Extinction of populations due to inbreeding depression with demographic disturbances

The process of population extinction due to inbreeding depression with constant demographic disturbances every generation is analysed using a population genetic and demographic model. The demographic disturbances introduced into the model represent loss of population size that is induced by any kind of human activities, e.g. through hunting and destruction of habitats. The genetic heterozygosity among recessive deleterious genes and the population size are assumed to be in equilibrium before the demographic disturbances start. The effects of deleterious mutations are represented by decreases in the growth rate and carrying capacity of a population. Numerical simulations indicate rapid extinction due to synergistic interaction between inbreeding depression and declining population size for realistic ranges of per-locus mutation rate, equilibrium population size, intrinsic rate of population growth, and strength of demographic disturbances. Large populations at equilibrium are more liable to extinction when disturbed due to inbreeding depression than small populations. This is a consequence of the fact that large populations maintain more recessive deleterious mutations than small populations. The rapid extinction predicted in the present study indicates the importance of the demographic history of a population in relation to extinction due to inbreeding depression.     

Drift load in populations of small size and low density

According to theory, drift load in randomly mating populations is determined by past population size, because enhanced genetic drift in small populations causes accumulation and fixation of recessive deleterious mutations of small effect. In contrast, segregating load due to mutations of low frequency should decline in smaller populations, at least when mutations are highly recessive and strongly deleterious. Strong local selection generally reduces both types of load. We tested these predictions in 13 isolated, outcrossing populations of Arabidopsis lyrata that varied in population size and plant density. Long-term size was estimated by expected heterozygosity at 20 microsatellite loci. Segregating load was assessed by comparing performance of offspring from selfings versus within-population crosses. Drift load was the heterosis effect created by interpopulation outbreeding. Results showed that segregating load was unrelated to long-term size. However, drift load was significantly higher in populations of small effective size and low density. Drift load was mostly expressed late in development, but started as early as germination and accumulated thereafter. The study largely confirms predictions of theory and illustrates that mutation accumulation can be a threat to natural populations.     

Population size and the nature of genetic load in Gentianella germanica

Abstract Theory predicts a significant relationship between the size of a population and the magnitude and composition of its genetic load, but few natural populations have been investigated. We examined the magnitude of genetic load due to recessive deleterious alleles (GL) both segregating and fixed within Gentianella germanica populations of varying size by selfing and reciprocally crossing plants within and between natural populations according to a partial diallel design and by comparing the performance of the experimental progeny in a common-garden experiment. The results show that GL for total fitness in small populations (fewer than 200 plants) was mainly due to fixed recessive deleterious alleles, whereas GL for total fitness in larger populations (more than 200 plants) appeared to be mainly due to segregating deleterious recessive alleles. The total fitness of selfed plants increased with decreasing population size, indicating some purging of deleterious alleles associated with declining population sizes. The magnitudes of GL due to fixed deleterious alleles in small populations and segregating deleterious alleles in large populations, however, were overall similar, suggesting that purging selection was an insignificant force when compared to genetic drift in determining the magnitude of GL in small natural populations in this species. The results of this study highlight the importance of population size in determining the dynamics of genetic loads of natural populations and are overall in line with a large body of theoretical work indicating that small populations may face higher extinction risks due to the fixation and accumulation of deleterious alleles of small effect.     

Bottlenecks in large populations: the effect of immigration on population viability

We model a large population that is subject to successive short bottlenecks, in order to investigate the impact of different extents of immigration on the change in genetic load and on viability. A first simple genetic model uncovers the opposite effects of immigration on fitness according to the type of deleterious mutations considered: immigration increases fitness if the genetic load is comprised of mildly deleterious mutations, whereas it decreases fitness if it is comprised of lethals. When considering both types of mutations and adding explicit stochastic demographic considerations, in which bottlenecks are engendered by random catastrophes, the global impact of immigration on viability is dependent upon a balance between its opposite effects on the two components of the genetic load and on demographic stochasticity. In this context, immigration tends to increase the probability of extinction if occurring preferentially when population density is high, while it decreases extinction if occurring preferentially towards low-density populations.     

