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.

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 Ne = 14) and Nanger dama (Ne = 11). No purging is detected in Ammotragus lervia (Ne = 4), in agreement with the notion that drift overcomes purging under fast inbreeding, nor in G. dorcas (Ne = 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.

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.

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 (Fa) 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.

An explicit model for the inbreeding load in the evolutionary analysis of selfing.

I present analytical predictions for the equilibrium inbreeding load expected in a population under mutation, selection, and a regular mating system for any population size and for any magnitude and recessivity of the deleterious effects. Using this prediction, I deduce the relative fitness of mutant alleles with small effect on selfing to explore the situations where selfing or outcrossing are expected to evolve. The results obtained are in agreement with previous literature, showing that natural selection is expected to lead to stable equilibria where populations show either complete outcrossing or complete selfing, and that selfing is promoted by large deleterious mutation rates. I find that the evolution of selfing is favored by a large recessivity of deleterious effects, while the magnitude of homozygous deleterious effects only becomes relevant in relatively small populations. This result contradicts the standard assumption that purging in large populations will only promote selfing when homozygous deleterious effects are large, and implies that previously published results obtained assuming lethal mutations in large populations can be extrapolated to nonlethal alleles of similar recessivity. This conclusion and the general approach used in this analysis can be useful in the study of the evolution of mating systems.

Understanding Inbreeding Depression, Purging, and Genetic Rescue.

Inbreeding depression, the reduction of fitness caused by inbreeding, is a nearly universal phenomenon that depends on past mutation, selection, and genetic drift. Recent estimates suggest that its impact on individual fitness is even greater than previously thought. Genomic information is contributing to its detection and can enlighten important aspects of its genetic architecture. In natural populations, purging and genetic rescue mitigate fitness decline during inbreeding periods, and might be critical to population survival, thus, both mechanisms should be considered when assessing extinction risks. However, deliberate purging and genetic rescue involve considerable risk in the short and medium term, so that neither appears to be a panacea against high inbreeding depression.

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.

Estimation of genetic purging under competitive conditions.

Inbreeding depression for fitness traits is a key issue in evolutionary biology and conservation genetics. The magnitude of inbreeding depression, though, may critically depend on the efficiency of genetic purging, the elimination or recessive deleterious mutations by natural selection after they are exposed by inbreeding. However, the detection and quantification of genetic purging for nonlethal mutations is a rather difficult task. Here, we present two comprehensive sets of experiments with Drosophila aimed at detecting genetic purging in competitive conditions and quantifying its magnitude. We obtain, for the first time in competitive conditions, an estimate for the predictive parameter, the purging coefficient (d), that quantifies the magnitude of genetic purging, either against overall inbreeding depression (d ≈ 0.3), or against the component ascribed to nonlethal alleles (dNL ≈ 0.2). We find that competitive fitness declines at a high rate when inbreeding increases in the absence of purging. However, in moderate size populations under competitive conditions, inbreeding depression need not be too dramatic in the medium to short term, as the efficiency of purging is also very high. Furthermore, we find that purging occurred under competitive conditions also reduced the inbreeding depression that is expressed in the absence of competition.

On the Consequences of Purging and Linkage on Fitness and Genetic Diversity.

Using computer simulation we explore the consequences of linkage on the inbreeding load of an equilibrium population, and on the efficiency of purging and the loss of genetic diversity after a reduction in population size. We find that linkage tends to cause increased inbreeding load due to the build up of coupling groups of (partially) recessive deleterious alleles. It also induces associative overdominance at neutral sites but rarely causes increased neutral genetic diversity in equilibrium populations. After a reduction in population size, linkage can cause some delay both for the expression of the inbreeding load and the corresponding purging. However, reasonable predictions can be obtained for the evolution of fitness under inbreeding and purging by using empirical estimates of the inbreeding depression rate. Purging selection against homozygotes for deleterious alleles affects the population's pedigree. Furthermore, it can slow the loss of genetic diversity compared to that expected from the variance of gametic contributions to the breeding group and even from pedigree inbreeding. Under some conditions, this can lead to a smaller loss of genetic diversity, even below that expected from population size in the absence of selection.

