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.     

The advantage of factorial mating under selection is uncovered by deterministically predicted rates of inbreeding

Rates of inbreeding (ΔF) in selected populations were predicted using the framework of long-term genetic contributions and validated against stochastic simulations. Deterministic predictions decomposed ΔF into four components due to: finite population size, directional selection, covariance of genetic contribution of mates, and deviation of variance of family size from that expected from a Poisson distribution. Factorial (FM) and hierarchical (HM) mating systems were compared under mass and sib-index selection. Prediction errors were in most cases for ΔF less than 10% and for rate of gain less than 5%. ΔF was higher with index than mass selection. ΔF was lower with FM than HM in all cases except random selection. FM reduced the variance of the average breeding value of the mates of an individual. This reduced the impact of the covariance of contributions of mates on ΔF. Thus, contributions of mates were less correlated with FM than HM, causing smaller deviations of converged contributions from the optimum contributions. With index selection, FM also caused a smaller variance of number of offspring selected from each parent. This reduced variance of family size reduced ΔF further. FM increases the flexibility in breeding schemes for achieving the optimum genetic contributions.     

Selection against genetic defects in conservation schemes while controlling inbreeding

We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.     

A combination of walk-back and optimum contribution selection in fish: a simulation study

The aim of this paper was to study the performance of a novel fish breeding scheme, which is a combination of walk-back and optimum contribution selection using stochastic simulation. In this walk-back selection scheme, batches of different sizes (50, 100, 1000, 5000 and 10 000) with the phenotypically superior fish from one tank with mixed families were genotyped to set up the pedigree. BLUP estimated breeding values were calculated. The optimum contribution selection method was used with the rate of inbreeding (ΔF) constrained to 0.005 or 0.01 per generation. If the constraint on ΔF could not be held, a second batch of fish was genotyped etc. Compared with the genotyping of all selection candidates (1000, 5000 or 10 000), the use of batches saves genotyping costs. The results show that two batches of 50 fish were often necessary. With a batch size of 100, genetic level was 76–92% of the genetic level achieved for schemes with all fish being genotyped and thus candidates for the optimum contribution selection step. More parents were selected for schemes with larger batches, resulting in a higher genetic gain, especially when all selection candidates were genotyped. There was little extra genetic gain in genotyping of 1000 fish instead of 100 for the larger schemes of 5000 and 10 000 candidates. The accuracy of breeding values was similar for all batch sizes (~0.30), but higher (~0.5) when all candidates were included. Since only the phenotypically most superior fish were genotyped, BLUP-EBV were biased. Compared with genotyping of all selection candidates, the use of batches saves genotyping costs, while simultaneously maintaining high genetic gains.     

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.     

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.     

Designing artificial selection experiments for specific objectives

The observed genetic gain (ΔP) from selection in a finite population is the possible expected genetic gain E(Δ G) minus the difference in inbreeding depression effects in the selected and control lines. The inbreeding depression can be avoided by crossing the control and selected ♂ and ♀ parents to unrelated mates and summing the observed gains. The possible expected gain will be reduced by an amount D from the predicted gain because of the effects of the genetic limit and random genetic drift, the magnitude of which is a function of effective population size, N. The expected value of D is zero in unselected control populations and in the first generation for selected populations. Therefore, this source of bias can be reduced by increasing N in the selected populations and can be avoided by selecting for a single generation. To obtain observed responses which are unbiased estimates of the predicted response from which to estimate the realized heritability (or regression) in the zero generation, or to test genetic theory based on infinite population size, single-generation selection with many replications would be most efficient. To measure the "total" effect or genetic efficiency of a selection criterion or method, including the effect of different selection intensities, effective population sizes, and space requirements, more than one generation of selection is required to estimate the expected response in breeding values. The efficiency, in the sense of minimum variance, of estimating the expected breeding values at any generation t will decline as the number of generations t increases. The variance of either the estimated mean gain or the regression of gain on selection differential can be reduced more by increasing the number of replicates K than by increasing the number of generations t. Also the general pattern of the response over t can be estimated if the N's are known. Therefore, two- or not more than three-generation selection experiments with many replications would be most efficient.     