Inbreeding rate modifies the dynamics of genetic load in small populations

The negative fitness consequences of close inbreeding are widely recognized, but predicting the long-term effects of inbreeding and genetic drift due to limited population size is not straightforward. As the frequency and homozygosity of recessive deleterious alleles increase, selection can remove (purge) them from a population, reducing the genetic load. At the same time, small population size relaxes selection against mildly harmful mutations, which may lead to accumulation of genetic load. The efficiency of purging and the accumulation of mutations both depend on the rate of inbreeding (i.e., population size) and on the nature of mutations. We studied how increasing levels of inbreeding affect offspring production and extinction in experimental Drosophila littoralis populations replicated in two sizes, N = 10 and N = 40. Offspring production and extinction were measured over 25 generations concurrently with a large control population. In the N = 10 populations, offspring production decreased strongly at low levels of inbreeding, then recovered only to show a consistent subsequent decline, suggesting early expression and purging of recessive highly deleterious alleles and subsequent accumulation of mildly harmful mutations. In the N = 40 populations, offspring production declined only after inbreeding reached higher levels, suggesting that inbreeding and genetic drift pose a smaller threat to population fitness when inbreeding is slow. Our results suggest that highly deleterious alleles can be purged in small populations already at low levels of inbreeding, but that purging does not protect the small populations from eventual genetic deterioration and extinction.     

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).     

MUTATION LOAD AND THE SURVIVAL OF SMALL POPULATIONS

Previous attempts to model the joint action of selection and mutation in finite populations have treated population size as being independent of the mutation load. However, the accumulation of deleterious mutations is expected to cause a gradual reduction in population size. Consequently, in small populations random genetic drift will progressively overpower selection making it easier to fix future mutations. This synergistic interaction, which we refer to as a mutational melt-down, ultimately leads to population extinction. For many conditions, the coefficient of variation of extinction time is less than 0.1, and for species that reproduce by binary fission, the expected extinction time is quite insensitive to population carrying capacity. These results are consistent with observations that many cultures of ciliated protozoans and vertebrate fibroblasts have characteristic extinction times. The model also predicts that clonal lineages are unlikely to survive more than 10⁴ to 10⁵ generations, which is consistent with existing data on parthenogenetic animals. Contrary to the usual view that Muller's ratchet does more damage when selection is weak, we show that the mean extinction time declines as mutations become more deleterious. Although very small sexual populations, such as self-fertilized lines, are subject to mutational meltdowns, recombination effectively eliminates the process when the effective population size exceeds a dozen or so. The concept of the effective mutation load is developed, and several procedures for estimating it are described. It is shown that this load can be reduced substantially when mutational effects are highly variable.     

Heterosis in an isolated, effectively small, and self-fertilizing population of the flowering plant Leavenworthia alabamica

Mildly deleterious mutations are thought to play a major role in the extinction of natural populations, especially those that are small, isolated, or inbred. Self-fertilization should reduce the effective size of populations and simultaneously reduce migration between populations. A history of self-fertilization should therefore cause a population to harbor a substantial "local drift load" caused by the fixation of mildly deleterious mutations. This hypothesis was tested in Leavenworthia alabamica, which contains large, self-incompatible populations and smaller self-compatible populations with adaptations for self-fertilization. The fitness of offspring from within- and between-population crosses was compared to quantify heterosis caused by the masking of deleterious alleles in the heterozygous state. Little heterosis was observed in crosses between five large, self-incompatible populations and two of the three small, self-fertilizing populations of L. alabamica. However, the most geographically isolated and genetically divergent self-fertilizing population (Tuscumbia) exhibited a 110.2% increase in germination and a 73.6% increase in fitness, which is consistent with a sizeable local drift load. The finding of substantial heterosis for fitness supports the idea that small effective size, reproductive isolation, and self-fertilization can make populations particularly vulnerable to mutation accumulation.     

