PARENT SESSION
Oral Session #74: Spatial Ecology: Models and Methods. Presiding: C. Loehle.
Friday, August 10, 2001. 8:00 AM to 11:30 AM. Hall of Ideas E.

Statistical mechanics of a continent-wide biological survey.

Keitt, Timothy¹, ¹

ABSTRACT- Ecologists, going back to Taylor, have long been interested in scaling phenomena. Motivated by recent studies of scaling in economic time series, I examine power-law scaling in population time series taken from the North American Breeding Bird Survey. For each species in the survey, I form a single time series by summing over all survey locations in a given year. I then estimate and remove from the time series the bias in these time series due to changes through time in the number and distribution of survey locations. I show that the standard deviation of population growth rates depends strongly on mean abundance and that this relationship is power-law with exponent 0.36+/-0.01. A null model for this relationship is that time series with higher means are sums of a greater number of independently fluctuating sub-populations. According the central limit theorem, we should see an exponent of 1/2, i.e., much less variability in highly abundance species. Two modifications of the null model can account for the greater variability of highly abundant species. The first is an increase in the size of sub-populations with increasing total population size which results in fewer sub-populations and higher variability in abundant species. The second is spatial synchrony in local population growth rates leading to a smaller effective number of sub-populations. I show that both these phenomena are present in the survey data. The resulting model predicts a wide range of macroecological patterns reported in the literature and present in the survey data. I also discuss why some species deviate widely from the overall scaling law.

KEY WORDS: metapopulations, statistical mechanics, scaling, stochastic population models