Evaluation of marker-assisted selection through computer simulation

Computer simulation was used to evaluate responses to marker-assisted selection (MAS) and to compare MAS responses with those typical of phenotypic recurrent selection (PRS) in an allogamous annual crop species such as maize (Zea mays L.). Relative to PRS, MAS produced rapid responses early in the selection process; however, the rate of these responses diminished greatly within three to five cycles. The gains from MAS ranged from 44.7 to 99.5% of the maximum potential, depending on the genetic model considered. Linkage distance between markers and quantitative trait loci (QTLs) was the factor which most limited the responses from MAS. When averaged across all models considered, flanking QTLs within two marker loci produced 38% more gain than did selection based on single markers if markers were loosely-linked to a QTL (20% recombination). Flanking markers were much less advantageous when markers were closely-linked to a QTL (5% recombination), producing an advantage over single markers of only 11%. Markers were most effective in fully exploiting the genetic potential when fewer QTLs controlled the trait. Large QTL numbers exacerbated the problem of marker-QTL recombination by requiring more generations for fixation. In annual crop species, MAS may offer a primary advantage of enabling two selection cycles per year versus the 2 years per cycle required by most PRS schemes for the evaluation of testcross progeny. MAS thus appears to allow very rapid gains for the first 2–3 years of recurrent selection, after which time conventional methods might replace MAS to achieve further responses.Publication number 19, 330 of the Minnesota Agricultural Experiment Station     

Divergence and evolution of assortative mating in a polygenic trait model of speciation with gene flow

Assortative mating is an important driver of speciation in populations with gene flow and is predicted to evolve under certain conditions in few‐locus models. However, the evolution of assortment is less understood for mating based on quantitative traits, which are often characterized by high genetic variability and extensive linkage disequilibrium between trait loci. We explore this scenario for a two‐deme model with migration, by considering a single polygenic trait subject to divergent viability selection across demes, as well as assortative mating and sexual selection within demes, and investigate how trait divergence is shaped by various evolutionary forces. Our analysis reveals the existence of sharp thresholds of assortment strength, at which divergence increases dramatically. We also study the evolution of assortment via invasion of modifiers of mate discrimination and show that the ES assortment strength has an intermediate value under a range of migration‐selection parameters, even in diverged populations, due to subtle effects which depend sensitively on the extent of phenotypic variation within these populations. The evolutionary dynamics of the polygenic trait is studied using the hypergeometric and infinitesimal models. We further investigate the sensitivity of our results to the assumptions of the hypergeometric model, using individual‐based simulations.     

Evaluation and retrospective optimization of genomic selection for yield and disease resistance in spring barley

The general applicability of genomic selection (GS) to plant breeding and principles guiding its use have been established by simulation and empirical cross-validation studies. More recently, studies have demonstrated genetic gains over multiple cycles of selection in a variety of crop species. In this study, we provide additional evidence for the effectiveness of GS in an actual breeding program by demonstrating significant gains of 186.1 kg ha^?1 and ??1.85 ppm for grain yield and deoxynivalenol, respectively, two unfavorably correlated quantitative traits, across 3 cycles of selection in a spring six-row barley breeding population. With its general effectiveness established, the next step is to increase the accuracy of predictions used in GS and thereby increase genetic gains. For this, we first showed that updating the training population (TP) with phenotyped lines from recent breeding cycles, specifically selected lines, had an overall positive effect on prediction accuracy. Additionally, we investigated four recently proposed algorithms that seek to optimize the composition of a TP. Overall, the optimization algorithms improved prediction accuracy when compared to a randomly selected TP subset of the same size, but which algorithm performed best was dependent on the trait being predicted and other factors discussed within. This retrospective investigation highlights the importance of maintaining and optimizing the TP when using GS in applied breeding to maximize prediction accuracy, thereby maximizing gain from selection and resource utilization efficiency.     

EVOLUTION OF DOMINANCE UNDER FREQUENCY-DEPENDENT INTRASPECIFIC COMPETITION IN AN ASSORTATIVELY MATING POPULATION

We study the evolution of higher levels of dominance as a response to negative frequency-dependent selection. In contrast to previous studies, we focus on the effect of assortative mating on the evolution of dominance under frequency-dependent intraspecific competition. We analyze a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under a mixture of frequency-independent stabilizing selection, density-dependent selection, and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The second (modifier) locus determines the degree of dominance at the trait level. Additionally, the population mates assortatively with respect to similarities in the ecological trait. Our analysis shows that the parameter region in which dominance can be established decreases if small levels of assortment are introduced. In addition, the degree of dominance that can be established also decreases. In contrast, if assortment is intermediate, sexual selection for extreme types can be established, which leads to evolution of higher levels of dominance than under random mating. For modifiers with large effects, intermediate levels of assortative mating are most favorable for the evolution of dominance. For large modifiers, the speed of fixation can even be higher for intermediate levels of assortative mating than for random mating.     

