A model of optimal timing for a predictive adaptive response

Predictive adaptive responses (PARs) are a form of developmental plasticity in which the developmental response to an environmental cue experienced early in life is delayed and yet, at the same time, the induced phenotype anticipates (i.e., is completely developed before) exposure to the eventual environmental state predicted by the cue, in which the phenotype is adaptive. We model this sequence of events to discover, under various assumptions concerning the cost of development, what lengths of delay, developmental time, and anticipation are optimal. We find that in many scenarios modeled, development of the induced phenotype should be completed at the exact same time that the environmental exposure relevant to the induced phenotype begins: that is, in contrast to our observed cases of PARs, there should be no anticipation. Moreover, unless slow development is costly, development should commence immediately after the cue: there should be no delay. Thus, PARs, which normally have non-zero delays and/or anticipation, are highly unusual. Importantly, the exceptions to these predictions of zero delays and anticipation occurred when developmental time was fixed and delaying development was increasingly costly. We suggest, therefore, that PARs will only evolve under three kinds of circumstances: (i) there are strong timing constraints on the cue and the environmental status, (ii) delaying development is costly, and development time is either fixed or slow development is costly, or (iii) when the period between the cue and the eventual environmental change is variable and the cost of not completing development before the change is high. These predictions are empirically testable.