system of small populations and its potential effects on genetic drift and genetic diversity is of high importance for their viability assessments. The traditional method for studying genetic mating systems is paternity analysis. Yet, as small populations are often rare and elusive, the genetic data required for paternity analysis are frequently unavailable. The endangered Asiatic wild ass (Equus hemionus), like all equids, displays a behaviourally polygynous mating system; however, the level of polygyny has never been measured genetically in wild equids. Combining noninvasive genetic data with stochastic modelling of shifts in allele frequencies, we developed an alternative approach to paternity analysis for studying the genetic mating system of the re-introduced Asiatic wild ass in the Negev Desert, Israel. We compared the shifts in allele frequencies (as a measure of genetic drift) that have occurred in the wild ass population since re-introduction onset to simulated scenarios under different proportions of mating males. We revealed a strongly polygynous mating system in which less than 25% of all males participate in the mating process each generation. This strongly polygynous mating system and its potential effect on the re-introduced population's genetic diversity could have significant consequences for the long-term persistence of the population in the Negev. The stochastic modelling approach and the use of allele-frequency shifts can be further applied to systems that are affected by genetic drift and for which genetic data are limited.

Molecular assessment of mating strategies in a population of Atlantic spotted dolphins

Similar to other small cetacean species, Atlantic spotted dolphins (Stenella frontalis) have been the object of concentrated behavioral study. Although mating and courtship behaviors occur often and the social structure of the population is well-studied, the genetic mating system of the species is unknown. To assess the genetic mating system, we genotyped females and their progeny at ten microsatellite loci. Genotype analysis provided estimates of the minimum number of male sires necessary to account for the allelic diversity observed among the progeny. Using the estimates of male sires, we determined whether females mated with the same or different males during independent estrus events. Using Gerud2.0, a minimum of two males was necessary to account for the genetic variation seen among progeny arrays of all tested females. ML-Relate assigned the most likely relationship between offspring pairs; half or full sibling. Relationship analysis supported the conservative male estimates of Gerud2.0 but in some cases, half or full sibling relationships between offspring could not be fully resolved. Integrating the results from Gerud2.0, ML-Relate with previous observational and paternity data, we constructed two-, three-, and four-male pedigree models for each genotyped female. Because increased genetic diversity of offspring may explain multi-male mating, we assessed the internal genetic relatedness of each offspring's genotype to determine whether parent pairs of offspring were closely related. We found varying levels of internal relatedness ranging from unrelated to closely related (range -0.136-0.321). Because there are several hypothesized explanations for multi-male mating, we assessed our data to determine the most plausible explanation for multi-male mating in our study system. Our study indicated females may benefit from mating with multiple males by passing genes for long-term viability to their young.

Molecular pedigree reconstruction and estimation of evolutionary parameters in a wild Atlantic salmon river system with incomplete sampling: a power analysis

Background

Pedigree reconstruction using genetic analysis provides a useful means to estimate fundamental population biology parameters relating to population demography, trait heritability and individual fitness when combined with other sources of data. However, there remain limitations to pedigree reconstruction in wild populations, particularly in systems where parent-offspring relationships cannot be directly observed, there is incomplete sampling of individuals, or molecular parentage inference relies on low quality DNA from archived material. While much can still be inferred from incomplete or sparse pedigrees, it is crucial to evaluate the quality and power of available genetic information a priori to testing specific biological hypotheses. Here, we used microsatellite markers to reconstruct a multi-generation pedigree of wild Atlantic salmon (Salmo salar L.) using archived scale samples collected with a total trapping system within a river over a 10 year period. Using a simulation-based approach, we determined the optimal microsatellite marker number for accurate parentage assignment, and evaluated the power of the resulting partial pedigree to investigate important evolutionary and quantitative genetic characteristics of salmon in the system.

Results

We show that at least 20 microsatellites (ave. 12 alleles/locus) are required to maximise parentage assignment and to improve the power to estimate reproductive success and heritability in this study system. We also show that 1.5 fold differences can be detected between groups simulated to have differing reproductive success, and that it is possible to detect moderate heritability values for continuous traits (h² ~ 0.40) with more than 80% power when using 28 moderately to highly polymorphic markers.

Conclusion

The methodologies and work flow described provide a robust approach for evaluating archived samples for pedigree-based research, even where only a proportion of the total population is sampled. The results demonstrate the feasibility of pedigree-based studies to address challenging ecological and evolutionary questions in free-living populations, where genealogies can be traced only using molecular tools, and that significant increases in pedigree assignment power can be achieved by using higher numbers of markers.

