Theoretical Population Biology最新文献

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.

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

Health perceptions and health-related behaviors can change at the population level as cultures evolve. In the last decade, despite the proven efficacy of vaccines, the developed world has seen a resurgence of vaccine-preventable diseases (VPDs) such as measles, pertussis, and polio. Vaccine hesitancy, which is influenced by historical, political, and socio-cultural forces, is believed to be a primary factor responsible for decreasing vaccine coverage, thereby increasing the risk and occurrence of VPD outbreaks. Behavior change models have been increasingly employed to understand disease dynamics and intervention effectiveness. However, since health behaviors are culturally influenced, it is valuable to examine them within a cultural evolution context. Here, using a mathematical modeling framework, we explore the effects of cultural evolution on vaccine hesitancy and vaccination behavior. With this model, we shed light on facets of cultural evolution (vertical transmission, community influences, homophily, etc.) that promote the spread of vaccine hesitancy, ultimately affecting levels of vaccination coverage and VPD outbreak risk in a population. In addition, we present our model as a generalizable framework for exploring cultural evolution when humans’ beliefs influence, but do not strictly dictate, their behaviors. This model offers a means of exploring how parents’ potentially conflicting beliefs and cultural traits could affect their children’s health and fitness. We show that vaccine confidence and vaccine-conferred benefits can both be driving forces of vaccine coverage. We also demonstrate that an assortative preference among vaccine-hesitant individuals can lead to increased vaccine hesitancy and lower vaccine coverage.

We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, $1-\varepsilon >0$ or $-(1+\varepsilon )<0$. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the second half of the period, that we refer as the $(\pm 1)$ model. In the absence of migration, the population goes to 0 exponentially fast in each environment. In this paper, we show that, when the period is sufficiently large, a small dispersal between the two patches is able to produce a very high positive exponential growth rate for the whole population, a phenomena called inflation. We prove in particular that the threshold of the dispersal rate at which the inflation appears is exponentially small with the period. We show that inflation is robust to random perturbation, by considering a model where the values of the growth rate in each patch are switched at random times: we prove that inflation occurs for low switching rate and small dispersal. We also consider another stochastic model, where after each period of time $T$, the values of the growth rates in each patch is chosen randomly, independently from the other patch and from the past. Finally, we provide some extensions to more complicated models, especially epidemiological and density dependent models.

Many traits in populations are well understood as being Mendelian effects at single loci or additive polygenic effects across numerous loci. However, there are important phenomena and traits that are intermediate between these two extremes and are known as oligogenic traits. Here we investigate digenic, or two-locus, traits and how their frequencies in populations are affected by non-random mating, specifically inbreeding, linkage disequilibrium, and selection. These effects are examined both separately and in combination to demonstrate how many digenic traits, especially double homozygous ones, can show significant, sometimes unexpected, changes in population frequency with inbreeding, linkage, and linkage disequilibrium. The effects of selection on deleterious digenic traits are also detailed. These results are applied to both digenic traits of medical significance as well as measuring inbreeding in natural populations.