Yukio Sakisaka

Power Law for Extinction Process in Multiple Contact Process

We deal with a multiple contact process, that is a modification of the contact process. This system contains N kinds of species ( N = 10) on a finite-sized square lattice. Simulations are carried out using two different methods: local and global interactions. It is found that the waiting time to the extinction of the first species follows a power law. Moreover, we find that local interaction promotes the coexistence of multiple species.

Finite Size Stability Analysis for Stochastic Cellular Automata

Real simulations are performed on a finite size of lattice. It is therefore very difficult to predict a phase diagram on an infinitely large lattice. Here, we present a Finite Size Stability Analysis (FSSA) to know whether the phase is sustainable or not. Although this analysis is a hypothesis, it enables us to determine the boundary of phase diagram. We apply FSSA to multi-state system. For example we study ten-species system in ecology. From computer simulations on various sizes of lattices, we obtain the waiting time i¾?to extinction. The system is found to have two phases: the coexistence of all species is either unstable or marginally (neutrally) stable. In the latter case, i¾?diverges on a power law with the increase of lattice size.

Evolution of gamete size in primitive taxa without mating types

An ESS model to better understand the evolutionary dynamics of a primitive non-mating type gamete size was developed with reference to the PBS (Parker, Baker and Smith’s) theory, which was based on total numbers of zygotes formed and the zygote survival rates. We did not include mating types since it has been suggested that primitive mating systems did not have mating types. As input parameters, we used experimental data on gamete motility of marine green algae. Based on hard sphere collision mechanics, we detailed the fertilization kinetics of gametes that swim in water prior to fusing with their partners through a set of coupled, non-linear differential equations. These equations were integrated numerically using typical values of the constant parameters. To estimate the relative zygote survival rate, we used a function that is sigmoid in shape and examined some evolutionarily stable strategies in mating systems that depend on optimizing values of the invasion success ratio.

Lattice Population and Optimality of Sex Ratio: Effect of Sterile Male

To know the optimality under given conditions is one of most important problems in various fields. In the present paper, we focus on the optimality of sex ratio i¾?in animals. So far, the optimal sex ratio has been obtained by evolutionarily stable strategy (ESS) in most cases. Recently, however, our coauthors have presented a lattice model of mating population to explain the optimality not by ESS but by the sustainability. They mainly studied the symmetrical case between male and female. In the present paper, we deal with asymmetrical cases: there are sterile male. Our results relatively well explain the evolution of animal sex ratio.

Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds

We investigate an epidemic model on a square lattice with two protection treatments: prevention and quarantine. To explore the effects of both treatments, we apply the site and bond percolations. Computer simulations reveal that the threshold between endemic and disease-free phases can be represented by a single scaling law. The mean-field theory qualitatively predicts such infection dynamics and the scaling law.

Effects of habitat destruction in model ecosystems: Parity law depending on species richness

Abstract Habitat destruction is one of the primary causes of recent mass extinction of biospecies. Even if the destruction is limited to a local and small area, the cumulative destruction increases the risk of extinction. In this paper, we explore the effect of habitat destruction in lattice ecosystems composed of multiple species. Simulations reveal a parity law: the response of the system shows different behaviors by whether the species richness of system is even or odd. The mean-field theory partially predicts such a parity law.

Population dynamics of a species with two or three types of males on a lattice

In any biological population, the individuals with low reproductive success appear recursively at every generation. This phenomenon is prominent in rearing animals and insects, such as aquaculture. We consider the variation in the fitness of male and assume that all individuals live on a lattice. Recently, lattice models have been applied to sexual populations. In these cases, simulations have been carried out by two methods: local and global interactions. In the former, birth process occurs between neighboring sites, whereas in the latter it occurs between any pair of lattice sites. In the present paper, we deal with the population dynamics of a single species that contains two or three types of males and one female. Our attention is paid on the conditions of both “stability” and “sustainability”. Here the stability means that the system reaches a surviving equilibrium in population dynamics. In contrast, the sustainability denotes that the population size at the equilibrium is sufficiently high. Simulation for two-male system exhibits the Allee effect: the population goes extinct, unless both densities of male and female are substantially high. For the stability, the high-fitness male is more important than the subordinate male. However, for the sustainability, our results shows that the low-fitness male plays more important role than high-fitness male. Especially if the low-fitness male is not reproductive, the population tends to go extinct. This tendency is conspicuous, when we consider the local interaction. Moreover, simulations are carried out for three-male system. It is found that the sustainability is influenced not by the fitness variation in male but the average of male fitness. Our results suggest that fitness reductions in individuals can become very critical for maintaining artificially breeding populations.