Discrete time spatial models arising in genetics, evolutionary game theory, and branching processes

A saddle point method is used to obtain the speed of first spread of new genotypes in genetic models and of new strategies in game theoretic models. It is also used to obtain the speed of the forward tail of the distribution of farthest spread for branching process models. The technique is applicable to a wide range of models. They include multiple allele and sex-linked models in genetics, multistrategy and bimatrix evolutionary games, and multitype and demographic branching processes. The speed of propagation has been obtained for genetics models (in simple cases only) by Weinberger [1, 2] and Lui [3–7], using exact analytical methods. The exact results were obtained only for two-allele, single-locus genetic models. The saddle point method agrees in these very simple cases with the results obtained by using the exact analytic methods. Of course, it can also be used in much more general situations far less tractable to exact analysis.The connection between genetic and game theoretic models is also briefly considered, as is the extent to which the exact analytic methods yield results for simple models in game theory.     

The long-term evolution of multilocus traits under frequency-dependent disruptive selection

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.     

An optimizing principle of natural selection in evolutionary population genetics

This paper brings together two themes in evolutionary population genetics theory. The first concerns Fisher's Fundamental Theorem of Natural Selection: a recent interpretation of this theorem claims that it is an exact result, relating to the so-called "partial" increase in mean fitness. The second theme concerns the desire to find an optimality principle in genetic evolution. Such a principle is found here: of all gene frequency changes which lead to the same partial increase in mean fitness as the natural selection gene frequency changes, the natural selection values minimize a generalized distance measure between parent and daughter generation gene frequency values.     

Computer simulations: tools for population and evolutionary genetics

Computer simulations are excellent tools for understanding the evolutionary and genetic consequences of complex processes whose interactions cannot be analytically predicted. Simulations have traditionally been used in population genetics by a fairly small community with programming expertise, but the recent availability of dozens of sophisticated, customizable software packages for simulation now makes simulation an accessible option for researchers in many fields. The in silico genetic data produced by simulations, along with greater availability of population-genomics data, are transforming genetic epidemiology, anthropology, evolutionary and population genetics and conservation. In this Review of the state-of-the-art of simulation software, we identify applications of simulations, evaluate simulator capabilities, provide a guide for their use and summarize future directions.     

The mind of primitive anthropologists: hemoglobin and HLA, patterns of molecular evolution

Frank Livingstone played a central role in defining the population genetics of the sickle cell mutation at position 6 of the human beta globin gene, the most famous amino acid substitution in evolutionary biology. Its discovery occurred at a time when traditional, 19th-century principles of natural selection were being joined with the newly discovered mechanics of DNA structure and protein synthesis to produce Neo-Darwinian theory. When combined with the epidemiology of malaria in Africa, differential mortality for both homozygotes, and the resulting advantage of the heterozygote, sickle cell became the classic balanced polymorphism. Human HLA-A has 237 molecular alleles. The histocompatibility system has as its primary function the presentation of peptides to T-cell receptors and plays an essential role in the immune system. Nearly all of the alleles are codominant and fully functional. Despite almost 30 years of disease-association studies with HLA-A, no convincing evidence has been found for differential fertility or mortality at this locus. Yet the dogma in the histocompatibility field is that this extensive human polymorphism is maintained by "balancing selection." Explaining HLA-A polymorphism is what one might call the sickle-cell-effect. This one mutation, coming as it did at the historical convergence of Darwinian theory and modern genetics, and carrying with it the strong relationship between mutation, disease, and allele frequency, has conditioned our discussion of human genetic variation and population genetics. Has the strength of this early idea made evolutionary biologists uncritical of systems like HLA-A and retarded the search for new mechanisms of molecular evolution? Is it now time to move away from a focus on mutation and polymorphism in evolutionary genetics and toward a systems theory that would explain the origin and evolution of hemoglobin and HLA-A and the biochemical pathways that surround them?     

Forward from the crossroads of ecology and evolution

Community genetics is a synthesis of community ecology and evolutionary biology. It examines how genetic variation within a species affects interactions among species to change ecological community structure and diversity. The use of community genetics approaches has greatly expanded in recent years and the evidence for ecological effects of genetic diversity is growing. The goal of current community genetics research is to determine the circumstances in which, and the mechanisms by which community genetic effects occur and is the focus of the papers in this special issue. We bring a new group of researchers into the community genetics fold. Using a mixture of empirical research, literature reviews and theoretical development, we introduce novel concepts and methods that we hope will enable us to develop community genetics into the future.     

