Models of biological invasion
In this chapter, we will brieﬂy review the main mathematical approaches that are used to describe biological invasions and species spread. Spatiotemporal models of population dynamics arise when the trade-oﬀ is considered between the change in population size or density due to the processes of birth and death and its change due to emigration/immigration into a given site or into a vicinity of certain position in space. There are, however, diﬀerent ways to describe this trade-oﬀ depending on peculiarities of ecological situation as well as diﬀerent features of population dynamics to be taken into account. This results in a wide variety of relevant mathematical models ranging from fully deterministic to purely stochastic, from single-species to multi-species, from continuous to discrete, etc. Some of them are presented below.