crowded conditions, the population experiences density-dependent forces of natural selection, called K-selection. Niche theory Metapopulations Spatial analysis of ecological systems often reveals that assumptions that are valid for spatially homogenous populations – and indeed, intuitive – may no longer be valid when migratory subpopulations moving from one patch to another are considered. In a simple one-species formulation, a subpopulation may occupy a patch, move from one patch to another empty patch, or die out leaving an empty patch behind. In such a case, the proportion of occupied patches may be represented as where m is the rate of colonization, and e is the rate of extinction. In this model, if e < m, the steady state value of p is 1 – (e/m) while in the other case, all the patches will eventually be left empty. This model may be made more complex by addition of another species in several different ways, including but not limited to game theoretic approaches, predator–prey interactions, etc. We will consider here an extension of the previous one-species system for simplicity. Let us denote the proportion of patches occupied by the first population as p1, and that by the second as p2. Then, In this case, if e is too high, p1 and p2 will be zero at steady state. However, when the rate of extinction is moderate, p1 and p2 can stably coexist. The steady state value of p2 is given by (p*1 may be inferred by symmetry). If e is zero, the dynamics of the system favor the species that is better at colonizing (i.e. has the higher m value). This leads to a very important result in theoretical ecology known as the Intermediate Disturbance Hypothesis, where the biodiversity (the number of species that coexist in the population) is maximized when the disturbance (of which e is a proxy here) is not too high or too low, but at intermediate levels. The form of the differential equations used in this simplistic modelling approach can be modified. For example: Colonization may be dependent on p linearly (m*(1-p)) as opposed to the non-linear m*p*(1-p) regime described above. This mode of replication of a species is called the “rain of propagules”, where there is an abundance of new individuals entering the population at every generation. In such a scenario, the steady state where the population is zero is usually unstable. Extinction may depend non-linearly on p