Long-term term growth rate predicted by the analytical model in a single patch as a function of random and responsive switching values,

and

(

**A–C**). Three contour plots show the combination of both strategies that maximizes the long-term growth rate, and how this combination depends on the signal reliability. Highly reliable signals select for types that have high values of responsive switching, and low values of random switching (

**A**). Unreliable signals select for types that have low values of responsive switching, and high values of random switching (

**C**). Signals of intermediate reliability select for types that have intermediate levels of both responsive and random switching (

**B**). These predictions are in line with the results of the individual-based model, where the dominant type after

generations is close to the combination of

and

predicted by the analytical model (yellow filled circles;

**A–C**). For each parameter combination (

**A–C**), the scaled Venn diagram (

**D–F**) depicts the probability of false positive (switch if there is no stress, probabilities are 0.11424, 0.22448, and 0.27585 for A, B, and C, respectively), false negative (do not switch if there is stress, probabilities are 0.01524, 0.02048, and 0.01935 for A, B, and C, respectively), and correct decisions (probabilities are 0.08391, 0.06385, and 0.06132 for A, B, and C, respectively) for the strategy that maximizes the long-term growth rate. In a situation with two patches (

**G**), the results of the individual-based model depend on the type of density regulation. When the population undergoes global density regulation (yellow filled circles), the dominant types are close to the combination of switching values that maximizes long-term growth rate according to the analytical model (

**G**; contour plot); when the population undergoes local density regulation (purple filled circles), the dominant types have higher values of random switching than predicted by the analytical model. Parameters used in all panels are

,

,

,

, and for individual-based runs we evolve the population for

generations at the population size

and repeat it

times. Mutation rates are

The resolution used is

.

values used are 0.03 for (

**A**), 0.01 for (

**B**) and (

**G**), and 0 for (

**C**).

## PubMed Commons