The evolution of self-fertilization in density-regulated populations

The evolution of selfing in hermaphrodites has been studied to reveal the demographic conditions that lead to intermediate selfing rates. Using a demographic model based on Ricker-type density regulation, we assume first that, independent of population density, inbred individuals survive less well than outbred individuals and second, that inbred and outbred individuals differ in their competitive abilities in density-regulated populations. The evolution of selfing, driven by inbreeding depression and the cost of outcrossing, is then analysed for three fundamentally different demographic scenarios: stable population densities, deterministically varying population densities (resulting from cyclical or chaotic population dynamics) and stochastic fluctuations of carrying capacities (resulting from environmental noise). We show that even under stable demographic conditions evolutionary outcomes are not confined to either complete selfing or full outcrossing. Instead, intermediate selfing rates arise under a wide range of conditions, depending on the nature of competitive interactions between inbred and outbred individuals. We also explore the evolution of selfing under deterministic and stochastic density fluctuations to demonstrate that such environmental conditions can evolutionarily stabilize intermediate selfing rates. This is the first study, to our knowledge, to consider in detail the effect of density regulation on the evolution of selfing rates.     

The frequency of consanguineous matings due to multiple use of donors in artificial insemination.

The amount of inadvertent inbreeding as a result of donor anonymity in artificial insemination has been estimated. A child from a first-cousin mating or closer is expected approximately once every 41/2 years in the United States as a result of artificial insemination by donor. Since a child with unknown paternity seems less likely to mate with paternal relatives than is a child with known paternity, artificial insemination by donor may actually reduce the average inbreeding of the population. Nevertheless, to reduce recessive diseases, inbreeding should be kept to a minimum by limiting the number of children produced by a single donor. Formulas are presented for local risks of inbreeding based on the number of children per donor.     

Association studies in consanguineous populations.

To study the genetic determinism of multifactorial diseases in large panmictic populations, a strategy consists in looking for an association with markers closely linked to candidate genes. A distribution of marker genotypes different in patients and controls may indicate that the candidate gene is involved in the disease. In panmictic populations, the power to detect the role of a candidate gene depends on the gametic disequilibrium with the marker locus. In consanguineous populations, we show that it depends on the inbreeding coefficient F as well. Inbreeding increases the power to detect the role of a recessive or quasi-recessive disease-susceptibility factor. The gain in power turns out to be greater for small values of the gametic disequilibrium. Moreover, even in the absence of gametic disequilibrium, the presence of inbreeding may allow to detect the role of a recessive factor. Ignoring inbreeding when it exists may lead to reject falsely a recessive model if the mode of inheritance is inferred on the distribution of genotypes among patients.     

The evolution of self-fertilization in perennials

Abstract Many plants are perennials, but studies of self-fertilization do not usually include features of perennial life histories. We therefore develop models that include selfing, a simple form of perenniality, adult inbreeding depression, and an adult survivorship cost to seed production. Our analysis shows that inbreeding depression in adults diminishes the genetic transmission advantage associated with selfing, especially in long-lived perennials that experience inbreeding depression over many seasons. Perennials also pay a cost when selfing increases total seed set at the expense of future survivorship and reproduction. Such life-history considerations shed new light on the generalization that annuals self-fertilize more than perennials. Past research suggested reproductive assurance as an explanation for this association, but common modes of selfing offer equal reproductive assurance to annuals and perennials. Instead, perennials may avoid selfing because of adult inbreeding depression and the cost to future survivorship and reproduction.     

The map expansion obtained with recombinant inbred strains and intermated recombinant inbred populations for finite generation designs

The generation of special crosses between different inbred lines such as recombinant inbred strains (RIS) and intermated recombinant inbred populations (IRIP) is being used to improve the power of QTL detection techniques, in particular fine mapping. These approaches acknowledge the fact that recombination of linked loci increases with every generation, caused by the accumulation of crossovers appearing between the loci at each meiosis. This leads to an expansion of the map distance between the loci. While the amount of the map expansion of RIS and IRIP is known for infinite inbred generations, it is not known for finite numbers of generations. This gap was closed here. Since the recursive evaluation of the map expansion factors turned out to be complex, a useful approximation was derived.     

