Non-random mating for selection with restricted rates of inbreeding and overlapping generations

Minimum coancestry mating with a maximum of one offspring per mating pair (MC1) is compared with random mating schemes for populations with overlapping generations. Optimum contribution selection is used, whereby ΔF is restricted. For schemes with ΔF restricted to 0.25% per year, 256 animals born per year and heritability of 0.25, genetic gain increased with 18% compared with random mating. The effect of MC1 on genetic gain decreased for larger schemes and schemes with a less stringent restriction on inbreeding. Breeding schemes hardly changed when omitting the iteration on the generation interval to find an optimum distribution of parents over age-classes, which saves computer time, but inbreeding and genetic merit fluctuated more before the schemes had reached a steady-state. When bulls were progeny tested, these progeny tested bulls were selected instead of the young bulls, which led to increased generation intervals, increased selection intensity of bulls and increased genetic gain (35% compared to a scheme without progeny testing for random mating). The effect of MC1 decreased for schemes with progeny testing. MC1 mating increased genetic gain from 11–18% for overlapping and 1–4% for discrete generations, when comparing schemes with similar genetic gain and size.     

Mating schemes for optimum contribution selection with constrained rates of inbreeding

The effect of non-random mating on genetic response was compared for populations with discrete generations. Mating followed a selection step where the average coancestry of selected animals was constrained, while genetic response was maximised. Minimum coancestry (MC), Minimum coancestry with a maximum of one offspring per mating pair (MC1) and Minimum variance of the relationships of offspring (MVRO) mating schemes resulted in a delay in inbreeding of about two generations compared with Random, Random factorial and Compensatory mating. In these breeding schemes where selection constrains the rate of inbreeding, ΔF, the improved family structure due to non-random mating increased genetic response. For schemes with ΔF constrained to 1.0% and 100 selection candidates, genetic response was 22% higher for the MC1 and MVRO schemes compared with Random mating schemes. For schemes with a less stringent constraint on ΔF or more selection candidates, the superiority of the MC1 and MVRO schemes was smaller (5–6%). In general, MC1 seemed to be the preferred mating method, since it almost always yielded the highest genetic response. MC1 mainly achieved these high genetic responses by avoiding extreme relationships among the offspring, i.e. fullsib offspring are avoided, and by making the contributions of ancestors to offspring more equal by mating least related animals.     

Mating animals by minimising the covariance between ancestral contributions generates less inbreeding without compromising genetic gain in breeding schemes with truncation selection

We reasoned that mating animals by minimising the covariance between ancestral contributions (MCAC mating) will generate less inbreeding and at least as much genetic gain as minimum-coancestry mating in breeding schemes where the animals are truncation-selected. We tested this hypothesis by stochastic simulation and compared the mating criteria in hierarchical and factorial breeding schemes, where the animals were selected based on breeding values predicted by animal-model BLUP. Random mating was included as a reference-mating criterion. We found that MCAC mating generated 4% to 8% less inbreeding than minimum-coancestry mating in the hierarchical and factorial breeding schemes without any loss in genetic gain. Moreover, it generated upto 28% less inbreeding and about 3% more genetic gain than random mating. The benefits of MCAC mating over minimum-coancestry mating are worthwhile because they can be achieved without extra costs or practical constraints. MCAC mating merely uses pedigree information to pair the animals more appropriately and is clearly a worthy alternative to minimum-coancestry mating and probably any other mating criterion. We believe, therefore, that MCAC mating should be used in breeding schemes where pedigree information is available.     

Mating strategies with genomic information reduce rates of inbreeding in animal breeding schemes without compromising genetic gain

We tested the hypothesis that mating strategies with genomic information realise lower rates of inbreeding (∆F) than with pedigree information without compromising rates of genetic gain (∆G). We used stochastic simulation to compare ∆F and ∆G realised by two mating strategies with pedigree and genomic information in five breeding schemes. The two mating strategies were minimum-coancestry mating (MC) and minimising the covariance between ancestral genetic contributions (MCAC). We also simulated random mating (RAND) as a reference point. Generations were discrete. Animals were truncation-selected for a single trait that was controlled by 2000 quantitative trait loci, and the trait was observed for all selection candidates before selection. The criterion for selection was genomic-breeding values predicted by a ridge-regression model. Our results showed that MC and MCAC with genomic information realised 6% to 22% less ∆F than MC and MCAC with pedigree information without compromising ∆G across breeding schemes. MC and MCAC realised similar ∆F and ∆G. In turn, MC and MCAC with genomic information realised 28% to 44% less ∆F and up to 14% higher ∆G than RAND. These results indicated that MC and MCAC with genomic information are more effective than with pedigree information in controlling rates of inbreeding. This implies that genomic information should be applied to more than just prediction of breeding values in breeding schemes with truncation selection.     

