Theoretical Population Biology最新文献

Given a labeled tree topology $t$, consider a population $P$ of $k$ leaves chosen among those of $t$. The clade of $P$ is the minimal subtree of $t$ containing $P$ and its size is given by the number of leaves in the clade. When $t$ is selected under the Yule or uniform distribution among the labeled topologies of size $n$, we study the “clade size” random variable determining closed formulas for its probability mass function, its mean, and its variance. Our calculations show that for large $n$ the clade size tends to be smaller under the uniform model than under the Yule model, with a larger variability in the first scenario for values of $k\ge 5$. We apply our probability formulas to investigate set-theoretic relationships between the clades of two populations in a random tree, determining how likely one clade is contained in or it is equal to the other. Our study relates to earlier calculations for the probability that under the Yule model the clade size of $P$ equals the size of $P$ – that is, the population $P$ forms a monophyletic group – and extends known results for the probability that the minimal (non-trivial) clade containing a random taxon has a given size.

Modern molecular technologies have revolutionized our understanding of bacterial epidemiology, but reported data across studies and different geographic endemic settings remain under-integrated in common theoretical frameworks. Pneumococcus serotype co-colonization, caused by the polymorphic bacteria Streptococcus pneumoniae, has been increasingly investigated and reported in recent years. While the global genomic diversity and serotype distribution of S. pneumoniae have been well-characterized, there is limited information on how co-colonization patterns vary globally, critical for understanding the evolution and transmission dynamics of the bacteria. Gathering a rich dataset of cross-sectional pneumococcal colonization studies in the literature, we quantified patterns of transmission intensity and co-colonization prevalence variation in children populations across 17 geographic locations. Linking these data to an SIS model with cocolonization under the assumption of quasi-neutrality among multiple interacting strains, our analysis reveals strong patterns of negative co-variation between transmission intensity ($R_0$) and susceptibility to co-colonization ($k$). In line with expectations from the stress-gradient-hypothesis in ecology (SGH), pneumococcus serotypes appear to compete more in co-colonization in high-transmission settings and compete less in low-transmission settings, a trade-off which ultimately leads to a conserved ratio of single to co-colonization $\mu =1/(R_0-1)k$. From the mathematical model’s behavior, such conservation suggests preservation of ‘stability-diversity-complexity’ regimes in coexistence of similar co-colonizing strains. We find no major differences in serotype compositions across studies, pointing to adaptation of the same set of serotypes across variable environments as an explanation for their differential interaction in different transmission settings. Our work highlights that the understanding of transmission patterns of Streptococcus pneumoniae from global scale epidemiological data can benefit from simple analytical approaches that account for quasi-neutrality among strains, co-colonization, as well as variable environmental adaptation.

In this paper, we investigate the consequences of dormancy in the ‘rare mutation’ and ‘large population’ regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second ‘small mutations’ limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011).

The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the ‘speed of adaptation’ of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

Mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. The most seminal example are the Wright–Fisher diffusion and the Kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. As well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. We employ the so-called Bernoulli factory – a celebrated tool in simulation-based computing – to derive duality relations for broad classes of genetics models. As concrete examples, we present Wright–Fisher diffusions with general drift functions, and Allen–Cahn equations with general, nonlinear forcing terms. The drift and forcing functions can be interpreted as the action of frequency-dependent selection. To our knowledge, this work is the first time a connection has been drawn between Bernoulli factories and duality in models of population genetics.

We develop a spatially realistic model of mutualistic metacommunities that exploits the joint structure of spatial and interaction networks. Assuming that all species have the same colonisation and extinction parameters, this model exhibits a sharp transition between stable non-null equilibrium states and a global extinction state. This behaviour allows defining a threshold on colonisation/extinction parameters for the long-term metacommunity persistence. This threshold, the ‘metacommunity capacity’, extends the metapopulation capacity concept and can be calculated from the spatial and interaction networks without needing to simulate the whole dynamics. In several applications we illustrate how the joint structure of the spatial and the interaction networks affects metacommunity capacity. It results that a weakly modular spatial network and a power-law degree distribution of the interaction network provide the most favourable configuration for the long-term persistence of a mutualistic metacommunity. Our model that encodes several explicit ecological assumptions should pave the way for a larger exploration of spatially realistic metacommunity models involving multiple interaction types.

Although cooperative hunting is widespread among animals, its benefits are unclear. At low frequencies, cooperative hunting may allow predators to escape competition and access bigger prey that could not be caught by a lone cooperative predator. Cooperative hunting is a more successful strategy when it is common, but its spread can result in overhunting big prey, which may have a lower per-capita growth rate than small prey. We construct a one-predator species, two-prey species model in which predators either learn to hunt small prey alone or learn to hunt big prey cooperatively. Predators first learn vertically from parents, then horizontally (i.e. socially) from random individuals or siblings. After horizontal transmission, they hunt with their learning partner if both are cooperative, and otherwise they hunt alone. Cooperative hunting cannot evolve when initially rare unless predators (a) interact with siblings, or (b) horizontally transmit the cooperative behavior to potential hunting partners. Whereas competition for small prey favors cooperative hunting when this cooperation is initially rare, the frequency of cooperative hunting cannot reach 100% unless big prey is abundant. Furthermore, a mutant that increases horizontal learning can invade if cooperative hunting is present, but not at 100%, because horizontal learning allows pairs of predators to have the same strategy. Our results reveal that the interactions between prey availability, social learning, and degree of cooperation among predators may have important effects on ecosystems.

Consider the problem of estimating the branch lengths in a symmetric 2-state substitution model with a known topology and a general, clock-like or star-shaped tree with three leaves. We show that the maximum likelihood estimates are analytically tractable and can be obtained from pairwise sequence comparisons. Furthermore, we demonstrate that this property does not generalize to larger state spaces, more complex models or larger trees. Our arguments are based on an enumeration of the free parameters of the model and the dimension of the minimal sufficient data vector. Our interest in this problem arose from discussions with our former colleague Freddy Bugge Christiansen.

Mathematical models of conformity and anti-conformity have commonly included a set of simplifying assumptions. For example, (1) there are $m=2$ cultural variants in the population, (2) naive individuals observe the cultural variants of $n=3$ adult “role models,” and (3) individuals’ levels of conformity or anti-conformity do not change over time. Three recent theoretical papers have shown that departures from each of these assumptions can produce new population dynamics. Here, we explore cases in which multiple, or all, of these assumptions are violated simultaneously: namely, in a population with $m$ variants of a trait where conformity (or anti-conformity) occurs with respect to $n$ role models, we study a model in which the conformity rates at each generation are random variables that are independent of the variant frequencies at that generation. For this model a class of symmetric constant equilibria exist, and it is possible that all of these equilibria are simultaneously stochastically locally stable. In such cases, the effect of initial conditions on subsequent evolutionary trajectories becomes very complicated.