Analysis of relative abundances with zeros on environmental gradients: a multinomial regression model.

Fiona Chong,Matthew Spencer

doi:10.7717/peerj.5643

Abstract

Ecologists often analyze relative abundances, which are an example of compositional data. However, they have made surprisingly little use of recent advances in the field of compositional data analysis. Compositions form a vector space in which addition and scalar multiplication are replaced by operations known as perturbation and powering. This algebraic structure makes it easy to understand how relative abundances change along environmental gradients. We illustrate this with an analysis of changes in hard-substrate marine communities along a depth gradient. We fit a quadratic multivariate regression model with multinomial observations to point count data obtained from video transects. As well as being an appropriate observation model in this case, the multinomial deals with the problem of zeros, which often makes compositional data analysis difficult. We show how the algebra of compositions can be used to understand patterns in dissimilarity. We use the calculus of simplex-valued functions to estimate rates of change, and to summarize the structure of the community over a vertical slice. We discuss the benefits of the compositional approach in the interpretation and visualization of relative abundance data.

Highlights

Mosimann (1962) and Martin & Mosimann (1965) discussed how the nature of compositional data affects the interpretation of correlations between relative abundances of pollen types, How to cite this article Chong and Spencer (2018), Analysis of relative abundances with zeros on environmental gradients: a multinomial regression model
Exceptions include Jackson (1997), who explained how the interpretation of correlation, ordination and cluster analysis is affected by the properties of relative abundance data, López-Flores et al (2014), who showed that redundancy analysis of phytoplankton relative abundances was more ecologically informative under a compositional data analysis approach than under the usual approach, Gross & Edmunds (2015), who used compositional data analysis to develop time series models for coral reef composition, and Yuan et al (2016), who used the principles of compositional data analyses in comparisons between measures of temporal change in relative abundances
We showed that the vector space structure of the simplex leads naturally to tangible, functional and intuitive summaries of the changes in community compositions with depth in a subtidal marine system

Summary

Introduction

These are sets of non-negative numbers with a fixed sum (typically 1 or 100), and are examples of compositional data, defined as equivalence classes of proportional vectors with positive components Compositional data present some special challenges, arising from their constrained multivariate nature, including the absence of an interpretable covariance structure and the inappropriateness of simple parametric models (Aitchison, 1986, chapter 3). Many of these challenges have been addressed in the last few decades, leading to a coherent set of principles for the analysis of compositional data (Pawlowsky-Glahn & Buccianti, 2011). Exceptions include Jackson (1997), who explained how the interpretation of correlation, ordination and cluster analysis is affected by the properties of relative abundance data, López-Flores et al (2014), who showed that redundancy analysis of phytoplankton relative abundances was more ecologically informative under a compositional data analysis approach than under the usual approach, Gross & Edmunds (2015), who used compositional data analysis to develop time series models for coral reef composition, and Yuan et al (2016), who used the principles of compositional data analyses in comparisons between measures of temporal change in relative abundances

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