Estimation of genetic purging under competitive conditions

Inbreeding Depression and Purging in Fertility and Longevity Traits in Sheep Breeds from Germany

In the present study, we analysed fertility and longevity traits of 22 sheep breeds from Germany with a suitable quantity of data in the national database OviCap. The data comprised merino, meat, country and milk sheep breeds with 62,198 ewes and about 173,000 lambing records, until the fifth lambing. Across-breed means of heritabilities reached estimates of 0.13, 0.17 and 0.18 for number of lambings, average number of lambs born per lambing and number of lambs per lifetime, respectively. For age at first lambing, length of lifetime and productive life, mean heritabilities over breeds were 0.34, 0.17 and 0.32, respectively. The across-breed means of the individual rate of inbreeding were significantly negative for the average number of lambs born per lambing and number of lambs born per lifetime, and for number of lambings it was close to the significance threshold. We found declining slopes for inbreeding depression for the average number of lambs born per lambing and number of lambs born per lifetime in 16 breeds, and significantly negative slopes in five and seven breeds. For lifetime and productive life, 9/22 and 8/22 breeds showed significant inbreeding depression, while for age at first lambing, only 1/22 breeds showed significant inbreeding depression. A significant reduction in inbreeding depression due to purging effects was found for eight breeds. Fitness traits may be subject to forced directional selection. Therefore, sheep breeding programmes should give special consideration to fertility and longevity traits. Fitness related traits seem to be essential in conservation of genetic diversity within sheep breeds.

Characterizing and Eliminating the Inbreeding Load

The authors evaluated the relevant literature related to purging, which is the interaction between selection and inbreeding in which the population may eliminate its inbreeding load at least partially. According to the relevant literature, the inbreeding load and the process of purging were evaluated via pedigree methods based on ancestral inbreeding, the inbreeding-purging model, and expressed opportunity of purging, along with genomic methods. Most ancestral inbreeding-related studies were performed in zoos, where only a small proportion of the studied populations show signs of purging. The inbreeding-purging model was developed with Drosophila, and it was used to evaluate different zoo ungulates and Pannon white rabbits. Purging was detected in both studies. The expressed opportunity of purging was applied in Jersey cattle and Pannon white rabbits. In the Jersey cattle, it had an effect of 12.6% for fitness, while in the Pannon white rabbits, the inbreeding load was between 40% and 80% of its original value. The genomic studies also signalled purging, but they also made it clear that, contrary to the detected purging, the evaluated populations still suffered from inbreeding depression. Therefore, especially for domesticated animals, it can be concluded that deliberate inbreeding with the purpose of generating purging is not advocated.

An empirical test of the estimation of historical effective population size using Drosophila melanogaster

The availability of a large number of high-density markers (SNPs) allows the estimation of historical effective population size (Ne ) from linkage disequilibrium between loci. A recent refinement of methods to estimate historical Ne from the recent past has been shown to be rather accurate with simulation data. The method has also been applied to real data for numerous species. However, the simulation data cannot encompass all the complexities of real genomes, and the performance of any estimation method with real data is always uncertain, as the true demography of the populations is not known. Here, we carried out an experimental design with Drosophila melanogaster to test the method with real data following a known demographic history. We used a population maintained in the laboratory with a constant census size of about 2800 individuals and subjected the population to a drastic decline to a size of 100 individuals. After a few generations, the population was expanded back to the previous size and after a few further generations again expanded to twice the initial size. Estimates of historical Ne were obtained with the software GONE both for autosomal and X chromosomes from samples of 17 individuals sequenced for the whole genome. Estimates of the historical effective size were able to infer the patterns of changes that occurred in the populations showing generally good performance of the method. We discuss the limitations of the method and the application of the software carried out so far.

