Metapopulation

A metapopulation describes a group of sub-populations ( subpopulations ), which differ to a limited gene exchange. It consists ( i.GG. to other populations, resulting from subpopulations composed ) the possibility that subpopulations become extinct (local extinction) and at the same or elsewhere subpopulations by new or re-colonization occur (local colonization ). The extinction of subpopulations can u.U. be prevented by immigration of individuals from other subpopulations ( rescue effect).

There are several definitions of the term metapopulation, which differ, for example, is whether it has actually lead to local extinctions, or whether the possibility of local extinctions already (which it then but, for example, does not come due to the rescue effect ) is sufficient for the existence of a metapopulation. There are also depending on the definition further conditions for the existence of metapopulation.

With the help of the concept of metapopulation can be used in population biology describe processes, on the one hand refer to individual subpopulations, on the other, the interactions of several of these subpopulations among themselves. In this way, a mosaic-like representation of the population dynamics, on the basis of gene flow can be determined. In addition, the Metapopulationsökologie found in nature conservation application, as can be described by their processes in fragmented landscapes.

Metapopulation by Levins

In the theoretical treatment of meta-populations whose members are spread over a large number of habitats, often one uses a spatially implicit approach. Assuming that the probability of extinction in each habitat is independent of the state of the remaining habitats and colonization rate depends linearly on the proportion already occupied habitats, we arrive at the following formulation: Be the proportion of the time t occupied habitats (patches ) and e and c is the extinction or colonization probability per time step. Then we have:

(1.1)

As can be seen from the differential equation is the expectation value E of the per inhabited Habitat emerging or re- occupied habitats. Equation ( 1.1) has two stable fixed points, a fixed reference points, and a further checkpoint in for

Loss of part L of the available habitats (that ) leads to

As discussed for E, is also here the threshold is at and thus.

Application

To illustrate the application of the metapopulation for the European tree frog is shown here. This is very strongly affected by a Verinselung its habitat by draining of fens and waters and the straightening of streams and rivers.

The large blue circles in the image opposite represent optimal habitats that act as refugia and dispersal centers of individual- rich " surplus populations ". Through emigration from there suboptimal secondary colonies ( "N") are stabilized in their environment, so that can keep smaller stocks there despite individually high mortality. In addition serve " stepping stones " ( "TB" ), which are as permanent habitat less suitable than biotopvernetzende temporary places for individuals who wander in the otherwise intensively farmed area. About exist side colonies and stepping stones so at least indirectly and population ecological interrelationships between the optimal habitats. Prerequisite for the functioning of this model is including the "biological permeability " of the landscape: Amphibians "friendly" line structures (hedges, etc. ) play an essential role. The graph also shows that the loss already selected adverse or stepping stones can interfere with or disrupt the grid sensitive. Even if an optimal habitat destabilized or destroyed, the entire environment is linked directly affected. The extinction also increases here due to lack of immigration significantly, although it has been there even any qualitative changes.

In mathematical epidemiology a close resemblance to the Metapopulationsansatz formalism is widely used under the name of SIS model.