1. 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.
2. 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.
3. 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.
4. 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.

中文翻译：

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测量误差模型揭示了沿着等速线梯度的消费者移动规模

1. 在移动消费者的同位素研究中，当只观察一次个体时，空间位置的测量误差几乎是不可避免的。该错误可能会对生态学重要特征（例如个体运动行为和饮食生态位宽度）的解释产生重大影响。这项研究引入了一种测量误差建模框架，用于为沿线性等速线梯度移动和进食的消费者估算运动规模和同位素分数。
2. 该模型假设移动消费者及其基线资源的空间同位素回归斜率差异的根本原因在于消费者空间位置中存在测量误差。假定测量误差是由消费者运动引起的，消费者运动由现实的运动内核表示。具有已知参数值的模拟用于评估在涉及消费者流动性和样本数量的不同组合的情况下模型的性能。该模型的几种变体适合于经验数据，并将它们的参数估计值与替代模型的参数估计值进行比较。
3. 在具有已知参数值的模拟中，运动比例的模型估计收敛到已知值，并且比替代模型具有更小的偏差和方差。经验数据的运动规模和分数的估计与先前报道的估计一致。
4. 忽略空间位置的测量误差可能会阻碍空间同位素分析的进展。所提出的框架为将空间位置中的测量误差纳入等值线分析提供了统计学上的原则基础，以提供对感兴趣的参数（例如运动尺度和分数）的改进估计。该框架具有足够的通用性，可适用于各种物种，同位素示踪剂，环境和空间尺度。扩展该框架的逻辑下一步可能涉及多个物种，非线性等值线梯度和二维等值线的建模。