Nonparametric Identifiability in Species Distribution and Abundance Models: Why it Matters and How to Diagnose a Lack of it Using Simulation

Strong parametric assumptions are often made when formulating statistical models in practice. In the field of ecology, these assumptions have sparked repeated debates about identifiability of species distribution and abundance models. We leverage econometrics literature to broaden the view of the problem. Nonparametric identifiability exists when a model could, in theory, be estimated without parametric assumptions. Even if in practice an ecologist will not fit a nonparametric model, the potential to do so means the data are informative for desired goals. Our approach for determining whether nonparametric identifiability holds in targeted parts of the model is based on relaxing particular parametric assumptions. We approximate a nonparametric relationship as a flexible, unpenalized spline fit to simulated data with increasing sample sizes. We show the importance of semi-parametric identifiability, nonparametric identifiability achieved in part of a model, with presence-only models, single-visit occupancy and abundance models, and capture-recapture models with detection heterogeneity. In each case, we use our simulation approach to illustrate that when nonparametric identifiability holds in a regression relationship, even a mis-specified parametric model may provide a useful approximation of properties of interest like prevalence and average occurrence and abundance, the fit of alternative models can be compared, and parametric assumptions can be checked. When semi-parametric identifiability does not hold, parametric assumptions create artificial identifiability, and alternative models cannot be distinguished empirically. We argue that ecologists, and modelers in general, should be most confident in results when a stronger form of identifiability holds.