Evolution of assortative mating in a population expressing dominance

In this article, we study the influence of dominance on the evolution of assortative mating. We perform a population-genetic analysis of a two-locus two-allele model. We consider a quantitative trait that is under a mixture of frequency-independent stabilizing selection and density- and frequency-dependent selection caused by intraspecific competition for a continuum of resources. The trait is determined by a single (ecological) locus and expresses intermediate dominance. The second (modifier) locus determines the degree of assortative mating, which is expressed in females only. Assortative mating is based on similarities in the quantitative trait ('magic trait' model). Analytical conditions for the invasion of assortment modifiers are derived in the limit of weak selection and weak assortment. For the full model, extensive numerical iterations are performed to study the global dynamics. This allows us to gain a better understanding of the interaction of the different selective forces. Remarkably, depending on the size of modifier effects, dominance can have different effects on the evolution of assortment. We show that dominance hinders the evolution of assortment if modifier effects are small, but promotes it if modifier effects are large. These findings differ from those in previous work based on adaptive dynamics.     

Reinforcement and divergence under assortative mating

Traits that cause assortative mating such as the flowering time in plants and body size in animals can produce reproductive isolation between hybridizing populations. Can selection against unfit hybrids cause two populations to diverge in their mean values for these kinds of traits? Here I present a haploid analytical model of one population that receives gene flow from another. The partial pre-zygotic isolation between the two populations is caused by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by selection against genetic incompatibilities that can involve any form of selection on individual genes and gene combinations (epistasis). The analysis assumes that the introgression rate and selection coefficients are small. The results show that the assortment trait mean will not diverge from the immigrants unless there is direct selection on the trait favouring it to do so or there are genes of very large effect. The amount of divergence at equilibrium is determined by a balance between direct selection on the assortment trait and introgression from the other population. Additional selection against hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discussed in the light of these results.     

Linkage disequilibrium in two European F<Subscript>2</Subscript> flint maize populations under modified recurrent full-sib selection

According to quantitative genetic theory, linkage disequilibrium (LD) can hamper the short- and long-term selection response in recurrent selection (RS) programs. We analyzed LD in two European flint maize populations, KW1265 × D146 (A × B) and D145 × KW1292 (C × D), under modified recurrent full-sib selection. Our objectives were to investigate (1) the decay of initial parental LD present in F₂ populations by three generations of intermating, (2) the generation of new LD in four (A × B) and seven (C × D) selection cycles, and (3) the relationship between LD changes and estimates of the additive genetic variance. We analyzed the F₂ and the intermated populations as well as all selection cycles with 104 (A × B) and 101 (C × D) simple sequence repeat (SSR) markers with a uniform coverage of the entire maize genome. The LD coefficient D and the composite LD measure Δ were estimated and significance tests for LD were performed. LD was reduced by intermating as expected from theory. A directional generation of negative LD between favorable alleles could not be observed during the selection cycles. However, considerable undirectional changes in D were observed, which we attributed to genetic sampling due to the finite population size used for recombination. Consequently, a long-term reduction of the additive genetic variance due to negative LD was not observed. Our experimental results support the hypothesis that in practical RS programs with maize, LD generated by selection is not a limiting factor for obtaining a high selection response.     

Testing for effects of recombination rate on nucleotide diversity in natural populations of Arabidopsis lyrata

We investigated DNA sequence diversity for loci on chromosomes 1 and 2 in six natural populations of Arabidopsis lyrata and tested for the role of natural selection in structuring genomewide patterns of variability, specifically examining the effects of recombination rate on levels of silent polymorphism. In contrast with theoretical predictions from models of genetic hitchhiking, maximum-likelihood-based analyses of diversity and divergence do not suggest reduction of diversity in the region of suppressed recombination near the centromere of chromosome 1, except in a single population from Russia, in which the pericentromeric region may have undergone a local selective sweep or demographic process that reduced variability. We discuss various possibilities that might explain why nucleotide diversity in most A. lyrata populations is not related to recombination rate, including genic recombination hotspots, and low gene density in the low recombination rate region.     

