The Mac ArthurWilson Equilibrium Theory

What was the revolution that MacArthur and Wilson effected in their 1967 book? The essence is that each island is in a state of species equilibrium, in which the number of new (not already on the island) species immigrating per unit time is balanced by the number of species becoming extinct per unit time. To see how this could be very different from previous theoretical constructs, we can examine the effect of an island's distance on its species count. Extensive collection of information on species distributions and compilation of faunal lists shows that number of species on far islands (those distant from a source of colonizing species) is less than the number on otherwise similar near islands. One possible explanation is that the far islands, so removed from the source, simply did not have time to acquire the number of species near islands possess but eventually would. An entirely different explanation was advanced by MacArthur and Wilson, who argued that far islands have fewer species because their low immigration rate is balanced at equilibrium by a low extinction rate; the fewer species on far islands means fewer to go extinct per time, thus achieving a balance at a smaller equilibrium number.

The model actualizing these ideas was first presented as a graph of gross extinction and immigration rates

Gross immigration or extinction

rate

Number of species present (b) (c)

Number of species present (b) (c)

Figure 1 (a) The graphical version of the MacArthur-Wilson equilibrium model. The model is for a particular island. S is the number of species at equilibrium (when gross immigration equals gross extinction), and P is the number of species in the source pool. Rate curves are monotonic but nonlinear. The intercept of the dashed line on the y-axis is the turnover rate at equilibrium. (b) The distance effect for the MacArthur-Wilson equilibrium model: far islands have lower immigration rates than near islands (for a given number of species present on the island), implying near islands at equilibrium have more species (SN) than do far islands at equilibrium (SF). (c) The area effect for the MacArthurWilson equilibrium model: small islands have higher extinction rates than large islands (for a given number of species present on the island), implying large islands at equilibrium have more species (S J than do small islands at equilibrium (SS).

Number of species present

Figure 1 (a) The graphical version of the MacArthur-Wilson equilibrium model. The model is for a particular island. S is the number of species at equilibrium (when gross immigration equals gross extinction), and P is the number of species in the source pool. Rate curves are monotonic but nonlinear. The intercept of the dashed line on the y-axis is the turnover rate at equilibrium. (b) The distance effect for the MacArthur-Wilson equilibrium model: far islands have lower immigration rates than near islands (for a given number of species present on the island), implying near islands at equilibrium have more species (SN) than do far islands at equilibrium (SF). (c) The area effect for the MacArthurWilson equilibrium model: small islands have higher extinction rates than large islands (for a given number of species present on the island), implying large islands at equilibrium have more species (S J than do small islands at equilibrium (SS).

against the number of species present on the island. In its most general form it makes two assumptions (Figure 1a):

A1. Rate of immigration of new species (those not yet on the island) decreases monotonically with increasing number of species already present. It reaches zero when all species in the source area (there are P of them) are on the island; and

A2. Rate of extinction of species increases monotonically as the number of species increases (the more species there are, the more to go extinct). These two assumptions imply

P1. An equilibrium between immigration and extinction will eventually occur, at which time the immigration and extinction rates will equal the same value, called the turnover rate at equilibrium.

Two additional assumptions allow some more predictions:

A3. Near islands have immigration rates higher than far, for the same number of species present (because near islands are closer to the source area); and

A4. Small islands have extinction rates higher than large, for the same number of species present (because average population size is smaller for the smaller islands, so the per-species extinction likelihood is greater). These imply the following predictions:

P2. Near islands of the same size as far have more species (Figure 1b); and

P3. Large islands of the same distance as small have more species (Figure 1c). This prediction is a version of the species-area relation, one for which there is much evidence, as discussed below.

Finally, certain assumptions lead to

P4. the colonization curve, or the curve relating number of species on the island to time since the colonization process begins, is convex.

Although the relation of extinction to area and the relation of immigration to distance are expected to be by far the dominant ones, the two other logically possible relations have also been proposed and documented. First, far islands may have extinction rates higher than near for the same number of species present (Brown and Kodric-Brown's 'rescue effect'). The rationale is that near islands have populations supplemented by immigration more than do far islands; thus population sizes of the species present on near islands average larger so are less extinction-prone than populations on far islands (and/or near-island populations have more genetic variation, so again are less extinction-prone). Second, large islands may have greater immigration rates than small, for the same number of species present (the 'target effect'). The rationale is that larger islands have a greater diameter or area to intercept laterally moving or vertically descending immigrants, respectively, so have a greater immigration rate. Evidence for both of these effects is widespread and will be discussed below, but we note here that all four postulates about rates, (A3) and (A4) and the two just mentioned, have been detected in the same system, spiders on subtropical islands of the Bahamas.

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