The Influence of the Mating System on the Maintenance of Genetic Variability in Polygenic Characters

The traditional models of the effect of assortative mating and inbreeding on the genetic variance of polygenic characters (Fisher 1918; Wright 1921) presume that there is no natural selection or mutation. In a large population, the genetic variance determined by additive genes may then increase by up to a factor of two with local inbreeding, and even more with assortative mating. The classical models are still used to interpret data from natural populations. But contrary to their assumptions, most metrical characters in natural populations are usually thought to be under a type of selection which depletes polygenic variation. Mutation is then necessary to maintain genetic variation. The present models show that with the additional features of mutation and selection, in a large population, the mating system has no influence on the amount of genetic variability maintained by additive genes.     

天敌-害虫系统中两种天敌与一种害虫相互作用形式的几个数学模型

本文运用简单的概率思考,对两种天敌与一种害虫的捕食行为或拟寄生行为给出互不相容的,相容的,及相互独立的统计描述。对近年来由Hassell、May、Beddington等人为了提供生物防治的理论依据,所提出的天敌与害虫相互作用数学模型中作用率(捕食率,拟寄生率)给以确切的概率涵义。并对两种天敌与一种害虫的不同形式的相互作用,提出5个数学模型,其中有的是改进前人的模型,有的是田间生态系统中常见的,而尚未有人提出过的。文中还分别就随机寻找和非随机寻找两种情况下,将模型参数的变动影响及种群动态的趋势进行了数值模拟。     

The Evolution of Selectively Similar Electro-Phoretically Detectable Alleles in Finite Natural Populations

Most of the models of population genetics are not realistic when applied to data on electrophoretic variants of proteins because the same net charge may result from any of several amino acid combinations. In the absence of realistic models they have, however, been widely used to test competing hypotheses about the origin and maintenance of genetic variation in populations. In this paper I present a general method for determining probability generating functions for electrophoretic state differences. Then I use the method to find allelic state difference distributions for selectively similar electrophoretically detectable alleles in finite natural populations.Predicted patterns of genetic variation, both within and among species, are in reasonable accord with those found in the Drosophila willistoni group by Ayala et al. (1972) and by Ayala and Tracey (1974).     

Natural selection, fitness entropy, and the dynamics of coevolution

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.     

Spatial heterogeneity,population “regulation” and local extinction in simulated host-parasitoid interactions

Summary Simulation models have recently been used to suggest that spatial heterogeneity, acting on small spatial scales within local populations, may allow parasitoids and other natural enemies to regulate host or prey populations in ways that would not be detected by conventional (k-factor) analyses of life table data. However, additional study of these models suggests that local extinction may be a frequent event in the simulated interactions. The spreading of risk concept appears more applicable to the simulated populations than a classical view emphasizing tight regulation around stable equilibrium points. The spreading of risk viewpoint also appears to shed additional light on questions raised in the recent debate between Dempster (1983); Hassel (1985); Dempster and Pollard (1986), concerning the modeling of spatial heterogeneity and regulation in temperate-zone insect populations.     

Mechanistic models of population-level phenomena

This paper is about mechanisms and models, and how they interact. In part, it is a response to recent discussion in philosophy of biology regarding whether natural selection is a mechanism. We suggest that this debate is indicative of a more general problem that occurs when scientists produce mechanistic models of populations and their behaviour. We can make sense of claims that there are mechanisms that drive population-level phenomena such as macroeconomics, natural selection, ecology, and epidemiology. But talk of mechanisms and mechanistic explanation evokes objects with well-defined and localisable parts which interact in discrete ways, while models of populations include parts and interactions that are neither local nor discrete in any actual populations. This apparent tension can be resolved by carefully distinguishing between the properties of a model and those of the system it represents. To this end, we provide an analysis that recognises the flexible relationship between a mechanistic model and its target system. In turn, this reveals a surprising feature of mechanistic representation and explanation: it can occur even when there is a mismatch between the mechanism of the model and that of its target. Our analysis reframes the debate, providing an alternative way to interpret scientists’ “mechanism-talk”, which initially motivated the issue. We suggest that the relevant question is not whether any population-level phenomenon such as natural selection is a mechanism, but whether it can be usefully modelled as though it were a particular type of mechanism.     

