Theoretical Population Biology最新文献

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on the complement of the Gini coefficient, Drewnowski’s index, which is a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model, and showing an example of application to Swedish life table data. Our experiments demonstrate how Drewnowski’s index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species.

Principal component analysis (PCA) is one of the most frequently-used approach to describe population structure from multilocus genotype data. Regarding geographic range expansions of modern humans, interpretations of PCA have, however, been questioned, as there is uncertainty about the wave-like patterns that have been observed in principal components. It has indeed been argued that wave-like patterns are mathematical artifacts that arise generally when PCA is applied to data in which genetic differentiation increases with geographic distance. Here, we present an alternative theory for the observation of wave-like patterns in PCA. We study a coalescent model – the umbrella model – for the diffusion of genetic variants. The model is based on genetic drift without any particular geographical structure. In the umbrella model, splits from an ancestral population occur almost continuously in time, giving birth to small daughter populations at a regular pace. Our results provide detailed mathematical descriptions of eigenvalues and eigenvectors for the PCA of sampled genomic sequences under the model. When variants uniquely represented in the sample are removed, the PCA eigenvectors are defined as cosine functions of increasing periodicity, reproducing wave-like patterns observed in equilibrium isolation-by-distance models. Including singleton variants in the analysis, the eigenvectors corresponding to the largest eigenvalues exhibit complex wave shapes. The accuracy of our predictions is further investigated with coalescent simulations. Our analysis supports the hypothesis that highly structured wave-like patterns could arise from genetic drift only, and may not always be artificial outcomes of spatially structured data. Genomic data related to the peopling of the Americas are reanalyzed in the light of our new theory.

Chan, Durrett, and Lanchier introduced a multitype contact process with temporal heterogeneity involving two species competing for space on the d-dimensional integer lattice. Time is divided into two seasons. They proved that there is an open set of the parameters for which both species can coexist when their dispersal range is sufficiently large. Numerical simulations suggested that three species can coexist in the presence of two seasons. The main point of this paper is to prove that this conjecture is incorrect. To do this we prove results for a more general ODE model and contrast its behavior with other related systems that have been studied in order to understand the competitive exclusion principle.

By providing additional opportunities for coalescence within families, the presence of consanguineous unions in a population reduces coalescence times relative to non-consanguineous populations. First-cousin consanguinity can take one of six forms differing in the configuration of sexes in the pedigree of the male and female cousins who join in a consanguineous union: patrilateral parallel, patrilateral cross, matrilateral parallel, matrilateral cross, bilateral parallel, and bilateral cross. Considering populations with each of the six types of first-cousin consanguinity individually and a population with a mixture of the four unilateral types, we examine coalescent models of consanguinity. We previously computed, for first-cousin consanguinity models, the mean coalescence time for X-chromosomal loci and the limiting distribution of coalescence times for autosomal loci. Here, we use the separation-of-time-scales approach to obtain the limiting distribution of coalescence times for X-chromosomal loci. This limiting distribution has an instantaneous coalescence probability that depends on the probability that a union is consanguineous; lineages that do not coalesce instantaneously coalesce according to an exponential distribution. We study the effects on the coalescence time distribution of the type of first-cousin consanguinity, showing that patrilateral-parallel and patrilateral-cross consanguinity have no effect on X-chromosomal coalescence time distributions and that matrilateral-parallel consanguinity decreases coalescence times to a greater extent than does matrilateral-cross consanguinity.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

For the two-patch logistic model, we study the effect of dispersal intensity and dispersal asymmetry on the total population abundance and its distribution. Two complete classifications of the model parameter space are given: one concerning when dispersal causes smaller or larger total biomass than no dispersal, and the other addressing how the total biomass changes with dispersal intensity and dispersal asymmetry. The dependencies of the population abundance of each individual patch on dispersal intensity and dispersal asymmetry are also fully characterized. In addition, the maximal and minimal total population sizes induced by dispersal are determined for the logistic model with an arbitrary number of patches, and a weak order-preserving result correlated the local population abundances with and without dispersal is established.

We revisit the Spatial $\Lambda$-Fleming–Viot process introduced in Barton and Kelleher (2010). Particularly, we are interested in the time $T_0$ to the most recent common ancestor for two lineages. We distinguish between the cases where the process acts on the two-dimensional plane and on a finite rectangle. Utilizing a differential equation linking $T_0$ with the physical distance between the lineages, we arrive at computationally efficient and reasonably accurate approximation schemes for both cases. Furthermore, our analysis enables us to address the question of whether the genealogical process of the model “comes down from infinity”, which has been partly answered before in Véber and Wakolbinger (2015).

The egalitarian allotment of gametes to each allele at a locus (Mendel’s law of segregation) is a near-universal phenomenon characterizing inheritance in sexual populations. As exceptions to Mendel’s law are known to occur, one can investigate why non-Mendelian segregation is not more common using modifier theory. Earlier work assuming sex-independent modifier effects in a random mating population with heterozygote advantage concluded that equal segregation is stable over long-term evolution. Subsequent investigation, however, demonstrated that the stability of the Mendelian scheme disappears when sex-specific modifier effects are allowed. Here I derive invasion conditions favoring the repeal of Mendelian law in mixed and obligate selfing populations. Oppositely-directed segregation distortion in the production of male and female gametes is selected for in the presence of overdominant fitness. The conditions are less restrictive than under panmixia in that strong selection can occur even without differential viability of reciprocal heterozygotes (i.e. in the absence of parent-of-origin effects at the overdominant fitness locus). Generalized equilibria are derived for full selfing.

In classical epidemic theory, behavior is assumed to be stationary. In recent years, epidemic models have been extended to include behaviors that transition in response to the current state of the epidemic. However, it is widely known that human behavior can exhibit strong history-dependence as a consequence of learned experiences. This history-dependence is similar to hysteresis phenomena that have been well-studied in control theory. To illustrate the importance of history-dependence for epidemic theory, we study dynamics of a variant of the SIRS model where individuals exhibit lazy-switch responses to prevalence dynamics, based on the Preisach hysteresis operator. The resulting model can possess a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We consider how the limit point of the epidemic trajectory and the infection peak along this trajectory depend on the degree of heterogeneity of the response. Our approach supports the argument that public health responses during the emergence of a new disease can have fundamental long-term consequences for subsequent management efforts.

Previous analyses have predicted that social learning should not evolve in a predator–prey system. Here we examine whether success-biased social learning, by which social learners copy successful demonstrators, allows social learning by foragers to evolve. We construct a one-predator, two-prey system in which foragers must learn how to feed on depletable prey populations in an environment where foraging information can be difficult to obtain individually. We analyze two models in which social learning is success-biased: in the first, individual learning does not depend on the resource dynamics, and in the second model it depends on the relative frequency of the resource. Unlike previous results, we find that social learning does not cause predators to over-harvest one type of prey over the other. Furthermore, increasing the probability of social learning increases the probability of learning a successful foraging behavior, especially when individually learned information tends to be inaccurate. Whereas social learning does not evolve among individual learners in the first model, the assumption of resource-dependent learning in the second model allows a mutant with an increased probability of social learning to spread through the forager population.