Jari Oksanen

Species spatial distributions are the result of population demography, behavioral traits, and species interactions in spatially heterogeneous environmental conditions. Hence the composition of species assemblages is an integrative response variable, and its variability can be explained by the complex interplay among several structuring factors. The thorough analysis of spatial variation in species assemblages may help infer processes shaping ecological communities. We suggest that ecological studies would benefit from the combined use of the classical statistical models of community composition data, such as constrained or unconstrained multivariate analyses of site‐by‐species abundance tables, with rapidly emerging and diversifying methods of spatial pattern analysis. Doing so allows one to deal with spatially explicit ecological models of beta diversity in a biogeographic context through the multiscale analysis of spatial patterns in original species data tables, including spatial characterization of fitted or residual variation from environmental models. We summarize here the recent progress for specifying spatial features through spatial weighting matrices and spatial eigenfunctions in order to define spatially constrained or scale‐explicit multivariate analyses. Through a worked example on tropical tree communities, we also show the potential of the overall approach to identify significant residual spatial patterns that could arise from the omission of important unmeasured explanatory variables or processes.

Summary 1. Tests of significance of the individual canonical axes in redundancy analysis allow researchers to determine which of the axes represent variation that can be distinguished from random. Variation along the significant axes can be mapped, used to draw biplots or interpreted through subsequent analyses, whilst the nonsignificant axes may be dropped from further consideration. 2. Three methods have been implemented in computer programs to test the significance of the canonical axes; they are compared in this paper. The simultaneous test of all individual canonical axes, which is appealing because of its simplicity, produced incorrect (highly inflated) levels of type I error for the axes following those corresponding to true relationships in the data, so it is invalid. The ‘marginal’ testing method implemented in the ‘vegan’ R package and the ‘forward’ testing method implemented in the program CANOCO were found to have correct levels of type I error and comparable power. Permutation of the residuals achieved greater power than permutation of the raw data. 3. R functions found in a Supplement to this paper provide the first formal description of the ‘marginal’ and ‘forward’ testing methods.

Joint Species Distribution Modelling (JSDM) is becoming an increasingly popular statistical method for analysing data in community ecology. Hierarchical Modelling of Species Communities (HMSC) is a general and flexible framework for fitting JSDMs. HMSC allows the integration of community ecology data with data on environmental covariates, species traits, phylogenetic relationships and the spatio-temporal context of the study, providing predictive insights into community assembly processes from non-manipulative observational data of species communities.The full range of functionality of HMSC has remained restricted to Matlab users only. To make HMSC accessible to the wider community of ecologists, we introduce Hmsc 3.0, a user-friendly r implementation.We illustrate the use of the package by applying Hmsc 3.0 to a range of case studies on real and simulated data. The real data consist of bird counts in a spatio-temporally structured dataset, environmental covariates, species traits and phylogenetic relationships. Vignettes on simulated data involve single-species models, models of small communities, models of large species communities and models for large spatial data. We demonstrate the estimation of species responses to environmental covariates and how these depend on species traits, as well as the estimation of residual species associations. We demonstrate how to construct and fit models with different types of random effects, how to examine MCMC convergence, how to examine the explanatory and predictive powers of the models, how to assess parameter estimates and how to make predictions. We further demonstrate how Hmsc 3.0 can be applied to normally distributed data, count data and presence-absence data.The package, along with the extended vignettes, makes JSDM fitting and post-processing easily accessible to ecologists familiar with r.