The spatial-temporal dynamics of animal competitions arise from the effective forces between the participants



To conserve and defend resources, animals often enter competitions that involve a complex trade-off between risk and reward. Although it is obvious to use cognitive decision-making schemes to analyze and model these competitions, such cognitive schemes are difficult to test in behavioral experiments and they do not address a directly observable aspect of competitions – the movement of participants in space. We study the dynamics of competitions in a globe-weaving spider in which males compete for mating opportunities in the confined arena of the female web. We show that physical rules of interaction, which amount to attraction and repulsion between competitors and determine their movement, can explain the real-time dynamics of animal competitions.


The competition between animals for resources, especially food, territories and partners, is omnipresent in all areas of life. This competition is often resolved through competitions between individuals who are generally understood based on their results and, in particular, the dependence of those results on the decision-making of the participants. Because they are limited to endpoint predictions, these approaches cannot predict real-time or real-time dynamics of animal competition behavior. This limitation can be overcome by examining systems that exhibit typical competitive behavior and at the same time are easy enough to track and model. Here we propose to use such systems to construct a theoretical framework describing real-time movements and behaviors of animal participants. We investigate the spatiotemporal dynamics of competitions in a ball-weaving spider in which all common elements of animal competitions come into play. The limited arena of the web, in which interactions are dominated by vibration signals in a two-dimensional space, simplifies the analysis of interactions between agents. We ask whether these seemingly complex decision-makers can be modeled as interacting active particles that, due to their interactions, only react to effective forces of attraction and repulsion. By analyzing the emerging dynamics of “competitive particles”, we provide mechanistic explanations for dynamic real-time aspects of animal competitions, thus explaining the competitive advantages of larger competitors and showing that animal competitions do not require complex decision-making in order to achieve adaptive results. Our results show that physics-based classification and modeling in terms of effective interaction rules provide a powerful framework for understanding animal competition behavior.


    • Accepted October 28, 2021.
  • Authors’ contributions: AH, SFGR, AJ and NSG designed research; AH, SFGR and DG conducted research; AH, RIE and NSG analyzed data; and AH, AJ and NSG wrote the paper.

  • The authors do not declare any competing interests.

  • This article is a PNAS direct submission.

  • This article provides supporting information online at

Data availability

All data relevant to this study are contained in the article and / or supporting information.


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