Population model based on individual dynamical cells

Abstract

Traditional population dynamics models, explaining separate aspects of observed ecological phenomena, are well understood mathematically, but their extension to a wider class of phenomena is difficult. Artificial life models represent another extreme, capable of simulating almost every biological phenomenon, but not accessible to mathematical analysis. A population model having a scope between the two extremes – but flexible, extensible, and within reach of mathematical analysis – is introduced in this paper. The model is based on piece-wise linear dynamical models of individual organisms. Parameter ranges in which the model meets natural ecological requirements is explored through analysis and simulations.