Radeva Tsvetomira, Dornhaus Anna, Lynch Nancy, Nagpal Radhika, Su Hsin-Hao
Electrical Engineering and Computer Science Department, Massachusetts Institute of Technology, Cambridge, MA, USA.
Department of Ecology and Evolutionary Biology, The University of Arizona, Tucson, AZ, USA.
PLoS Comput Biol. 2017 Dec 14;13(12):e1005904. doi: 10.1371/journal.pcbi.1005904. eCollection 2017 Dec.
Adaptive collective systems are common in biology and beyond. Typically, such systems require a task allocation algorithm: a mechanism or rule-set by which individuals select particular roles. Here we study the performance of such task allocation mechanisms measured in terms of the time for individuals to allocate to tasks. We ask: (1) Is task allocation fundamentally difficult, and thus costly? (2) Does the performance of task allocation mechanisms depend on the number of individuals? And (3) what other parameters may affect their efficiency? We use techniques from distributed computing theory to develop a model of a social insect colony, where workers have to be allocated to a set of tasks; however, our model is generalizable to other systems. We show, first, that the ability of workers to quickly assess demand for work in tasks they are not currently engaged in crucially affects whether task allocation is quickly achieved or not. This indicates that in social insect tasks such as thermoregulation, where temperature may provide a global and near instantaneous stimulus to measure the need for cooling, for example, it should be easy to match the number of workers to the need for work. In other tasks, such as nest repair, it may be impossible for workers not directly at the work site to know that this task needs more workers. We argue that this affects whether task allocation mechanisms are under strong selection. Second, we show that colony size does not affect task allocation performance under our assumptions. This implies that when effects of colony size are found, they are not inherent in the process of task allocation itself, but due to processes not modeled here, such as higher variation in task demand for smaller colonies, benefits of specialized workers, or constant overhead costs. Third, we show that the ratio of the number of available workers to the workload crucially affects performance. Thus, workers in excess of those needed to complete all tasks improve task allocation performance. This provides a potential explanation for the phenomenon that social insect colonies commonly contain inactive workers: these may be a 'surplus' set of workers that improves colony function by speeding up optimal allocation of workers to tasks. Overall our study shows how limitations at the individual level can affect group level outcomes, and suggests new hypotheses that can be explored empirically.
适应性集体系统在生物学及其他领域中很常见。通常，此类系统需要一种任务分配算法：即个体通过其选择特定角色的一种机制或规则集。在此，我们研究此类任务分配机制的性能，其衡量标准是个体分配到任务所需的时间。我们提出以下问题：（1）任务分配从根本上来说是否困难，因而成本高昂？（2）任务分配机制的性能是否取决于个体数量？以及（3）还有哪些其他参数可能会影响其效率？我们运用分布式计算理论的技术来构建一个群居昆虫群落的模型，其中工蚁必须被分配到一组任务；然而，我们的模型可推广到其他系统。首先，我们表明，工蚁快速评估其当前未从事任务的工作需求的能力，对能否快速实现任务分配至关重要。这表明，在诸如体温调节等群居昆虫任务中，例如温度可能提供一个全局且近乎即时的刺激来衡量冷却需求，那么使工蚁数量与工作需求相匹配应该很容易。在其他任务中，如巢穴修复，不在工作现场的工蚁可能无法知晓该任务需要更多工蚁。我们认为这会影响任务分配机制是否受到强烈选择。其次，我们表明在我们的假设下，群落规模不会影响任务分配性能。这意味着当发现群落规模的影响时，它们并非任务分配过程本身所固有，而是由于此处未建模的过程，例如较小群落任务需求的更高变异性、专业化工蚁的益处或固定的间接成本。第三，我们表明可用工蚁数量与工作量的比率对性能有至关重要的影响。因此，超出完成所有任务所需数量的工蚁会提高任务分配性能。这为群居昆虫群落通常包含不活跃工蚁这一现象提供了一种潜在解释：这些可能是一组“多余”的工蚁，它们通过加速工蚁向任务的最优分配来改善群落功能。总体而言，我们的研究展示了个体层面的局限性如何影响群体层面的结果，并提出了可通过实证探索的新假设。
