From behavioural to population level: Growth and competition

The aim of this work is to build models of population dynamics for growth and competition interaction by starting with detailed models at the individual level. At the individual level, we start with detailed models where the growth is described by linear terms. By considering individual interferences and by using aggregation methods, we show that the population level, different growth equation can emerge. We present an example of the emergence of logistic growth and an example of the emergence of logistic growth with Allee effect. Furthermore, in the case of two populations, we show that individual interferences can lead at the population level, to a model which has the same qualitative dynamics behaviour as the Lotka-Volterra competition model. Finally, we show that our model brings to light the effects of spatial heterogeneity on competition models. First, we find the stabilizing effects but also we show that destabilizing effects can occur.