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
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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.
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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?
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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
=
E
1 + l1h1 + l2h2T
=Simplifies tol1e1 + l2e2
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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
l1e1
1 + l1h1
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
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
l1e1
1 + l1h1
Holds true when
e1h2 - e2h1
> e2l1
1. WHAT FOOD ITEMS SHOULD A FORAGER EAT?
Should a predator each both types of prey or just prey 1?
e1h2 - e2h1>
e2l1
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
Net
foo
d in
take
Time between patches
•t1 T1
•t2
T2
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?
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
Searching timeTravelling time
1 prey
8 prey
7 prey
Optimum
How many insects should the parent take/trip?
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
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
Prof
itab
ilit
y
Perc
enta
ge o
f di
et
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?
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)
E1
h1
E2
h2
>- 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.
E1
S1 + h1
E2
h2
> or E1h2
E2
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
IDEAL FREE DISTRIBUTION
Two experiments
Sticklebacks
Daphnia Daphnia x 2
End A End B
IDEAL FREE DISTRIBUTION
Two experiments
Sticklebacks
Number of fish at end A
Time (min)
Introduce at rate x
Switch to rate 2x
2
4
0
predicted
IDEAL FREE DISTRIBUTION
Two experiments
Mallards
Number of ducks at site A
Time after start of experiment
predicted
predicted
IDEAL FREE DISTRIBUTION
Mating in Sarcophaga
Expectation
Relative numbers of males at each patch Expected number of arriving females
Time after pat deposition
Num
ber
of m
ales
on
pat
Staying time
Mal
e m
atin
g su
cces
s
