The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

上位性及其在遗传育种研究中的应用

上位性引入遗传学已有一个多世纪,直到近些年才受到广泛关注,成为复杂性状遗传研究体系的一个重要组成部分。上位性可分为统计上位性和功能上位性两类,前者具有群体特性,后者属于基因型现象。分子标记技术是研究上位性的一个有力工具,理论与实验研究证实上位性在动植物数量性状的表现中具有重要作用。上位性在作物育种中的应用因作物的繁殖方式,育种方法等不同而异,上位性是杂种优势形成的重要遗传基础。     

A symmetric two locus model with viability and fertility selection

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.Research supported in part by NIH grants GM 28106 and GM 10452     

Modeling Epistasis in Genomic Selection

Modeling epistasis in genomic selection is impeded by a high computational load. The extended genomic best linear unbiased prediction (EG-BLUP) with an epistatic relationship matrix and the reproducing kernel Hilbert space regression (RKHS) are two attractive approaches that reduce the computational load. In this study, we proved the equivalence of EG-BLUP and genomic selection approaches, explicitly modeling epistatic effects. Moreover, we have shown why the RKHS model based on a Gaussian kernel captures epistatic effects among markers. Using experimental data sets in wheat and maize, we compared different genomic selection approaches and concluded that prediction accuracy can be improved by modeling epistasis for selfing species but may not for outcrossing species.     

A general approach for the study of a population of testcross progenies and consequences for recurrent selection

Summary A model to study genetic effects at the level of a population of testcross progenies is presented. As there is no dominance for the testcross value, with the restriction of epistasis to pairs of loci, only additive x additive epistasis can contribute to the variance among progenies. To estimate the variance among progenies due to epistasis, it is necessary to have the population structured in families of full sibs, half sibs or S₁, with only a few plants per family tested in combination with the tester. Using a two-way mating design to produce the families, it is possible to estimate the variance due to additive x additive epistasis. The consequence of the presence of epistasis is studied at the level of recurrent selection for combining ability with the tester. It seems that epistasis itself does not change the efficiency of the breeding methods considered. However, when the population from intercrossing is structured in families, it could be efficient to use a combined selection when the heritability is very low. In this case it would be efficient to produce full-sib families (by single-pair matings) at the level of intercrossing. The best procedure is to produce such families at the same time as crossing with the tester. In comparison to the classical scheme of selection for combining ability with a tester, such a modification increases the efficiency of selection 41.1% if an off-season generation can be used.     

Epistasis affecting litter size in mice

Litter size is an important reproductive trait as it makes a major contribution to fitness. Generally, traits closely related to fitness show low heritability perhaps because of the corrosive effects of directional natural selection on the additive genetic variance. Nonetheless, low heritability does not imply, necessarily, a complete absence of genetic variation because genetic interactions (epistasis and dominance) contribute to variation in traits displaying strong heterosis in crosses, such as litter size. In our study, we investigated the genetic architecture of litter size in 166 females from an F2 intercross of the SM/J and LG/J inbred mouse strains. Litter size had a low heritability (h2 = 12%) and a low repeatability (r = 33%). Using interval-mapping methods, we located two quantitative trait loci (QTL) affecting litter size at locations D7Mit21 + 0 cM and D12Mit6 + 8 cM, on chromosomes 7 and 12 respectively. These QTL accounted for 12.6% of the variance in litter size. In a two-way genome-wide epistasis scan we found eight QTL interacting epistatically involving chromosomes 2, 4, 5, 11, 14, 15 and 18. Taken together, the QTL and their interactions explain nearly 49% (39.5% adjusted multiple r2) of the phenotypic variation for litter size in this cross, an increase of 36% over the direct effects of the QTL. This indicates the importance of epistasis as a component of the genetic architecture of litter size and fitness in our intercross population.     

Epistasis in natural populations of a predominantly selfing plant

Populations of predominantly selfing plant species often show spatial genetic structure but little is known whether epistatic gene interactions are spatially structured. To detect a possible epistatic effect and a spatial scale at which it operates, we created artificial crosses between plants spanning a range of fixed distances from 1 to 400 m in three populations of wild barley. The self-pollinated and crossed progeny (F₁) and two generations of segregated progeny (F₂ and F₃) were tested in experimentally simulated population environments for relative performance (RP). The measured fitness traits included number of seeds, total seed weight and seed germination. For any of these traits, there was no association between RP of F₁, F₂ and F₃ plants and either pairwise kinship coefficients or crossing distance. In contrast, in all three populations, we found lower seed viability of outcrossed as compared with self-pollinated genotypes in the first generation of segregation. However, in the F₃ generation this outbreeding effect disappeared in the two populations and greatly decreased in the third population. For seed production, heterosis in F₁ and outbreeding depression in F₂ were observed only in the population with unusually high number of heterozygotes. Our findings support the view that in selfing species a spatial mosaic of various locally abundant genotypes represents not randomly fixed combinations of alleles but the co-adapted gene complexes that were sieved by selection, while heterozygotes are characteristic for the transient phase of this process, when segregation and purging of maladaptive genotypes have not yet occurred.     

