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.     

Effects of Interference Between Selected Loci on the Mutation Load,Inbreeding Depression,and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.     

Familial versus mass selection in small populations

We used diffusion approximations and a Markov-chain approach to investigate the consequences of familial selection on the viability of small populations both in the short and in the long term. The outcome of familial selection was compared to the case of a random mating population under mass selection. In small populations, the higher effective size, associated with familial selection, resulted in higher fitness for slightly deleterious and/or highly recessive alleles. Conversely, because familial selection leads to a lower rate of directional selection, a lower fitness was observed for more detrimental genes that are not highly recessive, and with high population sizes. However, in the long term, genetic load was almost identical for both mass and familial selection for populations of up to 200 individuals. In terms of mean time to extinction, familial selection did not have any negative effect at least for small populations (N ≤ 50). Overall, familial selection could be proposed for use in management programs of small populations since it increases genetic variability and short-term viability without impairing the overall persistence times.     

Selection in a subdivided population with local extinction and recolonization

In a subdivided population, local extinction and subsequent recolonization affect the fate of alleles. Of particular interest is the interaction of this force with natural selection. The effect of selection can be weakened by this additional source of stochastic change in allele frequency. The behavior of a selected allele in such a population is shown to be equivalent to that of an allele with a different selection coefficient in an unstructured population with a different size. This equivalence allows use of established results for panmictic populations to predict such quantities as fixation probabilities and mean times to fixation. The magnitude of the quantity N(e)s(e), which determines fixation probability, is decreased by extinction and recolonization. Thus deleterious alleles are more likely to fix, and advantageous alleles less likely to do so, in the presence of extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Reduced population size can induce quick evolution of inbreeding depression in the invasive ladybird <Emphasis Type="Italic">Harmonia axyridis</Emphasis>

Understanding biological invasion is currently one of the main scientific challenges for ecologists. The introduction process is crucial for the success of an invasion, especially when it involves a demographic bottleneck. A small introduced population is expected to face a higher risk of extinction before the first stage of invasion is complete if inbreeding depression, caused by the expression of deleterious alleles, is important. Changes in mating regimes or in population size can induce the evolution of deleterious allele frequencies, either by selection or by drift, possibly resulting in the purging or the fixation of such alleles within the population. The harlequin ladybird Harmonia axyridis became invasive on several continents following a scenario including at least one event of demographic bottleneck. Although native populations suffered from severe inbreeding depression, it was greatly reduced in invasive ones suggesting that deleterious alleles were purged during the invasion process. In this study, we performed an experiment designed to manipulate the effective population size of H. axyridis across successive generations to mimic contrasting introduction events. We used the measurement of two fitness-related phenotypic traits in order to test (1) if inbreeding depression can evolve at the time-scale of an invasion; and (2) if the changes in inbreeding depression following a bottleneck in laboratory conditions are compatible with the purging of deleterious alleles observed in this species. We found that two generations of very low population size are enough to induce a substantial change in inbreeding depression. Although the genetic changes mostly consisted in fixation of deleterious alleles, purging did also occur, sometimes simultaneously with fixation.     

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).     

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.Subject terms: Evolutionary genetics, Inbreeding     

Genetic components of variation in Nemophila menziesii undergoing inbreeding: morphology and flowering time.

The standard approaches to estimation of quantitative genetic parameters and prediction of response to selection on quantitative traits are based on theory derived for populations undergoing random mating. Many studies demonstrate, however, that mating systems in natural populations often involve inbreeding in various degrees (i.e. , self matings and matings between relatives). Here we apply theory developed for estimating quantitative genetic parameters for partially inbreeding populations to a population of Nemophila menziesii recently obtained from nature and experimentally inbred. Two measures of overall plant size and two of floral size expressed highly significant inbreeding depression. Of three dominance components of phenotypic variance that are defined under partial inbreeding, one was found to contribute significantly to phenotypic variance in flower size and flowering time, while the remaining two components contributed only negligibly to variation in each of the five traits considered. Computer simulations investigating selection response under the more complete genetic model for populations undergoing mixed mating indicate that, for parameter values estimated in this study, selection response can be substantially slowed relative to predictions for a random mating population. Moreover, inbreeding depression alone does not generally account for the reduction in selection response.     

Effects of population size and metapopulation dynamics on a mating-system polymorphism

The evolutionary dynamics of neutral alleles under the Wright-Fisher model are well understood. Similarly, the effect of population turnover on neutral genetic diversity in a metapopulation has attracted recent attention in theoretical studies. Here we present the results of computer simulations of a simple model that considers the effects of finite population size and metapopulation dynamics on a mating-system polymorphism involving selfing and outcrossing morphs. The details of the model are based on empirical data from dimorphic populations of the annual plant Eichhornia paniculata, but the results are also of relevance to species with density-dependent selfing rates in general. In our model, the prior selfing rate is determined by two alleles segregating at a single diploid locus. After prior selfing occurs, some remaining ovules are selfed through competing self-fertilisation in finite populations as a result of random mating among gametes. Fitness differences between the mating-system morphs were determined by inbreeding depression and pollen discounting in a context-dependent manner. Simulation results showed evidence of frequency dependence in the action of pollen discounting and inbreeding depression in finite populations. In particular, as a result of selfing in outcrossers through random mating among gametes, selfers experienced a "fixation bias" through drift, even when the mating-system locus was selectively neutral. In a metapopulation, high colony turnover generally favoured the fixation of the outcrossing morph, because inbreeding depression reduced opportunities for colony establishment by selfers through seed dispersal. Our results thus demonstrate that population size and metapopulation processes can lead to evolutionary dynamics involving pollen and seed dispersal that are not predicted for large populations with stable demography.     