The action of stabilizing selection, mutation, and drift on epistatic quantitative traits.

For a quantitative trait under stabilizing selection, the effect of epistasis on its genetic architecture and on the changes of genetic variance caused by bottlenecking were investigated using theory and simulation. Assuming empirical estimates of the rate and effects of mutations and the intensity of selection, we assessed the impact of two-locus epistasis (synergistic/antagonistic) among linked or unlinked loci on the distribution of effects and frequencies of segregating loci in populations at the mutation-selection-drift balance. Strong pervasive epistasis did not modify substantially the genetic properties of the trait and, therefore, the most likely explanation for the low amount of variation usually accounted by the loci detected in genome-wide association analyses is that many causal loci will pass undetected. We investigated the impact of epistasis on the changes in genetic variance components when large populations were subjected to successive bottlenecks of different sizes, considering the action of genetic drift, operating singly (D), or jointly with mutation (MD) and selection (MSD). An initial increase of the different components of the genetic variance, as well as a dramatic acceleration of the between-line divergence, were always associated with synergistic epistasis but were strongly constrained by selection.

Allelic diversity and its implications for the rate of adaptation.

Genetic variation is usually estimated empirically from statistics based on population gene frequencies, but alternative statistics based on allelic diversity (number of allelic types) can provide complementary information. There is a lack of knowledge, however, on the evolutionary implications attached to allelic-diversity measures, particularly in structured populations. In this article we simulated multiple scenarios of single and structured populations in which a quantitative trait subject to stabilizing selection is adapted to different fitness optima. By forcing a global change in the optima we evaluated which diversity variables are more strongly correlated with both short- and long-term adaptation to the new optima. We found that quantitative genetic variance components for the trait and gene-frequency-diversity measures are generally more strongly correlated with short-term response to selection, whereas allelic-diversity measures are more correlated with long-term and total response to selection. Thus, allelic-diversity variables are better predictors of long-term adaptation than gene-frequency variables. This observation is also extended to unlinked neutral markers as a result of the information they convey on the demographic population history. Diffusion approximations for the allelic-diversity measures in a finite island model under the infinite-allele neutral mutation model are also provided.

Understanding and predicting the fitness decline of shrunk populations: inbreeding, purging, mutation, and standard selection.

The joint consequences of inbreeding, natural selection, and deleterious mutation on mean fitness after population shrinkage are of great importance in evolution and can be critical to the conservation of endangered populations. I present simple analytical equations that predict these consequences, improving and extending a previous heuristic treatment. Purge is defined as the "extra" selection induced by inbreeding, due to the "extra" fitness disadvantage (2d) of homozygotes for (partially) recessive deleterious alleles. Its effect is accounted for by using, instead of the classical inbreeding coefficient f, a purged inbreeding coefficient g that is weighed by the reduction of the frequency of deleterious alleles caused by purging. When the effective size of a large population is reduced to a smaller stable value N (with Nd ≥ 1), the purged inbreeding coefficient after t generations can be predicted as g(t) ≈ [(1 - 1/2N) g(t)(-1) + 1/2N](1 - 2d f(t)(-1)), showing how purging acts upon previously accumulated inbreeding and how its efficiency increases with N. This implies an early fitness decay, followed by some recovery. During this process, the inbreeding depression rate shifts from its ancestral value (δ) to that of the mutation-selection-drift balance corresponding to N (δ*), and standard selection cancels out the inbreeding depression ascribed to δ*. Therefore, purge and inbreeding operate only upon the remaining δ - δ*. The method is applied to the conservation strategy in which family contributions to the breeding pool are equal and is extended to make use of genealogical information. All these predictions are checked using computer simulation.

Regeneration of the variance of metric traits by spontaneous mutation in a Drosophila population.

