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.     

Strong Epistatic Selection on the RNA Secondary Structure of HIV

A key question in evolutionary genomics is how populations navigate the adaptive landscape in the presence of epistasis, or interactions among loci. This problem can be directly addressed by studying the evolution of RNA secondary structures, for which there is constraint to maintain pairing between Watson-Crick (WC) sites. Replacement of a nucleotide at one site of a WC pair reduces fitness by disrupting binding, which can be restored via a compensatory replacement at the interacting site. Here, I present the first genome-scale analysis of epistasis on the RNA secondary structure of human immunodeficiency virus type 1 (HIV-1). Comparison of polymorphism frequencies at ancestrally conserved sites reveals that selection against replacements is ∼2.7 times stronger at WC than at non-WC sites, such that nearly 50% of constraint can be attributed to epistasis. However, almost all epistatic constraint is due to selection against conversions of WC pairs to unpaired (UP) nucleotides, whereas conversions to GU wobbles are only slightly deleterious. This disparity is also evident in pairs with second-site compensatory replacements; conversions from UP nucleotides to WC pairs increase median fitness by ∼4.2%, whereas conversions from GU wobbles to WC pairs only increase median fitness by ∼0.3%. Moreover, second-site replacements that convert UP nucleotides to GU wobbles also increase median fitness by ∼4%, indicating that such replacements are nearly as compensatory as those that restore WC pairing. Thus, WC peaks of the HIV-1 epistatic adaptive landscape are connected by high GU ridges, enabling the viral population to rapidly explore distant peaks without traversing deep UP valleys.     

The Action of Purifying Selection,Mutation and Drift on Fitness Epistatic Systems

