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All of these constraints vary linearly with the proportion of each food type in the

diet (Fig. 5.5). The optimal solution will occur at one of the intersections of the linear

constraint lines. By multiplying the energy content of each prey type by the daily

intake of that item at each of the intersection points, we can assess which intersec-

tion point offers the greatest energy returns, while guaranteeing that moose main-

tain a minimum acceptable level of sodium intake. The optimal solution in this case

is to have a diet dominated by terrestrial plants, with a small fraction of aquatic plants.

Linear programming has been successfully applied to predict simple dietary pre-

ferences (e.g. forbs versus grasses) in a wide variety of species (Belovsky 1986). It

has proven less successful at predicting the actual mix of species in herbivore diets.

Like the contingency model, linear programming models are ultimately limited by

the reliability of parameter estimates and the degree to which proper constraints have

been identified. Nonetheless, it remains a very useful means of incorporating multi-

ple constraints into dietary predictions.

Many resources naturally have patchy patterns of spatial distribution. This presents

a number of problems for foragers, such as how to decide which patches or habitats

to exploit, how long to stay in each patch once chosen, and how to adjust habitat

preferences in light of choices made by other foragers. Optimality principles can be

usefully applied to each of these problems.

We start by considering how long an animal should stay in a given patch. Let us

take, for example, fig trees that are widely spaced throughout tropical rainforest.

A toucan that wishes to eat figs is faced with deciding how long to feed at a par-

ticular fig tree before moving on to look for another. We have already seen that

foragers must spend valuable time and energy looking for each food item that they

might exploit. As a consequence, there are diminishing returns the longer the tou-

can stays at the tree because most foragers have a functional response that declines

as resource density declines. After an initial period of rapid energy gain, the rate of

accumulation of further energy by the animal begins to slow down as resource

density drops lower and lower due to the animal’s feeding (Fig. 5.6).

We can denote the cumulative energy gain by the function G(t), meaning that cumu-

lative gain depends on the time tspent in each patch. For simplicity, we assume that

each patch is identical with respect to initial resource abundance and that the

66 Chapter 5

5.3 Optimal patch or habitat use

5.3.1Optimal patch

residence time

1.0

0.5

0

0 5 10 15 20

Time (travel + patch)

Cumulative energy gain

Fig. 5.6The cumulative gain of

energy from a patch (solid curve)

as a function of the time spent in

the patch plus the average time

spent traveling between patches.

The broken line indicates the

tangent to this gain curve that

passes through the origin (0,0 on

both axes). The slope of this

tangent represents the long-term

rate of energy gain relative to both

travel and patch residence time.

The point of intersection identifies

the optimal patch residence time.

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