Model-based ordination for phenological studies: from controlling sampling bias to inferring temporal associations

Hao Ran Lai 

Willig et al. (Methods in Ecology and Evolution, 15, 868--885, 2024) cautioned that unequal sampling effort and pseudoreplication can bias the characterisation of species phenology using circular statistics. Borrowing concepts from rarefaction, they proposed bootstrapping to control for time-varying marginal totals that arise from unequal sampling effort over time. This study extends their cautionary notes to regressions of phenological time series, where bootstrapping can be replaced by various built-in functionalities of generalised linear mixed-effect models. I further take this opportunity to borrow a key innovation in model-based ordination and joint species distribution modelling --- generalised linear latent variable models (GLLVM) --- to illustrate its ability in extracting more information out of multispecies phenological data beyond circular statistics. With sampling-bias adjustment, GLLVMs, or regressions in general, are robust predictive and inferential tools that enrich our phenological understandings in conjunction with circular statistics for hypothesis testing.