The effect of fast created inbreeding on litter size and body weights in mice

This study was designed to reveal any differences in effects of fast created versus total inbreeding on reproduction and body weights in mice. A line selected for large litter size for 124 generations (H) and a control line (K) maintained without selection for the same number of generations were crossed (HK) and used as a basis for the experiment. Within the HK cross, full sib, cousin or random mating were practised for two generations in order to create new inbreeding (IB_F) at a fast rate. In the first generation of systematic mating, old inbreeding was regenerated in addition to creation of new inbreeding from the mating design giving total inbreeding (IB_T). The number of pups born alive (NBA) and body weights of the animals were then analysed by a model including both IB_T and IB_F. The IB_T of the dam was in the present study found to reduce the mean NBA with -0.48 (± 0.22) (p < 0.05) pups per 10% increase in the inbreeding coefficient, while the additional effect of IB_F was -0.42 (± 0.27). For the trait NBA per female mated, the effect of IB_T was estimated to be -0.45 (± 0.29) per 10% increase in the inbreeding coefficient and the effect of IB_F was -0.90 (± 0.37) (p < 0.05) pups. In the present study, only small or non-significant effects of IB_F of the dam could be found on sex-ratio and body weights at three and six weeks of age in a population already adjusted for IB_T.     

The β Subunit of the Heterotrimeric G Protein Triggers the Kluyveromyces lactis Pheromone Response Pathway in the Absence of the γ Subunit

The Kluyveromyces lactis heterotrimeric G protein is a canonical Gαβγ complex; however, in contrast to Saccharomyces cerevisiae, where the Gγ subunit is essential for mating, disruption of the KlGγ gene yielded cells with almost intact mating capacity. Expression of a nonfarnesylated Gγ, which behaves as a dominant-negative in S. cerevisiae, did not affect mating in wild-type and ΔGγ cells of K. lactis. In contrast to the moderate sterility shown by the single ΔKlGα, the double ΔKlGα ΔKlGγ mutant displayed full sterility. A partial sterile phenotype of the ΔKlGγ mutant was obtained in conditions where the KlGβ subunit interacted defectively with the Gα subunit. The addition of a CCAAX motif to the C-end of KlGβ, partially suppressed the lack of both KlGα and KlGγ subunits. In cells lacking KlGγ, the KlGβ subunit cofractionated with KlGα in the plasma membrane, but in the ΔKlGα ΔKlGγ strain was located in the cytosol. When the KlGβ-KlGα interaction was affected in the ΔKlGγ mutant, most KlGβ fractionated to the cytosol. In contrast to the generic model of G-protein function, the Gβ subunit of K. lactis has the capacity to attach to the membrane and to activate mating effectors in absence of the Gγ subunit.     

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.     

Aerobic Growth of Escherichia coli Is Reduced,and ATP Synthesis Is Selectively Inhibited when Five C-terminal Residues Are Deleted from the ? Subunit of ATP Synthase

F-type ATP synthases are rotary nanomotor enzymes involved in cellular energy metabolism in eukaryotes and eubacteria. The ATP synthase from Gram-positive and -negative model bacteria can be autoinhibited by the C-terminal domain of its ϵ subunit (ϵCTD), but the importance of ϵ inhibition in vivo is unclear. Functional rotation is thought to be blocked by insertion of the latter half of the ϵCTD into the central cavity of the catalytic complex (F₁). In the inhibited state of the Escherichia coli enzyme, the final segment of ϵCTD is deeply buried but has few specific interactions with other subunits. This region of the ϵCTD is variable or absent in other bacteria that exhibit strong ϵ-inhibition in vitro. Here, genetically deleting the last five residues of the ϵCTD (ϵΔ5) caused a greater defect in respiratory growth than did the complete absence of the ϵCTD. Isolated membranes with ϵΔ5 generated proton-motive force by respiration as effectively as with wild-type ϵ but showed a nearly 3-fold decrease in ATP synthesis rate. In contrast, the ϵΔ5 truncation did not change the intrinsic rate of ATP hydrolysis with membranes. Further, the ϵΔ5 subunit retained high affinity for isolated F₁ but reduced the maximal inhibition of F₁-ATPase by ϵ from >90% to ∼20%. The results suggest that the ϵCTD has distinct regulatory interactions with F₁ when rotary catalysis operates in opposite directions for the hydrolysis or synthesis of ATP.     