Impact of Inbreeding and Ancestral Inbreeding on Longevity Traits in German Brown Cows

A recent study on the population structure of the German Brown population found increasing levels of classical and ancestral inbreeding coefficients. Thus, the aim of this study was to determine the effects of inbreeding depression and purging on longevity traits using classical and ancestral inbreeding coefficients according to Kalinowski (2002) (Fa_Kal, FNew), Ballou (1997) (Fa_Bal), and Baumung (2015) (Ahc). For this purpose, uncensored data of 480,440 cows born between 1990 and 2001 were available. We analyzed 17 longevity traits, including herd life, length of productive life, number of calvings, lifetime and effective lifetime production for milk, fat, and protein yield, the survival to the 2nd, 4th, 6th, 8th, and 10th lactation number, and the culling frequencies due to infertility, or udder and foot and leg problems. Inbreeding depression was significant and negative for all traits but for culling due to udder and to foot and leg problems. When expressed in percentages of genetic standard deviations, inbreeding depression per 1% increase in inbreeding was -3.61 to -10.98%, -2.42 to -2.99%, -2.21 to -4.58%, and 5.13% for lifetime production traits, lifetime traits, survival rates, and culling due to infertility, respectively. Heterosis and recombination effects due to US Brown Swiss genes were positive and counteracted inbreeding depression. The effects of FNew were not significantly different from zero, while Fa_Kal had negative effects on lifetime and lifetime production traits. Similarly, the interaction of F with Fa_Bal was significantly negative. Thus, purging effects could not be shown for longevity traits in German Brown. A possible explanation may be seen in the breed history of the German Brown, that through the introgression of US Brown Swiss bulls ancestral inbreeding increased and longevity decreased. Our results show, that reducing a further increase in inbreeding in mating plans is advisable to prevent a further decline in longevity due to inbreeding depression, as purging effects were very unlikely in this population.

An empirical evaluation of the estimation of inbreeding depression from molecular markers under suboptimal conditions

Inbreeding depression (ID), the reduction in fitness due to inbreeding, is typically measured by the regression of the phenotypic values of individuals for a particular trait on their corresponding inbreeding coefficients (F). While genealogical records can provide these coefficients, they may be unavailable or incomplete, making molecular markers a useful alternative. The power to detect ID and its accuracy depend on the variation of F values of individuals, the sample sizes available, and the accuracy in the estimation of individual fitness traits and F values. In this study, we used Drosophila melanogaster to evaluate the effectiveness of molecular markers in estimating ID under suboptimal conditions. We generated two sets of 100 pairs of unrelated individuals from a large panmictic population and mated them for two generations to produce non-inbred and unrelated individuals (F = 0) and inbred individuals (full-sib progeny; F = 0.25). Using these expected genealogical F values, we calculated inbreeding depression for two fitness-related traits, pupae productivity and competitive fitness. We then sequenced the males from 17 non-inbred pairs and 17 inbred pairs to obtain their genomic inbreeding coefficients and estimate ID for the two traits. The scenario assumed was rather restrictive in terms of estimation of ID because: (1) the individuals belonged to the same generation of a large panmictic population, leading to low variation in individual F coefficients; (2) the sample sizes were small; and (3) the traits measured depended on both males and females while only males were sequenced. Despite the challenging conditions of our study, we found that molecular markers provided estimates of ID that were comparable to those obtained from simple pedigree estimations with larger sample sizes. The results therefore suggest that genomic measures of inbreeding are useful to provide estimates of inbreeding depression even under very challenging scenarios.

Analysis of Inbreeding Effects on Survival at Birth of Pannon White Rabbits Using the Inbreeding-Purging Model

Mating between related animals is an inevitable consequence of a closed population structure especially when it coincides with a small population size. As a result, inbreeding depression may be encountered especially when considering fitness traits. However, under certain circumstances, the joint effects of inbreeding and selection may at least partly purge the detrimental genes from the population. In the course of this study, our objective was to determine the status of purging and to quantify the magnitude of the eliminated genetic load for the survival at birth of Pannon White rabbit kits maintained in a closed nucleus population. The evolution of the survival at birth was evaluated by applying the PurgeR R package based on the inbreeding-purging model. In the period from 1992 to 2017, 22.718 kindling records were analyzed. According to the heuristic approach, the purging coefficient reached the maximum possible value of 0.5 when estimating between 1992 and 1997. Based on the expected fitness over generations and on the expressed opportunity of purging, the beneficial effects of purging could be expected after 10 generations. The proportion of the purged genetic load could be between 20% and 60%. While the results obtained are not entirely conclusive, they do raise the possibility that some of the inbreeding load was caused, at least in part, by genes that could be successfully removed from the population by purging.

