Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their offspring. We use a biparental Moran model, which is characterized by its fixed number N of individuals. We fix an individual and consider the proportions of the genomes of all individuals living  n time steps later, that come from this individual. When n goes to infinity, these proportions all converge almost surely towards the same random variable. When N then goes to infinity, this random variable multiplied by N (i.e. the stationary weight of any ancestor in the whole population) converges in law towards the mixture of a Dirac measure in 0 and an exponential law with parameter 1/2, and the weights of several given ancestors are independent. This gives an explicit formula for the limiting (deterministic) distribution of all ancestors' weights.

This paper establishes the global attractivity of a positive constant equilibrium of a nonlocal and time-delayed diffusive malaria model in a homogeneous case. The same problem was achieved in a recent paper (Lou and Zhao in J Math Biol 62:543-568, 2011) by using the fluctuation method, but with a sufficient condition that the disease will become stable requires a sufficiently large basic reproduction number [Formula: see text]. The present study is devoted to remove the sufficient condition by utilizing an appropriate Lyapunov functional and shows that the disease will become stable when [Formula: see text] is exactly greater than one, which remarkably improves the known results in Lou and Zhao (2011).

The distribution of ticks is essentially determined by the presence of climatic conditions and ecological contexts suitable for their survival and development. We build a model that explicitly takes into account each physiological state through a system of infinite differential equations where tick population density are structured on an infinite discrete set. We suppose that intrastage development process is temperature dependent (Arrhenius temperatures function) and that larvae hatching and adult mortality are temperature and water vapor deficit dependent. We analysed mathematically the model and have explicit the [Formula: see text] of the tick population.

We derive a stochastic SIS pairwise model by considering the change of the variables of this system caused by an event. Based on approximations, we construct a low-dimensional deterministic system that can be used to describe the epidemic spread on a regular network. The mathematical treatment of the model yields explicit expressions for the variances of each variable at equilibrium. Then a comparison between the stochastic pairwise model and the stochastic mean-field SIS model is performed to indicate the effect of network structure. We find that the variances of the prevalence of infection for these two models are almost equal when the number of neighbors of every individual is large. Furthermore, approximations for the quasi-stationary distribution of the number of infected individuals and the expected time to extinction starting in quasi-stationary are derived. We analyze the approximations for the critical number of neighbors and the persistence threshold based on the stochastic model. The approximate performance is then examined by numerical and stochastic simulations. Moreover, during the early development phase, the temporal variance of the infection is also obtained. The simulations show that our analytical results are asymptotically accurate and reasonable.

Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to real-world "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define a biological and mathematical relationship between implicit and explicit control, and we provide mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow the optimal control and basic reproduction number analyses typically utilized in implicit control modeling to be interpreted directly in terms of real-world actions and real-world monetary costs. Our methods reveal that only certain sub-classes of explicit control protocols are able to be represented as implicit controls, and that implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple explicit controls have negligible effects on population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

We present a unified framework for modelling genomes and their rearrangements in a genome algebra, as elements that simultaneously incorporate all physical symmetries. Building on previous work utilising the group algebra of the symmetric group, we explicitly construct the genome algebra for the case of unsigned circular genomes with dihedral symmetry and show that the maximum likelihood estimate (MLE) of genome rearrangement distance can be validly and more efficiently performed in this setting. We then construct the genome algebra for a more general case, that is, for genomes that may be represented by elements of an arbitrary group and symmetry group, and show that the MLE computations can be performed entirely within this framework. There is no prescribed model in this framework; that is, it allows any choice of rearrangements that preserve the set of regions, along with arbitrary weights. Further, since the likelihood function is built from path probabilities-a generalisation of path counts-the framework may be utilised for any distance measure that is based on path probabilities.

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks that describe such complex processes have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of phylogenetic networks from empirical data.

This paper deals with a system of reaction-diffusion-advection equations for a generalist predator-prey model in open advective environments, subject to an unidirectional flow. In contrast to the specialist predator-prey model, the dynamics of this system is more complex. It turns out that there exist some critical advection rates and predation rates, which classify the global dynamics of the generalist predator-prey system into three or four scenarios: (1) coexistence; (2) persistence of prey only; (3) persistence of predators only; and (4) extinction of both species. Moreover, the results reveal significant differences between the specialist predator-prey system and the generalist predator-prey system, including the evolution of the critical predation rates with respect to the ratio of the flow speeds; the take-over of the generalist predator; and the reduction in parameter range for the persistence of prey species alone. These findings may have important biological implications on the invasion of generalist predators in open advective environments.

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. That is, whether parameters can be uniquely determined from perfect or realistic data in theory and practice. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

Evolutionary models used for describing molecular sequence variation suppose that at a non-recombining genomic segment, sequences share ancestry that can be represented as a genealogy-a rooted, binary, timed tree, with tips corresponding to individual sequences. Under the infinitely-many-sites mutation model, mutations are randomly superimposed along the branches of the genealogy, so that every mutation occurs at a chromosomal site that has not previously mutated; if a mutation occurs at an interior branch, then all individuals descending from that branch carry the mutation. The implication is that observed patterns of molecular variation from this model impose combinatorial constraints on the hidden state space of genealogies. In particular, observed molecular variation can be represented in the form of a perfect phylogeny, a tree structure that fully encodes the mutational differences among sequences. For a sample of n sequences, a perfect phylogeny might not possess n distinct leaves, and hence might be compatible with many possible binary tree structures that could describe the evolutionary relationships among the n sequences. Here, we investigate enumerative properties of the set of binary ranked and unranked tree shapes that are compatible with a perfect phylogeny, and hence, the binary ranked and unranked tree shapes conditioned on an observed pattern of mutations under the infinitely-many-sites mutation model. We provide a recursive enumeration of these shapes. We consider both perfect phylogenies that can be represented as binary and those that are multifurcating. The results have implications for computational aspects of the statistical inference of evolutionary parameters that underlie sets of molecular sequences.

In iterated games, a player can unilaterally exert influence over the outcome through a careful choice of strategy. A powerful class of such "payoff control" strategies was discovered by Press and Dyson (2012). Their so-called "zero-determinant" (ZD) strategies allow a player to unilaterally enforce a linear relationship between both players' payoffs. It was subsequently shown by Chen and Zinger (2014) that when the slope of this linear relationship is positive, ZD strategies are robustly effective against a selfishly optimizing co-player, in that all adapting paths of the selfish player lead to the maximal payoffs for both players (at least when there are certain restrictions on the game parameters). In this paper, we investigate the efficacy of selfish learning against a fixed player in more general settings, for both ZD and non-ZD strategies. We first prove that in any symmetric 2[Formula: see text]2 game, the selfish player's final strategy must be of a certain form and cannot be fully stochastic. We then show that there are prisoner's dilemma interactions for which selfish optimization does not always lead to maximal payoffs against fixed ZD strategies with positive slope. We give examples of selfish adapting paths that lead to locally but not globally optimal payoffs, undermining the robustness of payoff control strategies. For non-ZD strategies, these pathologies arise regardless of the original restrictions on the game parameters. Our results illuminate the difficulty of implementing robust payoff control and selfish optimization, even in the simplest context of playing against a fixed strategy.