Effects of population size and isolation on heterosis, mean fitness, and inbreeding depression in a perennial plant

? In small isolated populations, genetic drift is expected to increase chance fixation of partly recessive, mildly deleterious mutations, reducing mean fitness and inbreeding depression within populations and increasing heterosis in outcrosses between populations. ? We estimated relative effective sizes and migration among populations and compared mean fitness, heterosis, and inbreeding depression for eight large and eight small populations of a perennial plant on the basis of fitness of progeny produced by hand pollinations within and between populations. ? Migration was limited, and, consistent with expectations for drift, mean fitness was 68% lower in small populations; heterosis was significantly greater for small (mean?=?70%, SE?=?14) than for large populations (mean?=?7%, SE?=?27); and inbreeding depression was lower, although not significantly so, in small (mean?=?-0.29%, SE?=?28) than in large (mean?=?0.28%, SE?=?23) populations. ? Genetic drift promotes fixation of deleterious mutations in small populations, which could threaten their persistence. Limited migration will exacerbate drift, but data on migration and effective population sizes in natural populations are scarce. Theory incorporating realistic variation in population size and patterns of migration could better predict genetic threats to small population persistence.     

Rapid spread of immigrant genomes into inbred populations

When local populations are genetically differentiated from one another and partially inbred, as typically occurs in subdivided populations, immigrant genomes are predicted to be at a frequency-dependent fitness advantage due to heterosis (hybrid vigour) in their descendants. We tested this prediction with pedigreed laboratory populations of the butterfly Bicyclus anynana and report here on a rapid increase over five generations in the contribution of an initially rare immigrant genome to the local population gene pool. The replicated experimental design, including immigrant controls, demonstrates that the mechanism underlying immigrant genome spread is heterosis, and that the advantage to the immigrant genes is sustained over several generations. Our result suggests that effective migration rates may often be much higher than the numbers of individual migrants assumed by classical population genetics models, with implications for the persistence and evolution of metapopulations.     

Heterosis as an explanation for large amounts of genic polymorphism

By using both numerical and analytical approaches, we have shown that heterosis alone is not a mechanism for maintaining many alleles segregating at a locus. Even when all heterozygous are more fit than all homozygotes, the proportion of fitness arrays that will lead to a stable, feasible equilibrium of more than 6 or 7 alleles is vanishingly small. More alleles can be maintained if, in addition to heterosis, it is assumed that there is very little variation in fitness from heterozygote to heterozygote, with the ratio of mean heterosis to standard deviation of fitness among heterozygotes in the neighborhood of 10. When such conditions hold, the allelic frequency distribution and equilibrium will be very uniform, with all alleles very close to equal frequency (see PDF). It is much more likely that stable equilibria for multiple alleles will be best explained by multiple niche selection.     

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.     

Strong effects of heterosis on the evolution of dispersal rates

When dispersal is limited, crosses between different regions may generate progeny of higher fitness than crosses within regions, due to the fact that individuals from the same region are more likely to share the same recessive deleterious alleles. This phenomenon (termed heterosis) generates a selective force favouring dispersal; however, the importance of heterosis on dispersal evolution has been a subject for debate. In this paper, we use computer simulations representing deleterious mutations occurring over a whole genome (of arbitrary map length R) to explore the magnitude of heterosis, and its effect on the evolution of dispersal. These results show that heterosis may have important effects on dispersal when it is in the upper range of values observed in natural populations, which occurs in our simulations when the genomic deleterious mutation rate U is also in the upper range of observed values. Comparing the results with extrapolations from an analytical two‐locus model indicates that the effect of heterosis is mainly driven by pairwise associations between the locus affecting dispersal and selected loci when U is not too high (roughly, U < 0.5), whereas higher order associations become important for higher values of U.     

