Modelling of selection acting upon the pleioptropic locus in a population with two age classes

We created and examined a mathematical model describing the size and genetic composition dynamics in a population with two age classes, where the survival of both zygotes and adult individuals is determined by one pleioptropic locus. Even under present limitations, as the outside effects of a complex multigenic system are reduced to the case of single locus, our model demonstrates a wide range of different evolutionary scenarios for possible changes in the population dynamics. An increase in the reproductive potential and survival is accompanied by a transition from stable to oscillating population numbers. However, the evolutionary growth of these parameters may be nonmonotonic and may fluctuate significantly. In the case of antagonistic pleioptropy, an increase in one of these parameters usually leads to a predictable decrease in the other. This, in turn, may even stabilize the numbers and genetic compositions of the age groups. We demonstrated that selection acting on later stages of the life cycle is accompanied by violation of the Hardy-Weinberg equilibriums that link allele and genotype frequencies. We obtained a balance ratio, which allowed us to compare the combined fitness of the genotypes and to demonstrate that selection leads to the exclusion of the least adapted genotypes. Initial conditions may in some cases determine the genetic composition and pattern of population size dynamics.     

The population genetics of multistage carcinogenesis

Despite the many successes of cancer research, we lack the framework necessary to predict the ratio of familial (inherited) to sporadic (non-inherited) cancers. An evolutionary model of multistage carcinogenesis provides this framework by demonstrating that the number of tumour suppressor loci (TSLs) preventing cancer in a given tissue is expected to depend upon the tissue's vulnerability to pre-reproductive somatic mutation. Since this vulnerability increases with tissue size, single gene control of human cancer may be restricted to retinoblastoma, a cancer of the tiny embryonic retina. The model is used to estimate the frequency of mutant alleles causing inherited cancers, based on the population genetics of the mutation-selection balance between new mutations arising and selection that eliminates them. For each specific cancer, this balance is determined by the effectiveness with which pre-reproductive cancer is suppressed in the non-mutant genotype characteristic of that population. Effectiveness depends on an interaction between the number of TSLs suppressing the cancer and factors determining the tissue-wide somatic mutation rate, such as tissue size and number of pre-reproductive cell divisions. The model predicts that the commonest pre-reproductive cancers will have the lowest proportion of familial cases, and that cancers associated with the most TSLs will have the highest post-reproductive incidence but no elevated pre-reproductive risk (a pattern seen in human epithelial cancers).     

Gene frequency patterns in the levene subdivided population model

In the context of a multideme population structure subject to selection, migration, and mating forces, it is desired to ascertain the stable evolutionary outcomes for various classes of selection regimes. These include selection patterns as (i) a mosaic of local directed selection effects, (ii) overdominance throughout with varying intensities of the local heterozygote advantage, (iii) varying degrees of underdominance throughout, (iv) a mixed underdominant-overdominant regime. An accounting of the nature of the equilibrium configurations in the Levene population subdivision model was done with respect to the above classes of selection regimes. In particular, it is established that multiple polymorphic equilibria do not arise for selection structures (i) and (ii), while for the mixed underdominant-overdominant selection form (iv) with appropriate parameter ranges there can exist two stable internal equilibria. A surprising finding is that the number and/or character of the equilibria is not changed by increased population division beyond that of two habitats, while there is a significant difference in the equilibrium possibilities for a one- as against a two-deme population. These results appear to be a special limiting feature of the Levene population subdivision formulation.     

The evolution of social communication systems in a subdivided population

Evolution of social communication systems is modeled with a quantitative genetic model. The mathematical model describes the coevolutionary process of a social signal (a social character) and responsiveness (a social preference) to the signal. The responsiveness is postulated to influence fitness of senders of the signal. Considerations are extended to subdivided population structure by combining the social selection model with a group selection model. The numerical results derived from the models indicate that the evolutionary rate of social communication systems depends largely on genetic correlation between the signal and the responsiveness. Group selection can reinforce the evolutionary rate and relax its dependence on genetic correlation. The origin of genetic correlation is discussed in relation to group selection.     

Incorporating experimental design and error into coalescent/mutation models of population history

Coalescent theory provides a powerful framework for estimating the evolutionary, demographic, and genetic parameters of a population from a small sample of individuals. Current coalescent models have largely focused on population genetic factors (e.g., mutation, population growth, and migration) rather than on the effects of experimental design and error. This study develops a new coalescent/mutation model that accounts for unobserved polymorphisms due to missing data, sequence errors, and multiple reads for diploid individuals. The importance of accommodating these effects of experimental design and error is illustrated with evolutionary simulations and a real data set from a population of the California sea hare. In particular, a failure to account for sequence errors can lead to overestimated mutation rates, inflated coalescent times, and inappropriate conclusions about the population. This current model can now serve as a starting point for the development of newer models with additional experimental and population genetic factors. It is currently implemented as a maximum-likelihood method, but this model may also serve as the basis for the development of Bayesian approaches that incorporate experimental design and error.     