Single species models with logistic growth and dissymmetric impulse dispersal

In this paper, two classes of single-species models with logistic growth and impulse dispersal (or migration) are studied: one model class describes dissymmetric impulsive bi-directional dispersal between two heterogeneous patches; and the other presents a new way of characterizing the aggregate migration of a natural population between two heterogeneous habitat patches, which alternates in direction periodically. In this theoretical study, some very general, weak conditions for the permanence, extinction of these systems, existence, uniqueness and global stability of positive periodic solutions are established by using analysis based on the theory of discrete dynamical systems. From this study, we observe that the dynamical behavior of populations with impulsive dispersal differs greatly from the behavior of models with continuous dispersal. Unlike models where the dispersal is continuous in time, in which the travel losses associated with dispersal make it difficult for such dispersal to evolve e.g., [25], [26], [28], in the present study it was relatively easy for impulsive dispersal to positively affect populations when realistic parameter values were used, and a rich variety of behaviors were possible. From our results, we found impulsive dispersal seems to more nicely model natural dispersal behavior of populations and may be more relevant to the investigation of such behavior in real ecological systems.     

Frequency-dependent selection and competition: empirical approaches

When Darwin and Wallace first formulated the theory of evolution by natural selection, they were greatly influenced by the idea that populations tend to increase geometrically and rapidly outgrow the resources available to them. They argued that the ensuing competition among individuals would be a major agent of natural selection. Since their day, competition has become almost synonymous with the idea of natural selection or survival of the fittest. In this paper we examine the relation between competition and selection by using simple competition models, consider the interaction of density and frequency in determining competitive outcome, and review the literature on frequency-dependent competitive interactions among genotypes within populations.     

Dams and canyons disrupt gene flow among populations of a threatened riparian plant

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Estimating genetic parameters in natural populations using the "animal model"

Estimating the genetic basis of quantitative traits can be tricky for wild populations in natural environments, as environmental variation frequently obscures the underlying evolutionary patterns. I review the recent application of restricted maximum-likelihood "animal models" to multigenerational data from natural populations, and show how the estimation of variance components and prediction of breeding values using these methods offer a powerful means of tackling the potentially confounding effects of environmental variation, as well as generating a wealth of new areas of investigation.     

Distribution and fitness effects of the son-killer bacterium inNasonia

Summary Maternally inherited microorganisms that kill male (but not female) progeny are widespread in nature. Three hypotheses have been proposed for the evolution of male-killing microorganisms: inbreeding reduction, release of resources to remaining females and inoculum for horizontal transmission. The sonkiller bacterium,Arsenophonus nasoniae, is a maternally inherited bacterium that causes lethality of male embryos of infected females in the parasitoid wasp,Nasonia vitripennis. In this paper we describe the geographical distribution and frequency of the son-killer bacterium in North American populations ofN. vitripennis andNasonia longicornis. We tested the resource release hypothesis using the body size measurements of infected and uninfected females from natural populations. No evidence was found for a fitness increase of females infected with the bacterium compared to uninfected females. We propose a modification of the existing models, termed the incremental gain hypothesis. According to this model, the bacteria are maintained in host populations due to horizontal transmission and male killing provides an incremental gain in the fitness of infected females relative to females infected with non-male-killing bacteria.     

Genetic differentiation between clone collections and natural populations of European black poplar (<Emphasis Type="Italic">Populus nigra</Emphasis> L.) in turkey