Genetic loads under fitness‐dependent mutation rates

Abstract Although much theory depends on the genome‐wide rate of deleterious mutations, good estimates of the mutation rate are scarce and remain controversial. Furthermore, mutation rate may not be constant, and a recent study suggests that mutation rates are higher in mildly stressful environments. If mutation rate is a function of condition, then individuals carrying more mutations will tend to be in worse condition and therefore produce more mutations. Here I examine the mean fitnesses of sexual and asexual populations evolving under such condition‐dependent mutation rates. The equilibrium mean fitness of a sexual population depends on the shape of the curve relating fitness to mutation rate. If mutation rate declines synergistically with increasing condition the mean fitness will be much lower than if mutation rate declines at a diminishing rate. In contrast, asexual populations are less affected by condition‐dependent mutation rates. The equilibrium mean fitness of an asexual population only depends on the mutation rate of the individuals in the least loaded class. Because such individuals have high fitness and therefore a low mutation rate, asexual populations experience less genetic load than sexual populations, thus increasing the twofold cost of sex.     

Outbreeding depression and breeding system evolution in small,remnant populations of <Emphasis Type="Italic">Primula vulgaris</Emphasis>: consequences for genetic rescue

Many species suffer from anthropogenic habitat fragmentation. The resulting small and isolated populations are more prone to extinction due to, amongst others, genetic erosion, inbreeding depression and Allee-effects. Genetic rescue can help mitigate such problems, but might result in outbreeding depression. We evaluated offspring fitness after selfing and outcrossing within and among three very small and isolated remnant populations of the heterostylous plant Primula vulgaris. We used greenhouse-grown offspring from these populations to test several fitness components. One population was fixed for the pin-morph, and was outcrossed with another population in the field to obtain seeds. Genetic diversity of parent and offspring populations was studied using microsatellites. Morph and population-specific heterosis, inbreeding and outbreeding depression were observed for fruit and seed set, seed weight and cumulative fitness. Highest fitness was observed in the field-outcrossed F1-population, which also showed outbreeding depression following subsequent between-population (back)crossing. Despite outbreeding depression, fitness was still relatively high. Inbreeding coefficients indicated that the offspring were more inbred than their parent populations. Offspring heterozygosity and inbreeding coefficients correlated with observed fitness. One population is evolving homostyly, showing a thrum morph with an elongated style and high autonomous fruit and seed set. This has important implications for conservation strategies such as genetic rescue, as the mating system will be altered by the introduction of homostyles.     

Heterosis and outbreeding depression in crosses between natural populations of Arabidopsis thaliana

Understanding the causes and architecture of genetic differentiation between natural populations is of central importance in evolutionary biology. Crosses between natural populations can result in heterosis if recessive or nearly recessive deleterious mutations have become fixed within populations because of genetic drift. Divergence between populations can also result in outbreeding depression because of genetic incompatibilities. The net fitness consequences of between-population crosses will be a balance between heterosis and outbreeding depression. We estimated the magnitude of heterosis and outbreeding depression in the highly selfing model plant Arabidopsis thaliana, by crossing replicate line pairs from two sets of natural populations (C↔R, B↔S) separated by similar geographic distances (Italy↔Sweden). We examined the contribution of different modes of gene action to overall differences in estimates of lifetime fitness and fitness components using joint scaling tests with parental, reciprocal F₁ and F₂, and backcross lines. One of these population pairs (C↔R) was previously demonstrated to be locally adapted, but locally maladaptive quantitative trait loci were also found, suggesting a role for genetic drift in shaping adaptive variation. We found markedly different genetic architectures for fitness and fitness components in the two sets of populations. In one (C↔R), there were consistently positive effects of dominance, indicating the masking of recessive or nearly recessive deleterious mutations that had become fixed by genetic drift. The other set (B↔S) exhibited outbreeding depression because of negative dominance effects. Additional studies are needed to explore the molecular genetic basis of heterosis and outbreeding depression, and how their magnitudes vary across environments.     

