Escape in time: stay young or age gracefully?

We compare two modes of ‘escape in time’ from an unpredictable environment: developmental delay (‘stay young’) such as seed dormancy, and reproductive delay (‘age gracefully’) such as delayed flowering. We find that developmental delay and reproductive delay are symmetric with respect to fitness i.e. they have the same effect on growth rate if they have equal costs, and if the environmental pattern is time-reversible. We describe this property by saying that if one kind of delay is an ‘escape into the future’, the other is an ‘escape into the past’. When the costs of the two kinds of delay are equal, and we add a little delay to a life cycle that has none, the increase in growth rate is equal whether we add developmental delay, reproductive delay, or a combination of the two. When the costs of delay are equal, and we consider a life cycle that has just one form of delay, the largest gain in fitness tends to come from an increase in the delay that is already present. Thus, changes in the amount of delay tend to be self-reinforcing. Hence we expect evolution to lead to an entrainment so that life cycles will often contain mainly one or other kind of delay. As the amount of delay increases, the growth rate reaches a maximum that may be regarded as an ESS, and then falls. Geometrically, this maximum is a ‘ridge’ on the fitness surface when environments are moderately variable i.e. there are many combinations of delays that yield the maximum growth rate. When the environment becomes highly variable, or strongly positively autocorrelated, this ‘ridge’ is replaced by a pair of ‘peaks’. Two combinations of delay then lead to the highest growth rate, one where reproductive delay is dominant and one where developmental delay is dominant.