Fig 1.
Illustration of the trade-off between the mortality rates from obesity and predation when setting the target level of reserves during a glut (FG).
The two illustrated strategies have the same target under normal conditions (FN) but different FG values. The higher FG 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 FN. However, at such high reserves the mortality rate from obesity is higher. The lower FG avoids the period of very high reserves (labelled ‘extra obesity cost’) but reaches FN sooner, and so incurs extra mortality from predation (‘extra time exposed to predation’).
Fig 2.
Illustration of the mortality rates mi as a function of reserves x when foraging at the appropriate rate to maintain reserves at x (dashed line) and when resting (solid line) for a specific model implementation (see Appendix).
The mortality from starvation (mS, green line) declines rapidly with increasing fat reserves x, and so is only substantial at low reserves. The mortality from obesity (mB, blue line) is small at low reserves and increases at an accelerating rate. Mortality due to predation during foraging (mP, red line) increases with reserves. The optimal normal fat level is at the minimum of the sum of the mortality rates under normal conditions (mS + mB + αmP). During a glut, the animal should feed up to reserves level
where the mortality from obesity causes total mortality (not including mP, which is zero while resting) to equal that at
(dotted lines). It can then rest, avoiding the risk of predation, until its reserves fall to
, 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.
Fig 3.
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: , solid lines:
) and (c, d) the various sources of mortality under normal conditions (starvation mS, green lines; predation mP, red lines; obesity mB, blue lines), total mortality under normal conditions (dashed lines), and mortality from obesity in constant glut (solid lines).
Note that the mortality from obesity under normal conditions is always very small and that at low κ mortality under constant glut conditions increases (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.