Whether a species is present or absent from a patch of suitable habitat at any given time depends on the balance between the colonization of that patch by individuals of the species, and the extinction of the species in the patch. As we learned in Concept 42.5 of the textbook and in the Metapopulation simulation (Animated Tutorial 42.3), the chances of colonization and extinction vary both with the size of the patch of habitat and with its distance from a source of colonists. To summarize:

• Colonization rate increases as patch size increases and increases as the distance of a patch from a source of colonists decreases.
• Extinction rate is higher for small patches (which support smaller populations of the species because of smaller carrying capacity, K) and is lower for larger patches (which support larger populations).

In 1963, Robert MacArthur and E. O. Wilson published a conceptual model of island biogeography that takes a similar approach in predicting how many different species will be found in a patch of habitat, depending on size of the patch and its distance from a source of colonists. The patch in this case might be an island in the sea or an “island” of suitable habitat for the species in question surrounded by a “sea” of unsuitable habitat.

MacArthur and Wilson showed that their model successfully predicted two patterns seen with real oceanic islands: (1) islands closer to a mainland source of colonists support more species (higher species richness) than those more distant from the mainland and (2) larger islands support more species than smaller islands at the same distance from the mainland. This Animated Tutorial uses a probabilistic computer simulation to illustrate these main results of the MacArthur-Wilson model.

How the Simulation Model Works

The simulation model considers four islands, two of which (one small, one large) are close to a mainland, and two of which (again one small, one large) are more distant. The mainland supports ten equally abundant species of birds. Individuals of each species in this mainland species “pool” occasionally fly out to sea and may reach an island. The mainland population of each species is assumed to be so large that the supply of dispersers is not depleted by this occasional emigration out to sea, and the islands are assumed to be so far apart that dispersal between them doesn't occur.

The simulation begins with empty islands. In each time step, the simulation chooses a fixed number of individual birds at random from the 10 mainland species to fly out to sea from random points along the mainland shore. The chance that a given bird reaches an island depends on whether its flight path “runs into” the island; it also depends on whether the bird perishes before reaching the island. If the bird reaches an island that doesn't contain a population of its species, it is considered a “colonist” and establishes a new population, adding to the species richness of that island.

The population of each bird species on each island also has some chance of going extinct during each time interval. This probability is higher (and equal) for the two smaller islands because population size is proportional to island size, and lower (and equal) for the two larger islands. This feature agrees with the known fact that smaller populations are more at risk of extinction than larger ones.

Effects of Island Distance and Island Size on Species Richness

Go to the Simulation tab and click on “Reset” to set the system to its starting configuration. Now click on “Start/Stop” to begin the simulation. Birds fly out into the sea and some of them reach and colonize an island. When a bird successfully colonizes an island, the mainland is connected to the island with an arrow. The species present on an island at any time step are indicated by “pie segments” of different colors within the circle that represents the island, and the total number of species is indicated in the center of the circle. The size of the circle indicates whether the island is small or large, but circles aren't drawn to scale to make the pie segments large enough to see. The position of the island indicates whether it is far or near, but distances also aren't drawn to scale.

As the simulation runs, notice that arrows appear at different rates for the four islands, and that the numbers and colors of species present on the islands change as colonization and extinction processes occur—the island communities are dynamic, changing through time as resident species go extinct and new species colonize.

The number of time steps is shown in the upper right of the simulation image. Stop the simulation after a hundred time steps or so and click on the “Summary” button to see the number of species (species richness) on each island averaged over these time steps. Write down these numbers for the four islands. How do closer and more distant islands of the same size compare? How do smaller and larger islands of the same distance compare? Click “Start” to continue the simulation and “Stop” again after roughly another hundred time steps. Have the average species richness values on the four islands changed? Have their relative species richnesses changed? Why or why not? Are these results in agreement with predictions from the MacArthur-Wilson conceptual model of island biogeography (see Concept 44.4 and Figure 44.11 in the textbook)?

Effects of Island Distance and Island Size on Colonization and Extinction Rates

Note that the “Summary” tab shows the average extinction rate for each island—the average number of bird species that went extinct per time step. It also shows the average colonization rate—the average number of new species colonizing per time step. Write down these numbers for the four islands. What is the relationship between average colonization rate and average extinction rate on an island? How do these rates compare for closer and more distant islands of the same size? How do they compare for small and large islands at the same distance? Are these patterns in agreement with the MacArthur-Wilson model (see Concept 44.4 and Figure 44.11 in the textbook)?

The Approach to Equilibrium

You can use the simulation to explore how the equilibrium species richness is achieved by clicking “Reset” to empty the islands and then toggling “Start/Stop” in quick succession. Do this to run the simulation for 3–5 time steps. Pick one of the “near” islands and record how many species are on it, the average colonization rate and the average extinction rate. Are these rates the same? Now “Start” the simulation again and stop after 3–5 more time steps. Has the species number changed? What's happened to the average colonization and extinction rate? Repeat this a few more times. What happens to the colonization and extinction rates as the island fills with species?

Also note that the “Summary” button shows the average extinction rate for each island, that is, the average number of bird species that went extinct per time step. How do these values compare for closer and more distant islands, and for smaller and larger islands?

The MacArthur-Wilson model can be thought of as a model of a metacommunity as opposed to a metapopulation. It is a conceptual model of a dynamic system, just as the metapopulation model is. By this we mean that the processes of colonization and extinction are occurring continuously, as is realistic for actual ecological populations and communities. Although change is ongoing—the average species richness of each island fluctuates somewhat through time, as do the identities of the bird species present on the islands—each island reaches an equilibrium species richness, $\hat{S}$. This equilibrium is a dynamic equilibrium, a dynamic balance between colonization and extinction of different species.

Initially, new species arrive at a faster rate than go extinct on an empty island. As the island fills with species, however, fewer and fewer successful colonists found a new population—colonization rate decreases—and more and more species are present to go extinct—extinction rate increases. Eventually, average colonization rate converges on average extinction rate, and species richness becomes more-or-less constant—it reaches an equilibrium. This equilibrium species richness is predicted by the MacArthur-Wilson model to be greater for large than small islands, and for near than far islands because per-species extinction rates are greater for small than large islands, and per-species dispersal rates are greater for near than far islands. Because colonization and extinction are probabilistic, species richness fluctuates around the equilibrium value, $\hat{S}$, decreasing when by chance extinctions exceed colonizations in a time step, or increasing when by chance colonizations exceed extinctions.

Despite the relative constancy of species richness, the species composition on an island (see page 900 of the text) changes through time, at a rate of turnover that is equivalent to the average colonization or extinction rate at equilibrium. The MacArthur-Wilson model predicts higher turnover for smaller islands and for those closer to the mainland than for larger ones and more distant ones (contemplate the y-axis in Figure 44.11 of the textbook, as well as the turnover in actual arthropod species depicted in Apply the Concept, p. 910 of the textbook).

Textbook Reference: Concept 44.4 Diversity Patterns Provide Clues to What Determines Diversity