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（subordinates）会遭到优势个体（dominant individuals）的惩罚或驱逐出群体。优势个体驱逐威胁的可信度可能随群体层面之外的社会背景而变化：当从属个体可轻易在邻近领地繁殖时，优势个体较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对群体生产力贡献占比极高的小型群体中，优势个体强制从属个体合作的能力可能会被削弱。本研究构建了双人博弈论模型（game theoretic model），以探究社会背景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。与理论预测相悖的是，我们发现当优势个体难以替换被驱逐的从属个体时，其会要求更多帮助，这表明当优势个体无法弥补因驱逐从属个体而造成的损失时，会对其未尽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（fitness costs），且其帮助行为不会随群体外的繁殖机会变化而改变。不过，当从属个体可根据优势个体的要求可塑性地提升帮助水平（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，但随着群体外繁殖机会的增加，其提供的帮助会随之减少。本研究结果证明，将协商过程纳入帮助策略的理论模型具有重要意义，同时证实可塑性是合作繁殖中付费居留（pay-to-stay）机制的核心调控机制。