Metapopulation

A metapopulation describes a group of subpopulations (subpopulations) that have a restricted gene exchange among themselves . There is (in general to other populations that are composed of subpopulations) the possibility that subpopulations will die out (local extinction) and subpopulations will arise at the same or another location through new or re-colonization (local colonization). The extinction of subpopulations can u. U. can be prevented by the immigration of individuals from other subpopulations (rescue effect).

There are several definitions of the term metapopulation. For example, a distinction can be made between whether local extinctions actually have to occur or whether the possibility of local extinctions (which, however, then do not occur due to the rescue effect, for example) is sufficient for the existence of a metapopulation. In addition, depending on the definition, there are further requirements for the existence of metapopulations.

With the help of the term metapopulation, processes in population biology can be described that relate on the one hand to individual subpopulations and on the other hand to the interactions of several of these subpopulations with one another. This creates a mosaic-like representation of the population dynamics , on the basis of which the gene flow can be determined. In addition, metapopulation ecology is used in nature conservation, as it can be used to describe processes in fragmented landscapes.

Metapopulation model according to Levins

In the theoretical treatment of metapopulations, the members of which are distributed over a large number of habitats, one often uses a spatially implicit approach. Assuming that the probability of extinction in each individual habitat is independent of the condition of the remaining habitats and that the colonization rate is linearly dependent on the proportion of already occupied habitats, one arrives at the following formulation: Let the proportion of habitats ( patches ) occupied at time t and e the probability of extinction or c the probability of colonization per time step. Then we get: ${\displaystyle p}$

(1)

${\displaystyle {\frac {\mathrm {d} p}{\mathrm {d} t}}=cp(1-p)-ep}$.

As can be seen from the differential equation, the expected value E of the habitats newly or reoccupied per inhabited habitat is . Equation (1) has two stable fixed points , one fixed point at and another fixed point at ${\displaystyle {\frac {c}{e}}}$ ${\displaystyle p*=0}$

(2)

${\displaystyle p*=1-{\frac {e}{c}}}$for . ${\displaystyle 0<p<1}$

Loss of part L of the available habitats (thus ) lists . ${\displaystyle {\frac {\mathrm {d} p}{\mathrm {d} t}}=cp(1-(p+L))-ep}$ ${\displaystyle E_{L}={\frac {c(1-L)}{e}}}$

As discussed for E , the threshold value is also here at and therefore at . ${\displaystyle E_{L}=1}$ ${\displaystyle E=(1-L)^{-1}}$

Ultimately, this means that more patches have to be colonized (so that p *> 0, c> e must apply) so that a metapopulation does not die out. The Levins model forms a top-down approach, since the population dynamics per patch within the metapopulations is largely neglected.

application

Scheme of an idealized (virtual) metapopulation model from tree frog waters of different quality and priority (explanations in the text)

To illustrate the application, the metapopulation model for the European tree frog is shown here. This is very much affected by the islanding of its habitat through the draining of fens and bodies of water as well as the straightening of streams and rivers.

The large blue circles in the adjacent graphic represent optimal biotopes that function as refuges and centers of expansion for “surplus populations ” rich in individuals. By migrating from there, suboptimal secondary colonies ("N") in their vicinity are stabilized, so that smaller populations can be maintained there despite high individual mortality rates. In addition, “stepping stone biotopes” (“TB”), which are less suitable as permanent habitats, serve as biotope-networking temporary locations for individuals who wander around in the otherwise intensively cultivated area. Via secondary colonies and stepping stone biotopes, there are at least indirect population-ecological interrelationships between the optimal biotopes. The prerequisite for the functioning of this model is, among other things, the "biological permeability" of the landscape: amphibians "friendly" line structures (hedges etc.) play an essential role. The graphic also shows that the elimination of individual side or stepping stone biotopes can seriously impair or interrupt the network. If even an optimal biotope is destabilized or destroyed, the entire directly linked environment is affected. The risk of extinction increases considerably because of the lack of immigration, although there have been no qualitative changes there.

In mathematical epidemiology , a formalism that is very similar to the metapopulation approach is widely used under the name of the SIS model .

literature

• R. Levins: Some demographic and genetic consequences of environmental heterogenity for biological control. In: Bull. Entomol. Soc. At the. 15, 1969, pp. 237-240.
• K. Sternberg: Population ecological studies on a metapopulation of the raised moor mosaic damsel ( Aeshna subarctica elisabethae Djakonov, 1922) in the Black Forest. In: Z. Ökologie u. Natural reserve. 4, 1995, pp. 53-60.
• K. Sternberg: Regulation and stabilization of metapopulations in dragonflies, illustrated using the example of Aeshna subarctica elisabethae Djakonov, 1922 in the Black Forest (Anisoptera, Aeshnidae). In: Libellula. 14, 1995, pp. 1-39.
• Ilkka Hanski : Metapopulation ecology. Oxford University Press, Oxford 1999, ISBN 0-19-854066-3 .
• Nicholas F. Britton: Essential Mathematical Biology. Springer, ISBN 1-85233-536-X .