Data from: Dominant and subordinate outside options alter help and eviction in a pay-to-stay negotiation model

In several cooperatively breeding species, subordinates that do not help sufficiently are punished or evicted from the group by dominant individuals. The credibility of dominant eviction threats may vary with the social context beyond the group level: when subordinates can easily breed in a neighboring territory, dominant may be less able to demand help from subordinates. Further, dominant ability to enforce subordinate cooperation may be reduced when it is difficult to replace evicted subordinates or in small groups where each subordinate makes a large contribution to group productivity. Here, we develop a two-player game theoretic model to examine how the social context influences subordinate help and the threshold of help at which dominants evict subordinates. In contract to predictions, we found that dominants demand more help when dominants are less able to replace evicted subordinates, suggesting that dominants punish a dereliction of helping behavior more strongly when they are unable to compensate for the loss of an evicted subordinate. In single sealed-bid games, subordinates help less than the fitness costs they impose on dominants and help does not vary with subordinate breeding opportunities outside the group. However, when subordinates can plastically increase help in response to demanding dominants (akin to pay-to-stay dynamics), subordinates provide more help overall, but decrease their help as breeding opportunities outside of the group increase. Our results demonstrate the importance of incorporating negotiation into theoretical models of helping strategies and demonstrate that plasticity is a key mechanism underlying pay-to-stay mechanisms of cooperation.

在多种合作繁育物种中，未能充分履行帮助义务的从属个体，会受到优势个体的惩罚或从群体中被驱逐。优势个体驱逐威胁的可信度，可能随群体层面之外的社会情境发生变化：当从属个体可轻易在邻域领地繁育后代时，优势个体便更难要求从属个体提供帮助。此外，当难以替换被驱逐的从属个体，或是在每个从属个体都对群体生产力贡献显著的小型群体中，优势个体强制从属个体开展合作的能力可能会被削弱。本研究构建了双人博弈论（game theoretic）模型，用以探究社会情境如何影响从属个体的帮助行为，以及优势个体驱逐从属个体所需的帮助阈值。与预测结果相悖的是，我们发现当优势个体更难以替换被驱逐的从属个体时，它们会要求从属个体提供更多帮助，这表明当优势个体无法弥补因驱逐从属个体所造成的损失时，它们会对未履行帮助义务的行为施以更严厉的惩罚。在单次密封投标博弈中，从属个体提供的帮助少于其给优势个体带来的适应度成本，且其帮助行为不会随群体外繁育机会的多少发生变化。然而，当从属个体可根据优势个体的要求灵活调整帮助行为（类似于“付费留居”（pay-to-stay）机制）时，从属个体整体会提供更多帮助，但随着其群体外繁育机会的增加，帮助行为会相应减少。本研究结果表明，将协商机制纳入帮助策略理论模型的重要性，同时证实了可塑性是合作付费留居机制背后的核心调控机制。