The effect of reproductive compensation on recessive disorders within consanguineous human populations

We investigate the effects of consanguinity and population substructure on genetic health using the UK Asian population as an example. We review and expand upon previous treatments dealing with the deleterious effects of consanguinity on recessive disorders and consider how other factors, such as population substructure, may be of equal importance. For illustration, we quantify the relative risks of recessive lethal disorders by presenting some simple calculations that demonstrate the effect 'reproductive compensation' has on the maintenance of recessive alleles. The results show how reproductive compensation can effectively counteract the purging of deleterious alleles within consanguineous populations. Whereas inbreeding does not elevate the equilibrium frequency of affected individuals, reproductive compensation does. We suggest this effect must be built into interpretations of the incidence of genetic disease within populations such as the UK Asians. Information of this nature will benefit health care workers who inform such communities.     

Allee effect and self-fertilization in hermaphrodites: reproductive assurance in demographically stable populations

The fact that selfing increases seed set (reproductive assurance) has often been put forward as an important selective force for the evolution of selfing. However, the role of reproductive assurance in hermaphroditic populations is far from being clear because of a lack of theoretical work. Here, I propose a theoretical model that analyzes self-fertilization in the presence of reproductive assurance. Because reproductive assurance directly influences the per capita growth rate, I developed an explicit demographic model for partial selfers in the presence of reproductive assurance, specifically when outcrossing is limited by the possibility of pollen transfer (Allee effect). Mating system parameters are derived as a function of the underlying demographical parameters. The functional link between population demography and mating system parameters (reproductive assurance, selfing rate) can be characterized. The demographic model permits the analysis of the evolution of self-fertilization in stable populations when reproductive assurance occurs. The model reveals some counterintuitive results such as the fact that increasing the fraction of selfed ovules can, in certain circumstances, increase the fraction of outcrossed ovules. Moreover, I demonstrate that reproductive assurance per se cannot account for the evolution of stable mixed selfing rates. Also, the model reveals that the extinction of outcrossing populations depends on small changes in population density (ecological perturbations), while the transition from outcrossing to selfing can, in certain cases, lead the population to extinction (evolutionary suicide). More generally, this paper highlights the fact that self-fertilization affects both the dynamics of individuals and the dynamics of selfing genes in hermaphroditic populations.     

The effective size of fluctuating populations

We consider a Wright-Fisher model whose population size is an autocorrelated stochastic process. Our interest is in the effects of autocorrelated fluctuations of the population size on the effective size. We define the inbreeding effective size and the variance effective size and show that these effective sizes are the same for this model. In the literature, it is said that the effective size is equal to the harmonic mean of population size when the size fluctuates. We will show, however, that the effective size is not the same as the harmonic mean of population size unless the fluctuations of population size are uncorrelated. The effective size is larger (resp. smaller) than the harmonic mean when the fluctuations of population size are positively (resp. negatively) autocorrelated. Further, we obtain some asymptotic expressions for effective size when the population size is very large and/or the autocorrelation of the fluctuation is very strong.     

The effective size of bryophyte populations

Bryophytes with their dominant haploid stage conform poorly to the life cycles generally treated in population genetical models. Here we make a detailed analysis of what effective sizes bryophyte model populations have as a function of their breeding system. It is found that the effective size is rarely much smaller than the scored number of haploid gametophytic individuals, even when the limited number of diploids (sporophytes) formed is taken into account. The most severe decrease in effective size occurs when unisexual gametophytic females produce only a small number of fertile diploid sporophytes in male biased populations; this effect is due to the restricted sampling of male gametophytic individuals that then occurs. It is shown that the harmonic mean of diploid sporophytes formed per haploid gametophytic individuals is the relevant measure in these calculations and not the standard (and generally larger) arithmetic mean.     

Efficacy of population structure analysis with breeding populations and inbred lines

The objective was to assess by simulation the efficacy of population structure analysis in plant breeding. Twelve populations and 300 inbred lines were simulated and genotyped using 100 microsatellite loci. The experimental material included populations with and without admixture, ancestry relationship and linkage disequilibrium, and with distinct levels of genetic differentiation and effective sizes. The analyses were performed using Structure software and employed all available models. For all the group number (K) tested, for both populations and inbred lines, the admixture model with correlated allelic frequencies provided the highest value for the logarithm of the marginal likelihood. Fitting appropriate model and using adequate sample size for individuals and markers, Structure was effective in identifying the correct population structure, migrants and individuals with genome from distinct populations. The linkage model did not result in an improvement in clustering relative to the admixture model with correlated allelic frequencies. The inclusion of prior information did not change the results; for some K values the analyses showed slight higher values of the marginal likelihood. The reduction in the number of individuals and markers negatively affected the results. There was a high variation in the most probable K value between the evaluated methods.     