Inbreeding depression in self-incompatible North-American Arabidopsis lyrata: disentangling genomic and S-locus-specific genetic load

Newly formed selfing lineages may express recessive genetic load and suffer inbreeding depression. This can have a genome-wide genetic basis, or be due to loci linked to genes under balancing selection. Understanding the genetic architecture of inbreeding depression is important in the context of the maintenance of self-incompatibility and understanding the evolutionary dynamics of S-alleles. We addressed this using North-American subspecies of Arabidopsis lyrata. This species is normally self-incompatible and outcrossing, but some populations have undergone a transition to selfing. The goals of this study were to: (1) quantify the strength of inbreeding depression in North-American populations of A. lyrata; and (2) disentangle the relative contribution of S-linked genetic load compared with overall inbreeding depression. We enforced selfing in self-incompatible plants with known S-locus genotype by treatment with CO₂, and compared the performance of selfed vs outcrossed progeny. We found significant inbreeding depression for germination rate (δ=0.33), survival rate to 4 weeks (δ=0.45) and early growth (δ=0.07), but not for flowering rate. For two out of four S-alleles in our design, we detected significant S-linked load reflected by an under-representation of S-locus homozygotes in selfed progeny. The presence or absence of S-linked load could not be explained by the dominance level of S-alleles. Instead, the random nature of the mutation process may explain differences in the recessive deleterious load among lineages.     

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.     

Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming (Open Access publication)

An approach for optimising genetic contributions of candidates to control inbreeding in the offspring generation using semidefinite programming (SDP) was proposed. Formulations were done for maximising genetic gain while restricting inbreeding to a preset value and for minimising inbreeding without regard of gain. Adaptations to account for candidates with fixed contributions were also shown. Using small but traceable numerical examples, the SDP method was compared with an alternative based upon Lagrangian multipliers (RSRO). The SDP method always found the optimum solution that maximises genetic gain at any level of restriction imposed on inbreeding, unlike RSRO which failed to do so in several situations. For these situations, the expected gains from the solution obtained with RSRO were between 1.5–9% lower than those expected from the optimum solution found with SDP with assigned contributions varying widely. In conclusion SDP is a reliable and flexible method for solving contribution problems.     

A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression

The population outcrossing rate (t) and adult inbreeding coefficient (F) are key parameters in mating system evolution. The magnitude of inbreeding depression as expressed in the field can be estimated given t and F via the method of Ritland (1990). For a given total sample size, the optimal design for the joint estimation of t and F requires sampling large numbers of families (100–400) with fewer offspring (1–4) per family. Unfortunately, the standard inference procedure (MLTR) yields significantly biased estimates for t and F when family sizes are small and maternal genotypes are unknown (a common occurrence when sampling natural populations). Here, we present a Bayesian method implemented in the program BORICE (Bayesian Outcrossing Rate and Inbreeding Coefficient Estimation) that effectively estimates t and F when family sizes are small and maternal genotype information is lacking. BORICE should enable wider use of the Ritland approach for field-based estimates of inbreeding depression. As proof of concept, we estimate t and F in a natural population of Mimulus guttatus. In addition, we describe how individual maternal inbreeding histories inferred by BORICE may prove useful in studies of inbreeding and its consequences.     

The Effect of Inbreeding on Competitive Male-Mating Ability in DROSOPHILA MELANOGASTER

The effect of full-sib inbreeding on competitive male-mating ability (CI♂) in Drosophila melanogaster was investigated in two experiments. In the first, five inbred lines (with reserves) were assessed up to 18 generations. Linear inbreeding depression, of 5.9% per 10% increase in homozygosity, was observed. In a second experiment, 21 inbred lines were tested after three generations of full-sib mating (without reserves), and the decline with inbreeding was more severe, the male competitive index (CI♂) decreasing by 10.7% per 10% increase in F. The difference between these results is attributed to natural selection acting on variation within the inbred lines in extent of homozygosity, which can arise because of the peculiarly strong influence of linkage in Drosophila. Furthermore, differentiation between the lines may have reflected this variation rather than the various effects of different alleles fixed.—These results imply that the genetic variation in male-mating ability is largely due to dominance (no epistasis was detected) and are consonant with the proposition that intermale sexual selection is a very important component of fitness in D. melanogaster . There was no evidence of a positive correlation between male body size and competitive mating ability.     

