Examples

• Discrete-time models
  • Introduction to discrete time IBM. All birth-death events are synchronized.
    • Definition of individual and creation of an individual
    • Creating individuals and a population represented by list structure
    • Individuals give birth
    • Individuals can die
  • Galton-Watson process
    • A stochastic process in discrete time. An individual gives N birth (N = 0, 1, 2, ...) according to a probability P(N=n). An individual survives with a certain probability. Starting from a certain number of individuals, the population growth (decrease) is stochastically simulated.
    • As a spice, individuals are given "age" that is chronologically incremented as time t advances.
    • Corresponds to the determininstic exponential growth (decrease) given as difference equation.
• Continous-time models
  • Birth-death event occurs asynchronously to an individual. Interevent time is exponentially distributed.
  • Birth-death process with density dependency
    • A stochastic process in continous time. Each individual gives a birth or dies with the rate B1 - B2*N and D1 + D2*N, respectively. N is the total number of individuals as non-negative integer. B1, B2, D1 and D2 are positive constant.
    • Corresponds to the deterministic logistic equation described as ODE. But this stochastic process does not necessarily equate to the deterministic counterpart.
  • Birth-death process with local density dependency
    • Similar to the above birth-death process but differs in that individuals are located in two-dimensional torus space and birth and death rate depend on the "local" density, not the total number of individuals N.
    • Local density measures how many other individuals are located around the focal individual.
  • Birth-death process with local density dependency - OpenMP version using four cores.
    • OpenMP makes the simulation boost by parallel processing.

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takasu@ics.nara-wu.ac.jp

4/10/08