Presentation Information
[POS-36]Simulation analysis of two species point pattern dynamics with bi-stable local dynamics
*Ayaka Mori1 (1. Nara Women's University (Japan))
Keywords:
point pattern dynamics,spatial population dynamics,bi-stable local dynamics,individual-based model
Population dynamics focuses on how population size changes with time. Many population dynamics models are given by ODE that focuses only on population size. Some non-spatial models show bi-stability where there exist more than one locally stable equilibrium. Non-spatial ODE models can be easily extended to spatial models assuming random diffusion as reaction-diffusion models that explicitly consider spatial distribution. It has been well known that reaction-diffusion models with bistable reaction term can show spatially specific patterns such as stripes and spirals under a certain condition. In this study, we explore spatial population dynamics in terms of "point pattern approach".
A point pattern is a collection of points distributed over continuous space. Each point gives birth, dies, and moves with a certain rule.
We extend bi-stable ODE model to a point pattern dynamics to explore if spatially specific pattern emerges.
Individuals are represented as points on two-dimensional torus space. Each point has (x, y) coordinate, species index (0 or 1) and local densities. Local density is a measure of crowdedness, the number of individuals nearby, that is used to represent interactions among points. Because we construct two species point pattern dynamics, we consider two types of local densities; intra-species and inter-species. We assume a set of rules about birth, death and movement of a point that depend on the point's local densities.
We use Gillespie algorithm to implement these rules to simulate stochastic point pattern dynamics. Point pattern dynamics can be quantified by the number of points as 1st order structure and the number of pairs as the 2nd order structure.
Main findings are as follows:
1) Spatially specific patterns emerge under a certain condition.
2) Range of point movements is a key parameter that results in spatially specific patterns. In future study, parameter space need to be explored more extensively. We plan to derive the moment dynamics; dynamics of the singlet densities (species 0 and 1) and the pair densities (0-0, 0-1, 1-0 and 1-1). We ultimately aim to derive the condition that results in spatial pattern based on the moment dynamics.
A point pattern is a collection of points distributed over continuous space. Each point gives birth, dies, and moves with a certain rule.
We extend bi-stable ODE model to a point pattern dynamics to explore if spatially specific pattern emerges.
Individuals are represented as points on two-dimensional torus space. Each point has (x, y) coordinate, species index (0 or 1) and local densities. Local density is a measure of crowdedness, the number of individuals nearby, that is used to represent interactions among points. Because we construct two species point pattern dynamics, we consider two types of local densities; intra-species and inter-species. We assume a set of rules about birth, death and movement of a point that depend on the point's local densities.
We use Gillespie algorithm to implement these rules to simulate stochastic point pattern dynamics. Point pattern dynamics can be quantified by the number of points as 1st order structure and the number of pairs as the 2nd order structure.
Main findings are as follows:
1) Spatially specific patterns emerge under a certain condition.
2) Range of point movements is a key parameter that results in spatially specific patterns. In future study, parameter space need to be explored more extensively. We plan to derive the moment dynamics; dynamics of the singlet densities (species 0 and 1) and the pair densities (0-0, 0-1, 1-0 and 1-1). We ultimately aim to derive the condition that results in spatial pattern based on the moment dynamics.