Analysis of population structure in autotetraploid species.

Population structure parameters commonly used for diploid species are reexamined for the particular case of tetrasomic inheritance (autotetraploid species). Recurrence equations that describe the evolution of identity probabilities for neutral genes in an "island model" of population structure are derived assuming tetrasomic inheritance. The expected equilibrium value of FST is computed. In contrast to diploids, the correlation of genes between individuals within populations with respect to genes between populations (FST) may vary among loci due to the particular segregation patterns expected under tetrasomic inheritance and is consequently inappropriate for estimating demographic parameters in such populations. We thus define a new parameter (rho) and derive its relationship with Nm. This relationship is shown to be independent from both the selfing rate and the proportion of double reduction. Finally, the statistical procedure required to evaluate these parameters using data on gene frequencies distribution among autotetraploid populations is developed.     

ABSENCE OF POLLEN DISCOUNTING IN A GENOTYPE OF IPOMOEA PURPUREA EXHIBITING INCREASED SELFING

Throughout southeastern North America, the annual morning glory Ipomoea purpurea exhibits a polymorphism at a locus that influences the intensity of floral pigmentation. Previous studies have shown that when rare, the homozygous white genotype has a greater selfing rate than the homozygous dark genotype. In the absence of pollen discounting (a reduction in transmission of pollen to other plants by genotypes that exhibit increased selfing) and inbreeding depression, this increased selfing rate should favor the white allele. Experiments reported here confirm that the white genotype has elevated selfing rates when rare but indicate pollen discounting is not associated with elevated selfing. Rather, white genotypes contribute more pollen to the outcross pollen pool. The disparity between genotypes in both selfing rates and success at pollen contribution to other plants disappears at intermediate to high frequencies of the white allele. Pollinator movements are consistent with the pattern of selfing. These results suggest that elevated selfing and enhanced success at pollen donation contribute to maintenance of the white allele in natural populations of morning glories.     

GAMETOPHYTIC SELF-FERTILIZATION IN HOMOSPOROUS PLANTS: DEVELOPMENT,EVALUATION, AND APPLICATION OF A STATISTICAL METHOD FOR EVALUATING ITS IMPORTANCE

The methods described here make it possible to use data on sporophytic genotype frequencies to estimate the frequency of gametophytic self-fertilization in populations of homosporous plants. Bootstrap bias reduction is effective in reducing or eliminating the bias of the maximum likelihood estimate of the gametophytic selfing rate. The bias-corrected percentile method provides the most reliable confidence intervals for allele frequencies. The percentile method gives the most reliable confidence intervals for the gametophytic selfing rate when selfing is common. The maximum likelihood intervals, the percentile intervals, the bias-corrected percentile intervals, and the bootstrap t intervals are all overly conservative in their construction of confidence intervals for the gametophytic selfing rate when self-fertilization is rare. Application of the recommended methods indicates that gametophytic self-fertilization is quite rare in two sexually reproducing populations of Pellaea andromedifolia studied by Gastony and Gottlieb (1985).     

Selection caused by self-fertilization I. Four measures of self-fertilization and their effects on fitness

The standard models of selfing in seed plants consider only the ovules, which are assumed to have a constant selfing rate. It has recently become clear, however, that hermaphrodite or monoecious populations frequently show sexual asymmetry (nonconstant pollen:ovule fertilities among individuals). Such asymmetry usually results in pollen selfing rates which differ from those for the ovules and are frequency-dependent even for constant ovule selfing rates. A recent study of selfing rates for all gametes of an individual is extended here to include four selfing rates (for ovules, pollen, all gametes, and zygotes), and simple mathematical relationships linking the four rates are obtained. Unlike earlier models of selfing, it is not assumed that the ovule selfing rate is constant, but instead that this rate, like all the others, is determined by the mobility of the pollen, which in turn is determined by the floral biology and ecology. It is found that all four selfing rates are usually frequency-dependent. The selfing rate for all gametes (the combined selfing rate) is usually intermediate between those for the ovules and pollen, and the zygotic rate is usually the smallest of the four. The exceptions to the above statements occur for relatively extreme situations, such as complete selfing for pollen or ovules, no selfing, or sexual symmetry. Three modes of selfing are considered: prior (PS), competing (CS), and delayed (DS) self-fertilization. It is shown that if there are at least two types with different selfing rates in the population, then the ranking of their selfing rates may depend upon the frequencies of the types (for the combined and the zygotic rates), may be frequency-independent (ovule rate), or may be dependent or independent, according to the mode of selfing (pollen rate). The effects of the various influences on the amount of selfing are by no means negligible. Thus a numerical study shows pollen selfing rates for one type which vary from 0.09 to 0.96, according to its frequency. Another numerical result shows a change in combined selfing rate from 0.13 to 0.86, depending solely on the mode of selfing. Results for Scots Pine show that an ovule selfing rate of 0.5 was accompanied by a combined rate of 0.143.The population selfing rate is not the same as the mean of individual selfing rates, and can only be obtained if female fitnesses as well as ovule selfing rates are known for each type.Previous models of selfing have failed to distinguish between the effects of increased selfing and increased pollen fertility, with the result that increased selfing always resulted in greater fitness. In the present models the two effects are distinguishable, and it is found that increased selfing may result in increased or decreased fitness, depending also on population density and on a form of pollen density. Thus the old dogma that in the absence of viability and fertility selection increased selfing always results in increased fitness is finally refuted, and the importance of the influence of ecological parameters on selfing and fitness is emphasized, since population density and pollen density influence the selfing rates.     

