Nonepistatic Models Research Articles

Background Selection From Unlinked Sites Causes Nonindependent Evolution of Deleterious Mutations.

Background selection describes the reduction in neutral diversity caused by selection against deleterious alleles at other loci. It is typically assumed that the purging of deleterious alleles affects linked neutral variants, and indeed simulations typically only treat a genomic window. However, background selection at unlinked loci also depresses neutral diversity. In agreement with previous analytical approximations, in our simulations of a human-like genome with a realistically high genome-wide deleterious mutation rate, the effects of unlinked background selection exceed those of linked background selection. Background selection reduces neutral genetic diversity by a factor that is independent of census population size. Outside of genic regions, the strength of background selection increases with the mean selection coefficient, contradicting the linked theory but in agreement with the unlinked theory. Neutral diversity within genic regions is fairly independent of the strength of selection. Deleterious genetic load among haploid individuals is underdispersed, indicating nonindependent evolution of deleterious mutations. Empirical evidence for underdispersion was previously interpreted as evidence for global epistasis, but we recover it from a non-epistatic model.

The role of epistasis in protein evolution

An important question in molecular evolution is whether an amino acid that occurs at a given position makes an independent contribution to fitness, or whether its effect depends on the state of other loci in the organism's genome, a phenomenon known as epistasis. In a recent letter to Nature, Breen et al. (2012) argued that epistasis must be "pervasive throughout protein evolution" because the observed ratio between the per-site rates of non-synonymous and synonymous substitutions (dN/dS) is much lower than would be expected in the absence of epistasis. However, when calculating the expected dN/dS ratio in the absence of epistasis, Breen et al. assumed that all amino acids observed in a protein alignment at any particular position have equal fitness. Here, we relax this unrealistic assumption and show that any dN/dS value can in principle be achieved at a site, without epistasis. Furthermore, for all nuclear and chloroplast genes in the Breen et al. dataset, we show that the observed dN/dS values and the observed patterns of amino acid diversity at each site are jointly consistent with a non-epistatic model of protein evolution.

Characterization of epistasis influencing complex spontaneous obesity in the BSB model.

There is growing awareness that complex interactions among multiple genes and environmental factors play an important role in controlling obesity traits. The BSB mouse, which is produced by the backcross of (lean C57BL/6J x lean Mus spretus) x C57BL/6J, provides an excellent model of epistatic obesity. To evaluate potential epistatic interactions among six chromosomal regions previously determined to influence obesity phenotypes, we performed novel Bayesian analyses on the basis of both epistatic and nonepistatic models for four obesity traits: percentage of body fat, adiposity index, total fat mass, and body weight, and also for plasma total cholesterol. The epistatic analysis detected at least one more QTL than the nonepistatic analysis did for all obesity traits. These obesity traits were variously influenced by QTL on chromosomes 2, 7, 12, 15, and 16. Interaction between genes on chromosomes 2 and 12 was present for all obesity traits, accounting for 3-4.8% of the phenotypic variation. Chromosome 12 was found to have weak main effects on all obesity traits. Several different epistatic interactions were also detected for percentage of body fat, adiposity index, and total fat mass. Chromosomes 6 and 12 have not only main effects but also strong epistatic effects on plasma total cholesterol. Our results emphasize the importance of modeling epistasis for discovery of obesity genes.

Absence of Epistasis for Grain Yield in Elite Maize Hybrids

Certain maize (Zea mays L.) inbred lines are more successful than others in forming elite hybrids. This study was conducted to determine whether epistatic interactions play a significant role in hybrid performance. Statistical epistasis was measured with a modified generation means model using testcrosses. Six progeny generations (P1, P2, F1, F2, and a backcross from the F1 to each parent) were produced for all possible hybrids of a five-parent diallel in both the Iowa Stiff Stalk Synthetic (BSSS) and non-BSSS heterotic groups. Two testers were hybridized to each of the 10 possible hybrid progeny sets in both groups. Each testcross progeny set was evaluated in 10 environments. The nonepistatic model accounted for a large amount of the variation in generation means and fit the data well. Of the 40 maize testcross progeny sets studied, five resulted in a significant epistatic effect for grain yield. Four of the significant epistatic effects showed evidence of linkage, while one was due to unlinked epistatic effects. Our results suggest that parents in a hybrid cross need to be significantly different and testers need to bring out those differences to detect epistasis better by means of testcross generation means.