Patterns of pollen dispersal in a small population of the Canarian endemic palm (Phoenix canariensis)

The genetic diversity of small populations is greatly influenced by local dispersal patterns and genetic connectivity among populations, with pollen dispersal being the major component of gene flow in many plants species. Patterns of pollen dispersal, mating system parameters and spatial genetic structure were investigated in a small isolated population of the emblematic palm Phoenix canariensis in Gran Canaria island (Canary Islands). All adult palms present in the study population (n=182), as well as 616 seeds collected from 22 female palms, were mapped and genotyped at 8 microsatellite loci. Mating system analysis revealed an average of 5.8 effective pollen donors (Nep) per female. There was strong variation in correlated paternity rates across maternal progenies (ranging from null to 0.9) that could not be explained by the location and density of local males around focal females. Paternity analysis revealed a mean effective pollen dispersal distance of ∼71 m, with ∼70% of effective pollen originating from a distance of <75 m, and 90% from <200 m. A spatially explicit mating model indicated a leptokurtic pollen dispersal kernel, significant pollen immigration (12%) from external palm groves and a directional pollen dispersal pattern that seems consistent with local altitudinal air movement. No evidence of inbreeding or genetic diversity erosion was found, but spatial genetic structure was detected in the small palm population. Overall, the results suggest substantial pollen dispersal over the studied population, genetic connectivity among different palm groves and some resilience to neutral genetic erosion and subsequently to fragmentation.

Fractional parentage analysis and a scale-free reproductive network of brown trout

In this study, we developed a method of fractional parentage analysis using microsatellite markers. We propose a method for calculating parentage probability, which considers missing data and genotyping errors due to null alleles and other causes, by regarding observed alleles as realizations of random variables which take values in the set of alleles at the locus and developing a method for simultaneously estimating the true and null allele frequencies of all alleles at each locus. We then applied our proposed method to a large sample collected from a wild population of brown trout (Salmo trutta). On analyzing the data using our method, we found that the reproductive success of brown trout obeyed a power law, indicating that when the parent-offspring relationship is regarded as a link, the reproductive system of brown trout is a scale-free network. Characteristics of the reproductive network of brown trout include individuals with large bodies as hubs in the network and different power exponents of degree distributions between males and females.

Influence of long-distance seed dispersal on the genetic diversity of seed rain in fragmented Pinus densiflora populations relative to pollen-mediated gene flow

Long-distance dispersal (LDD) of seeds has a critical impact on species survival in patchy landscapes. However, relative to pollen dispersal, empirical data on how seed LDD affects genetic diversity in fragmented populations have been poorly reported. Thus, we attempted to indirectly evaluate the influence of seed LDD by estimating maternal and paternal inbreeding in the seed rain of fragmented 8 Pinus densiflora populations. In total, the sample size was 458 seeds and 306 adult trees. Inbreeding was estimated by common parentage analysis to evaluate gene flow within populations and by sibship reconstruction analysis to estimate gene flow within and among populations. In the parentage analysis, the observed probability that sampled seeds had the same parents within populations was significantly larger than the expected probability in many populations. This result suggested that gene dispersal was limited to within populations. In the sibship reconstruction, many donors both within and among populations appeared to contribute to sampled seeds. Significant differences in sibling ratios were not detected between paternity and maternity. These results suggested that seed-mediated gene flow and pollen-mediated gene flow from outside population contributed some extent to high genetic diversity of the seed rain (H E > 0.854). We emphasize that pine seeds may have excellent potential for gene exchange within and among populations.

Using pedigree reconstruction to estimate population size: genotypes are more than individually unique marks

Estimates of population size are critical for conservation and management, but accurate estimates are difficult to obtain for many species. Noninvasive genetic methods are increasingly used to estimate population size, particularly in elusive species such as large carnivores, which are difficult to count by most other methods. In most such studies, genotypes are treated simply as unique individual identifiers. Here, we develop a new estimator of population size based on pedigree reconstruction. The estimator accounts for individuals that were directly sampled, individuals that were not sampled but whose genotype could be inferred by pedigree reconstruction, and individuals that were not detected by either of these methods. Monte Carlo simulations show that the population estimate is unbiased and precise if sampling is of sufficient intensity and duration. Simulations also identified sampling conditions that can cause the method to overestimate or underestimate true population size; we present and discuss methods to correct these potential biases. The method detected 2–21% more individuals than were directly sampled across a broad range of simulated sampling schemes. Genotypes are more than unique identifiers, and the information about relationships in a set of genotypes can improve estimates of population size.

Can genetic estimators provide robust estimates of the effective number of breeders in small populations?

