INTRODUCTION

Most species live not in one large combined population, but in multiple distinct populations that are separated in space to varying degrees. The entire set of populations in a region is called a metapopulation, or “population of populations.” The component populations are often called subpopulations. Subpopulations may (or may not) be linked to one another by dispersal—the movement of individuals among populations. Dispersal strongly influences the dynamics of a metapopulation and its subpopulations. When individuals disperse out of a population (emigration), the population size decreases; and when individuals successfully disperse into a subpopulation (immigration), the recipient population size increases.

If there is no emigration or immigration, each subpopulation is a closed system that grows or decreases according to the BD model of population size. In the BD model, if a subpopulation goes extinct (the population size N reaches zero), it will remain extinct, even though that patch of habitat may still be suitable for the species in question. As subpopulations “wink off” one by one, an entire metapopulation can become extinct relatively quickly.

In contrast, if individuals can move among subpopulations, each subpopulation is an open system that grows or shrinks according to the BIDE model. In this case, immigration can “rescue” a subpopulation that is on the brink of extinction by adding new individuals, thereby moving N farther from zero. Further, a suitable patch of habitat that is unoccupied because its subpopulation went extinct can be recolonized by immigrants from other subpopulations and once again “wink on.” The metapopulation with dispersal will persist much longer before going extinct than will a metapopulation without any exchange of individuals.

Click Instructions to explore the effects of subpopulation size and isolation on metapopulation dynamics.

How the metapopulation simulation works

This simulation considers a metapopulation of a hypothetical species of butterfly that consists of four subpopulations surrounded by a “sea” of unsuitable habitat. The maximum sustainable size of each subpopulation (its carrying capacity, K) is indicated by the area of its circular habitat patch, and the size of the subpopulation at a particular time is indicated by the colored portion of the circle.

The simulation starts with all subpopulations at their carrying capacity. Through time, each subpopulation changes in size—decreasing when individuals die or emigrate and increasing when individuals are born or immigrate; all of these demographic processes are probabilistic, so the number of individuals added to or lost from a subpopulation varies through time. Each emigrant sets out from its source subpopulation in a random straight-line direction. Its chance of reaching another subpopulation before it starves depends on the diameters of the other subpopulations (and thus the chance that the path of the emigrant “runs into” that subpopulation). When subpopulations are farther apart, the chances of running into them decreases, and fewer emigrants reach another subpopulation. If an emigrant is successful in reaching another subpopulation, it is added to that subpopulation. A subpopulation goes extinct if no individuals give birth or immigrate, and all die or emigrate, during a time interval. When a subpopulation goes extinct, the circle is empty and the butterfly in the center disappears. Extinct subpopulations remain empty unless they are recolonized by immigration. The simulation stops when all four subpopulations go extinct.

To run the simulation, go to Simulation. Click “Reset” to set the four populations to their maximal sustainable size, K. Then click on “Start/Stop” to run the simulation. Notice that each subpopulation fills and empties through time. Stop the simulation by clicking the “Start/Stop” toggle, and then click on “Summary” to see more information on the history of each subpopulation up to that time—this will tell you the extinction rate for the subpopulation (the number of times the subpopulation went extinct divided by the number of time steps when its size was greater than zero), and its average size when it wasn’t extinct (expressed as a fraction of its K).

Now click “Reset” to rerun the simulation, and stop it after approximately the same time as the first simulation. Examine the summary. Are the results exactly the same as the first simulation run? Do you expect them to be the same?

This illustrates an important property of probabilistic simulations: they do not produce exactly the same results in repeated runs, because the demographic processes of birth, death, and dispersal contain an element of chance, just as nature does. This means that a single simulation run can be viewed as a single observation, much like the observation of the weight of a single fish (see Appendix B of the textbook). What does this tell you about the value of increasing your sample of simulations? (Hint: See Activity B1 Standard Deviations, Standard Errors, and Confidence Intervals Simulation.)

Metapopulation dynamics without dispersal

To explore metapopulation dynamics in the absence of dispersal, click on the “No dispersal” box underneath the four circles, and choose “Less” for “Distance” (the distance between subpopulations of the metapopulation). Then click the “Start/Stop” button to start the simulation and notice that the subpopulations change in size.

The simulation will probably end pretty quickly with the entire metapopulation going extinct. Notice the number of time steps that elapse before this happens. Write this number down. Click the “Summary” button to learn more about the fate of each subpopulation. The extinction rate for each subpopulation without dispersal can be thought of as unity divided by the number of time steps until it went extinct. Do larger populations (indicated by larger circles) persist longer and therefore have lower extinction rates than smaller ones do? To detect patterns it is important to repeat the simulation many times to obtain averages. This is true for all of the versions of the simulation that you try.

Now “Reset” and select “More” for the “Distance” and repeat the simulation. Were the same subpopulations still more or less prone to extinction? Which subpopulations were more likely to go extinct? Why? Did increasing the distance between subpopulations alter the outcome of the simulation or the time to extinction of the entire metapopulation? Why or why not?

Metapopulation dynamics with dispersal

Click again the “No dispersal” box to uncheck it and allow dispersal, click “Reset,” again choose “Less” for “Distance” and run the simulation. What happens this time? Does the simulation stop by itself? If you grow tired of watching, you can stop the simulation at any point by clicking the “Start/Stop”“ button. Now look at the “Summary” button and the number of time steps. How do the values of extinction rate and average population size compare with those for the system without dispersal? What can you conclude about the effect of dispersal on subpopulation dynamics and how long the metapopulation persists?

The effect of distance

To see how the isolation of subpopulations (the distance between them) affects metapopulation dynamics, re-run the simulation allowing dispersal but choose “More” for “Distance.” Recall that the chance of successful immigration into a new subpopulation decreases as distance between subpopulations increases. Compare the results with what you just saw with less distance. What happens to overall time to extinction of the metapopulation? What happens to the average population sizes and extinction rates of the different subpopulations (now you can interpret the extinction rate as the fraction of the total number of time steps in which a subpopulation was extinct)?

When demographic processes like birth, death, and dispersal are probabilistic, or affected by chance, then populations can go extinct even when the average per-capita growth rate is positive. Smaller populations are more likely than large populations to go extinct by chance.

Dispersal affects the dynamics of a metapopulation system dramatically. If there is no dispersal, then there are no immigrants to recolonize subpopulations that go extinct. Subpopulations will “wink off” one by one, and the metapopulation itself may go extinct quite quickly.

Dispersal among subpopulations allows immigration to “rescue” subpopulations that are in danger of extinction, and to repopulate patches of suitable habitat where previous subpopulations have gone extinct. This allows the entire metapopulation to persist for much longer. In the simulation, you may have observed that the simple system of four subpopulations did eventually go extinct even when there was dispersal—but it may have taken a long time. Consider how much longer it would have taken with many more than four subpopulations or with a greater chance of successful dispersal!

Insights from simulations such as the one you have just explored have helped biologists to understand changes in the abundance of species in real ecological communities and landscapes. They also inform conservation ecologists and restoration ecologists who are trying to find ways to preserve endangered species or to restore ecological systems from which certain species have been lost.