Rates of formation and dissipation of clumping reveal lagged responses in tropical tree populations.

The dynamics of spatial patterns of plant populations can provide important information about underlying processes, yet they have received relatively little attention to date. Here we investigate the rates of formation and dissipation of clusters and the relationship of these rates to the degree of aggregation (clumping) in models and in empirical data for tropical trees. In univariate models, exact solutions and simulations show that the rate of change of spatial patterns has a specific, linear relationship to the degree of aggregation at all scales. Shorter dispersal and/or weaker negative density dependence (NDD) result in both denser and longer-lasting clusters. In multivariate host-parasite models in contrast, the rate of change of spatial pattern is faster relative to the level of aggrega- tion. We then analyzed the dynamics of spatial patterns of stems ≥ 1 cm diameter in 221 tropical tree species from seven censuses spanning 28 yr. We found that for most species, the rates of change in spatial patterns were faster than predicted from univariate models given their aggregation. This indicates that more complex dynamics involving multivariate interactions induce time lags in responses to aggregation in these species. Such lags could arise, for example, if it takes time for natural enemies to locate aggregations of their hosts. This combination of theoretical and empirical results thus shows that complex multilevel models are needed to capture spatiotemporal dynamics of tropical forests and provides new insights into the processes structuring tropical plant communities.