Selfing Model Research Articles

Joint evolution of differential seed dispersal and self-fertilization.

Differential seed dispersal, in which selfed and outcrossed seeds possess different dispersal propensities, represents a potentially important individual-level association. A variety of traits can mediate differential seed dispersal, including inflorescence and seed size variation. However, how natural selection shapes such associations is poorly known. Here, we developed theoretical models for the evolution of mating system and differential seed dispersal in metapopulations, incorporating heterogeneous pollination, dispersal cost, cost of outcrossing and environment-dependent inbreeding depression. We considered three models. In the 'fixed dispersal model', only selfing rate is allowed to evolve. In the 'fixed selfing model', in which selfing is fixed but differential seed dispersal can evolve, we showed that natural selection favours a higher, equal or lower dispersal rate for selfed seeds to that for outcrossed seeds. However, in the 'joint evolution model', in which selfing and dispersal can evolve together, evolution necessarily leads to higher or equal dispersal rate for selfed seeds compared to that for outcrossed. Further comparison revealed that outcrossed seed dispersal is selected against by the evolution of mixed mating or selfing, whereas the evolution of selfed seed dispersal undergoes independent processes. We discuss the adaptive significance and constraints for mating system/dispersal association.

Genetic structure and diversity of the selfing model grass Brachypodium stacei (Poaceae) in Western Mediterranean: out of the Iberian Peninsula and into the islands.

Annual Mediterranean species of the genus Brachypodium are promising model plants for energy crops since their selfing nature and short-life cycles are an advantage in breeding programs. The false brome, B. distachyon, has already been sequenced and new genomic initiatives have triggered the de-novo genome sequencing of its close relatives such as B. stacei, a species that was until recently mistaken for B. distachyon. However, the success of these initiatives hinges on detailed knowledge about the distribution of genetic variation within and among populations for the effective use of germplasm in a breeding program. Understanding population genetic diversity and genetic structure is also an important prerequisite for designing effective experimental populations for genomic wide studies. However, population genetic data are still limited in B. stacei. We therefore selected and amplified 10 nuclear microsatellite markers to depict patterns of population structure and genetic variation among 181 individuals from 19 populations of B. stacei occurring in its predominant range, the western Mediterranean area: mainland Iberian Peninsula, continental Balearic Islands and oceanic Canary Islands. Our genetic results support the occurrence of a predominant selfing system with extremely high levels of homozygosity across the analyzed populations. Despite the low level of genetic variation found, two different genetic clusters were retrieved, one clustering all SE Iberian mainland populations and the island of Minorca and another one grouping all S Iberian mainland populations, the Canary Islands and all Majorcan populations except one that clustered with the former group. These results, together with a high sharing of alleles (89%) suggest different colonization routes from the mainland Iberian Peninsula into the islands. A recent colonization scenario could explain the relatively low levels of genetic diversity and low number of alleles found in the Canary Islands populations while older colonization events are hypothesized to explain the high genetic diversity values found in the Majorcan populations. Our study provides widely applicable information about geographical patterns of genetic variation in B. stacei. Among others, the genetic pattern and the existence of local alleles will need to be adequately reflected in the germplasm collection of B. stacei for efficient genome wide association studies.

Inbreeding Affects Gene Expression Differently in Two Self-Incompatible Arabidopsis lyrata Populations with Similar Levels of Inbreeding Depression.

Knowledge of which genes and pathways are affected by inbreeding may help understanding the genetic basis of inbreeding depression, the potential for purging (selection against deleterious recessive alleles), and the transition from outcrossing to selfing. Arabidopsis lyrata is a predominantly self-incompatible perennial plant, closely related to the selfing model species A. thaliana. To examine how inbreeding affects gene expression, we compared the transcriptome of experimentally selfed and outcrossed A. lyrata originating from two Scandinavian populations that express similar inbreeding depression for fitness (∂ ≈ 0.80). The number of genes significantly differentially expressed between selfed and outcrossed individuals were 2.5 times higher in the Norwegian population (≈ 500 genes) than in the Swedish population (≈ 200 genes). In both populations, a majority of genes were upregulated on selfing (≈ 80%). Functional annotation analysis of the differentially expressed genes showed that selfed offspring were characterized by 1) upregulation of stress-related genes in both populations and 2) upregulation of photosynthesis-related genes in Sweden but downregulation in Norway. Moreover, we found that reproduction- and pollination-related genes were affected by inbreeding only in Norway. We conclude that inbreeding causes both general and population-specific effects. The observed common effects suggest that inbreeding generally upregulates rather than downregulates gene expression and affects genes associated with stress response and general metabolic activity. Population differences in the number of affected genes and in effects on the expression of photosynthesis-related genes show that the genetic basis of inbreeding depression can differ between populations with very similar levels of inbreeding depression.

