Small population effects in stochastic population dynamics

The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results. Supported in part by DOE Office of Basic Science, Chemical Division. Reported at SMB03, the August 2003 meeting of the Society for Mathematical Biology.     

From population genetics to population genomics of forest trees: integrated population genomics approach

Early works by Altukhov and his associates on pine and spruce laid the foundation for Russian population genetic studies on tree species with the use of molecular genetic markers. In recent years, these species have become especially popular as nontraditional eukaryotic models for population and evolutionary genomic research. Tree species with large, cross-pollinating native populations, high genetic and phenotypic variation, growing in diverse environments and affected by environmental changes during hundreds of years of their individual development, are an ideal model for studying the molecular genetic basis of adaptation. The great advance in this field is due to the rapid development of population genomics in the last few years. In the broad sense, population genomics is a novel, fast-developing discipline, combining traditional population genetic approaches with the genomic level of analysis. Thousands of genes with known function and sometimes known genomic localization can be simultaneously studied in many individuals. This opens new prospects for obtaining statistical estimates for a great number of genes and segregating elements. Mating system, gene exchange, reproductive population size, population disequilibrium, interaction among populations, and many other traditional problems of population genetics can be now studied using data on variation in many genes. Moreover, population genomic analysis allows one to distinguish factors that affect individual genes, alleles, or nucleotides (such as, for example, natural selection) from factors affecting the entire genome (e.g., demography). This paper presents a brief review of traditional methods of studying genetic variation in forest tree species and introduces a new, integrated population genomics approach. The main stages of the latter are : (1) selection of genes, which are tentatively involved in variation of adaptive traits, by means of a detailed examination of the regulation and the expression of individual genes and genotypes, with subsequent determination of their complete allelic composition by direct nucleotide sequencing; (2) examination of the phenotypic effects of individual alleles by, e.g., association mapping; and (3) determining the frequencies of the selected alleles in natural population for identification of the adaptive variation pattern in the heterogeneous environment. Through decoding the phenotypic effects of individual alleles and identification of adaptive variation patterns at the population level, population genomics in the future will serve as a very helpful, efficient, and economical tool, essential for developing a correct strategy for conserving and increasing forests and other commercially valuable plant and animal species.     

From population genetics to population genomics of forest trees: Integrated population genomics approach

Early works by Altukhov and his associates on pine and spruce laid the foundation for Russian population genetic studies on tree species with the use of molecular genetic markers. In recent years, these species have become especially popular as nontraditional eukaryotic models for population and evolutionary genome-wide research. Tree species with large, cross-pollinating native populations, high genetic and phenotypic variation, growing in diverse environments and affected by environmental changes during hundreds of years of their individual development, are an ideal model for studying the molecular genetic basis of adaptation. The great advance in this field is due to the rapid development of population genomics in the last few years. In the broad sense, population genomics is a novel, fast-developing discipline, combining traditional population genetic approaches with the genome-wide level of analysis. Thousands of genes with known function and sometimes known genome-wide localization can be simultaneously studied in many individuals. This opens new prospects for obtaining statistical estimates for a great number of genes and segregating elements. Mating system, gene exchange, reproductive population size, population disequilibrium, interaction among populations, and many other traditional problems of population genetics can be now studied using data on variation in many genes. Moreover, population genome-wide analysis allows one to distinguish factors that affect individual genes, allelles, or nucleotides (such as, for example, natural selection) from factors affecting the entire genome (e.g., demography). This paper presents a brief review of traditional methods of studying genetic variation in forest tree species and introduces a new, integrated population genomics approach. The main stages of the latter are: (1) selection of genes, which are tentatively involved in variation of adaptive traits, by means of a detailed examination of the regulation and the expression of individual genes and genotypes, with subsequent determination of their complete allelic composition by direct nucleotide sequencing; (2) examination of the phenotypic effects of individual alleles by, e.g., association mapping; and (3) determining the frequencies of the selected alleles in natural population for identification of the adaptive variation pattern in the heterogeneous environment. Through decoding the phenotypic effects of individual alleles and identification of adaptive variation patterns at the population level, population genomics in the future will serve as a very helpful, efficient, and economical tool, essential for developing a correct strategy for conserving and increasing forests and other commercially valuable plant and animal species.     

A population balance model for fish population dynamics

A population balance model of fish population dynamics for batch systems was developed. A growth rate expression was introduced and coupled with the population balance. Solutions of the model provide predictions of such fish size distribution characteristics as average size, standard deviation and coefficient of variation. A growth diffusivity mechanism was found to be inapplicable to systems where a terminal size is reached. A study of the two parameter growth rate expression was conducted, illustrating that conditions conducive to high growth rates also resulted in broadening of size distributions. The model was compared to data found in the literature to demonstrate its predictive capabilities.     

Perfect simulation from nonneutral population genetic models: variable population size and population subdivision

We show how the idea of monotone coupling from the past can produce simple algorithms for simulating samples at a nonneutral locus under a range of demographic models. We specifically consider a biallelic locus and either a general variable population size mode or a general migration model for population subdivision. We investigate the effect of demography on the efficacy of selection and the effect of selection on genetic divergence between populations.     

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.     

