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.     

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.     

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.     

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.     

Coupling-induced population synchronization in an excitatory population of subthreshold Izhikevich neurons

We consider an excitatory population of subthreshold Izhikevich neurons which exhibit noise-induced firings. By varying the coupling strength J, we investigate population synchronization between the noise-induced firings which may be used for efficient cognitive processing such as sensory perception, multisensory binding, selective attention, and memory formation. As J is increased, rich types of population synchronization (e.g., spike, burst, and fast spike synchronization) are found to occur. Transitions between population synchronization and incoherence are well described in terms of an order parameter $\mathcal{O}$ . As a final step, the coupling induces oscillator death (quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. The oscillator death leads to a transition from firing to non-firing states at the population level, which may be well described in terms of the time-averaged population spike rate $\overline{R}$ . In addition to the statistical-mechanical analysis using $\mathcal{O}$ and $\overline{R}$ , each population and individual state are also characterized by using the techniques of nonlinear dynamics such as the raster plot of neural spikes, the time series of the membrane potential, and the phase portrait. We note that population synchronization of noise-induced firings may lead to emergence of synchronous brain rhythms in a noisy environment, associated with diverse cognitive functions.     

Markov population processes as models of primate social and population dynamics

Thanks to recently developed theory of Markov population processes, models of how an individual primate migrates from one casual social group to another or from one breeding troop to another can now deal exactly with transition rates which depend nonlinearly on the sizes of both the group (or troop) left and the group (or troop) entered. Examples of such models presented here are consistent with existing observations of primate social and population dynamics and are more plausible as explanations of these data than previous linear models.     

Reanalysis of Eurasian population history: ancient DNA evidence of population affinities

Mitochondrial hypervariable region I genetic data from ancient populations at two sites in Asia-Linzi in Shandong (northern China) and Egyin Gol in Mongolia-were reanalyzed to detect population affinities. Data from 51 modern populations were used to generate distance measures (Fst's) to the two ancient populations. The tests first analyzed relationships at the regional level and then compiled the top regional matches for an overall comparison to the two probe populations. The reanalysis showed that the Egyin Gol and Linzi populations have clear distinctions in genetic affinity. The Egyin Gol population as a whole appears to bear close affinities with modern populations of northern East Asia. The Linzi population seems to have some genetic affinities with the West, as suggested by the original analysis, although the original attribution of "European-like" seems to be misleading. We suggest that the Linzi individuals are potentially related to early Iranians, who are thought to have been widespread in parts of Central Eurasia and the steppe regions in the first millennium B.C., although some significant admixture between a number of populations of varying origin cannot be ruled out. We also examine the effect of sequence length on this type of genetic data analysis and discuss the results of previous studies on the Linzi sample.     

The effect of population density on the growth of an animal population

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Contribution from the Department of Fisheries, Kyoto University.

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Contribution from the Entomological Laboratory, Kyoto University, No. 201.     

Isomorphism of population models

Population models are represented as measure preserving transformations and characterized by the entropy of these transformations. Isomorphism invariants of these mappings are discussed and an upper bound for the entropy of a population model is derived.