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.

Tuber melanosporum outcrosses: analysis of the genetic diversity within and among its natural populations under this new scenario

Tuber melanosporum is an ectomycorrhizal ascomycete producing edible ascocarps. The prevalent view is that this species strictly selfs, since genetic analyses have never detected heterozygotic profiles in its putatively diploid/dikaryotic gleba. The selfing model has also forged the experimental approaches to assess the population genetic variability. Here, the hypothesis that T. melanosporum outcrosses was tested. To this end, SSR (simple sequence repeats) and ITS (internal transcribed spacer) markers were employed to fingerprint asci and the surrounding gleba within single ascocarps. The distribution of genetic variability was also investigated at different geographical levels using single (SSR and ITS) and multilocus (AFLP, amplified fragment length polymorphism) markers. It is shown that T. melanosporum outcrosses since asci display additional alleles besides those present in the surrounding, uniparental, gleba. Furthermore, SSR and AFLP data reveal a high rate of intrapopulation diversity within samples from the same ground and root apparatus and the highest rate of genetic variability within the southernmost populations of the distributional range. These data call for a profound re-examination of T. melanosporum mating system, life cycle and strategies for managing man-made plantations. They also strongly support the idea that the last glaciation restricted the species distribution to the Italian and Spanish peninsulas.

Kin selection and coefficients of relatedness in family-structured populations with inbreeding

We consider family specific fitnesses that depend on mixed strategies of two basic phenotypes or behaviours. Pairwise interactions are assumed, but they are restricted to occur between sibs. To study the change in frequency of a rare mutant allele, we consider two different forms of weak selection, one applied through small differences in genotypic values determining individual mixed strategies, the other through small differences in viabilities according to the behaviours chosen by interacting sibs. Under these two specific forms of weak selection, we deduce conditions for initial increase in frequency of a rare mutant allele for autosomal genes in the partial selfing model as well as autosomal and sex-linked genes in the partial sib-mating model with selection before mating or selection after mating. With small differences in mixed strategies, we show that conditions for protection of a mutant allele are tantamount to conditions for initial increase in frequency obtained in additive kin selection models. With particular reference to altruism versus selfishness, we provide explicit ranges of values for the selfing or sib-mating rate based on a fixed cost–benefit ratio and the dominance scheme that allow the spreading of a rare mutant allele into the population. This study confirms that more inbreeding does not necessarily promote the evolution of altruism. Under the hypothesis of small differences in viabilities, the situation is much more intricate unless an additive model is assumed. In general however, conditions for initial increase in frequency of a mutant allele can be obtained in terms of fitness effects that depend on the genotypes of interacting individuals or their mates and generalized conditional coefficients of relatedness according to the inbreeding condition of the interacting individuals.

Selfing and biparental inbreeding: a mating system analysis in Lymnaea peregra (Gastropoda: Lymnaeidae)

The mating system was analysed in three populations of Lymnaea peregra, under the mixed-mating model (MMM) and the effective selfing model (ESM), using progeny array data and allozyme markers. The results revealed variation among populations for the outcrossing rate (tm ranged from 0.646 to 0.983). This finding modifies the earlier classification of L. peregra as a predominantly outcrossing species. The occurrence of biparental inbreeding and population substructure in one of three populations was suggested from positive (tm—ts) under the MMM, covariation of the effective selfing rate with parental fixation index, as well as the great difference between the effective selfing rate of inbred and outbred parents under the ESM. The within-population distribution of the outcrossing rates varied extensively and may involve different patterns of selection and levels of inbreeding depression among the populations studied. Consistently, the estimation of correlated matings showed different levels of the correlation of selfing within progenies in the three populations. Levels of multiple paternity for the outcrossed progeny were positively associated with higher population outcrossing rates, which may reflect the propensity of preferential outcrossers to copulate actively.

WHOLE- AND PART-FLOWER SELF-POLLINATION IN GLYCINE CLANDESTINA AND G. ARGYREA AND THE EVOLUTION OF AUTOGAMY.

The overall rate of self-fertilization can be viewed as the sum of two distinct processes: 1) self-pollination of all ovules in a flower (whole-flower self-pollination); and 2) self-pollination of some of the ovules in a flower, occurring together with outcrossing of the remaining ovules (part-flower self-pollination). In some situations these processes may be equated with different modes of self-pollination. A model of the mating system in which the progeny of separate fruits serve as the unit of observation is presented. The model partitions the overall rate of self-pollination into components attributable to whole- and part-flower selfing. When the mating system is estimated using information on marker genotypes from chasmogamous fruits in two species of Glycine together with the whole- and part-flower selfing model, the results indicate that the chasmogamous flowers in a subalpine population of G. clandestina underwent a significant level of whole-flower selfing, whereas in another, lower elevation population of G. clandestina and in a subtropical population of G. argyrea, they did not. This difference is thought to be related to the contrast in the variability of environmental conditions for insect-mediated pollination between the habitats sampled. In particular, the large component of whole-flower selfing observed in the subalpine population of G. clandestina may be due to self-pollination that is induced during periods unfavorable to insect-mediated pollination. It can be demonstrated that such induced selfing will be selected whenever environmental conditions are such that pollinator activity limits seed set, and moreover that induced selfing can result in the selection of overall levels of self-pollination that are intermediate between 0 and 1. Monte Carlo simulation is employed to show that ignoring the correlation of self-fertilization events that result from whole- and part-flower selfing may lead to biased estimates of mating system parameters.

