Metapopulation

Metapopulations are important in fisheries. The local population (1.) serves as a source for hybridization with surrounding subspecies populations (1.a, 1.b, and 1.c).The populations are normally spatially separated and independent but spatial overlap between them during breeding times allows for gene flow between the populations.

A metapopulation consists of a group of spatially separated populations of the same species which interact at some level. The term metapopulation was coined by Richard Levins in 1969 to describe a model of population dynamics of insect pests in agricultural fields, but the idea has been most broadly applied to species in naturally or artificially fragmented habitats.

A metapopulation is generally considered to consist of several distinct populations together with areas of suitable habitat which are currently unoccupied. Each population cycles in relative independence of the other populations and eventually goes extinct as a consequence of demographic stochasticity (fluctuations in population size due to random demographic events); the smaller the population, the more prone it is to extinction.

Although individual populations have finite life-spans, the population as a whole is often stable because immigrants from one population (which may, for example, be experiencing a population boom) are likely to re-colonize habitat which has been left open by the extinction of another population. They may also immigrate into to a small population and rescue that population from extinction (called the rescue effect).

The development of metapopulation theory, in conjunction with the development of source-sink dynamics, emphasised the importance of connectivity between seemingly isolated populations. Although no single population may be able to guarantee the long-term survival of a given species, the combined effect of many populations may be able to do this.

The most important contributor to metapopulation theory is the Finnish biologist, Ilkka Hanski [1], of the University of Helsinki.

Predation and Oscillations

The first experiments with predation and spatial heterogeneity were conducted by G.F. Gause in the 1930's, based off of the Lotka-Volterra equation, which was formulated in the mid-1920s, but no further application had been conducted . The Lotka-Volterra equation suggested that the relationship between predators and their prey would result in population oscillations over time based on the initial densities of predator and prey. Gause's early experiments to prove the predicted oscillations of this theory failed because the predator-prey interactions were not influenced by immigration. However, once immigration was introduced, the population cycles accurately depicted the oscillations predicted by the Lotka-Volterra equation, with the peaks in prey abundance shifted slightly to the left of the peaks of the predator densities. Huffaker's experiments expanded on those of Gause by examining how both the factors of migration and spatial heterogeneity lead to predator-prey oscillations.

Huffaker's experiments on predator-prey interactions (1958)

In order to study predation and population oscillations, Huffaker used mite species, one being the predator and the other being the prey. He set up a controlled experiment using oranges, which the prey fed on, as the spatially structured habitat in which the predator and prey would interact. At first, Huffaker experienced difficulties similar to those of Gause in creating a stable predator-prey interaction. By using oranges only, the prey species quickly went extinct followed consequently with predator extinction. However, he discovered that by modifying the spatial structure of the habitat, he could manipulate the population dynamics and allow the overall survival rate for both species to increase. He did this by altering the distance between the prey and oranges (their food), establishing barriers to predator movement, and creating corridors for the prey to disperse. These changes resulted in increased habitat patches and in turn provided more areas for the prey to seek temporary protection. When the prey would go extinct locally at one habitat patch, they were able to reestablish by migrating to new patches before being attacked by predators. This habitat spatial structure of patches allowed for coexistence between the predator and prey species and promoted a stable population oscillation model. Although the term metapopulation had not yet been coined, the environmental factors of spatial heterogeneity and habitat patchiness would later describe the conditions of a metapopulation relating to how groups of spatially separated populations of species interact with one another. Huffaker's experiment is significant because it showed how metapopulations can directly affect the predator-prey interactions and in turn influence population dynamics.

Aggregation effect and stability of predator-prey interactions

The stability of predator-prey interactions in patchy environments is reinforced when an aggregation effect occurs. Aggregation effect is when predators are more greatly attracted to habitat patches with high prey densities, therefore, areas with low prey densities are relieved from the pressure of predation and are able to generate a larger population and avoid extinction.

The Levins model

Levins' original model applied to a metapopulation distributed over many patches of suitable habitat with significantly less interaction between patches than within a patch. Population dynamics within a patch were simplified to the point where only presence and absence were considered. Each patch in his model is either populated or not.

Let N be the fraction of patches occupied at a given time. During a time step, each occupied patch can become unoccupied with an extinction probability e. Additionally, 1 − N of the patches are unoccupied. Each of these may become populated by colonization. Let c be a constant rate of propagule generation for each of the N occupied patches. This yields a probability of cN for each unoccupied patch to be colonized. So for each time step, the change in the proportion of occupied patches, dN/dt, is

${\frac {dN}{dt}}=(1-N)cN-eN.\,$

This takes on a sigmoid shape similar to the logistic model. The equilibrium value of N can be calculated by setting dN to be equal to zero. Solving for N gives either N = 0 or

$N=1-{\frac {e}{c}}.\,$

This result, that N is always less than one, implies that some fraction of a species habitat will always be unoccupied.

Stochastic patch occupancy models (SPOMs)

One major drawback of the Levins model is that it is deterministic, whereas the fundamental metapopulation processes are stochastic. Metapopulations are particularly useful when discussing species in disturbed habitats, and the viability of their populations, i.e., how likely they are to become extinct in a given time interval. The Levins model cannot address this issue.

For conservation biology purposes, metapopulation models must include (a) the finite nature of metapopulations (how many patches are suitable for habitat), and (b) the probabalistic nature of extinction and colonisation. Also, note that in order to apply these models, the extinctions and colonisations of the patches must be asynchronous.

Stochasticity and Metapopulations

Huffaker's studies of spatial structure and species interactions are an example of early experimentation in metapopulation dynamics. Since the experiments of Huffaker and Levins, models have been created which integrate stochastic factors. These models have proven that the combination of environmental variability (stochascity) and relatively small migration rates cause indefinite or unpredictable persistence. However, Huffaker's experiment almost guaranteed infinite persistence because of the controlled immigration variable.

Attribution

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Footnotes

Other references:

• Hanski, I. Metapopulation Ecology Oxford University Press. 1999. ISBN 0-19-854065-5
• Huffaker, C.B. 1958. Experimental Studies on Predation: Dispersion factors and predator-prey oscillations. Hilgardia. 27: 343, p. 83
• Fahrig, L. 2003. Effects of Habitat Fragmentation on Biodiversity. Annual Review of ecology, evolution, and systematics. 34:1, p.487.
• Janssen, A. et al. 1997. Metapopulation Dynamics of a Persisting Predator-Prey system.
• Kareiva, P. 1987. Habitat Fragmentation and the Stability of Predator-Prey Interactions. Nature. 326:6111, p. 388.
• Legendre, P. and Fortin, M.J. 1989. Spatial pattern and ecological analysis. Plant Ecology. 80:2, p.107.
• Levins, R. (1969) "Some demographic and genetic consequences of environmental heterogeneity for biological control." Bulletin of the Entomological Society of America, 15, 237-240
• Levin, S.A. 1974. Dispersion and Population Interactions. The American Naturalist. 108:960, p.207.
• Real, Leslie A. and Brown, James H. 1991. Foundations of Ecology: Classic papers with commentaries. The University of Chicago Press, Chicago.