A comparison of two methods for prediction of response and rates of inbreeding in selected populations with the results obtained in two selection experiments

Selection programmes are mainly concerned with increasing genetic gain. However, short-term progress should not be obtained at the expense of the within-population genetic variability. Different prediction models for the evolution within a small population of the genetic mean of a selected trait, its genetic variance and its inbreeding have been developed but have mainly been validated through Monte Carlo simulation studies. The purpose of this study was to compare theoretical predictions to experimental results. Two deterministic methods were considered, both grounded on a polygenic additive model. Differences between theoretical predictions and experimental results arise from differences between the true and the assumed genetic model, and from mathematical simplifications applied in the prediction methods. Two sets of experimental lines of chickens were used in this study: the Dutch lines undergoing true truncation mass selection, the other lines (French) undergoing mass selection with a restriction on the representation of the different families. This study confirmed, on an experimental basis, that modelling is an efficient approach to make useful predictions of the evolution of selected populations although the basic assumptions considered in the models (polygenic additive model, normality of the distribution, base population at the equilibrium, etc.) are not met in reality. The two deterministic methods compared yielded results that were close to those observed in real data, especially when the selection scheme followed the rules of strict mass selection: for instance, both predictions overestimated the genetic gain in the French experiment, whereas both predictions were close to the observed values in the Dutch experiment.     

Family level inbreeding depression and the evolution of plant mating systems

Variation in the magnitude of inbreeding depression (ID) among families may have important consequences for mating system evolution. Experimental studies have shown that such variation is a common feature of natural plant populations. Unfortunately, the genetic and evolutionary significance of family level estimates remains obscure. Almost any kind of genetic variation will generate differences in ID among families, and as a consequence, a non-zero variance in family level ID is not sufficient to distinguish genetic architectures with wholly different implications for mating system evolution. Quantitative genetic methods provide a means to extract more information from ID experiments. Estimates of quantitative genetic variance components directly inform questions about the genetic basis of ID and should ultimately allow tests of alternative theories of mating system evolution.     

When it comes to inbreeding: slower is better

The extent to which genetic diversity is lost from inbred populations is important for conservation biology, evolutionary ecology, and plant and animal breeding. This importance stems from the fact that the amount of genetic diversity a population has is expected to correlate with evolutionary potential. A population's ability to avert extinction during rapidly changing environmental conditions, or the magnitude of response to selection on a trait, depend on the ability of the genome to maintain potentially adaptive genetic variation in the face of random genetic drift. Although a few previous studies have demonstrated that the rate of inbreeding affects the amount of genetic diversity maintained, the elegant work of Demontis et al. , in this issue, clearly demonstrates that slow inbreeding maintains more genetic diversity than fast inbreeding and that the primary mechanism could be balancing selection. In their study, populations that took 19 generations, rather than one generation, to reach the same level of inbreeding maintained 10% higher levels of allelic richness and 25% higher levels of heterozygosity. The use of specifically chosen molecular markers not expected to be neutral makes this study especially noteworthy, as the study provides evidence concerning the mechanisms underlying the maintenance of genetic diversity in the face of inbreeding.     

Reduction of inbreeding in commercial females by rotational mating with several sire lines

A mating system to reduce the inbreeding of commercial females in the lower level was examined theoretically, assuming a hierarchical breed structure, in which favorable genes are accumulated in the upper level by artificial selection and the achieved genetic progress is transferred to the lower level through migration of males. The mating system examined was rotational mating with several closed sire lines in the upper level. Using the group coancestry theory, we derived recurrence equations for the inbreeding coefficient of the commercial females. The asymptotic inbreeding coefficient was also derived. Numerical computations showed that the critical factor for determining the inbreeding is the number of sire lines, and that the size of each sire line has a marginal effect. If four or five sire lines were available, rotational mating was found to be quite an effective system to reduce the short- and long-term inbreeding of the commercial females, irrespective of the effective size of each sire line. Oscillation of the inbreeding coefficient under rotational mating with initially related sire lines could be minimized by avoiding the consecutive use of highly related lines. Extensions and perspectives of the system are discussed in relation to practical application.     

Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.     

Evolution and genetic architecture of disassortative mating at a locus under heterozygote advantage

The evolution of mate choice is a major topic in evolutionary biology because it is thought to be a key factor in trait and species diversification. Here, we aim at uncovering the ecological conditions and genetic architecture enabling the puzzling evolution of disassortative mating based on adaptive traits. This rare form of mate choice is observed for some polymorphic traits but theoretical predictions on the emergence and persistence of this behavior are largely lacking. Thus, we developed a mathematical model to specifically understand the evolution of disassortative mating based on mimetic color pattern in the polymorphic butterfly Heliconius numata. We confirm that heterozygote advantage favors the evolution of disassortative mating and show that disassortative mating is more likely to emerge if at least one allele at the trait locus is free from any recessive deleterious mutations. We modeled different possible genetic architectures underlying mate choice behavior, such as self‐referencing alleles, or specific preference or rejection alleles. Our results showed that self‐referencing or rejection alleles linked to the color pattern locus enable the emergence of disassortative mating. However, rejection alleles allow the emergence of disassortative mating only when the color pattern and preference loci are tightly linked.     

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.     

Optimal mass selection policies for schemes with overlapping generations and restricted inbreeding

Optimum breeding schemes for maximising the rate of genetic progress with a restriction on the rate of inbreeding (per year or per generation) are investigated for populations with overlapping generations undergoing mass selection. The optimisation is for the numbers of males and females to be selected and for their distribution over age classes. Expected rates of genetic progress (ΔG) are combined with expected rates of inbreeding (ΔF) in a linear objective function (Φ = ΔG - λΔF) which is maximised. A simulated annealing algorithm is used to obtain the solutions. The restriction on inbreeding is achieved by increasing the number of parents and, in small schemes with severe restrictions, by increasing the generation interval. In the latter case the optimum strategy for obtaining the maximum genetic gain is far from truncation selection across age classes. In most situations, the optimum mating ratio is one but the differences in genetic gain obtained with different mating ratios are small. Optimisation of schemes when restricting the rate of inbreeding per generation leads to shorter generation intervals than optimisation when restricting the rate of inbreeding per year.     

Evolution of mating types in finite populations: The precarious advantage of being rare

Sexually reproducing populations with self‐incompatibility bear the cost of limiting potential mates to individuals of a different type. Rare mating types escape this cost since they are unlikely to encounter incompatible partners, leading to the deterministic prediction of continuous invasion by new mutants and an ever‐increasing number of types. However, rare types are also at an increased risk of being lost by random drift. Calculating the number of mating types that a population can maintain requires consideration of both the deterministic advantages and the stochastic risks. By comparing the relative importance of selection and drift, we show that a population of size N can maintain a maximum of approximately N^1/3 mating types for intermediate population sizes, whereas for large N, we derive a formal estimate. Although the number of mating types in a population is quite stable, the rare‐type advantage promotes turnover of types. We derive explicit formulas for both the invasion and turnover probabilities in finite populations.     

Sex‐specific effects of inbreeding in wild‐caught Drosophila melanogaster under benign and stressful conditions

In animal populations, sib mating is often the primary source of inbreeding depression (ID). We used recently wild‐caught Drosophila melanogaster to test whether such ID is amplified by environmental stress and, in males, by sexual selection. We also investigated whether increased ID because of stress (increased larval competition) persisted beyond the stressed stage and whether the effects of stress and sexual selection interacted. Sib mating resulted in substantial cumulative fitness losses (egg to adult reproduction) of 50% (benign) and 73% (stressed). Stress increased ID during the larval period (23% vs. 63%), but not during post‐stress reproductive stages (36% vs. 31%), indicating larval stress may have purged some adult genetic load (although ID was uncorrelated across stages). Sexual selection exacerbated inbreeding depression, with inbred male offspring suffering a higher reproductive cost than females, independent of stress (57% vs. 14% benign, 49% vs. 11% stress).     