The European black poplar (Populus nigra L.) is an ecologically and economically important tree species for Turkey. The important and major genetic resources of species for future breeding and ex situ conservation purposes have been archived in a clone bank in Ankara by selecting clones from natural populations and old plantations throughout Turkey. There is no study to date assessing genetic composition these materials. Two-hundred-thirty-three P. nigra clones from six geographic region of Turkey (clone collection populations), and 32 trees from two natural populations (Tunceli and Melet) were genotyped by using 12 nuclear microsatellite DNA markers. There were nine clones which duplicated in various frequencies. The analysis carried out with removal of the duplicated clones revealed a moderately high genetic diversity in studied populations. The observed heterozygosities ranged from 0.59 in Tunceli natural to 0.69 in Central Anatolia clone collection populations. In general, there was excess of heterozygosity in the studied populations. Populations composed of clone collections were significantly differentiated from natural populations (F _ST = 0.17), while there was little differentiation among those populations in the clone collection (F _ST = 0.03). Two distantly located natural populations with small sizes also differed from each other (F _ST = 0.17). Genetic structure analysis revealed two distinct groups (clone collection vs natural populations) with very high membership values (>92%). Clone collection populations had high level of admixture while natural populations had homogenous genetic structure. The presence of large number of clonal duplication, reduced genetic differentiation, and high level of admixture in clone collection populations indicate that genetic resources of European black poplar were highly degraded through genetic erosion and pollution caused by intensive cultural practices and extensive dispersal of clonal materials. To understand genetic diversity and its structural pattern thoroughly in the six clone collection populations, a further study with extensive and systematic sampling of European black poplar populations in major river ecosystems in Turkey will be useful.     

From survivors to replicators: evolution by natural selection revisited

For evolution by natural selection to occur it is classically admitted that the three ingredients of variation, difference in fitness and heredity are necessary and sufficient. In this paper, I show using simple individual-based models, that evolution by natural selection can occur in populations of entities in which neither heredity nor reproduction are present. Furthermore, I demonstrate by complexifying these models that both reproduction and heredity are predictable Darwinian products (i.e. complex adaptations) of populations initially lacking these two properties but in which new variation is introduced via mutations. Later on, I show that replicators are not necessary for evolution by natural selection, but rather the ultimate product of such processes of adaptation. Finally, I assess the value of these models in three relevant domains for Darwinian evolution.     

Molecular phylogeography and population evolution analysis of <Emphasis Type="Italic">Citrus ichangensis</Emphasis> (Rutaceae)

Ichang papeda (Citrus ichangensis), a wild and endemic perennial plant in Rutaceae, is characterized by the existence of wild and natural populations in southwestern and middle-west China. We analyzed a total of 231 individuals across 16 natural populations using chloroplast SSR markers, nuclear SSR markers, and single-copy nuclear genes. Standard population genetic analyses as well as Bayesian and maximum likelihood models were used to clarify the genetic diversity, population differentiation, barriers to gene flow, bottleneck events, isolation by distance, history migration, demographic history among populations, and phylogeny evolution. The chloroplast and nuclear genome analyses revealed a low level of genetic diversity in C. ichangensis. Clear signals of recent bottlenecks and strong patterns of isolation by distance were detected among different subpopulations, indicating a low extent of historical gene flow for this species and that genetic drift would occur after population differentiation. Bayesian clustering analyses revealed a clear pattern of genetic structure, with one cluster spanning the potential refugia in Wuling Mountains and Ta-pa Mountains, and other two clusters covering a more limited distribution range. The demographic history also supported the scenario that two isolated clusters originated in parallel from the genetic diversity center. Taxonomically, Ichang papeda may be a member of subgenus Citrus. Owing to the complicated topography, the mountainous regions and the Yangtze River have provided long-term stable habitats for C. ichangensis and acted as main barriers for its expansion, which might facilitate the process of speciation. Statistical population models and genetic data indicated strong genetic structure in C. ichangensis, which might result from the restricted gene flow, genetic drift, and population bottlenecks.     