Two's company, three's a crowd: experimental evaluation of the evolutionary maintenance of trioecy in Mercurialis annua (Euphorbiaceae)

Trioecy is an uncommon sexual system in which males, females, and hermaphrodites co-occur as three clearly different gender classes. The evolutionary stability of trioecy is unclear, but would depend on factors such as hermaphroditic sex allocation and rates of outcrossing vs. selfing. Here, trioecious populations of Mercurialis annua are described for the first time. We examined the frequencies of females, males and hermaphrodites across ten natural populations and evaluated the association between the frequency of females and plant densities. Previous studies have shown that selfing rates in this species are density-dependent and are reduced in the presence of males, which produce substantially more pollen than hermaphrodites. Accordingly, we examined the evolutionary stability of trioecy using an experiment in which we (a) indirectly manipulated selfing rates by altering plant densities and the frequency of males in a fully factorial manner across 20 experimental plots and (b) examined the effect of these manipulations on the frequency of the three sex phenotypes in the next generation of plants. In the parental generation, we measured the seed and pollen allocations of hermaphrodites and compared them with allocations by unisexual plants. In natural populations, females occurred at higher frequencies in denser patches, a finding consistent with our expectations. Under our experimental conditions, however, no combination of plant densities and male frequencies was associated with increased frequencies of females. Our results suggest that the factors that regulate female frequencies in trioecious populations of M. annua are independent of those regulating male frequencies (density), and that the stable co-existence of all three sex phenotypes within populations is unlikely.     

SEX CHANGE WITH INBREEDING: EXPERIMENTS ON SEPARATE VERSUS COMBINED SEXES

Ipomopsis rubra plants grown in the laboratory initially produced hermaphrodite flowers, but some self- or sib-mated individuals switched to produce large numbers of pistillate (male sterile) flowers. The sex change did not occur with outcrossing. Plants with extreme male sterility were also observed in natural populations, usually in smaller individuals. Male sterility may be compensated by more seeds (resource reallocation), better seeds (avoidance of selfing), or both. Pistillate flowers were smaller, so savings could be used for additional seeds. Selfed seeds had reduced survival and fecundity, so avoidance of selfing could produce better quality offspring. We explored costs and benefits of sex change with two fitness models. The first assumes randomoutcross matings. Estimates of resource reallocation and inbreeding (selfing) depression are sufficient for pistillate inflorescences to have equal or greater fitness than hermaphrodite inflorescences if the selfing rate is high. Frequencies of sex change with intensive self-pollination were consistent with this model. The second model assumes all nonself matings are between sibs in “local mating” groups. Parents may benefit by male sterility in offspring, but gains would be higher if sex change occurred earlier and at higher than observed frequencies.     