Evolution of selfing syndrome and its influence on genetic diversity and inbreeding: A range-wide study in Oenothera primiveris

PREMISE

To avoid inbreeding depression, plants have evolved diverse breeding systems to favor outcrossing, such as self-incompatibility. However, changes in biotic and abiotic conditions can result in selective pressures that lead to a breakdown in self-incompatibility. The shift to increased selfing is commonly associated with reduced floral features, lower attractiveness to pollinators, and increased inbreeding. We tested the hypothesis that the loss of self-incompatibility, a shift to self-fertilization (autogamy), and concomitant evolution of the selfing syndrome (reduction in floral traits associated with cross-fertilization) will lead to increased inbreeding and population differentiation in Oenothera primiveris. Across its range, this species exhibits a shift in its breeding system and floral traits from a self-incompatible population with large flowers to self-compatible populations with smaller flowers.

METHODS

We conducted a breeding system assessment, evaluated floral traits in the field and under controlled conditions, and measured population genetic parameters using RADseq data.

RESULTS

Our results reveal a bimodal transition to the selfing syndrome from the west to the east of the range of O. primiveris. This shift includes variation in the breeding system and the mating system, a reduction in floral traits (flower diameter, herkogamy, and scent production), a shift to greater autogamy, reduced genetic diversity, and increased inbreeding.

CONCLUSIONS

The observed variation highlights the importance of range-wide studies to understand breeding system variation and the evolution of the selfing syndrome within populations and species.

Purging of deleterious burden in the endangered Iberian lynx

SignificanceThe dynamics of deleterious variation under contrasting demographic scenarios remain poorly understood in spite of their relevance in evolutionary and conservation terms. Here we apply a genomic approach to study differences in the burden of deleterious alleles between the endangered Iberian lynx (Lynx pardinus) and the widespread Eurasian lynx (Lynx lynx). Our analysis unveils a significantly lower deleterious burden in the former species that should be ascribed to genetic purging, that is, to the increased opportunities of selection against recessive homozygotes due to the inbreeding caused by its smaller population size, as illustrated by our analytical predictions. This research provides theoretical and empirical evidence on the evolutionary relevance of genetic purging under certain demographic conditions.

Genomic evidence for inbreeding depression and purging of deleterious genetic variation in Indian tigers

Increasing habitat fragmentation leads to wild populations becoming small, isolated, and threatened by inbreeding depression. However, small populations may be able to purge recessive deleterious alleles as they become expressed in homozygotes, thus reducing inbreeding depression and increasing population viability. We used whole-genome sequences from 57 tigers to estimate individual inbreeding and mutation load in a small-isolated and two large-connected populations in India. As expected, the small-isolated population had substantially higher average genomic inbreeding (FROH = 0.57) than the large-connected (FROH = 0.35 and FROH = 0.46) populations. The small-isolated population had the lowest loss-of-function mutation load, likely due to purging of highly deleterious recessive mutations. The large populations had lower missense mutation loads than the small-isolated population, but were not identical, possibly due to different demographic histories. While the number of the loss-of-function alleles in the small-isolated population was lower, these alleles were at higher frequencies and homozygosity than in the large populations. Together, our data and analyses provide evidence of 1) high mutation load, 2) purging, and 3) the highest predicted inbreeding depression, despite purging, in the small-isolated population. Frequency distributions of damaging and neutral alleles uncover genomic evidence that purifying selection has removed part of the mutation load across Indian tiger populations. These results provide genomic evidence for purifying selection in both small and large populations, but also suggest that the remaining deleterious alleles may have inbreeding-associated fitness costs. We suggest that genetic rescue from sources selected based on genome-wide differentiation could offset any possible impacts of inbreeding depression.

