In Encyclopedia of Biodiversity (Second Edition), 2013, Peter Chesson studied metapopulations. Metapopulation deals with the patchiness of populations in space. He also studied in the book the role of this patchiness in the population dynamics, the population stability, and coexistence of different species, and thus the maintenance of diversity. If we talk about strict metapopulation studies, it will only focus on the patchiness which is due to colonization and extinction of local populations in a region.

The Studies of metapopulations emphasize that patchiness which alters the population dynamics by which also changes the outcomes of the species interactions. Further, we will proceed on to studying more about ‘Metapopulation’.

### Metapopulation Definition

Metapopulation or Metapopulation ecology is a regional group of populations that are connected with species. For a single species, each of the metapopulations is continually modified by the increase in births and immigrations and it gets continually decreased by deaths and emigrations of the present individuals in the group. These local populations of a given species quite fluctuate in their size, they become very much vulnerable to its extinction in the periods when their numbers are quite low. The Extinction of local populations is evident in some species. The elimination of the metapopulation of the structure of these species can increase the prosperity of regional extinction of these species.

This structure of metapopulations quite varies among the species. Particularly in some species, this is quite stable over time and they act as the source of recruits into the other, they are the less stable populations.

### Metapopulation Dynamics

Metapopulation Dynamics definition, as previously defined by Levin’s includes the extinction and colonization of the local populations. His theory suggested that the process can be affected by demographic persistence, its existence of interacting species, its genetic variation, and evolution.

Metapopulation biology is very much concerned with its dynamic consequences of the migration among the local people and the conditions of its regional persistence of the species with the unstable local population growth. This is a well-established habitat patch area and the isolation on migration, colonization and population extinction became integrated with classic metapopulation dynamics. Metapopulation Dynamics has led the models which have been used to predict the movement patterns of the individuals, the dynamics of the species, and also the distributional patterns in the multispecies of communities in the real fragmented landscapes.

### Mainland Island Metapopulation

We adapt to different ecological environments, through divergent selection and generate phenotypic and genetic differences between these populations. The changes eventually give rise to these new species. The speciation process is generally quantitative in nature. This is being represented by a lot of studies that show that divergence during the speciation quite varies continuously, and this sequence of genetically-based changes occur as two lineages on the pathway to reproductive isolation diverge from each other. Divergent evolution and reproductive isolation are the two primary elements of speciation which many have recognized that reproductive isolation is generally a signature effect that is rather than a primary cause of speciation.

Further detailing about the Levin’s’ metapopulation study, we get to know the generalization majorly consists of the introduction of immigration, which is generally from a mainland and the assumption of the dynamics is stochastic, rather than deterministic.

We will derive an equation for this probability is – n of the patches that are occupied, is derived and Ps(n) is the stationary probability, which together means and higher moments in the stationary state, determined.

The time dependence of this probability distribution is also studied: through the Gaussian approximation which is generally n when the boundary is at n = 0 and has little effect, thus, by calculating P (0, t), the probability got no patches. They are occupied at a time which is denoted by t, and by using the linearization procedure. These analytic calculations are then supplemented by calculating the numerical solutions of the master equation and simulations of the stochastic process. All these various approaches are quite consistent with each other.

We can use the forms for Ps and P (0, t) which are in the linearization and approximation which are the bases for calculating the meantime for a metapopulation to get extinct. We also give an analytical expression which is for the meantime to extinct the derived that is within the mean-field approach. We chalk out a simple method in order to apply our mean-field approach which is even complex patch networks in the realistic model metapopulations. Also, after studying a lattice metapopulation model and also a spatially realistic model, we can thereby conclude the analytical formula required for the mean extinction time is normally applicable to those metapopulations that are really endangered.