Joint effects of self-fertilization and population structure on mutation load, inbreeding depression and heterosis

Both the spatial distribution of organisms and their mode of reproduction have important effects on the change in allele frequencies within populations. In this article, we study the combined effect of population structure and the rate of partial selfing of organisms on the efficiency of selection against recurrent deleterious mutations. Assuming an island model of population structure and weak selection, we express the mutation load, the within- and between-deme inbreeding depression, and heterosis as functions of the frequency of deleterious mutants in the metapopulation; we then use a diffusion model to calculate an expression for the equilibrium probability distribution of this frequency of deleterious mutants. This allows us to derive approximations for the average mutant frequency, mutation load, inbreeding depression, and heterosis, the simplest ones being Equations 35-39 in the text. We find that population structure can help to purge recessive deleterious mutations and reduce the load for some parameter values (in particular when the dominance coefficient of these mutations is <0.2-0.3), but that this effect is reversed when the selfing rate is above a given value. Conversely, within-deme inbreeding depression always decreases, while heterosis always increases, with the degree of population subdivision, for all selfing rates.     

A Markov chain Monte Carlo approach for joint inference of population structure and inbreeding rates from multilocus genotype data

Nonrandom mating induces correlations in allelic states within and among loci that can be exploited to understand the genetic structure of natural populations (Wright 1965). For many species, it is of considerable interest to quantify the contribution of two forms of nonrandom mating to patterns of standing genetic variation: inbreeding (mating among relatives) and population substructure (limited dispersal of gametes). Here, we extend the popular Bayesian clustering approach STRUCTURE (Pritchard et al. 2000) for simultaneous inference of inbreeding or selfing rates and population-of-origin classification using multilocus genetic markers. This is accomplished by eliminating the assumption of Hardy-Weinberg equilibrium within clusters and, instead, calculating expected genotype frequencies on the basis of inbreeding or selfing rates. We demonstrate the need for such an extension by showing that selfing leads to spurious signals of population substructure using the standard STRUCTURE algorithm with a bias toward spurious signals of admixture. We gauge the performance of our method using extensive coalescent simulations and demonstrate that our approach can correct for this bias. We also apply our approach to understanding the population structure of the wild relative of domesticated rice, Oryza rufipogon, an important partially selfing grass species. Using a sample of n = 16 individuals sequenced at 111 random loci, we find strong evidence for existence of two subpopulations, which correlates well with geographic location of sampling, and estimate selfing rates for both groups that are consistent with estimates from experimental data (s approximately 0.48-0.70).     

Chiasmata and the breeding system in wild populations of diploid wheats

Seven populations of the selfer Triticum longissimum (= Aegilops longissima) and five populations of the closely related outbreeder T. speltoides (= Ae. speltoides) were scored for chiasma frequencies in pollen mother cells. The populations of the selfer have significantly higher frequencies of chiasmata than the outbreeding populations. This difference becomes even clearer when interstitial chiasmata alone are compared. It is argued that an optimal degree of effective recombination is achieved by the balance between outbreeding and interstitial chiasmata. — There are wider differences between the selfing populations than between the outbreeding populations, but the differences between families (within populations) are small in both species. Variation between plants within families seems to be lower in the selfer, but nevertheless high enough to be inexplicable on the basis of selfing alone. — Small populations subject to hardship conditions show a higher frequency of chiasmata than others.     

The consequences of rare sexual reproduction by means of selfing in an otherwise clonally reproducing species

Clonal reproduction of diploids leads to an increase in heterozygosity over time. A single round of selfing will then create new homozygotic genotypes. Given the same allele frequencies, heritable genetic variation is larger when there are more extreme, i.e. homozygotic genotypes. So after a long clonal expansion, one round of selfing increases heritable genetic variation, but any fully or partially recessive deleterious alleles simultaneously impose a fitness cost. Here we calculate that the cost of selfing in the yeast Saccharomyces is experienced only by a minority of zygotes. This allows a round of selfing to act as an evolutionary capacitor to unlock genetic variation previously found in a cryptic heterozygous form. We calculate the evolutionary consequences rather than the evolutionary causes of sex. We explore a range of parameter values describing sexual frequencies, focusing especially on the parameter values known for wild Saccharomyces. Our results are largely robust to many other parameter value choices, so long as meiosis is rare relative to the strength of selection on heterozygotes. Results may also be limited to organisms with a small number of genes. We therefore expect the same phenomenon in some other species with similar reproductive strategies.     

