Dependence of the Lyapunov's exponent on the parameter for alternative environmental inputs.

<p>A: Results for model (1) with the stochastic input (5). The curves correspond to . For negative the growth rate decreases with . B: Results for model (1) with the periodic environmental input . The curves correspond to . Again, for negative the growth rate decreases with . Other parameters are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103241#pone-0103241-g004" target="_blank">Figure 4</a>.</p

Illustration of random phenotype switching.

<p>The S-shaped curve consists of two horizontal segments and a slanted segment whose slope may be randomly changing. Stable phenotype states can be found on the horizontal segments of this curve. For a given value of the environmental input , the transition from the state on the lower part of the curve to the upper part occurs when the meeting point of the slanted segment with the lower state line shifts to the left of ; the transition from the upper to the lower branch occurs when the meeting point of the slanted segment with the upper state line shifts to the right of . When , transitions from state 0 to state 1 occur with higher probability than transitions from state 1 to the state 0. When , transitions from state 0 to state 1 are less likely than transitions from state 1 to state 0.</p

Convergence of the growth rate to the Lyapunov exponent.

<p>A typical evolution of the time average of the growth rate (8) over the increasing time interval from 0 to . For the process asymptotically approaches a stationary value (6). Deviations are within . The plot was obtained using system (7) with OU input (4).</p

The effect of changes in the parameters and on the Lyapunov's exponent .

<p>Each plot demonstrates a positive optimal value of the threshold parameter , which maximizes for model (1). A: The effect of altering the average lag time . The curves correspond to . The growth rate increases with . Solid lines are plotted for , a relatively slow transition rate; dashed lines are plotted for , a high transition rate. Other parameters are , , and . B: The effect of varying the stiffness of the potential well . The lines correspond to . The growth rate decreases with . Other parameters are , , , and .</p

The Lyapunov's exponent for different values.

<p>Plots on panels A and B were obtained for systems (9) and (1), respectively, with OU environmental input (4). A: The curves correspond to . For the growth rate increases with . B: The curves are for . For negative the growth rate decreases with . Other parameters are , , , , .</p

Results of modifying the difference of the growth rates.

<p>The parameter measures the difference of the growth rates of the fully favored and fully unfavored phenotypes. The growth rate increases with . The curves correspond to . Other parameters are , , , and .</p