Variance and variability,uncovering an underappreciated component of reproductive isolation

Estimating the fitness of line crosses has been a key element in studies of inbreeding depression, hybridization, and speciation. Fitness values are typically compared using differences in the arithmetic mean of a fitness component between types of crosses. One aspect of fitness that is often overlooked is variance in offspring fitness over time. In the majority of studies, ignoring this aspect of fitness is unavoidable because it is impossible to estimate variance in offspring fitness over long time periods. Here, I describe a method of estimating variance in offspring fitness by substituting spatial variation for temporal variation and provide an empirical example. The method is based on Levene's test of homogeneity of variances. It is implemented by quantifying differences in residual variation among cross types. In a previous study, I performed crosses between populations of the annual plant Diodia teres and quantified hybrid fitness. In this study, another component of isolation and heterosis was revealed when considering variance in offspring fitness. When taking into account variance in offspring fitness using geometric mean fitness as the measure of performance, hybrids between populations from different habitats showed less heterosis than when calculating fitness based on arithmetic mean. This study demonstrates that variance in offspring fitness can be an important aspect of fitness that should be measured more frequently.     

Parasites promote host gene flow in a metapopulation

Local adaptation is a powerful mechanism to maintain genetic diversity in subdivided populations. It counteracts the homogenizing effect of gene flow because immigrants have an inferior fitness in the new habitat. This picture may be reversed in host populations where parasites influence the success of immigrating hosts. Here we report two experiments testing whether parasite abundance and genetic background influences the success of host migration among pools in a Daphnia magna metapopulation. In 22 natural populations of D. magna, immigrant hosts were found to be on average more successful when the resident populations experienced high prevalences of a local microsporidian parasite. We then determined whether this success is due to parasitism per se, or the genetic background of the parasites. In a common garden competition experiment, we found that parasites reduced the fitness of their local hosts relatively more than the fitness of allopatric host genotypes. Our experiments are consistent with theoretical predictions based on coevolutionary host-parasite models in metapopulations. A direct consequence of the observed mechanism is an elevated effective migration rate for the host in the metapopulation.     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

The different sources of variation in inbreeding depression, heterosis and outbreeding depression in a metapopulation of Physa acuta

Understanding how parental distance affects offspring fitness, i.e., the effects of inbreeding and outbreeding in natural populations, is a major goal in evolutionary biology. While inbreeding is often associated with fitness reduction (inbreeding depression), interpopulation outcrossing may have either positive (heterosis) or negative (outbreeding depression) effects. Within a metapopulation, all phenomena may occur with various intensities depending on the focal population (especially its effective size) and the trait studied. However, little is known about interpopulation variation at this scale. We here examine variation in inbreeding depression, heterosis, and outbreeding depression on life-history traits across a full-life cycle, within a metapopulation of the hermaphroditic snail Physa acuta. We show that all three phenomena can co-occur at this scale, although they are not always expressed on the same traits. A large variation in inbreeding depression, heterosis, and outbreeding depression is observed among local populations. We provide evidence that, as expected from theory, small and isolated populations enjoy higher heterosis upon outcrossing than do large, open populations. These results emphasize the need for an integrated theory accounting for the effects of both deleterious mutations and genetic incompatibilities within metapopulations and to take into account the variability of the focal population to understand the genetic consequences of inbreeding and outbreeding at this scale.     

Effects of genetic distance on heterosis in a <Emphasis Type="Italic">Drosophila melanogaster</Emphasis> model system

Habitat fragmentation and small population sizes can lead to inbreeding and loss of genetic variation, which can potentially cause inbreeding depression and decrease the ability of populations to adapt to altered environmental conditions. One solution to these genetic problems is the implementation of genetic rescue, which re-establishes gene flow between separated populations. Similar techniques are being used in animal and plant breeding to produce superior production animals and plants. To optimize fitness benefits in genetic rescue programs and to secure high yielding domestic varieties in animal and plant breeding, knowledge on the genetic relatedness of populations being crossed is imperative. In this study, we conducted replicated crosses between isogenic Drosophila melanogaster lines from the Drosophila Genetic Reference Panel. We grouped lines in two genetic distance groups to study the effect of genetic divergence between populations on the expression of heterosis in two fitness components; starvation resistance and reproductive output. We further investigated the transgenerational effects of outcrossing by investigating the fitness consequences in both the F₁- and the F₃-generations. High fitness enhancements were observed in hybrid offspring compared to parental lines, especially for reproductive output. However, the level of heterosis declined from the F₁- to the F₃-generation. Generally, genetic distance did not have strong impact on the level of heterosis detected, although there were exceptions to this pattern. The best predictor of heterosis was performance of parental lines with poorly performing parental lines showing higher hybrid vigour when crossed, i.e. the potential for heterosis was proportional to the level of inbreeding depression. Overall, our results show that outcrossing can have very strong positive fitness consequences for genetically depauperate populations.     

