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PubMed2006

The genetic analysis of family structured inbreeding depression studies.

An important question emerging from theoretical studies of mating system evolution is whether the fitness of a randomly extracted, fully inbred genotype will exceed the mean of outbred individuals. We introduce two statistics (I(1) and I(2)) related to the probability of extracting a high line. I(1) and I(2) can be estimated from the family structured experimental designs typically used to estimate inbreeding depression (ID). Maximum likelihood procedures are developed from an explicit genetic model. These yield parameter estimates and provide the likelihoods necessary to test hypotheses, for example, whether population-level ID is nonzero. Finally, we describe a new publicly available computer program titled 'IDG' (Inbreeding Depression Genetics) to execute these procedures.

Analysis of Variance↗
PubMed1998

Measuring departures from Hardy-Weinberg: a Markov chain Monte Carlo method for estimating the inbreeding coefficient.

Many well-established statistical methods in genetics were developed in a climate of severe constraints on computational power. Recent advances in simulation methodology now bring modern, flexible statistical methods within the reach of scientists having access to a desktop workstation. We illustrate the potential advantages now available by considering the problem of assessing departures from Hardy-Weinberg (HW) equilibrium. Several hypothesis tests of HW have been established, as well as a variety of point estimation methods for the parameter which measures departures from HW under the inbreeding model. We propose a computational, Bayesian method for assessing departures from HW, which has a number of important advantages over existing approaches. The method incorporates the effects-of uncertainty about the nuisance parameters--the allele frequencies--as well as the boundary constraints on f (which are functions of the nuisance parameters). Results are naturally presented visually, exploiting the graphics capabilities of modern computer environments to allow straightforward interpretation. Perhaps most importantly, the method is founded on a flexible, likelihood-based modelling framework, which can incorporate the inbreeding model if appropriate, but also allows the assumptions of the model to he investigated and, if necessary, relaxed. Under appropriate conditions, information can be shared across loci and, possibly, across populations, leading to more precise estimation. The advantages of the method are illustrated by application both to simulated data and to data analysed by alternative methods in the recent literature.

Algorithms↗
PubMed2003

Inbreeding depression influences genet size distribution in a marine angiosperm.

Although inbreeding depression is a major genetic phenomena influencing individual fitness, it is difficult to measure in wild populations. An alternative approach is to correlate heterozygosity, measured using highly polymorphic markers, with a fitness-correlated trait. In clonal plants, genet size is predicted to be fitness correlated. Here we test the prediction that the genet size distribution of the marine clonal plant Zostera marina (eelgrass) is influenced by inbreeding depression. We used nine polymorphic microsatellite markers to access the fine scale clonal structure and to measure individual heterozygosity within 4 plots (each corresponds to 256 m2, sampled at 1-m intervals) in two populations along the German Baltic Coast. The same plots were also sampled for flowering and vegetative shoots to obtain estimates for sexual reproductive output at the level of the genetic individual. We found substantial differences in the genet size distribution between the two populations that may be explained by different disturbance frequency. In both populations, clone size was significantly positively correlated with the total number of flowering shoots, indicating that larger clones have a higher reproductive output. Individual heterozygosity was significantly positively associated with clone size. The effect was much stronger in Falkenstein (low disturbance) than in Maasholm (high disturbance). The results indicate that in a low disturbance population the relatively outbred clones occupy a higher proportion of the available space, possibly because they outcompete relatively inbred neighbours.

Alleles↗
PubMed2004

Inbreeding avoidance in cunningham's skinks (Egernia cunninghami) in natural and fragmented habitat.

Habitat fragmentation/alteration has been proposed as a distinct process threatening the viability of populations of many organisms. One expression of its impact may be the disruption of core population processes such as inbreeding avoidance. Using the experimental design outlined in our companion paper, we report on the impact of habitat alteration (deforestation) on inbreeding in the rock-dwelling Australian lizard Egernia cunninghami. Ten microsatellite loci were used to calculate relatedness coefficients of potential and actual breeding pairs, and to examine mate-choice and heterozygosity. Despite significantly less dispersal and higher within-group relatedness between potential mates in deforested than in natural habitats, this did not result in significantly more inbred matings. Average relatedness amongst breeding pairs was low, with no significant difference between natural and fragmented populations in relatedness between breeding pairs, or individual heterozygosity. Active avoidance of close kin as mates was indicated by the substantially and significantly lower relatedness in actual breeding pairs than potential ones. These facts, and heterozygote excesses in all groups of immature lizards from both habitats, show that E. cunninghami maintained outbreeding in the face of increased accumulation of relatives.

