A model for genetic relationship in areally continous plant populations.

Representations are based on plant populations, continuously distributed over their habitats according to specified density patterns. Migration of genetic material takes place via pollen and seed dispersal. Monoecious plants with arbitrary rates of self-fertilization and dioecious plants are considered. The model was constructed with the intention of determining coefficients of inbreeding and kinship for all locations within the seed population after its dispersal over the habitat, assuming the respective genetic relationships of the parental generation to be known. To display the consequences of single components hidden in the general result, the following specifications have been treated: finite population size combined with random dispersal of seed, equilibrium states for hypothetically infinite population size with “limited” dispersal of pollen and seed, random dispersal of pollen, and random dispersal of seed.     

Pedigree analysis of the closed nucleus of Iranian Baluchi sheep

A study was conducted to characterise genetic diversity in the closed nucleus of Baluchi sheep using pedigree analysis. Herdbook information collected between 1979 and 2008, including pedigree records on 21,721 animals, was used to compute inbreeding and average generation intervals. Effective population size and parameters derived from probability of gene origin were computed for ewes born between 2005 and 2008 with both parents known (female reference population). The average complete generation equivalent of the female reference population was 5.47. The mean generation interval was 3.33 years in the studied period. From 1983 to 1994, the rate of increase in inbreeding was approximately 0.2% per year, but, after 1994, inbreeding did not increase as in the preceding years and had an approximately flat trend over time. The mean relationship coefficients among rams, among ewes and between rams and ewes in active animals were calculated to predict the future level of inbreeding. The effective number of founders, effective number of ancestors and founder genome equivalent of the reference population were 80, 47 and 19.5, respectively. The realised effective population size was 134 animals. The results of this study indicated that the population under study has fairly good genetic variability.     

A model for genetic relationship in areally continuous plant populations

Representations are based on plant populations, continuously distributed over their habitats according to specified density patterns. Migration of genetic material takes place via pollen and seed dispersal. Monoecious plants with arbitrary rates of self-fertilization and dioecious plants are considered. The model was constructed with the intention of determining coefficients of inbreeding and kinship for all locations within the seed population after its dispersal over the habitat, assuming the respective genetic relationships of the parental generation to be known. To display the consequences of single components hidden in the general result, the following specifications have been treated: finite population size combined with random dispersal of seed, equilibrium states for hypothetically infinite population size with “limited” dispersal of pollen and seed, random dispersal of pollen, and random dispersal of seed.     

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.     

Mate choice for nonadditive genetic benefits and the maintenance of genetic diversity in song sparrows

The lek paradox asserts that strong directional selection via female choice should deplete additive genetic variation in fitness and consequently any benefit to females expressing the preference. Recently, we have provided a novel resolution to the paradox by showing that nonadditive genetic effects such as overdominance can be inherited from parent to offspring, and populations with females that express a mating preference for outbred males maintain higher genetic variation than populations with females that mate randomly. Here, we test our dynamic model using empirical data previously published from a small island population of song sparrows (Melospiza melodia). The model assumes that fitness and male trait expression display overdominance effects. The results demonstrate that female choice for outbred males mediated by directional selection on song repertoire size provides a heritable benefit to offspring through reduced inbreeding depression. Within the population, we estimate the heritability of the inbreeding coefficient to be 0.18 ± 0.08 (SD). Furthermore, we show that mate choice for outbred males increases fitness‐related genetic variation in the population by 12% and thereby reduces inbreeding depression by 1% per generation in typical years and upwards of 15% in severe years. Thus, mate choice may help to stave off population extinction in this and other small populations.     

