When does modelling dependence change the target of biodiversity indicators?

Oliver L. Pescott 

Recent biodiversity trend analyses have modelled uncertainty arising from temporal, spatial and phylogenetic dependence. For descriptive indicators such as the Living Planet Index (LPI) however, a prior question is whether dependence modelling improves estimation of a fixed quantity or risks changing the quantity being reported. Using the high-profile case of Johnson et al. (2024), the current paper argues that covariance-rich hierarchical models can make this relationship ambiguous. When aggregate trends are estimated as common coefficients in latent models with structured covariance, observations contribute unequal independent information through assumed redundancy among related units. The reported collective trend may therefore be a model-based coefficient (e.g. a mean over a latent-effect distribution) shaped by partial pooling and dependence structure, rather than the sampled panel average under declared weights that indicator users may assume. A further ambiguity is whether the reported coefficient summarises the analysed panel or supports claims about a broader spatial, taxonomic or other policy-relevant domain. The defensible reply, that the model is merely a more efficient estimator of a panel average, requires explicit statement of the estimand, weighting scheme, relationship between the model output and that estimand, and evidence of performance for that target; predictive success alone is insufficient for this descriptive claim. The implication is that covariance-rich indicator analyses should state the estimand, the role of dependence modelling, missing data assumptions and domain of inference before interpreting the resulting trend for scientific applications.