Genetic recombination and adaptation to fluctuating environments: selection for geotaxis in Drosophila melanogaster

Heritable variation in fitness is the fuel of adaptive evolution, and sex can generate new adaptive combinations of alleles. If the generation of beneficial combinations drives the evolution of recombination, then the level of recombination should result in changes in the response to selection. Three types of lines of Drosophila melanogaster varying in their level of genetic recombination were selected over 38 generations for geotaxis. The within-chromosome recombination level of these lines was controlled for 60% of the genome: chromosome X and chromosome II. The full recombination lines had normal, unmanipulated levels of recombination on these two chromosomes. Conversely, nonrecombination lines had recombination effectively eliminated within the X and second chromosomes. Finally, partial recombination lines had the effective rate of within-chromosome recombination lowered to 10% of natural levels for these two chromosomes. The rate of response to selection was measured for continuous negative geotaxis and for a fluctuating environment (alternating selection for negative and positive geotaxis). All selected Drosophila lines responded to selection and approximately 36% of the response to selection was because of the X and second chromosomes. However, recombination did not accelerate adaptation during either directional or fluctuating selection for geotaxis.     

Dynamics of long-term genomic selection

Background

Simulation and empirical studies of genomic selection (GS) show accuracies sufficient to generate rapid gains in early selection cycles. Beyond those cycles, allele frequency changes, recombination, and inbreeding make analytical prediction of gain impossible. The impacts of GS on long-term gain should be studied prior to its implementation.

Methods

A simulation case-study of this issue was done for barley, an inbred crop. On the basis of marker data on 192 breeding lines from an elite six-row spring barley program, stochastic simulation was used to explore the effects of large or small initial training populations with heritabilities of 0.2 or 0.5, applying GS before or after phenotyping, and applying additional weight on low-frequency favorable marker alleles. Genomic predictions were from ridge regression or a Bayesian analysis.

Results

Assuming that applying GS prior to phenotyping shortened breeding cycle time by 50%, this practice strongly increased early selection gains but also caused the loss of many favorable QTL alleles, leading to loss of genetic variance, loss of GS accuracy, and a low selection plateau. Placing additional weight on low-frequency favorable marker alleles, however, allowed GS to increase their frequency earlier on, causing an initial increase in genetic variance. This dynamic led to higher long-term gain while mitigating losses in short-term gain. Weighted GS also increased the maintenance of marker polymorphism, ensuring that QTL-marker linkage disequilibrium was higher than in unweighted GS.

Conclusions

Losing favorable alleles that are in weak linkage disequilibrium with markers is perhaps inevitable when using GS. Placing additional weight on low-frequency favorable alleles, however, may reduce the rate of loss of such alleles to below that of phenotypic selection. Applying such weights at the beginning of GS implementation is important.     

The conditions for speciation through intraspecific competition

Abstract It has been shown theoretically that sympatric speciation can occur if intraspecific competition is strong enough to induce disruptive selection. However, the plausibility of the involved processes is under debate, and many questions on the conditions for speciation remain unresolved. For instance, is strong disruptive selection sufficient for speciation? Which roles do genetic architecture and initial composition of the population play? How strong must assortative mating be before a population can split in two? These are some of the issues we address here. We investigate a diploid multilocus model of a quantitative trait that is under frequency‐dependent selection caused by a balance of intraspecific competition and frequency‐independent stabilizing selection. This trait also acts as mating character for assortment. It has been established previously that speciation can occur only if competition is strong enough to induce disruptive selection. We find that speciation becomes more difficult for very strong competition, because then extremely strong assortment is required. Thus, speciation is most likely for intermediate strengths of competition, where it requires strong, but not extremely strong, assortment. For this range of parameters, however, it is not obvious how assortment can evolve from low to high levels, because with moderately strong assortment less genetic variation is maintained than under weak or strong assortment sometimes none at all. In addition to the strength of frequency‐dependent competition and assortative mating, the roles of the number of loci, the distribution of allelic effects, the initial conditions, costs to being choosy, the strength of stabilizing selection, and the particular choice of the fitness function are explored. A multitude of possible evolutionary outcomes is observed, including loss of all genetic variation, splitting in two to five species, as well as very short and extremely long stable limit cycles. On the methodological side, we propose quantitative measures for deciding whether a given distribution reflects two (or more) reproductively isolated clusters.     