For different fitness mutational models, with epistasis introduced, we simulated the consequences of drift (D scenario) or mutation, selection, and drift (MSD scenario) in populations at the MSD balance subsequently subjected to bottlenecks of size N = 2, 10, 50 during 100 generations. No “conversion” of nonadditive into additive variance was observed, all components of the fitness genetic variance initially increasing with the inbreeding coefficient F and subsequently decreasing to zero (D) or to an equilibrium value (MSD). In the D scenario, epistasis had no appreciable effect on inbreeding depression and that on the temporal change of variance components was relevant only for high rates of strong epistatic mutation. In parallel, between-line differentiation in mean fitness accelerated with F and that in additive variance reached a maximum at F ∼ 0.6–0.7, both processes being intensified by strong epistasis. In the MSD scenario, however, the increase in additive variance was smaller, as it was used by selection to purge inbreeding depression (N ≥ 10), and selection prevented between-line differentiation. Epistasis, either synergistic or antagonistic (this leading to multiple adaptive peaks), had no appreciable effect on MSD results nor, therefore, on the evolutionary rate of fitness change.THE roles of genetic drift and natural selection in shaping the genetic variation of fitness due to segregation at epistatic loci have often been discussed since Wright''s (1931) pioneering treatment of the subject. In general, the pertinent analyses have been usually elaborated within an analytical framework where changes in the mean and the components of the genetic variance exclusively due to drift were first considered, this being followed by an examination of the conditions that may subsequently allow for a more rapid selection response and/or facilitate the movement of populations to new adaptive peaks.Theoretically, it is well known that the contribution of neutral additive loci to the additive genetic variance of metric traits in populations decreases linearly as the inbreeding coefficient F increases, until it ultimately vanishes when fixation is attained (Wright 1951). For neutral nonadditive loci, however, that contribution may initially increase until a critical F value is reached and then subsequently decline to zero. This is the case of simple dominant loci (Robertson 1952; Willis and Orr 1993), and it also applies to two-locus models showing either additive × additive epistasis (Cockerham and Tachida 1988; Goodnight 1988) or more complex epistasis involving dominance at the single-locus level (Cheverud and Routman 1996; López-Fanjul et al. 1999, 2000; Goodnight 2000). Furthermore, those models have been extended to cover multiple additive × additive epistatic systems (Barton and Turelli 2004, López-Fanjul et al. 2006).In parallel, laboratory experiments have also studied the impact of population bottlenecks on the additive variance of metric traits (see reviews by López-Fanjul et al. 2003 and Van Buskirk and Willi 2006). For morphological traits not strongly correlated with fitness, a decrease in their additive variance together with little or no inbreeding depression was often observed, both results being compatible with the corresponding additive expectations and suggesting that the standing variation of those traits is mainly controlled by quasi-neutral additive alleles. Using typical estimates of mutational parameters, Zhang et al. (2004) showed that these experimental results can be explained by assuming a model of pleiotropic and real stabilizing selection acting on the pertinent trait. On the other hand, life-history traits closely connected to fitness usually show strong inbreeding depression and a dramatic increase in additive variance after a brief period of inbreeding or bottlenecking, indicating that much of that variance should be due to deleterious recessive alleles segregating at low frequencies. However, it should be kept in mind that experimental results cannot discern between simple dominance and dominance with additional epistasis as causes of inbreeding-induced changes in the additive variance.In their discussion of the shifting-balance theory (Wright 1931), Wade and Goodnight emphasized the evolutionary importance of the “conversion” of epistatic variance into additive variance, proposing that drift-induced excesses in the additive variance for fitness available to selection could enhance the potential for local adaptation, a phenomenon that was not discussed in the original formulation of Wright''s theory (Wade and Goodnight 1998; Goodnight and Wade 2000; but see Coyne et al. 1997, 2000). However, the additive variance is inflated only under restrictive conditions that often involve low-frequency deleterious recessive alleles (Robertson 1952; López-Fanjul et al. 2002), so that a drift-induced excess in the additive variance of fitness will be associated with inbreeding depression and, therefore, it is unlikely to produce a net increase in the adaptive potential of populations. In addition, previous considerations were based on the theoretical analysis of the behavior of neutral genetic variation after bottlenecks, and the role of selection acting on epistatic systems controlling fitness has not been studied.In this article we used analytical and simulation methods to investigate the contribution of epistatic systems to the change in the mean and the genetic components of variance of fitness during bottlenecking, due to the joint action of mutation, natural selection, and genetic drift (MSD). To develop a biologically reasonable model, we assumed that mutations show a distribution of homozygous and heterozygous effects close to those experimentally observed in Drosophila melanogaster, and we imposed different types of epistasis on this basic system. The pattern and strength of epistatic effects on fitness is largely unknown, but synergism between homozygous deleterious mutations at different loci has often been reported in Drosophila mutation-accumulation experiments (Mukai 1969; Ávila et al. 2006). Therefore, we studied the consequences of synergistic epistasis in pairs of loci by increasing the deleterious effect of the double homozygote above that expected from the deleterious effects of the homozygotes at both loci involved. However, to explore the consequences of bottlenecking in a multiple-peak adaptive surface, we also considered cases of antagonistic epistasis where, at each pair of loci, the fitness of the double homozygote for the deleterious alleles was larger than expected. Of course, other epistatic models could also be considered, including those showing higher-order interaction effects, but the severe shortage of relevant empirical data makes the choice highly subjective and, consequently, we restricted our analysis to the simplest case. On the other hand, our procedure has the practical advantage of allowing the definition of epistasis by the addition of a single parameter to those describing the properties of individual loci.Our aim was to describe and analyze drift-induced changes in the components of the genetic variance of fitness, where neutral predictions will be reliable only during extreme and brief bottlenecks. For moderate bottleneck sizes or long-term inbreeding, it becomes necessary to consider the concurrent effects of natural selection both on the standing variation and on that arisen by new mutation. Moreover, the nature of the genetic variability of fitness in the base population, arisen by mutation and shaped by natural selection and drift, is critical for the assessment of the consequences of subsequent bottlenecks. For nonepistatic models, the genetic properties of the trait can be theoretically inferred from the pertinent mutational parameters and effective population sizes by assuming a balance between mutation, selection, and drift. This can be numerically achieved using diffusion theory, and reliable approximations can be easily calculated by analytical methods (García-Dorado 2007). Notwithstanding, the analytical study of the contribution of epistasis to the genetic properties of fitness at the MSD balance becomes particularly difficult and it must be complemented with computer simulation.     