Genetic purging in captive endangered ungulates with extremely low effective population sizes

Inbreeding threatens the survival of small populations by producing inbreeding depression, but also exposes recessive deleterious effects in homozygosis allowing for genetic purging. Using inbreeding-purging theory, we analyze early survival in four pedigreed captive breeding programs of endangered ungulates where population growth was prioritized so that most adult females were allowed to contribute offspring according to their fitness. We find evidence that purging can substantially reduce inbreeding depression in Gazella cuvieri (with effective population size N_e = 14) and Nanger dama (N_e = 11). No purging is detected in Ammotragus lervia (N_e = 4), in agreement with the notion that drift overcomes purging under fast inbreeding, nor in G. dorcas (N_e = 39) where, due to the larger population size, purging is slower and detection is expected to require more generations. Thus, although smaller populations are always expected to show smaller fitness (as well as less adaptive potential) than larger ones due to higher homozygosis and deleterious fixation, our results show that a substantial fraction of their inbreeding load and inbreeding depression can be purged when breeding contributions are governed by natural selection. Since management strategies intended to maximize the ratio from the effective to the actual population size tend to reduce purging, the search for a compromise between these strategies and purging could be beneficial in the long term. This could be achieved either by allowing some level of random mating and some role of natural selection in determining breeding contributions, or by undertaking reintroductions into the wild at the earliest opportunity.

Reviewing the consequences of genetic purging on the success of rescue programs

Genetic rescue is increasingly considered a promising and underused conservation strategy to reduce inbreeding depression and restore genetic diversity in endangered populations, but the empirical evidence supporting its application is limited to a few generations. Here we discuss on the light of theory the role of inbreeding depression arising from partially recessive deleterious mutations and of genetic purging as main determinants of the medium to long-term success of rescue programs. This role depends on two main predictions: (1) The inbreeding load hidden in populations with a long stable demography increases with the effective population size; and (2) After a population shrinks, purging tends to remove its (partially) recessive deleterious alleles, a process that is slower but more efficient for large populations than for small ones. We also carry out computer simulations to investigate the impact of genetic purging on the medium to long term success of genetic rescue programs. For some scenarios, it is found that hybrid vigor followed by purging will lead to sustained successful rescue. However, there may be specific situations where the recipient population is so small that it cannot purge the inbreeding load introduced by migrants, which would lead to increased fitness inbreeding depression and extinction risk in the medium to long term. In such cases, the risk is expected to be higher if migrants came from a large non-purged population with high inbreeding load, particularly after the accumulation of the stochastic effects ascribed to repeated occasional migration events. Therefore, under the specific deleterious recessive mutation model considered, we conclude that additional caution should be taken in rescue programs. Unless the endangered population harbors some distinctive genetic singularity whose conservation is a main concern, restoration by continuous stable gene flow should be considered, whenever feasible, as it reduces the extinction risk compared to repeated occasional migration and can also allow recolonization events.

Long-term exhaustion of the inbreeding load in Drosophila melanogaster

Inbreeding depression, the decline in fitness of inbred individuals, is a ubiquitous phenomenon of great relevance in evolutionary biology and in the fields of animal and plant breeding and conservation. Inbreeding depression is due to the expression of recessive deleterious alleles that are concealed in heterozygous state in noninbred individuals, the so-called inbreeding load. Genetic purging reduces inbreeding depression by removing these alleles when expressed in homozygosis due to inbreeding. It is generally thought that fast inbreeding (such as that generated by full-sib mating lines) removes only highly deleterious recessive alleles, while slow inbreeding can also remove mildly deleterious ones. However, a question remains regarding which proportion of the inbreeding load can be removed by purging under slow inbreeding in moderately large populations. We report results of two long-term slow inbreeding Drosophila experiments (125-234 generations), each using a large population and a number of derived lines with effective sizes about 1000 and 50, respectively. The inbreeding load was virtually exhausted after more than one hundred generations in large populations and between a few tens and over one hundred generations in the lines. This result is not expected from genetic drift alone, and is in agreement with the theoretical purging predictions. Computer simulations suggest that these results are consistent with a model of relatively few deleterious mutations of large homozygous effects and partially recessive gene action.

