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.Subject terms: Population genetics, Evolutionary biology, Molecular ecology     

Simultaneous estimation of null alleles and inbreeding coefficients

Although microsatellites are a very efficient tool for many population genetics applications, they may occasionally produce "null" alleles, which, when present in high proportion, may affect estimates of key parameters such as inbreeding and relatedness coefficients or measures of genetic differentiation. In order to account for the presence of null alleles, it is first necessary to estimate their frequency within studied populations. However, the commonly used null allele frequency estimators are not of general applicability because they can produce upwardly biased estimates when a population under study experiences some inbreeding. In such a case, 2 formerly described approaches, population inbreeding model and individual inbreeding model, can be applied for simultaneous estimation of null allele frequencies and of the inbreeding coefficient. In this study, we demonstrate the properties and utility of these 2 methods and show that they outperform the commonly used approaches in the estimation of null allele frequencies based on genotypic data. The methods are applied to empirical data from a natural population of European beech (Fagus sylvatica L.), and results are briefly discussed. The methods presented in this paper are implemented in the Windows-based user-friendly INEST computer program (available free of charge at http://genetyka.ukw.edu.pl/INEst10_setup.exe).     

Exact inbreeding coefficients in populations with overlapping generations

A theory is given that allows inbreeding coefficients to be calculated exactly for populations with overlapping generations. Emphasis is placed on providing equations well suited for computer iteration. Both monoecious and dioecious populations are considered and family size is not restricted to being Poisson. One-locus and two-locus inbreeding coefficients are evaluated, although the reader may omit the two-locus sections. The exact treatment is shown to be preferable to approximate treatments in that it applies to both early and late generations for all populations sizes. Inbreeding effective numbers found by the exact treatment are compared to various approximate numbers, and the approximate values are found to be generally very good.     

Spawning, copulation and inbreeding coefficients in marine invertebrates

Patterns of population genetic variation have frequently been understood as consequences of life history covariates such as dispersal ability and breeding systems (e.g. selfing). For example, marine invertebrates show enormous variation in life history traits that are correlated with the extent of gene flow between populations and the magnitude of differentiation among populations at neutral genetic markers (FST). Here we document an unexpected correlation between marine invertebrate life histories and deviation from Hardy-Weinberg equilibrium (non-zero values of FIS, the inbreeding coefficient). FIS values were significantly higher in studies of species with free-spawned planktonic sperm than in studies of species that copulate or have some form of direct sperm transfer to females or benthic egg masses. This result was robust to several different analytical approaches. We note several mechanisms that might contribute to this pattern, and appeal for more studies and ideas that might help to explain our observations.     

A spectral theory for Wright’s inbreeding coefficients and related quantities

Wright’s inbreeding coefficient, F_ST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright’s inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of F_ST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright’s F_ST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of F_ST approximates the proportion of genetic variation explained by the first (K − 1) principal components accurately. The new definition of F_ST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.     

Linkage and inbreeding coefficients in a finite random mating population

The notion of inbreeding coefficient associated with one single locus introduced by G. Malecot can be extended to two loci. For a panmictic model with separate generation the recurrence equations are given therein allowing to calculate the coefficients in the event of migration and mutation, or loss of kinship.Hence it is derived particularly that the limit genetic distance of two groups associated with two loci is, under specific hypotheses, little different from the sum of marginal genetic distances.For an isolat this paper studies, in terms of crossing over, mutations, and population size, the evolution of the inbreading coefficients of order 2 and especially the difference of this evolution from the evolution to independence of the two loci.     

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.     

An analytical model for calculating internal dose conversion coefficients for non-human biota

To assess the radiation burden of non-human living organisms, dose coefficients are available in the literature, precalculated by assuming an ellipsoidal shape of each organism. A previously developed analytical method was applied for the determination of absorbed fractions inside ellipsoidal volumes from alpha, beta, and gamma radiations to the calculation of dose conversion coefficients (DCCs) for 15 reference organisms, animals and plants, either terrestrial, amphibian, or aquatic, and six radionuclides (¹⁴C, ⁹⁰Sr, ⁶⁰Co, ¹³⁷Cs, ²³⁸U, and ²⁴¹Am). The results were compared with the reference values reported in Publication 108 of the International Commission on Radiological Protection, in which a different calculation approach for DCCs was employed. The results demonstrate that the present analytical method, originally intended for applications in internal dosimetry of nuclear medicine therapy, gives consistent results for all the beta-, beta–gamma-, and alpha-emitting radionuclides tested in a wide range of organism masses, between 8 mg and 1.3 kg. The applicability of the method proposed can take advantage from its ease of implementation in an ordinary electronic spreadsheet, allowing to calculate, for virtually all possible radionuclide emission spectra, the DCCs for ellipsoidal models of non-human living organisms in the environment.     

