Theoretical Population Biology最新文献

About 50 years ago, Keyfitz (1971) asked how much further a growing human population would increase if its fertility rate were immediately to be reduced to replacement level and remain there forever. The reason for demographic momentum is an age–structure inertia due to relatively many potential parents because of past high fertility. Although nobody expects such a miraculous reduction in reproductive behavior, a gradual decline in fertility in rapidly growing populations seems inevitable. As any delay in fertility decline to a stationary level leads to an increase in the momentum, it makes sense to think about the timing and the quantum of the reduction in reproduction. More specifically, we consider an intertemporal trade-off between costly pro- and anti-natalistic measures and the demographic momentum at the end of the planning period. This paper uses the McKendrick–von Foerster partial differential equation of age–structured population dynamics to study a sketched problem in a distributed parameter control framework. Among the results obtained by applying an appropriate extension of Pontryagin’s Maximum Principle are the following: (i) monotony of adaptation efforts to net reproduction rate and convex decrease/concave increase (if initial net reproduction rate exceeds 1/is below 1); and (ii) oscillating efforts and reproduction rate if, additionally, the size of the total population does not deviate from a fixed level.

Consider the diffusion process defined by the forward equation $u_t(t,x)=\frac{1}{2}{\left\{xu(t,x)\right\}}_{xx}-\alpha {\left\{xu(t,x)\right\}}_x$ for $t,x\ge 0$ and $-\infty <\alpha <\infty$, with an initial condition $u(0,x)=\delta (x-x_0)$. This equation was introduced and solved by Feller to model the growth of a population of independently reproducing individuals. We explore important coalescent processes related to Feller’s solution. For any $\alpha$ and $x_0>0$ we calculate the distribution of the random variable $A_n(s;t)$, defined as the finite number of ancestors at a time $s$ in the past of a sample of size $n$ taken from the infinite population of a Feller diffusion at a time $t$ since its initiation. In a subcritical diffusion we find the distribution of population and sample coalescent trees from time $t$ back, conditional on non-extinction as $t\to \infty$. In a supercritical diffusion we construct a coalescent tree which has a single founder and derive the distribution of coalescent times.

Cooperation usually becomes harder to sustain as groups become larger because incentives to shirk increase with the number of potential contributors to collective action. But is this always the case? Here we study a binary-action cooperative dilemma where a public good is provided as long as not more than a given number of players shirk from a costly cooperative task. We find that at the stable polymorphic equilibrium, which exists when the cost of cooperation is low enough, the probability of cooperating increases with group size and reaches a limit of one when the group size tends to infinity. Nevertheless, increasing the group size may increase or decrease the probability that the public good is provided at such an equilibrium, depending on the cost value. We also prove that the expected payoff to individuals at the stable polymorphic equilibrium (i.e., their fitness) decreases with group size. For low enough costs of cooperation, both the probability of provision of the public good and the expected payoff converge to positive values in the limit of large group sizes. However, we also find that the basin of attraction of the stable polymorphic equilibrium is a decreasing function of group size and shrinks to zero in the limit of very large groups. Overall, we demonstrate non-trivial comparative statics with respect to group size in an otherwise simple collective action problem.

By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for $r$, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

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.