Theoretical Population Biology最新文献

A population experiencing habitat loss can avoid extinction by undergoing genetic adaptation—a process known as evolutionary rescue. Here we analytically approximate the probability of evolutionary rescue via a niche-constructing mutation that allows carriers to convert a novel, unfavorable reproductive habitat to a favorable state at a cost to their fecundity. We analyze competition between mutants and non-niche-constructing wild types, who ultimately require the constructed habitats to reproduce. We find that over-exploitation of the constructed habitats by wild types can generate damped oscillations in population size shortly after mutant invasion, thereby decreasing the probability of rescue. Such post-invasion extinction is less probable when construction is infrequent, habitat loss is common, the reproductive environment is large, or the population’s carrying capacity is small. Under these conditions, wild types are less likely to encounter the constructed habitats and, consequently, mutants are more likely to fix. These results suggest that, without a mechanism that deters wild type inheritance of the constructed habitats, a population undergoing rescue via niche construction may remain prone to short-timescale extinction despite successful mutant invasion.

Research shows that geographic disparities in life expectancy between leading and lagging states are increasing over time while racial disparities between Black and White Americans have been going down. In the 65+ age strata morbidity is the most common cause of death, making differences in morbidity and associated adverse health-related outcomes between advantaged and disadvantaged groups an important aspect of disparities in life expectancy at age 65 (LE65). In this study, we used Pollard’s decomposition to evaluate the disease-related contributions to disparities in LE65 for two types of data with distinctly differing structures: population/registry and administrative claims. To do so, we analyzed Pollard’s integral, which is exact by construction, and developed exact analytic solutions for both types of data without the need for numerical integration. The solutions are broadly applicable and easily implemented. Applying these solutions, we found that the largest relative contributions to geographic disparities in LE65 were chronic lower respiratory diseases, circulatory diseases, and lung cancer; and, to racial disparities: arterial hypertension, diabetes mellitus, and cerebrovascular diseases. Overall, the increase in LE65 observed over 1998–2005 and 2010–2017 was primarily due to a reduction in the contributions of acute and chronic ischemic diseases; this was partially offset by increased contributions of diseases of the nervous system including dementia and Alzheimer’s disease.

Dispersal can enable access to resources in new locations. Consequently, traits that govern dispersal probability and dispersal distance may impact an individual’s ability to acquire resources. However, spatial variation in the quality or quantity of resources may mediate potential adaptive benefits of novel dispersal traits. Ecological traits (i.e., those that determine how an individual processes resources) will also, by definition, affect how an individual interacts with the resource landscape. In a spatially heterogeneous environment, this creates potential for evolutionary feedbacks between dispersal-related traits and ecological traits. For example, dispersal may introduce individuals to novel resources, at which point there may be selection for local adaptation of ecological traits. Conversely, an individual’s ability to utilize different resource types may determine how dispersal impacts fitness. Here, we develop an individual-based model to investigate co-evolution of dispersal and ecological traits in a landscape where multiple resources vary independently across space. We find that: (1) resource specialists can emerge and tend to evolve dispersal strategies suited to the structure of their preferred resource type and (2) generalists, when they emerge, tend to possess intermediate dispersal strategies. Lastly, we note that the effect of dispersal on the evolution of the ecological trait is weaker than vice versa and, as a result, appreciable heterogeneity in the abundance of resources across a landscape will likely obscure a signal of co-evolution.

Our understanding of aposematism (the conspicuous signalling of a defence for the deterrence of predators) has advanced notably since its first observation in the late nineteenth century. Indeed, it extends the scope of a well-established game-theoretical model of this very same process both from the analytical standpoint (by considering regimes of varying background mortality and colony size) and from the practical standpoint (by assessing its efficacy and limitations in predicting the evolution of prey traits in finite simulated populations). The nature of the manuscript at hand is more mathematical and its aim is two-fold: first, to determine the relationship between evolutionarily stable levels of defence and signal strength under various regimes of background mortality and colony size. Second, to compare these predictions with simulations of finite prey populations that are subject to random local mutation. We compare the roles of absolute resident fitness, mutant fitness and stochasticity in the evolution of prey traits and discuss the importance of population size in the above.

Multiple-merger coalescents, also known as $\Lambda$-coalescents, have been used to describe the genealogy of populations that have a skewed offspring distribution or that undergo strong selection. Inferring the characteristic measure $\Lambda$, which describes the rates of the multiple-merger events, is key to understand these processes. So far, most inference methods only work for some particular families of $\Lambda$-coalescents that are described by only one parameter, but not for more general models. This article is devoted to the construction of a non-parametric estimator of the density of $\Lambda$ that is based on the observation at a single time of the so-called Site Frequency Spectrum (SFS), which describes the allelic frequencies in a present population sample. First, we produce estimates of the multiple-merger rates by solving a linear system, whose coefficients are obtained by appropriately subsampling the SFS. Then, we use a technique that aggregates the information extracted from the previous step through a kernel type of re-construction to give a non-parametric estimation of the measure $\Lambda$. We give a consistency result of this estimator under mild conditions on the behavior of $\Lambda$ around 0. We also show some numerical examples of how our method performs.

