Metapopulation dynamics of two local populations

Recall that in the discrete-time population model, when r was set > 2.69 (Fig. 2.19) the population underwent chaotic behavior (May 1974, 1976b). However, if two such populations are connected to each other by migration a number of interesting and unexpected changes occur (Hanski 1999).

In this example the Ricker model, is used:

In populations one and two, shown in Fig. 5.4, r = 3 and K = 3. Population one is initiated with one individual (N0 = 1), while for population two N0 = 2. Each population and the metapopulation (Fig. 5.5) behave chaotically. The metapopulation is simply the sum of populations one and two. At time = 49 the two populations are connected by allowing 30% of the individuals to emigrate. The emigrants are divided equally between the

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Figure 5.4 Two local populations. (a) Population one: N0 = 1, r = 3, K = 3. (b) Population two: N0 = 2, r = 3, K = 3. The two populations are connected at t = 49.

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Figure 5.4 Two local populations. (a) Population one: N0 = 1, r = 3, K = 3. (b) Population two: N0 = 2, r = 3, K = 3. The two populations are connected at t = 49.

two populations. The migrations calm the chaotic behavior, and by time = 55 the two populations (Fig. 5.4) have moved to a two-point limit cycle. The two populations go through cycles out of phase with each other, and the metapopulation (Fig. 5.5) is completely stabilized (Hanski 1999).

Gyllenberg et al. (1993) have confirmed that migration can help stabilize local population dynamics, although some mortality must occur during migration to have a stabilizing effect. Similarly, migration from a permanent (mainland) population or from a population with a low growth rate also has a stabilizing effect. Movement of individuals between local populations has, at least theoretically, a stabilizing effect on the local populations themselves as well as on the metapopulation. We are well advised, however, not to push this theoretical point too far in field populations (Hanski 1999).

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Figure 5.5 Metapopulation of populations one and two from Fig. 5.4. The two populations are connected at t = 49. The metapopulation is stabilized at t = 55.

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Figure 5.5 Metapopulation of populations one and two from Fig. 5.4. The two populations are connected at t = 49. The metapopulation is stabilized at t = 55.

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