An overview of modeling approaches
The great variety of diﬀerent environmental settings and ecological interactions existing in mother nature requires, in order to make their theoretical study more eﬀective, an equally broad range of modeling approaches. Quite typically, an adequate model choice depends not only on the ecosystem or community type, but also on the goals of the study, in particular, on the spatial and/or temporal scales where the given phenomena are developing. Discreteness of populations is a fundamental property (cf. Durrett and Levin, 1994), yet on a spatial scale much larger than the size of a typical individual description of the population dynamics by a continuous quantity such as the population density (the number of individuals of a given species per unit area or unit volume) was proved to be eﬀective, e.g., see Murray (1989) and Shigesada and Kawasaki (1997). On a larger scale, however, environmental heterogeneity and habitat fragmentation become important, which may make space-discrete models more appropriate. A similar duality arises in the temporal dynamics. Moreover, due to the possible overlapping of spatial and/or temporal scales associated with diﬀerent processes, sometimes a hybrid approach might be required that describes some of the processes continuously and some of them discretely; one example is given by a ﬁsh school feeding on plankton (Medvinsky et al., 2002).