What do we need to construct a theory of landscape demography? As a first step, we have developed an analytical framework that allows us to examine how the behavior of an ensemble of populations emerges from information about individual populations and their covariances. We adapt ideas from modern portfolio theory, a framework heavily used in finance.
This framework allows us to describe how the means, standard deviations, and covariances of growth rates for a number of individual populations can combine (based on the relative sizes of the populations) to give a set of means and standard deviations of growth of the entire ensemble. We can calculate the limiting values of this set from the theory, and from this one can find such things as the combination that gives the globally minimum variance, or the maximum (and minimum) ensemble growth rates for any standard deviation. There are simple graphical methods for asking how different nearby values are, so we are not restricted to examining optima.
Results/Conclusions
Using this approach, we can ask a number of biological questions with considerable importance for conservation and invasion biology. These include: How does the addition of new populations, or loss of existing populations, change the shape or location of the ensemble set of growth rates and sd’s? How do changes in the relative sizes of the individual populations change the ensemble mean and sd? How do these affect estimates of quasi-extinction risk?
The data required are time series of multiple local populations, which are becoming increasingly available to ecologists. We illustrate the approach with some examples from freely available data sets. The examples demonstrate that the estimates of the limiting sets are rather robust to violations of assumptions of normality in the underlying theory.