MUTATION AND EXTINCTION: THE ROLE OF VARIABLE MUTATIONAL EFFECTS,SYNERGISTIC EPISTASIS,BENEFICIAL MUTATIONS,AND DEGREE OF OUTCROSSING

Recent theoretical studies have illustrated the potential role of spontaneous deleterious mutation as a cause of extinction in small populations. However, these studies have not addressed several genetic issues, which can in principle have a substantial influence on the risk of extinction. These include the presence of synergistic epistasis, which can reduce the rate of mutation accumulation by progressively magnifying the selective effects of mutations, and the occurrence of beneficial mutations, which can offset the effects of previous deleterious mutations. In stochastic simulations of small populations (effective sizes on the order of 100 or less), we show that both synergistic epistasis and the rate of beneficial mutation must be unrealistically high to substantially reduce the risk of extinction due to random fixation of deleterious mutations. However, in analytical calculations based on diffusion theory, we show that in large, outcrossing populations (effective sizes greater than a few hundred), very low levels of beneficial mutation are sufficient to prevent mutational decay. Further simulation results indicate that in populations small enough to be highly vulnerable to mutational decay, variance in deleterious mutational effects reduces the risk of extinction, assuming that the mean deleterious mutational effect is on the order of a few percent or less. We also examine the magnitude of outcrossing that is necessary to liberate a predominantly selfing population from the threat of long-term mutational deterioration. The critical amount of outcrossing appears to be greater than is common in near-obligately selfing plant species, supporting the contention that such species are generally doomed to extinction via random drift of new mutations. Our results support the hypothesis that a long-term effective population size in the neighborhood of a few hundred individuals defines an approximate threshold, below which outcrossing populations are vulnerable to extinction via fixation of deleterious mutations, and above which immunity is acquired.     

Theoretical aspects of extinction by inbreeding depression

Populational extinction due to inbreeding depression is analyzed with simple population genetic and population ecological models. Two alternative genetic mechanisms of inbreeding depression, i.e. recessive deleterious genes and overdominant genes, are assumed in separate analyses in order to examine their relative importance. With both mechanisms the population size and the coefficient of inbreeding are maintained at stable equilibria if there is no non-genetic demographic disturbance or stress. With a certain amount of demographic disturbance the population declines rapidly due to interaction between the decrease of population size and the increase of inbreeding coefficient. Such rapid extinction occurs with both genetic mechanisms. However, in the case of overdominant genes extinction happens only if the equilibrium population size is small and the selection coefficient is large such that segregation load is large. In nature, extinction due to overdominant genes is considered to be much less likely than extinction due to recessive deleterious genes.     

The influence of neighborhood size and habitat shape on the accumulation of deleterious mutations.

To examine the impact of genetic neighborhood size and habitat shape on genetic load and the accumulation of deleterious mutation, individual-based simulations were performed in continuously distributed habitats. The risk of extinction increased as both the area of the habitat and the neighborhood size decreased. When the neighborhood area became smaller than the habitat area, habitat shape also began to influence the risk of extinction by mutation loads, expected time to extinction being shorter in longer and narrower habitats than in a square habitat. Both the number of homozygous deleterious loci per individual and the mutation load in the population increased as the neighborhood size and total population size decreased. Neighborhood size and total population size both independently affected the average number of homozygous deleterious loci per individual. In addition, as the ratio of the long to the short side of the rectangle of a habitat increased, the average number of homozygous deleterious loci increased. When the areas of the habitats were held constant, the average number of homozygous loci and the mutation loads were smallest for a regular square and largest for the longest, narrowest habitat. These results suggest that the spatial genetic structure of an individual is an important factor in the accumulation of deleterious mutations and the risk of extinction by mutation meltdown.     