In the C1 population of Drosophila melanogaster of moderate effective size ( approximately 500), which was genetically invariant in its origin, we studied the regeneration by spontaneous mutation of the genetic variance for two metric traits [abdominal (AB) and sternopleural (ST) bristle number] and that of the concealed mutation load for viability, together with their temporal stability, using alternative selection models based on mutational parameters estimated in the C1 genetic background. During generations 381-485 of mutation accumulation (MA), the additive variances of AB and ST approached the levels observed in standing laboratory populations, fluctuating around their expected equilibrium values under neutrality or under relatively weak causal stabilizing selection. This type of selection was required to simultaneously account for the observed additive variance in our population and for those previously reported in natural and laboratory populations, indicating that most mutations affecting bristle traits would only be subjected to weak selective constraints. Although gene action for bristles was essentially additive, transient situations occurred where inbreeding resulted in a depression of the mean and an increase of the additive variance. This was ascribed to the occasional segregation of mutations of large recessive effects. On the other hand, the observed non-lethal inbreeding depression for viability must be explained by the segregation of alleles of considerable and largely recessive deleterious effects, and the corresponding load concealed in the heterozygous condition was found to be temporally stable, as expected from tighter constraints imposed by natural selection.

The action of purifying selection, mutation and drift on fitness epistatic systems.

For different fitness mutational models, with epistasis introduced, we simulated the consequences of drift (D scenario) or mutation, selection, and drift (MSD scenario) in populations at the MSD balance subsequently subjected to bottlenecks of size N = 2, 10, 50 during 100 generations. No "conversion" of nonadditive into additive variance was observed, all components of the fitness genetic variance initially increasing with the inbreeding coefficient F and subsequently decreasing to zero (D) or to an equilibrium value (MSD). In the D scenario, epistasis had no appreciable effect on inbreeding depression and that on the temporal change of variance components was relevant only for high rates of strong epistatic mutation. In parallel, between-line differentiation in mean fitness accelerated with F and that in additive variance reached a maximum at F approximately 0.6-0.7, both processes being intensified by strong epistasis. In the MSD scenario, however, the increase in additive variance was smaller, as it was used by selection to purge inbreeding depression (N > or = 10), and selection prevented between-line differentiation. Epistasis, either synergistic or antagonistic (this leading to multiple adaptive peaks), had no appreciable effect on MSD results nor, therefore, on the evolutionary rate of fitness change.

A simple method to account for natural selection when predicting inbreeding depression.

It has been widely appreciated that natural selection opposes the progress of inbreeding in small populations, thus limiting the actual inbreeding depression for fitness traits. However, no method to account for the consequences of this process has been given so far. I give a simple and intuitive method to predict inbreeding depression, taking into account the increase in selection efficiency against recessive alleles during inbreeding. It is based on the use of a "purged inbreeding coefficient" g(t) that accounts for the reduction of the probability of the deleterious homozygotes caused by the excess d of detrimental effect for deleterious alleles in the homozygous condition over its additive expectation. It is shown that the effect of purging can be important even for relatively small populations. For between-loci variable deleterious effects, accurate predictions can be obtained using the effective homozygous deleterious excess d(e), which can be estimated experimentally and is robust against variation of the ancestral effective population size. The method can be extended to any trait and it is used to predict the evolution of the mean viability or fecundity in a conservation program with equal or random family contributions.

The dynamics of the roo transposable element in mutation-accumulation lines and segregating populations of Drosophila melanogaster.

We estimated the number of copies for the long terminal repeat (LTR) retrotransposable element roo in a set of long-standing Drosophila melanogaster mutation-accumulation full-sib lines and in two large laboratory populations maintained with effective population size approximately 500, all of them derived from the same isogenic origin. Estimates were based on real-time quantitative PCR and in situ hybridization. Considering previous estimates of roo copy numbers obtained at earlier stages of the experiment, the results imply a strong acceleration of the insertion rate in the accumulation lines. The detected acceleration is consistent with a model where only one (maybe a few) of the approximately 70 roo copies in the ancestral isogenic genome was active and each active copy caused new insertions with a relatively high rate ( approximately 10(-2)), with new inserts being active copies themselves. In the two laboratory populations, however, a stabilized copy number or no accelerated insertion was found. Our estimate of the average deleterious viability effects per accumulated insert [E(s) < 0.003] is too small to account for the latter finding, and we discuss the mechanisms that could contain copy number.

