Model-based analysis of species composition (mvabund modeling) provides many advantages for hypothesis testing and model evaluation. One is that these approaches explicitly model the relationship between mean and variance of abundance. However, producing an overall summary plot of changes in multivariate species composition has been difficult. Most plots focus on individual species, although mixture models can be used to provide plots that show certain changes in multivariate species composition. I develop a mostly model-free approach to plotting multivariate species composition. This approach retains the variance-to-mean relationship and data-distribution from a model-based analysis but makes no additional assumptions about the mean structure.
Results/Conclusions
The variance-to-mean and data distribution models define a new likelihood-based distance between each pair of observations. nMDS is then used to portray those distances. The approach can be extended to overlay model-based predictions of multivariate species composition on an nMDS plot of the raw data. This approach is illustrated using the temporal trend in bird abundance on Skokholm Island. The results clearly demonstrate that a linear trend model does not describe the overall pattern of changes in abundance.