Diploids in the Cryptococcus neoformans Serotype A Population Homozygous for the α Mating Type Originate via Unisexual Mating

The ubiquitous environmental human pathogen Cryptococcus neoformans is traditionally considered a haploid fungus with a bipolar mating system. In nature, the α mating type is overwhelmingly predominant over a. How genetic diversity is generated and maintained by this heterothallic fungus in a largely unisexual α population is unclear. Recently it was discovered that C. neoformans can undergo same-sex mating under laboratory conditions generating both diploid intermediates and haploid recombinant progeny. Same-sex mating (α-α) also occurs in nature as evidenced by the existence of natural diploid αADα hybrids that arose by fusion between two α cells of different serotypes (A and D). How significantly this novel sexual style contributes to genetic diversity of the Cryptococcus population was unknown. In this study, ∼500 natural C. neoformans isolates were tested for ploidy and close to 8% were found to be diploid by fluorescence flow cytometry analysis. The majority of these diploids were serotype A isolates with two copies of the α MAT locus allele. Among those, several are intra-varietal allodiploid hybrids produced by fusion of two genetically distinct α cells through same-sex mating. The majority, however, are autodiploids that harbor two seemingly identical copies of the genome and arose via either endoreplication or clonal mating. The diploids identified were isolated from different geographic locations and varied genotypically and phenotypically, indicating independent non-clonal origins. The present study demonstrates that unisexual mating produces diploid isolates of C. neoformans in nature, giving rise to populations of hybrids and mixed ploidy. Our findings underscore the importance of same-sex mating in shaping the current population structure of this important human pathogenic fungus, with implications for mechanisms of selfing and inbreeding in other microbial pathogens.     

Selection Response in Finite Populations

Formulae were derived to predict genetic response under various selection schemes assuming an infinitesimal model. Account was taken of genetic drift, gametic (linkage) disequilibrium (Bulmer effect), inbreeding depression, common environmental variance, and both initial segregating variance within families (σ(AW0)(2)) and mutational (σ(M)(2)) variance. The cumulative response to selection until generation t(CR(t)) can be approximated as & where N(e) is the effective population size, σ(AW &)(2) = N(e)σ(M)(2) is the genetic variance within families at the steady state (or one-half the genic variance, which is unaffected by selection), and D is the inbreeding depression per unit of inbreeding. R(0) is the selection response at generation 0 assuming preselection so that the linkage disequilibrium effect has stabilized. β is the derivative of the logarithm of the asymptotic response with respect to the logarithm of the within-family genetic variance, i.e., their relative rate of change. R(0) is the major determinant of the short term selection response, but σ(M)(2), N(e) and β are also important for the long term. A selection method of high accuracy using family information gives a small N(e) and will lead to a larger response in the short term and a smaller response in the long term, utilizing mutation less efficiently.     

Optimization of selection contribution and mate allocations in monoecious tree breeding populations

Background

The combination of optimized contribution dynamic selection and various mating schemes was investigated over seven generations for a typical tree breeding scenario. The allocation of mates was optimized using a simulated annealing algorithm for various object functions including random mating (RM), positive assortative mating (PAM) and minimization of pair-wise coancestry between mates (MCM) all combined with minimization of variance in family size and coancestry. The present study considered two levels of heritability (0.05 and 0.25), two restrictions on relatedness (group coancestry; 1 and 2%) and two maximum permissible numbers of crosses in each generation (100 and 400). The infinitesimal genetic model was used to simulate the genetic architecture of the trait that was the subject of selection. A framework of the long term genetic contribution of ancestors was used to examine the impacts of the mating schemes on population parameters.

Results

MCM schemes produced on average, an increased rate of genetic gain in the breeding population, although the difference between schemes was small but significant after seven generations (up to 7.1% more than obtained with RM). In addition, MCM reduced the level of inbreeding by as much as 37% compared with RM, although the rate of inbreeding was similar after three generations of selection. PAM schemes yielded levels of genetic gain similar to those produced by RM, but the increase in the level of inbreeding was substantial (up to 43%).

Conclusion

The main reason why MCM schemes yielded higher genetic gains was the improvement in managing the long term genetic contribution of founders in the population; this was achieved by connecting unrelated families. In addition, the accumulation of inbreeding was reduced by MCM schemes since the variance in long term genetic contributions of founders was smaller than in the other schemes. Consequently, by combining an MCM scheme with an algorithm that optimizes contributions of the selected individuals, a higher long term response is obtained while reducing the risk within the breeding program.