untitled

forager has no means of knowing exactly how long it will take to get to the next

suitable patch, only how long it takes on average, based on its previous experience.

The long-term rate of energy gain, E(t), can be expressed as the total energy gained,

G(t), divided by the time spent within each patch (t) plus the average time it takes

the forager to find a new patch (1/λ):

Long-term intake is usually maximized at an intermediate amount of time spent within

each patch. The optimal residence time can be found graphically by drawing the

tangent to the gain curve that passes through the origin (Fig. 5.6). This tangent is

known as the “marginal value” in economic jargon, so the optimal patch use model

has come to be known as the marginal value theorem(Charnov 1976b).

The marginal value theorem makes a number of useful predictions:

1 Foragers should leave all patches when the rate of intake in those patches reaches

a threshold value. This will typically occur at a particular density of prey.

2 Foragers should leave resource-poor patches much sooner than resource-rich

patches.

3 The average distance among patches should influence the optimal time to leave a

patch, the giving-up time(and by analogy the optimal giving-up densityof prey).

The optimal decision would be to stay in each patch longer when the distance among

patches is long than when the distance is short.

Several studies have tested these predictions. Out of 45 published studies, 70% showed

patterns of patch departure consistent with these predictions. In 25% of these

studies, precise numerical predictions were upheld (Stephens and Krebs 1986). One

of the most elegant examples is Cowie’s (1977) study of patch use by great tits. Cowie

built a series of perches in an aviary on which small containers with tight-fitting

covers were attached. Several mealworms were placed in each container, and covered

with sawdust. Birds learned to prise the lid off each container before searching for

mealworms within it, the container being the “patch.” By changing the tightness of

lids, Cowie could control the time between cessation of foraging in one patch

and the initiation of a bout of foraging in a new patch. He showed that birds were

sensitive to travel time between patches, staying longer at patches when travel time

was long than when it was short. Changes in departure time were well predicted by

the marginal value theorem (Fig. 5.7).

For most large herbivores, food is continuously distributed across the landscape, rather

than in definable patches. Nonetheless, local abundance of food still varies consid-

erably from place to place. A slight modification to the marginal value theorem can

readily accommodate this situation (Arditi and Dacorogna 1988). This model pre-

dicts that animals should feed whenever the cropping rate exceeds the average rate

of cropping. A small herd of fallow deer (Dama dama) confined to a small pasture,

grazed according to the marginal value rule, concentrating their feeding in sites where

food abundance was higher than average (Focardi et al. 1996). However, a second deer

herd which roamed over a much larger area showed little evidence of being sensitive

to the marginal value of grazing. The marginal value rule seemed most applicable to

Et

Gt

t

Gt

t

()

()

()

=

⎛

⎝

⎜

⎞

⎠

⎟+

=

1 1 +

λ

λ

λ

THE ECOLOGY OF BEHAVIOR 67

5.3.2Patch use by

herbivores

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