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1.
For the Levene model with soft selection in two demes, the maintenance of polymorphism at two diallelic loci is studied. Selection is nonepistatic and dominance is intermediate. Thus, there is directional selection in every deme and at every locus. We assume that selection is in opposite directions in the two demes because otherwise no polymorphism is possible. If at one locus there is no dominance, then a complete analysis of the dynamical and equilibrium properties is performed. In particular, a simple necessary and sufficient condition for the existence of an internal equilibrium and sufficient conditions for global asymptotic stability are obtained. These results are extended to deme-independent degree of dominance at one locus. A perturbation analysis establishes structural stability within the full parameter space. In the absence of genotype-environment interaction, which requires deme-independent dominance at both loci, nongeneric equilibrium behavior occurs, and the introduction of arbitrarily small genotype-environment interaction changes the equilibrium structure and may destroy stable polymorphism. The volume of the parameter space for which a (stable) two-locus polymorphism is maintained is computed numerically. It is investigated how this volume depends on the strength of selection and on the dominance relations. If the favorable allele is (partially) dominant in its deme, more than 20% of all parameter combinations lead to a globally asymptotically stable, fully polymorphic equilibrium.  相似文献   

2.
Evolution under the multilocus Levene model is investigated. The linkage map is arbitrary, but epistasis is absent. The geometric-mean fitness, , depends only on the vector of gene frequencies, ρ; it is nondecreasing, and the single-generation change is zero only on the set, Λ, of gametic frequencies at gene-frequency equilibrium. The internal gene-frequency equilibria are the stationary points of . If the equilibrium points of ρ(t) (where t denotes time in generations) are isolated, as is generic, then ρ(t) converges as t to some . Generically, ρ(t) converges to a local maximum of . Write the vector of gametic frequencies, p, as , where d represents the vector of linkage disequilibria. If is a local maximum of , then the equilibrium point is asymptotically stable. If either there are only two loci or there is no dominance, then d(t)→0 globally as t. In the second case, has a unique maximum and is globally asymptotically stable. If underdominance and overdominance are excluded, and if at each locus, the degree of dominance is deme independent for every pair of alleles, then the following results also hold. There exists exactly one stable gene-frequency equilibrium (point or manifold), and it is globally attracting. If an internal gene-frequency equilibrium exists, it is globally asymptotically stable. On Λ, (i) the number of demes, Γ, is a generic upper bound on the number of alleles present per locus; and (ii) if every locus is diallelic, generically at most Γ−1 loci can segregate. Finally, if migration and selection are completely arbitrary except that the latter is uniform (i.e., deme independent), then every uniform selection equilibrium is a migration-selection equilibrium and generically has the same stability as under pure selection.  相似文献   

3.
The Levene model is the simplest mathematical model to describe the evolution of gene frequencies in spatially subdivided populations. It provides insight into how locally varying selection promotes a population’s genetic diversity. Despite its simplicity, interesting problems have remained unsolved even in the diallelic case.In this paper we answer an open problem by establishing that for two alleles at one locus and J demes, up to 2J−1 polymorphic equilibria may coexist. We first present a proof for the case of stable monomorphisms and then show that the result also holds for protected alleles. These findings allow us to prove that any odd number (up to 2J−1) of equilibria is possible, before we extend the proof to even numbers. We conclude with some numerical results and show that for J>2, the proportion of parameter space affording this maximum is extremely small.  相似文献   

4.
Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r2 (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r2 are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.  相似文献   

5.
Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.  相似文献   

6.
Wahlund's inequality informally states that if a structured and an unstructured population have the same allele frequencies at a locus, the structured population contains more homozygotes. We show that this inequality holds generally for ploidy level P, that is, the structured population has more P-polyhomozygotes. Further, for M randomly chosen loci (M >or= 2), the structured population is also expected to contain more M-multihomozygotes than an unstructured population with the same single-locus homozygosities. The extended inequalities suggest multilocus identity coefficients analogous to F(ST). Using microsatellite genotypes from human populations, we demonstrate that the multilocus Wahlund inequality can explain a positive bias in "identity-in-state excess".  相似文献   

7.
The dynamics and equilibrium structure of a deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. Various limiting cases are derived in which one or more of the three evolutionary forces, selection, migration, and recombination, are weak relative to the others. Two are particularly interesting. If migration and recombination are strong relative to selection, the dynamics can be conceived as a perturbation of the so-called weak-selection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weak-selection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weak-selection limit and has the same stability properties. The number of equilibria is the same in both systems, equilibria in the full (perturbed) system are in quasi-linkage equilibrium, and differences among allele frequencies across demes are small. If migration is weak relative to recombination and epistasis is also weak, then every equilibrium is a perturbation of an equilibrium of the corresponding system without migration, has the same stability properties, and is in quasi-linkage equilibrium. In both cases, every trajectory converges to an equilibrium, thus no cycling or complicated dynamics can occur.   相似文献   