The diffusion model for migration and selection in a plant population

 The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies. The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations. Received 30 August 1995; received in revised form 23 February 1996     

Linkage Modification with Mixed Random Mating and Selfing: A Numerical Study

Although recombination cannot increase under conditions of random mating or complete selfing in regimes of constant selection, with mixed random mating and selfing, selection for increased recombination can occur. For some fitness regimes there may be selection for reduced recombination with both low and high degrees of selfing but selection for increased recombination with moderate degrees of selfing. With some fitness regimes there is a historical effect: depending on which equilibrium a population starts from, there may be selection for either increased or decreased recombination. In other cases the direction of selection may be determined by the present state of individuals within the population. If recombination is already fairly limited, there may be selection for further reduction. If recombination is already fairly frequent, there may be selection for increased recombination. For certain symmetric viability systems there may be an intermediate value of the recombination fraction between 0 and 0.5 toward which the population will evolve. Although it is not yet possible to classify precisely those fitness matrices that can exhibit selection for increased recombination, it does appear that selection for increased recombination can occur only if at least two of the double homozygotes are less fit than would be expected on the basis of a comparison of the fitnesses of the single and double heterozygotes on an additive scale.     

The consequences of rare sexual reproduction by means of selfing in an otherwise clonally reproducing species

Clonal reproduction of diploids leads to an increase in heterozygosity over time. A single round of selfing will then create new homozygotic genotypes. Given the same allele frequencies, heritable genetic variation is larger when there are more extreme, i.e. homozygotic genotypes. So after a long clonal expansion, one round of selfing increases heritable genetic variation, but any fully or partially recessive deleterious alleles simultaneously impose a fitness cost. Here we calculate that the cost of selfing in the yeast Saccharomyces is experienced only by a minority of zygotes. This allows a round of selfing to act as an evolutionary capacitor to unlock genetic variation previously found in a cryptic heterozygous form. We calculate the evolutionary consequences rather than the evolutionary causes of sex. We explore a range of parameter values describing sexual frequencies, focusing especially on the parameter values known for wild Saccharomyces. Our results are largely robust to many other parameter value choices, so long as meiosis is rare relative to the strength of selection on heterozygotes. Results may also be limited to organisms with a small number of genes. We therefore expect the same phenomenon in some other species with similar reproductive strategies.     

The genetic mating structure of subdivided populations I. Open-mating model

The genetic mating structure of a subdivided population can describe how parental genotypes gave rise to zygotes. When parents of the same genotype are considered together as one class (“open-mating”), three independent parameters of inbreeding and mating structure are needed to describe this structure at a diallelic locus. One is Wright's fixation index F. The other two are mating structure parameters, derived herein and termed the “effective selfing” rate E and the “inbreeding assortative selfing” rate D. E is the genetically equivalent proportion of self-fertilization at a single locus, and is given by standardized second and third central moments of gene frequencies of mates. E is a summary measure of inbreeding that includes effects due to self-fertilization and mating to relatives, as well as correlations between mates induced by Wahlund effects and/or selective diversification among neighborhoods. The second parameter D measures the tendency of inbred or more homozygous individuals to effectively self more (or less) than outbred or more heterozygous individuals. D is related to the maintenance of variation of inbreeding among individuals and/or to the prevalence of spatial variation of selection. D is independent of E, but together with E controls the generational change of inbreeding, ΔF. Extensions of the model to unequal allele frequencies in male vs female mates, and to multi-allelic loci, are also examined.     

植物种群交配系统、亲本分析以及基因流动研究

 在过去的二十年中,有关植物种群交配与散布过程的研究与日俱增,重点集中在利用母本子代系列(Maternal progeny arrays)来估计种群间自交与异交的相对比例,种群的花粉散布与雄性育性变异的模式。早期的研究主要依靠排除法来确定亲本,但几乎同时也意识到基因流动事件几乎是检测不到的。在大多数估计中,难以做到为大多数非迁移子代确定唯一的亲本。因此,基因流动与雄性育性的最大似然性方法得以引入该领域的研究。本文介绍了用单位点和多位点模型来估计家系与种群自交与异交的相对频率,着重阐述了目前可用于亲本分析与基因流的估计方法。最后介绍了我们对木根麦冬交配系统与亲本分析的研究以及亲本分析将来的研究方向。     

HIGH INBREEDING DEPRESSION,SELECTIVE INTERFERENCE AMONG LOCI,AND THE THRESHOLD SELFING RATE FOR PURGING RECESSIVE LETHAL MUTATIONS

