Evolution of fitnesses and allele frequencies in a population with spatially heterogeneous selection pressures

The level of gene flow considerably influences the outcome of evolutionary processes in structured populations with spatial heterogeneity in selection pressures; low levels of gene flow may allow local adaptation whereas high levels of gene flow may oppose this process thus preventing the stable maintenance of polymorphism. Indeed, proportions of fitness space that successfully maintain polymorphism are substantially larger in spatially heterogenous populations with lower to moderate levels of gene flow when compared to single-deme models. Nevertheless, the effect of spatial heterogeneity on the evolutionary construction of polymorphism is less clear. We have investigated the levels of polymorphism resulting from a simple two-deme construction model, which incorporates recurrent mutation as well as selection. We further compared fitness properties, stability of equilibria, and frequency distribution patterns emerging from the construction approach and compared these to the static fitness-space approach. The construction model either promotes or constrains the level of polymorphisms, depending on the levels of gene flow. Comparison of the fitness properties resulting from both approaches shows that they maintain variation in different parts of fitness space. The part of fitness space resulting from construction is more stable than that implied by the ahistoric fitness-space approach. Finally, the equilibrium allele-frequency distribution patterns vary substantially with different levels of gene flow, underlining the importance of correctly sampling spatial structure if these patterns are to be used to estimate population-genetic processes.     

A simple completion of Fisher’s fundamental theorem of natural selection

Fisher''s fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher''s original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher''s concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations.     

THE EVOLUTION OF CANALIZATION AND THE BREAKING OF VON BAER'S LAWS: MODELING THE EVOLUTION OF DEVELOPMENT WITH EPISTASIS

Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters. A contour on such a “phenotype landscape” is a set of states of developmental characters that produce the same adult phenotype. Epistasis induces curvature of this surface, and degree of canalization is represented by the slope along a contour. I first discuss the geometric properties of phenotype landscapes, relating epistasis to canalization. I then impose a fitness function on the phenotype and model evolution of developmental characters as a function of the fitness function and the local geometry of the surface. This model shows how canalization evolves as a population approaches an optimum phenotype. It further shows that under some circumstances, “decanalization” can occur, in which the expression of adult phenotype becomes increasingly sensitive to developmental variation. This process can cause very similar populations to diverge from one another developmentally even when their adult phenotypes experience identical selection regimes.     

Variable selection in nonlinear modeling based on RBF networks and evolutionary computation

In this paper a novel variable selection method based on Radial Basis Function (RBF) neural networks and genetic algorithms is presented. The fuzzy means algorithm is utilized as the training method for the RBF networks, due to its inherent speed, the deterministic approach of selecting the hidden node centers and the fact that it involves only a single tuning parameter. The trade-off between the accuracy and parsimony of the produced model is handled by using Final Prediction Error criterion, based on the RBF training and validation errors, as a fitness function of the proposed genetic algorithm. The tuning parameter required by the fuzzy means algorithm is treated as a free variable by the genetic algorithm. The proposed method was tested in benchmark data sets stemming from the scientific communities of time-series prediction and medicinal chemistry and produced promising results.     

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.     

Some natural viability systems for a multiallelic locus: a theoretical study

The maintenance of genetic polymorphism under various natural structured viability regimes vs. general unrestricted fitness assignments are compared. The selection models considered include a generalized dominance fitness system, a generalized viability model based on allelic activity values, viability matrices based on multilocus activity levels, viability matrices defined by partitioned "resource" or "substrate" variables, and circulant-type viability matrices. A number of examples that support these formulations are discussed. Detailed results on the nature of the genotype frequency equilibrium configurations for the specified viability models are presented. An increased likelihood for a globally stable equilibrium is predicted for the more structured viability models.     

Evolutionary genetics of maternal effects

Maternal genetic effects (MGEs), where genes expressed by mothers affect the phenotype of their offspring, are important sources of phenotypic diversity in a myriad of organisms. We use a single‐locus model to examine how MGEs contribute patterns of heritable and nonheritable variation and influence evolutionary dynamics in randomly mating and inbreeding populations. We elucidate the influence of MGEs by examining the offspring genotype‐phenotype relationship, which determines how MGEs affect evolutionary dynamics in response to selection on offspring phenotypes. This approach reveals important results that are not apparent from classic quantitative genetic treatments of MGEs. We show that additive and dominance MGEs make different contributions to evolutionary dynamics and patterns of variation, which are differentially affected by inbreeding. Dominance MGEs make the offspring genotype‐phenotype relationship frequency dependent, resulting in the appearance of negative frequency‐dependent selection, while additive MGEs contribute a component of parent‐of‐origin dependent variation. Inbreeding amplifies the contribution of MGEs to the additive genetic variance and, therefore enhances their evolutionary response. Considering evolutionary dynamics of allele frequency change on an adaptive landscape, we show that this landscape differs from the mean fitness surface, and therefore, under some condition, fitness peaks can exist but not be “available” to the evolving population.     

