  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.