On the Classification of Epistatic Interactions

Modern genomewide association studies are characterized by the problem of “missing heritability.” Epistasis, or genetic interaction, has been suggested as a possible explanation for the relatively small contribution of single significant associations to the fraction of variance explained. Of particular concern to investigators of genetic interactions is how to best represent and define epistasis. Previous studies have found that the use of different quantitative definitions for genetic interaction can lead to different conclusions when constructing genetic interaction networks and when addressing evolutionary questions. We suggest that instead, multiple representations of epistasis, or epistatic “subtypes,” may be valid within a given system. Selecting among these epistatic subtypes may provide additional insight into the biological and functional relationships among pairs of genes. In this study, we propose maximum-likelihood and model selection methods in a hypothesis-testing framework to choose epistatic subtypes that best represent functional relationships for pairs of genes on the basis of fitness data from both single and double mutants in haploid systems. We gauge the performance of our method with extensive simulations under various interaction scenarios. Our approach performs reasonably well in detecting the most likely epistatic subtype for pairs of genes, as well as in reducing bias when estimating the epistatic parameter (ɛ). We apply our approach to two available data sets from yeast (Saccharomyces cerevisiae) and demonstrate through overlap of our identified epistatic pairs with experimentally verified interactions and functional links that our results are likely of biological significance in understanding interaction mechanisms. We anticipate that our method will improve detection of epistatic interactions and will help to unravel the mysteries of complex biological systems.UNDERSTANDING the nature of genetic interactions is crucial to obtaining a more complete picture of complex biological systems and their evolution. The discovery of genetic interactions has been the goal of many researchers studying a number of model systems, including but not limited to Saccharomyces cerevisiae, Caenorhabditis elegans, and Escherichia coli (You and Yin 2002; Burch et al. 2003; Burch and Chao 2004; Tong et al. 2004; Drees et al. 2005; Sanjuán et al. 2005; Segre et al. 2005; Pan et al. 2006; Zhong and Sternberg 2006; Jasnos and Korona 2007; St. Onge et al. 2007; Decourty et al. 2008). Recently, high-throughput experimental approaches, such as epistatic mini-array profiles (E-MAPs) and genetic interaction analysis technology for E. coli (GIANT-coli), have enabled the study of epistasis on a large scale (Schuldiner et al. 2005, 2006; Collins et al. 2006, 2007; Typas et al. 2008). However, it remains unclear whether the computational and statistical methods currently in use to identify these interactions are indeed the most appropriate.The study of genetic interaction, or “epistasis,” has had a long and somewhat convoluted history. Bateson (1909) first used the term epistasis to describe the ability of a gene at one locus to “mask” the mutational influence of a gene at another locus (Cordell 2002). The term “epistacy” was later coined by Fisher (1918) to denote the statistical deviation of multilocus genotype values from an additive linear model for the value of a phenotype (Phillips 1998, 2008).These origins are the basis for the two main current interpretations of epistasis. The first, as introduced by Bateson (1909), is the “biological,” “physiological,” or “compositional” form of epistasis, concerned with the influence of an individual''s genetic background on an allele''s effect on phenotype (Cheverud and Routman 1995; Phillips 1998, 2008; Cordell 2002; Moore and Williams 2005). The second interpretation, attributed to Fisher, is “statistical” epistasis, which in its linear regression framework places the phenomenon of epistasis in the context of a population (Wagner et al. 1998; Wade et al. 2001; Wilke and Adami 2001; Moore and Williams 2005; Phillips 2008). Each of these approaches is equally valid in studying genetic interactions; however, confusion still exists about how to best reconcile the methods and results of the two (Phillips 1998, 2008; Cordell 2002; Moore and Williams 2005; Liberman and Feldman 2006; Aylor and Zeng 2008).Aside from the distinction between the statistical and the physiological definitions of epistasis, inconsistencies exist when studying solely physiological epistasis. For categorical traits, physiological epistasis is clear as a “masking” effect. When noncategorical or numerical traits are measured, epistasis is defined as the deviation of the phenotype of the multiple mutant from that expected under independence of the underlying genes.The “expectation” of the phenotype under independence, that is, in the absence of epistasis, is not defined consistently between studies. For clarity, consider epistasis between pairs of genes and, without loss of generality, consider fitness as the phenotype. The first commonly used definition of independence, originating from additivity, defines the effect of two independent mutations to be equal to the sum of the individual mutational effects. A second, motivated by the use of fitness as a phenotype, defines the effect of the two mutations as the product of the individual effects (Elena and Lenski 1997; Desai et al. 2007; Phillips 2008). A third definition of independence has been referred to as “minimum,” where alleles at two loci are independent if the double mutant has the same fitness as the less-fit single mutant. Mani et al. (2008) claim that this has been used when identifying pairwise epistasis by searching for synthetic lethal double mutants (Tong et al. 2001, 2004; Pan et al. 2004, 2006; Davierwala et al. 2005). A fourth is the “Log” definition presented by Mani et al. (2008) and Sanjuan and Elena (2006). The less-frequently used “scaled ɛ” (Segre et al. 2005) measure of epistasis takes the multiplicative definition of independence with a scaling factor.These different definitions of independence are partly due to distinct measurement “scales.” For some traits, a multiplicative definition of independence may be necessary to identify epistasis between two genes, whereas for other traits, additivity may be appropriate (Falconer and Mackay 1995; Wade et al. 2001; Mani et al. 2008; Phillips 2008). An interaction found under one independence definition may not necessarily be found under another, leading to different biological conclusions (Mani et al. 2008).Mani et al. (2008) suggest that there may be an “ideal” definition of independence for all gene pairs for identifying functional relationships. However, it is plausible that different representations of independence for two genes may reflect different biological properties of the relationship (Kupper and Hogan 1978; Rothman et al. 1980). “Two categories of general interest [the additive and multiplicative definitions, respectively] are those in which etiologic factors act interchangeably in the same step in a multistep process, or alternatively act at different steps in the process” (Rothman et al. 1980, p. 468). In some cases, the discovery of epistasis may merely be an artifact of using an incorrect null model (Kupper and Hogan 1978). It may be necessary to represent “independence” differently, resulting in different statistical measures of interactions, for different pairs of genes depending on their functions.Previous studies have suggested that different pairs of loci may have different modes of interaction and have attempted to subclassify genetic interactions into regulatory hierarchies and mutually exclusive “interaction subtypes” to elucidate underlying biological properties (Avery and Wasserman 1992; Drees et al. 2005; St. Onge et al. 2007). We suggest that epistatic relationships can be divided into several subtypes, or forms, corresponding to the aforementioned definitions of independence. As a particular gene pair may deviate from independence according to several criteria, we do not claim that these subtypes are necessarily mutually exclusive. We attempt to select the most likely epistatic subtype that is the best statistical representation of the relationship between two genes. To further subclassify interactions, epistasis among deleterious mutations can take one of two commonly used forms: positive (equivalently alleviating, antagonistic, or buffering) epistasis, where the phenotype of the double mutant is less severe than expected under independence, and negative (equivalently aggravating, synergistic, or synthetic), where the phenotype is more severe than expected (Segre et al. 2005; Collins et al. 2006; Desai et al. 2007; Mani et al. 2008).Another objective of such distinctions is to reduce the bias of the estimator of the epistatic parameter (ɛ), which measures the extent and direction of epistasis for a given gene pair. Mani et al. (2008), assuming that the overall distribution of ɛ should be centered around 0, find that inaccurately choosing a definition of independence can result in increased bias when estimating ɛ. For example, using the minimum definition results in the most severe bias when single mutants have moderate fitness effects, and the additive definition results in the largest positive bias when at least one gene has an extreme fitness defect (Mani et al. 2008). Therefore, it is important to select an optimal estimator for ɛ for each pair of genes from among the subtypes of epistatic interactions.Epistasis may be important to consider in genomic association studies, as a gene with a weak main effect may be identified only through its interaction with another gene or other genes (Frankel and Schork 1996; Culverhouse et al. 2002; Moore 2003; Cordell 2009; Moore and Williams 2009). Epistasis has also been studied extensively in the context of the evolution of sex and recombination. The mutational deterministic hypothesis proposes that the evolution of sex and recombination would be favored by negative epistatic interactions (Feldman et al. 1980; Kondrashov 1994); many other studies have also studied the importance of the form of epistasis (Elena and Lenski 1997; Otto and Feldman 1997; Burch and Chao 2004; Keightley and Otto 2006; Desai et al. 2007; MacCarthy and Bergman 2007). Indeed, according to Mani et al. (2008, p. 3466), “the choice of definition [of epistasis] alters conclusions relevant to the adaptive value of sex and recombination.”Given fitness data from single and double mutants in haploid organisms, we implement a likelihood method to determine the subtype that is the best statistical representation of the epistatic interaction for pairs of genes. We use maximum-likelihood estimation and the Bayesian information criteria (BIC) (Schwarz 1978) with a likelihood-ratio test to select the most appropriate null or epistatic model for each putative interaction. We conduct extensive simulations to gauge the performance of our method and demonstrate that it performs reasonably well under various interaction scenarios. We apply our method to two data sets with fitness measurements obtained from yeast (Jasnos and Korona 2007; St. Onge et al. 2007), whose authors assume only multiplicative epistasis for all interactions. By examining functional links and experimentally validated interactions among epistatic pairs, we demonstrate that our results are biologically meaningful. Studying a random selection of genes, we find that minimum epistasis is more prevalent than both additive and multiplicative epistasis and that the overall distribution of ɛ is not significantly different from zero (as Jasnos and Korona 2007 suggest). For genes in a particular pathway, we advise selecting among fewer epistatic subtypes. We believe that our method of epistatic subtype classification will aid in understanding genetic interactions and their properties.