Cooperation is considered a mysterious phenomenon from the perspective of adaptive evolution. However, if an individual can separate from an unsatisfactory group and join another, then this can facilitate positive assortment between cooperative types and promote the evolution of cooperation. What kind of disbandment rule most facilitates the evolution of cooperation? A previous study investigated exogenous disbandment rules and showed that, when games are played between two players, a rule where heterogeneous groups disband facilitates the evolution of cooperation. However, in groups of more than two individuals, a rule strictly requiring homogeneity applied if and only if the expected number of rounds played in a group was greater than some critical value. How large is the critical value? In this study, we make a mathematical analysis using evolutionary game theory. Our results show that the critical number of rounds increases greatly as the group size increases. Consequently, for species with large group sizes, e.g., Homo sapiens, under plausible parameter values, the strict homogeneity rule is unlikely to facilitate the evolution of cooperation. We find instead that a disbandment rule that requires a threshold level of homogeneity outperformed the strict homogeneity rule. Furthermore, we calculate the position of internal equilibria at which cooperators and defectors coexist and show that the initial evolution of cooperation is most encouraged when cooperators are tolerant (intolerant) of defectors if the benefit-to-cost ratio is large (small).

We developed a simple linear stochastic model for Dalbulus maidis dependent exclusively on temperature, whose parameters were determined from published field and laboratory studies performed at different temperatures. This model takes into account the principal stages and events of the life cycle of this pest, which is vector of maize diseases. We implemented the effect of distributed delays or Linear Chain Trick (LCT) considering a fixed number of sub-stages for egg and nymph stages of Dalbulus maidis in order to accurately represent what is observed in nature. A sensitivity analysis allows us to observe that the speed of the dynamics is sensitive to changes in the development rates, but not to the longevity of each stage or the fecundity, which almost exclusively affect insect abundance. We used our model to study its predictive and explanatory capacity considering a published experiment as a case study. Although the simulation results show a behavior qualitatively equivalent to that observed in the experimental results it is not possible to explain accurately the magnitude, nor the times in which the maximum abundances of second-generation nymphs and adults are reached. Therefore, we evaluated three possible scenarios for the insect that allow us to glimpse some of the advantages of having a computational model in order to find out what processes, taken into account in the model, may explain the differences observed between published experimental results and model results. The three proposed scenarios, based on variations in the parameterized rates of the model, can satisfactorily explain the experimental observations. We observed that in order to better simulate the experimental results it is not necessary to modify fecundity or mortality rates. However, it is necessary to accelerate the average development rates of our model by 20 to 40 %, compatible with extreme values of the rates close to the upper edges of the confidence bands of our parameterization rate curves, according to insects with faster development rates already reported in literature.

The Structured Coalescent was introduced to describe the coalescent process in spatially subdivided populations with migration. Here, we re-interpret migration routes of individuals in the original model as “migration routes” of single genes in tandemly arranged gene arrays. A gene copy may change its position within the array via unequal recombination. Hence, in a coalescent framework, two copies sampled from two chromosomes may coalesce only if they are at exactly homologous positions. Otherwise, one or multiple recombination events have to occur before they can coalesce, thereby increasing mean coalescence time and expected genetic diversity among the copies in a gene array.

We explicitly calculate the transition probabilities on these routes backward in time. We simulate the structured coalescent with migration and coalescence rates informed by the unequal recombination process of gene copies. With this novel interpretation of population structure models we determine coalescence times and expected genetic diversity in samples of orthologous and paralogous copies from a gene family. As a case study, we discuss the site frequency spectrum of a small gene family in the two scenarios of high and of no gene copy number variation among individuals. These examples underline the significance of our model, since standard test-statistics may lead to misinterpretations when analyzing sequence data of multi-copy genes due to their different expected genetic diversity.

Parentage exclusion probability is usually calculated to evaluate the informativeness of a set of markers for, and the statistical power of, a parentage analysis. Equations for parentage exclusion probability have been derived in various scenarios such as paternity exclusion when maternity is known or unknown or when candidate males are unrelated or loosely related (being from the same subpopulation) to the father. All previous work assumes a diploid species. Although marker-based parentage analyses have been conducted in haploidiploid species (such as ants, bees and wasps) for diploid offspring at the individual level or haploid offspring at the class level, rigorously derived formulations of parentage exclusion probability for haploid offspring at the individual level are lacking, which prevents the precise evaluation of the informativeness for and the statistical power of a parentage analysis. In this study we derive equations for the exclusion probability of maternity of a haploid male when multiple mother candidates (workers or queens) are unrelated or fullsibs to the mother. The usefulness of the equations is exemplified by numerical examples, and the results are discussed in the context of the study of worker reproductivity in eusocial haplodiploid species. The results are especially valuable for an optimal experimental design in determining sampling intensities (e.g. number of markers and number of individuals) to achieve satisfactory statistical power of a parentage analysis in investigating workers’ reproductivity in eusocial haplodiploid species.

Recombination is a powerful evolutionary process that shapes the genetic diversity observed in the populations of many species. Reconstructing genealogies in the presence of recombination from sequencing data is a very challenging problem, as this relies on mutations having occurred on the correct lineages in order to detect the recombination and resolve the ordering of coalescence events in the local trees. We investigate the probability of reconstructing the true topology of ancestral recombination graphs (ARGs) under the coalescent with recombination and gene conversion. We explore how sample size and mutation rate affect the inherent uncertainty in reconstructed ARGs, which sheds light on the theoretical limitations of ARG reconstruction methods. We illustrate our results using estimates of evolutionary rates for several organisms; in particular, we find that for parameter values that are realistic for SARS-CoV-2, the probability of reconstructing genealogies that are close to the truth is low.