POWSIM: a computer program for assessing statistical power when testing for genetic differentiation

Knowledge of statistical power is essential for sampling design and data evaluation when testing for genetic differentiation. Yet, such information is typically missing in studies of conservation and evolutionary genetics, most likely because of complex interactions between the many factors that affect power. powsim is a 32‐bit Windows/DOS simulation‐based computer program that estimates power (and α error) for chi‐square and Fisher's exact tests when evaluating the hypothesis of genetic homogeneity. Optional combinations include the number of samples, sample sizes, number of loci and alleles, allele frequencies, and degree of differentiation (quantified as F_ST). powsim is available at http://www.zoologi.su.se/~ryman .     

Quantitative genetics of behavioural reaction norms: genetic correlations between personality and behavioural plasticity vary across stickleback populations

Behavioural ecologists have proposed various evolutionary mechanisms as to why different personality types coexist. Our ability to understand the evolutionary trajectories of personality traits requires insights from the quantitative genetics of behavioural reaction norms. We assayed > 1000 pedigreed stickleback for initial exploration behaviour of a novel environment, and subsequent changes in exploration over a few hours, representing their capacity to adjust their behaviour to changes in perceived novelty and risk. We found heritable variation in both the average level of exploration and behavioural plasticity, and population differences in the sign of the genetic correlation between these two reaction norm components. The phenotypic correlation was not a good indicator of the genetic correlation, implying that quantitative genetics are necessary to appropriately evaluate evolutionary hypotheses in cases such as these. Our findings therefore have important implications for future studies concerning the evolution of personality and plasticity.     

From genes to ecosystems: a genetic basis to ecosystem services

Ecosystems provide services, many of which are regulated through species interactions. Emerging research in the fields of community and ecosystem genetics indicate that genetic variation in one species can influence species interactions and affect subsequent patterns of energy flow and nutrient cycles. Because there can be a genetic basis to community- and ecosystem-level processes, evolutionary processes that alter standing genetic variation can have extended consequences that matter to patterns of biodiversity and ecosystem function that exist on the landscape. Here we explore some emerging areas of research in the field of community and ecosystem genetics and discuss the general importance of this approach to evolutionary ecology.     

Mimulus is an emerging model system for the integration of ecological and genomic studies

The plant genus Mimulus is rapidly emerging as a model system for studies of evolutionary and ecological functional genomics. Mimulus contains a wide array of phenotypic, ecological and genomic diversity. Numerous studies have proven the experimental tractability of Mimulus in laboratory and field studies. Genomic resources currently under development are making Mimulus an excellent system for determining the genetic and genomic basis of adaptation and speciation. Here, we introduce some of the phenotypic and genetic diversity in the genus Mimulus and highlight how direct genetic studies with Mimulus can address a wide spectrum of ecological and evolutionary questions. In addition, we present the genomic resources currently available for Mimulus and discuss future directions for research. The integration of ecology and genetics with bioinformatics and genome technology offers great promise for exploring the mechanistic basis of adaptive evolution and the genetics of speciation.     

Fundamentals of fungal molecular population genetic analyses

The last two decades have seen tremendous growth in the development and application of molecular methods in the analyses of fungal species and populations. In this paper, I provide an overview of the molecular techniques and the basic analytical tools used to address various fundamental population and evolutionary genetic questions in fungi. With increasing availability and decreasing cost, DNA sequencing is becoming a mainstream data acquisition method in fungal evolutionary genetic studies. However, other methods, especially those based on the polymerase chain reaction, remain powerful in addressing specific questions for certain groups of taxa. These developments are bringing fungal population and evolutionary genetics into mainstream ecology and evolutionary biology.     

The co-evolutionary genetics of ecological communities

Co-evolution has produced many intriguing adaptations and made significant contributions to biodiversity through the co-adaptive radiations of interacting groups, such as pollinating insects and flowering plants or hosts and endosymbionts. New methods from molecular genetics and comparative genomics, in conjunction with advances in evolutionary genetic theory, are for the first time providing tools for detecting, investigating and understanding the genetic bases of the co-adaptive process and co-speciation. Advances in the emerging field of community genetics, which integrates genetics and community ecology, could revolutionize how co-evolution is studied, how genes are functionally annotated and how conservation geneticists implement preservation strategies.     

