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.在多种合作繁殖物种（cooperatively breeding species）中，未充分提供帮助的从属个体将受到优势个体的惩罚，或被逐出群体。优势个体的驱逐威胁可信度可能受群体层面之外的社会情境影响：当从属个体可轻易在邻域领地繁殖时，优势个体便较难要求从属个体提供帮助。此外，当难以替换被逐出的从属个体，或是在每个从属个体对群体生产力贡献占比较大的小型群体中，优势个体强制从属个体开展合作的能力可能会减弱。本研究构建了两人博弈论模型（two-player game theoretic model），以探究社会情境如何影响从属个体的帮助行为，以及优势个体实施驱逐行为的帮助阈值。与理论预测相悖的是，我们发现当优势个体难以替换被逐出的从属个体时，其会要求更多的帮助，这表明当优势个体无法弥补被驱逐从属个体的缺失所带来的损失时，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（sealed-bid games）中，从属个体提供的帮助少于其给优势个体带来的适合度成本，且其帮助行为不会随群体外繁殖机会的多少而变化。然而，当从属个体可根据优势个体的要求可塑性地调整帮助行为（类似于付费居留（pay-to-stay）机制）时，从属个体整体会提供更多帮助，但会随着群体外繁殖机会的增加而减少帮助投入。本研究结果证实了将协商机制纳入帮助策略理论模型的重要性，同时表明可塑性是合作行为中付费居留机制的核心底层机制。