Influence of Harvest on the Dynamics of Populations with Age and Sex Structures

The paper investigates influence of sex- and age-specific harvest on the dynamics of structured populations based on the mathematical model with discrete time. We assume birth rate depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by decreasing juvenile survival rate with growth of sex-age class sizes. The aim is to study the mechanisms of formation and evolution of dynamic modes for the exploited structured population models due to harvesting intensity. Conditions for sustainable development of the exploited population are received. Dynamic modes of the population models are studied. Influence of birth, survival, and self-regulation rates, the formation process of the mating pairs, and sex- and age-specific harvest on transitions between different dynamic modes are investigated. Sex-specific harvest of mature females or males will change the pair formation if the sex class, whose number of individuals is more, is exploited. Depending on values of the population parameters, the sex- and age-specific harvest (juveniles, mature females or males) can result in both damping of the oscillations, which stabilizes population dynamics, and the oscillation appearance, including two-year or quasiperiodic population fluctuations. The model of exploited population reveals the phenomenon of multistability, which is typical for a population without harvesting. The multistability is the result of complex bifurcations occurring due to both the system nonlinearity and the changing pair formation principle.

Mate limitation and sex ratio evolution

Sex ratio evolution has been one of the most successful areas of evolutionary theory. Pioneered by Düsing and Fisher under panmixia, and later extended by Hamilton to cover local mate competition (LMC), these models often assume, either implicitly or explicitly, that all females are fertilized. Here, we examine the effects of relaxing this assumption, under both panmictic and LMC models with diploid genetics. We revisit the question of the mathematical relationship between sex ratio and probability of fertilization, and use these results to model sex ratio evolution under risk of incomplete fertilization. We find that (i) under panmixia, mate limitation has no effect on the evolutionarily stable strategy (ESS) sex allocation; (ii) under LMC, mate limitation can make sex allocation less female-biased than under complete fertilization; (iii) contrary to what is occasionally stated, a significant fraction of daughters can remain unfertilized at the ESS in LMC with mate limitation; (iv) with a commonly used mating function, the fraction of unfertilized daughters can be quite large, and (v) with more realistic fertilization functions, the deviation becomes smaller. The models are presented in three equivalent forms: individual selection, kin selection and group selection. This serves as an example of the equivalence of the methods, while each approach has their own advantages. We discuss possible extensions of the model to haplodiploidy.

A Schistosomiasis Model with Mating Structure

A schistosomiasis model is proposed including single schistosomes, paired schistosomes, snails, and the latent period of infected snails. A reasonable sex ratio of schistosomes and the minimum mating function are considered. A threshold condition determining the stability of the system is given, and the stability of equilibrium for the model is shown. The impact of the latent period of infected snails on schistosomiasis transmission can be found through numerical simulations. Finally, preferable control strategies are obtained by sensitivity analyses. Killing snails may be the preferred control measure. If we choose chemotherapy, we should use some drugs which are sufficient for reducing egg-associated pathology, since paired schistosomes are mostly harmful to definitive hosts.

Two-Sex Branching Processes with Offspring and Mating in a Random Environment

We introduce a class of discrete-time two-sex branching processes where the offspring probability distribution and the mating function are governed by an environmental process. It is assumed that the environmental process is formed by independent but not necessarily identically distributed random vectors. For such a class, we determine some relationships among the probability generating functions involved in the mathematical model and derive expressions for the main moments. Also, by considering different probabilistic approaches we establish several results concerning the extinction probability. A simulated example is presented as an illustration.

Two-Sex Branching Processes with Offspring and Mating in a Random Environment

We introduce a class of discrete-time two-sex branching processes where the offspring probability distribution and the mating function are governed by an environmental process. It is assumed that the environmental process is formed by independent but not necessarily identically distributed random vectors. For such a class, we determine some relationships among the probability generating functions involved in the mathematical model and derive expressions for the main moments. Also, by considering different probabilistic approaches we establish several results concerning the extinction probability. A simulated example is presented as an illustration.

Phosphorylation of the MAPKKK Regulator Ste50p in Saccharomyces cerevisiae: a Casein Kinase I Phosphorylation Site Is Required for Proper Mating Function

ABSTRACT The Ste50 protein of Saccharomyces cerevisiae is a regulator of the Ste11p protein kinase. Ste11p is a member of the MAP3K (or MEKK) family, which is conserved from yeast to mammals. Ste50p is involved in all the signaling pathways that require Ste11p function, yet little is known about the regulation of Ste50p itself. Here, we show that Ste50p is phosphorylated on multiple serine/threonine residues in vivo. Threonine 42 (T42) is phosphorylated both in vivo and in vitro, and the protein kinase responsible has been identified as casein kinase I. Replacement of T42 with alanine (T42A) compromises Ste50p function. This mutation abolishes the ability of overexpressed Ste50p to suppress either the mating defect of a ste20 ste50 deletion mutant or the mating defect of a strain with a Ste11p deleted from its sterile-alpha motif domain. Replacement of T42 with a phosphorylation-mimetic aspartic acid residue (T42D) permits wild-type function in all assays of Ste50p function. These results suggest that phosphorylation of T42 of Ste50p is required for proper signaling in the mating response. However, this phosphorylation does not seem to have a detectable role in modulating the high-osmolarity glycerol synthesis pathway.

Bisexual Galton-Watson branching process with population-size-dependent mating

In this paper, we introduce a bisexual Galton-Watson branching process with mating function dependent on the population size in each generation. Necessary and sufficient conditions for the process to become extinct with probability 1 are investigated for two possible conditions on the sequence of mating functions. Some results for the probability generating functions associated with the process are also given.