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In this paper we present a discrete dynamical population modeling of invasivespecies, with reference to the swamp crayfish Procambarus clarkii. Since thisspecies can cause environmental damage of various kinds, it is necessary toevaluate its expected in not yet infested areas. A structured discrete model isbuilt, taking into account all biological information we were able to find,including the environmental variability implemented by means of stochasticparameters (coefficients of fertility, death, etc.). This model is based on astructure with 7 age classes, i.e. a Leslie mathematical population modelingtype and it is calibrated with laboratory data provided by the Department ofEvolutionary Biology (DEB) of Florence (Italy). The model presents manyinteresting aspects: the population has a high initial growth, then itstabilizes similarly to the logistic growth, but then it exhibits oscillations(a kind of limit-cycle attractor in the phase plane). The sensitivity analysisshows a good resilience of the model and, for low values of reproductive femalefraction, the fluctuations may eventually lead to the extinction of thespecies: this fact might be exploited as a controlling factor. Moreover, theprobability of extinction is valuated with an inverse Gaussian that indicates ahigh resilience of the species, confirmed by experimental data and fieldobservation: this species has diffused in Italy since 1989 and it has shown anatural tendency to grow. Finally, the spatial mobility is introduced in themodel, simulating the movement of the crayfishes in a virtual lake ofelliptical form by means of simple cinematic rules encouraging the movementtowards the banks of the catchment (as it happens in reality) while a randomwalk is imposed when the banks are reached.

A dynamical population modeling of invasive species with reference to the crayfish Procambarus Clarkii