A class of models of selectively neutral alleles

Using exchangeability as a statistical analog of neutrality, we derive a generalized sampling distribution for neutral alleles. The distribution depends upon a parameter that determines the underlying marginal distribution of the number of copies of a neutral allele and that can range from zero to infinity. The sampling model of Ewens (1972) is a special case characterized by an extreme value (0) of this parameter. Two other special cases are considered, one of which seems to be applicable to populations with a structure like that of the Yanomama Indians of South America. We then investigate the expected frequency spectra under these three special cases and discover that all three models yield a broad range of possible spectra with overlap between the special cases. We finally show that Ewens' sampling model cannot be used to construct tests of neutrality versus selection tending to maintain polymorphisms, but it can be used to construct tests of directional selection versus neutrality plus selection tending to yield polymorphic states.     

Diversity of benzimidazole-resistance alleles in populations of small ruminant parasites

The resistance of gastro-intestinal nematodes of small ruminants (sheep and goat) to benzimidazole anthelmintic drugs seems to be linked primarily to a single mutation in the isotype 1 beta-tubulin gene. This study was carried out to investigate the origin and diversity of benzimidazole-resistance alleles in trichostrongylid nematodes. We sequenced a 550 bp fragment of the isotype 1 beta-tubulin gene from several benzimidazole-resistant Teladorsagia circumcincta populations isolated from dairy goat farms in the central and south-western France. We also sequenced the same beta-tubulin fragment from Trichostrongylus colubriformis and Haemonchus contortus populations in south-western France. We found eight benzimidazole-resistance alleles in all T. circumcincta populations studied, six in H. contortus populations, and only one in T. colubriformis populations. In most cases, only one benzimidazole-resistance allele was present in T. circumcincta and H. contortus populations, but two alleles were found in a fewer number of them. Some T. circumcincta populations shared the same benzimidazole-resistance allele whereas some others had a specific benzimidazole-resistance allele. Similar findings were obtained for H. contortus. As no parasites are introduced once the flock of dairy goat farms has been constituted, these data indicate for the three studied species that rare pre-existing benzimidazole-resistance alleles already present before the isolation of populations had been selected. On the other hand, the fact that some benzimidazole-resistance alleles were specific to one population of T. circumcincta or H. contortus, seems to be in agreement with the hypothesis of the selection of spontaneous mutations. Thus, the origin of benzimidazole-resistance alleles in trichostrongylid nematodes seems to involve primarily the selection of rare alleles and possibly of spontaneous mutations.     

Estimation of mating system parameters in plant populations using marker loci with null alleles

Summary An Expectation-Maximization (EM)-algorithm procedure is presented that extends Cheliak et al. (1983) method of maximum-likelihood estimation of mating system parameters of mixed mating system models. The extension permits the estimation of the rate of self-fertilization (s) and allele frequencies (Pi) at loci in outcrossing pollen, at marker loci having recessive null alleles. The algorithm makes use of maternal and filial genotypic arrays obtained by the electrophoretic analysis of cohorts of progeny. The genotypes of maternal plants must be known. Explicit equations are given for cases when the genotype of the maternal gamete inherited by a seed can (gymnosperms) or cannot (angiosperms) be determined. The procedure can accommodate any number of codominant alleles, but only one recessive null allele at each locus. An example, using actual data from Pinus banksiana, is presented to illustrate the application of this EM algorithm to the estimation of mating system parameters using marker loci having both codominant and recessive alleles.Issued as AECL-8745     

Genetic variability and distribution of mating type alleles in field populations of Leptosphaeria maculans from France

Leptosphaeria maculans is the most ubiquitous fungal pathogen of Brassica crops and causes the devastating stem canker disease of oilseed rape worldwide. We used minisatellite markers to determine the genetic structure of L. maculans in four field populations from France. Isolates were collected at three different spatial scales (leaf, 2-m2 field plot, and field) enabling the evaluation of spatial distribution of the mating type alleles and of genetic variability within and among field populations. Within each field population, no gametic disequilibrium between the minisatellite loci was detected and the mating type alleles were present at equal frequencies. Both sexual and asexual reproduction occur in the field, but the genetic structure of these populations is consistent with annual cycles of randomly mating sexual reproduction. All L. maculans field populations had a high level of gene diversity (H = 0.68 to 0.75) and genotypic diversity. Within each field population, the number of genotypes often was very close to the number of isolates. Analysis of molecular variance indicated that >99.5% of the total genetic variability was distributed at a small spatial scale, i.e., within 2-m2 field plots. Population differentiation among the four field populations was low (GST < 0.02), suggesting a high degree of gene exchange between these populations. The high gene flow evidenced here in French populations of L. maculans suggests a rapid countrywide diffusion of novel virulence alleles whenever novel resistance sources are used.     

