Predicting the relationship between local and regional species richness from a patch occupancy dynamics model

1. A linear relationship between the number of species in ecological communities (local richness) and the species pools from which the communities are drawn (regional richness) suggests that species interactions are not sufficient to limit local richness and that communities are not saturated with species. Instead, this relationship implies that communities are open to regional influences and are interlinked by dispersal. 2. Here we show how the linear relationship between local and regional richness in real, noninteractive, assemblages of cynipid gall wasps on California oaks, can be predicted from a simple patch-occupancy model. 3. One cynipid assemblage has been surveyed for 3 years, allowing for crude estimates of colonization and extinction rates per patch. Using the mainland/island model of patch occupancy dynamics, these rates are combined with the observed number of cynipid species associated with each oak species (regional richness) to predict the expected local species richness in each patch. Assuming that species are independently distributed among localities, the expected variance in species richness among localities is also computed. 4. The model is then tested on an independent data set. When differences in sampling effort (number of surveyed trees per locality) were accounted for, the regression equation relating observed (n = 41) to predicted local species richness does not differ statistically from the line of perfect agreement. The residuals are also distributed according to the predicted variance. 5. Although not statistically significant, the variance in local richness appears to be slightly underestimated by the model. One explanation may be that cynipid species display some positive covariance in their distribution among localities, that is, groups of species occur together in given localities more frequently than would be expected by chance. Variance ratio tests identified statistically positive covariance within cynipid assemblages for three oaks species. 6. The close fit of the model to the data supports the theoretical scenario for noninteractive communities, that the slope of the local-regional richness relationship and patch-occupancy processes are different expressions of the same phenomenon.