FORAGING. ASK THE FOLLOWING QUESTION: 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? Diet Selection Models...

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FORAGING

ASK THE FOLLOWING QUESTION:

1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?

Diet Selection Models

Imagine a predator seeking prey:

Finds either prey type

Eat?? Move on??

Currency: Maximize rate of energy intake

The RULES!!!

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

Predator knows all this

ei = energy provided by prey type i

hi = handling time and effort associated with prey type i

li = encounter rate with prey type i

Ts = 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.

Assume predator always take prey with the higher ei/hi value

i.e. a more favourable energy gain : handling effort ratio

Low ei/hi value Higher ei/hi value

Assume predator always take prey with the higher ei/hi value

Assume that the higher ei/hi value is prey type 1 (or e1/h1)

Question : Should forager take prey 1 alone or take prey 1 and 2 as they are encountered?

Begin by calculating the total energy (E) per unit time associated with prey 1

E Ts l1e1

Ts + Ts l1h1T

=Total energy obtained from prey 1

Total handling time + Search time

E l1e1

1 + l1h1T

=Simplifies to

Now calculate the total energy (E) per unit time associated both prey 1 and 2

E Ts (l1e1 + l2e2)

Ts + Ts l1h1 + Ts l2h2 T

1 + l1h1 + l2h2T

=Simplifies tol1e1 + l2e2

1 + l1h1 + l2h2

>l1e1 + l2e2

Should a predator each both types of prey or just prey 1?

Mathematically, a predator should eat prey 1 if the following is true

1 + l1h1

1 + l1h1 + l2h2

>l1e1 + l2e2

Mathematically, a predator should eat prey 1 if the following is true

1 + l1h1

Holds true when

e1h2 - e2h1

> e2l1

e1h2 - e2h1>

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)

Patch Models

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

PATCH MODELS

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

Time in patch

Time between patches

•t1 T1

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 spendmore time in a patch (the t1: T1 situation).

If there is a shorter time between patches, you should spend

less time in a patch (the t1: T1 situation).

Modifications to Optimal Foraging Models

Central Place Foraging

Feeding area

Nesting area

Cost - energy getting to feeding area

Cost - energy returning from feeding area-carrying load of food

FORAGING STARLINGS

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

Searching time

Give up too early? – lots of travelling time for a small load

Give up too late? – spend time in ineffective search

Searching timeTravelling time

1 prey

8 prey

7 prey

Optimum

Searching timeTravelling time

Long travel time

Optimum for long

travel time

Short travel time

Optimum for short

travel time

What happens if we change the travel 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

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

Time in copulaTime spent searching and guarding

156 min

Predicted

Actual

Economics of food type

Shore crabs – choice of different sized mussels

Size of mussel Size of mussel

1.0 2.0 3.01.0 2.0 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?

Large prey – contain E1 energy with handling time of h1

Small prey – contain E2 energy with handling time of h2

So, the profitability (energy gain/unit handling time)

>- 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.

S1 + h1

> or E1h2

S1 > - h1

Choice of prey 2 (less profitable) depends on the abundance of prey 1(as expressed by S1)

Three predictions

1) Predator should eithera) Just eat prey 1 (specialize)b) Eat both (generalize)

2) Decision to specialize depends on S1 and not S2

3) Switch from specialist to generalist – should be sudden- occur when S1 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

Reward/individual

Number of competitors

Rich habitat

Poor habitat

Reward is same in both

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

Two experiments

Sticklebacks

Daphnia Daphnia x 2

End A End B

Two experiments

Sticklebacks

Number of fish at end A

Time (min)

Introduce at rate x

Switch to rate 2x

predicted

Two experiments

Mallards

Number of ducks at site A

Time after start of experiment

predicted

Mating in Sarcophaga

Expectation

Relative numbers of males at each patch Expected number of arriving females

Time after pat deposition

Staying time

FORAGING. ASK THE FOLLOWING QUESTION: 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? Diet Selection Models...

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