Nariyuki Nakagiri

Indirect relation between species extinction and habitat destruction

To study local destruction of habitat, we present a lattice ecosystem composed of prey (X) and predator (Y). This system corresponds to a lattice version of the Lotka–Volterra model, where interaction is allowed between neighboring lattice points. The lattice is partly destroyed, and destructed sites or barriers are randomly located between adjacent lattice points with the probability p. The barrier interrupts the reproduction of X, but the species Y suffers no direct damage by barriers. This system exhibits an extinction due to an indirect effect: when the density p of barriers increases, the species Y goes extinct. On the other hand, an initial suppression of X may later lead to the increase of X. The predator Y decreases in spite of the increase of X. These results cannot be explained by a mean-field theory such as the Lotka–Volterra equation. We discuss that endangered species may become extinct by a slight perturbation to their habitat.

Segregation in an interacting particle system

Abstract We present a lattice system composed of three kinds of particles which interact following a rule combining the contact process with Rock–Paper–Scissors game. Depending on value of a parameter, this system naturally evolves into a specific pattern, where segregation of three species occurs. We discuss that such a segregation phenomenon associates with a habitat isolation of biospecies.

The Effect of Mutualism on Community Stability

The so-called Lotka–Volterra model, which is thought to be appropriate for the dynamics of mutualistic relationship, tells us that mutualism does not play positive roles for the stability of ecosys...

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.

Bond and Site Percolation and Habitat Destruction in Model Ecosystems

Habitat destruction is one of the primary causes of species extinction. In the present article, we apply bond and site destructions to a prey–predator system. Predator reproduction is disturbed by these destructions, while prey sustains no direct damage. It is found for both bond and site destructions that the number of predators increases in spite of the increase in destruction. However, if the destruction is too great, the predators decreases and eventually goes extinct. The mean-field theories for both type of destruction predict the same extinction threshold values. In contrast, the simulations for bond and site destructions reveal that extinction thresholds are much smaller than the mean-field theory predicts. This may be the result of the fragmentation of habitat via the percolation of habitat destruction.

Spatial pattern formation in a model ecosystem: exchange between symbiosis and competition

Abstract Spatial pattern dynamics in a lattice ecosystem composed of two species is studied. Depending on values of a parameter, the exchange of relationship between competition and symbiosis takes place. While interaction parameters between species are fixed, spatial distribution of species naturally evolves into a specific pattern of either competition or mutualism.

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.

Monte Carlo Simulation in Lattice Ecosystem: Top-Predator Conservation and Population Uncertainty

The conservation of biodiversity is one of the most important problems in this century. Under human management, ecosystems suffer perturbations or disturbances. The investigation of perturbation experiments is essential to conserve species and habitat. We carry out Monte-Carlo simulations on finite-size lattices composed of species (n ≤ 4). The value of mortality rate m of top predator is altered to a higher or lower level and a fluctuation enhancement (FE) is explored. Here FE means an uncertainty in population dynamics. It is found for that FE is observed when m is decreased. Namely, when we protect the top predator, its population dynamics becomes very difficult to predict.