Department of Mathematics, Nanjing University of Science and Technology, Nanjing, 210094, People's Republic of China.
Sciences and Mathematics Faculty, College of Integrative Sciences and Arts, Arizona State University, Mesa, AZ, 85212, USA.
J Math Biol. 2021 Mar 29;82(5):42. doi: 10.1007/s00285-021-01589-z.
The mechanisms through which work is organized are central to understanding how complex systems function. Previous studies suggest that task organization can emerge via nonlinear dynamical processes wherein individuals interact and modify their behavior through simple rules. However, there is very limited theory about how those processes are shaped by behavioral variation within social groups. In this work, we propose an adaptive modeling framework on task allocation by incorporating variation both in task performance and task-related metabolic rates. We study the scaling effects of colony size on the resting probability as well as task allocation. We also numerically explore the effects of stochastic noise on task allocation in social insect colonies. Our theoretical and numerical results show that: (a) changes in colony size can regulate the probability of colony resting and the allocation of tasks, and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks; (b) increased response thresholds may cause colonies to rest in varied patterns such as periodicity. In this case, we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time; (c) stochastic noise can cause work activities and task demand to fluctuate within a range, where the amplitude of the fluctuation is positively correlated with the intensity of noise.
工作组织的机制是理解复杂系统如何运作的核心。先前的研究表明，任务组织可以通过非线性动力过程出现，其中个体通过简单规则相互作用并改变其行为。然而，关于这些过程如何受到社会群体内部行为变化的影响，理论非常有限。在这项工作中，我们通过将任务表现和与任务相关的代谢率的变化都纳入到任务分配的自适应建模框架中，提出了一种任务分配的自适应建模框架。我们研究了群体大小对休息概率和任务分配的缩放效应。我们还通过数值方法研究了随机噪声对社会昆虫群体任务分配的影响。我们的理论和数值结果表明：(a) 群体大小的变化可以调节群体休息的概率和任务的分配，调节的方向取决于任务的非线性代谢缩放效应；(b) 增加的响应阈值可能导致群体以周期性等不同的模式休息。在这种情况下，我们首次在社会昆虫群体的任务分配中观察到了一个有趣的泡沫现象；(c) 随机噪声会导致工作活动和任务需求在一定范围内波动，波动的幅度与噪声的强度成正比。