REVIEW: Optimality models in the age of experimental evolution and genomics

Optimality models have been used to predict evolution of many properties of organisms. They typically neglect genetic details, whether by necessity or design. This omission is a common source of criticism, and although this limitation of optimality is widely acknowledged, it has mostly been defended rather than evaluated for its impact. Experimental adaptation of model organisms provides a new arena for testing optimality models and for simultaneously integrating genetics. First, an experimental context with a well‐researched organism allows dissection of the evolutionary process to identify causes of model failure – whether the model is wrong about genetics or selection. Second, optimality models provide a meaningful context for the process and mechanics of evolution, and thus may be used to elicit realistic genetic bases of adaptation – an especially useful augmentation to well‐researched genetic systems. A few studies of microbes have begun to pioneer this new direction. Incompatibility between the assumed and actual genetics has been demonstrated to be the cause of model failure in some cases. More interestingly, evolution at the phenotypic level has sometimes matched prediction even though the adaptive mutations defy mechanisms established by decades of classic genetic studies. Integration of experimental evolutionary tests with genetics heralds a new wave for optimality models and their extensions that does not merely emphasize the forces driving evolution.     

What is parallelism?

Although parallel and convergent evolution are discussed extensively in technical articles and textbooks, their meaning can be overlapping, imprecise, and contradictory. The meaning of parallel evolution in much of the evolutionary literature grapples with two separate hypotheses in relation to phenotype and genotype, but often these two hypotheses have been inferred from only one hypothesis, and a number of subsidiary but problematic criteria, in relation to the phenotype. However, examples of parallel evolution of genetic traits that underpin or are at least associated with convergent phenotypes are now emerging. Four criteria for distinguishing parallelism from convergence are reviewed. All are found to be incompatible with any single proposition of homoplasy. Therefore, all homoplasy is equivalent to a broad view of convergence. Based on this concept, all phenotypic homoplasy can be described as convergence and all genotypic homoplasy as parallelism, which can be viewed as the equivalent concept of convergence for molecular data. Parallel changes of molecular traits may or may not be associated with convergent phenotypes but if so describe homoplasy at two biological levels-genotype and phenotype. Parallelism is not an alternative to convergence, but rather it entails homoplastic genetics that can be associated with and potentially explain, at the molecular level, how convergent phenotypes evolve.     

Simulating natural selection in landscape genetics

Linking landscape effects to key evolutionary processes through individual organism movement and natural selection is essential to provide a foundation for evolutionary landscape genetics. Of particular importance is determining how spatially-explicit, individual-based models differ from classic population genetics and evolutionary ecology models based on ideal panmictic populations in an allopatric setting in their predictions of population structure and frequency of fixation of adaptive alleles. We explore initial applications of a spatially-explicit, individual-based evolutionary landscape genetics program that incorporates all factors--mutation, gene flow, genetic drift and selection--that affect the frequency of an allele in a population. We incorporate natural selection by imposing differential survival rates defined by local relative fitness values on a landscape. Selection coefficients thus can vary not only for genotypes, but also in space as functions of local environmental variability. This simulator enables coupling of gene flow (governed by resistance surfaces), with natural selection (governed by selection surfaces). We validate the individual-based simulations under Wright-Fisher assumptions. We show that under isolation-by-distance processes, there are deviations in the rate of change and equilibrium values of allele frequency. The program provides a valuable tool (cdpop v1.0; http://cel.dbs.umt.edu/software/CDPOP/) for the study of evolutionary landscape genetics that allows explicit evaluation of the interactions between gene flow and selection in complex landscapes.     

Metapodial bones of Ursus gr. spelaeus from selected caves of the North Italy. A biometrical study and evolutionary trend

The cave bear evolution is characterized by some specific trends, including the increase in size, the progressive complication of the tooth surface and the gradual strengthening of the metapodial bones. Important indicators of the evolutionary level are the morphodynamic index of P⁴/₄ and the plumpness index of the metapodial bones. Only recently, the morphological and morphometric analysis was complemented by genetic analysis – particularly of mtDNA. As a consequence, mainly based on genetics, new taxa have been proposed, for some of whom the exact taxonomic rank (species or subspecies?) is still under discussion. However, the new evolutionary model presents some problems because the genetic data alone are not sufficient to ensure a specific distinction and the morphodynamic and morphometric data do not support a specific distinction between the cave bear populations. The morphometric analysis performed on numerous metapodial bones belonging to some Italian (Buco dell’Orso, Covoli Velo and S. Donà di Lamon) and European populations seems to confirm, on the whole, a level of diversity not higher than that of a subspecies, allowing at most the identification of some local evolutionary trends, as assumed for the populations which have been living in the Italian peninsula.