Joint Maximum Likelihood Estimation of Genetic and Mating Structure Using Open-Pollinated Progenies

SUMMARY Maximum likelihood estimation is described for parameters of genetic and mating structure under two plant mating system models, the mixed-mating model and the effective selfing model. Genetic structure is described by Wright's gene fixation index, which measures excess homozygosity at a single locus, and mating structure is described by selfing rates. The unit of observation is treated as the entire array of open-pollinated progeny genotypes at a single locus, descended from a maternal parent of unknown genotype. For the mixed-mating model, recursions are given for joint estimates of selffertilization rate s, fixation index of parents F, and allele frequencies of each sex. For the effective selfing model, recursions are given for joint estimates of effective selfing rate of inbred parents si, effective selfing rate of outbred parents so, fixation index F, and allele frequency among both sexes. Two alternate forms are given for each recursion. The first is the single-variable Newton-Raphson (Fisher scoring) method, where information divides the score. The second is the expectationmaximization (EM) method, which can be derived from the first method by increasing the information to that expected if the underlying variables of incomplete data could be directly observed. The EM form is more numerically stable, whereas the Newton-Raphson form gives faster convergence and allows negative estimates. Consideration of the progeny array as the unit of sampling allows asymptotic variances to be a function of progeny array size, for fixed total zygote sample size. The optimal number of progeny per array, which minimizes variance of estimates, is from 4 to 8 zygotes for F and the generational change of gene fixation, AF. It is near 4 for inbred and/or substructured populations and for more alleles/ more extreme allele frequencies, and near 8 for outbred populations. Optimal number is large for s, while in contrast, optimal number can be 4-5 for the effective selfing rate E (an average of si and so) because of variation of selfing rate among plants in substructured populations. Progeny sizes as low as 2 give information but a minimum size of 3 is recommended.

THE EFFECTIVE PROPORTION OF SELF-FERTILIZATION WITH CONSANGUINEOUS MATINGS IN INBRED POPULATIONS

Allelic segregation at a single locus among offspring derived from matings, including those between inbred relatives, is a combination of two patterns, corresponding to self-fertilization and random outcrossing. The proportion of effective self-fertilization is termed the "effective selfing rate," and it is specified with identity coefficients. The description of the offspring genotypic distribution for a population with mating among relatives requires a set of three independent parameters of genetic and mating structure. One such set is the inbreeding coefficient of parents, the coefficient of kinship between mates and the effective selfing rate. The model used to derive the effective selfing rate distinguishes between the effective selfing rates of inbred vs. outbred parents; the mixed mating model does not distinguish between these two rates. As a result, the mixed mating model usually gives biased estimates of effective selfing, if there is mating among inbred relatives. The procedure for estimation of effective selfing, based upon progeny array data distributed according to the "effective selfing model," is presented, and an example is given.

Some aspects of a stochastic two locus selfing genetic model with selection and computer simulation

The present paper examines a specific genetic model as a finite Markov process, using the normal matrix approach. This model is the two locus selfing model with selection studied by Tan (1973), who used an eigenvalue approach. The properties of the process are analytically and numerically investigated and the effects of selection and crossover on the transition from a heterozygotic parent through several generations of heterozygotic progeny are assessed. These results enlarge upon Tan's work and, in addition, present two new aspects of the model. In particular (1) the expected number of generations of heterozygotic progeny of genotype j that will descend from a heterozygotic parent of genotype i and (2) the variance of this number of generations about the mean value have not been previously considered.

Applications of Some Finite Markov Chain Theories to Two Locus Selfing Model with Selection

In this paper, we apply some finite Markov chain theories to study the two locus selfing model with selection. Specifically, the effects of selection and linkage on the ultimate absorption probabilities, the first time absorption probabilities, the mean absorption times and the variances of first absorption times, are assessed. Also discussed are the effects of selection on the absolute probability distributions, the variances of the nth generation and the covariances between the nith and the (n, + n2)th generations. Some formulas using the spectral expansion of matrix are given for the absorption probabilities, the mean absorption times and the variances of the first time absorptions.