South Australian Branch SSA December 2019 Meeting

The SA Branch was pleased to welcome Distinguished Professor Marti J. Anderson, a fellow of the Royal Society of New Zealand and a recent recipient of a prestigious James Cook Fellowship, to give the tenth E.A. Cornish Memorial Lecture. Marti holds the Professorial Chair in Statistics in the New Zealand Institute for Advanced Study (NZIAS) at Massey University in Auckland. She is an ecological statistician whose research is inter-disciplinary: from ecology to mathematical statistics. Her core research is in community ecology, biodiversity, multivariate analysis, models of ecological count data, experimental design and resampling methods, with a special focus on creating new applied statistics for ecology that can yield new insights into global patterns of biodiversity.

Her talk was based on a fundamental question in ecology – How do species respond to spatial or environmental gradients? To answer this question, one needs to think about how to best model these responses. A typical response is unimodal and a couple of classical models including generalized linear models (GLM) with one or more polynomial term(s) and a bell-shaped (Gaussian) curve were discussed to fit unimodal response patterns in ecology. However, there are problems with polynomial models because they are quite constrained and can generate unrealistic predictions (even yielding negative numbers). Meanwhile, Gaussian models don’t account for asymmetry.

Instead, something more flexible like generalized additive models, e.g. splines may be considered, but these do not provide interpretable parameters. Such flexible spline-type models also have only previously been applied to binary-type data.

Marti showed examples of real data of depth gradient distributions of different fish species in the NE Pacific. She explained her first principle of modelling is to re-visit data-types commonly encountered and re-visit genuinely observed patterns in such variables along large-scale gradients. The data were very messy and contained large numbers of zero values at certain depths.

The goal was to decide on a flexible nonlinear parametric mathematical form to model the mean response of species to environmental gradients. This needs to be coupled with a suitable statistical distribution to model the error structure. Model frameworks were discussed and four mean functions were introduced: Beta (modified), Sech (modified), HOF (Huisman, Olf, Fresco) and Gaussian mixtures. Various error distributions which could account for excess zeros and overdispersion were coupled with these four mean functions and models were compared using the AICc. Marti showed an example of the best fitting model for the Shortspine thornyhead (Sebastolobus alascanus), which was the Sech function combined with a zero-inflated negative binomial (ZINB).

Visualisations of these models for multiple species simultaneously were also discussed, including overlays of mean distributions, ordered ‘floating’ distributions and ordered ‘strip’ distributions.  A further example was given using data from the Continuous Plankton Recorder (CPR) from the North Atlantic. Beautiful visualizations displayed northern shifts in the latitudinal distributions of plankton species, showing how these have changed between 1960 and 2005: a cold-water species has contracted polewards, while a warm-water species has extended its range northwards.

Developments and extensions of these models are an area of current research and include cross-validation, estimation of variation in parameters, Bayesian approaches; extension of error distributions to include linked zero-inflated models, contagious distributions, under-dispersion, etc; modelling simultaneous responses of multiple species(Y), accounting for inter-specific associations; consideration of more than one gradient (X), including interactions; and ordination of species (modes, dispersions) in environmental space.

For more information contact m.j.anderson@massey.ac.nz

Yiwen (Wendy) Li