Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

Rank-invariant estimation of inbreeding coefficients

The two alleles an individual carries at a locus are identical by descent (ibd) if they have descended from a single ancestral allele in a reference population, and the probability of such identity is the inbreeding coefficient of the individual. Inbreeding coefficients can be predicted from pedigrees with founders constituting the reference population, but estimation from genetic data is not possible without data from the reference population. Most inbreeding estimators that make explicit use of sample allele frequencies as estimates of allele probabilities in the reference population are confounded by average kinships with other individuals. This means that the ranking of those estimates depends on the scope of the study sample and we show the variation in rankings for common estimators applied to different subdivisions of 1000 Genomes data. Allele-sharing estimators of within-population inbreeding relative to average kinship in a study sample, however, do have invariant rankings across all studies including those individuals. They are unbiased with a large number of SNPs. We discuss how allele sharing estimates are the relevant quantities for a range of empirical applications.

How to estimate kinship

The concept of kinship permeates many domains of fundamental and applied biology ranging from social evolution to conservation science to quantitative and human genetics. Until recently, pedigrees were the gold standard to infer kinship, but the advent of next‐generation sequencing and the availability of dense genetic markers in many species make it a good time to (re)evaluate the usefulness of genetic markers in this context. Using three published data sets where both pedigrees and markers are available, we evaluate two common and a new genetic estimator of kinship. We show discrepancies between pedigree values and marker estimates of kinship and explore via simulations the possible reasons for these. We find these discrepancies are attributable to two main sources: pedigree errors and heterogeneity in the origin of founders. We also show that our new marker‐based kinship estimator has very good statistical properties and behaviour and is particularly well suited for situations where the source population is of small size, as will often be the case in conservation biology, and where high levels of kinship are expected, as is typical in social evolution studies.

Genetic and genomic monitoring with minimally invasive sampling methods

The decreasing cost and increasing scope and power of emerging genomic technologies are reshaping the field of molecular ecology. However, many modern genomic approaches (e.g., RAD-seq) require large amounts of high-quality template DNA. This poses a problem for an active branch of conservation biology: genetic monitoring using minimally invasive sampling (MIS) methods. Without handling or even observing an animal, MIS methods (e.g., collection of hair, skin, faeces) can provide genetic information on individuals or populations. Such samples typically yield low-quality and/or quantities of DNA, restricting the type of molecular methods that can be used. Despite this limitation, genetic monitoring using MIS is an effective tool for estimating population demographic parameters and monitoring genetic diversity in natural populations. Genetic monitoring is likely to become more important in the future as many natural populations are undergoing anthropogenically driven declines, which are unlikely to abate without intensive adaptive management efforts that often include MIS approaches. Here, we profile the expanding suite of genomic methods and platforms compatible with producing genotypes from MIS, considering factors such as development costs and error rates. We evaluate how powerful new approaches will enhance our ability to investigate questions typically answered using genetic monitoring, such as estimating abundance, genetic structure and relatedness. As the field is in a period of unusually rapid transition, we also highlight the importance of legacy data sets and recommend how to address the challenges of moving between traditional and next-generation genetic monitoring platforms. Finally, we consider how genetic monitoring could move beyond genotypes in the future. For example, assessing microbiomes or epigenetic markers could provide a greater understanding of the relationship between individuals and their environment.

Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.

Estimating inbreeding coefficients from NGS data: Impact on genotype calling and allele frequency estimation

Most methods for next-generation sequencing (NGS) data analyses incorporate information regarding allele frequencies using the assumption of Hardy–Weinberg equilibrium (HWE) as a prior. However, many organisms including those that are domesticated, partially selfing, or with asexual life cycles show strong deviations from HWE. For such species, and specially for low-coverage data, it is necessary to obtain estimates of inbreeding coefficients (F) for each individual before calling genotypes. Here, we present two methods for estimating inbreeding coefficients from NGS data based on an expectation-maximization (EM) algorithm. We assess the impact of taking inbreeding into account when calling genotypes or estimating the site frequency spectrum (SFS), and demonstrate a marked increase in accuracy on low-coverage highly inbred samples. We demonstrate the applicability and efficacy of these methods in both simulated and real data sets.