The effective population size (N(e)) is proportional to the loss of genetic diversity and the rate of inbreeding, and its accurate estimation is crucial for the monitoring of small populations. Here, we integrate temporal studies of the gecko Oedura reticulata, to compare genetic and demographic estimators of N(e). Because geckos have overlapping generations, our goal was to demographically estimate N(bI), the inbreeding effective number of breeders and to calculate the N(bI)/N(a) ratio (N(a) =number of adults) for four populations. Demographically estimated N(bI) ranged from 1 to 65 individuals. The mean reduction in the effective number of breeders relative to census size (N(bI)/N(a)) was 0.1 to 1.1. We identified the variance in reproductive success as the most important variable contributing to reduction of this ratio. We used four methods to estimate the genetic based inbreeding effective number of breeders N(bI(gen)) and the variance effective populations size N(eV(gen)) estimates from the genotype data. Two of these methods - a temporal moment-based (MBT) and a likelihood-based approach (TM3) require at least two samples in time, while the other two were single-sample estimators - the linkage disequilibrium method with bias correction LDNe and the program ONeSAMP. The genetic based estimates were fairly similar across methods and also similar to the demographic estimates excluding those estimates, in which upper confidence interval boundaries were uninformative. For example, LDNe and ONeSAMP estimates ranged from 14-55 and 24-48 individuals, respectively. However, temporal methods suffered from a large variation in confidence intervals and concerns about the prior information. We conclude that the single-sample estimators are an acceptable short-cut to estimate N(bI) for species such as geckos and will be of great importance for the monitoring of species in fragmented landscapes.

Estimation of mating system parameters in an evolving gynodioecous population of cultivated sunflower (Helianthus annuus L.)

Cultivated plants have been molded by human-induced selection, including manipulations of the mating system in the twentieth century. How these manipulations have affected realized parameters of the mating system in freely evolving cultivated populations is of interest for optimizing the management of breeding populations, predicting the fate of escaped populations and providing material for experimental evolution studies. To produce modern varieties of sunflower (Helianthus annuus L.), self-incompatibility has been broken, recurrent generations of selfing have been performed and male sterility has been introduced. Populations deriving from hybrid-F1 varieties are gynodioecious because of the segregation of a nuclear restorer of male fertility. Using both phenotypic and genotypic data at 11 microsatellite loci, we analyzed the consanguinity status of plants of the first three generations of such a population and estimated parameters related to the mating system. We showed that the resource reallocation to seed in male-sterile individuals was not significant, that inbreeding depression on seed production averaged 15-20% and that cultivated sunflower had acquired a mixed-mating system, with ∼50% of selfing among the hermaphrodites. According to theoretical models, the female advantage and the inbreeding depression at the seed production stage were too low to allow the persistence of male sterility. We discuss our methods of parameter estimation and the potential of such study system in evolutionary biology.

On the choice of prior density for the Bayesian analysis of pedigree structure

This article is concerned with the choice of structural prior density for use in a fully Bayesian approach to pedigree inference. It is found that the choice of prior has considerable influence on the accuracy of the estimation. To guide this choice, a scale invariance property is introduced. Under a structural prior with this property, the marginal prior distribution of the local properties of a pedigree node (number of parents, offspring, etc.) does not depend on the number of nodes in the pedigree. Such priors are found to arise naturally by an application of the Minimum Description Length (MDL) principle, under which construction of a prior becomes equivalent to the problem of determining the length of a code required to encode a pedigree, using the principles of information theory. The approach is demonstrated using simulated and actual data, and is compared to two well-known applications, CERVUS and COLONY.

A new version of PRT software for sibling groups reconstruction with comments regarding several issues in the sibling reconstruction problem

Pedigree reconstruction using genotypic markers has become an important tool for the study of natural populations. The nonstandard nature of the underlying statistical problems has led to the necessity of developing specialized statistical and computational methods. In this article, a new version of pedigree reconstruction tools (PRT 2.0) is presented. The software implements algorithms proposed in Almudevar & Field (Journal of Agricultural Biological and Environmental Statistics, 4, 1999, 136) and Almudevar (Biometrics, 57, 2001a, 757) for the reconstruction of single generation sibling groups (SG). A wider range of enumeration algorithms is included, permitting improved computational performance. In particular, an iterative version of the algorithm designed for larger samples is included in a fully automated form. The new version also includes expanded simulation utilities, as well as extensive reporting, including half-sibling compatibility, parental genotype estimates and flagging of potential genotype errors. A number of alternative algorithms are described and demonstrated. A comparative discussion of the underlying methodologies is presented. Although important aspects of this problem remain open, we argue that a number of methodologies including maximum likelihood estimation (COLONY 1.2 and 2.0) and the set cover formulation (KINALYZER) exhibit undesirable properties in the sibling reconstruction problem. There is considerable evidence that large sets of individuals not genetically excluded as siblings can be inferred to be a true sibling group, but it is also true that unrelated individuals may be genetically compatible with a true sibling group by chance. Such individuals may be identified on a statistical basis. PRT 2.0, based on these sound statistical principles, is able to efficiently match or exceed the highest reported accuracy rates, particularly for larger SG. The new version is available at http://www.urmc.rochester.edu/biostat/people/faculty/almudevar.cfm.