Optimal mass selection policies for schemes with overlapping generations and restricted inbreeding

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG - λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.     

Individual Variation in Inbreeding Depression: The Roles of Inbreeding History and Mutation

We use mutation-selection recursion models to evaluate the relative contributions of mutation and inbreeding history to variation among individuals in inbreeding depression and the ability of experiments to detect associations between individual inbreeding depression and mating system genotypes within populations. Poisson mutation to deleterious additive or recessive alleles generally produces far more variation among individuals in inbreeding depression than variation in history of inbreeding, regardless of selfing rate. Moreover, variation in inbreeding depression can be higher in a completely outcrossing or selfing population than in a mixed-mating population. In an initially random mating population, the spread of a dominant selfing modifier with no pleiotropic effects on male outcross success causes a measurable increase in inbreeding depression variation if its selfing rate is large and inbreeding depression is caused by recessive lethals. This increase is observable during a short period as the modifier spreads rapidly to fixation. If the modifier alters selfing rate only slightly, it fails to spread or causes no measurable increase in inbreeding depression variance. These results suggest that genetic associations between mating loci and inbreeding depression loci could be difficult to demonstrate within populations and observable only transiently during rapid evolution to a substantially new selfing rate.     

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.     

Inbreeding and extinction: Effects of rate of inbreeding

Deleterious alleles may be removed (purged) bynatural selection in populations undergoinginbreeding. However, there is controversyregarding the effectiveness of selection inreducing the risk of extinction due toinbreeding, especially in relation to the rateof inbreeding. We evaluated the effect of therate of inbreeding on reducing extinction risk,in populations of Drosophila melanogastermaintained using full-sib mating (160replicates), or at effective population sizes(N _e) of 10 (80) or 20 (80).Extinction rates in the populations maintainedusing full-sib mating occurred at lower levelsof inbreeding than in the larger populations,whereas the two larger populations did notdiffer significantly from each other.Inbreeding coefficients at 50% extinction were0.62, 0.79 and 0.77 for the full-sib (N _e = 2.6), N _e = 10 and N _e = 20 treatments, respectively. Populations of N _e = 20 that remained extant after 60 generations, showed inbreeding depression, with the mean fitness of these populations being only 45% of the outbredcontrols. There was considerable variationamong the 31 inbred populations in fitness, butnone of the N _e = 20 populations hadfitness that was higher than the outbredcontrol. We conclude that purging may slow therate of extinction slightly, but it cannot berelied on to eliminate the deleterious effectsof inbreeding.     

Microsatellite support for active inbreeding in a cichlid fish

In wild animal populations, the degree of inbreeding differs between species and within species between populations. Because mating with kin often results in inbreeding depression, observed inbreeding is usually regarded to be caused by limited outbreeding opportunities due to demographic factors like small population size or population substructuring. However, theory predicts inclusive benefits from mating with kin, and thus part of the observed variation in inbreeding might be due to active inbreeding preferences. Although some recent studies indeed report kin mating preferences, the evidence is still highly ambiguous. Here, we investigate inbreeding in a natural population of the West African cichlid fish Pelvicachromis taeniatus which showed clear kin mating preferences in standardized laboratory experiments but no inbreeding depression. The presented microsatellite analysis reveals that the natural population has, in comparison to two reference populations, a reduced allelic diversity (A = 3) resulting in a low heterozygosity (H_o = 0.167) pointing to a highly inbred population. Furthermore, we found a significant heterozygote deficit not only at population (F_is = 0.116) but also at subpopulation level (F_is = 0.081) suggesting that inbreeding is not only a by-product of population substructuring but possibly a consequence of behavioral kin preferences.     

