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2 results

  • 7 - Models with Individual Variability

  • from Part II - Ecological Modelling
  • Martin Drechsler
  • Book:
    Ecological-Economic Modelling for Biodiversity Conservation
    Published online:
    29 February 2020
    Print publication:
    26 March 2020, pp 88-97

  • Summary

    Individuals differ in many characteristics such as sex and age, which implies that they usually have different chances of reproducing and surviving. Even stronger differences are usually observed if individuals belong to different species. This chapter presents two types of model for the consideration of individual variability. The first is equation-based models that differ from the models of Chapter 4 by the fact that several equations (one for each age class or each species, etc.) are needed. If the dimensions along which individuals differ are too numerous, or if additional features such as adaptive behaviour are included, individual-based models are more appropriate. An example demonstrates that equation-based models and individual-based models, when considering the same features of the modeled population, lead to the same results. It is argued that individual-based models are generally more complex than equation-based models but also more flexible and able to consider more details.

  • Oriented graphs generated by random points on a circle

  • Part of
  • Yoshiaki Itoh, Hiroshi Maehara, Norihide Tokushige
  • Journal:
    Journal of Applied Probability / Volume 37 / Issue 2 / June 2000
    Published online by Cambridge University Press:
    14 July 2016, pp. 534-539
    Print publication:
    June 2000

  • Extending the cascade model for food webs, we introduce a cyclic cascade model which is a random generation model of cyclic dominance relations. Put n species as n points Q1,Q2,…, Qn on a circle. If the counterclockwise way from Qi to Qj on the circle is shorter than the clockwise way, we say Qi dominates Qj. Consider a tournament whose dominance relations are generated from the points on a circle by this rule. We show that when we take n mutually independently distributed points on the circle, the probability of getting a regular tournament of order 2r+1 as the largest regular tournament is equal to (n/(2r+1))/2n-1. This probability distribution is for the number of existing species after a sufficiently long period, assuming a Lotka-Volterra cyclic cascade model.