Animals↗
PubMed2004

Functionally reproductive diploid and haploid males in an inbreeding hymenopteran with complementary sex determination.

It has become a matter of orthodoxy that among wasps, ants, bees, and other insects in the order Hymenoptera, only uniparental haploid males that arise from unfertilized eggs are capable of reproduction. This idea is of interest because the best understood and perhaps most widespread sex determination system among these insects [known as single locus complementary sex determination (sl-CSD)] does not depend on ploidy alone and, paradoxically, consistently results in small numbers of diploid biparental males. To date, the reproductive potential of diploid males has been studied in 13 of the perhaps 200,000 hymenopterans world-wide; in each of these instances, the diploid males are genetic dead ends because they are inviable or sterile. The data from these species have resulted in a general conclusion that has been invoked for virtually all species with sl-CSD and has become the basis for assumptions regarding conservation biology, sex ratio analysis, and the evolution of social behavior. Here, we report that in the solitary vespid wasp Euodynerus foraminatus, both diploid and haploid males are fertile, which documents normal fertility in diploid males of a hymenopteran with sl-CSD. This wasp has high levels of inbreeding because of frequent brother-sister mating in nature; therefore, diploid males are more frequently produced and thus more likely exposed to selection favoring their fertility. Because inbreeding and diploid male production may be important features of the population biology of many hymenopterans, we sound a cautionary note regarding ideas about the evolutionary ecology of these insects.

Animals↗
PubMed1979

Genetic and phenotypic consequences of inbreeding.

The effects of inbreeding on heterozygosity, mean performance, variation within and between lines, and fixation or loss of genes are discussed. Theoretical predictions for degree of pedigree inbreeding and consequences for genes neutral with respect to fitness are outlined first, and then the likely modifications necessary to account for natural selection during inbred line development are considered. For illustration, some results from experiments with laboratory animals are reviewed. Inbred lines or F1 crosses between them are special genotypes, not representative of the population from which they were derived. Similarly, outbred stocks of laboratory animals that have a long history in the laboratory, or narrow base, or are maintained in small numbers, will lack variation and become like inbred lines. The efficacy of using either inbreds or such outbred stocks in toxicological screening is questioned on the ground that the range of genotypes is inadequate.

Animals↗
PubMed2004

The robustness of Hamilton's rule with inbreeding and dominance: kin selection and fixation probabilities under partial sib mating.

Assessing the validity of Hamilton's rule when there is both inbreeding and dominance remains difficult. In this article, we provide a general method based on the direct fitness formalism to address this question. We then apply it to the question of the evolution of altruism among diploid full sibs and among haplodiploid sisters under inbreeding resulting from partial sib mating. In both cases, we find that the allele coding for altruism always increases in frequency if a condition of the form rb>c holds, where r depends on the rate of sib mating alpha but not on the frequency of the allele, its phenotypic effects, or the dominance of these effects. In both examples, we derive expressions for the probability of fixation of an allele coding for altruism; comparing these expressions with simulation results allows us to test various approximations often made in kin selection models (weak selection, large population size, large fecundity). Increasing alpha increases the probability of fixation of recessive altruistic alleles (h<1/2), while it can increase or decrease the probability of fixation of dominant altruistic alleles (h>1/2).

Altruism↗
PubMed1984

Deviations from Hardy-Weinberg proportions: sampling variances and use in estimation of inbreeding coefficients.

An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients (f) obtained from these deviations. If f is small, the best estimate of f in large samples is shown to be 2 sigma i(Tii/Ni)/(k - 1), where Tii is an unbiased measure of the excess of the ith homozygote and Ni the number of the ith allele in the sample [frequency = Ni/(2N)]. No extra information is obtained from the Tij, where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the Tij, ignoring the Tii. Also (1) the variance of the estimate of f equals 1/(N(k - 1] when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n, the variance is increased by a proportion (n - 1)/4 but is not increased by a half-sib relationship. If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.

Alleles↗
PubMed1987

On the theory of partially inbreeding finite populations. I. Partial selfing.

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is Ne = N'/(1 + FIS), where FIS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is found to be 2(N'/N)(FISS1 + (1 - FIS)S2), where S1 and S2 are the selective advantages of AA and AA in comparison with AA. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions Ne = N/(1 + 3FIS).

Alleles↗
PubMed1990

Assessment of inbreeding by DNA fingerprinting: development of a calibration curve using defined strains of chickens.

