Rates of decay of linkage disequilibrium under two-locus models of selection

The effect of selection and linkage on the decay of linkage disequilibrium, D, is investigated for a hierarchy of two-locus models. The method of analysis rests upon a qualitative classification of the dynamic of D under selection relative to the neutral dynamic. To eliminate the confounding effects of gene frequency change, the behavior of D is first studied with gene frequencies fixed at their invariant values. Second, the results are extended to certain special situations where gene frequencies are changing simultaneously.A wide variety of selection regimes can cause an acceleration of the rate of decay of D relative to the neutral rate. Specifically, the asymptotic rate of decay is always faster than the neutral rate in the neighborhood of a stable equilibrium point, when viabilities are additive or only one locus is selected. This is not necessarily the case for models in which there is nonzero additive epistasis. With multiplicative viabilities, decay is always accelerated near a stable boundary equilibrium, but decay is only faster near the stable central equilibrium (with = 0) if linkage is sufficiently loose. In the symmetric viability model, decay may even be retarded near a stable boundary equilibrium. Decay is only accelerated near a stable corner equilibrium when the double homozygote is more fit than the double heterozygotes. Decay near a stable edge equilibrium may be retarded if there is loose linkage. With symmetric viabilities there is usually an acceleration of the decay process for gene frequencies near 1/2 when the central equilibrium (with = 0) is stable. This is always the case when the sign of the epistasis is negative or zero.Conversely, the decay ofD is retarded in the neighborhood of a stable equilibrium in the multiplicative and symmetric viability models if any of the conditions above are violated. Near an unstable equilibrium of any of the models considered,D may either increase or decay at a rate slower than, equal to, or faster than the neutral rate. These analytic results are supplemented by numerical studies of the symmetric viability model.     

A FORTRAN program for the calculation and analysis of two-locus linkage disequilibrium coefficients

Summary A FORTRAN program was written that calculates composite linkage disequilibrium coefficients from genotypic data. Chi-square tests determine whether coefficients calculated for allele and locus pairs are significantly greater than zero. A subroutine is provided that partitions the variance in linkage disequilibrium into within- and between-subpopulation components. Output obtained from analysis of allozyme data collected from natural subpopulations of the house fly (Musca domestica L.) are included to illustrate features of the program.Journal Paper No. J-11345 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2411     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

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.     

Comparing clines on molecular and phenotypic traits in hybrid zones: a window on tension zone models

The study of zones of secondary contact provides insight into the maintenance of reproductive isolation. Tension zone theory supplies powerful tools for assessing how dispersal and selection shape hybrid zones. We present a multimodal analysis of phenotypic clines in conjunction with clines at molecular markers in a hybrid zone between Larus glaucescens and Larus occidentalis. We developed a new method to analyze simultaneously clines of quantitative traits and molecular data. Low linkage disequilibrium and the lack of coincidence between clines at six microsatellites, a mitochondrial DNA region, and two phenotypic traits indicated introgression. However, the hypothesis of neutral diffusion was rejected based on evidence that all of the clines were concordant and narrower than expected for neutral clines, indicating some indirect selection. The analysis of phenotypic variance gave evidence of restricted phenotypic introgression and together with the bimodal distribution of phenotypes suggested that disruptive selection is acting across the hybrid zone, especially on the coloration of bare parts. Multimodal analysis of phenotypic clines also highlighted a shift between the peak of intermediates and the cline center, left behind by hybrid zone motion. High-resolution analysis of phenotypes distribution thus proved useful for detecting hybrid zone movement even without temporal data.     

The two-locus model of Gaussian stabilizing selection

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the strength of selection and the recombination rate may also be arbitrary. We find that 16 different equilibrium patterns exist, having up to 11 equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal effects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model.     