Absence of Epistasis for Grain Yield in Elite Maize Hybrids

Certain maize (Zea mays L.) inbred lines are more successful than others in forming elite hybrids. This study was conducted to determine whether epistatic interactions play a significant role in hybrid performance. Statistical epistasis was measured with a modified generation means model using testcrosses. Six progeny generations (P1, P2, F1, F2, and a backcross from the F1 to each parent) were produced for all possible hybrids of a five‐parent diallel in both the Iowa Stiff Stalk Synthetic (BSSS) and non‐BSSS heterotic groups. Two testers were hybridized to each of the 10 possible hybrid progeny sets in both groups. Each testcross progeny set was evaluated in 10 environments. The nonepistatic model accounted for a large amount of the variation in generation means and fit the data well. Of the 40 maize testcross progeny sets studied, five resulted in a significant epistatic effect for grain yield. Four of the significant epistatic effects showed evidence of linkage, while one was due to unlinked epistatic effects. Our results suggest that parents in a hybrid cross need to be significantly different and testers need to bring out those differences to detect epistasis better by means of testcross generation means.

Muller's ratchet, epistasis and mutation effects.

In this study, computer simulation is used to show that despite synergistic epistasis for fitness, Muller's ratchet can lead to lethal fitness loss in a population of asexuals through the accumulation of deleterious mutations. This result contradicts previous work that indicated that epistasis will halt the ratchet. The present results show that epistasis will not halt the ratchet provided that rather than a single deleterious mutation effect, there is a distribution of deleterious mutation effects with sufficient density near zero. In addition to epistasis and mutation distribution, the ability of Muller's ratchet to lead to the extinction of an asexual population under epistasis for fitness depends strongly on the expected number of offspring that survive to reproductive age. This strong dependence is not present in the nonepistatic model and suggests that interpreting the population growth parameter as fecundity is inadequate. Because a continuous distribution of mutation effects is used in this model, an emphasis is placed on the dynamics of the mutation effect distribution rather than on the dynamics of the number of least mutation loaded individuals. This perspective suggests that current models of gene interaction are too simple to apply directly to long-term prediction for populations undergoing the ratchet.

Comparison of Testcrosses Produced from F2 and First Backcross Populations in Maize

Single crosses and backcrosses from established lines are importeat parental sources for developing new inbred lines in hybrid maize (Zea mays L.) breeding. The objectives of this study were (i) compare, both theoretically and experimentally, the testcross properties of F2 vs. first backcross populations; and (ii) to outline criteria for choosing between these two types of base populations in recycling breeding programs. Two homozygous lines (P1, P2) and individual plants from their F2 and first backcross (BC1, BC2) generations were mated to an unrelated single‐cross tester. A total of 186 testcross progenies were evaluated for grain and forage traits at three and two locations, respectively. The five generations (P1, P2, F2, BC1, BC2) differed significantly (P < 0.05) in their testcross means (X̄) for grain (GY) and forage (FY) yield. A nonepistatic model accounted for 92 to 99% of the variation among testcross generation means for five of the six traits examined, yet the presence of epistasis was indicated in several instances. In accordance with theory, the ratio of BC (the pooled estimate of BC1 and BC2) to F2 genotypic variance among testcross progenies (σ2g) was close to 0.50 for all traits but one. Heterogeneous σ2g estimates in BC1 and BC2 were found for GY, FY, and grain dry matter content, suggesting the presence of epistasis. Predicted selection response for testcross performance (ΔG) was greatest in the F2. Testcross progenies of the F2, BC1, and BC2 generations displayed similar phenotypic and genotypic correlations as expected by theory. The “usefulness” criterion U = x̄ + ΔG was employed to assess the breeding prospects of each generation. With weak selection, the better backcross had superior usefulness for four traits, whereas with strong selection the F2 had highest usefulness for all traits except GY.

