Intermediate Selfing Rates Research Articles

Cyclical dynamics under constant selection against mutations in haploid and diploid populations with facultative selfing.

We have found that constant selection against mutations can cause cyclical dynamics in a population with facultative selfing. When this happens, the distribution of the number of deleterious mutations per genotype fluctuates with the period approximately 1/sHe generations, where sHe is the coefficient of selection against a heterozygous mutation. The amplitude of oscillations of the mean population fitness often exceeds an order of magnitude. Cyclical dynamics can occur under intermediate selfing rates if selection against heterozygous mutations is weak and selection against homozygous mutations is much stronger. Cycling is possible without epistasis or with diminishing-returns epistasis, but not with synergistic epistasis. Under multiplicative selection, cycling might happen if the haploid mutation rate exceeds 1.9 in the case of selfing of haploids, and if this diploid mutation rate exceeds 4.5 in the case of selfing of diploids. We propose a heuristic explanation for cycling under facultative selfing and discuss its possible relevance.

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 distribution of individual inbreeding coefficients and pairwise relatedness in a population of mimulus guttatus

In order to infer population structure at the individual level, we estimated individual inbreeding coefficients and examined the relationship between geographical distance and genetic relatedness from polymorphic microsatellite data for a population of Mimulus guttatus that has an intermediate selfing rate. Expected heterozygosities for five microsatellites ranged from 0.79 to 0.93. The population inbreeding coefficient was calculated to be 0.19 (SE=0.023). A method-of-moments estimator developed by Ritland (1996b) was used to estimate the distribution of inbreeding among and relatedness between individuals of a natural population. The mean individual inbreeding coefficient (F=0.16) did not differ significantly from the population-level estimate. Most of the individuals appeared to be outbred, and there were very few plants that had estimated inbreeding coefficients greater than one-half. Individuals sampled from one transect showed significantly more inbreeding than individuals sampled along the other (P=0.005). There was no apparent relationship between interplant distance (range: 0-14 m) and mean genetic relatedness between individuals. These results represent the first application of polymorphic microsatellites to estimate fine-scale genetic population structure.

The mutation load under tetrasomic inheritance and its consequences for the evolution of the selfing rate in autotetraploid species

Single-locus equilibrium frequencies of a partially recessive deleterious mutation under the mutation–selection balance model are derived for partially selfing autotetraploid populations. Assuming multiplicative fitness interactions among loci, approximate solutions for the mean fitness and inbreeding depression values are also derived for the multiple locus case and compared with expectations for the diploid model. As in diploids, purging of deleterious mutations through consanguineous matings occurs in autotetraploid populations, i.e. the equilibrium mutation load is a decreasing function of the selfing rate. However, the variation of inbreeding depression with the selfing rate depends strongly on the dominance coefficients associated with the three heterozygous genotypes. Inbreeding depression can either increase or decrease with the selfing rate, and does not always vary monotonically. Expected issues for the evolution of the selfing rate consequently differ depending on the dominance coefficients. In some cases, expectations for the evolution of the selfing rate resemble expectations in diploids; but particular sets of dominance coefficients can be found that lead to either complete selfing or intermediate selfing rates as unique evolutionary stable state.

Evolution of intermediate selfing rates in plants: pollination ecology versus deleterious mutations

The evolutionarily stable rate of self-fertilzation is studied in phenotypic models that incorporate pollination ecology as well as the correlated evolution of inbreeding depression and the population mean selfing rate. Inbreeding depression is assumed to be caused by continual mutation to deleterious, partially recessive alleles. Several mutation rates and dominance levels are included. Two separate ecological cases are studied: how selfing rate affects proportion of ovules fertilized (pollination assurance, seed discounting) and how selfing rate affects male outcrossing success through pollen discounting. Evolutionarily stable rates are invariably zero or intermediate in two circumstances, namely when increased selfing causes (1) a decrease in the proportion of ovules fertilized or (2) an increase in pollen discounting and, therefore, a disproportionate decrease in male outcrossing success. Complete selfing is stable when selfing increases the proportion of ovules fertilized for all selfing rates. Stable selfing is zero or one in cases where the selfing rate has no effect on the proportion of ovules fertilized or when pollen discounting does not increase with selfing. Higher inbreeding depression tends to decrease the optimal selfing rate, and lower inbreeding depression (higher dominance coefficients and lower mutation rates) is more favorable to the existence of stable intermediate selfing rates. Approaches such as this that explicitly incorporate the interdependence of selfing, ovule fertilization, and male outcrossing may help explain the persistence of intermediate selfing rates in animal-pollinated plants.

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.

