antsc5_new.txt from Occupancy patterns in superorganisms: a spin-glass approach to ant exploration

Emergence of collective, as well as superorganism-like, behavior in biological populations requires the existence of rules of communication, either direct or indirect, between organisms. Since reaching an understanding of such rules at the individual level can be often difficult, approaches carried out at higher, or effective, levels of description can represent a useful alternative. In the present work, we show how a spin-glass approach characteristic of statistical physics can be used as a tool to characterize the properties of the spatial occupancy patterns of a biological population. We exploit the presence of pairwise interactions in spin-glass models for detecting correlations between occupancies at different sites in the media. Such correlations, we claim, represent a proxy to the existence of planned and/or social strategies in the spatial organization of the population. Our spin-glass approach does not only identify those correlations but produces a statistical <i>replica</i> of the system (at the level of occupancy patterns) that can be subsequently used for testing alternative conditions/hypothesis. Here, this methodology is presented and illustrated for a particular case of study: we analyze occupancy patterns of <i>Aphaenogaster senilis</i> ants during foraging through a simplified environment consisting of a discrete (tree-like) artificial lattice. Our spin-glass approach consistently reproduces the experimental occupancy patterns across time, and besides, an intuitive biological interpretation of the parameters is attainable. Likewise, we prove that pairwise correlations are important for reproducing this dynamics by showing how a null model, where such correlations are neglected, would perform much worse; this provides a solid evidence to the existence of superorganism-like strategies in the colony.

生物种群中集体行为乃至类超有机体行为的涌现，离不开个体间直接或间接的通信规则。由于在个体层面解析此类规则往往难度颇高，采用更高层级或有效层级的描述方法，便可成为颇具价值的替代方案。本研究展示了统计物理学经典的自旋玻璃（spin-glass）方法，可作为刻画生物种群空间占据模式特征的工具。我们利用自旋玻璃模型中的成对相互作用，检测介质中不同位点的占据情况相关性。我们认为，此类相关性可作为种群空间组织中存在计划性和/或社会性策略的替代指标。该自旋玻璃方法不仅能够识别此类相关性，还可生成系统在占据模式层面的统计复本（replica），后续可用于检验不同条件或假说。本文针对特定研究案例对该方法进行了介绍与演示：我们分析了*Aphaenogaster senilis*在以离散树状人工格点构建的简化环境中觅食时的占据模式。我们的自旋玻璃方法能够一致复现随时间变化的实验占据模式，此外还可对模型参数给出直观的生物学解释。同理，我们通过对比验证了成对相关性对复现该动态的重要性——若采用忽略此类相关性的零模型，其表现会大幅劣于我们的方法，这为蚁群存在类超有机体策略提供了坚实的证据。