History and fate of a small isolated population of Weddell seals at White Island,Antarctica

Weddell seals (Leptonychotes weddellii Lesson) at White Island, Antarctica form a small, completely enclosed, natural population hypothesized to be of recent origin, likely founded by individuals from nearby Erebus Bay. This population constitutes an ideal model to document a founder event and ensuing genetic drift, with implications for conservation. Here we combined historical accounts, census and tagging data since the late 1960s, and genetic data (41 microsatellite loci and mitochondrial DNA sequences) from 84 individuals representing nearly all individuals present between 1990 and 2000 to investigate the history of the founding of the White Island population, document its population dynamics and evaluate possible future threats. We fully resolved parental relationships over three overlapping generations. Cytonuclear disequilibrium among the first generation suggested that it comprised the direct descendants of a founding group. We estimated that the White Island population was founded by a small group of individuals that accessed the island during a brief break in the surrounding sea ice in the mid-1950s, consistent with historical accounts. Direct and indirect methods of calculating effective population size were highly congruent and suggested a minimum founding group consisting of three females and two males. The White Island population showed altered reproductive dynamics compared to Erebus Bay, including highly skewed sex ratio, documented inbred mating events, and the oldest known reproducing Weddell seals. A comparison with the putative source population showed that the White Island population has an effective inbreeding coefficient (F _e) of 0.29. Based on a pedigree analysis including the hypothesized founding group, 86% of the individuals for whom parents were known had inbreeding coefficients ranging 0.09–0.31. This high level of inbreeding was correlated with reduced pup survival. Seals at White Island therefore face the combined effects of low genetic variability, lack of immigration, and inbreeding depression. Ultimately, this study provides evidence of the effects of natural isolation on a large, long-lived vertebrate and can provide clues to the potential effects of anthropogenic-caused isolation of similar taxa.     

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extend of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.     

Comparison of ancestral and current-generation inbreeding in an experimental strawberry breeding population

Progenies from first-generation self, half-sib, full-sib, and cross fertilizations were generated to evaluate the magnitude of inbreeding depression for vegetative and production traits in strawberry. Tests were conducted to determine the linearity of trait mean depression with inbreeding rate (F) over this range of inbreeding values, as an indication of the presence of non-additive epistasis. A control population, for which a similar range of coancestry had accumulated over several cycles of breeding and selection, was also generated to compare the consequences of ancestral and current-generation inbreeding. Trait means for crosses among current-generation half-sibs, full-sibs, and selfs were 2–17%, 3–12%, and 14–45% lower than for unrelated crosses among the same set of parents, respectively. Linear regression of progeny means on current generation F was significantly negative for all traits and explained 17–44% of the variance among progeny means. Mean depression was largely linear over the range of inbreeding rates tested in this population, indicating the absence of epistasis for the traits evaluated. Conversely, (F) regressions of progeny means on pedigree inbreeding coefficients, where coancestry had accumulated over several cycles of breeding and selection, were uniformly non-significant and explained 0–10% of the variance among cross means. Further, multiple regression of progeny means for current-generation relatives on pedigree F failed to improve fit significantly over regression on current-generation F alone for all traits. Together, these results suggest that pedigree inbreeding coefficients are poor predictors of changes in homozygosity when populations are developed through multiple cycles of breeding and selection. They also imply that inbreeding depression will be of minor importance for strawberry breeding populations managed with adequate population sizes and strong directional selection.     

Quantifying gene flow from spatial genetic structure data in a metapopulation of Chamaecrista fasciculata (Leguminosae)

Abstract An extensive allozyme survey was conducted within a natural "meta" population of the native North American annual legume, Chamaecrista fasciculata (Leguminosae) to quantify genetic structure at different spatial scales. Gene flow was then estimated by a recently developed indirect method based on a continuous population model, using pairwise kinship coefficients between individuals. The indirect estimates of gene flow, quantified in terms of neighborhood size, with an average value on the order of 150 individuals, were concordant among different spatial scales (subpopulation, population, metapopulation). This gene-flow value lies within the range of direct estimates previously documented from observations of pollen and seed dispersal for the same metapopulation. Monte Carlo simulations using the direct measures of gene flow as parameters further demonstrated that the observed spatial pattern of allozyme variation was congruent with a model of isolation by distance. Combining previously published estimates of pollen dispersal distances with kinship coefficients from this study, we quantified biparental inbreeding relative to either a single subpopulation or the whole metapopulation. At the level of a neighborhood, little biparental inbreeding was observed and most departure from Hardy-Weinberg genotypic proportions was explained by self-fertilization, whereas both selfing and biparental inbreeding contributed to nonrandom mating at the metapopulation level. Gene flow was also estimated from indirect methods based on a discontinuous population structure model. We discuss these results with respect to the effect of a patchy population structure on estimation of gene flow.     

