Parameter and uncertainty estimation for process-oriented population and distribution models: data, statistics and the niche
Abstract
The spatial distribution of a species is determined by dynamic processes such as reproduction, mortality and dispersal. Conventional static species distribution models (SDMs) do not incorporate these processes explicitly. This limits their applicability, particularly for non‐equilibrium situations such as invasions or climate change. In this paper we show how dynamic SDMs can be formulated and fitted to data within a Bayesian framework. Our focus is on discrete state‐space Markov process models which provide a flexible framework to account for stochasticity in key demographic processes, including dispersal, growth and competition. We show how to construct likelihood functions for such models (both discrete and continuous time versions) and how these can be combined with suitable observation models to conduct Bayesian parameter inference using computational techniques such as Markov chain Monte Carlo. We illustrate the current state‐of‐the‐art with three contrasting examples using both simulated and empirical data. The use of simulated data allows the robustness of the methods to be tested with respect to deficiencies in both data and model. These examples show how mechanistic understanding of the processes that determine distribution and abundance can be combined with different sources of information at a range of spatial and temporal scales. Application of such techniques will enable more reliable inference and projections, e.g. under future climate change scenarios than is possible with purely correlative approaches. Conversely, confronting such process‐oriented niche models with abundance and distribution data will test current understanding and may ultimately feedback to improve underlying ecological theory.
What the paper shows and why it matters
(AI-generated)
Species’ distributions arise from dynamic processes such as reproduction, mortality and dispersal. Most statistical species distribution models, however, are static: they relate recorded occurrences to environmental variables, which is quick, but they assume that the species is in equilibrium with its environment and usually ignore dispersal. Ignoring dispersal matters for invasions and climate change, the paper notes, since a species may be absent from a site more because it has not arrived than because the site is unsuitable. Process-based models exist, but fitting them to the data at hand (maps, counts, prior knowledge) has been difficult. The problem the paper takes on is how to confront such dynamic models with these data and quantify the uncertainty.
The paper shows that process-based species distribution models, static or dynamic, can be fitted to data with one generic Bayesian scheme that quantifies uncertainty. The likelihood is built from a process model, for population change, and an observation model, for detection. Combined with priors (what is known beforehand), the posterior is sampled by Markov chain Monte Carlo, a sampling algorithm; in stochastic models the unobserved population history is inferred along with the parameters. Three examples illustrate the scheme; the first uses a static equilibrium niche model. In a simulation with presence/absence data from one time point, the 95% credibility intervals contained the true parameter values. For Rhododendron ponticum in Britain, 1970–2000, a colonisation model (Catterall et al. 2012; the application to this species was previously unpublished) matched the observed 1987 colonisations by visual comparison and gave a risk map for 2030. In a virtual study taken from Pagel and Schurr (2012), combining maps and abundance time series, the fitted model forecast ranges accurately even under severe dispersal limitation.
The paper argues that fitting process-oriented niche models allows more reliable inference and projections under climate change than purely correlative models, and that confronting them with data will test, and may improve, ecological theory about the niche. Limits remain: calculating the likelihood exactly may become costly as models grow, so the paper names likelihood-free and particle Markov chain Monte Carlo methods as possible alternatives. Caley et al. (2015) cite the paper for the point that exact likelihood calculation is impractical for invasion models, which motivates their approximate Bayesian computation.
References
- Catterall et al. (2012). Accounting for uncertainty in colonisation times: a novel approach to modelling the spatio‐temporal dynamics of alien invasions using distribution data. Ecography 35, 901–911. doi:10.1111/j.1600-0587.2011.07190.x
- Pagel & Schurr (2012). Forecasting species ranges by statistical estimation of ecological niches and spatial population dynamics. Global Ecology and Biogeography 21, 293–304. doi:10.1111/j.1466-8238.2011.00663.x
- Caley et al. (2015). Inferring the Distribution and Demography of an Invasive Species from Sighting Data: The Red Fox Incursion into Tasmania. PLOS ONE 10, e0116631. doi:10.1371/journal.pone.0116631