8.
Linkage disequilibrium (LD) reflects coinheritance of an ancestral segment by chromosomes in a population. To begin to understand the effects of population history on the extent of LD, we model the length of a tract of identity-by-descent (IBD) between two chromosomes in a finite, random mating population. The variance of an IBD tract is large: a model described by (Genet. Res. Cambridge 35 (1980) 131) underestimates this variance. Using Fisher's concept of junctions, we predict the mean length of an IBD tract, given the age of the population and the population sizes over time. We derive results also for subdivided populations, given times of subdivision events and sizes of the resulting subpopulations. The model demonstrates that population growth and subdivision strongly affect the expected length of an IBD tract in small populations. These effects are less dramatic in large populations.  相似文献   

9.
10.
11.
The potential of maintaining multilocus polymorphism by migration-selection balance is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, selection may vary across demes, and loci are multiallelic. It is shown that if migration and recombination are strong relative to selection, then with weak or no epistasis and intermediate dominance at every locus and in every deme, arbitrarily many alleles can be maintained at arbitrarily many loci at a stable equilibrium. If migration is weak relative to selection and recombination, then with weak or no epistasis and intermediate dominance at every locus and in every deme, as many alleles as there are demes can be maintained at arbitrarily many loci at equilibrium. In both cases open sets of such parameter combinations are constructed, thus the results are robust with respect to small, but arbitrary, perturbations in the parameters. For weak migration, the number of demes is, in fact, a generic upper bound to the number of alleles that can be maintained at any locus. Thus, several scenarios are identified under which multilocus polymorphism can be maintained by migration-selection balance when this is impossible in a panmictic population.   相似文献   

12.
The maintenance of genetic variation in a spatially heterogeneous environment has been one of the main research themes in theoretical population genetics. Despite considerable progress in understanding the consequences of spatially structured environments on genetic variation, many problems remain unsolved. One of them concerns the relationship between the number of demes, the degree of dominance, and the maximum number of alleles that can be maintained by selection in a subdivided population. In this work, we study the potential of maintaining genetic variation in a two-deme model with deme-independent degree of intermediate dominance, which includes absence of G×E interaction as a special case. We present a thorough numerical analysis of a two-deme three-allele model, which allows us to identify dominance and selection patterns that harbor the potential for stable triallelic equilibria. The information gained by this approach is then used to construct an example in which existence and asymptotic stability of a fully polymorphic equilibrium can be proved analytically. Noteworthy, in this example the parameter range in which three alleles can coexist is maximized for intermediate migration rates. Our results can be interpreted in a specialist-generalist context and (among others) show when two specialists can coexist with a generalist in two demes if the degree of dominance is deme independent and intermediate. The dominance relation between the generalist allele and the specialist alleles play a decisive role. We also discuss linear selection on a quantitative trait and show that G×E interaction is not necessary for the maintenance of more than two alleles in two demes.  相似文献   

13.
This study analyzes population structure and linkage disequilibrium (LD) among 187 commonly used Chinese maize inbred lines, representing the genetic diversity among public, commercial and historically important lines for corn breeding. Seventy SSR loci, evenly distributed over 10 chromosomes, were assayed for polymorphism. The identified 290 alleles served to estimate population structure and analyze the genome-wide LD. The population of lines was highly structured, showing 6 subpopulations: BSSS (American BSSS including Reid), PA (group A germplasm derived from modern U.S. hybrids in China), PB (group B germplasm derived from modern U.S. hybrid in China), Lan (Lancaster Surecrop), LRC (derivative lines from Lvda Reb Cob, a Chinese landrace) and SPT (derivative lines from Si-ping-tou, a Chinese landrace). Forty lines, which formerly had an unknown and/or miscellaneous origin and pedigree record, were assigned to the appropriate group. Relationship estimates based on SSR marker data were quantified in a Q matrix, and this information will inform breeder’s decisions regarding crosses. Extensive inter- and intra-chromosomal LD was detected between 70 microsatellite loci for the investigated maize lines (2109 loci pairs in LD with D′ > 0.1 and 93 out of them at P < 0.01).This suggests that rapidly evolving microsatellites may track recent population structure. Interlocus LD decay among the diverse maize germplasm indicated that association studies in QTLs and/or candidate genes might avoid nonfunctional and spurious associations since most of the LD blocks were broken between diverse germplasm. The defined population structure and the LD analysis present the basis for future association mapping. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