Influence of Gene Flow and Breeding Tactics on Gene Diversity within Populations

Expressions describing the accumulation of gene correlations within and among lineages and individuals of a population are derived. The model permits different migration rates by males and females and accounts for various breeding tactics within lineages. The resultant equations enable calculation of the probabilistic quantities for the fixation indices, rates of loss of genetic variation, accumulation of inbreeding, and coefficients of relationship for the population at any generation. All fixation indices were found to attain asymptotic values rapidly despite the consistent loss of genetic variation and accumulation of inbreeding within the population. The time required to attain asymptotic values, however, was prolonged when gene flow among lineages was relatively low (less than 20%). The degree of genetic differentiation among breeding groups, inbreeding coefficients, and gene correlations within lineages were found to be primarily functions of breeding tactics within groups rather than gene flow among groups. Thus, the asymptotic value of S. Wright's island model is not appropriate for describing genetic differences among groups within populations. An alternative solution is provided that under limited conditions will reduce to the original island model. The evolution of polygynous breeding tactics appears to be more favorable for promoting intragroup gene correlations than modification of migration rates. Inbreeding and variance effective sizes are derived for populations that are structured by different migration and breeding tactics. Processes that reduce the inbreeding effective population size result in a concomitant increase in variance effective population size.     

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.     

Population structure of the Trakehner Horse breed

The objective of this study was to examine the population structure of the Trakehner Horse breed. A total of 13 793 pedigree records were used for analysing the active breeding population and their ancestors dating back to 1950. Ancestors that were born before 1950 were called as base animals. The average generation interval was calculated as 10.2 years. The effective population size (Ne) was estimated by the increase in average year-wise inbreeding coefficient and average coancestry, respectively. Two methods were applied to estimate the effective population size: 1. Numerator-relationship-matrix (NRM), which did not consider missing ancestries. 2. Uncertain-parentage-matrix (UPM), which considered a probabilistic correction for unknown ancestors. There were no major differences between these two methods with respect to the rate of increase in inbreeding although the global levels using the UPM method were observed to be higher. Estimates for the inbreeding coefficients and the average coancestries varied little between both methods. The estimates of the effective population size per generation based on the rate of inbreeding ranged from 169 (NRM) to 150 (UPM) and 158 (NRM) to 144 (UPM) calculated by the average coancestry. From the early 1990s onwards, a strong increase in the rate of inbreeding was observed. This may be due to an increasing variance of the family size of sires and may be interpreted as a consequence of the growing use of artificial insemination. Analysing coancestries within and between the centrally managed regional breeding societies in Germany further revealed the Trakehner horse breed to be a genetically fragmented population with a main partition corresponding to formerly divided East and West Germany. The average rate of gene contributions (Thoroughbred (xx), Arab Horse breed (ox)) to the defined actual breeding population was calculated to be 22.3% xx-genes and 11.7% ox-genes.     

Increased inbreeding but not homozygosity in small populations of Sabatia angularis (Gentianaceae)

Understanding how the mating system varies with population size in plant populations is critical for understanding their genetic and demographic fates. We examined how the mating system, characterized by outcrossing rate, biparental inbreeding rate, and inbreeding coefficient, and genetic diversity varied with population size in natural populations of the biennial Sabatia angularis. We found a significant, positive relationship between outcrossing and population size. Selfing was as high as 40% in one small population but was only 7% in the largest population. Despite this pattern, observed heterozygosity did not vary with population size, and we suggest that selection against inbred individuals maintains observed heterozygosity in small populations. Consistent with this hypothesis, we found a trend of lower inbreeding coefficients in the maternal than progeny generation in all of the populations, and half of the populations exhibited significant excesses of adult heterozygosity. Moreover, genetic diversity was not related to population size and was similar across all populations examined. Our results suggest that the consequences of increased selfing for population fitness in S. angularis, a species that experiences significant inbreeding depression, will depend on the relative magnitude and consistency of inbreeding depression and the demographic cost of selection for outcrossed progeny in small populations.     