Diffusion approximations of the two-locus Wright-Fisher model

Diffusion approximations are established for the multiallelic, two-locus Wright-Fisher model for mutation, selection, and random genetic drift in a finite, panmictic, monoecious, diploid population. All four combinations of weak or strong selection and tight or loose linkage are treated, though the proof in the case of strong selection and loose linkage is incomplete. Under certain conditions, explicit formulas are obtained for the stationary distributions of the two diffusions with loose linkage.Supported in part by NSF Grant DMS-8704369Supported in part by NSF Grant BSR-8512844     

Index versus tandem selection after repeated generations of selection

Summary A theoretical comparison between two multiple-trait selection methods, index and tandem selection, after several generations of selection was carried out. An infinite number of loci determining the traits, directional and truncation selection, discrete generations and infinite population size were assumed. Under these assumptions, changes in genetic parameters over generations are due to linkage disequilibrium generated by selection. Changes continue for several generations until equilibrium is approached. Algebraic expressions for asymptotic responses from index selection can be derived if index weights are maintained constant across generations. Expressions at equilibrium for genetic parameters and responses are given for the index and its component traits. The loss in response by using initial index weights throughout all generations, instead of updating them to account for changes in genetic parameters, was analyzed. The benefit of using optimum weights was very small ranging from 0% to about 1.5% for all cases studied. Recurrence formulae to predict genetic parameters and responses at each generation of selection are given for both index and tandem selection. A comparison between expected response in the aggregate genotype at equilibrium from index and tandem selection is made considering two traits of economic importance. The results indicate that although index selection is more efficient for improving the aggregate breeding value, its relative efficiency with respect to tandem selection decreases after repeated cycles of selection. The reduction in relative efficiency is highest with the highest selection intensity and heritabilities and with negative correlations between the two traits. The advantage of index over tandem selection might be further reduced if changes in genetic parameters due to gene frequency changes produced by selection, random fluctuations due to the finite size of the population, and errors in estimation of parameters, were also considered.     

NATURAL SELECTION ON QUANTITATIVE TRAITS IN THE BOMBINA HYBRID ZONE

Observations on the means, variances, and covariances of quantitative traits across hybrid zones can give information similar to that from Mendelian markers. In addition, they can identify particular traits through which the cline is maintained. We describe a survey of six traits across the hybrid zone between Bombina bombina and Bombina variegata (Amphibia: Discoglossidae) near Pe??enica in Croatia. We obtained laboratory measuments of the belly pattern, skin thickness, mating call, skeletal form, egg size, and the developmental time of tadpoles. Although offspring from hybrid populations showed no evidence of reduced viability, a third of the F₁ families failed completely, irrespective of the direction of the cross. All traits differed significantly between the taxa. Clines in belly pattern, skin thickness, mating call, and skeletal form were closely concordant with clines in four diagnostic enzyme loci. However, the cline in developmental time was displaced towards bombina, and the cline in egg size was displaced towards variegata. This discordance could be because the traits are not inherited additively or because they are subject to different selection pressures. We favor the latter explanation in the case of developmental time. We show that moderate selection acting directly on a trait suffices to shift its position; rather stronger selection is needed to change its width appreciably. Within hybrid populations, there are significant associations among quantitative traits, and between traits and enzymes. Phenotypic variances also increase in hybrid populations. These observations can be explained by linkage disequilibria among the underlying loci. However, the average magnitude of the covariance between traits is about half that expected from the linkage disequilibria between enzyme loci. The discrepancy is not readily explained by nonadditive gene action. This puzzle is now unresolved and calls for further investigation.     

A quantitative method to assess the ecological indicator system's effectiveness: a case study of the Ecological Province Construction Indicators of China

The ecological indicator system (EIS) is widely used. It is vital to develop a scientific and rational EIS for practical application. Assessment of an EIS's effectiveness is important to understand the gaps between practical indicators and indicators that are considered theoretically ideal. In this paper we develop a conceptual method to quantitatively assess the effectiveness of a practical EIS by comparing it with the ideal EIS that is considered perfect by using three assessment indices: linkage, coverage and representation degrees. Linkage degree reveals the relevance of individual indicators to the ideal system. Coverage degree shows the integrity of the practical indicator system compared with the ideal system. Representation degree is the ultimate goal of the quantitative assessment and can detect the gap and overlap between the practical indicator system and the ideal one. Case study on the Ecological Province Construction Indicators (EPCI) proved that our conceptual method is useful to assess the effectiveness of a practical EIS. Compared with an ideal EIS, the EPCI has a high linkage and coverage degree but biased representation. Although the practical EIS covers most of the objectives detailed in the Fujian eco-province construction documents, many social development indicators are overlooked, including ecological culture and green consumption. Using the quantitative method will improve the practical application of an EIS by detecting its redundancy and weakness.     