Detecting purging of inbreeding depression by a slow rate of inbreeding for various traits: the impact of environmental and experimental conditions

Inbreeding depression (ID) has since long been recognized as a significant factor in evolutionary biology. It is mainly the consequence of (partially) recessive deleterious mutations maintained by mutation-selection balance in large random mating populations. When population size is reduced, recessive alleles are increasingly found in homozygous condition due to drift and inbreeding and become more prone to selection. Particularly at slow rates of drift and inbreeding, selection will be more effective in purging such alleles, thereby reducing the amount of ID. Here we test assumptions of the efficiency of purging in relation to the inbreeding rate and the experimental conditions for four traits in D. melanogaster. We investigated the magnitude of ID for lines that were inbred to a similar level, F ≈ 0.50, reached either by three generations of full-sib mating (fast inbreeding), or by 12 consecutive generations with a small population size (slow inbreeding). This was done on two different food media. We observed significant ID for egg-to-adult viability and heat shock mortality, but only for egg-to-adult viability a significant part of the expressed inbreeding depression was effectively purged under slow inbreeding. For other traits like developmental time and starvation resistance, however, adaptation to the experimental and environmental conditions during inbreeding might affect the likelihood of purging to occur or being detected. We discuss factors that can affect the efficiency of purging and why empirical evidence for purging may be ambiguous.

How Depressing Is Inbreeding? A Meta-Analysis of 30 Years of Research on the Effects of Inbreeding in Livestock

Inbreeding depression has been widely documented for livestock and other animal and plant populations. Inbreeding is generally expected to have a stronger unfavorable effect on fitness traits than on other traits. Traditionally, the degree of inbreeding depression in livestock has been estimated as the slope of the linear regression of phenotypic values on pedigree-based inbreeding coefficients. With the increasing availability of SNP-data, pedigree inbreeding can now be replaced by SNP-based measures. We performed a meta-analysis of 154 studies, published from 1990 to 2020 on seven livestock species, and compared the degree of inbreeding depression (1) across different trait groups, and (2) across different pedigree-based and SNP-based measures of inbreeding. Across all studies and traits, a 1% increase in pedigree inbreeding was associated with a median decrease in phenotypic value of 0.13% of a trait’s mean, or 0.59% of a trait’s standard deviation. Inbreeding had an unfavorable effect on all sorts of traits and there was no evidence for a stronger effect on primary fitness traits (e.g., reproduction/survival traits) than on other traits (e.g., production traits or morphological traits). p-values of inbreeding depression estimates were smaller for SNP-based inbreeding measures than for pedigree inbreeding, suggesting more power for SNP-based measures. There were no consistent differences in p-values for percentage of homozygous SNPs, inbreeding based on runs of homozygosity (ROH) or inbreeding based on a genomic relationship matrix. The number of studies that directly compares these different measures, however, is limited and comparisons are furthermore complicated by differences in scale and arbitrary definitions of particularly ROH-based inbreeding. To facilitate comparisons across studies in future, we provide the dataset with inbreeding depression estimates of 154 studies and stress the importance of always reporting detailed information (on traits, inbreeding coefficients, and models used) along with inbreeding depression estimates.