Combining markers into haplotypes can improve population structure inference

High-throughput genotyping and sequencing technologies can generate dense sets of genetic markers for large numbers of individuals. For most species, these data will contain many markers in linkage disequilibrium (LD). To utilize such data for population structure inference, we investigate the use of haplotypes constructed by combining the alleles at single-nucleotide polymorphisms (SNPs). We introduce a statistic derived from information theory, the gain of informativeness for assignment (GIA), which quantifies the additional information for assigning individuals to populations using haplotype data compared to using individual loci separately. Using a two-loci-two-allele model, we demonstrate that combining markers in linkage equilibrium into haplotypes always leads to nonpositive GIA, suggesting that combining the two markers is not advantageous for ancestry inference. However, for loci in LD, GIA is often positive, suggesting that assignment can be improved by combining markers into haplotypes. Using GIA as a criterion for combining markers into haplotypes, we demonstrate for simulated data a significant improvement of assigning individuals to candidate populations. For the many cases that we investigate, incorrect assignment was reduced between 26% and 97% using haplotype data. For empirical data from French and German individuals, the incorrectly assigned individuals can, for example, be decreased by 73% using haplotypes. Our results can be useful for challenging population structure and assignment problems, in particular for studies where large-scale population-genomic data are available.

Reproductive success of male Atlantic spotted dolphins (Stenella frontalis) revealed by noninvasive genetic analysis of paternity

Cetaceans are known to frequently engage in sexual behavior; however, the lack of male parental investment in offspring makes assessment of male reproductive success difficult. We assessed paternity in a small population (mean individuals sighted per year = 93) of Atlantic spotted dolphins ( Stenella frontalis (G. Cuvier, 1829)) utilizing noninvasively collected fecal material. Samples (n = 88) were collected from dolphins from four social clusters. Of the 29 offspring tested, 34.5% were assigned paternity, resulting in 10 paternities assigned to seven males. Our study indicates that achieving a certain age is a potential precursor for males to mate successfully, as 18 years was the youngest estimated age of a male at the time of calf conception. In all pairings but one, the males were older than the female (mean age difference = 7.7+ years). Successful males were from two of the four social clusters and males most often mated within their social group or with females from the next geographically closest group. The study combines genetic data with known maternal pedigree information and reveals patterns in the overall mating system in a cetacean species where reproductive success of males was previously unknown.

Mating patterns and determinants of individual reproductive success in brown trout (Salmo trutta) revealed by parentage analysis of an entire stream living population

Reproductive success and its determinants are difficult to infer for wild populations of species with no parental care where behavioural observations are difficult or impossible. In this study, we characterized the breeding system and provide estimates of individual reproductive success under natural conditions for an exhaustively sampled stream-resident brown trout (Salmo trutta) population. We inferred parentage using a full probability Bayesian model that combines genetic (microsatellite) with phenotypic data. By augmenting the potential parents file with inferred parental genotypes from sib-ship analysis in cases where large families had unsampled parents, we could make more precise inference on variance of family size. We observed both polygamous and monogamous matings and large reproductive skew for both sexes, particularly in males. Correspondingly, we found evidence for sexual selection on body size for both sexes. We show that the mating system of brown trout has the potential to be very flexible and we conjecture that environmental uncertainty could be driving the evolution and perhaps select for the maintenance of plasticity of the mating system in this species.

Reconstruction of pedigrees in clonal plant populations

We present a Bayesian method for the reconstruction of pedigrees in clonal populations using co-dominant genomic markers such as microsatellites and single nucleotide polymorphisms (SNPs). The accuracy of the algorithm is demonstrated for simulated data. We show that the joint estimation of parameters of interest such as the rate of self-fertilization is possible with high accuracy even with marker panels of moderate power. Classical methods can only assign a very limited number of statistically significant parentages in this case and would therefore fail. Statistical confidence is estimated by Markov Chain Monte Carlo (MCMC) sampling. The method is implemented in a fast and easy to use open source software that scales to large datasets with many thousand individuals.