Speciation in peripheral populations: effects of drift load and mating systems

Speciation in peripheral populations has long been considered one of the most plausible scenarios for speciation with gene flow. In this study, however we identify two additional problems of peripatric speciation, as compared to the parapatric case, that may impede the completion of the speciation process for most parameter regions. First, with (predominantly) unidirectional gene flow, there is no selection pressure to evolve assortative mating on the continent. We discuss the implications of this for different mating schemes. Second, genetic load can build up in small populations. This can lead to extinction of the peripheral species, or generate selection pressure for lower assortative mating to avoid inbreeding. In this case, either a stable equilibrium with intermediate assortment evolves or there is cycling between phases of hybridization and phases of complete isolation.     

Minimising inbreeding in small populations by rotational mating with frozen semen

Mating plans are investigated in order to minimize inbreeding in small populations when frozen semen is available. For a single dam line it was found that specific sire rotations minimized the asymptotic level of inbreeding when semen is used repeatedly from certain generations. When semen of N foundation (G0) sires is used rotationally over generations it is shown that the inbreeding level asymptotes to 1/(2(N+1) - 2). However, if only G0 sires are used then all genes will eventually descend from the founder sires. Inbreeding can be reduced further by using sires from generation one (G1) and later as this retains genes from the founder dams in the long-term gene pool. If semen from NG0 sires and N unrelated G1 sons is used rotationally then inbreeding asymptotes to (2(N-1) + 1)/(2(2N+1) - 2). When there are more founder dams than sires, the asymptotic inbreeding can be reduced even further by using the semen of half-sib G1 sires in rotation. Optimal rotations using full-sib G1 sires or generation 2 (or later) sires will lower the asymptotic inbreeding also, but generally not by much. It was found that when unlimited frozen semen from a specified group of sires was available, the optimal mating plan was achieved by selecting each generation the sire with the least co-ancestry with the current female of the dam line.     

How phenotypic matching based on neutral mating cues enables speciation in locally adapted populations

Maynard Smith's (American Naturalist, 1966, 100, 637) suggestion that in some cases a prerequisite for speciation is the existence of local ecological adaptations has not received much attention to date. Here, we test the hypothesis using a model like that of Maynard Smith but differing in the way animals disperse between niches. In previous studies, males disperse randomly between niches but females stay put in their natal niche. As a first step toward generalizing the model, we here analyze the case that equal proportions of the two sexes disperse between niches before breeding. Supporting Maynard Smith's (1966) hypothesis, we find that once local adaptations are established, a neutral mating cue at an independent locus can rapidly enable speciation in populations with a suitable mechanism for phenotype matching. We find that stable ecological polymorphisms are relatively insensitive to the strength of selection, but depend crucially on the extent of dispersal between niches, with a threshold of ~5% if population sizes in two niches are equal. At higher levels of dispersal, ecological differentiation is lost. These results contrast with those of earlier studies and shed light on why parapatric speciation is limited by the extent of gene flow. Our testable model provides a candidate explanation for the rapid speciation rates, diversity of appearance and occurrence of “species flocks” observed among some African cichlids and neotropical birds and may also have implications for the occurrence of punctuational change on phylogenies.     

Sexual selection and alternative mating behaviours generate demographic stochasticity in small populations.

Recent theory predicts that environmental variation and small population size facilitate the coexistence of alternative phenotypes despite unequal mean fitness. However, traditional studies of reproductive strategies often assume that the stability of alternative mating behaviours relies on equal male fitness. We present results from field observations and experimental manipulations of thermal resources on territories demonstrating the coexistence of alternative reproductive behaviours with unequal fitness. The side-blotched lizard Uta stansburiana exhibits two alternative strategies for territoriality: "usurp" and "defend". Paternity analysis revealed significantly greater mean fitness for "usurpers" than "defenders" in our study of natural variation. Moreover, variance in fitness was significantly higher for usurpers on both experimental and natural plots, implying that "usurp" is a risky strategy with potentially large pay-offs or none at all. We show theoretically that significantly higher variance in usurper fitness can allow for coexistence with defenders despite higher mean fitness of usurpers. This coexistence is facilitated by small population size. Our results have general implications for the evolution of alternative strategies and the maintenance of genetic diversity in small populations.     

Fixation of new alleles and the extinction of small populations: drift load, beneficial alleles, and sexual selection

With a small effective population size, random genetic drift is more important than selection in determining the fate of new alleles. Small populations therefore accumulate deleterious mutations. Left unchecked, the effect of these fixed alleles is to reduce the reproductive capacity of a species, eventually to the point of extinction. New beneficial mutations, if fixed by selection, can restore some of this lost fitness. This paper derives the overall change in fitness due to fixation of new deleterious and beneficial alleles, as a function of the distribution of effects of new mutations and the effective population size. There is a critical effective size below which a population will on average decline in fitness, but above which beneficial mutations allow the population to persist. With reasonable estimates of the relevant parameters, this critical effective size is likely to be a few hundred. Furthermore, sexual selection can act to reduce the fixation probability of deleterious new mutations and increase the probability of fixing new beneficial mutations. Sexual selection can therefore reduce the risk of extinction of small populations.     