St. Onge et al. (2007) data set:

St. Onge et al. (2007) examined 26 nonessential genes known to confer resistance to MMS, constructed double-deletion strains for 323 double-mutant strains (all but two of the total possible pairs), and assumed the multiplicative form of epistasis for all interactions (see Methods: Analysis of experimental data). Following these authors, we focus on single- and double-mutant fitnesses measured in the presence of MMS. (For results in the absence of MMS, see File S1 and File S1_2.)Using the resampling method described in Analysis of experimental data and File S1, 222 gene pairs pass the cutoff of having epistasis inferred in at least 900 of 1000 replicates. This does not include 5 synthetic lethal gene pairs. Hypothesis testing and a multiple-testing procedure (for 222 simultaneous hypotheses) are necessary to determine the final epistatic pairs.To select one among the three multiple-testing procedures, we follow St. Onge et al. (2007) and examine gene pairs that share specific functional links (see Analysis of experimental data). The Bonferroni method is likely too conservative, yielding only 25 significantly epistatic pairs with only one functional link among them; alternatively, the pFDR procedure appears to be too lenient in rejecting independence for all 222 pairs. Therefore, we use the FDR procedure (although the number of functional links is not significant) and detect 193 epistatic pairs, of which 5 (2.6%) are synthetic lethals, 19 (9.8%) have additive epistasis, 33 (17.1%) have multiplicative epistasis, and 136 (70.5%) have minimum epistasis (File S1_1). We find 29 gene pairs with positive (alleviating) epistasis and 159 gene pairs with negative (aggravating) epistasis.

TABLE 2

Summary of gene pairs with the indicated epistatic subtypes, inferred using the FDR procedure with the BIC method that considers all three epistatic subtypes and their corresponding null models

选择作用下家鸡淀粉酶的遗传多态性研究--基因频率分化、相关效应估计和标记辅助选择试验

对“三黄”鸡4个品系的血液淀粉酶（Amy-l）基因频率进行了估计,结果表明：Amy-l基因频率具有明显的品系特异性,父系Amy－lA高;母系Amy-lB频率高．人工选择可能是导致两个具有相同遗传来源的品系（Ⅱ系和Ⅲ系）Amy-l基因频率发生分化的原因．利用线性模型估计了Amy－l基因的加性效应,结果表明：Amy-lB有利于产蛋性能,而Amy－l4有利于体重和蛋重的提高。标记辅助选择试验结果表明,选择Amy-l传型来改变家禽品系类型是可能的,但效果有限,因此,对Amy-l的选择应结合于综合的选择方案之中．     

Differentiation of Muller''s Chromosomal Elements D and E in the Obscura Group of Drosophila

Twenty-two markers located on Muller's elements D or E have been mapped by in situ hybridization in six species of the obscura group of Drosophila and in D. melanogaster. The obscura species can be grouped into a Palearctic cluster (D. subobscura, D. madeirensis and D. guanche) and a Nearctic one (D. pseudoobscura, D. persimilis and D. miranda). Eleven of the probes contain known genes: E74, Acp70A, Est5, hsp28/23, hsp83, emc, hsp70, Xdh, Acph-1, Cec and rp49. The remaining probes are recombinant phages isolated from a D. subobscura genomic library. All these markers hybridize to the putative homologous chromosome or chromosomal arm of elements D and E. Thus, these elements have conserved their genic content during species divergence. Chromosomal homologies proposed previously for each element among the species of the same cluster have been compared with the present results. The distribution of markers within each element has changed considerably as inferred from pairwise comparisons of obscura species included in the two different clusters. Only chromosomal segments defined by closely linked markers have been conserved: one such segment has been detected in element D and three in element E between D. subobscura and D. pseudoobscura.     