Representation of Nonepistatic selection models and analysis of multilocus Hardy-Weinberg Equilibrium configurations.

The paper develops conditions for the existence and the stability of central equilibria emanating from selection recombination interaction with generalized nonepistatic selection forms operating in multilocus multiallele systems. The selection structure admits a natural representation as simple sums of Kronecker products based on a common set of marginal selection components. A flexible parametrization of the recombination process is introduced leading to a canonical derivation of the transformation equations connecting gamete frequency states over successive generations. Conditions for the existence and stability of multilocus Hardy-Weinberg (H.W.) type equilibria are elaborated for the classical nonepistatic models (multiplicative and additive viability effects across loci) as well as for generalized nonepistatic selection expressions. It is established that the range of recombination distributions maintaining a stable H.W. polymorphic equilibrium is confined to loose linkage in the pure multiplicative case, but is not restricted in the additive model. In the bisexual case we ascertain for the generalized nonepistatic model the stability conditions of a common H.W polymorphism.

Simulation of cyclic single cross selection

Computer simulation was used to compare Hallauer's cyclic single cross selection (CSCS) with reciprocal recurrent selection (RRS). Three epistatic and three non-epistatic models with 60 loci determining a single character provided the genetic base. The rate of advance over seven cycles was always greater for CSCS than for RRS on either a cycle or generation basis. No genetic conditions were found where CSCS failed to respond. The advantages of CSCS increases as the proportion of non-additive genetic variance increases. Genetic advance of the hybrid population was shown to result from the joint effects of an average change in gene frequency and complementary effects (nicking) of selection. Nicking effects accounted for most of the advance for some starting conditions. RRS generally had higher selection limits with no epistasis or low gene frequency of the dominant allele. CSCS generally had higher limits with epistasis or high frequency of the dominant allele. We suggested that CSCS begin with divergent genetic populations and strong selection intensity for three cycles. Final selection of superior single crosses was indicated when the lines were completely inbred.

Genetic Effects Estimated from Generation Means in Four Diallel Sets of Maize Inbreds1

Genetic parameters were estimated from generation means in four types of maize (Zea mays L.) inbred lines: first cycle lines, isolated from open‐pollinated varieties; second cycle lines, isolated from either planned pedigree crosses or synthetic varieties; good lines per se; and poor line per se. Nine generations were available for each cross: parents, F1, F2, F3, backcrosses, and backcrosses selfed. Parameters estimated were additive, dominance, and digenic epistatic effects.Second‐cycle inbreds demonstrated significantly more epistasis for yield than did first‐cycle inbreds. Good and poor inbreds were similar and intermediate to first‐ and second‐cycle inbreds in the occurence of epistasis, which occurred in 30% of the crosses. Interactions of environments ✕ additive and dominance effects were significant in more than two‐thirds of the crosses. The environments ✕ epistasis interactions were significant in 25% of the cases for the poor inbreds.Dominance effects were several times larger than additive effects for all crosses. Pooling of effects over loci is discussed as the reason for disagreement with results of variance analyses. Additive ✕ additive and dominance ✕ dominance interactions were present in half the crosses of the poor inbreds. Significance of epistatic effects and additive effects was found in about the same frequency in the other types of inbreds.Correlation analyses indicated the nonepistatic model sufficient to describe the gene action, since all r values exceeded 0.9**. The full model including epistatic terms was of value in describing a particular environment, but the epistatic terms were of no value when predicting yield in one environment from trials in a different environment.