By analyzing DNA fingerprints of chickens from seven well-defined genetic groups, a calibration curve was established relating the degree of inbreeding with the average band frequency, allelic frequency and band sharing. The probe used was bacteriophage M13 DNA and digestion of the genomic DNA was carried out with the MspI restriction enzyme. The analysis also provided an estimate of the average allelic frequency at a hypervariable locus and the average mutation frequency per locus and generation. The values of 0.24 and 1.7 X 10(-3), respectively, are similar to the estimates for humans using other probes and hybridization protocols. It is suggested that the calibration curve established can be used for determining inbreeding not only in chickens, but also in other species.

Alleles↗
PubMed1992

Effects of partial inbreeding on fixation rates and variation of mutant genes.

Diffusion methods were used to investigate the fixation probability, average time until fixation and extinction, and cumulative heterozygosity and genetic variance for single mutant genes in finite populations with partial inbreeding. The critical parameters in the approximation are the coefficient of inbreeding due to nonrandom mating (F) and the effective population size (Ne), which also depends on F and the variance of family size. For large Ns, the fixation probability (u) is u = 2(Ne/N)s (F + h - Fh), where N is the population census, s is the coefficient of selection of the mutant homozygote and h is the coefficient of dominance. For Poisson family size (independent Poisson distributions of selfed and nonselfed offspring with partial selfing, and independent Poisson distributions of male and female numbers with partial sib mating), Ne = N/(1 + F), and the time until fixation is approximately equal to Ne/N times the time to fixation with random mating, but this relation does not hold, however, for other distributions of family size. The cumulative nonadditive variance until fixation or loss for dominant genes is reduced with increasing F while for recessive genes it is increased with intermediate values of F. The average time until extinction of deleterious mutations is reduced by increasing F. This reduction, when expressed as a proportion, is approximately independent of the initial gene frequency as well as the selective disadvantage if this is large.

Animals↗
PubMed1996

Marker-based inferences about epistasis for genes influencing inbreeding depression.

We describe a multilocus, marker-based regression method for inferring interactions between genes controlling inbreeding depression in self-fertile organisms. It is based upon selfing a parent heterozygous for several unlinked codominant markers, then analyzing the fitness of progeny marker genotypes. If loci causing inbreeding depression are linked to marker loci, then viability selection is manifested by distorted segregation of markers, and fecundity selection by dependence of the fecundity character upon the marker genotype. To characterize this selection, fitness is regressed on the proportion of loci homozygous for markers linked to deleterious alleles, and epistasis is detected by nonlinearity of the regression. Alternatively, fitness can be regressed on the proportion of heterozygous loci. Other modes of selection can be incorporated with a bivariate regression involving both homozygote and heterozygote marker genotypes. The advantage of this marker-based approach is that "purging" is minimized and specific chromosomal segments are identified; its disadvantage lies in low statistical power when linkage is not strong and/or the linkage phase between marker and selected loci is uncertain. Using this method in the wildflower Mimulus guttatus, we found predominant multiplicative gene interaction determining fecundity and some negative synergistic (nonmultiplicative) interaction for viability.

Epistasis, Genetic↗
PubMed1997

Fixation, segregation and linkage of allozyme loci in inbred families of the Pacific oyster Crassostrea gigas (Thunberg): implications for the causes of inbreeding depression.

The effect that inbreeding has on the fixation and segregation of genes has rarely been confirmed by direct observation. Here, fixation, segregation, and linkage of allozymes is investigated in the progeny of self-fertilized hermaphrodites of the normally outcrossing Pacific oyster Crassostrea gigas. The estimate of fixation pooled over loci, individuals, and families, F = 0.462, is significantly lower than the expected value of 0.5. Log-likelihood ratios reveal significant heterogeneity in fixation among individuals, among families, and among loci. In addition, the grand pooled segregation ratio, 127:243:54, deviates significantly from 1:2:1, with a bias against homozygotes for alleles of lesser frequency in the natural population. Segregation ratios for 11 of 14 loci are significantly heterogeneous among families, and exact tests for segregation within families reveal 16 significant results out of 51 tests. Thus, fixation and segregation of allozyme markers in inbred oyster families deviates from the expectations of neutral inbreeding theory. Di-genic disequilibria are significant for four of 74 di-locus pairs revealing two linkage groups. Strong viability selection is apparently conditional on the genotype of the hermaphrodite-founders and is largely focused on these two linkage groups. These genetic effects are explained by interaction between cis-linked factors and polymorphic regulatory backgrounds.

Animals↗
PubMed1997

Inbreeding depression and inferred deleterious-mutation parameters in Daphnia.

