An ecological network is a presentation of the biotic interactions in an ecosystem, in which species(nodes) are connected by pairwise interactions(links). Species compete, evolve and disperse simply for the purpose of seeking resources to sustain their struggle for their very existence. Depending on their specific settings of applications, they can take the forms of resource-consumer, plant-herbivore, parasite-host interactions etc. When seemingly competitive interactions are carefully examined, they are often in fact some forms of predator-prey interaction in disguise. Thus these predator-prey interaction models give the building blocks of large and complex ecological networks.
Generic Predator-Prey Model:
Consider two populations whose sizes at a reference time t are denoted by x(t), y(t) respectively. The functions x and y might denote population numbers or concentrations (number per area) or some other scaled measure of the population sizes, but are taken to be continuous functions. Changes in population size with time are described by the time derivatives dx/dt and dy/dt respectively, and a general model of interacting populations is written in terms of two autonomous differential equations:
dx/dt = xf(x, y)
dy/dt = yg(x,y )
The functions f and g denote the respective per capita growth rates of the two species. It is assumed that df/dy < 0 and dg/dx > 0. This general model is often called Kolmogorov's predator-prey model.