Shortcut predictions for fitness properties at the mutation-selection-drift balance and for its buildup after size reduction under different management strategies.

For populations at the mutation-selection-drift (MSD) balance, I develop approximate analytical expressions giving expectations for the number of deleterious alleles per gamete, the number of loci at which any individual is homozygous for deleterious alleles, the inbreeding depression rate, and the additive and dominant components of fitness variance. These predictions are compared to diffusion ones, showing good agreement under a wide range of situations. I also give approximated analytical predictions for the changes in mean and additive variance for fitness when a population approaches a new equilibrium after its effective size is reduced to a stable value. Results are derived for populations maintained with equal family contribution or with no management after size reduction, when selection acts through viability or fertility differences. Predictions are compared to previously published results obtained from transition matrices or stochastic simulations, a good qualitative fit being obtained. Predictions are also obtained for populations of various sizes under different sets of plausible mutational parameters. They are compared to available empirical results for Drosophila, and conservation implications are discussed.

The build up of mutation-selection- drift balance in laboratory Drosophila populations.

The build up of an equilibrium between mutation, selection, and drift in populations of moderate size is an important evolutionary issue, and can be critical in the conservation of endangered populations. We studied this process in two Drosophila melanogaster populations initially lacking genetic variability (C1 and C2) that were subsequently maintained during 431 or 165 generations with effective population size N(e) approximately 500 (estimated by lethal complementation analysis). Each population originated synchronously to a companion set of full-sib mutation accumulation (MA) lines, C1 and MA1 were derived from an isogenic origin and C2 and MA2 from a single MA1 line at generation 265. The results suggest that both C1 and C2 populations were close to the mutation-selection-drift balance for viability and bristle traits, and are consistent with a 2.5-fold increase of the mutation rate in C2 and MA2. Despite this increase, the average panmictic viability in C2 was only slightly below that of C1, indicating that the expressed loads due to segregating deleterious mutation were small, in agreement with the low deleterious mutation rate (0.015-0.045) previously reported for the MA1 lines. In C1, the nonlethal inbreeding depression rate for viability was 30% of that usually estimated in segregating populations. The genetic variance for bristles regenerated in C1 and C2 was moderately smaller than the average value reported for natural populations, implying that they have accumulated a substantial adaptive potential. In light of neutral and selective predictions, these results suggest that bristle additive variance was predominantly due to segregation of mutations with deleterious effects of the order of 10(-3), and is consistent with relatively weak causal stabilizing selection (V(s) approximately 30).

Increase of the spontaneous mutation rate in a long-term experiment with Drosophila melanogaster.

In a previous experiment, the effect of 255 generations of mutation accumulation (MA) on the second chromosome viability of Drosophila melanogaster was studied using 200 full-sib MA1 lines and a large C1 control, both derived from a genetically homogeneous base population. At generation 265, one of those MA1 lines was expanded to start 150 new full-sib MA2 lines and a new C2 large control. After 46 generations, the rate of decline in mean viability in MA2 was approximately 2.5 times that estimated in MA1, while the average degree of dominance of mutations was small and nonsignificant by generation 40 and moderate by generation 80. In parallel, the inbreeding depression rate for viability and the amount of additive variance for two bristle traits in C2 were 2-3 times larger than those in C1. The results are consistent with a mutation rate in the line from which MA2 and C2 were derived about 2.5 times larger than that in MA1. The mean viability of C2 remained roughly similar to that of C1, but the rate of MA2 line extinction increased progressively, leading to mutational collapse, which can be ascribed to accelerated mutation and/or synergy after important deleterious accumulation.