Island biogeography predicts that species will be stochastically lost and gained as a dynamic equilibrium is maintained.  Typically, island biogeography is used to make predictions about the resulting patterns in a landscape and data is collected at a single time period.  However, repeated measurements of diversity over time enable an examination of the mechanisms of island biogeography, not just the consequences.  Specifically, many communities in natural environments will be subject to environmental variation which may change rates of colonization and extinction over time.  In this research, we analyze data from a series of 1900 prairie quadrates from Cedar Creek Natural History Area which were repeatedly sampled over a 23-year time span.  The sampling interval varied from 3 years to 5 years, dependent on the availability of research funding—a common issue with long-term data sets.  In order to compare rates of colonization and extinction across sample periods of different lengths, colonization and extinction curves must be compared in a common time frame—most naturally on an annual basis.  This can factor out the confounding effect of time—for example, on the observed number of species lost over 3 years versus 5 years.

Results/Conclusions

A stochastic process model is used to extend an annual model of colonization and extinction over multiple years.  The model is computationally intensive as rates of colonization and extinction were found to be dependent on species richness and species richness probabilistically varies during unobserved years.  For example, the model accounts for all possible combinations of unobserved levels of richness that might be achieved by species colonizing a quadrant, and then going extinct before it is ever observed at the next sampling period.  This model is compared with empirical data using maximum likelihood techniques. We find that, when adjusted for different time intervals, average annual rates of colonization and extinction vary considerably among time periods.  As a consequence, the predicted long-term equilibrium species richness varies among time periods.  Furthermore, communities move toward the equilibrium richness, but do not attain the equilibrium.  As a consequence, communities are at times under-saturated and at times over-saturated.