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.     

Prediction of response with overlapping generations accounting for multistage selection

Summary A generalization of Hill's equations predicting response to selection is developed that accounts for multiple stage selection in either or both sexes. The method accounts for the flow of genes for animals selected at later stages. This allows for the use of genetic gains from later stages, which explains the reduction in variance due to previous selection. Genetic gains from different selection differentials in each reproductive pathway are incorporated into the equations. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory.The method is applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. Two models were compared: (1) the first model accounted for two-stage selection of males, the first stage being based on pedigree information and the second stage on both pedigree and progeny test information; and (2) the second model assumed single-stage male selection. Selection was based on milk volume, milk fat, and milk protein yields. The predicted asymptotic rates for a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% by assuming singlestage male selection.Journal Paper No. J14146 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa; Project No. 1053     

Methods for minimizing the loss of genetic diversity in conserved populations with overlapping generations

Minimization of the average coancestry in a population has been theoretically proven to be the most efficient method to preserve genetic diversity. In the present study, based on a population genetic model, two methods to minimize the average coancestry in populations with overlapping generations were developed. For a given parental coancestry structure, the first method (OG) minimizes the average coancestry in the next generation, and the second method (LT) is designed to minimize the long-term accumulation of coancestry. The efficiencies of the two methods were examined by stochastic simulation. Compared to random choice of parents, the annual effective population sizes under the two proposed methods increased 2–3 folds. The difference among the two methods was small in a population with short generation interval. For populations with long generation intervals, the OG method showed a slightly larger annual effective size in an initial few years. However, in the subsequent years, the LT method gave a 5–15% larger annual effective size than the OG method. From these results, it is suggested that the LT method would be preferred to the OG method in most practical situations.     

Evolution of dispersal in a stepping-stone population with overlapping generations

We use Hamilton's inclusive fitness method to calculate the evolutionarily stable dispersal rate in 1- and 2-dimensional stepping-stone populations. This extends previous results by introducing a positive probability for adults to survive into the next generation and breed again. Relatedness between nearby individuals generally decreases with increasing survival, decreasing competition with kin and favouring greater dispersal rates.     

On the relation between gene flow theory and genetic gain

In conventional gene flow theory the rate of genetic gain is calculated as the summed products of genetic selection differential and asymptotic proportion of genes deriving from sex-age groups. Recent studies have shown that asymptotic proportions of genes predicted from conventional gene flow theory may deviate considerably from true proportions. However, the rate of genetic gain predicted from conventional gene flow theory was accurate. The current note shows that the connection between asymptotic proportions of genes and rate of genetic gain that is embodied in conventional gene flow theory is invalid, even though genetic gain may be predicted correctly from it.     

Marker assisted selection with optimised contributions of the candidates to selection

The benefits of marker assisted selection (MAS) are evaluated under realistic assumptions in schemes where the genetic contributions of the candidates to selection are optimised for maximising the rate of genetic progress while restricting the accumulation of inbreeding. MAS schemes were compared with schemes where selection is directly on the QTL (GAS or gene assisted selection) and with schemes where genotype information is not considered (PHE or phenotypic selection). A methodology for including prior information on the QTL effect in the genetic evaluation is presented and the benefits from MAS were investigated when prior information was used. The optimisation of the genetic contributions has a great impact on genetic response but the use of markers leads to only moderate extra short-term gains. Optimised PHE did as well as standard truncation GAS (i.e. with fixed contributions) in the short-term and better in the long-term. The maximum accumulated benefit from MAS over PHE was, at the most, half of the maximum benefit achieved from GAS, even with very low recombination rates between the markers and the QTL. However, the use of prior information about the QTL effects can substantially increase genetic gain, and, when the accuracy of the priors is high enough, the responses from MAS are practically as high as those obtained with direct selection on the QTL.     

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.     