Pedigree and marker information requirements to monitor genetic variability

There are several measures available to describe the genetic variability of populations. The average inbreeding coefficient of a population based on pedigree information is a frequently chosen option. Due to the developments in molecular genetics it is also possible to calculate inbreeding coefficients based on genetic marker information. A simulation study was carried out involving ten sires and 50 dams. The animals were mated over a period of 20 discrete generations. The population size was kept constant. Different situations with regard to the level of polymorphism and initial allele frequencies and mating scheme (random mating, avoidance of full sib mating, avoidance of full sib and half sib mating) were considered. Pedigree inbreeding coefficients of the last generation using full pedigree or 10, 5 and 2 generations of the pedigree were calculated. Marker inbreeding coefficients based on different sets of microsatellite loci were also investigated. Under random mating, pedigree-inbreeding coefficients are clearly more closely related to true autozygosity (i.e., the actual proportion of loci with alleles identical by descent) than marker-inbreeding coefficients. If mating is not random, the demands on the quality and quantity of pedigree records increase. Greater attention must be paid to the correct parentage of the animals.     

A comparison of inbreeding rates in India, Japan, Europe and China.

This is a report on an application of a new method for estimating inbreeding rates in large, semi-isolated populations over time. This study is intended to further show the versatility of the method. In a previous study, the method was shown to be useful in analysing the effect of details in a single population curve on inbreeding. In this study, the method is applied to the population curves of India, Japan, Europe and China over the past two millennia, to allow inter-comparisons of the inbreeding within those populations. Anthropologists traditionally concentrate on small isolates within a country for the estimation of inbreeding. Those isolates, however, might not be representative of the country as a whole. The method used in this study attempts to estimate inbreeding over large regions over an extended period of time. The method models the genealogical 'paradox' and yields estimates of the average inbreeding in terms of Pearl's coefficient Z, as a function of time. It is first assumed that the whole population of each country is the adult (breeding) population, corresponding to minimum inbreeding. It is found that the more complex the population curve examined, the greater the precision of the Z curves obtained. The effect of incorporating a single known value of inbreeding into the analyses is also investigated. This procedure produces a more realistic situation where the adult (breeding) population is considerably less than the entire population. It is shown, that if it is assumed that the whole population of the country is the adult (breeding) population, then a present day person from one of the four regions/countries studied is descended from between 72% and 97% of the early medieval population of the particular country. On the other hand, if a known value of inbreeding for Britain is incorporated into the analysis, these values become of the order of 1% for the older-settled regions/countries, and about 16% for Japan. However, that value for Japan is reduced to about 1% when a known value of inbreeding for this country is used. Although some uncertainty in these results remains, the versatility of the method demonstrated here will provide more accurate results, as better input-data become available.     

Potential bias in inbreeding depression estimates when using pedigree relationships to assess the degree of homozygosity for loci under selection

A potential bias in estimation of inbreeding depression when using pedigree relationships to assess the degree of homozygosity for loci under selection is indicated. A comparison of inbreeding coefficients based on either pedigree or genotypic frequencies indicated that, as a result of selection, the inbreeding coefficient based on pedigree might not correspond with the random drift of allelic frequencies. Apparent differences in average levels of both inbreeding coefficients were obtained depending on the genetic model (additive versus dominance, initial allelic frequencies, heritability) and the selection system assumed (no versus mass selection). In the absence of selection, allelic frequencies within a small population change over generations due to random drift, and the pedigree-based inbreeding coefficient gives a proper assessment of the accompanying probability of increased homozygosity within a replicate by indicating the variance of allelic frequencies over replicates. With selection, in addition to random drift, directional change in allelic frequencies is not accounted for by the pedigree-based inbreeding coefficient. This result implies that estimation of inbreeding depression for traits under either direct or indirect selection, estimated by a regression of performance on pedigree-based coefficients, should be carefully interpreted.Deceased     

Genetic characterization of free-ranging Asiatic wild ass in Central Asia as a basis for future conservation strategies

