The University of Western Australia, Department of Mathematics and Statistics, Crawley, 6009, Australia.
The University of Western Australia, Department of Mathematics and Statistics, Crawley, 6009, Australia; Potsdam Institute for Climate Impact Research (PIK), Potsdam 14473, Germany.
J Theor Biol. 2019 Jun 21;471:82-90. doi: 10.1016/j.jtbi.2019.03.021. Epub 2019 Mar 27.
The selfish herd hypothesis provides an explanation for group aggregation via the selfish avoidance of predators. Conceptually, and as was first proposed, this movement should aim to minimise the danger domain of each individual. Whilst many reasonable proxies have been proposed, none have directly sought to reduce the danger domain. In this work we present a two dimensional stochastic model that actively optimises these domains. The individuals' dynamics are determined by sampling the space surrounding them and moving to achieve the largest possible domain reduction. Two variants of this idea are investigated with sampling occurring either locally or globally. We simulate our models and two of the previously proposed benchmark selfish herd models: k-nearest neighbours (kNN); and local crowded horizon (LCH). The resulting positions are analysed to determine the benefit to the individual and the group's ability to form a compact group. To do this, the group level metric of packing fraction and individual level metric of domain size are observed over time for a range of noise levels. With these measures we show a clear stratification of the four models when noise is not included. kNN never resulted in centrally compacted herd, while the local active selfish model and LCH did so with varying levels of success. The most centralised groups were achieved with our global active selfish herd model. The inclusion of noise improved aggregation in all models. This was particularly so with the local active selfish model with a change to ordering of performance so that it marginally outperformed LCH in aggregation. By more closely following Hamilton's original conception and aligning the individual's goal of a reduced danger domain with the movement it makes increased cohesion is observed, thus confirming his hypothesis, however, these findings are dependent on noise. Moreover, many features originally conjectured by Hamilton are also observed in our simulations.
自利群体假说通过自利逃避捕食者来解释群体聚集。从概念上讲，正如最初提出的那样，这种运动应该旨在最小化每个个体的危险域。虽然已经提出了许多合理的替代方案，但没有一个方案直接试图缩小危险域。在这项工作中，我们提出了一个二维随机模型，该模型主动优化这些域。个体的动态由在其周围空间采样并移动以实现最大可能的域减少来决定。两种变体都进行了调查，采样发生在局部或全局。我们模拟了我们的模型和两个先前提出的自利群体模型的基准：k-最近邻（kNN）；以及局部拥挤视野（LCH）。分析所得位置，以确定个体和群体形成紧凑群体的能力的益处。为此，观察一段时间内不同噪声水平下的群体水平度量填充分数和个体水平度量域大小。通过这些措施，当不包括噪声时，我们清楚地对四个模型进行了分层。kNN 从未导致中心密集的畜群，而局部主动自私模型和 LCH 则以不同的成功程度做到了这一点。具有全局主动自私群体模型的最集中群体。所有模型的聚集都因噪声的加入而得到改善。对于局部主动自私模型尤其如此，其性能排序发生了变化，从而使其在聚集方面略微优于 LCH。通过更紧密地遵循 Hamilton 的原始概念，并使个体的减少危险域的目标与它所做出的运动相一致，观察到了凝聚力的提高，从而证实了他的假说，然而，这些发现取决于噪声。此外，Hamilton 最初推测的许多特征也在我们的模拟中观察到。