The Role of Life Cycle and Migration in Selection for Variance in Offspring Number

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the fixationprobability of mutant strategies has been calculated under several scenarios with the general conclusion that variance in offspring number reduces fitness in proportion to the inverse of the population size [Gillespie, J., Genetics 76:601–606, 1974; Proulx, S.R., Theor. Popul. Biol. 58:33–47, 2000]. This relationship becomes more complicated under a metapopulation scenario where the “effective” population size depends on migration rate, population structure, and lifecycle. It is shown that in a life cycle where reproduction and migration (the birth-migration-regulation life cycle, or BMR)occur prior to density regulation within every deme, the fitness of a strategy depends on migration rate. When migration rates are near zero, the fitness of the strategy is determined by the size of individual demes, so that the strategy favoredin small populations tends to be fixed. As migration rate increases and approaches panmixis between demes, the fitness ofa reproductive strategy approaches what its value would be in a single, panmictic deme with a population size correspondingtothe census size of the metapopulation. Interestingly, when the life cycle is characterized by having density regulation in each deme prior to migration (the BRM life cycle) the fixation probability of a strategy is independent of migration rate. These results are found to be qualitatively consistent with the individual-based simulation results in Shpak [Theor. Biosci.124:65–85, 2005]. An erratum to this article can be found at     

Heterosis is common and inbreeding depression absent in natural populations of Arabidopsis thaliana

The importance of genetic drift in shaping patterns of adaptive genetic variation in nature is poorly known. Genetic drift should drive partially recessive deleterious mutations to high frequency, and inter‐population crosses may therefore exhibit heterosis (increased fitness relative to intra‐population crosses). Low genetic diversity and greater genetic distance between populations should increase the magnitude of heterosis. Moreover, drift and selection should remove strongly deleterious recessive alleles from individual populations, resulting in reduced inbreeding depression. To estimate heterosis, we crossed 90 independent line pairs of Arabidopsis thaliana from 15 pairs of natural populations sampled across Fennoscandia and crossed an additional 41 line pairs from a subset of four of these populations to estimate inbreeding depression. We measured lifetime fitness of crosses relative to parents in a large outdoor common garden (8,448 plants in total) in central Sweden. To examine the effects of genetic diversity and genetic distance on heterosis, we genotyped parental lines for 869 SNPs. Overall, genetic variation within populations was low (median expected heterozygosity = 0.02), and genetic differentiation was high (median F_ST = 0.82). Crosses between 10 of 15 population pairs exhibited significant heterosis, with magnitudes of heterosis as high as 117%. We found no significant inbreeding depression, suggesting that the observed heterosis is due to fixation of mildly deleterious alleles within populations. Widespread and substantial heterosis indicates an important role for drift in shaping genetic variation, but there was no significant relationship between fitness of crosses relative to parents and genetic diversity or genetic distance between populations.     

PEAK SHIFTS AND POLYMORPHISM DURING PHASE THREE OF WRIGHT'S SHIFTING-BALANCE PROCESS

The third phase of Wright's shifting-balance theory involves the export of adaptive gene combinations from one subpopulation to another. Previous results have demonstrated that this can occur at very low migration rates, but it has been argued that this simply reflects the ability of migration to overcome selection and fix any (even deleterious) alleles. Here, previous analyses are extended by concentrating on the critical balance between forward and reverse migration rates that still allows phase III to proceed. It is shown that selective advantage, dominance, recombination rate, and the number of loci all affect the ability of a genotype to invade and become fixed in a new subpopulation, but it is unlikely that phase III will occur in the absence of differential migration unless the invading genotype consists of a few dominant loci with a large selection advantage, spreading into a few populations of lower fitness. Therefore, as was envisioned by Wright, differential migration from more to less fit populations will be necessary for phase III to occur under most circumstances.     