Inbreeding and extinction: Effects of purging

Deleterious alleles may be removed (purged) bynatural selection in populations undergoinginbreeding. However, there is controversyregarding the effectiveness of purging inreducing the extinction risk due to inbreeding,particularly in conservation contexts. Weevaluated the effects of purging on theextinction risk due to inbreeding in Drosophila melanogaster using two basepopulations, an outbred population (non-purged)and four-way crosses between highly inbredlines derived from the same population(purged). The inbred lines used in the four-waycrosses were previously subjected to 20generations of full-sib mating. The impact offull-sib inbreeding over a further 12generations was compared in 200 populationsfrom each of the two base populations. Therewas a small and non-significant differencebetween the extinction rates at an inbreedingcoefficient of 0.93 in the non-purged (0.74± 0.03) and purged (0.69 ± 0.03)treatments. This is consistent with otherevidence indicating that the effects of purgingare often small. Purging using rapid inbreedingin very small populations cannot be relied uponto eliminate the deleterious effects ofinbreeding.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

Interpopulation variation in mating system and late-stage inbreeding depression in Magnolia stellata

Inbreeding has the potential to cause evolutionary changes in populations, although these changes are likely to drive populations to extinction through inbreeding depression and reductions in genetic diversity. We investigated the mating system and late-stage inbreeding depression (δ) in 10 populations of Magnolia stellata using nine microsatellite markers and evaluated the effects of population size and the degree of population isolation through inbreeding and inbreeding depression on the persistence of populations. The outcrossing rates were very similar (~0.7) among populations, but the correlations of paternity, fractions of biparental inbreeding and inbreeding coefficients at the seed stage ( F _S) varied among populations, suggesting that the level of outcrossing was similar among populations, while the quality of it was not. A significant negative correlation was detected between F _S and population size. The average value of δ was 0.709, and the values in six of the 10 populations were significant. The values of δ differed among populations, although clear relationships with population size and the degree of population isolation were not detected. However, in one population, which was very small and located in the edge of the species' range, we obtained a very low value of δ (–0.096), which may be indicative of purging or the fixation of deleterious alleles. Existing M. stellata populations that are small (and thus might be expected to have higher frequencies of inbreeding) and have large values of δ may be in danger of declining, even if the populations are located within the central region of the species' range.     

Non-random mating for selection with restricted rates of inbreeding and overlapping generations

Minimum coancestry mating with a maximum of one offspring per mating pair (MC1) is compared with random mating schemes for populations with overlapping generations. Optimum contribution selection is used, whereby ΔF is restricted. For schemes with ΔF restricted to 0.25% per year, 256 animals born per year and heritability of 0.25, genetic gain increased with 18% compared with random mating. The effect of MC1 on genetic gain decreased for larger schemes and schemes with a less stringent restriction on inbreeding. Breeding schemes hardly changed when omitting the iteration on the generation interval to find an optimum distribution of parents over age-classes, which saves computer time, but inbreeding and genetic merit fluctuated more before the schemes had reached a steady-state. When bulls were progeny tested, these progeny tested bulls were selected instead of the young bulls, which led to increased generation intervals, increased selection intensity of bulls and increased genetic gain (35% compared to a scheme without progeny testing for random mating). The effect of MC1 decreased for schemes with progeny testing. MC1 mating increased genetic gain from 11–18% for overlapping and 1–4% for discrete generations, when comparing schemes with similar genetic gain and size.     

Hitchhiking of Deleterious Alleles and the Cost of Adaptation in Partially Selfing Species

Self-fertilization is generally seen to be disadvantageous in the long term. It increases genetic drift, which subsequently reduces polymorphism and the efficiency of selection, which also challenges adaptation. However, high selfing rates can increase the fixation probability of recessive beneficial mutations, but existing theory has generally not accounted for the effect of linked sites. Here, we analyze a model for the fixation probability of deleterious mutants that hitchhike with selective sweeps in diploid, partially selfing populations. Approximate analytical solutions show that, conditional on the sweep not being lost by drift, higher inbreeding rates increase the fixation probability of the deleterious allele, due to the resulting reduction in polymorphism and effective recombination. When extending the analysis to consider a distribution of deleterious alleles, as well as the average fitness increase after a sweep, we find that beneficial alleles generally need to be more recessive than the previously assumed dominance threshold (h < 1/2) for selfing to be beneficial from one-locus theory. Our results highlight that recombination aiding the efficiency of selection on multiple loci amplifies the fitness benefits of outcrossing over selfing, compared to results obtained from one-locus theory. This effect additionally increases the parameter range under which obligate outcrossing is beneficial over partial selfing.     

Inbreeding,inbreeding depression and extinction

Inbreeding is unavoidable in small, isolated populations and can cause substantial fitness reductions compared to outbred populations. This loss of fitness has been predicted to elevate extinction risk giving it substantial conservation significance. Inbreeding may result in reduced fitness for two reasons: an increased expression of deleterious recessive alleles (partial dominance hypothesis) or the loss of favourable heterozygote combinations (overdominance hypothesis). Because both these sources of inbreeding depression are dependent upon dominance variance, inbreeding depression is predicted to be greater in life history traits than in morphological traits. In this study we used replicate inbred and control lines of Drosophila simulans to address three questions:1) is inbreeding depression greater in life history than morphological traits? 2) which of the two hypotheses is the major underlying cause of inbreeding depression? 3) does inbreeding elevate population extinction risk? We found that inbreeding depression was significantly greater in life history traits compared to morphological traits, but were unable to find unequivocal support for either the overdominance or partial dominance hypotheses as the genetic basis of inbreeding depression. As predicted, inbred lines had a significantly greater extinction risk.