A model for the evolution of assortative mating

Abstract: Many animals and plants show a correlation between the traits of the individuals in the mating pair, implying assortative mating. Given the ubiquity of assortative mating in nature, why and how it has evolved remain open questions. Here we attempt to answer these questions in those cases where the trait under assortment is the same in males and females. We consider the most favorable scenario for assortment to evolve, where the same trait is under assortment and viability selection. We find conditions for assortment to evolve using a multilocus formalism in a haploid population. Our results show how epistasis in fitness between the loci that control the focal trait is crucial for assortment to evolve. We then assume specific forms of assortment in haploids and diploids and study the limiting cases of selective and nonselective mating. We find that selection for increased assortment is weak and that where increased assortment is costly, it does not invade.     

Genotype-assisted optimum contribution selection to maximize selection response over a specified time period

Genotype-assisted selection (GAS), i.e. selection for an identified quantitative trait locus (QTL) and polygenic background genes, has been shown to increase short-term genetic gain but may reduce long-term genetic gains. In order to avoid this reduction of long-term gain, multi-generation optimization of truncation selection schemes is needed. This paper presents a multi-generation optimization of optimum contribution (OC) selection with selection on an identified QTL. This genotype-assisted optimum contribution (GAOC) selection method assumes that the optimum selection differential at the QTL is constant over the time horizon, and achieves this by controlling the increase of the frequency of the positive QTL allele. Implementation was straightforward by an additional linear restriction in the OC algorithm. GAOC achieved 35.2%, 2.3% and 1.1%, respectively, more cumulative genetic gain than OC selection (ignoring the QTL) using time horizons of 5, 10 and 15 generations. When one-generation optimization of GAS was used instead of multi-generation optimization, these figures were 2.8%, 3.1% and 3.2%, respectively. Simulated annealing was used to optimize the increases of the frequency of the positive QTL allele in order to test the optimality of GAOC. This latter resulted in genetic gains that were always within 0.4% of those of GAOC. In practice, short-term genetic gains are also important, which makes one-generation optimization of genetic gain closer to optimal.     

Recombination and Response to Selection in DROSOPHILA MELANOGASTER

Most biologists beleive that recombination speeds response to selection for traits determined by polygenic loci. To test this hypothesis, sixteen Drosophila melanogaster populations were selected for positive phototaxis for twenty-one generations. In some populations, balancer chromosomes were used to suppress autosomal recombination, and in others the autosomes were free to recombine. Suppression of recombination had no effect on mean rate of response to selection, though it may have increased variability in the rate of response among replicate lines. Suppressed recombination lines did not shift selection response to the freely recombining X chromosomes, despite fairly large increased in X chromosome recombination. The results suggest that in populations of moderate size, sex does not accelerate short term response to selection.     

Single versus subdivided population strategies in breeding against an adverse genetic correlation

In advanced conifer breeding programmes, the simultaneous genetic improvement of adversely correlated traits constitutes a major challenge. Population subdivision strategies have been proposed to deal with breeding objective uncertainty, to reduce inbreeding depression in production populations and to reduce genetic correlation adversity. We used Monte Carlo simulations based on a finite locus model to study the effect of a two-breeding-population strategy applying selection for each trait in each breeding population on the genetic correlation and on genetic gains in breeding populations (BP) and the production population (PP) within a time frame of ten generations. A single-BP and a two-subline strategy both applying multitrait index selection with equal trait weights were used as references. Two BP strategy simulations indicated that simultaneous genetic gain for the two traits could be achieved in the PP despite adverse pleiotropy. The adversity of the genetic correlations decreased in BPs of the two-BP strategy, in contrast to single-BP and subline strategies, but the adversity reduction came at the cost of a lower rate of aggregated (summed) genetic gain in the PP for the two-BP strategy compared to the single-BP or subline strategies. The subline strategy exhibited increased genetic gain in the PP at equal levels of inbreeding as intended. Two BP strategies could be useful to develop breeds specialised on different traits and to simultaneously reduce adverse genetic correlations. However, if the aggregated genetic gain should be maximised, the single-BP strategy appears a better choice.     

Open-nucleus breeding strategies compared with population-wide positive assortative mating

