When does modelling dependence change the interpretation of biodiversity indicators?

Oliver L. Pescott 

Recent biodiversity trend analyses have modelled uncertainty arising from temporal, spatial and phylogenetic dependence. For primarily descriptive indicators such as the Living Planet Indices (LPI) however, a prior question is whether dependence modelling improves estimation of a fixed quantity or actually changes 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 the relationship between a reported model coefficient and an intended estimand ambiguous. When aggregate trends are estimated from common coefficients in latent models with structured covariance, observations contribute unequal independent information to the estimator through assumed redundancy among related units. The reported collective trend is then a model-based coefficient (e.g. a mean over a latent-effect distribution) shaped by partial pooling and dependence; this is not automatically an average under declared estimand or “aggregation” weights that indicator trend users may assume. A further ambiguity is whether the reported coefficient summarises the analysed sample or supports claims about a broader spatial, taxonomic or other policy-relevant domain. One defensible reply, that the model is merely a more efficient estimator of a sample 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 not sufficient for this descriptive claim. Claims concerning broader generalisability require accompanying risk-of-bias assessments where evaluation against the true target (e.g. a time trend in some facet of global biodiversity) is unobtainable. The implication is that covariance-rich hierarchical indicator analyses should state the estimand, the role of dependence modelling, missing data assumptions and domain of inference clearly before interpreting the resulting trend for scientific or policy applications.