reply ‘Raise the stakes’ evolves into a defector

Abstract

Sherratt and Roberts reply — Killingback and Doebeli argue that our cooperative strategy ‘raise the stakes’¹ (RTS) can be continually undermined by selection for less generous strategies. They suggest that the “lack of robustness of RTS” arises from our use of a discontinuous strategy. However, this cannot be the case because the instability they report was in their reformulation of our model in continuous terms. Whether a continuous model is “essential” is debatable. Discontinuous strategies can be more realistic, particularly when resources are not infinitely divisible, hence our notion of a minimal non-zero investment of one unit.

Main

We have also considered the relative success of rare, mutant continuous RTS strategies, but our analyses show that the mean initial investment parameter a will always evolve upwards. Simulations confirm this. Therefore, after trying to replicate their approach, we can find no evidence that even the continuous form of RTS-based cooperation can be eroded in the way they suggest. From this, we cannot exclude the possibility that they have misinterpreted the way RTS operates.

Killingback and Doebeli appear to agree that cooperation can thrive in variable investment systems and that successful strategies would tend to exhibit some initial build up of ‘trust’. However, they claim that a strategy that depends on responding to the payoff would be more stable, which we question for two reasons. First, payoff dependency can lead to unnecessary investment in a sucker. Second, in a recent payoff-dependent model², negative payoffs always resulted in the end of cooperation, whereas RTS can rebuild relationships. These sources of instability are highlighted by the need for spatial structuring before payoff-dependent mutualism could evolve². Such assumptions are not required when cost-dependent mutualistic strategies are considered (unpublished data). (Further details are available from T.N.S.)

See also — Killingback et al.