Dose-structured population dynamics

Applied population dynamics modeling is relied upon with increasing frequency to quantify how human activities affect human and non-human populations. Current techniques include variously the population's spatial transport, age, size, and physiology, but typically not the life-histories of exposure to other important things occurring in the ambient environment, such as chemicals, heat, or radiation. Consequently, the effects of such 'abiotic' aspects of an ecosystem on populations are only currently addressed through individual-based modeling approaches that despite broad utility are limited in their applicability to realistic ecosystems [V. Grimm, Ten years of individual-based modeling in ecology: what have we learned and what could we learn in the future? Ecol. Model. 115 (1999) 129-148][1]. We describe a new category of population dynamics modeling, wherein population dynamical states of the biotic phases are structured on dose, and apply this framework to demonstrate how chemical species or other ambient aspects can be included in population dynamics in three separate examples involving growth suppression in fish, inactivation of microorganisms with ultraviolet irradiation, and metabolic lag in population growth. Dose-structuring is based on a kinematic approach that is a simple generalization of age-structuring, views the ecosystem as a multi-component mixture with reacting biotic/abiotic components. The resulting model framework accommodates (a) different memories of exposure as in recovery from toxic ambient conditions, (b) differentiation between exogenous and endogenous sources of variation in population response, and (c) quantification of acute or sub-acute effects on populations arising from life-history exposures to abiotic species. Classical models do not easily address the very important fact that organisms differ and have different experiences over their life cycle. The dose structuring is one approach to incorporate some of these elements into the existing structures of the classical models, while retaining many of the features (and other limitations) of classical models.     

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Effective population size and population subdivision in demographically structured populations

A fast-timescale approximation is applied to the coalescent process in a single population, which is demographically structured by sex and/or age. This provides a general expression for the probability that a pair of alleles sampled from the population coalesce in the previous time interval. The effective population size is defined as the reciprocal of twice the product of generation time and the coalescence probability. Biologically explicit formulas for effective population size with discrete generations and separate sexes are derived for a variety of different modes of inheritance. The method is also applied to a nuclear gene in a population of partially self-fertilizing hermaphrodites. The effects of population subdivision on a demographically structured population are analyzed, using a matrix of net rates of movement of genes between different local populations. This involves weighting the migration probabilities of individuals of a given age/sex class by the contribution of this class to the leading left eigenvector of the matrix describing the movements of genes between age/sex classes. The effects of sex-specific migration and nonrandom distributions of offspring number on levels of genetic variability and among-population differentiation are described for different modes of inheritance in an island model. Data on DNA sequence variability in human and plant populations are discussed in the light of the results.     

Bacterial population genetics

Bacterial population genetics is the study of natural bacterial genetic diversity arising from evolutionary processes. The roles of molecular mistakes, restriction–modification, plasmids and gene transfer in bacteria are also important components of population genetics. These aspects are of considerable scientific importance from a fundamental perspective, because of the short generation times of bacteria, their microscopic cell size, the large population sizes bacteria can achieve and their different mechanisms of gene transfer.     

Genetic structure in an expanding cervid population after population reduction

The Norwegian red deer population (Cervus elaphus) was from the mid eighteenth to the early twentieth century drastically reduced in size and distribution but has the last century expanded both demographically and spatially. We have investigated genetic variation, differentiation and admixture in this spatially expanding ungulate population, using 14 microsatellites. The present genetic structure is moderate to strong with an average F _ST = 0.08. Low M-ratios indicate loss of genetic variation in all localities and signals of a recent bottleneck was identified in 14 of 15 localities. Genetic distances between the localities indicate two main routes of dispersal during expansion, from the north–west and south–west, respectively. Bayesian assignment tests verify a break of the dataset in two, and demonstrate 99.9% probability for the existence of five sub-populations, which coincide well with five relict populations described by historic records. Computer simulations suggest that the observed genetic differentiation is recent rather than ancient, and that it may be explained by models of fragmentation or of founder events and subsequent merging rather than by models of recent bottlenecks in some particular demes within an ancient genetic structure.     

Assessing minimum viable population size: Demography meets population genetics

The discussion of a population's minimum viable size provides a focus for the study of ecological and genetic factors that influence the persistence of a threatened population. There are many causes of extinction and the fate of a specific population cannot generally be predicted. This uncertainty has been dealt with in two ways: through stochastic demographic models to determine how to minimize extinction probabilities; and through population genetic theory to determine how best to maintain genetic variation, in the belief that the ability to evolve helps buffer a population against the unknown. Recent work suggests that these two very different approaches lead to very similar conclusions, at least under panmictic conditions. However, defining the ideal spatial distribution for an endangered species remains an important challenge.     

Collapsing population cycles

During the past two decades population cycles in voles, grouse and insects have been fading out in Europe. Here, we discuss the cause and implication of these changes. Several lines of evidence now point to climate forcing as the general underlying cause. However, how climate interacts with demography to induce regime shifts in population dynamics is likely to differ among species and ecosystems. Herbivores with high-amplitude population cycles, such as voles, lemmings, snowshoe hares and forest Lepidoptera, form the heart of terrestrial food web dynamics. Thus, collapses of these cycles are also expected to imply collapses of important ecosystem functions, such as the pulsed flows of resources and disturbances.     

Bacterial population genetics

Bacterial population genetics is the study of natural bacterial genetic diversity arising from evolutionary processes. The roles of molecular mistakes, restriction–modification, plasmids and gene transfer in bacteria are also important components of population genetics. These aspects are of considerable scientific importance from a fundamental perspective, because of the short generation times of bacteria, their microscopic cell size, the large population sizes bacteria can achieve and their different mechanisms of gene transfer.