ABSTRACT
We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal invasion stopping. We consider possible values of model parameters for zebra mussels. The general N-lake control problem has to be solved numerically, and we show a number of typical features of solutions: distribution of control efforts in space and optimal stopping configurations related with the clusters in lake connection structure.
Subject(s)
Dreissena/physiology , Fresh Water , Models, Biological , Algorithms , Animals , Cost-Benefit Analysis , Ecosystem , Population Control/economics , Population Control/methods , Population Dynamics , Rivers , ShipsABSTRACT
Predictions for climate change include movement of temperature isoclines up to 1000 m/year, and this is supported by recent empirical studies. This paper considers effects of a rapidly changing environment on competitive outcomes between species. The model is formulated as a system of nonlinear partial differential equations in a moving domain. Terms in the equations describe competition interactions and random movement by individuals. Here the critical patch size and travelling wave speed for each species, calculated in the absence of competition and in a stationary habitat, play a role in determining the outcome of the process with competition and in a moving habitat. We demonstrate how habitat movement, coupled with edge effects, can open up a new niche for invaders that would be otherwise excluded.