Comparative study of mathematical models for the relationship between water temperature and brood development time of Gammarus fossarum and G. roeseli (Crustacea: Amphipoda)

SUMMARY. 1. The relationship between water temperature ( T°C ) and brood development time (d days for embryonic development time plus 'post-hatch time') was investigated experimentally using animals from four populations of Gammarus fossarum (populations 1–4) and two populations of G. roeseli (populations 5 and 6) in Austrian streams.
2. Eleven mathematical models were examined as suitable functions to describe the relationship between d and T . The models were compared with respect to their goodness-of-fit and suitability for further quantitative, statistical analyses of intra- and interspecific differences between natural populations of G. fossarum and G. roeseli .
3. Statistical analyses were performed with logarithmically transformed values of d , in order to provide homogeneous variances between the different constant temperatures used. The following three-parameter model was found to be the most suitable for the data:
This equation was fitted in its linear form:      

Simple assumptions on age composition lead to erroneous conclusions on the nature of density dependence in age-structured populations

Ecologists have debated the nature of density dependence in natural populations for decades, and efforts to detect density dependence from time series of abundance data have paralleled these debates. Yet due to the correlative nature of time series data, these undertakings have been statistically problematic. Most analyses of density dependence have focused on simple population models (i.e., non-overlapping generations), but in reality most vertebrates exhibit more complex life histories, and this complexity has been incorporated into population models in a variety of ways. Unfortunately, adding complexity to population models can further exacerbate efforts to detect density dependence. We examined the effect of adding age structure when inadequate data exist in support; to demonstrate this effect, we adopted Pacific salmon (Oncorhynchus spp.) as our study organism. Most salmon populations are semelparous and have variable age at maturity. Salmon populations (and many other fish species populations) are typically modeled in terms of numbers of recruits arising from spawners in a given brood year. Recruits are enumerated as they return as adults to spawn, and proper assignment of recruits to brood year requires age information. Unfortunately, while adult counts are common, detailed age information is not. A common practice is to apply long-term averages of age composition to returning adults to "reconstruct" time series of recruits. Here, by conducting simulations and analyzing data from natural populations, we demonstrated that this practice leads to a biased portrayal of density dependence by overestimating recruits from small spawning classes and underestimating recruits from large spawning classes. Also, productivity was overestimated and variance was underestimated, which could lead to overly optimistic predictions of extinction risk or overharvesting.     

Resource partitioning among competing species—A coevolutionary approach

A reasonably general theory for predicting the outcome of coevolution among interacting species is developed. It is applied to a model for resource partitioning among competing species.Current theory for resource partitioning is based on derivations of a “limiting similarity”—i.e., a limit to how similar competitors can be to one another consistent with coexistence. This theory presumes there is a mechanism, perhaps invasion and extinction, which causes competitors to attain the limiting similarity. The view taken in this paper is that partitioning is an evolutionary compromise between pressures for character displacement and disadvantages inherent in the shift to different resource types.A set of principles is offered for the evolution of the parameters in ecological models. (1) For single population models natural selection causes the parameters ultimately to assume those values which produce the highest equilibrium population size. (2) For models of interacting populations, but without interspecific frequency-dependence, natural selection causes the parameters to assume values which produce either the highest or lowest equilibrium population size for any species depending on the sign of the “feedback” in the community obtained by deleting that species. (3) For models of interacting populations with interspecific frequency dependence natural selection leads to parameter values which produce intermediate equilibrium population sizes. A function called the conditional equilibrium population size is introduced. Provided (a) the mean fitness is a maximum in each species at a stable coevolutionary equilibrium and (b) there is negative density-dependence in each species then natural selection causes the parameters to assume values which produce the highest conditional equilibrium population size for each species.These coevolutionary principles, applied to a model for resource partitioning, entail that the niche separation between species relative to given niche widths, increases with the variety of available resources and decreases with the number of competing populations. Also, the evolution of character displacement between two species does not proceed far enough to maximize the equilibrium population sizes of the species involved. These results imply that the relationship between the niche overlap (of nearest neighbors) and species diversity is qualitatively different depending on whether the variety of resources at any place covaries with the species diversity there. Without covariation niche overlap increases with species diversity; with covariation overlap may decrease with species diversity. This study provides the beginning of a theory for the convergent evolution of community structure.     

