Statistical performance and information content of time lag analysis and redundancy analysis in time series modeling

Time lag analysis (TLA) is a distance-based approach used to study temporal dynamics of ecological communities by measuring community dissimilarity over increasing time lags. Despite its increased use in recent years, its performance in comparison with other more direct methods (i.e., canonical ordination) has not been evaluated. This study fills this gap using extensive simulations and real data sets from experimental temporary ponds (true zooplankton communities) and landscape studies (landscape categories as pseudo-communities) that differ in community structure and anthropogenic stress history. Modeling time with a principal coordinate of neighborhood matrices (PCNM) approach, the canonical ordination technique (redundancy analysis; RDA) consistently outperformed the other statistical tests (i.e., TLAs, Mantel test, and RDA based on linear time trends) using all real data. In addition, the RDA-PCNM revealed different patterns of temporal change, and the strength of each individual time pattern, in terms of adjusted variance explained, could be evaluated. It also identified species contributions to these patterns of temporal change. This additional information is not provided by distance-based methods. The simulation study revealed better Type I error properties of the canonical ordination techniques compared with the distance-based approaches when no deterministic component of change was imposed on the communities. The simulation also revealed that strong emphasis on uniform deterministic change and low variability at other temporal scales is needed to result in decreased statistical power of the RDA-PCNM approach relative to the other methods. Based on the statistical performance of and information content provided by RDA-PCNM models, this technique serves ecologists as a powerful tool for modeling temporal change of ecological (pseudo-) communities.