Size structured populations: Dispersion effects due to stochastic variability of the individual growth rate
✍ Scribed by G Buffoni; A Cappelletti
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 551 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0895-7177
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✦ Synopsis
Let z = ~(a), a = chronological age, be a biometric descriptor of the individuals of a population, such as weight, a characteristic length, . . . , of the individuals. The variable z may be considered ss a physiological age and r = 2 is defined ss the growth rate (growth velocity) of the individuals. The z-size structure of the population is obtained by distributing the individuals into z-classes: (zi, zi+r), i = 0, 1, . . . $71, where ti = zo + iAz and AZ is the size class. The class (zo, 21) is the recruitment clsss. The discrete model for the dynamics of a z-size structured population presented here is based on the following main assumptions. l The growth plasticity of the individuals is taken into account by assuming that the growth rate r is a random variable, with values rj = jAz/At, j E J = { m, m + 1,. , M -1, M}. If I-"' c 0, then processes of shrinking or fragmentation may occur, for example, in the case of organisms with highly variable development (ss clonal invertebrates and plants).
l The basic feedback, due to the population size, only occurs in survival of the recruitment in the first t-class.
We obtain that the evolution equations are based on a generalized nonlinear Leslie matrix operator. Necessary and sufficient conditions for the existence of positive steady state solutions are given. An algorithm for computing these solutions is described. A local stability analysis around the equilibrium has also been performed. The (t, t)-continuous analogue of the discrete model has been derived: it consists of a first-order hyperbolic system.