A New Stochastic Individual-Based Model for Pattern Formation and its Application to Predator-Prey Systems
Authored by Seido Nagano, Atsushi Yokoyama, Yoshika Noguchi
Date Published: 2008
DOI: 10.1007/s10867-008-9055-6
Sponsors:
Japanese Ministry of Education, Culture, Sports, Science and Technology
Japanese Ministries
Platforms:
No platforms listed
Model Documentation:
Other Narrative
Mathematical description
Model Code URLs:
Model code not found
Abstract
Reaction-diffusion theory has played a very important role in the study
of pattern formation in biology. However, a group of individuals is
described by a single state variable representing population density in
reaction-diffusion models, and interaction between individuals can be
included only phenomenologically. In this paper, we propose a new scheme
that seamlessly combines individual-based models with elements of
reaction-diffusion theory and apply it to predator-prey systems as a
test of our scheme. In the model, starvation periods and the time to
reproductive maturity are modeled for individual predators. Similarly, the life cycle and time to reproductive maturity of an individual prey
are modeled. Furthermore, both predators and prey migrate through a
two-dimensional space. To include animal migration in the model, we use
a relationship between the diffusion and the random numbers generated
according to a two-dimensional bivariate normal distribution. Despite
the simplicity of this model, our scheme successfully produces logistic
patterns and oscillations in the population size of both predator and
prey. The peak for the predator population oscillation lags slightly
behind the prey peak. The simplicity of this scheme will aid additional
study of spatially distributed negative-feedback systems.
Tags
Dynamics
Population persistence