Evolution of the Selfing Rate and Resource Allocation Models

Abstract First, evolutionary theories of selfing of terrestrial plants are reviewed briefly. The evolution of the selfing rate is controlled mainly by (1) the benefit of enhanced genetic relatedness to seeds and (2) the cost of lowered fitness of selfed offspring (inbreeding depression), being modified by (3) fertility assurance under pollen limitation, (4) reduced performance as pollen donor, (5) reduced expenditure to male function, and (6) lowered genetic recombination. Models of the joint evolution of selfing and inbreeding depression predict either strong outcrossing or predominant selfing. Although wind‐pollinated plants fit the prediction, some animal‐pollinated species have intermediate selfing rates, refuting the theory.Second, three resource allocation models are analyzed, in which an individual plant optimally allocates limited resources to outcrossed seeds, selfed seeds, and to energy reserves for the next year. The first model explains how the number of outcrossed and selfed offspring change with plant size when they differ in dispersal distance. The second model predicts that, in a disturbed habitat, the plant is likely to be annual and to produce both selfed and outcrossed seeds; in contrast, in a stable habitat, the plant tends to be perennial and to abort selfed seeds selectively. Hand pollination may increase seed production for perennials but not for annuals. The third model explains the observed difference between animal and wind pollinated plants in the out‐crossing rate pattern by the difference in the way pollen acquisition increases with investment.

FITNESS CONSEQUENCES OF OUTCROSSING IN IMPATIENS CAPENSIS: TESTS OF THE FREQUENCY-DEPENDENT AND SIB-COMPETITION MODELS.

Using field and greenhouse experiments, we tested two hypotheses that could account for the maintenance of outcrossing in Impatiens capensis. Seedlings derived from cleistogamous (CL) and chasmogamous (CH) flowers were grown under competitive conditions while flanked by neighbors that were either related or unrelated. In both experiments, CH progeny sometimes expressed more phenotypic variability than CL progeny. In the greenhouse experiment, CH progeny attained the same weight as CL progeny, and the relatedness of neighboring plants did not affect the growth of either type. In the field experiment, CL and CH progeny performed similarly when grown with related competitors. However, CH progeny were somewhat larger when planted with nonsibs, while CL progeny were somewhat smaller under those conditions. Thus, there is no evidence that either frequency-dependent selection or the avoidance of competition among siblings favors the maintenance of outcrossing in this species. We also modeled the relative variability of selfed and outcrossed progeny under several reproductive systems. When females mate with one male (progeny are full sibs), selfed progeny are often more variable than outcrossed progeny. When females engage in both selfing and outcrossing, variation among progeny is frequently maximized at an intermediate selfing rate. The sib-competition mechanism, under a range of genetic models, is not apt to promote outcrossing, since selfed progeny are commonly more variable than outcrossed progeny.

On sex allocation and selfing in higher plants

Sex allocation (male allocation/female allocation) as a function of selfing rate is studied in the wild riceOryza perennis. Using dry weight measures, the male/female ratio is linearly related to the selfing rate. This linear relationship may have a fairly radical interpretation in terms of current sex allocation theory. It suggests that the intermediate selfing rates are themselves maintained by a form of frequency dependence. In particular, the linearity suggests: (i) the relative fitness of a selfed versus outcrossed offspring decreases with increased selfing; (ii) in equilibrium, a selfed offspring is approximately half as fit as an outcrossed offspring; (iii) the frequency dependence, being the opposite of that proposed in most selfing models, may result from the same forces thought to be involved in the maintenance of sex itself, and (iv) the position of the fitted line contains information about the plant's use of wind pollination for male reproduction. It suggests that wind shows much less mixing of pollen than previously assumed, and/or that there are severe morphological constraints on pollen presentation. The above interpretations are clearly speculative and tentative. Possible problems in the analysis, and some alternatives for data interpretation are discussed.

Deleterious mutations as an evolutionary factor. II. Facultative apomixis and selfing.

A population with u deleterious mutations per genome per generation is considered in which only those individuals that carry less than a critical number k of mutations are viable. Besides a large number of loci subject to mutation and selection, the genome contains one or two special loci responsible for the mode of reproduction. Amphimixis vs. apomixis and amphimixis vs. selfing are considered separately. In the first case, the genome degradation rate v (= u/square root k) is found to play the decisive role, as in the case of recombination. When v greater than 1.25, obligate amphimixis is established. If v decreases below this value, the alleles with first low and then larger penetrance are fixed, until alleles conferring obligate asexual reproduction become advantageous. The proportion of resources allocated to produce seeds also increases with decrease of v. These results are unlikely to depend on the genetic basis of the mode of reproduction. The result of competition between outcrossing and selfing depends on both u and k, as well as on whether the mutations are recessive. The alleles for selfing with low penetrance are selected against if the mutations are at all recessive. The fitness of alleles with high penetrance depends primarily on u, decreasing when u increases. There may exist conditions when only the alleles providing intermediate selfing rates can be fixed in a population. In other cases a population may exist with either obligate outcrossing or selfing at a high rate. Thus, truncation selection against deleterious mutations may be a factor supporting obligate or facultative sex despite the twofold advantage of apomixis or selfing.

Selection in plant populations of effectively infinite size: IV. The maintenance of males among hermaphrodites for a biallelic model

Conditions for the maintenance of males in androdioecious populations (populations with both male and hermaphrodite individuals) have been derived for four different one-locus two-allele models of inheritance of androdioecy. The results are not in general accordance with those already known: depending on the mode of inheritance, males can be maintained irrespective of their fertilities. If males are sufficiently fertile, it may happen that they are maintained only for intermediate selfing rates of the hermaphrodites. A result already found for gynodioecy is confirmed for androdioecy, namely, that a 1∶1 sex ratio is immediately established among zygotes if hermaphrodites appear as heterozygotes only.