DENG and LYNCH recently proposed a method for estimating deleterious genomic mutation parameters from changes in the mean and genetic variance of fitness traits upon inbreeding in outcrossing populations. Such observations are readily acquired in cyclical parthenogens. Selfing and life-table experiments were performed for two such Daphnia populations. We observed a significant inbreeding depression and an increase of genetic variance for all traits analyzed. DENG and LYNCH's original procedures were extended to estimate genomic mutation rate (U), mean dominance coefficient (h), mean selection coefficient (s), and scaled genomic mutational variance (Vm/Ve). On average, U, h, s and Vm/Ve (indicates an estimate) are 0.84 [corrected], 0.30, 0.14 and 4.6E-4, respectively. For the true values, the U and h are lower bounds, and s and Vm/Ve upper bounds. The present U, h and Vm/Ve are in general concordance with earlier results. The discrepancy between the present s and that from mutation-accumulation experiments in Drosophila (approximately 0.04) is discussed. It is shown that different reproductive modes do not affect gene frequency at mutation-selection equilibrium if mutational effects on fitness are multiplicative and not completely recessive.

Animals↗
PubMed2000

Predicting rates of inbreeding in populations undergoing selection.

Tractable forms of predicting rates of inbreeding (DeltaF) in selected populations with general indices, nonrandom mating, and overlapping generations were developed, with the principal results assuming a period of equilibrium in the selection process. An existing theorem concerning the relationship between squared long-term genetic contributions and rates of inbreeding was extended to nonrandom mating and to overlapping generations. DeltaF was shown to be approximately (1)/(4)(1 - omega) times the expected sum of squared lifetime contributions, where omega is the deviation from Hardy-Weinberg proportions. This relationship cannot be used for prediction since it is based upon observed quantities. Therefore, the relationship was further developed to express DeltaF in terms of expected long-term contributions that are conditional on a set of selective advantages that relate the selection processes in two consecutive generations and are predictable quantities. With random mating, if selected family sizes are assumed to be independent Poisson variables then the expected long-term contribution could be substituted for the observed, providing (1)/(4) (since omega = 0) was increased to (1)/(2). Established theory was used to provide a correction term to account for deviations from the Poisson assumptions. The equations were successfully applied, using simple linear models, to the problem of predicting DeltaF with sib indices in discrete generations since previously published solutions had proved complex.

Inbreeding↗
PubMed2000

Prediction of rates of inbreeding in populations selected on best linear unbiased prediction of breeding value.

Predictions for the rate of inbreeding (DeltaF) in populations with discrete generations undergoing selection on best linear unbiased prediction (BLUP) of breeding value were developed. Predictions were based on the concept of long-term genetic contributions using a recently established relationship between expected contributions and rates of inbreeding and a known procedure for predicting expected contributions. Expected contributions of individuals were predicted using a linear model, u(i)(()(x)()) = alpha + betas(i), where s(i) denotes the selective advantage as a deviation from the contemporaries, which was the sum of the breeding values of the individual and the breeding values of its mates. The accuracy of predictions was evaluated for a wide range of population and genetic parameters. Accurate predictions were obtained for populations of 5-20 sires. For 20-80 sires, systematic underprediction of on average 11% was found, which was shown to be related to the goodness of fit of the linear model. Using simulation, it was shown that a quadratic model would give accurate predictions for those schemes. Furthermore, it was shown that, contrary to random selection, DeltaF less than halved when the number of parents was doubled and that in specific cases DeltaF may increase with the number of dams.

Animal Husbandry↗
PubMed2003

Minimizing inbreeding by managing genetic contributions across generations.

Here we present the strategy that achieves the lowest possible rate of inbreeding (DeltaF) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a DeltaF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and consequently DeltaF is minimized. Using the concept of long-term genetic contributions, the asymptotic DeltaF of the new strategy for random mating, M sires and d dams per sire, is phi/(12M), where phi = [1 + 2((1)/(4))(d)]. Predictions were validated using Monte Carlo simulations. The scheme was shown to achieve the lowest possible DeltaF using pedigree alone and showed that further reductions in DeltaF below that obtained from random mating arise from preferential mating of relatives and not from their avoidance.

Animal Husbandry↗
PubMedDate not supplied

Changes in genetic variances with increased inbreeding of beef cattle.

Data on performance traits from a herd of Hereford cattle composed of inbred lines and linecross groups were analyzed to estimate within- and among-line genetic variances and to evaluate how these variances changed with increased inbreeding. Within-line variances were highly erratic while among-line variances tended to be somewhat more consistent. Changes in variances with increased inbreeding did not generally follow the theoretical expectations for the redistribution of genetic variances.

Animals↗