Inbreeding under a cyclical mating system

Summary General recursion formulae for the coefficient of inbreeding under a cyclical mating system were derived in which one male and one female are selected from each of the n families per generation (population size N = 2 n). Each male is given the family number of his sire in each generation, while his mate comes from another family, varying systematically in different generations. Males of the r-th family in generations 1, 2, 3,..., t = n–1 within each cycle mate with females from families r+1, r+2, r+3,..., r+t to produce generations 2, 3, 4,..., t+1=1, respectively. The change in heterozygosity shows a cyclical pattern of rises and falls, repeating in cycles of n–1 generations. The rate of inbreeding oscillates between <-3% to >6% in different generations within each cycle, irrespective of the population size. The average rate of inbreeding per generation is approximately 1/[4 N-(Log₂N+1)], which is the rate for the maximum avoidance of inbreeding. The average inbreeding effective population size is approximately 2 N–2.     

Inbreeding depression and heterosis in populations of Schiedea viscosa, a highly selfing species

Progeny from self-pollinations and intrapopulation crosses were examined in Schiedea viscosa to determine the extent of inbreeding depression in this highly selfing species. Progeny of interpopulation crosses were also investigated to determine whether deleterious alleles have been fixed in populations of S. viscosa. There was no inbreeding depression at early life history stages, including seeds per capsule, seed mass, or germination. Inbreeding depression was detected for the later life history stage of fruit biomass, although not for survival or life span. Heterosis for vegetative biomass and fruit biomass was detected in progeny from crosses between populations. Levels of inbreeding depression in S. viscosa are low relative to out-crossing species of Schiedea, especially when early life history stages are compared.     

Inbreeding depression and mixed mating in Leptosiphon jepsonii: a comparison of three populations

BACKGROUND AND AIMS: Inbreeding depression is thought to play a central role in the evolution and maintenance of cross-fertilization. Theory indicates that inbreeding depression can be purged with self-fertilization, resulting in positive feedback for the selection of selfing. Variation among populations of Leptosiphon jepsonii in the timing and rate of self-fertilization provides an opportunity to study the evolution of inbreeding depression and mating systems. In addition, the hypothesis that differences in inbreeding depression for male and female fitness can stabilize mixed mating in L. jepsonii is tested. METHODS: In a growth room experiment, inbreeding depression was measured in three populations with mean outcrossing rates ranging from 0.06 to 0.69. The performance of selfed and outcrossed progeny is compared at five life history stages. To distinguish between self-incompatibility and early inbreeding depression, aborted seeds and unfertilized ovules were counted in selfed and outcrossed fruits. In one population, pollen and ovule production was quantified to estimate inbreeding depression for male and female fitness. KEY RESULTS: Both prezygotic barriers and inbreeding depression limited self seed set in the most outcrossing population. Cumulative inbreeding depression ranged from 0.297 to 0.501, with the lowest value found in the most selfing population. Significant inbreeding depression for early life stages was found only in the more outcrossing populations. Inbreeding depression was not significant for pollen or ovule production. CONCLUSIONS: The results provide modest support for the hypothesized relationship between inbreeding depression and mating systems. The absence of early inbreeding depression in the more selfing populations is consistent with theory on purging. Differences in male and female expression of inbreeding depression do not appear to stabilize mixed mating in L. jepsonii. The current estimates of inbreeding depression for L. jepsonii differ from those of previous studies, underscoring the effects of environmental variation on its expression.     

Inbreeding depression in perennial Lychnis viscaria (Caryophyllaceae): effects of population mating history and nutrient availability

We studied inbreeding depression in a perennial plant, Lychnis viscaria, in three populations differing in their inbreeding history and population size by measuring several traits at two nutrient levels over the plant's life cycle. The observed levels of inbreeding depression (cumulative inbreeding depression, from -0.057 to 0.629) were high for a plant with a mixed mating system. As expected, the population with a low level of isozyme variation expressed the least inbreeding depression for seed germination. Highest inbreeding depression for germination was found in the largest and genetically most variable population. No clear differences between populations in expression of inbreeding depression in the later life stages were found. The population level inbreeding depression varied with the nutrient conditions and among populations and life stages, but we found no evidence that inbreeding depression increased with lower nutrient availability. These results emphasize the importance of measuring inbreeding depression under several environmental conditions and over life stages.     