Evolution of coadaptation in a two-locus epistatic system

Although recent advances in genome biology have dramatically increased our understanding of the contribution of gene interactions to the development of complex phenotypes, we still lack general agreement on the process and mechanisms responsible for the evolution of epistatic systems. Even if genes in a species are indeed integrated into coadapted complexes of interacting components, simple additive evolution may eventually result in epistatic differentiation of populations. Consequently, the prevalence of epistatic gene action does not tell us anything about the role of epistatic selection in the history of population divergence. To elucidate the contribution of epistatic selection in the evolution of coadaptation, we investigate the fixation process of two mutations that interact synergistically to enhance fitness. We show by diffusion analysis and simulations that epistatic selection on cosegregating variants does not by itself promote the evolution of epistatic systems; rather, accumulation of neutral mutations may play a crucial role, creating an appropriate genetic milieu for adaptive evolution in the future generations.     

Study on ecological restoration in near-shore zone of a eutrophic lake, Wuli Bay, Taihu Lake

A two-year restoration period, large-scale ecological restoration demonstration engineering project was carried out in the near-shore zones of Wuli Bay, Taihu Lake. Various methods to restore the aquatic biodiversity and prevent ecological degradation were employed and their effects on water quality and aquatic plants were investigated. The results showed that water quality had been significantly improved in the demonstration zones. The concentrations of TN and TP were about half of those of the reference site in Wuli Bay. The water transparency was 30 cm higher than that in the reference site. The species, cover and biomass of aquatic plants were also significantly increased in the demonstration zones.     

Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Genetic variation for shell traits in a direct-developing marine snail involved in a putative sympatric ecological speciation process

Populations of the marine gastropod Littorina saxatilis from exposed rocky shores of NW Spain provide one of the few putative cases of sympatric ecological speciation. Two ecotypes with large differences in shell morphology and strong assortative mating are living at different vertical levels of the shore separated by a few meters. It has been hypothesized that shell size is the main determinant for the reproductive isolation observed between the ecotypes, and that several shell shape traits are subject to divergent natural selection and are responsible for the adaptation of each ecotype to its respective habitat. Using embryos extracted from wild females we obtain estimates of genetic variation for shell size and shape and compare them with those from neutral molecular markers. Estimates of heritability are significantly larger for the ecotype found in the upper shore than for that in the lower shore, in concordance with a similar result observed for heterozygosity of neutral markers. The large genetic differentiation between ecotypes for the shell traits, contrasting the smaller close to neutral differentiation between populations of the same ecotype, supports the implication of the traits in adaptation.     

Polymorphism in the two-locus Levene model with nonepistatic directional selection

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.     

Identification and characterization of coding single-nucleotide polymorphisms within a human olfactory receptor gene cluster

Single-nucleotide polymorphisms (SNPs) were studied in 15 olfactory receptor (OR) coding regions, one control region and two noncoding sequences all residing within a 412 kb OR gene cluster on human chromosome 17p13.3, as well as in other G-protein coupled receptors (GPCRs). A total of 26 SNPs were identified in ORs, 21 of which are coding SNPs (cSNPs). The mean nucleotide diversity of OR coding regions was 0.078% (ranging from 0 to 0.16%), which is about twice higher than that of other GPCRs, and similar to the nucleotide diversity levels of noncoding regions along the human genome. The high polymorphism level in the OR coding regions might be due to a weak positive selection pressure acting on the OR genes. In two cases, OR genes have been found to share the same cSNP. This could be explained by recent gene conversion events, which might be a part of a concerted evolution mechanism acting on the OR superfamily. Using the genotype data of 85 unrelated individuals in 15 SNPs, we found linkage disequilibrium (LD) between pairs of SNPs located on the centromeric part of the cluster. On the other hand, no LD was found between SNPs located on the telomeric part of the cluster, suggesting the presence of several hot-spots for recombination within this cluster. Thus, different regions of this gene cluster may have been subject to different recombination rates.     