Loss of genetic diversity due to drift and inbreeding reduces a population’s ability to respond to environmental change and may result in inbreeding depression. The Asiatic wild ass (Equus hemionus), regionally also known as Gobi khulan, Turkmen kulan, or Persian onager, has become confined to less than 3% of its historic distribution range. Remaining populations in Central Asia outside of the Mongolian Gobi are small and fragmented. Questions concerning subpopulation status remain disputed and concerns over the viability of these populations have been raised because of small size, past bottlenecks, or recent founder events. We used non-invasive faecal samples to assess the genetic diversity and divergence among Turkmen kulan and Persian onager from five free-ranging and one captive population from Turkmenistan, Kazakhstan and Iran and compared their genetic constitution to the large autochthonous population in the Mongolian Gobi. We observed loss of genetic diversity (drift and inbreeding) in the captive and reintroduced populations as well as in one rapidly declining autochthonous population. Population differentiation and structure using microsatellites and mtDNA based phylogenetic analysis do not support the current separation of the autochthonous populations of Turkmen kulan and Persian onager into different subspecies, but rather suggest a cline with the Iranian population in Bahram-e-Goor at the southern end and the Turkmen population in Badhyz at the northern end falling into two distinct clusters, and the northern Iranian population in Touran being intermediate. We compare our findings to other population genetics studies of equids and discuss the implications of our findings for the future conservation of the Asiatic wild ass in the region.     

Genetic Differentiation in Populations with Different Classes of Individuals

I formulate and analyse a model of population structure with different classes of individuals. These different classes may be age classes, other demographic classes, or different types of habitats homogeneously distributed over a geographical area. The value of population differentiation under an island model of dispersal and the increase of differentiation with geographical distance in one- and two-dimensional "isolation by distance" models are then obtained for a generalization of the FST measure of population structure, as a function of "effective" mutation, migration, and population size parameters. The relevant effective subpopulation size is related to the "mutation effective population size" of a single isolated subpopulation and, in models of age-structured populations, to the inbreeding effective population size.     

Evaluation of ancestral inbreeding coefficients: Ballou’s formula versus gene dropping

Estimation of the purging of detrimental effects through inbreeding and selection is an important issue in conservation genetics opening new perspectives for the management of small populations. In 1997 Ballou proposed the ancestral inbreeding coefficient, which is calculated recursively via pedigree inbreeding coefficients, as a tool for evaluating the purging of deleterious alleles in zoo populations. The formula of Ballou assumes independence of inbreeding and ancestral inbreeding coefficients at any stage of the recursion. This study investigates the consequences of this inaccuracy on the estimation of true ancestral inbreeding, i.e. the proportion of alleles within a genome that has undergone inbreeding in the past. As an alternative we propose the estimation of ancestral inbreeding by the method of gene dropping. The methods are compared by stochastic simulation for various models with respect to mode of inheritance (neutral, detrimental and lethal alleles) and different settings for population size and initial allele frequencies. In all scenarios the proportion of alleles within a genome that has undergone inbreeding in the past was overestimated by Ballou’s formula. The overestimation was more pronounced in smaller populations but was not affected by genetic model or initial allele frequency. In contrast, the ancestral inbreeding coefficient calculated by gene dropping provided a robust estimate of ancestral inbreeding in most models and settings. A marginal overestimation was observed only in models with lethal alleles. Therefore, we recommend applying the gene dropping approach to estimate ancestral inbreeding coefficients.     

Incorporation of new founders into captive populations

This report describes preliminary studies intended to develop generalizations for the optimal incorporation of newcomers into breeding pools. Small populations, which grow from four to a stable size of 16 animals per generation, were simulated on a computer. New founders were introduced and various breeding schemes tried and evaluated for their effect on inbreeding coefficients and founder representation. Two variables were examined for their effects on inbreeding and founder representation: number of progeny produced by crossing new founders with the established population, and number of mates the new founder had from the established population. Increasing the value of these variables to the point at which new-founder representation was equal to the original founders' representations decreased inbreeding. Beyond this point, inbreeding increased.