The phylogeographical clade trade: tracing the impact of human-mediated dispersal on the colonization of northern Europe by the oak gallwasp Andricus kollari

Human dispersal of organisms is an important process modifying natural patterns of biodiversity. Such dispersal generates new patterns of genetic diversity that overlie natural phylogeographical signatures, allowing discrimination between alternative dispersal mechanisms. Here we use allele frequency and DNA sequence data to distinguish between alternative scenarios (unassisted range expansion and long range introduction) for the colonization of northern Europe by an oak-feeding gallwasp, Andricus kollari. Native to Mediterranean latitudes from Portugal to Iran, this species became established in northern Europe following human introduction of a host plant, the Turkey oak Quercus cerris. Colonization of northern Europe is possible through three alternative routes: (i) unassisted range expansion from natural populations in the Iberian Peninsula; (ii) unassisted range expansion from natural populations in Italy and Hungary; or (iii) descent from populations imported to the UK as trade goods from the eastern Mediterranean in the 1830s. We show that while populations in France were colonized from sources in Italy and Hungary, populations in the UK and neighbouring parts of coastal northern Europe encompass allozyme and sequence variation absent from the known native range. Further, these populations show demographic signatures expected for large stable populations, rather than signatures of rapid population growth from small numbers of founders. The extent and spatial distribution of genetic diversity in the UK suggests that these A. kollari populations are derived from introductions of large numbers of individuals from each of two genetically divergent centres of diversity in the eastern Mediterranean. The strong spatial patterning in genetic diversity observed between different regions of northern Europe, and between sites in the UK, is compatible with leptokurtic models of population establishment.     

Evidence for gene flow between wild and cultivated Medicago sativa (Leguminosae)based on allozyme markers andquantitative traits

Genetic differentiation between co-occurring crops and their wild relatives will be greatly modified by crop-to-weed gene flow and variation between human and natural selective pressures. The maintenance of original morphological features in most natural populations of Medicago sativa in Spain questions the relative extent of these antagonistic forces. In this paper, we measured and compared the pattern of population differentiation within and among the wild and cultivated gene pool with respect to both allozymes and quantitative traits. Patterns of diversity defined three kinds of natural populations. First, some populations were intermediate with respect to both allozymes and quantitative traits. This suggests that crop-to-weed gene flow may have created hybrid populations in some locations. Second, some populations were different from all the cultivated landraces with respect to both allozymes and quantitative traits. This probably results from variable gene flow in space and in time, due to demographic stochasticity in either natural or cultivated populations. Third, differentiation from cultivated landraces was only achieved for the quantitative traits but not for allozymes in two populations. This suggests that natural selection in some locations may oppose gene flow to establish cultivated traits into the natural introgressed populations.     

Selection-delayed population dynamics in baleen whales and beyond

While it is known that population cycles are driven by delayed density-dependent feedbacks, the search for a common feedback mechanism in natural populations with cyclic dynamics has remained unresolved for almost a century. To identify the existence and cause of delayed feedbacks I apply six age- and sex-structured population dynamics models to seven species of baleen whales (suborder Mysticeti) that were heavily depleted by past commercial whaling. The six models include a predator–prey model with killer whale (Orcinus orca) as the predator, and five singe-species models based on (1) exponential growth, (2) density-regulated growth, (3) density-regulated growth with depensation, (4) delayed density-regulated growth and (5) selection-delayed dynamics. The latter model has a density-regulated growth rate that is accelerated and decelerated by the intra-specific natural selection that arises from the density-dependent competitive interactions between the individuals in the population. Essential parameters are estimated by a Bayesian statistical framework, and it is shown that baleen whales have a delayed recovery relative to density-regulated growth. The time-lag is not explained by depensation, or by interactions with prey or predators. It is instead resolved by a selection-delayed acceleration of the intrinsic growth rate. The results are discussed in relation to the literature on cyclic dynamics, and it is noted (1) that selection-delayed dynamics is both theoretically and empirically sufficient for cyclic population dynamics, (2) that it is widespread in natural populations owing to the widespread occurrence of otherwise unexplained phenotypic cycles in populations with cyclic dynamics, and (3) that there is a lack of empirical evidence showing that predator–prey interactions is a sufficient cause for the cyclic dynamics of natural populations. The conclusion stresses the importance of intra-specific delays in cyclic dynamics, and suggests that it is the acceleration of the growth rate, and not the growth rate itself, that is determined by the density-dependent environment.