Inbreeding depression and low between-population heterosis in recently diverged experimental populations of a selfing species

In fragmented populations, genetic drift and selection reduce genetic diversity, which in turn results in a loss of fitness or in a loss of evolvability. Genetic rescue, that is, controlled input of diversity from distant populations, may restore evolutionary potential, whereas outbreeding depression might counteract the positive effect of this strategy. We carried out self-pollination and crosses within and between populations in an experimental subdivided population of a selfing species, Triticum aestivum L., to estimate the magnitude of these two phenomena. Surprisingly, for a self-fertilizing species, we found significant inbreeding depression within each population for four of the six traits studied, indicating that mildly deleterious mutations were still segregating in these populations. The progeny of within- and between-population crosses was very similar, indicating low between-population heterosis and little outbreeding depression. We conclude that relatively large population effective sizes prevented fixation of a high genetic load and that local adaptation was limited in these recently diverged populations. The kinship coefficient estimated between the parents using 20 neutral markers was a poor predictor of the progeny phenotypic values, indicating that there was a weak link between neutral diversity and genes controlling fitness-related traits. These results show that when assessing the viability of natural populations and the need for genetic rescue, the use of neutral markers should be complemented with information about the presence of local adaptation in the subdivided population.     

Inbreeding depression is high in a self‐incompatible perennial herb population but absent in a self‐compatible population showing mixed mating

High inbreeding depression is thought to be one of the major factors preventing evolutionary transitions in hermaphroditic plants from self‐incompatibility (SI) and outcrossing toward self‐compatibility (SC) and selfing. However, when selfing does evolve, inbreeding depression can be quickly purged, allowing the evolution of complete self‐fertilization. In contrast, populations that show intermediate selfing rates (a mixed‐mating system) typically show levels of inbreeding depression similar to those in outcrossing species, suggesting that selection against inbreeding might be responsible for preventing the transition toward complete self‐fertilization. By implication, crosses among populations should reveal patterns of heterosis for mixed‐mating populations that are similar to those expected for outcrossing populations. Using hand‐pollination crosses, we compared levels of inbreeding depression and heterosis between populations of Linaria cavanillesii (Plantaginaceae), a perennial herb showing contrasting mating systems. The SI population showed high inbreeding depression, whereas the SC population displaying mixed mating showed no inbreeding depression. In contrast, we found that heterosis based on between‐population crosses was similar for SI and SC populations. Our results are consistent with the rapid purging of inbreeding depression in the derived SC population, despite the persistence of mixed mating. However, the maintenance of outcrossing after a transition to SC is inconsistent with the prediction that populations that have purged their inbreeding depression should evolve toward complete selfing, suggesting that the transition to SC in L. cavanillesii has been recent. SC in L. cavanillesii thus exemplifies a situation in which the mating system is likely not at an equilibrium with inbreeding depression.     

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.     

Inbreeding depression in Solanum carolinense (Solanaceae) under field conditions and implications for mating system evolution

The clonal weed Solanum carolinense exhibits plasticity in the strength of its self-incompatibility (SI) system and suffers low levels of inbreeding depression (δ) in the greenhouse. We planted one inbred and one outbred plant from each of eight maternal plants in a ring (replicated twice) and monitored clonal growth, herbivory, and reproduction over two years. Per ramet δ was estimated to be 0.63 in year one and 0.79 in year two, and outbred plants produced 2.5 times more ramets than inbred plants in the spring of year two. Inbred plants also suffered more herbivore damage than outbred plants in both fields, suggesting that inbreeding compromises herbivore resistance. Total per genet δ was 0.85 over the two years, indicating that S. carolinense is unlikely to become completely self-compatible, and suggesting that plasticity in the SI system is part of a stable mixed-mating system permitting self-fertilization when cross pollen limits seed production.     

