Evolutionary game theory is a powerful mathematical framework to study how phenotypes evolve by natural selection. Both birth and death are key in classic models in evolutionary games. The conflict between the two is fundamental in life history theory. The conflict between birth and death has been shown to change the evolutionary outcome for continuous traits. However, it is not clear how the conflict reshapes the evolutionary outcome for discrete strategies. An allocation model is proposed, in which part of the payoff is mapped to reproduction and the rest is mapped to illness. For non-evolving allocation, it is proved that the allocation does not change the fixation probability if and only if the illness is an inverse exponential function and the product of reproduction function and illness function is a constant. The necessary and sufficient condition implies that the allocation dramatically alters the evolutionary stability for a wide class of evolutionary processes. This is also verified by alternative construction proofs and numerical examples. Furthermore, the illness and reproduction function also ensures that every allocation is a neutral stable regime, if the allocation evolves to maximize the invasion probability. A deviation can lead to a non-trivial evolutionary branching. These results explicitly show that the reproduction and illness functions are restrictive to ensure the invariance of evolutionary outcome. Thus it implies that the demographic and life history need to be considered together to understand patterns of evolutionary dynamics.

Dispersal-induced growth (DIG) occurs when several populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect, and the corresponding conditions on the parameters involved.

Erratum in J Math Biol. 2023 Jan 10;86(2):27.

Assuming that there are multiple batches of sterile males reared and released during the maturation period, we derive a switching delay differential model to study the fate of wild females under an impulsive and periodic release of sterile males. For the release magnitude of each batch c, we find two threshold values [Formula: see text] and [Formula: see text], and prove that when [Formula: see text], the model admits exactly two periodic solutions, among which one is asymptotically stable and the other is unstable. The trivial equilibrium, corresponding to the elimination of wild females, is locally asymptotically stable, and it becomes globally asymptotically stable when [Formula: see text]. One key step is to prove that every solution is sandwiched between two "good" solutions.

methods seek to infer a species tree from a set of gene trees. A desirable property of such methods is that of statistical consistency; that is, the probability of inferring the wrong species tree (the error probability) tends to 0 as the number of input gene trees becomes large. A popular paradigm is to infer a species tree that agrees with the maximum number of quartets from the input set of gene trees; this has been proved to be statistically consistent under several models of gene evolution. In this paper, we study the asymptotic behaviour of the error probability of such methods in this limit, and show that it decays exponentially. For a 4-taxon species tree, we derive a closed form for the asymptotic behaviour in terms of the probability that the gene evolution process produces the correct topology. We also derive bounds for the sample complexity (the number of gene trees required to infer the true species tree with a given probability), which outperform existing bounds. We then extend our results to bounds for the asymptotic behaviour of the error probability for any species tree, and compare these to the true error probability for some model species trees using simulations.

In this paper, we focus on the global dynamics of a multiscale hepatitis C virus model. The model takes into account the evolution of the virus in cells and RNA. For the model, we establish the globally asymptotical stability of both infection-free and infected equilibria. We first give the basic reproduction number [Formula: see text] of the model, and then find that the system holds infected equilibrium when [Formula: see text]. Using eigenvalue analysis, Lyapunov functional, persistence theory and so on, it is proved that infection-free and infected equilibria are globally asymptotically stable when [Formula: see text] and [Formula: see text], respectively. Thus, extinction and persistence of viruses in cells are theoretically judged. Finally, we show our theoretical results by means of numerical simulation.

Although ecological networks are typically constructed based on a single type of interaction, e.g. trophic interactions in a food web, a more complete picture of ecosystem composition and functioning arises from merging networks of multiple interaction types. In this work, we consider tripartite networks constructed by merging two bipartite networks, one mutualistic and one antagonistic. Taking the interactions within each sub-network to be distributed randomly, we consider the stability of the dynamics of the network based on the spectrum of its community matrix. In the asymptotic limit of a large number of species, we show that the spectrum undergoes an eigenvalue phase transition, which leads to an abrupt destabilisation of the network as the ratio of mutualists to antagonists is increased. We also derive results that show how this transition is manifest in networks of finite size, as well as when disorder is introduced in the segregation of the two interaction types. Our random-matrix results will serve as a baseline for understanding the behaviour of merged networks with more realistic structures and/or more detailed dynamics.

We considered an SIS functional partial differential model cooperated with spatial heterogeneity and lag effect of media impact. The wellposedness including existence and uniqueness of the solution was proved. We defined the basic reproduction number and investigated the threshold dynamics of the model, and discussed the asymptotic behavior and monotonicity of the basic reproduction number associated with the diffusion rate. The local and global Hopf bifurcation at the endemic steady state was investigated theoretically and numerically. There exists numerical cases showing that the larger the number of basic reproduction number, the smaller the final epidemic size. The meaningful conclusion generalizes the previous conclusion of ordinary differential equation.