## The development of metapopulation theory islands and metapopulations

The classic book, The Theory of Island Biogeography by MacArthur and Wilson (1967), was an important catalyst in radically changing ecological theory in general. The authors developed their ideas in the context of the dynamics of the animals and plants on real (maritime) islands, which they interpreted as reflecting a balance between the opposing forces of extinctions and colonizations. They emphasized that some species (or local populations) spend most of their time either recovering from past crashes or in phases of invasion of new territories (islands), while others spend much of their time at or around their carrying capacity. These two ends of a continuum are the r- and K-species of Section 4.12. At one extreme (r-species), individuals are good colonizers and have characteristics favoring rapid population growth in an empty habitat. At the other end of the continuum (K-species) individuals are not such good colonizers but have characteristics favoring long-term persistence in a crowded environment. K-species therefore have relatively low rates of both colonization and extinction, whereas r-species have relatively high rates. These ideas are developed further in the discussion of island biogeography in Chapter 21.

At about the same time as MacArthur and Wilson's book was published, a simple model of 'metapopulation' dynamics was proposed by Levins (1969, 1970). Like MacArthur and Wilson, he sought to incorporate into ecological thinking the essential patchiness of the world around us. MacArthur and Wilson were more concerned with whole communities of species, and envisaged a 'mainland' that could provide a regular source of colonists for the islands. Levins focused on populations of a single species and awarded none of his patches special mainland status. Levins introduced the variable p(t), the fraction of habitat patches occupied at time t, reflecting an acceptance that not all habitable patches are always inhabited.

The rate of change in the fraction of occupied habitat (patches, p) is given in Levins' model as:

in which \ is the rate of local extinction of patches and m is the rate of recolonization of empty patches. That is, the rate of recolonizations increases both with the fraction of empty patches prone to recolonization (1 - p) and with the fraction of occupied patches able to provide colonizers, p, whereas the rate of extinctions increases simply with the fraction of patches prone to extinction, p. Rewriting this equation, Hanski (1994a) showed

Levins' model that it is structurally identical to the logistic equation (see Section 5.9):

Hence, as long as the intrinsic rate of recolonization exceeds the intrinsic rate of extinction ((m -p) > 0), the total metapopulation will reach a stable equilibrium, with a fraction, 1 - (p/m), of the patches occupied.

The most fundamental message from taking a metapopulation perspective, then, which emerges from even the simplest models, is that a metapopulation can persist, stably, as a result of the balance between random extinctions and recolonizations even though none of the local populations are stable in their own right. An example of this is shown in Figure 6.16, where within a persistent, highly fragmented metapopulation of the Glanville fritillary butterfly (Melitaea cinxia) in Finland, even the largest local populations had a high probability of declining to extinction within 2 years. To re-state the message another way: if we wish to understand the long-term persistence of a population, or indeed that population's dynamics, then we may need to look beyond the local rates of birth and death (and what determines them), or even the local rates of immigration and emigration. If the population as a whole functions as a metapopulation, then the rates of subpopulation extinction and colonization may be of at least comparable importance.

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Log population size in 1991 |

Figure 6.16 Comparison of the local population sizes in June 1991 (adults) and August 1993 (larvae) of the Glanville fritillary butterfly (Melitaea cinxia) on Aland island in Finland. Multiple data points are indicated by numbers. Many 1991 populations, including many of the largest, had become extinct by 1993. (After Hanski et al., 1995.)

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