THE ADDITIVE GENETIC VARIANCE AFTER BOTTLENECKS IS AFFECTED BY THE NUMBER OF LOCI INVOLVED IN EPISTATIC INTERACTIONS

Genetic variability and founder effect in the pitcher plant Sarracenia purpurea (Sarraceniaceae) in populations introduced into Switzerland: from inbreeding to invasion

BACKGROUND AND AIMS

The long-lived and mainly outcrossing species Sarracenia purpurea has been introduced into Switzerland and become invasive. This creates the opportunity to study reactions to founder effect and how a species can circumvent deleterious effects of bottlenecks such as reduced genetic diversity, inbreeding and extinction through mutational meltdown, to emerge as a highly invasive plant.

METHODS

A population genetic survey by random amplified polymorphism DNA markers (RAPD) together with historical insights and a field pollination experiment were carried out.

KEY RESULTS

At the regional scale, S. purpurea shows low structure (thetast=0.072) due to a recent founder event and important subsequent growth. Nevertheless, multivariate statistical analyses reveal that, because of a bottleneck that shifted allele frequencies, most of the variability is independent among populations. In one population (Tenasses) the species has become invasive and genetic analysis reveals restricted gene flow and family structure (thetast=0.287). Although inbreeding appears to be high (Fis >0.410 from a Bayesian estimation), a field pollination experiment failed to detect significant inbreeding depression upon F1 seed number and seed weight fitness-traits. Furthermore, crosses between unrelated individuals produced F1 seeds with significantly reduced fitness, thus showing local outbreeding depression.

CONCLUSIONS

The results suggest that, under restricted gene flow among families, the species may not only have rapidly purged deleterious alleles, but also have undergone some form of selection for inbreeding due to co-adaptation between loci.

EFFECTS OF GENETIC DRIFT ON VARIANCE COMPONENTS UNDER A GENERAL MODEL OF EPISTASIS

We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.