Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas, São Paulo, Brazil.
Philos Trans A Math Phys Eng Sci. 2010 Dec 28;368(1933):5661-77. doi: 10.1098/rsta.2010.0270.
We investigated the phenomenon of population outbreaks in a spatial predator-prey model, and we found that pattern formation and outbreaks occur if the predators have a limited neighbourhood of interaction with the preys. The outbreaks can display a scale-invariant power-law tail, indicating self-organized criticality. We have also studied the system from an evolutionary point of view, where the predator home range is a hereditary trait subjected to mutations. We found that mutation drives the predator home range area to an optimal value where pattern formation and outbreaks are still present, but the latter are much less frequent. We developed analytical approximations using mean field and pair correlation techniques that indicate that the predation strategy is crucial for existence of this optimal home range area.
我们研究了空间捕食者-猎物模型中的种群爆发现象，发现如果捕食者与猎物的相互作用范围有限，则会出现模式形成和爆发。爆发可以显示具有标度不变幂律尾巴的自组织临界性。我们还从进化的角度研究了该系统，其中捕食者的活动范围是一个遗传特征，会发生突变。我们发现，突变会将捕食者的活动范围驱动到一个最佳值，在这个最佳值下仍然存在模式形成和爆发，但后者发生的频率要低得多。我们使用平均场和配对相关技术开发了分析近似值，表明捕食策略对于这种最佳活动范围的存在至关重要。