Reduced inbreeding depression due to historical inbreeding in Drosophila melanogaster: evidence for purging

An important issue in conservation biology and the study of evolution is the extent to which inbreeding depression can be reduced or reversed by natural selection. If the deleterious recessive alleles causing inbreeding depression can be 'purged' by natural selection, outbred populations that have a history of inbreeding are expected to be less susceptible to inbreeding depression. This expectation, however, has not been realized in previous laboratory experiments. In the present study, we used Drosophila melanogaster as a model system to test for an association between inbreeding history and inbreeding depression. We created six 'purged' populations from experimental lineages that had been maintained at a population size of 10 male-female pairs for 19 generations. We then measured the inbreeding depression that resulted from one generation of full-sib mating in the purged populations and in the original base population. The magnitude of inbreeding depression in the purged populations was approximately one-third of that observed in the original base population. In contrast to previous laboratory experiments, therefore, we found that inbreeding depression was reduced in populations that have a history of inbreeding. The large purging effects observed in this study may be attributable to the rate of historical inbreeding examined, which was slower than that considered in previous experiments.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

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.     

Phenotypic response to selection for traits with direct and maternal components when generations overlap

Summary Prediction of response to selection for traits with direct and maternal components is described for discrete and overlapping generations. Expected phenotypic response is the sum of direct and maternal contributions, the latter having a genetic and an environmental component. With overlapping generations the selection differentials achieved on these components are added to respective updated vectors containing age-sex distributions with values of previous selection rounds. An example demonstrates that in the early stages, results may be considerably affected by environmental correlations between direct and maternal effects. The method could be helpful in interpreting phenotypic changes in a population selected for traits with maternal effects.     

Variation of selfing rate and inbreeding depression among individuals and across generations within an admixed Cedrus population

We investigated the variation and short-term evolution of the selfing rate and inbreeding depression (ID) across three generations within a cedar forest that was established from admixture ca 1860. The mean selfing rate was 9.5%, ranging from 0 to 48% among 20 seed trees (estimated from paternally inherited chloroplast DNA). We computed the probability of selfing for each seed and we investigated ID by comparing selfed and outcrossed seeds within progenies, thus avoiding maternal effects. In all progenies, the germination rate was high (88–100%) and seedling mortality was low (0–12%). The germination dynamics differed significantly between selfed and outcrossed seeds within progenies in the founder gene pool but not in the following generations. This transient effect of selfing could be attributed to epistatic interactions in the original admixture. Regarding the seedling growth traits, the ID was low but significant: 8 and 6% for height and diameter growth, respectively. These rates did not vary among generations, suggesting minor gene effects. At this early stage, outcrossed seedlings outcompeted their selfed relatives, but not necessarily other selfed seedlings from other progenies. Thus, purging these slightly deleterious genes may only occur through within-family selection. Processes that maintain a high level of genetic diversity for fitness-related traits among progenies also reduce the efficiency of purging this part of the genetic load.     

Local effects of inbreeding on embryo number and consequences for genetic diversity in Kerguelen mouflon

A classical paradigm in population genetics is that homozygosity or inbreeding affects individual fitness through increased disease susceptibility and mortality, and diminished breeding success. Using data from an insular population of mouflon (Ovis aries) founded by a single pair of individuals, we compare embryo number of ewes with different levels of inbreeding. Contrary to expectations, ewes with the highest levels of homozygosity showed the largest number of embryos. Using two different statistical approaches, we showed that this relationship is probably caused by heterozygosity at specific genes. The genetics of embryo number coupled with cyclic dynamics could play a central role in promoting genetic variation in this population.     

Fluctuating asymmetry in a secondary sexual trait: no associations with individual fitness, environmental stress or inbreeding, and no heritability

It has been suggested that fluctuating asymmetry (FA) in secondary sexual traits may be a useful indicator of either individual quality or environmental stress. We tested this concept using a series of analyses of FA in male antler size in a wild red deer (Cervus elaphus) population, using four measures of size repeated across successive years on the same individuals. We found no consistent evidence of correlations between traits in levels of FA, nor of any associations between known environmental or developmental conditions. None of the four measures of FA showed a significant heritability (average h2 = 0.041), nor was there any evidence of inbreeding depression. For three of the four traits, fluctuating asymmetry did not predict either annual or lifetime breeding success. However there were significant associations between breeding success and FA in antler length. Given the series of null results in our other tests, it seems likely that this was a direct mechanistic effect rather than because measures of FA were indicative of individual quality or condition.     