Allee effects, mating systems and the extinction risk in populations with two sexes

The Allee effect is one of the population consequences of sexual reproduction that has received increased attention in recent years. Due to its impact on small population dynamics, it is commonly accepted that Allee effects should render populations more extinction prone. In particular, monogamous species are considered more susceptible to the Allee effect and hence, more extinction prone, than polygamous species. Although this hypothesis has received theoretical support, there is little empirical evidence. In this study, we investigate (1) how variation in tertiary sex ratio affects the presence and intensity of the Allee effect induced by mating system, as well as (2) how this effect contributes to extinction risk. In contrast with previous predictions, we show that all mating systems are likely to experience a strong Allee effect when the operational sex ratio (OSR) is balanced. This strong Allee effect does not imply being exceptionally extinction prone because it is associated with an OSR that result in a relatively small extinction risk. As a consequence, the impact of Allee effects on overall extinction risk is buffered. Moreover, the OSR of natural populations appears to be often male biased, thus making it unlikely that they will suffer from an Allee effect induced by mating system.     

High resolution analysis of mating systems: inbreeding in natural populations of Pinus radiata

Pinus radiata has a history of population bottlenecks and is currently restricted to five relatively small populations, three in mainland California, and two on islands off the coast of Baja California. Using highly polymorphic microsatellite markers and a newly developed statistical approach, we were able to estimate individual inbreeding coefficients and can thus analyse the mating system with high resolution. We find a bimodal distribution of inbreeding coefficients: most individuals result from selfing whereas few (in the mainland populations) to a modest number (in the island populations) are likely selfed. In most other pine species and presumably in the ancestral P. radiata population, occurrence of mature selfed individuals would be impossible because of the high genetic load. We therefore conclude that inbreeding depression has been purged in P. radiata and that the mating system has changed as a consequence.     

On the hypothesis that polymorphic enzyme alleles are selectively neutral. I. The evenness of allele frequency distribution

Using the theory developed by Ewens (1972, Theor. Pop. Biol.3, 87–112), some properties of the ratio of the observed to effective number of alleles are investigated. In particular the expected value of this ratio, as a function of the observed number of alleles, is seen to increase markedly under the neutral hypothesis. However, the corresponding values from field data for some drosophila species decrease as a function of the observed number of alleles.     

Ancestry-related assortative mating in Latino populations

Background

While spouse correlations have been documented for numerous traits, no prior studies have assessed assortative mating for genetic ancestry in admixed populations.

Results

Using 104 ancestry informative markers, we examined spouse correlations in genetic ancestry for Mexican spouse pairs recruited from Mexico City and the San Francisco Bay Area, and Puerto Rican spouse pairs recruited from Puerto Rico and New York City. In the Mexican pairs, we found strong spouse correlations for European and Native American ancestry, but no correlation in African ancestry. In the Puerto Rican pairs, we found significant spouse correlations for African ancestry and European ancestry but not Native American ancestry. Correlations were not attributable to variation in socioeconomic status or geographic heterogeneity. Past evidence of spouse correlation was also seen in the strong evidence of linkage disequilibrium between unlinked markers, which was accounted for in regression analysis by ancestral allele frequency difference at the pair of markers (European versus Native American for Mexicans, European versus African for Puerto Ricans). We also observed an excess of homozygosity at individual markers within the spouses, but this provided weaker evidence, as expected, of spouse correlation. Ancestry variance is predicted to decline in each generation, but less so under assortative mating. We used the current observed variances of ancestry to infer even stronger patterns of spouse ancestry correlation in previous generations.

Conclusions

Assortative mating related to genetic ancestry persists in Latino populations to the current day, and has impacted on the genomic structure in these populations.     

Mutation-selection balance in mixed mating populations

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.     

Competitive divergence in non-random mating populations

A haploid model of frequency-dependent selection and assortative mating is introduced and analyzed for the case of a single multiallelic autosomal locus. Frequency-dependent selection is due to intraspecific competition mediated by a quantitative character under stabilizing or directional selection. Assortment is induced by the same trait. We analyze the equilibrium structure and the local stability properties of all possible equilibria. In the limit of weak selection we obtain global stability properties by finding a Lyapunov function. We provide necessary and sufficient conditions for the maintenance of polymorphism in terms of the strength of stabilizing selection, intraspecific competition and assortment. Our results also include criteria for the ability of extreme types to invade the population. Furthermore, we study the occurrence of disruptive selection and provide necessary and sufficient conditions for intraspecific divergence to occur.     

Hardy-Weinberg equilibria in random mating populations

The structure of multiloci random mating populations is examined. Sufficient conditions for the existence of stable local Hardy-Weinberg equilibria for n loci and an arbitrary number of alleles per locus, are then derived for specified situations under the assumption of multiplicative gene action between loci. It is shown that a stable Hardy-Weinberg equilibrium can not be a local maximum of the mean fitness function with multiplicative gene action between loci. The stability of Hardy-Weinberg type border points and the condition for the increase of newly introduced genes are topics on which some n-loci results are also obtained for an arbitrary number of alleles per locus in systems that allow Hardy-Weinberg equilibria.