Measurement error models reveal the scale of consumer movements along an isoscape gradient

Abstract

In isotopic studies of mobile consumers, measurement error in spatial location is almost inevitable when individuals are observed only once. This error can have considerable impacts on the interpretation of ecologically important features, such as individual movement behaviour and dietary niche breadth. This study introduces a measurement error modelling framework for estimating movement scale and isotopic fractionation for consumers that move and feed along a linear isoscape gradient. The model assumes that the key mechanism underlying the difference in spatial isotopic regression slopes of mobile consumers and their baseline resources is the presence of measurement error in the spatial location of consumers. Measurement error is assumed to arise from consumer movements, which are represented by realistic movement kernels. Simulations with known parameter values are used to evaluate the performance of the models under scenarios involving different combinations of consumer mobility and sample size. Several variants of the model are fit to empirical data, and their parameter estimates are compared with those of alternative models. In simulations with known parameter values, model estimates of movement scale converged to the known values and had substantially smaller bias and variance than those of alternative models. Estimates of movement scale and fractionation for empirical data were consistent with previously reported estimates. Neglecting measurement error in spatial location is likely to hinder progress in spatial isotopic analyses. The proposed framework provides a statistically principled basis for incorporating measurement error in spatial location into isoscape analyses to provide improved estimates of parameters of interest, such as movement scale and fractionation. The framework is sufficiently general to be applicable to a variety of species, isotopic tracers, environments and spatial scales. Logical next steps to extend the framework could involve modelling of multiple species, nonlinear isoscape gradients and 2‐dimensional isoscapes.