The Effect of Deleterious Mutations on Neutral Molecular Variation

Selection against deleterious alleles maintained by mutation may cause a reduction in the amount of genetic variability at linked neutral sites. This is because a new neutral variant can only remain in a large population for a long period of time if it is maintained in gametes that are free of deleterious alleles, and hence are not destined for rapid elimination from the population by selection. Approximate formulas are derived for the reduction below classical neutral values resulting from such background selection against deleterious mutations, for the mean times to fixation and loss of new mutations, nucleotide site diversity, and number of segregating sites. These formulas apply to random-mating populations with no genetic recombination, and to populations reproducing exclusively asexually or by self-fertilization. For a given selection regime and mating system, the reduction is an exponential function of the total mutation rate to deleterious mutations for the section of the genome involved. Simulations show that the effect decreases rapidly with increasing recombination frequency or rate of outcrossing. The mean time to loss of new neutral mutations and the total number of segregating neutral sites are less sensitive to background selection than the other statistics, unless the population size is of the order of a hundred thousand or more. The stationary distribution of allele frequencies at the neutral sites is correspondingly skewed in favor of rare alleles, compared with the classical neutral result. Observed reductions in molecular variation in low recombination genomic regions of sufficiently large size, for instance in the centromere-proximal regions of Drosophila autosomes or in highly selfing plant populations, may be partly due to background selection against deleterious mutations.     

Patterns of inbreeding depression and architecture of the load in subdivided populations

Inbreeding depression is a general phenomenon that is due mainly to recessive deleterious mutations, the so-called mutation load. It has been much studied theoretically. However, until very recently, population structure has not been taken into account, even though it can be an important factor in the evolution of populations. Population subdivision modifies the dynamics of deleterious mutations because the outcome of selection depends on processes both within populations (selection and drift) and between populations (migration). Here, we present a general model that permits us to gain insight into patterns of inbreeding depression, heterosis, and the load in subdivided populations. We show that they can be interpreted with reference to single-population theory, using an appropriate local effective population size that integrates the effects of drift, selection, and migration. We term this the "effective population size of selection" (NS(e)). For the infinite island model, for example, it is equal to NS(e) = N1 + m/hs, where N is the local population size, m the migration rate, and h and s the dominance and selection coefficients of deleterious mutation. Our results have implications for the estimation and interpretation of inbreeding depression in subdivided populations, especially regarding conservation issues. We also discuss the possible effects of migration and subdivision on the evolution of mating systems.     

MUTATIONAL MELTDOWNS IN SEXUAL POPULATIONS

Although it is widely acknowledged that the gradual accumulation of mildly deleterious mutations is an important source of extinction for asexual populations, it is generally assumed that this process is of little relevance to sexual species. Here we present results, based on computer simulations and supported by analytical approximations, that indicate that mutation accumulation in small, random-mating monoecious populations can lead to mean extinction times less than a few hundred to a few thousand generations. Unlike the situation in obligate asexuals in which the mean time to extinction (t?_e) increases more slowly than linearly with the population carrying capacity (K), t?_e increases approximately exponentially with K in outcrossing sexual populations. The mean time to extinction for obligately selfing populations is shown to be equivalent to that for asexual populations of the same size, but with half the mutation rate and twice the mutational effect; this suggests that obligate selfing, like obligate asexuality, is inviable as a long-term reproductive strategy. Under all mating systems, the mean time to extinction increases relatively slowly with the logarithm of fecundity, and mutations with intermediate effects (similar to those observed empirically) cause the greatest risk of extinction. Because our analyses ignore sources of demographic and environmental stochasticity, which have synergistic effects that exacerbate the accumulation of deleterious mutations, our results should yield liberal upper bounds to the mean time to extinction caused by mutational degradation. Thus, deleterious mutation accumulation cannot be ruled out generally as a significant source of extinction vulnerability in small sexual populations or as a selective force influencing mating-system evolution.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Genetic variability and drift load in populations of an aquatic snail

Abstract Population genetic theory predicts that in small populations, random genetic drift will fix and accumulate slightly deleterious mutations, resulting in reduced reproductive output. This genetic load due to random drift (i.e., drift load) can increase the extinction risk of small populations. We studied the relationship between genetic variability (indicator of past population size) and reproductive output in eight isolated, natural populations of the hermaphroditic snail Lymnaea stagnalis . In a common laboratory environment, snails from populations with the lowest genetic variability mature slower and have lower fecundity than snails from genetically more variable populations. This result suggests that past small population size has resulted in increased drift load, as predicted. The relationship between genetic variability and reproductive output is independent of the amount of nonrandom mating within populations. However, reproductive output and the current density of snails in the populations were not correlated. Instead, data from the natural populations suggest that trematode parasites may determine, at least in part, population densities of the snails.     