The ecological causes and consequences of hard and soft selection

Interactions between natural selection and population dynamics are central to both evolutionary-ecology and biological responses to anthropogenic change. Natural selection is often thought to incur a demographic cost that, at least temporarily, reduces population growth. However, hard and soft selection clarify that the influence of natural selection on population dynamics depends on ecological context. Under hard selection, an individual's fitness is independent of the population's phenotypic composition, and substantial population declines can occur when phenotypes are mismatched with the environment. In contrast, under soft selection, an individual's fitness is influenced by its phenotype relative to other interacting conspecifics. Soft selection generally influences which, but not how many, individuals survive and reproduce, resulting in little effect on population growth. Despite these important differences, the distinction between hard and soft selection is rarely considered in ecology. Here, we review and synthesize literature on hard and soft selection, explore their ecological causes and implications and highlight their conservation relevance to climate change, inbreeding depression, outbreeding depression and harvest. Overall, these concepts emphasise that natural selection and evolution may often have negligible or counterintuitive effects on population growth-underappreciated outcomes that have major implications in a rapidly changing world.

On the estimation of inbreeding depression using different measures of inbreeding from molecular markers

The inbreeding coefficient (F) of individuals can be estimated from molecular marker data, such as SNPs, using measures of homozygosity of individual markers or runs of homozygosity (ROH) across the genome. These different measures of F can then be used to estimate the rate of inbreeding depression (ID) for quantitative traits. Some recent simulation studies have investigated the accuracy of this estimation with contradictory results. Whereas some studies suggest that estimates of inbreeding from ROH account more accurately for ID, others suggest that inbreeding measures from SNP-by-SNP homozygosity giving a large weight to rare alleles are more accurate. Here, we try to give more light on this issue by carrying out a set of computer simulations considering a range of population genetic parameters and population sizes. Our results show that the previous studies are indeed not contradictory. In populations with low effective size, where relationships are more tight and selection is relatively less intense, F measures based on ROH provide very accurate estimates of ID whereas SNP-by-SNP-based F measures with high weight to rare alleles can show substantial upwardly biased estimates of ID. However, in populations of large effective size, with more intense selection and trait allele frequencies expected to be low if they are deleterious for fitness because of purifying selection, average estimates of ID from SNP-by-SNP-based F values become unbiased or slightly downwardly biased and those from ROH-based F values become slightly downwardly biased. The noise attached to all these estimates, nevertheless, can be very high in large-sized populations. We also investigate the relationship between the different F measures and the homozygous mutation load, which has been suggested as a proxy of inbreeding depression.

Effects of Long-Term Selection in the Border Collie Dog Breed: Inbreeding Purge of Canine Hip and Elbow Dysplasia

Simple Summary

For dog breeders, health is one of the main criteria when choosing a breeding animal; thus, selection for good anatomy is the key to reduce orthopedic disorders. In many dog breeds, radiographic screening for canine hip and elbow dysplasia is a compulsory test for breeding; however, these multifactorial traits are determined by genetic and environmental factors. Therefore, it is extremely difficult to eliminate these disorders from the population. In natural selection, such traits can be “purged” out of the population with inbreeding. The study aimed to examine the inbreeding-purge of canine hip and elbow dysplasia in the border collie breed. The main conclusion was that over-representation of homozygous individuals may have a positive effect on hip and elbow conformation.

Abstract

Pedigree data of 13,339 border collie dog was collected along with canine hip dysplasia (CHD) and canine elbow dysplasia (CED) records (1352 CHD and 524 CED), and an inbreeding–purging (IP) model was created. Ancestral inbreeding coefficients were calculated by using a gene dropping simulation method with GRain 2.2 software. Cumulative logit models (CLM) for CHD and CED were fitted using a logit-link Poisson distribution and the classical (F__W), and ancestral inbreeding (F__BAL, F__KAL, and F__{KAL_NEW}) coefficients as linear regression coefficients. The effective population size was calculated from F__W and decreased in the examined period along with an increase of F__W; however, slight differences were found as a consequence of breeding dog imports. CHD values were lowered by the expansion of F__BAL, as the alleles had been inbred in the past. For CHD, signs of purging were obtained. There was a positive trend regarding the breeding activity (both sire and dam of the future litters should be screened and certified free from CHD and CED), as years of selection increased the frequency of alleles with favorable hip and elbow conformation. Division of the ancestral inbreeding coefficient showed that alleles that had been identical by descent (IBD) for the first time (F__{KAL_NEW}) had a negative effect on both traits, while F__KAL has shown favorable results for alleles IBD in past generations. Some authors had proven this phenomenon in captive populations or experimental conditions; however, no evidence of inbreeding purge has ever been described in dog populations. Despite the various breeding practices, it seems that alleles of these polygenic disorders could be successfully purged out of the population with long-term selection.