Sex-differential effects of inbreeding on overwinter survival, birth date and mass of bighorn lambs

Although it is generally expected that inbreeding would lower fitness, few studies have directly quantified the effects of inbreeding in wild mammals. We investigated the effects of inbreeding using long-term data from bighorn sheep on Ram Mountain, Alberta, Canada, over 20 years. This population underwent a drastic decline from 1992 to 2002 and has since failed to recover. We used a pedigree to calculate inbreeding coefficients and examined their impact on lamb growth, birth date and survival. Inbreeding had a substantial effect on female survival: for a given mass in September, the probability of overwinter survival for inbred female lambs was about 40% lower than that of noninbred ones. Contrary to our expectations, inbred female lambs were born earlier than noninbred ones. Earlier birth led to inbred female lambs being heavier by mid-September than noninbred ones. There was a nonsignificant trend for inbred female yearlings to weigh more than noninbred ones. A stronger mass-dependent viability selection for inbred compared to noninbred female lambs may explain why surviving inbred females were heavier than noninbred ones. Survival of male lambs was not affected by inbreeding. Sex-differential effects of inbreeding may be a general pattern in sexually dimorphic mammals, because of sex-biased maternal care or sexual differences in early development strategies.     

Cumulative frequency-dependent selective episodes allow for rapid morph cycles and rock-paper-scissors dynamics in species with overlapping generations

Rock-paper-scissors (RPS) dynamics, which maintain genetic polymorphisms over time through negative frequency-dependent (FD) selection, can evolve in short-lived species with no generational overlap, where they produce rapid morph frequency cycles. However, most species have overlapping generations and thus, rapid RPS dynamics are thought to require stronger FD selection, the existence of which yet needs to be proved. Here, we experimentally demonstrate that two cumulative selective episodes, FD sexual selection reinforced by FD selection on offspring survival, generate sufficiently strong selection to generate rapid morph frequency cycles in the European common lizard Zootoca vivipara, a multi-annual species with major generational overlap. These findings show that the conditions required for the evolution of RPS games are fulfilled by almost all species exhibiting genetic polymorphisms and suggest that RPS games may be responsible for the maintenance of genetic diversity in a wide range of species.     

Comparison of selection methods for improvement of the population hybrid

Summary The objective of this study was to compare several selection procedures with respect to expected genetic gain in the population hybrid across a range of initial allelic frequencies, degrees of dominance, and environmental variances. The methods compared were intrapopulation recurrent selection using full-sib or S₁ families, full-sib and two half-sib reciprocal recurrent selection procedures, and convergent improvement applied to populations. Comparisons were made by calculating expected allelic frequency changes for each method. The optimal selection method for a given set of allelic frequencies and degree of dominance depended little on the environmental variance. Partly because of its short cycle, full-sib intrapopulation selection was the most effective method for the majority of allelic frequency combinations when the degree of dominance was small and an off-season nursery could be used to make recombinations. With larger values for the degree of dominance, S₁ and reciprocal full-sib methods became optimal, the former method especially when favorable alleles had a high frequency and the latter when populations were highly divergent. When off-season nursery use was restricted to making self-pollinations or was absent, S₁ selection was optimal for the majority of allelic frequency combinations. Convergent improvement was superior only for extremely divergent allelic frequencies and then only when the degree of dominance was less than 0.10. Half-sib reciprocal methods were never optimal, although the gain for the standard half-sib reciprocal procedure differed little from that of full-sib reciprocal selection when the degree of dominance was 0.75.     

COANCESTRY: a program for simulating, estimating and analysing relatedness and inbreeding coefficients

The software package COANCESTRY implements seven relatedness estimators and three inbreeding estimators to estimate relatedness and inbreeding coefficients from multilocus genotype data. Two likelihood estimators that allow for inbred individuals and account for genotyping errors are for the first time included in this user-friendly program for PCs running Windows operating system. A simulation module is built in the program to simulate multilocus genotype data of individuals with a predefined relationship, and to compare the estimators and the simulated relatedness values to facilitate the selection of the best estimator in a particular situation. Bootstrapping and permutations are used to obtain the 95% confidence intervals of each relatedness or inbreeding estimate, and to test the difference in averages between groups.