The inflationary effects of environmental fluctuations in source-sink systems

Abstract

Ecological communities are open to the immigration of individuals and are variable through time. In open habitats immigration may permit populations of a species to persist locally even though local biotic and abiotic processes tend to exclude such "sink" populations. A general model for a sink population reveals that autocorrelated environmental variation can dramatically inflate local abundance and that such populations display a characteristic "outbreak" pattern. An experimental protist microcosm exhibits these predicted effects. Because the many ecological and environmental processes that set the rate of exclusion are typically autocorrelated, these theoretical and empirical results have broad implications for our understanding of community structure and highlight a previously unsuspected potential effect of anthropogenic climate change.

Fig 1.

Examples of time series of population size in a variable sink environment, using model 1, with f(t) = r(t) − dN(t). In these examples, the mean intrinsic growth 〈 r 〉 = −1, the immigration rate I = 1, and the strength of density dependence d = 0.001, so in a constant environment N* = 0.999. Examples are shown for two different magnitudes of serial autocorrelation [the SD of r(t) is σ_r = 1.5]; the autocorrelation time constant = 0.25 in the weakly correlated environment and 2 in the strongly correlated environment. Because we assume weak density dependence in the sink environment, during runs of favorable years the population can outbreak to high densities. See Appendix for technical details and definitions of parameters.

Fig 2.

(Left) Surface plot of time-averaged population size in variable sink environments, as a function of the magnitude of variation (right horizontal axis) and the strength of autocorrelation, t_c (left horizontal axis). Other parameters are the same as in Fig. 1. The vertical axis is density on a log scale. (Right) Surface plot of the coefficient of variation (N) as a function of magnitude of variation and the strength of autocorrelation.

Fig 3.

Experimental time series of P. tetraurelia (•, daily densities) under differing temperature regimes (continuous lines; e.g., horizontal for constant temperature treatment). a and b correspond to a replicate from each of the treatments W1 and R1 described in the text. c and d correspond to a replicate from each of the treatments W2 and R2. e and f correspond to the two constant, low-temperature sink controls.