Interpopulation variation in inbreeding is primarily driven by tolerance of mating with relatives in a spermcasting invertebrate

The degree to which individuals inbreed is a fundamental aspect of population biology shaped by both passive and active processes. Yet, the relative influences of random and non-random mating on the overall magnitude of inbreeding are not well characterized for many taxa. We quantified variation in inbreeding among qualitatively accessible and isolated populations of a sessile marine invertebrate (the colonial ascidian Lissoclinum verrilli) in which hermaphroditic colonies cast sperm into the water column for subsequent uptake and internal fertilization. We compared estimates of inbreeding to simulations predicting random mating within sites to evaluate if levels of inbreeding were (1) less than expected because of active attempts to limit inbreeding, (2) as predicted by genetic subdivision and passive inbreeding tolerance, or (3) greater than simulations due to active attempts to promote inbreeding via self-fertilization or a preference for related mates. We found evidence of restricted gene flow and significant differences in the genetic diversity of L. verrilli colonies among sites, indicating that on average colonies were weakly related in accessible locations, but their levels of relatedness matched that of first cousins or half-siblings on isolated substrates. Irrespective of population size, progeny arrays revealed variation in the magnitude of inbreeding across sites that tracked with the mean relatedness of conspecifics. Biparental reproduction was confirmed in most offspring (86%) and estimates of total inbreeding largely overlapped with simulations of random mating, suggesting that interpopulation variation in mother–offspring resemblance was primarily due to genetic subdivision and passive tolerance of related mates. Our results highlight the influence of demographic isolation on the genetic composition of populations, and support theory predicting that tolerance of biparental inbreeding, even when mates are closely related, may be favoured under a broad set of ecological and evolutionary conditions.     

The transition to social inbred mating systems in spiders: role of inbreeding tolerance in a subsocial predecessor

The social spiders are unusual among cooperatively breeding animals in being highly inbred. In contrast, most other social organisms are outbred owing to inbreeding avoidance mechanisms. The social spiders appear to originate from solitary subsocial ancestors, implying a transition from outbreeding to inbreeding mating systems. Such a transition may be constrained by inbreeding avoidance tactics or fitness loss due to inbreeding depression. We examined whether the mating system of a subsocial spider, in a genus with three social congeners, is likely to facilitate or hinder the transition to inbreeding social systems. Populations of subsocial Stegodyphus lineatus are substructured and spiders occur in patches, which may consist of kin groups. We investigated whether male mating dispersal prevents matings within kin groups in natural populations. Approximately half of the marked males that were recovered made short moves (< 5m) and mated within their natal patch. This potential for inbreeding was counterbalanced by a relatively high proportion of immigrant males. In mating experiments, we tested whether inbreeding actually results in lower offspring fitness. Two levels of inbreeding were tested: full sibling versus non-sib matings and matings of individuals within and between naturally occurring patches of spiders. Neither full siblings nor patch mates were discriminated against as mates. Sibling matings had no effect on direct fitness traits such as fecundity, hatching success, time to hatching and survival of the offspring, but negatively affected offspring growth rates and adult body size of both males and females. Neither direct nor indirect fitness measures differed significantly between within patch and between-patch pairs. We tested the relatedness between patch mates and nonpatch mates using DNA fingerprinting (TE-AFLP). Kinship explained 30% of the genetic variation among patches, confirming that patches are often composed of kin. Overall, we found limited male dispersal, lack of kin discrimination, and tolerance to low levels of inbreeding. These results suggest a history of inbreeding which may reduce the frequency of deleterious recessive alleles in the population and promote the evolution of inbreeding tolerance. It is likely that the lack of inbreeding avoidance in subsocial predecessors has facilitated the transition to regular inbreeding social systems.     

Resolving the conundrum of inbreeding depression but no inbreeding avoidance: Estimating sex‐specific selection on inbreeding by song sparrows (Melospiza melodia)

Inbreeding avoidance among interacting females and males is not always observed despite inbreeding depression in offspring fitness, creating an apparent “inbreeding paradox.” This paradox could be resolved if selection against inbreeding was in fact weak, despite inbreeding depression. However, the net magnitude and direction of selection on the degree to which females and males inbreed by pairing with relatives has not been explicitly estimated. We used long‐term pedigree data to estimate phenotypic selection gradients on the degree of inbreeding that female and male song sparrows (Melospiza melodia) expressed by forming socially persistent breeding pairs with relatives. Fitness was measured as the total numbers of offspring and grand offspring contributed to the population, and as corresponding expected numbers of identical‐by‐descent allele copies, thereby accounting for variation in offspring survival, reproduction, and relatedness associated with variation in parental inbreeding. Estimated selection gradients on the degree to which individuals paired with relatives were weakly positive in females, but negative in males that formed at least one socially persistent pairing. However, males that paired had higher mean fitness than males that remained socially unpaired. These analyses suggest that net selection against inbreeding may be weak in both sexes despite strong inbreeding depression, thereby resolving the “inbreeding paradox.”     