Epistasis, phenotypic disequilibrium and contrasting associations with climate in the land snail Theba pisana

Hotter conditions favour effectively unbanded (EUB) shells in the snail Theba pisana. T. pisana is also polymorphic for colour of the shell's apex, determined by a pair of alleles at a locus linked to the banding locus. Apex colour is epistatic to shell banding, such that banded snails with a dark apex have darker bands. Annual censuses over 22 years across an ecotone between a sheltered Acacia thicket and open dune vegetation showed a persistent association of both EUB shells and pale apex with the Open habitat. The parallel variation was due partly to strong phenotypic disequilibrium, as the combination of EUB with dark apex was rare. Nevertheless, in fully banded shells the frequency of pale apex was also higher in the Open habitat, confirming independent, parallel associations of the two contributors to paleness. Within the Acacia habitat, temporal variation of the frequencies of banding morphs was much greater than for apex colour, and EUB shells were associated with hotter summers. Consistent with its primary effect only on the very small snails, apex colour did not vary with summer conditions, but instead, higher frequencies of pale apices were associated with sunnier winters. The intensity of selection was lower on apex colour than shell banding, due partly to the constraint of phenotypic disequilibrium. The shell traits in T. pisana are an example of complex responses to climatic variation, in which phenotypic disequilibrium constrains evolution of apex colour, but separate mechanisms of selection are evident.     

Developmental rate and viability of rainbow trout with a null allele at a lactate dehydrogenase locus

We show that a previously described isozyme polymorphism in rainbow trout(Salmo gairdneri) is the result of an enzymatically inactive (i.e., null) allele(n). Ldh3 null homozygotes(n/n) and heterozygotes(100/n) have reductions of about 20 and 12% in total lactate dehydrogenase (LDH) activity at hatching, respectively. As juveniles,(100/n) fish have reductions in LDH activity of 15, 37, and 21% in brain, heart, and white muscle, respectively. Embryos with differntLdh3 phenotypes from 11 families do not differ significantly in either survival or hatching time. However, a second measure of developmental rate, the amount of malate dehydrogenase (MDH) and phosphoglucomutase (PGM) activity in 33-day-old embryos, suggests that(100/n) embryos develop more slowly than(100/100) embryos. In three of four families examined,(100/n) embryos have significantly lower amounts of total MDH activity (8–10%). In one of these,(100/n) embryos also have significantly lower total PGM activity (15%). These data suggest that the reduction in total LDH activity is associated with small but detectable delays in developmental rate but nondetectable differences in survival to hatching.This research was supported by NSF Grant BSR-8300039 to F. W. Allendorf and a postgraduate scholarship from the NSERC (Canada) to M. M. Ferguson.     

损毁大鼠双侧蓝斑引起多脏器出血

目的和方法：用直流电极毁大鼠双侧蓝斑,观察膀胱及各内脏组织的出血性变化。结果：完全损毁双侧蓝斑枷恒定地引起严重的膀胱出血,并伴有其它脏器不规律性发生的充血或轻微出血。部分损毁双侧蓝斑亦可引起多脏器轻微的充血和出血,但膀胱出血不再恒定发生。切除肾上腺减轻应激反应,或应用组织按H2受体拮抗剂,对完全损毁双侧蓝斑引起的膀胱出血或其它脏器的组织学出血性变化无明显影响。结论：损毁大鼠双侧蓝斑引起的多脏器出血并非由于手术应激引起;也与组织胺H2受 体无关,其机制有待进一步研究。     

Epistasis and genotype-by-environment interaction of grain protein content in durum wheat

Parental, F(1) , F (2) , BC (1) and BC (2) generations of four crosses involving four cultivars of durum wheat (Triticum durum Desf.) were evaluated at two sites in Tunisia. A three-parameter model was found inadequate for all cases except crosses Chili x Cocorit 71 at site Sidi Thabet and Inrat 69 x Karim at both sites. In most cases a digenic epistatic model was sufficient to explain variation in generation means. Dominance effects (h) and additive x additive epistasis (i) (when significant) were more important than additive (d) effects and other epistatic components. Considering the genotype-by-environment interaction, the non-interactive model (m, d, h, e) was found adequate. Additive variance was higher than environmental variance in three crosses at both sites. The estimated values of narrow-sense heritability were dependent upon the cross and the sites and were 0%-85%. The results indicate that appropriate choice of environment and selection in later generations would increase grain protein content in durum wheat.     