Inbreeding depression in an asexual population of Mimulus guttatus

The reproductive mechanism, that is whether an organism outcrosses, selfs or asexually reproduces, has a substantial impact on the amount and pattern of genetic variation. In this study, we estimate genetic variation and genetic load for a predominately asexual population of Mimulus guttatus, and then compare our results to other studies of predominately sexually reproducing (outcrossing and selfing) populations of M. guttatus. The asexual population had low levels of heterozygosity (H_e = 0.03) and low (but significantly non‐zero) inbreeding load, especially when compared with other M. guttatus populations. This differs greatly from the sexual populations of Mimulus that display substantial inbreeding depression. We discuss a variety of reasons why we see such low load in this study and suggest future research projects to further explore the questions.     

Evolution of coadaptation in a subdivided population

The interplay between population subdivision and epistasis is investigated by studying the fixation probability of a coadapted haplotype in a subdivided population. Analytical and simulation models are developed to study the evolutionary fate of two conditionally neutral mutations that interact epistatically to enhance fitness. We find that the fixation probability of a coadapted haplotype shows a marked increase when the population is genetically subdivided and subpopulations are loosely connected by migration. Moderate migration and isolation allow the propagation of the mutant alleles across subpopulations, while at the same time preserving the favorable allelic combination established within each subpopulation. Together they create the condition most favorable for the ultimate fixation of the coadapted haplotype. On the basis of the analytical and simulation results, we discuss the fundamental role of population subdivision and restricted gene flow in promoting the evolution of functionally integrated systems, with some implications for the shifting-balance theory of evolution.     

Inbreeding depression in two species of Mimulus (Scrophulariaceae) with contrasting mating systems

We examined the effect of self- and cross-pollination on germination success, flowering probability, pollen and ovule production, survivorship, and adult aboveground biomass in two species of Mimulus with contrasting mating systems: the highly seifing M. micranthus and an outcrossing population of M. guttatus. Cross-pollinations were performed both within and between populations in order to examine the scale at which the genetic load is distributed. We found significant inbreeding depression in M. guttatus in four of the six traits, with the highest inbreeding depression observed in biomass (68% and 69% based on within- and between-population crosses, respectively) and lowest in ovule production (21% based on between-population crosses only). M. micranthus displayed significant inbreeding depression in only two of the six traits examined. Again, we observed the highest inbreeding depression in biomass (47–60% based on within- and between-population crosses, respectively), but both traits showing significant differences between self and outcross progeny expressed lower inbreeding depression than in M. guttatus. We detected no significant inbreeding depression for either pollen or ovule production in M. micranthus. An estimate of total inbreeding depression based on the multiplicative effects of all traits was also lower in M. micanthus than∗∗∗ in M. guttatus. Our results are consistent with the expected purging of genetic load in populations with high selfing rates. The absence of inbreeding depression in M. micranthus pollen and ovule production, two traits with strong links to fitness in a selfing annual, further suggests the important role of directional selection in determining the population's genetic load. Comparison of cross-pollinations made within and between populations revealed little evidence of divergence of genetic load among the M. micranthus and M. guttatus populations examined.     

Inbreeding depression and purging in a haplodiploid: gender-related effects

Compared with diploid species, haplodiploids suffer less inbreeding depression because male haploidy imposes purifying selection on recessive deleterious alleles. However, alleles of genes only expressed in the diploid females are protected in heterozygous individuals. This leads to the prediction that haplodiploids suffer more from inbreeding effects on life-history traits controlled by genes with female-limited expression. To test this, we used a wild population of the haplodiploid mite Tetranychus urticae. First, negative effects of inbreeding were investigated by comparing maturation rate, juvenile survival, oviposition rate and longevity between lines created by three generations of either outbreeding or mother–son inbreeding. Second, purging through inbreeding was investigated by comparing the intensity of inbreeding depression between outbred families with known inbreeding/outbreeding mating histories. Negative effects of inbreeding and evidence for purging were found for the female trait oviposition rate, but not for juvenile survival and longevity. Both male and female maturation rate were negatively affected by inbreeding, most likely due to maternal effects because inbred offspring of outbred mothers was not affected. These results support the hypothesis that, in haplodiploids inbreeding effects and genetic variation due to deleterious recessive alleles may depend on gender.     