Geographical patterns of adaptation within a species' range: interactions between drift and gene flow

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.     

Heterosis for viability,fecundity, and male fertility in Drosophila melanogaster: comparison of mutational and standing variation.

If genetic variation for fitness traits in natural populations ("standing" variation) is maintained by recurrent mutation, then quantitative-genetic properties of standing variation should resemble those of newly arisen mutations. One well-known property of standing variation for fitness traits is inbreeding depression, with its converse of heterosis or hybrid vigor. We measured heterosis for three fitness traits, pre-adult viability, female fecundity, and male fertility, among a set of inbred Drosophilia melanogaster lines recently derived from the wild, and also among a set of lines that had been allowed to accumulate spontaneous mutations for over 200 generations. The inbred lines but not the mutation-accumulation (MA) lines showed heterosis for pre-adult viability. Both sets of lines showed heterosis for female fecundity, but heterosis for male fertility was weak or absent. Crosses among a subset of the MA lines showed that they were strongly differentiated for male fertility, with the differences inherited in autosomal fashion; the absence of heterosis for male fertility among the MA lines was therefore not caused by an absence of mutations affecting this trait. Crosses among the inbred lines also gave some, albeit equivocal, evidence for male fertility variation. The contrast between the results for female fecundity and those for male fertility suggests that mutations affecting different fitness traits may differ in their average dominance properties, and that such differences may be reflected in properties of standing variation. The strong differentiation among the MA lines in male fertility further suggests that mutations affecting this trait occur at a high rate.     

The adaptive value of epigenetic mutation: Limited in large but high in small peripheral populations

The fate of populations during range expansions, invasions and environmental changes is largely influenced by their ability to adapt to peripheral habitats. Recent models demonstrate that stable epigenetic modifications of gene expression that occur more frequently than genetic mutations can both help and hinder adaptation in panmictic populations. However, these models do not consider interactions between epimutations and evolutionary forces in peripheral populations. Here, we use mainland–island mathematical models and simulations to explore how the faster rate of epigenetic mutation compared to genetic mutations interacts with migration, selection and genetic drift to affect adaptation in peripheral populations. Our model focuses on cases where epigenetic marks are stably inherited. In a large peripheral population, where the effect of genetic drift is negligible, our analyses suggest that epimutations with random fitness impacts that occur at rates as high as 10^–3 increase local adaptation when migration is strong enough to overwhelm divergent selection. When migration is weak relative to selection and epimutations with random fitness impacts decrease adaptation, we find epigenetic modifications must be highly adaptively biased to enhance adaptation. Finally, in small peripheral populations, where genetic drift is strong, epimutations contribute to adaptation under a wider range of evolutionary conditions. Overall, our results suggest that epimutations can change outcomes of adaptation in peripheral populations, which has implications for understanding conservation and range expansions and contractions, especially of small populations.     

Deleterious mutations in a hybrid zone: can mutational load decrease the barrier to gene flow?

The aim of this paper is to investigate the effect of deleterious mutations in a hybrid zone maintained by selection against hybrids. In such zones, linkage disequilibria among hybrid depression loci, resulting from a balance between migration and selection, are crucial in maintaining the barrier because they allow each locus, in addition to its own selection coefficient, to cumulate indirect selective effects from other loci. Deleterious alleles produce heterosis and increase by this means the effective migration rate in structured populations. In a hybrid zone, they therefore contribute to decrease linkage disequilibria as well as the barrier to gene flow imposed by hybrid depression. However, deleterious mutations have no effect: (i) when selection against hybrids is weak, because linkage disequilibria are small even without heterosis in this case, or (ii) when selection against hybrids is so strong that it overwhelms heterosis. On the other hand, with moderate selection against hybrids, the decrease in the strength of the barrier due to heterosis may reach detectable levels, although it requires relatively small population sizes and/or migration rates. The effect is expected to be small and only within small genomes where loci are tightly linked can it become strong. Nevertheless, neglecting mutational load may to some extent obscure the estimations of selective parameters based either on artificial F1 crosses or on cline characteristics.