O8 - Parameter estimation for reaction-diffusion models of biological invasions
SESSION 5
SESSION 5
Reaction-diffusion models have been deeply exploited to advance theory in biological invasions. They can also be exploited to infer parameters governing biological invasions based on spatial and temporal data collected during the invasions. In the latter case, we studied the two following questions :
How to link the reaction-diffusion model representing the invasion dynamics with monitored data that are more or less directly connected with the dynamics?
How to carry out parameter estimation with a proper statistical approach?
The approach that we will present in this talk uses mechanistic-statistical models that combine (1) a submodel based on partial-dfferential équations and describing the dynamic under study, and (2) a stochastic submodel describing the observation process conditional on the dynamics. This class of models is included in state-space models. Consequently, statistical tools adapted to state-space models can be applied, especially estimation algorithms such as Markov chain Monte Carlo algorithms. In the talk, we will present two examples of mechanistic-statistical models adapted to invasions dynamics and we will fit them to simulated data corresponding to impacts of the invading species towards the environment. These impacts are measured at discrete times and at discrete locations. In the first example, we will estimate the dispersal rate, the effect of competition and the spatially heterogeneous intrinsic growth rate of the species. In the second example, we will estimate the date and location of the introduction of an invading species, i.e. the initial invasion conditions.