Population genetics and social organization of the sperm whale (Physeter macrocephalus) in the Azores inferred by microsatellite analyses

In the northeast Atlantic Ocean, the archipelago of the Azores is frequented by female–offspring groups of sperm whales ( Physeter macrocephalus L., 1758), as well as large males. The Azores apparently constitute both a feeding ground and a reproduction site. Little is known about the population and group structure of sperm whales in the area. We analysed 151 sloughed skin and biopsy samples collected from 2002 to 2004. Molecular analyses involved genetic tagging using 11 microsatellite loci and molecular sexing. Our objectives were to determine the population genetic structure, compare relatedness within and between social groups, infer kinship, and estimate the age of males at dispersal. Results suggest that individuals visiting the archipelago of the Azores belong to a single population. High genetic diversity and absence of inbreeding suggest that the population is recovering from whaling. Individuals sampled in close association are highly related, as well as those observed in the same area on the same day, suggesting that secondary social groups (i.e., the union of primary social units) are largely but not exclusively composed of relatives. Probable mother–offspring and full-sibling pairs were identified. Age of males at dispersal was estimated at 16.6 years, which was well above previous estimates for this species.

The influence of distinct pollinators on female and male reproductive success in the Rocky Mountain columbine

Although there are many reasons to expect distinct pollinator types to differentially affect a plant's reproductive success, few studies have directly examined this question. Here, we contrast the impact of two kinds of pollinators on reproductive success via male and female functions in the Rocky Mountain columbine, Aquilegia coerulea. We set up pollinator exclusion treatments in each of three patches where Aquilegia plants were visited by either day pollinators (majority bumble bees), by evening pollinators (hawkmoths), or by both (control). Day pollinators collected pollen and groomed, whereas evening pollinators collected nectar but did not groom. Maternal parents, potential fathers and progeny arrays were genotyped at five microsatellite loci. We estimated female outcrossing rate and counted seeds to measure female reproductive success and used paternity analysis to determine male reproductive success. Our results document that bumble bees frequently moved pollen among patches of plants and that, unlike hawkmoths, pollen moved by bumble bees sired more outcrossed seeds when it remained within a patch as opposed to moving between patches. Pollinator type differentially affected the outcrossing rate but not seed set, the number of outcrossed seeds or overall male reproductive success. Multiple visits to a plant and more frequent visits by bumble bees could help to explain the lack of impact of pollinator type on overall reproductive success. The increase in selfing rate with hawkmoths likely resulted from the abundant pollen available in experimental flowers. Our findings highlighted a new type of pollinator interactions that can benefit a plant species.

Parentage and sibship inference from multilocus genotype data under polygamy

Likelihood methods have been developed to partition individuals in a sample into sibling clusters using genetic marker data without parental information. Most of these methods assume either both sexes are monogamous to infer full sibships only or only one sex is polygamous to infer full sibships and paternal or maternal (but not both) half sibships. We extend our previous method to the more general case of both sexes being polygamous to infer full sibships, paternal half sibships, and maternal half sibships and to the case of a two-generation sample of individuals to infer parentage jointly with sibships. The extension not only expands enormously the scope of application of the method, but also increases its statistical power. The method is implemented for both diploid and haplodiploid species and for codominant and dominant markers, with mutations and genotyping errors accommodated. The performance and robustness of the method are evaluated by analyzing both simulated and empirical data sets. Our method is shown to be much more powerful than pairwise methods in both parentage and sibship assignments because of the more efficient use of marker information. It is little affected by inbreeding in parents and is moderately robust to nonrandom mating and linkage of markers. We also show that individually much less informative markers, such as SNPs or AFLPs, can reach the same power for parentage and sibship inferences as the highly informative marker simple sequence repeats (SSRs), as long as a sufficient number of loci are employed in the analysis.

FRANz: reconstruction of wild multi-generation pedigrees

SUMMARY

We present a software package for pedigree reconstruction in natural populations using co-dominant genomic markers such as microsatellites and single nucleotide polymorphisms (SNPs). If available, the algorithm makes use of prior information such as known relationships (sub-pedigrees) or the age and sex of individuals. Statistical confidence is estimated by Markov Chain Monte Carlo (MCMC) sampling. The accuracy of the algorithm is demonstrated for simulated data as well as an empirical dataset with known pedigree. The parentage inference is robust even in the presence of genotyping errors.

AVAILABILITY

The C source code of FRANz can be obtained under the GPL from http://www.bioinf.uni-leipzig.de/Software/FRANz/.