Propagation and suppression of environmental fluctuations.

<p>(a) Linear birth-death process in a fluctuation environment. The birth-rate is assumed to be linearly modulated by its environment modeled as a CIR process (see Eq. 19). (b) Calculation of suppressed and effective noise. Individual components were computed analytically by solving an ordinary differential equation (see Eq. 22 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003942#pcbi.1003942.s001" target="_blank">S1 Text</a>) with , , and . For orientation, we also show the information gain between and , computed using the marginal simulation algorithm (green); it can be understood as the gain in information about through observing and it exhibits a monotone relationship with the effective noise. (c) Relation between the effective noise and the speed of the environmental fluctuations. Noise contributions were computed by numerically solving Eq. 22 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003942#pcbi.1003942.s001" target="_blank">S1 Text</a> for , , and different values of . Note that the results are independent of the death rate . Also shown are realizations of and for the case for two different time-scales. If is fast, the output is able to suppress most of the variability in . In contrast, if is slow, fluctuations are largely transferred to (i.e., has a large effective noise) such that extrinsic noise in is substantial.