Linear Processes in Stochastic Population Dynamics: Theory and Application to Insect Development

Hernán Solari, Mario Natiello

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

Sammanfattning

We consider stochastic population processes (Markov jump processes)
that develop as consequence of the occurrence of randon events at
random time-inervals. The population is divided into sub-populations or compartments. The events occur at rates that depend linearly with the number of individuals in the different described compartments. The dynamics is presented in terms of a Kolmogorov Forward Equation in the space of events and projected onto the space of populations when needed. The general properties of the problem are discussed. Solutions are obtained using a revised version of the Method of Characteristics. After a few examples of exact solutions we systematically develop short-time-approximations to the problem. While the lowest order approximation matches the Poisson and multinomial heuristics previously
proposed, higher-order approximations are completely new. Further, we
analyse a model for insect development as a sequence of E developmental
stages regulated by rates that are linear in the implied subpopulations. Transitions to the next stage compete with death at all times. The process ends at a predetermined stage, for example pupation or adult emergence. In its simpler version all the stages are distributed with the same characteristic time.
Originalspråkengelska
Artikelnummer873624
TidskriftThe Scientific World Journal
Volym2014
DOI
StatusPublished - 2014

Ämnesklassifikation (UKÄ)

  • Matematik

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