Theoretical Population Biology最新文献

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.

The site frequency spectrum (SFS) is an important statistic that summarizes the molecular variation in a population, and is used to estimate population-genetic parameters and detect natural selection. Here, we study the SFS in a randomly mating, diploid population in which both the population size and selection coefficient vary periodically with time using a diffusion theory approach, and derive simple analytical expressions for the time-averaged SFS in slowly and rapidly changing environments. We show that for strong selection and in slowly changing environments where the population experiences both positive and negative cycles of the selection coefficient, the time-averaged SFS differs significantly from the equilibrium SFS in a constant environment. The deviation is found to depend on the time spent by the population in the deleterious part of the selection cycle and the phase difference between the selection coefficient and population size, and can be captured by an effective population size.

Game theory has emerged as an important tool to understand interacting populations in the last 50 years. Game theory has been applied to study population dynamics with optimal behavior in simple ecosystem models, but existing methods are generally not applicable to complex systems. In order to use game-theory for population dynamics in heterogeneous habitats, habitats are usually split into patches and game-theoretic methods are used to find optimal patch distributions at every instant. However, populations in the real world interact in continuous space, and the assumption of decisions based on perfect information is a large simplification. Here, we develop a method to study population dynamics for interacting populations, distributed optimally in continuous space. A continuous setting allows us to model bounded rationality, and its impact on population dynamics. This is made possible by our numerical advances in solving multiplayer games in continuous space. Our approach hinges on reformulating the instantaneous game, applying an advanced discretization method and modern optimization software to solve it. We apply the method to an idealized case involving the population dynamics and vertical distribution of forage fish preying on copepods. Incorporating continuous space and time, we can model the seasonal variation in the migration, separating the effects of light and population numbers. We arrive at qualitative agreement with empirical findings. Including bounded rationality gives rise to spatial distributions corresponding to reality, while the population dynamics for bounded rationality and complete rationality are equivalent. Our approach is general, and can easily be used for complex ecosystems.

Cell division is a necessity of life which can be either mitotic or amitotic. While both are fundamental, amitosis is sometimes considered a relic of little importance in biology. Nevertheless, eukaryotes often have polyploid cells, including cancer cells, which may divide amitotically. To understand how amitosis ensures the completion of cell division, we turn to the macronuclei of ciliates. The grand scheme governing the proliferation of the macronuclei of ciliate cells, which involves chromosomal replication and amitosis, is currently unknown, which is crucial for developing population genetics model of ciliate populations. Using a novel model that encompasses a wide range of mechanisms together with experimental data of the composition of mating types at different stages derived from a single karyonide of Tetrahymena thermophila, we show that the chromosomal replication of the macronucleus has a strong head-start effect, with only about five copies of chromosomes replicated at a time and persistent reuse of the chromosomes involved in the early replication. Furthermore the fission of a fully grown macronucleus is non-random with regard to chromosome composition, with a strong tendency to push chromosomes and their replications to the same daughter cell.

We study the effect of variability in payoffs on the evolution of cooperation ($C$) against defection ($D$) in multi-player games in a finite well-mixed population. We show that an increase in the covariance between any two payoffs to $D$, or a decrease in the covariance between any two payoffs to $C$, increases the probability of ultimate fixation of $C$ when represented once, and decreases the corresponding fixation probability for $D$. This is also the case with an increase in the covariance between any payoff to $C$ and any payoff to $D$ if and only if the sum of the numbers of $C$-players in the group associated with these payoffs is large enough compared to the group size. In classical social dilemmas with random cost and benefit for cooperation, the evolution of $C$ is more likely to occur if the variances of the cost and benefit, as well as the group size, are small, while the covariance between cost and benefit is large.

Inbreeding results from the mating of related individuals and has negative consequences because it brings together deleterious variants in one individual. Genomic estimates of the inbreeding coefficients are preferred to pedigree-based estimators as they measure the realized inbreeding levels and they are more robust to pedigree errors. Several methods identifying homozygous-by-descent (HBD) segments with hidden Markov models (HMM) have been recently developed and are particularly valuable when the information is degraded or heterogeneous (e.g., low-fold sequencing, low marker density, heterogeneous genotype quality or variable marker spacing). We previously developed a multiple HBD class HMM where HBD segments are classified in different groups based on their length (e.g., recent versus old HBD segments) but we recently observed that for high inbreeding levels with many HBD segments, the estimated contributions might be biased towards more recent classes (i.e., associated with large HBD segments) although the overall estimated level of inbreeding remained unbiased. We herein propose a new model in which the HBD classification is modelled in successive nested levels with decreasing expected HBD segment lengths, the underlying exponential rates being directly related to the number of generations to the common ancestor. The non-HBD classes are now modelled as a mixture of HBD segments from later generations and shorter non-HBD segments (i.e., both with higher rates). The new model has improved statistical properties and performs better on simulated data compared to our previous version. We also show that the parameters of the model are easier to interpret and that the model is more robust to the choice of the number of classes. Overall, the new model results in an improved partitioning of inbreeding in different HBD classes and should be preferred.