Inbreeding depression and its effect on intrinsic population dynamics in engraver beetles

Abstract.  1. Phloem-feeding bark beetles (Coleoptera: Curculionidae, Scolytinae) generally disperse before mating, leading to expectations of outbreeding. New York and British Columbia populations of engraver beetles ( Ips pini ) were tested for inbreeding depression using different methods. Among several traits measured, only the number of offspring surviving to adulthood was strongly reduced by inbreeding.
2. There was no evidence of avoidance of inbreeding depression in two possible mechanisms considered: differential male and female emergence times within full sib broods, and early termination of brood construction in forced sib mating.
3. Sib-mated females lay more eggs and have longer galleries than those in outbred crosses, despite a low rate of survival to adulthood for such eggs. This difference may be due to the ability of engraver beetles to assess crowding in broods as larvae begin to feed, and allows partial compensation for the effects of inbreed depression.
4. Population models assuming density-dependent generational effects were modified to account for inbreeding depression. Inbreeding depression makes populations less prone to cyclical behaviour, particularly at lower carrying capacities.
5. Inbreeding depression has not been previously measured in scolytids, nor has inbreeding-related behaviour been explicitly considered outside of exclusively inbreeding tribes.     

Inbreeding in a french peasant population

Genealogical pedigrees were collected from 976 farming couples who lived in a canton of central France in the XIXth and XXth century. Several methods (genealogical, isonymic and probability of origin of genes) were used to appraise the evolution of the biological structure of this population, which has gone through two phases. The first phase from 1800 to the World War I, shows gene flows between the farming population of the canton and those of neighbouring rural districts which are linked to an increase in consanguineous marriages. The second phase, from 1920 onwards, shows important gene flow from distant areas. This trend implies a decrease in consanguineous marriages.     

Host mating system and the prevalence of disease in a plant population

A modified susceptible-infected-recovered (SIR) host-pathogen model is used to determine the influence of plant mating system on the outcome of a host-pathogen interaction. Unlike previous models describing how interactions between mating system and pathogen infection affect individual fitness, this model considers the potential consequences of varying mating systems on the prevalence of resistance alleles and disease within the population. If a single allele for disease resistance is sufficient to confer complete resistance in an individual and if both homozygote and heterozygote resistant individuals have the same mean birth and death rates, then, for any parameter set, the selfing rate does not affect the proportions of resistant, susceptible or infected individuals at equilibrium. If homozygote and heterozygote individual birth rates differ, however, the mating system can make a difference in these proportions. In that case, depending on other parameters, increased selfing can either increase or decrease the rate of infection in the population. Results from this model also predict higher frequencies of resistance alleles in predominantly selfing compared to predominantly outcrossing populations for most model conditions. In populations that have higher selfing rates, the resistance alleles are concentrated in homozygotes, whereas in more outcrossing populations, there are more resistant heterozygotes.     

Host mating system and the spread of a disease-resistant allele in a population

The model presented here modifies a susceptible-infected (SI) host–pathogen model to determine the influence of mating system on the outcome of a host–pathogen interaction. Both deterministic and stochastic (individual-based) versions of the model were used. This model considers the potential consequences of varying mating systems on the rate of spread of both the pathogen and resistance alleles within the population. We assumed that a single allele for disease resistance was sufficient to confer complete resistance in an individual, and that both homozygote and heterozygote resistant individuals had the same mean birth and death rates. When disease invaded a population with only an initial small fraction of resistant genes, inbreeding (selfing) tended to increase the probability that the disease would soon be eliminated from a small population rather than become endemic, while outcrossing greatly increased the probability that the population would become extinct due to the disease.