Accounting for cryptic population substructure enhances detection of inbreeding depression with genomic inbreeding coefficients: an example from a critically endangered marsupial

Characterizing inbreeding depression in wildlife populations can be critical to their conservation. Coefficients of individual inbreeding can be estimated from genome‐wide marker data. The degree to which sensitivity of inbreeding coefficients to population genetic substructure alters estimates of inbreeding depression in wild populations is not well understood. Using generalized linear models, we tested the power of two frequently used inbreeding coefficients that are calculated from genome‐wide SNP markers, F_H and F^^III, to predict four fitness traits estimated over two decades in an isolated population of the critically endangered Leadbeater's possum. F_H estimates inbreeding as excess observed homozygotes relative to equilibrium expectations, whereas F^^III quantifies allelic similarity between the gametes that formed an individual, and upweights rare homozygotes. We estimated F_H and F^^III from 1,575 genome‐wide SNP loci in individuals with fitness trait data (N = 179–237 per trait), and computed revised coefficients, F_H^{by group} and F^^{IIIby group}, adjusted for population genetic substructure by calculating them separately within two different genetic groups of individuals identified in the population. Using F_H or F^^III in the models, inbreeding depression was detected for survival to sexual maturity, longevity and whether individuals bred during their lifetime. F^^{IIIby group} (but not F_H^{by group}) additionally revealed significant inbreeding depression for lifetime reproductive output (total offspring assigned to each individual). Estimates of numbers of lethal equivalents indicated substantial inbreeding load, but differing between inbreeding estimators. Inbreeding depression, declining population size, and low and declining genetic diversity suggest that genetic rescue may assist in preventing extinction of this unique Leadbeater's possum population.     

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.     

Identity coefficients and covariances between relatives in a parent-offspring inbreeding system

Summary A one-locus operator for a younger parent-offspring inbreeding system is obtained by a generation matrix method in which 14 classes of matings are defined. The eigenvalues and a set of eigenvectors for the generation matrix and, also, the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab x cd are given. The operator gives the genotypic array of descendants of a given mating an arbitrary number of generations later. Using this operator, an algorithm is developed for calculating identity coefficients between any two relatives in a possibly branching younger parent-off spring mating system. Application to obtaining covariances between relatives for a one-locus model is illustrated.Journal article (74-3-73) of the Kentucky Agricultural Experiment Station published with approval of the Director.     

Kin selection and coefficients of relatedness in family-structured populations with inbreeding

We consider family specific fitnesses that depend on mixed strategies of two basic phenotypes or behaviours. Pairwise interactions are assumed, but they are restricted to occur between sibs. To study the change in frequency of a rare mutant allele, we consider two different forms of weak selection, one applied through small differences in genotypic values determining individual mixed strategies, the other through small differences in viabilities according to the behaviours chosen by interacting sibs. Under these two specific forms of weak selection, we deduce conditions for initial increase in frequency of a rare mutant allele for autosomal genes in the partial selfing model as well as autosomal and sex-linked genes in the partial sib-mating model with selection before mating or selection after mating. With small differences in mixed strategies, we show that conditions for protection of a mutant allele are tantamount to conditions for initial increase in frequency obtained in additive kin selection models. With particular reference to altruism versus selfishness, we provide explicit ranges of values for the selfing or sib-mating rate based on a fixed cost-benefit ratio and the dominance scheme that allow the spreading of a rare mutant allele into the population. This study confirms that more inbreeding does not necessarily promote the evolution of altruism. Under the hypothesis of small differences in viabilities, the situation is much more intricate unless an additive model is assumed. In general however, conditions for initial increase in frequency of a mutant allele can be obtained in terms of fitness effects that depend on the genotypes of interacting individuals or their mates and generalized conditional coefficients of relatedness according to the inbreeding condition of the interacting individuals.     

Simple method for calculating confidence limits around inbreeding rate and effective population size estimates from pedigrees

An important concept in population genetics is effective population size (N_e), which describes the expected rate of loss of genetic variability from a population. One way to estimate N_e is using a pedigree. However, there are no methods for comparing the N_e estimated from a pedigree with that expected from life-history models. In the paper we show how N_e can be estimated from the change in inbreeding rate (f) estimated from a pedigree. The mean individual inbreeding rate in a population at a given time must be calculated from averaged values for males and females, where each age class is weighted by its reproductive value. We show an exact method for placing confidence intervals around f and N_e using a binomial distribution, and present a method for approximating this interval for large N_es using a Poisson distribution. These confidence intervals can be used to compare f and N_e from a pedigree to expected values from demographic models, and to compare N_es of two populations.     

Bayesian multilevel modelling of compositional data for simultaneous inferences on Allele compositions and inbreeding coefficients

Sample data from a number of sub-populations are often investigated in order to integrate the findings of different research studies on a particular area. In case of compositional samples, like the allele frequencies collected at a single locus in different surveys, the data are independent multinomial vectors. Each multinomial distribution depends on a specific probability vector, that is, the unknown relative composition of the sub-population. A Bayesian hierarchy approach is proposed here to model the variability of the sub-composition vectors around a common mean with possibly different scales. The common mean can be seen as the relative composition of the aggregated population. Scale parameters are well known in Biology as the Wright's inbreeding coefficients. The method presented here extends some previous work by assuming less prior knowledge on the subject and constraints on the model. A relatively simple Monte Carlo algorithm is described to perform joint inferences on general and local compositions and inbreeding coefficients. The method is applied on two case studies. The first one is based on DNA samples from ten Italian regions at the loci TH01 and FES, obtained from a database currently used for forensic identification, in which inbreeding assessments can be crucial. The second application is based on a set of colour-blind sample rates in North-East Indian populations collected by Choudhury (1994). The Author found some controversial results from the classical test for comparing proportions. A clearer picture, instead, is obtained by the current Bayesian approach.