Positive assortative mating (PAM) can enhance the additive genetic variance in a breeding population(BP). This increases the potential for gains in the production population (PP, selected subset of the BP) for recurrent selection programs in forest trees. The assortment of mates can be either: (1) by individual tree rank across the whole BP (PAM), or (2) trees of similar rank can be merged into larger hierarchical groups and then mated randomly within group ("open"-nucleus breeding,NB). The objective of this study was to compare PAM and NB in quantitative terms. The NB simulation model assumed two tiers (nucleus, main) with unrestricted migration between the tiers. Clonal tests were used to predict breeding values and test resources per mate were kept constant for all mates. Both gain and diversity were combined into a single selection criterion, "group-merit selection." Alternatives were compared over five breeding cycles by considering genetic gain and diversity in a selected PP established in a seed orchard. The assortment of mates in both alternatives enhanced additive variance and increased the additive effect in the BP, leading to additional gain in the PP. Gains generated under PAM always exceeded gains under NB. Thus, the main message from this study is that PAM in both the short- and long-term results in more gain at any target level of diversity in the PP (the breeder's target) than is achieved by the NB alternative. The optimum size of the nucleus varies with the desired level of seed orchard diversity. At lower target diversity, smaller nucleus sizes are favorable, while larger sizes result in more gain when seed orchard diversity is considered more important.     

Recombination and Assortment in the Macronucleus of TETRAHYMENA THERMOPHILA: A Theoretical Study by Computer Simulation

The compound nature of the macronucleus of Tetrahymena thermophila presents multiple opportunities for recombination between genes on the same macronuclear chromosome. Such recombinants should be detectable through their assortment at subsequent amitotic macronuclear divisions. Thus, a macronucleus that is initially AB/ab should produce recombinant assortees of the genotypes Ab/aB. Computer simulation shows that, when the recombination frequency is two or fewer times per cell cycle, recombinant assortees are produced at experimentally measurable frequencies of less than 40%. At higher recombination frequencies, linked genes appear to assort independently. The simulations also show that recombination during macronuclear development can be distinguished from recombination in subsequent cell cycles only if the first appearance of recombinant assortees is 100 or more fissions after conjugation. The use of macronuclear recombination and assortment as a means of mapping macronuclear genes is severely constrained by the large variances in assortment outcomes; with experimentally small sample sizes, such mapping is impossible.     

Differential Adhesion between Moving Particles as a Mechanism for the Evolution of Social Groups

The evolutionary stability of cooperative traits, that are beneficial to other individuals but costly to their carrier, is considered possible only through the establishment of a sufficient degree of assortment between cooperators. Chimeric microbial populations, characterized by simple interactions between unrelated individuals, restrain the applicability of standard mechanisms generating such assortment, in particular when cells disperse between successive reproductive events such as happens in Dicyostelids and Myxobacteria. In this paper, we address the evolutionary dynamics of a costly trait that enhances attachment to others as well as group cohesion. By modeling cells as self-propelled particles moving on a plane according to local interaction forces and undergoing cycles of aggregation, reproduction and dispersal, we show that blind differential adhesion provides a basis for assortment in the process of group formation. When reproductive performance depends on the social context of players, evolution by natural selection can lead to the success of the social trait, and to the concomitant emergence of sizeable groups. We point out the conditions on the microscopic properties of motion and interaction that make such evolutionary outcome possible, stressing that the advent of sociality by differential adhesion is restricted to specific ecological contexts. Moreover, we show that the aggregation process naturally implies the existence of non-aggregated particles, and highlight their crucial evolutionary role despite being largely neglected in theoretical models for the evolution of sociality.     

Efficiency of genomic selection with models including dominance effect in the context of Eucalyptus breeding

We developed a simulation study to test the efficiency of genomic selection (GS) in the case of Eucalyptus breeding. We simulated a recurrent selection scheme for clone production over four breeding cycles. Scenarios crossing broad sense heritabilities (H ²?=?0.6 and 0.1) and dominance to additive variance ratios (R?=?0.1; 0.5; and 1) were compared. GS was performed with 1,000 SNPs and 22 QTLs per Morgan and tested against phenotypic selection (PS) based on best linear unbiased prediction of parents and clones. When the training population was made up of the first cycle progeny tests and the candidate populations were the progeny tests of three successive cycles, GS accuracy decreased with breeding cycles (e.g., from 0.9 to 0.4 with H ²?=?0.6 and R?=?0.1), whereas PS presented constant performances (accuracy of 0.8 with H ²?=?0.6 and R?=?0.1). When the training population set was updated by associating data of previous cycles, GS accuracy was improved from 25 % to 418 %, especially with H ²?=?0.1. The GS model including dominance effects performed better in clone selection (genotypic value) when dominance effects were preponderant (R?=?1), heritability was high (H ²?=?0.6 and with an updated training set), but no improvement was detected for parent selection (breeding value). The genetic gains over cycles were lower with the GS method without updating the data set but, with an updated training set, were similar to PS. However, the genetic gain per unit time with GS was 1.5 to 3 times higher than with PS for breeding and clone populations. These results highlight the value of GS in Eucalyptus breeding.