Martinez-Garcia Ricardo, Fleming Christen H, Seppelt Ralf, Fagan William F, Calabrese Justin M
ICTP South American Institute for Fundamental Research & Instituto de Física Teórica - UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco 2 - Barra Funda 01140-070 São Paulo, SP Brazil; Dept. of Ecology & Evolutionary Biology, Princeton University, Princeton NJ 08544, USA.
Smithsonian Conservational Biology Institute, National Zoological Park, 1500 Remount Road, Front Royal, Virginia 22630 USA; Dept. of Biology, University of Maryland, College Park MD 20742, USA.
J Theor Biol. 2020 Aug 7;498:110267. doi: 10.1016/j.jtbi.2020.110267. Epub 2020 Apr 7.
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.
相遇率将运动策略与种内和种间相互作用联系起来，从而将个体运动行为转化为更高层次的生态过程。实际上，大量相互作用的种群理论基于质量作用定律，该定律可从封闭容器中仅具有局部感知的布朗运动假设推导得出。这些假设意味着完全均匀的空间利用、与种群范围相当的个体活动范围，以及相遇取决于实际交叉的运动路径。然而，越来越多的实证证据表明，动物并非均匀地利用空间，占据的活动范围远小于种群范围，并且通常具有非局部感知能力。在此，我们探讨这些经实证支持的行为如何改变成对相遇率。具体而言，我们推导了奥恩斯坦 - 乌伦贝克运动下相遇率的新解析表达式，该运动具有非均匀空间利用特征，并允许个体活动范围与种群范围不同。我们将基于奥恩斯坦 - 乌伦贝克运动的相遇预测与反射布朗运动的预测进行比较，质量作用定律可从反射布朗运动推导得出。对于这两种模型，我们进一步探讨感知尺度和活动范围大小之间的相互作用如何影响相遇率。我们发现，忽略现实的运动和感知行为会导致相遇率预测中出现系统性的、不可忽略的偏差。