Restriction fragment alleles of the rabbit IGHG genes with reference to the rabbit IGHGCH2 or e locus polymorphism

Among domesticated mammals, rabbit (Oryctolagus cuniculus) is the only species possessing not more than one subclass of immunoglobulin (IgG) antibodies. The rabbit IGHGCH2 or e locus presents two serologically defined alleles, the e14 and e15 allotypes, which are correlated with amino acid variation at the IgG CH2-CH3 interface. Genetic studies, while revealing the adaptive value of this polymorphism, have relied so far entirely upon allo-antisera. Here we show how these alleles can be distinguished by polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) methods. The proposed PCR-RFLP approach allows the monitoring of IGHG locus diversity in rabbit.     

Epistasis can lead to fragmented neutral spaces and contingency in evolution

In evolution, the effects of a single deleterious mutation can sometimes be compensated for by a second mutation which recovers the original phenotype. Such epistatic interactions have implications for the structure of genome space--namely, that networks of genomes encoding the same phenotype may not be connected by single mutational moves. We use the folding of RNA sequences into secondary structures as a model genotype-phenotype map and explore the neutral spaces corresponding to networks of genotypes with the same phenotype. In most of these networks, we find that it is not possible to connect all genotypes to one another by single point mutations. Instead, a network for a phenotypic structure with n bonds typically fragments into at least 2(n) neutral components, often of similar size. While components of the same network generate the same phenotype, they show important variations in their properties, most strikingly in their evolvability and mutational robustness. This heterogeneity implies contingency in the evolutionary process.     

A model for marker-assisted selection among single crosses with multiple genetic markers

 Trait means of marker genotypes are often inconsistent across experiments, thereby hindering the use of regression techniques in marker-assisted selection. Best linear unbiased prediction based on trait and marker data (TM-BLUP) does not require prior information on the mean effects associated with specific marker genotypes and, consequently, may be useful in applied breeding programs. The objective of this paper is to present a flanking-marker, TM-BLUP model that is applicable to interpopulation single crosses that characterize maize (Zea mays L.) breeding programs. The performance of a single cross is modeled as the sum of testcross additive and dominance effects at unmarked quantitative trait loci (QTL) and at marked QTL (MQTL). The TM-BLUP model requires information on the recombination frequencies between flanking markers and the MQTL and on MQTL variances. A tabular method is presented for calculating the conditional probability that MQTL alleles in two inbreds are identical by descent given the observed marker genotypes (G ^k _obs) at the kth MQTL. Information on identity by descent of MQTL alleles can then be used to calculate the conditional covariance of MQTL effects between single crosses given G ^k _obs. The inverse of the covariance matrix for dominance effects at unmarked QTL and MQTL can be written directly from the inverse of the covariance matrices of the corresponding testcross additive effects. In practice, the computations required in TM-BLUP may be prohibitive. The computational requirements may be reduced with simplified TM-BLUP models wherein dominance effects at MQTL are excluded, only the single crosses that have been tested are included, or information is pooled across several MQTL. Received: 22 June 1997 / Accepted: 25 February 1998     

The effect of variable environments on polymorphism at loci with several alleles I. A symmetric model

Much of the extant polymorphism has been attributed to spatial and temporal variation among selection regimes. Analysis of models entailing two alleles at a single locus has demonstrated that polymorphism may result from variation among selection regimes which prescribe monomorphism if constant. This relationship is studied in the context of several alleles at a locus.One result which is not valid with only two alleles is that variation among selection regimes which specify polymorphic equilibria may lead to a stable monomorphic equilibrium. The analyses of temporal variation and total panmixia spatial variation among environments show that temporal variation allows the simultaneous stability of equilibrium configurations which cannot be simultaneously stable under total panmixia spatial variation (hard or soft selection). The principle that polymorphism is more readily maintained with spatial than temporal variation is invalidated.Supported in part by Purdue Research Foundation and National Science Foundation (USA) grant MCS-8002227