Covariate-adjusted species response curves derived from long-term macroinvertebrate monitoring data using classical and contemporary model-based ordination methods

Abstract Species response curves describe the change in species abundance or probability of occurrence along an environmental gradient and can be useful tools for understanding the consequences of environmental change. I compare species (taxa) response curves to electrical conductivity derived by two multivariate methods—one based on a principal coordinates analysis (the “classical” method) and the other on latent variable models (the “contemporary” method)—from long-term (33-years) of aquatic macroinvertebrate and water quality data collected at six sites along 2200 km of the Murray River, Australia. In both cases the models included other environmental variables, and the response curves to electrical conductivity were adjusted for these covariates. The response curves were very similar by the two methods, but the contemporary method has many advantages. Unlike the classical method, the contemporary method explicitly accounts for the statistical properties of the data, and in particular the mean-variance relationship, thus enabling valid inference, and it provides interval estimates for the parameters of the model, allowing inferences to be drawn regarding the statistical significance of an individual taxon's relationship with electrical conductivity. For the data set used here with 104 taxa and 269 samples, the classical method, with 999 permutations to compute percentile confidence bands, took 12 min to execute on a laptop running a 2.8 GHz i7-7600U dual core CPU with 16 GB RAM, whereas the contemporary method (using the gllvm R package) took 6 min.