Epistatic association mapping in homozygous crop cultivars

The genetic dissection of complex traits plays a crucial role in crop breeding. However, genetic analysis and crop breeding have heretofore been performed separately. In this study, we designed a new approach that integrates epistatic association analysis in crop cultivars with breeding by design. First, we proposed an epistatic association mapping (EAM) approach in homozygous crop cultivars. The phenotypic values of complex traits, along with molecular marker information, were used to perform EAM. In our EAM, all the main-effect quantitative trait loci (QTLs), environmental effects, QTL-by-environment interactions and QTL-by-QTL interactions were included in a full model and estimated by empirical Bayes approach. A series of Monte Carlo simulations was performed to confirm the reliability of the new method. Next, the information from all detected QTLs was used to mine novel alleles for each locus and to design elite cross combination. Finally, the new approach was adopted to dissect the genetic basis of seed length in 215 soybean cultivars obtained, by stratified random sampling, from 6 geographic ecotypes in China. As a result, 19 main-effect QTLs and 3 epistatic QTLs were identified, more than 10 novel alleles were mined and 3 elite parental combinations, such as Daqingdou and Zhengzhou790034, were predicted.     

Ratchet riposte: more on gastropod burrowing sculpture

Recent warnings concerning paleobiological inferences based upon gastropod shell morphology (Houbrick 1991) merit serious consideration, although the dangers have been overstated. Ratchet sculpture, an asymmetrical sculpture that assists marine invertebrates in burrowing, is not qualitatively different from sculptures that apparently do not aid in burrowing. Therefore, the interpretation of such sculpture might be problematical. Nevertheless, the large body of empirical evidence demonstrating the function of ratchet sculpture in burrowing by bivalves, gastropods, carpoid echinoderms, brachiopods, and arthropods and the lack of evidence supporting alternative functions in the Gastropoda warrant the continued, although cautious, association of ratchet sculpture with burrowing in marine gastropods. □ Functional morphology, Gastropoda, ratchet sculpture, burrowing.     

Epistatic contributions to quantitative traits in Tribolium castaneum

Summary Triple-testcross experiments were used to analyze epistatic contributions to % hatchability of eggs, age of pupation, number of eggs laid in 24-hour period, and survival from hatching to day 35. Seven diverse inbred lines and the F₁ produced by crossing the two tester lines were examined for the presence of epistasis. There was evidence of epistasis for each of the 4 traits in at least one of the 8 lines tested. Epistasis was a major source of variation in survival in all of the lines tested.     

Epistatic association and linkage analysis in human families

Summary A new method is given to test for phenotypic association using related individuals in pedigree analysis. It is also shown how an extension of this method allows analyses of genetic linkage in the presence of epistatic associations. A published pedigree with strong evidence for linkage between Lp and ESD is reanalyzed, resulting in a considerable drop of the lod score for linkage.Dr. Falk is supported by a grant from the National Institutes of Health (GM 29177)     

Epistatic interactions alter dynamics of multilocus gene-for-gene coevolution

Fitness costs associated with resistance or virulence genes are thought to play a key role in determining the dynamics of gene-for-gene (GFG) host-parasite coevolution. However, the nature of interactions between fitness effects of multiple resistance or virulence genes (epistasis) has received less attention. To examine effects of the functional form of epistasis on the dynamics of GFG host-parasite coevolution we modified a classic multilocus GFG model framework. We show that the type of epistasis between virulence genes largely determines coevolutionary dynamics, and that coevolutionary fluctuations are more likely with acceleratingly costly (negative) than with linear or deceleratingly costly (positive) epistasis. Our results demonstrate that the specific forms of interaction between multiple resistance or virulence genes are a crucial determinant of host-parasite coevolutionary dynamics.     