The evolutionary dynamics of recessive or slightly dominant lethal mutations in partially self-fertilizing plants are analyzed using two models. In the identity-equilibrium model, lethals occur at a finite number of unlinked loci among which genotype frequencies are independent in mature plants. In the Kondrashov model, lethals occur at an infinite number of unlinked loci with identity disequilibrium produced by partial selfing. If the genomic mutation rate to (nearly) recessive lethal alleles is sufficiently high, such that the mean number of lethals (or lethal equivalents) per mature plant maintained at equilibrium under complete outcrossing exceeds 10, selective interference among loci creates a sharp discontinuity in the mean number of lethals maintained as a function of the selfing rate. Virtually no purging of the lethals occurs unless the selfing rate closely approaches or exceeds a threshold selfing rate, at which there is a precipitous drop in the mean number of lethals maintained. Identity disequilibrium lowers the threshold selfing rate by increasing the ratio of variance to mean number of lethals per plant, increasing the opportunity for selection. This theory helps to explain observations on plant species that display very high inbreeding depression despite intermediate selfing rates.     

Reliable selfing rate estimates from imperfect population genetic data

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.     

Population Dynamics Inferred from Temporal Variation at Microsatellite Loci in the Selfing Snail Bulinus Truncatus

We analyzed short-term forces acting on the genetics of subdivided populations based on a temporal survey of the microsatellite variability in the hermaphrodite freshwater snail Bulinus truncatus. This species inhabits temporary habitats, has a short generation time and exhibits variable rates of selfing. We studied the variability over three sampling dates in 12 Sahelian populations (1161 individuals). Classical genetic parameters (estimators of H(o), H(e), f, selfing rate and Fst) showed limited change over time whereas important temporal changes of allelic frequencies were detected for 10 of the ponds studied. These variations are not easily explained by selection, sampling drift and genetic drift alone and may be due to periodic migration. Indeed the habitats occupied by the populations studied are subject to large temporal fluctuations owing to annual cycles of drought and flood. In such ponds our results support a demographic model of population expansions and contractions under which available habitats, after the rainy season, are colonized by individuals originating from a smaller number of refuges (areas that never dry out in the deepest parts of the ponds). In contrast, selfing appeared to be an important force affecting the genetic structure in permanent ponds.     

Multilocus estimation of selfing and its heritability

We describe a new method of estimating the selfing rate (S) in a mixed mating population based on a population structure approach that accounts for possible intergenerational correlation in selfing rate, giving rise to an estimate of the upper limit for heritability of selfing rate (h(2)). A correlation between generations in selfing rate is shown to affect one- and two-locus probabilities of identity by descent. Conventional estimates of selfing rate based on a population structure approach are positively biased by intergenerational correlation in selfing. Multilocus genotypes of individuals are used to give maximum-likelihood estimates of S and h(2) in the presence of scoring artifacts. Our multilocus estimation of selfing rate and its heritability (MESH) method was tested with simulated data for a range of conditions. Selfing rate estimates from MESH have low bias and root mean squared error, whereas estimates of the heritability of selfing rate have more uncertainty. Increasing the number of individuals in a sample helps to reduce bias and root mean squared error more than increasing the number of loci of sampled individuals. Improved estimates of selfing rate, as well as estimates of its heritability, can be obtained with this method, although a large number of loci and individuals are needed to achieve best results.     

The evolutionary response of mating system to heterosis

Isolation allows populations to diverge and to fix different alleles. Deleterious alleles that reach locally high frequencies contribute to genetic load, especially in inbred or selfing populations, in which selection is relaxed. In the event of secondary contact, the recessive portion of the genetic load is masked in the hybrid offspring, producing heterosis. This advantage, only attainable through outcrossing, should favour evolution of greater outcrossing even if inbreeding depression has been purged from the contributing populations. Why, then, are selfing‐to‐outcrossing transitions not more common? To evaluate the evolutionary response of mating system to heterosis, we model two monomorphic populations of entirely selfing individuals, introduce a modifier allele that increases the rate of outcrossing and investigate whether the heterosis among populations is sufficient for the modifier to invade and fix. We find that the outcrossing mutation invades for many parameter choices, but it rarely fixes unless populations harbour extremely large unique fixed genetic loads. Reversions to outcrossing become more likely as the load becomes more polygenic, or when the modifier appears on a rare background, such as by dispersal of an outcrossing genotype into a selfing population. More often, the outcrossing mutation instead rises to moderate frequency, which allows recombination in hybrids to produce superior haplotypes that can spread without the mutation's further assistance. The transience of heterosis can therefore explain why secondary contact does not commonly yield selfing‐to‐outcrossing transitions.