The effect of positive assortative mating at one locus on a second linked locus

Summary A model for positive assortative mating based on genotype for one locus is employed to investigate the effect of this mating system on the genotypic structure of a second linked locus as well as on the joint genotypic structure of these two loci. It is shown that the second locus does not attain a precise positive assortative mating structure, but yet it shares a property that is characteristic of positive assortative mating, namely an increase in the frequency of homozygotes over that typically found in panmictic structures. Given any arbitrary genotypic structure for the parental population, the resulting offspring generation possesses a structure at the second locus that does not depend on the recombination frequency, while the joint structure of course does. In case assortative mating as well as linkage are not complete, there exists a unique joint equilibrium state for the two loci, which is characterized by complete stochastic independence between the two loci as well as by Hardy-Weinberg proportions at the second locus. For the second locus alone, Hardy-Weinberg equilibrium is realized if and only if gametic linkage equilibrium and an additionally specified condition are realized.     

中国海洋生态保护制度的转型发展--从海洋保护区走向海洋生态红线区

海洋生态环境的持续恶化与生态学认知的提高使海洋生态红线区管理制度成为必然。总结了中国海洋保护区现状与存在问题;分析了发展海洋生态红线的必要性、区划原则、概念及组成体系;提出海洋保护区与海洋生态红线区可分别籍空间统一性、决策统一性、工作内容与管理要求的一致性相关联,海洋保护区的核心、关键和重要因素与海洋生态红线的范围划定、宏观应对策略制定、微观管理规定一一对应。对海洋保护区管理向海洋生态红线区划与管理的转变给出了若干建议,认为海洋生态红线区划指标体系可以参照海洋保护区绩效评估、保护区选划与评估指标;并从海洋生态红线的尺度,陆海统筹的生态系统格局-结构\过程-机理,复杂生态系统与海洋生态红线的结合,海洋生态红线基点观测等方面对海洋生态红线的研究和工作方向进行了展望。     

农牧交错带系统生产力概念及其对生态重建的意义

论证了黄土高原农牧交错带在全球所有同纬度(39°～41°N)地区中是作物生长盛期内光、温及降水条件组合最好的地带,并以初步的实证和观测支持了这一论点,阐述了通过开发能很好地适应自然条件,特别是能扬长避短,充分利用总体上虽较严酷而局部具有优势的气候资源的“系统生产力”的新思路;中心选择和应用生物量高、水分效率高、覆盖作用好的新作物和相应的种植制度,围绕生物量“为牧而农”式地实行农牧结合;重“料”于粮草,相应改变传统农业的格局,以大幅度地提高黄土高原地区的系统生产力,探索走出一条生态重建和支柱产业协调发展新路的可能性。     

Conditional dispersal, clines, and the evolution of dispersiveness

Conditional dispersal, in which an individual’s decision over whether to disperse is a response to environmental conditions, features prominently in studies of dispersal evolution. Using models of clines, I examine how one widely discussed cost of dispersal, namely, that dispersal impedes local adaptation, changes with conditional dispersal and what this implies for dispersal evolution. I examine the consequences for dispersal evolution of the responsiveness of dispersal to the environment, the accuracy of any proximal cues that individuals rely upon to assess habitat quality, and whether dispersal responds to fitness itself or only to some fitness components (juvenile survivorship). All of the conditional dispersal behaviors that I consider weaken the indirect cost of dispersal inhibiting local adaptation. However, if individuals rely on imprecise cues to assess habitat quality and base dispersal decisions on juvenile survivorship, then conditional dispersal can incur additional costs by exacerbating overcrowding. Conditional dispersal initially leads to steeper clines in traits under direct selection, but when dispersiveness can itself evolve, conditional dispersal allows sigmoidal clines to persist long after those obtained with unconditional movement would become stepped. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.