An allometric relationship is of the form $B \propto M^{\alpha} $, where $B$ and $M$ are biological parameters, $M$ being typically a mass, and $\alpha$ is called the allometric coefficient. These allometries are a key ingredient for modelling ecological dynamics.

We design a simple individual-based model, structured by the mass of individuals. This gives rise to a Piecewise Deterministic Markov Process with allometric features.

First, we enforce with basic probabilistic tools some bounds for the allometric coefficients involved in our model. We refine these bounds thanks to a property of asymptotic pseudotrajectory. This concept comes from the work of Benaïm and Hirsch. We do not simply use their results, but adapt them to compare our process to the integral curves associated to a time-heterogeneous flow.