A general population genetic framework for antagonistic selection that accounts for demography and recurrent mutation

Antagonistic selection--where alleles at a locus have opposing effects on male and female fitness ("sexual antagonism") or between components of fitness ("antagonistic pleiotropy")--might play an important role in maintaining population genetic variation and in driving phylogenetic and genomic patterns of sexual dimorphism and life-history evolution. While prior theory has thoroughly characterized the conditions necessary for antagonistic balancing selection to operate, we currently know little about the evolutionary interactions between antagonistic selection, recurrent mutation, and genetic drift, which should collectively shape empirical patterns of genetic variation. To fill this void, we developed and analyzed a series of population genetic models that simultaneously incorporate these processes. Our models identify two general properties of antagonistically selected loci. First, antagonistic selection inflates heterozygosity and fitness variance across a broad parameter range--a result that applies to alleles maintained by balancing selection and by recurrent mutation. Second, effective population size and genetic drift profoundly affect the statistical frequency distributions of antagonistically selected alleles. The "efficacy" of antagonistic selection (i.e., its tendency to dominate over genetic drift) is extremely weak relative to classical models, such as directional selection and overdominance. Alleles meeting traditional criteria for strong selection (N(e)s > 1, where N(e) is the effective population size, and s is a selection coefficient for a given sex or fitness component) may nevertheless evolve as if neutral. The effects of mutation and demography may generate population differences in overall levels of antagonistic fitness variation, as well as molecular population genetic signatures of balancing selection.     

A spatial and temporal approach to microevolutionary forces affecting population biology in the freshwater snail Biomphalaria pfeifferi

The limitations of both population demography and genetics highlight the need to combine these approaches when inferring the influence of demographic processes and modes of migration on genetic structure. The aim of this study was to use spatiotemporal genetic and demographic surveys to reveal the microevolutionary forces acting on the metapopulation dynamics of the freshwater snail Biomphalaria pfeifferi. We also analyzed the consequences of population turnover on temporal genetic differentiation, an aspect that has been little explored. Genetic drift was revealed by both the demographic survey, which indicated severe bottlenecks or extinction during the rainy (resp. dry) season in open (resp. closed) habitats, and the genetic approach, which indicated high selfing rates and strong temporal differentiation. Genetic reassignments and temporal differentiation both confirmed the results of the demographic survey, which suggests that migration occurs in closed (resp. open) habitats during the hot and dry (resp. rainy) season, and indicated that source-sink functioning may be envisaged. A propagule pool mode of colonization was inferred in the open habitats during the rainy season and a migrant pool in the closed habitats during the dry season. Our study also suggests that selection might be inferred from patterns of neutral genetic markers when recombination is limited.     

Classical metapopulation dynamics and eco‐evolutionary feedbacks in dendritic networks

Eco‐evolutionary dynamics are now recognized to be highly relevant for population and community dynamics. However, the impact of evolutionary dynamics on spatial patterns, such as the occurrence of classical metapopulation dynamics, is less well appreciated. Here, we analyse the evolutionary consequences of spatial network connectivity and topology for dispersal strategies and quantify the eco‐evolutionary feedback in terms of altered classical metapopulation dynamics. We find that network properties, such as topology and connectivity, lead to predictable spatio‐temporal correlations in fitness expectations. These spatio‐temporally stable fitness patterns heavily impact evolutionarily stable dispersal strategies and lead to eco‐evolutionary feedbacks on landscape level metrics, such as the number of occupied patches, the number of extinctions and recolonizations as well as metapopulation extinction risk and genetic structure. Our model predicts that classical metapopulation dynamics are more likely to occur in dendritic networks, and especially in riverine systems, compared to other types of landscape configurations. As it remains debated whether classical metapopulation dynamics are likely to occur in nature at all, our work provides an important conceptual advance for understanding the occurrence of classical metapopulation dynamics which has implications for conservation and management of spatially structured populations.     

Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.     

