Analyzing compositional data (sum of proportions = 1) using mixed models with explanatory variables for each proportion

Question

I aim to investigate how the relative abundance of species across communities is associated with the functional traits of each species. For each location ($>250$), I have compositional data that represents the relative abundances of various species, with the sum amounting to $100 \%$ for each location. I also have the values of three functional traits for each combination of location and species.

The challenge is in addressing the analysis given the compositional nature of the relative abundance data (where proportions are not independent). If I understood well, the methods I've encountered so far treat compositional data in aggregate (for example, modeling the entire composition of the community with some explanatory variables; e.g. book Analyzing Compositional Data with R, Van den Boogaart & Tolosana-Delgado. 2013; Chapter 5: Linear Models for Compositions), without allowing for modeling the relative abundance of each individual species in relation to its traits.

If my data were not compositional, my model might look something like this if using a mixed model in R with glmmTMB:

Prop.Abundance ~ Trait1 + Trait2 + Trait3 + (1|Species), family= beta

I had considered modeling the relative richness with the three traits as fixed effects, while treating species as a random effect to account for repeated measures. However, I am hesitant to include location as a random effect since it might regularize the values across species for the same community, which I believe does not make biological sense.

The dataset would consist of six variables: Location, Species, Relative Abundance, Trait1, Trait2, and Trait3. The number of observations would equal the sum of the number of species across locations. Note that not all species are always present (resulting in unbalanced data).

Could anyone guide me on how to approach this type of analysis, preferably using R?

Answer 1

See my answer on compositional response to https://stats.stackexchange.com/a/638757/284766 that includes a discussion on the book "Analyzing Compositional Data with R." Section 5.3 "Compositions as Dependent Variables" shows how to model the relative abundance of each individual species in relation to its traits. The method transforms the response variable of several columns of proportions using an isometric log-ratio transformation (ilr) into orthonormal coordinates before employing OLS linear regression. Because not all species are present in all locations, there will be some zero proportions. This will challenge the model fitting, as the transformation is based on log ratios and neither log(.../0) nor log(0/...) is defined. Chapter 7 discusses how to deal with zeroes. Also because of zero proportions, Dirichlet regression, not discussed in the book, is not directly usable. One method to circumvent zero proportions is to add a tiny amount to this proportion. See https://maartenbuis.nl/presentations/berlin10.pdf.

Because of zero proportions, the best choice might be fractional multinomial logit models using fmlogit as mentioned in my answer. I do not think that you should use models of random or mixed effects, unless you feel that proportions measured at different locations are correlated (spatial correlation) or multiple measurements of all species are taken at each location (longitudinal data). Although each species are measured more than 250 times, but these observations are independent unless there are spatial correlation among locations or temporal correlation among measurements. Species-specific intercepts in a multinomial logit model will assess the mean unobserved deviation by species. If random intercepts and slopes are somehow needed, you can check out the package mlogit, but I do not think this package accepts fractional response, so you may have to crack the original script.

If you concern that some species are similar and share unobserved traits, you could consider nested logit models. See https://cran.r-project.org/web/packages/mlogit/vignettes/e2nlogit.html.