F. Guillaume Blanchet

This paper proposes a new way of using forward selection of explanatory variables in regression or canonical redundancy analysis. The classical forward selection method presents two problems: a highly inflated Type I error and an overestimation of the amount of explained variance. Correcting these problems will greatly improve the performance of this very useful method in ecological modeling. To prevent the first problem, we propose a two-step procedure. First, a global test using all explanatory variables is carried out. If, and only if, the global test is significant, one can proceed with forward selection. To prevent overestimation of the explained variance, the forward selection has to be carried out with two stopping criteria: (1) the usual alpha significance level and (2) the adjusted coefficient of multiple determination (Ra(2)) calculated using all explanatory variables. When forward selection identifies a variable that brings one or the other criterion over the fixed threshold, that variable is rejected, and the procedure is stopped. This improved method is validated by simulations involving univariate and multivariate response data. An ecological example is presented using data from the Bryce Canyon National Park, Utah, U.S.A.

Community ecology aims to understand what factors determine the assembly and dynamics of species assemblages at different spatiotemporal scales. To facilitate the integration between conceptual and statistical approaches in community ecology, we propose Hierarchical Modelling of Species Communities (HMSC) as a general, flexible framework for modern analysis of community data. While non-manipulative data allow for only correlative and not causal inference, this framework facilitates the formulation of data-driven hypotheses regarding the processes that structure communities. We model environmental filtering by variation and covariation in the responses of individual species to the characteristics of their environment, with potential contingencies on species traits and phylogenetic relationships. We capture biotic assembly rules by species-to-species association matrices, which may be estimated at multiple spatial or temporal scales. We operationalise the HMSC framework as a hierarchical Bayesian joint species distribution model, and implement it as R- and Matlab-packages which enable computationally efficient analyses of large data sets. Armed with this tool, community ecologists can make sense of many types of data, including spatially explicit data and time-series data. We illustrate the use of this framework through a series of diverse ecological examples.

There is a rich amount of information in co-occurrence (presence-absence) data that could be used to understand community assembly. This proposition first envisioned by Forbes (1907) and then Diamond (1975) prompted the development of numerous modelling approaches (e.g. null model analysis, co-occurrence networks and, more recently, joint species distribution models). Both theory and experimental evidence support the idea that ecological interactions may affect co-occurrence, but it remains unclear to what extent the signal of interaction can be captured in observational data. It is now time to step back from the statistical developments and critically assess whether co-occurrence data are really a proxy for ecological interactions. In this paper, we present a series of arguments based on probability, sampling, food web and coexistence theories supporting that significant spatial associations between species (or lack thereof) is a poor proxy for ecological interactions. We discuss appropriate interpretations of co-occurrence, along with potential avenues to extract as much information as possible from such data.