ASK THE FOLLOWING QUESTION:
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Imagine a predator seeking prey:
Finds either prey type
Eat?? Move on??
Currency: Maximize rate of energy intake

Predator knows all this
1. We can measure some standard currency
2. There is a cost in handling prey
3. A predator can
’ t handle one prey and search for another at the same time.
4. Prey are encountered sequentially
5. Prey are recognized instantly and accurately

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
e i
= energy provided by prey type i h i
= handling time and effort associated with prey type i l i
= encounter rate with prey type i
T s
= amount of time devoted to searching for prey type i
T = total time
For this example, we will assume that there are two prey types.

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Assume predator always take prey with the higher e i
/h i value i.e. a more favourable energy gain : handling effort ratio
Low e i
/h i value Higher e i
/h i value

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Assume predator always take prey with the higher e i
/h i value
Assume that the higher e i
/h i value is prey type 1
(or e
1
/h
1
)

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Begin by calculating the total energy (E) per unit time associated with prey 1
E
T
=
T s l
1 e
1
T s
+ T s l
1 h
1
Total energy obtained from prey 1
Total handling time + Search time
Simplifies to
E
T
= l
1 e
1
1 + l
1 h
1

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Now calculate the total energy (E) per unit time associated both prey 1 and 2
E
T
=
T s
( l
1 e
1
+ l
2 e
2
)
T s
+ T s l
1 h
1
+ T s l
2 h
2
Simplifies to
E
T
= l
1 e
1
+ l
2 e
2
1 + l
1 h
1
+ l
2 h
2

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Should a predator each both types of prey or just prey 1?
Mathematically, a predator should eat prey 1 if the following is true l
1 e
1
1 + l
1 h
1
> l
1 e
1
+ l
2 e
2
1 + l
1 h
1
+ l
2 h
2

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Should a predator each both types of prey or just prey 1?
Mathematically, a predator should eat prey 1 if the following is true l
1 e
1
1 + l
1 h
1
> l
1 e
1
+ l
2 e
2
1 + l
1 h
1
+ l
2 h
2
Holds true when l
1
> e
2 e
1 h
2
- e
2 h
1

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Should a predator each both types of prey or just prey 1?
l
1
> e
2 e
1 h
2
- e
2 h
1
Two predictions:
1. Once a critical encounter rate with prey 1 is reached, it alone should be taken
2. The decision about whether or not to take prey 2 does not depend on how common it is (i.e. it
’ s encounter rate)

Most food has a clumped distribution (or exists in patches)

HOW LONG SHOULD A FORAGER STAY IN A CERTAIN PATCH?
Problem :
Imagine a hummingbird on a flower
?
?
?
?
?

2. HOW LONG SHOULD A FORAGER STAY IN A CERTAIN PATCH?
Charnov - Marginal Value Theorem
- to determine how long an animal should stay in a patch t
•
1
Time between patches t
•
2
T
2
T
1
Time in patch

2. HOW LONG SHOULD A FORAGER STAY IN A CERTAIN PATCH?
Charnov - Marginal Value Theorem
- to determine how long an animal should stay in a patch
From previous graph:
If there is a longer time between patches, you should spend more time in a patch (the t
1
: T
1 situation).
If there is a shorter time between patches, you should spend less time in a patch (the t
1
: T
1 situation
).

Modifications to Optimal Foraging Models
Central Place Foraging
Cost - energy returning from feeding area
-carrying load of food
Nesting area
Feeding area
Cost - energy getting to feeding area

FORAGING STARLINGS
How many insects should the parent take/trip?
400 times/day

How many insects should the parent take/trip?
Size of the load

Rate of delivery of food

Survival of young

Reproductive success
First prey – retrieved easily
Later prey – retrieved less easily – prey already in beak
Yields a ‘loading’ or ‘gain’ curve
Load
Searching time

How many insects should the parent take/trip?
Give up too early? – lots of travelling time for a small load
Give up too late? – spend time in ineffective search
Travelling time
8 prey
1 prey
Optimum
Searching time
7 prey

How many insects should the parent take/trip?
What happens if we change the travel time?
Short travel time
Long travel time
Travelling time
Optimum for short travel time
Optimum for long travel time
Searching time

We did three things in formulating this model
1. Assumed starlings are good parents and will maximize energy delivery
2. Made a guess about the proper currency (max. net rate of food delivery)
3. Specified constrains – shape of load curve and travel time

Another example – Honey bee – Apis mellifera

Another example – Honey bee – Apis mellifera
Number of flowers visited (= number of loads)
Interflower time (= increase in carrying effort)

Sarcophaga on cow dung

Sarcophaga mating behaviour
% eggs fertilized
Time in copula

Sarcophaga
% eggs fertilized
Predicted
156 min
Time spent searching and guarding
Actual
Time in copula

Economics of food type
Shore crabs – choice of different sized mussels
1.0
2.0
Size of mussel
3.0
1.0
2.0
Size of mussel
3.0

Economics of food type
Shore crabs – choice of different sized mussels
Why this choice?
Very large prey – very long time and energy to open

Net gain is lower
Very small prey – easy to open but little energy
Why do they sometimes take less preferred prey?

Why do they sometimes take less preferred prey?
Large prey – contain E
1 energy with handling time of h
1
Small prey – contain E
2 energy with handling time of h
2
So, the profitability (energy gain/unit handling time)
E
1 h
1
>
E
2 h
2
- Large prey are more profitable

How does predator choose prey to maximize E/h?
a) If encounter prey 1, always eat it.
 choice of more profitable prey doesn’t depend on the abundance of prey 2 b) If encounter prey 2, should eat it if gain from eating prey 2 > gain from rejecting and searching for more profitable prey.
E
2 h
2
>
S
1
E
1
+ h
1 or
S
1
>
E
1 h
2
E
2
h
1
Choice of prey 2 (less profitable) depends on the abundance of prey 1(as expressed by S
1
)

Three predictions
1) Predator should either a) Just eat prey 1 (specialize) b) Eat both (generalize)
2) Decision to specialize depends on S
1 and not S
2
3) Switch from specialist to generalist – should be sudden
- occur when S
1 increases to the point where the equation is true

Extension of the Argument
So far – considered efforts of single animals
What happens when competition is involved?
Scenario:
Two habitats – one rich in resources, one poor
No territoriality, no fighting

As more competitors occupy rich habitat – deplete resources
Rich habitat
Reward/individual
Poor habitat
Reward is same in both
Number of competitors
PREDICTION: Competitors adjust their distribution so that all individuals have the same rate of resource acquisition.

IDEAL FREE DISTRIBUTION
-animals are FREE to go where they want
-animals are IDEAL in having complete information about resource availability

IDEAL FREE DISTRIBUTION
Two experiments
Sticklebacks
Daphnia
End A
Daphnia x 2
End B

IDEAL FREE DISTRIBUTION
Two experiments
Sticklebacks
Number of fish at end A
4
2
Introduce at rate x
Switch to rate 2x
0
Time (min) predicted

IDEAL FREE DISTRIBUTION
Two experiments
Mallards predicted
Number of ducks at site A
Time after start of experiment predicted

IDEAL FREE DISTRIBUTION
Mating in Sarcophaga

Expectation
Relative numbers of males at each patch

Expected number of arriving females
Time after pat deposition Staying time