Community surveys through space and time: testing the space-time interaction in the absence of replication

In order to test hypotheses about changes in the environment induced by man, including climatic change, ecologists are sampling portions of the environment repeatedly across time. This paper describes a method for testing a space-time interaction in repeated ecological survey data, when there is no replication at the level of individual sampling units (sites). This methodological development is important for the analysis of long-term monitoring data, including systems under anthropogenic influence. In these systems, an interaction may indicate that the spatial structure of community composition has changed in the course of time or that the temporal evolution is not the same at all sites. This paper describes ANOVA models corresponding to the steps leading to a solution to the problem, which is based on the representation of space and time by principal coordinates of neighbor matrices (PCNM eigenfunctions) in the ANOVA. Numerical simulations showed that ANOVA Model 5 was the model of choice for the analysis of the space-time interaction because it always had correct rates of Type I error, and its power was always equal to or higher than those of other possible models of analysis. If the hypothesis of absence of interaction is not rejected, one cannot conclude that a change has occurred in the spatial structure of the response data across time; one should follow the ordinary rules of two-way ANOVA if testing the significance of the main factors is of interest. If the hypothesis of absence of interaction is rejected, one should model the spatial structure of each time period in a separate way. One can also conduct a single test involving a separate model of the spatial structure for each time period. This paper presents two applications to real ecological data.