Theoretical Population Biology最新文献

We consider the dynamics of a collection of $n>1$ populations in which each population has its own rate of growth or decay, fixed in continuous time, and migrants may flow from one population to another over a fixed network, at a rate, fixed over time, times the size of the sending population. This model is represented by an ordinary linear differential equation of dimension $n$ with constant coefficients arrayed in an essentially nonnegative matrix. This paper identifies conditions on the parameters of the model (specifically, conditions on the eigenvalues and eigenvectors) under which the variance of the $n$ population sizes at a given time is asymptotically (as time increases) proportional to a power of the mean of the population sizes at that given time. A power-law variance function is known in ecology as Taylor’s Law and in physics as fluctuation scaling. Among other results, we show that Taylor’s Law holds asymptotically, with variance asymptotically proportional to the mean squared, on an open dense subset of the class of models considered here.

Plasmids may carry genes coding for beneficial traits and thus contribute to adaptation of bacterial populations to environmental stress. Conjugative plasmids can horizontally transfer between cells, which a priori facilitates the spread of adaptive alleles. However, if the potential recipient cell is already colonized by another incompatible plasmid, successful transfer may be prevented. Competition between plasmids can thus limit horizontal transfer. Previous modeling has indeed shown that evolutionary rescue by a conjugative plasmid is hampered by incompatible resident plasmids in the population. If the rescue plasmid is a mutant variant of the resident plasmid, both plasmids transfer at the same rates. A high conjugation rate then has two, potentially opposing, effects – a direct positive effect on spread of the rescue plasmid and an increase in the fraction of resident plasmid cells. This raises the question whether a high conjugation rate always benefits evolutionary rescue. In this article, we systematically analyze three models of increasing complexity to disentangle the benefits and limits of increasing horizontal gene transfer in the presence of plasmid competition and plasmid costs. We find that the net effect can be positive or negative and that the optimal transfer rate is thus not always the highest one. These results can contribute to our understanding of the many facets of plasmid-driven adaptation and the wide range of transfer rates observed in nature.

Recombination often concentrates in small regions called recombination hotspots where recombination is much higher than the genome’s average. In many vertebrates, including humans, gene PRDM9 specifies which DNA motifs will be the target for breaks that initiate recombination, ultimately determining the location of recombination hotspots. Because the sequence that breaks (allowing recombination) is converted into the sequence that does not break (preventing recombination), the latter sequence is over-transmitted to future generations and recombination hotspots are self-destructive. Given their self-destructive nature, recombination hotspots should eventually become extinct in genomes where they are found. While empirical evidence shows that individual hotspots do become inactive over time (die), hotspots are abundant in many vertebrates: a contradiction called the Recombination Hotspot Paradox. What saves recombination hotspots from their foretold extinction? Here we formulate a co-evolutionary model of the interaction among sequence-specific gene conversion, fertility selection, and recurrent mutation. We find that allelic frequencies oscillate leading to stable limit cycles. From a biological perspective this means that when fertility selection is weaker than gene conversion, it cannot stop individual hotspots from dying but can save them from extinction by driving their re-activation (resuscitation). In our model, mutation balances death and resuscitation of hotspots, thus maintaining their number over evolutionary time. Interestingly, we find that multiple alleles result in oscillations that are chaotic and multiple targets in oscillations that are asynchronous between targets thus helping to maintain the average genomic recombination probability constant. Furthermore, we find that the level of expression of PRDM9 should control for the fraction of targets that are hotspots and the overall temperature of the genome. Therefore, our co-evolutionary model improves our understanding of how hotspots may be replaced, thus contributing to solve the Recombination Hotspot Paradox. From a more applied perspective our work provides testable predictions regarding the relation between mutation probability and fertility selection with life expectancy of hotspots.

Many species that are birthed in one location and become reproductive in another location can be treated as if in a one-dimensional habitat where dispersal is biased downstream. One example of such is planktonic larvae that disperse in coastal oceans, rivers, and streams. In these habitats, the dynamics of the dispersal are dominated by the movement of offspring in one direction and the distance between parents and offspring in the other direction does not matter. We study an idealized species with non-overlapping generations in a finite linear habitat that has no larval input from outside of the habitat and is therefore isolated from other populations. The most non-realistic assumption that we make is that there are non-overlapping generations, and this is an assumption to be considered in future work. We find that a biased dispersal in the habitat reduces the average time to the most recent common ancestor and causes the average location of the most recent common ancestor to move from the center of the habitat to the upstream edge of the habitat. Due to the decrease in the time to the most recent common ancestor and the shift of the average location to the upstream edge, the effective population size (N${}_e$) no longer depends on the census size and is dependent on the dispersal statistics. We determine the average time and location of the most recent common ancestor as a function of the larval dispersal statistics. The location of the most recent common ancestor becomes independent of the length of the habitat and is only dependent on the location of the upstream edge and the larval dispersal statistics.

The evolution of a cultural trait may be affected by niche construction, or changes in the selective environment of that trait due to the inheritance of other cultural traits that make up a cultural background. This study investigates the evolution of a cultural trait, such as the acceptance of the idea of contraception, that is both vertically and horizontally transmitted within a homogeneous social network. Individuals may conform to the norm, and adopters of the trait have fewer progeny than others. In addition, adoption of this trait is affected by a vertically transmitted aspect of the cultural background, such as the preference for high or low levels of education. Our model shows that such cultural niche construction can facilitate the spread of traits with low Darwinian fitness while providing an environment that counteracts conformity to norms. In addition, niche construction can facilitate the ‘demographic transition’ by making reduced fertility socially accepted.

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.