Illustration of the mortality rates <i>m</i>_<i>i</i> as a function of reserves <i>x</i> when foraging at the appropriate rate to maintain reserves at <i>x</i> (dashed line) and when resting (solid line) for a specific model implementation (see Appendix).

<p>The mortality from starvation (<i>m</i>_<i>S</i>, green line) declines rapidly with increasing fat reserves <i>x</i>, and so is only substantial at low reserves. The mortality from obesity (<i>m</i>_<i>B</i>, blue line) is small at low reserves and increases at an accelerating rate. Mortality due to predation during foraging (<i>m</i>_<i>P</i>, red line) increases with reserves. The optimal normal fat level <math><mrow><msubsup><mi>F</mi><mi>N</mi><mi>*</mi></msubsup></mrow></math> is at the minimum of the sum of the mortality rates under normal conditions (<i>m</i>_<i>S</i> + <i>m</i>_<i>B</i> + <i>αm</i>_<i>P</i>). During a glut, the animal should feed up to reserves level <math><mrow><msubsup><mi>F</mi><mi>G</mi><mi>*</mi></msubsup></mrow></math> where the mortality from obesity causes total mortality (not including <i>m</i>_<i>P</i>, which is zero while resting) to equal that at <math><mrow><msubsup><mi>F</mi><mi>N</mi><mi>*</mi></msubsup></mrow></math> (dotted lines). It can then rest, avoiding the risk of predation, until its reserves fall to <math><mrow><msubsup><mi>F</mi><mi>N</mi><mi>*</mi></msubsup></mrow></math>, whereupon it must start to forage again before it suffers a large increase in mortality due to low reserves. Parameter values: γ = 10, ψ = 3, μ = 0.005, ϕ = 2, β = 3, κ = 0.01, ρ = 0.0001.</p

Effects of varying (a, c) risk of predation μ and (b, d) the cost of obesity κ on (a, b) the optimal strategy (dashed lines: FN*, solid lines: FG*) and (c, d) the various sources of mortality under normal conditions (starvation <i>m</i>_<i>S</i>, green lines; predation <i>m</i>_<i>P</i>, red lines; obesity <i>m</i>_<i>B</i>, blue lines), total mortality under normal conditions (dashed lines), and mortality from obesity in constant glut (solid lines).

<p>Note that the mortality from obesity under normal conditions is always very small and that at low κ mortality under constant glut conditions <i>increases</i> (to a small extent) as κ decreases. Baseline parameter values: γ = 10, ψ = 3, μ = 0.005, ϕ = 2, β = 3, κ = 0.01, ρ = 0.0001.</p

Illustration of the trade-off between the mortality rates from obesity and predation when setting the target level of reserves during a glut (<i>F</i>_<i>G</i>).

<p>The two illustrated strategies have the same target under normal conditions (<i>F</i>_<i>N</i>) but different <i>F</i>_<i>G</i> values. The higher <i>F</i>_<i>G</i> means that when a glut occurs reserves increase by a larger amount, which enables the animal to avoid foraging for a long time before reserves decrease to <i>F</i>_<i>N</i>. However, at such high reserves the mortality rate from obesity is higher. The lower <i>F</i>_<i>G</i> avoids the period of very high reserves (labelled ‘extra obesity cost’) but reaches <i>F</i>_<i>N</i> sooner, and so incurs extra mortality from predation (‘extra time exposed to predation’).</p

Mortality of mildly and highly defended prey types.

<p>Proportion of mildly defended α and highly defended β prey consumed by predators in the four experimental treatments (Mildly defended prey α alone; Highly defended prey β alone; α and β both present but distinguishably coloured; α and β both present and perfect mimics) for three values of the availability of alternative prey <i>f</i>γ (a, b) <i>f</i>γ = 0.1, (c, d) <i>f</i>γ = 0.2, (e, f) <i>f</i>γ = 0.3, and for whether detoxification is (a, c, e) cost-free (κ = 0) or (b, d, f) costly (κ = 1).</p

Impact of alternative prey on predator strategy and -state when defended prey are non-mimetic.

<p>Effect of availability of alternative prey (<i>f</i>γ) on predator strategy (a, c, e) and stationary distribution of predator state (b, d, f) in the non-mimetic treatment. Results are shown for three values of availability of alternative prey (a, b) γ = 0.1, (c, d) γ = 0.2, (e, f) γ = 0.3. The shaded areas show the states where: the predators reject all prey including alternative prey (black); reject only the mildly defended prey (pale grey); reject only the highly defended prey (intermediate grey) reject both defended prey (dark grey) (a, c, e). In the white areas, all prey are accepted. Distribution of predator states are shown from high (white) to zero (black) (b, d, f).</p

Parameters of the predator and the values explored.

<p>Parameters of the predator and the values explored.</p

Optimal foraging strategies when detoxification is not costly.

<p>Optimal foraging strategy for predators, shown as which prey types are rejected as a function of energy reserves <i>R</i> and toxin burden <i>D</i> for the four treatments: (a) mildly defended prey, α alone; (b) highly defended prey, β alone; (c) α and β both present and visually distinguishable; (d) α and β both present and perfect mimics. Here, there is no detoxification cost (κ = 0) and alternative prey are at intermediate availability (γ = 0.2). The shaded areas show the states where: the predators reject all prey including alternative prey (black); reject only the mildly defended prey (pale grey); reject only the highly defended prey (intermediate grey) reject both defended prey (dark grey). In the white areas, all prey are accepted.</p

Masquerade Appendix 1

Data from Porter (1997) and others on the ecological traits of the larvae of all of the British Geometridae and Drepanidae, including body length, and the number of host plant families, genera, and species

An illustration of data and explanatory models.

<p>(A) Prevalence of antidepressant purchases in divorced individuals in divorce-centred time (solid line) and in others in ordinary time (dashed line). The thick vertical line indicates the time of divorce. (B) The data points for model fitting and 95% Wald confidence intervals for prevalence; the general linear trend in non-divorced people and the baseline prevalence in divorced people was removed from prevalence data of the divorced individuals. (C) The stress-relief model (i.e. function <i>g</i>(<i>t</i>)) in the divorce-centred time t. (D) The stress-induction model. (E) The peak-stress model. (F) The adaptive model. Although all the model functions are shown here for illustration, their parametrisation is the one implied by the fitted models of the Results section.</p

Possible state transitions in the evolutionary state-dependent model.

<p>Note that it is also possible to stay in the same state for longer than one time step, but for clarity the self-loops are not shown (but see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179495#pone.0179495.s001" target="_blank">S1 Text</a>). A ‘strategy’ π(<i>x</i>,<i>t</i>) defines whether to be in a ‘depressed’ mode <i>u</i>₁ or not (mode <i>u</i>₀) given the state <i>x</i> and time <i>t</i>. The star superscript refers specifically to the optimal strategy that maximizes the reproductive value. The choice of mode dictates the transition-probability structure for the next time step. The effect of the ‘depressed’ mode is to decrease the probability of a divorce-like transition from the relationship-at-risk state to the unpartnered state by the value <i>s</i>, to increase the probability of death <i>m</i> by <i>z</i>, and to remove the probability of marrying <i>ρ</i> (removal of <i>ρ</i> had no consequences here, but to some, it seems a logical outcome of depression). We assumed that as many relationships at risk end up in divorce as in reconciliation on average (<i>d</i>₂); the function <i>f</i>(<i>d</i>₁, <i>d</i>₂) captured the overall divorce rate, as illustrated in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179495#pone.0179495.s001" target="_blank">S1 Text</a>.</p