Multivariate Tweedie distribution for predicting diet proportions

Using regression methods to analyze diet proportions for a marked point process

Details

Diet samples often measure a count or biomass for different prey categories. Rather than converting these data to a proportion and fitting these proportions as data, we can instead represent diet samples as an outcome from a thinnned and double-marked point process, where marks include prey category and size per encounter, and thinning represents variation in attack and capture rates and is conceptually similar to detectability/catchability in other point-count sampling analyses. Analyzing raw prey measurements (rather than proportions) allows a wide range of models (and associated off-the-shelf software), predictions can still be converted to proportions (with associated standard errors) after the model is fitted, and we can represent covariance in prey measurements within a sample using covariates that explain sample-specific attack/capture rates.

     If the prey densities follow a 

     a Poisson point-process, and prey size per encounter follows a gamma 

     distribution, then the resulting distribution for biomass of each prey

     follows a multivariate Tweedie distribution. We therefore interpret

     the multivariate Tweedie distribution as a "process-based" model

     for prey samples.

References

Thorson, J. T., Arimitsu, M. L., Levi, T., & Roffler, G. H. (2022). Diet analysis using generalized linear models derived from foraging processes using R package mvtweedie. Ecology, 103(5), e3637. doi:10.1002/ecy.3637