New inferences from tree shape: numbers of missing taxa and population growth rates

The relative positions of branching events in a phylogeny contain information about evolutionary and population dynamic processes. We provide new summary statistics of branching event times and describe how these statistics can be used to infer rates of species diversification from interspecies trees or rates of population growth from intraspecies trees. We also introduce a phylogenetic method for estimating the level of taxon sampling in a clade. Different evolutionary models and different sampling regimes can produce similar patterns of branching events, so it is important to consider explicitly the model assumptions involved when making evolutionary inferences. Results of an analysis of the phylogeny of the mosquito-borne flaviviruses suggest that there could be several thousand currently unidentified viruses in this clade.     

Territorial defense, territory size, and population regulation

The carrying capacity of an environment is determined partly by how individuals compete over the available resources. To territorial animals, space is an important resource, leading to conflict over its use. We build a model where the carrying capacity for an organism in a given environment results from the evolution of territorial defense effort and the consequent space use. The same evolutionary process can yield two completely different modes of population regulation. Density dependence arises through expanding and shrinking territories if fecundity is low, breeding success increases gradually with territory size, and/or defense is cheap. By contrast, when fecundity is high, breeding success sharply saturates with territory size, and/or defense is costly, we predict fixed territory sizes and regulation by floaters. These "surplus" individuals form a buffer against population fluctuations. Yet floaters can also harm breeder performance, and by comparing population growth of a territorial population to a nonterritorial (and individually suboptimal) alternative, we can quantify the harmful effect of evolutionary conflict on population performance. Territoriality has often been found to increase population stability, but this may come at a cost of reduced equilibrium densities.     

Structural genomics: correlation blocks, population structure, and genome architecture

An integration of the pattern of genome-wide inter-site associations with evolutionary forces is important for gaining insights into the genomic evolution in natural or artificial populations. Here, we assess the inter-site correlation blocks and their distributions along chromosomes. A correlation block is broadly termed as the DNA segment within which strong correlations exist between genetic diversities at any two sites. We bring together the population genetic structure and the genomic diversity structure that have been independently built on different scales and synthesize the existing theories and methods for characterizing genomic structure at the population level. We discuss how population structure could shape correlation blocks and their patterns within and between populations. Effects of evolutionary forces (selection, migration, genetic drift, and mutation) on the pattern of genome-wide correlation blocks are discussed. In eukaryote organisms, we briefly discuss the associations between the pattern of correlation blocks and genome assembly features in eukaryote organisms, including the impacts of multigene family, the perturbation of transposable elements, and the repetitive nongenic sequences and GC-rich isochores. Our reviews suggest that the observable pattern of correlation blocks can refine our understanding of the ecological and evolutionary processes underlying the genomic evolution at the population level.     

Resolving the tragedy of the commons: the feedback between intraspecific conflict and population density

Competition and conflict among individuals can favour exploitative strategies that undermine the common good. Theory suggests that this can lead to a tragedy of the commons and ultimately population extinction, a phenomenon known as evolutionary suicide. Here, I present a model of the evolutionary tragedy of the commons that explicitly considers the population dynamics where individuals invest in individually costly competitive traits. In the simplest form, this supports the notion that selection for high levels of conflict can cause evolutionary suicide. However, as competition comes with survival and fecundity costs, a feedback between the investment in competition and population density can act to reduce the level of conflict and prevent the population from going extinct. This suggests that the interaction between population ecology and the evolution of competition and conflict among individuals may be an important mechanism in resolving the level of competition and conflict among individuals.     

Complexity and demographic stability in population models

This article is concerned with relating the stability of a population, as defined by the rate of decay of fluctuations induced by demographic stochasticity, with its heterogeneity in age-specific birth and death rates. We invoke the theory of large deviations to establish a fluctuation theorem: The demographic stability of a population is positively correlated with evolutionary entropy, a measure of the variability in the age of reproducing individuals in the population. This theorem is exploited to predict certain correlations between ecological constraints and evolutionary trends in demographic stability, namely, (i) bounded growth constraints--a uni-directional increase in stability, (ii) unbounded growth constraints (large population size)--a uni-directional decrease in stability, (iii) unbounded growth constraints (small population size)--random, non-directional change in stability. These principles relating ecological constraints with trends in demographic stability are shown to be far reaching generalizations of the tenets derived from classical studies of stability in an evolutionary context. These results thus provide a new conceptual framework for explaining patterns of variation in population numbers observed in natural populations.     