Exploring the genetics of aging in a wild passerine bird

Senescence is the decline in survival and reproduction as an organism ages and is known to occur in collared flycatchers Ficedula albicollis. We consider annual fitness (the estimated genetic contribution that an individual makes to next year's gene pool) as a measure of age-specific fitness. We apply a restricted maximum likelihood linear mixed-model approach on 25 years of data on 3,844 male and 4,992 female collared flycatchers. Annual fitness had a significant additive genetic component (h2 of about 4%). Annual fitness declined at later ages in both sexes. Using a random regression animal model, we show that the observed age-related phenotypic changes in annual fitness were not present on the additive genetic level, contrary to predictions of genetic hypotheses of senescence. Our study suggests that patterns of aging in the wild need to be interpreted with caution in terms of underlying genetics because they may be largely determined by environmental processes.     

The Maintenance of Genetic Variability in Two-Locus Models of Stabilizing Selection

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.     

Simulated evolution and artificial selection

A highly simplified evolving system was investigated by computer simulation. The genetic complement of each simulated organism in the population was represented by a single chromosome that consisted of a string of symbols. Individual fitness was measured as the number of symbols that corresponded to a specified rule. Reproduction was simulated with a non-breeding algorithm and two variants of a breeding algorithm, and was subject to random point mutations. In each generation, selection was effected by replacing the less fit members of the population with offspring of the more fit. The size of the population and the fraction replaced, though under experimental control, were constant for each simulation run. It was found that even such a simplified system is able to mimic a variety of properties observed in natural systems. In addition, the effect of the simulation parameters on the course of fitness increase provides a basis for using a genetic algorithm as an optimization technique.     

GENETIC COVARIANCE OF FITNESS CORRELATES: WHAT GENETIC CORRELATIONS ARE MADE OF AND WHY IT MATTERS

The genetic variance-covariance matrix, G, is determined in part by functional architecture, the pathways by which variation in genotype influences phenotype. I develop a simple architectural model for G for two traits under directional selection constrained by their dependence on a common limiting resource. I assume that genetic variance is maintained by mutation-selection balance. The relative numbers of loci that play a role in acquiring versus allocating a limiting resource play a crucial role in determining genetic covariance. If many loci are involved in acquiring a resource, genetic covariance may be either negative or positive at equilibrium, depending on the fitness function and the input of mutational variance. The form of G does not necessarily reveal the constraint on resource acquisition inherent in the system, and therefore studies estimating G do not test for the existence of life-history tradeoffs. Characters may evolve in patterns that are unpredictable from G. Experiments are suggested that would indicate if this model could explain observations of positive genetic covariance.     

The Search for the Spatial and Electronic Requirements of a Drug

A new program called GAMMA (genetic algorithm for multiple molecule alignment) has been developed for the superimposition of several three-dimensional chemical structures. Superimposition of molecules and evaluation of structural similarity is an important task in drug design and pharmaceutical research. Similarities of compounds are determined by this program either based on their structural or their physicochemical properties by defining different matching criteria. These matching criteria are atomic properties such as atomic number or partial atomic charges. The program is based on a combination of a genetic algorithm with a numerical optimization process. A major goal of this hybrid procedure is to address the conformational flexibility of ligand molecules adequately. Thus, only one conformation per structure is necessary and the program can work even when only one conformation of a compound is stored in a database. The genetic algorithm optimizes in a nondeterministic process the size and the geometric fit of the overlay. The geometric fit of the conformations is further improved by changing torsional angles combining the genetic algorithm and the directed tweak method. The determination of the fitness of a superimposition is based on the Pareto optimization. As an application the superimposition of a set of Cytochrome P450c17 enzyme inhibitors has been performed.Electronic Supplementary Material available.     

A genetic algorithm based molecular modeling technique for RNA stem-loop structures.

A new modeling technique for arriving at the three dimensional (3-D) structure of an RNA stem-loop has been developed based on a conformational search by a genetic algorithm and the following refinement by energy minimization. The genetic algorithm simultaneously optimizes a population of conformations in the predefined conformational space and generates 3-D models of RNA. The fitness function to be optimized by the algorithm has been defined to reflect the satisfaction of known conformational constraints. In addition to a term for distance constraints, the fitness function contains a term to constrain each local conformation near to a prepared template conformation. The technique has been applied to the two loops of tRNA, the anticodon loop and the T-loop, and has found good models with small root mean square deviations from the crystal structure. Slightly different models have also been found for the anticodon loop. The analysis of a collection of alternative models obtained has revealed statistical features of local variations at each base position.     

遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。     

Intragenomic bet-hedging

The notion of intragenomic bet-hedging is introduced by modeling a system where one locus is seen as setting the “environment” for selection in a two-locus genetic system. Using a spatially structured simulation model I show that bet-hedging alleles with a lower mean fitness and lower variance of fitness across genotypes at a different locus can go to fixation, potentially providing a mechanism for the reduction of severe heterozygote advantage.