Encounter rates link movement strategies to intra- and inter-specific interactions, and therefore translate individual movement behavior into higher-level ecological processes. Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range, and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially smaller than the population range, and are often capable of nonlocal perception. Here, we explore how these empirically supported behaviors change pairwise encounter rates. Specifically, we derive novel analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range. We compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived. For both models, we further explore how the interplay between the scale of perception and home-range size affects encounter rates. We find that neglecting realistic movement and perceptual behaviors can lead to systematic, non-negligible biases in encounter-rate predictions.

中文翻译：

---

远程居住和远程感知如何改变遭遇率。

遭遇率将运动策略与种内和种间相互作用联系起来，因此将个体运动行为转化为更高层次的生态过程。事实上，大量相互作用的人口理论都依赖于质量作用定律，这可以从具有完全局部感知的封闭容器中的布朗运动假设推导出来。这些假设意味着完全统一的空间使用，个体家庭范围相当于人口范围，并且遭遇依赖于实际穿越的移动路径。然而，越来越多的经验证据表明，动物不均匀地使用空间，占据的家庭范围远小于种群范围，并且通常能够进行非局部感知。在这里，我们探索这些经验支持的行为如何改变成对相遇率。具体来说，我们推导出 Ornstein-Uhlenbeck 运动下相遇率的新解析表达式，其特点是空间使用不均匀，并允许个体家庭范围与人口范围不同。我们将基于 OU 的遭遇预测与反射布朗运动的预测进行比较，从中可以推导出质量作用定律。对于这两种模型，我们进一步探讨了感知规模和家庭范围大小之间的相互作用如何影响遭遇率。我们发现，忽视现实运动和感知行为会导致遭遇率预测中出现系统的、不可忽视的偏差。我们将基于 OU 的遭遇预测与反射布朗运动的预测进行比较，从中可以推导出质量作用定律。对于这两种模型，我们进一步探讨了感知规模和家庭范围大小之间的相互作用如何影响遭遇率。我们发现，忽视现实运动和感知行为会导致遭遇率预测中出现系统的、不可忽视的偏差。我们将基于 OU 的遭遇预测与反射布朗运动的预测进行比较，从中可以推导出质量作用定律。对于这两种模型，我们进一步探讨了感知规模和家庭范围大小之间的相互作用如何影响遭遇率。我们发现，忽视现实运动和感知行为会导致遭遇率预测中出现系统的、不可忽视的偏差。