Accelerated inbreeding depression suggests synergistic epistasis for deleterious mutations in Drosophila melanogaster

Epistasis may have important consequences for a number of issues in quantitative genetics and evolutionary biology. In particular, synergistic epistasis for deleterious alleles is relevant to the mutation load paradox and the evolution of sex and recombination. Some studies have shown evidence of synergistic epistasis for spontaneous or induced deleterious mutations appearing in mutation-accumulation experiments. However, many newly arising mutations may not actually be segregating in natural populations because of the erasing action of natural selection. A demonstration of synergistic epistasis for naturally segregating alleles can be achieved by means of inbreeding depression studies, as deleterious recessive allelic effects are exposed in inbred lines. Nevertheless, evidence of epistasis from these studies is scarce and controversial. In this paper, we report the results of two independent inbreeding experiments carried out with two different populations of Drosophila melanogaster. The results show a consistent accelerated inbreeding depression for fitness, suggesting synergistic epistasis among deleterious alleles. We also performed computer simulations assuming different possible models of epistasis and mutational parameters for fitness, finding some of them to be compatible with the results observed. Our results suggest that synergistic epistasis for deleterious mutations not only occurs among newly arisen spontaneous or induced mutations, but also among segregating alleles in natural populations.

Detection of genetic purging and predictive value of purging parameters estimated in pedigreed populations

The consequences of inbreeding for fitness are important in evolutionary and conservation biology, but can critically depend on genetic purging. However, estimating purging has proven elusive. Using PURGd software, we assess the performance of the Inbreeding-Purging (IP) model and of ancestral inbreeding (F_a) models to detect purging in simulated pedigreed populations, and to estimate parameters that allow reliably predicting the evolution of fitness under inbreeding. The power to detect purging in a single small population of size N is low for both models during the first few generations of inbreeding (t ≈ N/2), but increases for longer periods of slower inbreeding and is, on average, larger for the IP model. The ancestral inbreeding approach overestimates the rate of inbreeding depression during long inbreeding periods, and produces joint estimates of the effects of inbreeding and purging that lead to unreliable predictions for the evolution of fitness. The IP estimates of the rate of inbreeding depression become downwardly biased when obtained from long inbreeding processes. However, the effect of this bias is canceled out by a coupled downward bias in the estimate of the purging coefficient so that, unless the population is very small, the joint estimate of these two IP parameters yields good predictions of the evolution of mean fitness in populations of different sizes during periods of different lengths. Therefore, our results support the use of the IP model to detect inbreeding depression and purging, and to estimate reliable parameters for predictive purposes.

Detection of barriers to dispersal is masked by long lifespans and large population sizes

Population genetic analyses of species inhabiting fragmented landscapes are essential tools for conservation. Occasionally, analyses of fragmented populations find no evidence of isolation, even though a barrier to dispersal is apparent. In some cases, not enough time may have passed to observe divergence due to genetic drift, a problem particularly relevant for long‐lived species with overlapping generations. Failing to consider this quality during population structure analyses could result in incorrect conclusions about the impact of fragmentation on the species. We designed a model to explore how lifespan and population size influence perceived population structure of isolated populations over time. This iterative model tracked how simulated populations of variable lifespan and population size were affected by drift alone, using a freshwater mussel, Quadrula quadrula (mapleleaf), as a model system. In addition to exhibiting dramatic lifespan variability among species, mussels are also highly imperiled and exhibit fragmentation by dams throughout the range of many species. Results indicated that, unless population size was small (<50 individuals) or lifespan short (<22 years), observing genetic divergence among populations was unlikely. Even if wild populations are isolated, observing population structure in long‐lived mussels from modern damming practices is unlikely because it takes longer for population structure to develop in these species than most North American dams have existed. Larger population sizes and longer lifespans increase the time needed for significant divergence to occur. This study helps illuminate the factors that influence genetic responses by populations to isolation and provides a useful model for conservation‐oriented research.

