  Researchers and managers model ecological communities to infer the biotic and
abiotic variables that shape species' ranges, habitat use, and co-occurrence
which, in turn, are used to support management decisions and test ecological
theories. Recently, species distribution models were developed for and applied
to data from ecological communities. Model development and selection for
ecological community data is difficult because a high level of complexity is
desired and achieved by including numerous parameters, which can degrade
predictive accuracy and be challenging to interpret and communicate. Like other
statistical models, multi-species distribution models can be overparameterized.
Regularization is a technique that optimizes predictive accuracy by shrinking
or eliminating model parameters. For Bayesian models, the prior distribution
automatically regularizes parameters. We propose a tree shrinkage prior for
Bayesian multi-species distributions models that performs regularization and
reduces the number of regression coefficients associated with predictor
variables. Using this prior, the number of regression coefficients in
multi-species distributions models is reduced by estimation of unique
regression coefficients for a smaller number of guilds rather than a larger
number of species. We demonstrated our tree shrinkage prior using examples of
presence-absence data for six species of aquatic vegetation and relative
abundance data for 15 species of fish. Our results show that the tree shrinkage
prior can increase the predictive accuracy of multi-species distribution models
and enable researchers to infer the number and species composition of guilds
from ecological community data.