Negative environmental perturbations may improve species persistence

Among the factors proximally involved in the extinction of small isolated populations, genetic deterioration and temporal variation in environmental quality have been the subjects of intensive research in ecological and evolutionary sciences. However, previous theoretical studies and population viability assessments generally assumed a strict dichotomy between these two types of threat. Yet a number of empirical studies have recently suggested that the effects of genetic deterioration and environmental variation should not be considered independently, by demonstrating that the main effect of inbreeding depression lies with its tendency to exacerbate the deleterious consequences of environmental stress. Capitalizing on these results, I developed a stochastic model to examine the impact of random environmental perturbations on the persistence time of small isolated populations subject to inbreeding depression and mutation accumulation. The model assumes that spontaneous deleterious mutations have more severe effects when perturbations occur, which results in more efficient purging of the mutation load. Under this assumption, I find that negative perturbations may paradoxically improve middle- and long-term species persistence for realistic frequency of occurrence and severity distribution.     

Muller’s ratchet in symbiont populations

Muller’s ratchet, the inevitable accumulation of deleterious mutations in asexual populations, has been proposed as a major factor in genome degradation of obligate symbiont organisms. Essentially, if left unchecked the ratchet will with certainty cause extinction due to the ever increasing mutational load. This paper examines the evolutionary fate of insect symbionts, using mathematical modelling to simulate the accumulation of deleterious mutations. We investigate the effects of a hierarchical two level population structure. Since each host contains its own subpopulation of symbionts, there will be a large number of small symbiont populations linked indirectly via selection on the host level. We show that although the separate subpopulations will accumulate deleterious mutations quickly, the symbiont population as a whole will be protected from extinction by selection acting on the hosts. As a consequence, the extent of genome degradation observed in present day symbionts is more likely to represent loss of functions that were (near-) neutral to the host, rather than a snap shot of a decline towards complete genetic collapse.     

High mutation rates, bottlenecks, and robustness of RNA viral quasispecies

Population bottlenecks are stochastic events that strongly condition the structure and evolution of natural populations. Their effects are readily observable in highly heterogeneous populations, such as RNA viruses, since bottlenecks cause a fast accumulation of mutations. Considering that most mutations are deleterious, it was predicted that the frequent application of bottlenecks would yield a population unable to replicate. However, in vitro as well as in vivo systems evolving through bottlenecks present a remarkable resistance to extinction. This observation reveals the robustness of RNA viruses and points to the existence of internal mechanisms which must confer a high degree of adaptability to fast mutating populations. In this contribution, we review experimental observations regarding the survival of RNA viruses, both in laboratory experiments and in natural populations. By means of a simple theoretical model of evolution which incorporates strong reductions of the population size, we explore the relationship between the number of replication rounds that a single founder particle undergoes before the next bottleneck is applied, and the mutation rate in a particular environment. Our numerical results reveal that the mutation rate has evolved in a concerted way with the degree of optimization achieved by the population originated from the founder particle. We hypothesize that this mechanism generates a mutation-selection equilibrium in natural populations that maximizes adaptability while maintaining their structure.     

Accumulation of deleterious mutations in small abiotic populations of RNA

The accumulation of slightly deleterious mutations in populations leads to the buildup of a genetic load and can cause the extinction of populations of small size. Mutation-accumulation experiments have been used to study this process in a wide variety of organisms, yet the exact mutational underpinnings of genetic loads and their fitness consequences remain poorly characterized. Here, we use an abiotic system of RNA populations evolving continuously in vitro to examine the molecular events that can instigate a genetic load. By tracking the fitness decline of ligase ribozyme populations with bottleneck sizes between 100 and 3000 molecules, we detected the appearance and subsequent fixation of both slightly deleterious mutations and advantageous mutations. Smaller populations went extinct in significantly fewer generations than did larger ones, supporting the notion of a mutational meltdown. These data suggest that mutation accumulation was an important evolutionary force in the prebiotic RNA world and that mechanisms such as recombination to ameliorate genetic loads may have been in place early in the history of life.