Figure 5. Sufficient and optimal strategies for growth in environments of stress and growth durations (, ).

(A) To ensure survival over environmental cycles () populations must downregulate their death rate by a factor during the stress phases. At long growth and short stress durations a positive time-averaged growth rate can be maintained without adopting a protected state (). Here the growth benefit during exceeds the death cost during for all levels . For long stress and short growth durations no net growth is possible because the benefits during growth are outweighed by the costs during the stress phase (). (B) Optimal downregulation levels that maximize the time-averaged growth rate . For sufficiently short stress durations the survival-benefits of stress-protected states are always outweighed by the costs of longer growth-lags after stress. In this regime, limited by the black line, populations need not trade off against survival. The optimal strategy is to remain vegetative upon stress exposure (). When typical stress durations lay above the black line, populations must reconcile fast recovery with survival. Populations which do not downregulate sufficiently have too large death rates, and eventually go extinct, whereas populations that downregulate too much cannot resume growth sufficiently fast. Such populations can increase long term fitness by decreasing short term fitness, see also Fig. 4B. When the typical growth durations fall below the full white line the optimal strategy is to adopt the state of highest stress resistance, i.e., dormancy, even if this implies to not resume growth during the typical growth durations . Note that populations with particular downregulation levels are optimal on a line in parameter space (see dashed white line on which ).