Mathematical modelling for variations of inbreeding populations fitness with single and polygenic traits

BACKGROUND

Inbreeding mating has been widely accepted as the key mechanism to enhance homozygosity which normally will decrease the fitness of the population. Although this result has been validated by a large amount of biological data from the natural populations, a mathematical proof of these experimental discoveries is still not complete. A related question is whether we can extend the well-established result regarding the mean fitness from a randomly mating population to inbreeding populations. A confirmative answer may provide insights into the frequent occurrence of self-fertilization populations.

RESULTS

This work presents a theoretic proof of the result that, for a large inbreeding population with directional relative genotype fitness, the mean fitness of population increases monotonically. However, it cannot be extended to the case with over-dominant genotype fitness. In addition, by employing multiplicative intersection hypothesis, we prove that inbreeding mating does decrease the mean fitness of polygenic population in general, but does not decrease the mean fitness with mixed dominant-recessive genotypes. We also prove a novel result that inbreeding depression depends on not only the mating pattern but also genetic structure of population.

CONCLUSIONS

For natural inbreeding populations without serious inbreeding depression, our theoretical analysis suggests the majority of its genotypes should be additive or dominant-recessive genotypes. This result gives a reason to explain why many hermaphroditism populations do not show severe inbreeding depression. In addition, the calculated purging rate shows that inbreeding mating purges the deleterious mutants more efficiently than randomly mating does.

Inbreeding load and purging: implications for the short-term survival and the conservation management of small populations

Using computer simulations, we evaluate the effects of genetic purging of inbreeding load in small populations, assuming genetic models of deleterious mutations which account for the typical amount of load empirically observed. Our results show that genetic purging efficiently removes the inbreeding load of both lethal and non-lethal mutations, reducing the amount of inbreeding depression relative to that expected without selection. We find that the minimum effective population size to avoid severe inbreeding depression in the short term is of the order of Ne≈70 for a wide range of species' reproductive rates. We also carried out simulations of captive breeding populations where two contrasting management methods are performed, one avoiding inbreeding (equalisation of parental contributions (EC)) and the other forcing it (circular sib mating (CM)). We show that, for the inbreeding loads considered, CM leads to unacceptably high extinction risks and, as a result, to lower genetic diversity than EC. Thus we conclude that methods aimed at enhancing purging by intentional inbreeding should not be generally advised in captive breeding conservation programmes.

Predictive Model and Software for Inbreeding-Purging Analysis of Pedigreed Populations

The inbreeding depression of fitness traits can be a major threat to the survival of populations experiencing inbreeding. However, its accurate prediction requires taking into account the genetic purging induced by inbreeding, which can be achieved using a “purged inbreeding coefficient”. We have developed a method to compute purged inbreeding at the individual level in pedigreed populations with overlapping generations. Furthermore, we derive the inbreeding depression slope for individual logarithmic fitness, which is larger than that for the logarithm of the population fitness average. In addition, we provide a new software, PURGd, based on these theoretical results that allows analyzing pedigree data to detect purging, and to estimate the purging coefficient, which is the parameter necessary to predict the joint consequences of inbreeding and purging. The software also calculates the purged inbreeding coefficient for each individual, as well as standard and ancestral inbreeding. Analysis of simulation data show that this software produces reasonably accurate estimates for the inbreeding depression rate and for the purging coefficient that are useful for predictive purposes.