Dynamics of genetic rescue in inbred Drosophila melanogaster populations

Genetic rescue has been proposed as a management strategy to improve the fitness of genetically eroded populations by alleviating inbreeding depression. We studied the dynamics of genetic rescue in inbred populations of Drosophila. Using balancer chromosomes, we show that the force of heterosis that accompanies genetic rescue is large and allows even a recessive lethal to increase substantially in frequency in the rescued populations, particularly at stress temperatures. This indicates that deleterious alleles present in the immigrants can increase significantly in frequency in the recipient population when they are in linkage disequilibrium with genes responsible for the heterosis. In a second experiment we rescued eight inbred Drosophila populations with immigrants from two other inbred populations and observe: (i) there is a significant increase in viability both 5 and 10 generations after the rescue event, showing that the increase in fitness is not transient but persists long-term. (ii) The lower the fitness of the recipient population the larger the fitness increase. (iii) The increase in fitness depends significantly on the origin of the rescuers. The immigrants used were fixed for a conditional lethal that was mildly deleterious at 25°C but lethal at 29°C. By comparing fitness at 25°C (the temperature during the rescue experiment) and 29°C, we show that the lethal allele reached significant frequencies in most rescued populations, which upon renewed inbreeding became fixed in part of the inbred lines. In conclusion, in addition to the fitness increase genetic rescue can easily result in a substantial increase in the frequency of mildly deleterious alleles carried by the immigrants. This can endanger the rescued population greatly when it undergoes recurrent inbreeding. However, using a sufficient number of immigrants and to accompany the rescue event with the right demographic measures will overcome this problem. As such, genetic rescue still is a viable option to manage genetically eroded populations.     

Genotypic selection in Daphnia populations consisting of inbred sibships

The genetic basis of fitness reduction associated with inbreeding is still poorly understood. Here we use associations between allozyme genotypes and fitness to investigate the genetic basis of inbreeding depression in experimental outdoor populations of the water flea, Daphnia magna. In Daphnia, a phase of clonal reproduction follows hatching from sexually produced resting eggs, and changes in genotype frequencies during the clonal phase can be used to estimate fitness. Our experiment resembles natural colonization of ponds in that single clones colonize an empty pool, expand asexually and produce sexual offspring by selfing (sisters mate with their clonal brothers). These offspring diapause and form populations consisting of selfed sibships in the following spring. In 12 of 13 experimental populations, genotypes of selfed hatchlings after diapause conformed to Mendelian expectations. During the subsequent ca. 10 asexual generations, however, genotype frequencies changed significantly at 19 of 27 single loci studied within populations, mostly in favour of heterozygotes, with heterozygosity at multiple loci affecting the change in genotype frequency multiplicatively. Because variance in heterozygosity among siblings at a given marker reflects only heterozygosity in the chromosomal region around this marker, our results suggest that selection at fitness-associated loci in the chromosomal regions near the markers were responsible for these changes. The genotype frequency changes were more consistent with selection acting on linked loci than on the allozymes themselves. Taken together, the evidence for abundant selection in the chromosomal regions of the markers and the fact that changes in genotype frequencies became apparent only after several generations of clonal selection, point to a genetic load consisting of many alleles of small or intermediate effects, which is consistent with the strong genetic differentiation and repeated genetic bottlenecks in the metapopulation from which the animals for this study were obtained.     

The distribution of the proportion of the genome which is homozygous by descent in inbred individuals.

The expected proportion of loci which are homozygous by descent in an inbred individual is the inbreeding coefficient of that individual. Confidence limits on this proportion depend on the number of loci controlling the trait under investigation and the linkage relationships among the loci. Such information is generally not available. If it is assumed that the number of loci is large, the variance of the proportion of homozygous loci is approximated by the variance of the total map length which is homozygous by descent; this is calculated for several regular mating systems, including selfing, sib mating, and parent-off-spring mating. In particular, the confidence interval on the proportion of homozygous loci in Drosophila is likely to be large, and this has a number of implications to the interpretation and analysis of experimental data.     

The effective population size of some age-structured populations

It was shown in a previous paper that if generations are discrete, then the effective population size of a large population can be derived from the theory of multitype branching processes. It turns out to be proportional to the reciprocal of a term that appears in the denominator of expressions for survival probabilities when there is a supercritical positively regular branching process for which the dominant positive eigenvalue of the first moment matrix is slightly larger than 1. If there is an age-structured population with unchanging proportions among sexes and age groups, then the effective population size is shown to be also obtainable from the theory of multitype branching processes. The expression for this parameter has the same form as in the corresponding model for discrete generations, multiplied by an appropriate measure of the average length of a generation. Results are obtained for dioecious random mating populations, populations reproducing partly by selfing, and populations reproducing partly by full-sib mating.     

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.