Nagatani Takashi, Tainaka Kei-Ichi, Ichinose Genki
Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
Graduate School of Science and Technology, Shizuoka University, Hamamatsu 432-8561, Japan.
Biosystems. 2017 Dec;162:75-80. doi: 10.1016/j.biosystems.2017.09.015. Epub 2017 Sep 28.
Migration is observed across many species. Several authors have studied ecological migration by applying cellular automaton (CA). In this paper, we present a directional migration model with desert on a one-dimensional lattice where a traffic CA model and a lattice Lotka-Volterra system are connected. Here predators correspond to locomotive animals while prey is immobile plants. Predators migrate between deserts and fertile lands repeatedly. Computer simulations reveal the two types of phase transition: coexistence of both species and prey dominance, which is caused by both benefit and cost of migration. In the coexistence phase, the steady-state density of predators usually increases by migration as long as the desert size is small and their mortality rate is low. In contrast, the prey density increases, even if the desert size becomes large. Such a paradox comes from the indirect effect: predators go extinct by the increase of desert size, so that the plant density can increase. Moreover, we find several self-organized spatial patterns: 1) predators form a stripe pattern; namely swarms. 2) The velocity of predators is high on deserts, but very low on fertile land. 3) Predators give birth only on fertile lands.
许多物种都存在迁移现象。几位作者通过应用细胞自动机（CA）研究了生态迁移。在本文中，我们提出了一个在一维晶格上带有沙漠的定向迁移模型，其中交通CA模型与晶格Lotka-Volterra系统相连接。这里捕食者对应于移动的动物，而猎物是固定不动的植物。捕食者在沙漠和肥沃土地之间反复迁移。计算机模拟揭示了两种相变类型：物种共存和猎物占主导，这是由迁移的收益和成本共同导致的。在共存阶段，只要沙漠面积小且捕食者死亡率低，捕食者的稳态密度通常会因迁移而增加。相反，即使沙漠面积变大，猎物密度也会增加。这种悖论源于间接效应：捕食者因沙漠面积增加而灭绝，从而植物密度得以增加。此外，我们发现了几种自组织空间模式：1）捕食者形成条纹模式；即群体。2）捕食者在沙漠上的速度很高，但在肥沃土地上非常低。3）捕食者只在肥沃土地上繁殖。