Effective Size of Populations under Selection

Equations to approximate the effective size (N(e)) of populations under continued selection are obtained that include the possibility of partial full-sib mating and other systems such as assortative mating. The general equation for the case of equal number of sexes and constant number of breeding individuals (N) is N(e) = 4N/[2(1 - α(I)) + (S(k)(2) + 4Q(2)C(2)) (1 + α(I) + 2α(O))], where S(k)(2) is the variance of family size due to sampling without selection, C(2) is the variance of selective advantages among families (the squared coefficient of variation of the expected number of offspring per family), α(I) is the deviation from Hardy-Weinberg proportions, α(O) is the correlation between genes of male and female parents, and Q(2) is the term accounting for the cumulative effect of selection on an inherited trait. This is obtained as Q = 2/[2 - G(1 + r)], where G is the remaining proportion of genetic variance in selected individuals and r is the correlation of the expected selective values of male and female parents. The method is also extended to the general case of different numbers of male and female parents. The predictive value of the formulae is tested under a model of truncation selection with the infinitesimal model of gene effects, where C(2) and G are a function of the selection intensity, the heritability and the intraclass correlation of sibs. Under random mating r = α(I) = -1/(N - 1) and α(O) = 0. Under partial full-sib mating with an average proportion β of full-sib matings per generation, r & β and α(O) & α(I) & β/ (4 - 3β). The prediction equation is compared to other approximations based on the long-term contributions of ancestors to descendants. Finally, based on the approach followed, a system of mating (compensatory mating) is proposed to reduce rates of inbreeding without loss of response in selection programs in which selected individuals from the largest families are mated to those from the smallest families.     

Evolution under Fertility and Viability Selection

Evolution at a single multiallelic locus under arbitrary weak selection on both fertility and viability is investigated. Discrete, nonoverlapping generations are posited for autosomal and X-linked loci in dioecious populations, but monoecious populations are studied in both discrete and continuous time. Mating is random. The results hold after several generations have elapsed. With an error of order s [i.e., O(s)], where s represents the selection intensity, the population evolves in Hardy-Weinberg proportions. Provided the change per generation of the fertilities and viabilities due to their explicit time dependence (if any) is O(s2), the rate of change of the deviation from Hardy-Weinberg proportions is O(s2). If the change per generation of the viabilities and genotypic fertilities is smaller than second order [i.e., o(s2)], then to O(s2) the rate of change of the mean fitness is equal to the genic variance. The mean fitness is the product of the mean fertility and the mean viability; in dioecious populations, the latter is the unweighted geometric mean of the mean viabilities of the two sexes. Hence, as long as there is significant gene frequency change, the mean fitness increases. If it is the fertilities of matings that change slowly [at rate o(s2)], the above conclusions apply to a modified mean fitness, defined as the product of the mean viability and the square root of the mean fertility.     

Epistatic interactions between four rad loci in yeast

Haploid yeast strains carrying mutations in two or more of four ad genes were contrusted by tetrad dissection, and the UV survival of these strains was measured. It was found that (with one exception) double mutant strains were not significantly more sensitive than the most sensitive single mutants, for strains involving mutant loci rad 1, rad 3 and rad 4. The exception was the double mutant rad 1–5 rad 4-4, but another double mutant involving different alleles of the the same loci did not show an enhanced UV sensitivity. Triple and quadruple mutants also failed to show a significantly increased UV sensitivity with respect to the single mutants. The results indicate that all these four mutant loci confer UV sensitivity by the same mechanism, and it is suggested that the wild-type alleles mediate excision-repair of UV-induced DNA lesions. Enhanced sensitivity of the genotype rad 1–5 rad 4-4 is attributed to leakiness of these alleles.     

Epistatic contributions to quantitative traits in Tribolium castaneum

Summary Triple-testcross experiments were used to analyze epistatic contributions to larva weight, pupa weight, pupa width and adult weight in Tribolium castaneum. Seven diverse inbred lines and the F₁. produced by crossing the two tester lines were examined for indications of epistasis. Larva weight was the only trait for which no significant epistasis was detected. There was significant epistasis for pupa weight in three of the inbred lines; for pupa width in four of the inbred lines; for adult weight in five of the inbred lines. Only one inbred line and the F₁ line failed to exhibit significant epistasis for any trait. Each inbred line had a unique pattern of epistasis, suggesting that a number of different loci were contributing to the detected epistasis.This paper (No. 76-5-158) is published with the approval of the Director of the Kentucky Agricultural Experiment Station.