Anticipation: an effective evolutionary strategy for a sub-optimal population in a cyclic environment

We built a two-state model of an asexually reproducing organism in a periodic environment endowed with the capability to anticipate an upcoming environmental change and undergo pre-emptive switching. By virtue of these anticipatory transitions, the organism oscillates between its two states that is a time $\theta$ out of sync with the environmental oscillation. We show that an anticipation-capable organism increases its long-term fitness over an organism that oscillates in-sync with the environment, provided $\theta$ does not exceed a threshold. We also show that the long-term fitness is maximized for an optimal anticipation time that decreases approximately as $1/n$, $n$ being the number of cell divisions in time $T$. Furthermore, we demonstrate that optimal "anticipators" outperforms "bet-hedgers" in the range of parameters considered. For a sub-optimal ensemble of anticipators, anticipation performs better to bet-hedging only when the variance in anticipation is small compared to the mean and the rate of pre-emptive transition is high. Taken together, our work suggests that anticipation increases overall fitness of an organism in a periodic environment and it is a viable alternative to bet-hedging provided the error in anticipation is small.