The joint modelling of many variables in community ecology is a new and technically challenging area with many opportunities for future developments. The possibility of extending joint models to deal with imperfect detection has been highlighted by Beissinger et al. as an important problem worthy of further investigation [1]. We agree, and previously pointed to this potential extension as an outstanding question [2], alongside models that can estimate phylogenetic repulsion or attraction, nonlin...

Technological advances have enabled a new class of multivariate models for ecology, with the potential now to specify a statistical model for abundances jointly across many taxa, to simultaneously explore interactions across taxa and the response of abundance to environmental variables. Joint models can be used for several purposes of interest to ecologists, including estimating patterns of residual correlation across taxa, ordination, multivariate inference about environmental effects and envir...

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evalua...

Classical gradient analysis continues to be used to explore and test theories and models in community ecology. Yet the foundations of classical gradient analysis were developed at a time when computational power was limited, relative to current computational power. I argue that this history has left a lasting legacy on the field. Consequently, many gradient analyses do not to take advantage of current computer technology. Here I show how to use computationally intensive Markov-chain Monte Carlo ...

The gypsy moth is considered one of the most harmful invasive forest insects in North America. It has been suggested that gypsy moth may indirectly impact native caterpillar communities via shared parasitoids. However, the impact of gypsy moth on forest insect food webs in general remains unstudied. Here we assess such potential impacts by surveying forest insect food webs in Ontario, Canada. We systematically collected caterpillars using burlap bands at sites with and without histories of gypsy...

Data frames are integral to R. They provide a standard format for passing data to model-fitting and plotting functions, and this standard makes it easier for experienced users to learn new functions that accept data as a single data frame. Still, many data sets do not easily fit into a single data frame; data sets in ecology with a so-called fourth- corner problem provide important examples. Manipulating such inherently multiple-table data using several data frames can result in long and difficu...

Ecology is inherently multivariate, but high-dimensional data are difficult to understand. Dimension reduction with ordination analysis helps with both data exploration and clarification of the meaning of inferences (e.g., randomization tests, variation partitioning) about a statistical population. Most such inferences are asymmetric, in that variables are classified as either response or explanatory (e.g., factors, predictors). But this asymmetric approach has limitations (e.g., abiotic variabl...

Functional diversity is an important concept in community ecology because it captures information on functional traits absent in measures of species diversity. One popular method of measuring functional diversity is the dendrogram-based method, FD. To calculate FD, a variety of methodological choices are required, and it has been debated about whether biological conclusions are sensitive to such choices. We studied the probability that conclusions regarding FD were sensitive, and that patterns i...

Studies in biodiversity-ecosystem function and conservation biology have led to the development of diversity indices that take species' functional differences into account. We identify two broad classes of indices: those that monotonically increase with species richness (MSR indices) and those that weight the contribution of each species by abundance or occurrence (weighted indices). We argue that weighted indices are easier to estimate without bias but tend to ignore information provided by rar...

SUMMARY 1. As a result of the role that temperature plays in many aquatic processes, good predictive models of annual maximum near-surface lake water temperature across large spatial scales are needed, particularly given concerns regarding climate change. Comparisons of suitable modelling approaches are required to determine their relative merit and suitability for providing good predictions of current conditions. We developed models predicting annual maximum near-surface lake water temperatures...