14.
One hundred and ninety three parental lines obtained from 26 countries for an international rice molecular breeding program were evaluated using 101 well-distributed simple sequence repeat (SSR) markers. An overall genetic diversity of 0.68 and an average of 6.3 alleles per locus were revealed, indicating a high level of genetic variation in these lines. Cluster analysis of the 193 accessions showed three major groups and nine subgroups. Group I corresponded to the classical indica subspecies, whereas groups II and III belong to the japonica subspecies. Indica and japonica differentiation accounted for only 6.5% of the total variation in the entire sample and 93.5% was due to within-subspecies diversity. Differentiation among eco-geographic regions accounted for 24% of the diversity within the subspecies. Larger amounts of the eco-geographical differentiation were resolved within japonica than within indica. The largest indica-japonica differentiation based on the single locus level was detected by markers on chromosomes 9 and 12, while the smallest differentiation was detected by markers on chromosomes 4 and 8. Furthermore, genetic differences at the single-locus and two-locus levels, as well as components due to allelic and gametic differentiation, were revealed between indica and japonica and among the main geographic regions. The multilocus analysis in genetic diversity showed a higher proportion of variation caused by predominant non-random associations of different loci within and among the classified subspecies and geographic subdivisions. The results suggest that selection for eco-geographical adaptation on multilocus associations was largely responsible for the maintenance of the extensive variation in the primary gene pool of rice.Communicated by Q. ZhangS.B. Yu and W.J. Xu contributed equally to the work  相似文献   

15.
This paper is concerned with the “isolation with migration” model, where a panmictic ancestral population gave rise to a symmetric n-island model, time τ ago. Explicit analytical expressions are derived for the probability density function of the coalescence time of a pair of genes sampled at random from the same subpopulation or from different subpopulations, and for the probability distribution of the number of pairwise nucleotide differences.  相似文献   

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17.
This paper is concerned with a model of “isolation with an initial period of migration”, where a panmictic ancestral population split into n descendant populations which exchanged migrants symmetrically at a constant rate for a period of time and subsequently became completely isolated. In the limit as the population split occurred an infinitely long time ago, the model becomes an “isolation after migration” model, describing completely isolated descendant populations which arose from a subdivided ancestral population. The probability density function of the coalescence time of a pair of genes and the probability distribution of the number of pairwise nucleotide differences are derived for both models. Whilst these are theoretical results of interest in their own right, they also give an exact analytical expression for the likelihood, for data consisting of the numbers of nucleotide differences between pairs of DNA sequences where each pair is at a different, independent locus. The behaviour of the distribution of the number of pairwise nucleotide differences under these models is illustrated and compared to the corresponding distributions under the “isolation with migration” and “complete isolation” models. It is shown that the distribution of the number of nucleotide differences between a pair of DNA sequences from different descendant populations in the model of “isolation with an initial period of migration” can be quite different from that under the “isolation with migration model”, even if the average migration rate over time (and hence the total number of migrants) is the same in both scenarios. It is also illustrated how the results can be extended to other demographic scenarios that can be described by a combination of isolated panmictic populations and “symmetric island” models.  相似文献   

18.
CD14 is a lipopolysaccharide receptor known to be an important modulator of Th1–Th2 response during early childhood. Genetic association studies of the CD14 gene with asthma and atopic disorders have shown positive as well as negative results in different ethnic populations. The aim of this study was to test for association of C-159T functional promoter polymorphism with atopic asthma and serum IgE levels in northern and northwestern Indian populations. DNA was assayed for the CD14 C-159T polymorphism in a case-control study involving atopic asthmatics (n=187) and healthy normal controls (n=227), and in a family-based association study of 106 trios. The case-control study showed an association at the genotypic (P=0.0146) as well as the allelic level (P=0.0048). Moreover, we observed a deviation of allelic transmission from random proportions (P=0.024) in the transmission disequilibrium test analysis. When we analyzed our results for serum total IgE levels, against this polymorphism, we observed a difference at the genotypic (P=0.0026) as well as at the allelic level (P=0.0016) in a case-control study, whereas no association in the quantitative transmission disequilibrium test analysis was obtained. These findings provide suggestive evidence of association of the CD14 gene locus with atopic asthma in northern and northwestern Indian populations.  相似文献   

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