The power and promise of population genomics: from genotyping to genome typing

Population genomics has the potential to improve studies of evolutionary genetics, molecular ecology and conservation biology, by facilitating the identification of adaptive molecular variation and by improving the estimation of important parameters such as population size, migration rates and phylogenetic relationships. There has been much excitement in the recent literature about the identification of adaptive molecular variation using the population-genomic approach. However, the most useful contribution of the genomics model to population genetics will be improving inferences about population demography and evolutionary history.     

Evolutionary and population dynamics of host–parasitoid interactions

The role of evolutionary dynamics in understanding host–parasitoid interactions is interlinked with the population dynamics of these interactions. Here, we address the problems in coupling evolutionary and population dynamics of host–parasitoid interactions. We review previous theoretical and empirical studies and show that evolution can alter the ecological dynamics of a host–parasitoid interaction. Whether evolution stabilizes or destabilizes the interaction depends on the direction of evolutionary changes, which are affected by ecological, physiological, and genetic details of the insect biology. We examine the effect of life history correlations on population persistence and stability, embedding two types, one of which is competitively inferior but superior in encapsulation (for parasitoid, virulence), in a Nicholson–Bailey model with intraspecific resource competition for host. If a trade-off exists between intraspecific competitive ability and encapsulation (or virulence, as a countermeasure) in both the host and parasitoid, the trade-off or even positive correlation in the parasitoid is less influential to ecological stability than the trade-off in the host. We comment on the bearing this work has on the broader issues of understanding host–parasitoid interactions, including long-term biological control. Received: November 10, 1998 / Accepted: January 18, 1999     

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.     

Evolutionary games and population dynamics: maintenance of cooperation in public goods games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.     

Habitat geometry, population viscosity and the rate of genetic drift

In all natural populations, individuals located close to one another tend to interact more than those further apart. The extent of population viscosity can have important implications for ecological and evolutionary processes. Here we develop a spatially explicit population model to examine how the rate of genetic drift depends upon both spatial population structure and habitat geometry. The results show that the time to fixation for a new and selectively neutral mutation is dramatically increased in viscous populations. Furthermore, in viscous populations the time to fixation depends critically on habitat geometry. Fixation time for populations of identical size increases markedly as landscape width decreases and length increases. We suggest that similar effects will also be important in metapopulations, with the spatial arrangement of subpopulations and their connectivity likely to determine the rate of drift. We argue that the recent increases in computer power should facilitate major advances in our understanding of evolutionary landscape ecology over the next few years, and suggest that the time is ripe for a unification of spatial population dynamics theory, landscape ecology and population genetics.     

Can possible evolutionary outcomes be determined directly from the population dynamics?

Traditionally, to determine the possible evolutionary behaviour of an ecological system using adaptive dynamics, it is necessary to calculate the fitness and its derivatives at a singular point. We investigate the claim that the possible evolutionary behaviour can be predicted directly from the population dynamics, without the need for calculation, by applying three criteria — one based on the form of the density dependent rates and two on the role played by the evolving parameters. Taking a general continuous time model, with broad ecological range, we show that the claim is true. Initially, we assume that individuals enter in class 1 and move through population classes sequentially; later we relax these assumptions and find that the criteria still apply. However, when we consider models where the evolving parameters appear non-linearly in the dynamics, we find some aspects of the criteria fail; useful but weaker results on possible evolutionary behaviour now apply.     

Plant population dynamics, pollinator foraging, and the selection of self-fertilization

Many flowering plants rely on pollinators, self-fertilization, or both for reproduction. We model the consequences of these features for plant population dynamics and mating system evolution. Our mating systems-based population dynamics model includes an Allee effect. This often leads to an extinction threshold, defined as a density below which population densities decrease. Reliance on generalist pollinators who primarily visit higher density plant species increases the extinction threshold, whereas autonomous modes of selfing decrease and can eliminate the threshold. Generalist pollinators visiting higher density plant species coupled with autonomous selfing may introduce an effect where populations decreasing in density below the extinction threshold may nonetheless persist through selfing. The extinction threshold and selfing at low density result in populations where individuals adopting a single reproductive strategy exhibit mating systems that depend on population density. The ecological and evolutionary analyses provide a mechanism where prior selfing evolves even though inbreeding depression is greater than one-half. Simultaneous consideration of ecological and evolutionary dynamics confirms unusual features (e.g., evolution into extinction or abrupt increases in population density) implicit in our separate consideration of ecological and evolutionary scenarios. Our analysis has consequences for understanding pollen limitation, reproductive assurance, and the evolution of mating systems.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.