1. Mathematical analysis of partial differential equations (PDEs) has led to many insights regarding the effect of organism movements on spatial population dynamics. However, their use has mainly been confined to the community of mathematical biologists, with less attention from statistical and empirical ecologists. We conjecture that this is principally due to the inherent difficulties in fitting PDEs to data.
2. To help remedy this situation, in the context of movement ecology, we show how the popular technique of step selection analysis (SSA) can be used to parametrize a class of PDEs, called diffusion‐taxis models, from an animal's trajectory. We examine the accuracy of our technique on simulated data, then demonstrate the utility of diffusion‐taxis models in two ways. First, for non‐interacting animals, we derive the steady‐state utilization distribution in a closed analytic form. Second, we give a recipe for deriving spatial pattern formation properties that emerge from interacting animals: specifically, do those interactions cause heterogeneous spatial distributions to emerge and if so, do these distributions oscillate at short times or emerge without oscillations? The second question is applied to data on concurrently tracked bank voles Myodes glareolus.
3. Our results show that SSA can accurately parametrize diffusion‐taxis equations from location data, providing the frequency of the data is not too low. We show that the steady‐state distribution of our diffusion‐taxis model, where it is derived, has an identical functional form to the utilization distribution given by resource selection analysis (RSA), thus formally linking (fine scale) SSA with (broad scale) RSA. For the bank vole data, we show how our SSA‐PDE approach can give predictions regarding the spatial aggregation and segregation of different individuals, which are difficult to predict purely by examining results of SSA.
4. Our methods provide a user‐friendly way into the world of PDEs, via a well‐used statistical technique, which should lead to tighter links between the findings of mathematical ecology and observations from empirical ecology. By providing a non‐speculative link between observed movement behaviours and space use patterns on larger spatio‐temporal scales, our findings will also aid integration of movement ecology into understanding spatial species distributions.

中文翻译：

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使用步选择分析从动物运动轨迹参数化扩散出租车方程

1. 偏微分方程（PDE）的数学分析已引起有关生物运动对空间种群动态的影响的许多见解。但是，它们的使用主要局限于数学生物学家社区，而统计学和经验生态学家对此的关注较少。我们推测这主要是由于将PDE拟合到数据中的固有困难。
2. 为了纠正这种情况，我们在运动生态学的背景下，展示了如何使用流行的步选择分析（SSA）技术对一类PDE（称为扩散出租车）进行参数化。动物轨迹的模型。我们检查了我们的技术在模拟数据上的准确性，然后以两种方式证明了扩散出租车模型的实用性。首先，对于非交互性动物，我们以封闭的分析形式得出稳态利用率分布。其次，我们给出了从交互动物中得出的空间模式形成特性的诀窍：具体而言，这些交互作用会导致异质空间分布的出现吗？如果是的话，这些分布是否会在短时间内振荡或出现而没有振荡？第二个问题适用于同时跟踪的田鼠“ Myodes glareolus”的数据。
3. 我们的结果表明，只要数据的频率不太低，SSA可以根据位置数据准确地参数化扩散出租车方程。我们证明了我们所得到的扩散出租车模型的稳态分布与资源选择分析（RSA）给出的利用率分布具有相同的功能形式，因此正式将（精细规模）SSA与（大规模）联系起来。 ）RSA。对于银行田鼠数据，我们展示了我们的SSA-PDE方法如何能够提供有关不同个体的空间聚集和分离的预测，而仅通过检查SSA的结果很难完全预测这些预测。
4. 通过一种常用的统计技术，我们的方法为PDE的世界提供了一种用户友好的方法，这将导致数学生态学的发现与经验生态学的观察之间的紧密联系。通过在较大的时空尺度上提供观察到的运动行为与空间利用模式之间的非推测性联系，我们的发现还将有助于将运动生态学整合到理解空间物种分布中。