[Paper Review] Point process models for spatio-temporal distance sampling data

Yun Yuan, Fabian E. Bachl+6 more|arXiv (Cornell University)|Apr 20, 2016

Point processes and geometric inequalities48 references5 citations

TL;DR

This paper proposes a model-based inference framework using a spatial log-Gaussian Cox process and SPDE-INLA to estimate blue whale density at fine spatial scales from distance sampling data, enabling simultaneous modeling of detection and spatially structured density while revealing unexplained spatial variation not captured by covariates.

ABSTRACT

Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.

Motivation & Objective

• Address the limitation of conventional distance sampling in estimating animal density at fine spatial resolutions, particularly for endangered species like the blue whale.
• Overcome the design-based constraints of traditional methods that restrict density estimation to survey stratum levels.
• Model temporal and spatial variation in blue whale density using a flexible, stochastic approach that accounts for unexplained spatial structure.
• Simultaneously fit detection and density models to improve inference accuracy and enable prediction at arbitrary spatial scales.
• Assess the influence of environmental covariates such as sea surface temperature on blue whale distribution and abundance trends over 22 years.

Proposed method

• Formulate the generation of distance sampling data as a thinned spatial point process to link detection and spatial distribution.
• Use a spatial log-Gaussian Cox process (LGCP) to model the underlying intensity of animal detections, allowing flexible spatial correlation structure.
• Apply the stochastic partial differential equation (SPDE) approach to represent the latent Gaussian field governing spatial variation in density.
• Employ integrated nested Laplace approximation (INLA) for fast, accurate Bayesian inference without MCMC sampling.
• Simultaneously estimate detection function parameters and spatially varying density using a hierarchical model framework.
• Enable prediction of density at any desired spatial resolution by leveraging the GP representation and SPDE approximation.

Experimental results

Research questions

• RQ1 Can a model-based approach improve spatial resolution in density estimation beyond the stratum level in distance sampling?
• RQ2 How does spatially structured variation in blue whale density relate to environmental covariates such as sea surface temperature?
• RQ3 What is the temporal trend in blue whale density across 22 years of surveys in the Eastern Tropical Pacific Ocean?
• RQ4 To what extent is unexplained spatial variation in density present after accounting for observed covariates?
• RQ5 How well do detection and density models co-estimate when fitted jointly using SPDE-INLA?

Key findings

• Higher blue whale density is significantly associated with colder sea surface temperatures in space, indicating a preference for cooler waters.
• There is a positive but weak association between mean annual temperature and blue whale density, though the overall trend over 22 years is consistent with no significant change.
• Substantial spatially structured variation in density remains unexplained by available covariates, highlighting the importance of latent spatial processes.
• The SPDE-INLA framework successfully enables fine-scale density prediction and joint modeling of detection and spatial distribution.
• The model reveals complex spatial patterns in blue whale distribution that are not captured by stratum-level estimates or simple covariate models.
• The method provides a robust, scalable approach for population estimation in data-limited, endangered species with sparse survey coverage.