Response to selection on cold tolerance is constrained by inbreeding

The evolutionary potential of any given population is of fundamental importance for its longer term prospects. Modern land-use practices often result in small and isolated populations, increasing the risk of extinction through reduced genetic diversity as a consequence of inbreeding or drift. Such genetic erosion may also interfere with a population's evolutionary potential. In this study, we investigate the consequences of inbreeding on evolutionary potential (the ability to increase cold resistance) in a laboratory population of the tropical butterfly Bicyclus anynana. To explore constraints on evolution, we applied artificial selection to chill-coma recovery time, starting from three levels of inbreeding (outbred control, one or two full-sibling matings). Ten generations of selection produced highly divergent phenotypes, with the lines selected for increased cold tolerance showing about 28% shorter recovery times after cold exposure relative to unselected controls. Correlated responses to selection in 10 different life-history and stress-resistance traits were essentially absent. Inbred lines showed a weaker response to selection, indicating reduced evolutionary potential and thereby constraints on evolution. Inbreeding depression was still measurable in some traits after the course of selection. Traits more closely related to fitness showed a clear fitness rebound, suggesting a trait-specific impact of purging. Our findings have important implications for the longer term survival of small populations in fragmented landscapes.     

Assortative mating by size: A meta-analysis of mating patterns in water striders

Summary Assortative mating by size is a common mating pattern that can be generated by several different behavioural mechanisms, with different evolutionary implications. Assortative mating is typically associated with sexual selection and has been regarded as an attribute of populations, species, mating systems or even higher order taxa. In most animal groups, however, appropriate analyses of assortative mating at these different levels are lacking and the causes and forms of assortative mating are poorly understood. Here, we analyse 45 different population level estimates of assortative mating and non-random mating by size in seven confamiliar species of water striders that share a common mating system. A hierarchical comparative analysis shows that virtually all the variance within the clade occurs among samples within species. We then employ meta-analysis to estimate the overall strength of assortative mating, to determine the form of assortative mating and to further assess potential differences among species as well as the probable causes of assortative mating in this group of insects. We found overall weak but highly significant positive assortative mating. We show that analyses of the degree of heteroscedasticity in plots of male versus female size are critical, since the evolutionary implications of true and apparent assortative mating differ widely and conclude that the positive assortative mating observed in water striders was of the true rather than the apparent form. Further, within samples, mating individuals were significantly larger than non-mating individuals in both males and females. All of these non-random mating patterns were consistent among species and we conclude that weak positive assortative mating by size is a general characteristic of those water strider species that share this mating system. We use our results to illustrate the importance of distinguishing between different forms of assortative mating, to discriminate between various behavioural causes of assortative mating and to assess potential sources of interpopulational variance in estimates of assortative mating. Finally, we discuss the value of using meta-analytic techniques for detecting overall patterns in multiple studies of non-random mating.     

Anther-stigma separation is associated with inbreeding depression in Datura stramonium,a predominantly self-fertilizing annual

Abstract.— Genetically based variation in outcrossing rate generates lineages within populations that differ in their history of inbreeding. According to some models, mating-system modifiers in such populations will demonstrate both linkage and identity disequilibrium with fitness loci, resulting in lineage-specific inbreeding depression. Other models assert that differences among families in levels of inbreeding depression are mainly attributable to random accumulation of genetic load, unrelated to variation at mating-system loci. We measured female reproductive success of selfed and outcrossed progeny from naturally occurring lineages of Datura stramonium , a predominantly self-fertilizing annual weed that has heritable variation in stigma-anther separation, a trait that influences selfing rates. Progeny from inbred lineages (as identified by high degree of anther-stigma overlap) showed equal levels of seed production, regardless of cross type. Progeny from mixed lineages (as identified by relatively high separation between anthers and stigma) showed moderate levels of inbreeding depression. We found a significant correlation between anther-stigma separation and relative fitness of selfed and outcrossed progeny, suggesting that family-level inbreeding depression may be related to differences among lineages in inbreeding history in this population. Negative inbreeding depression in putatively inbred lineages may be due in part to additive effects or to epistatic interactions among loci.