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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.

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Presentation on theme: "FORAGING. ASK THE FOLLOWING QUESTION: 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? Diet Selection Models Imagine a predator seeking prey: Finds either prey."— Presentation transcript:

1 FORAGING

2 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

3 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

4 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 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.

5 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 valueHigher e i /h i value

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

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

8 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 s ( 1 e e 2 ) T s + T s 1 h 1 + T s 2 h 2 T = E h h 2 T = Simplifies to 1 e e 2

9 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? h h 2 > 1 e e 2 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 e h 1

10 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? h h 2 > 1 e e 2 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 e h 1 Holds true when e 1 h 2 - e 2 h 1 > e2e2 1

11 1. WHAT FOOD ITEMS SHOULD A FORAGER EAT? Should a predator each both types of prey or just prey 1? e 1 h 2 - e 2 h 1 > e2e2 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)

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

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

14 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 food intake Time between patches  T1T1  T2T2

15 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     situation). If there is a shorter time between patches, you should spend less time in a patch (the      situation ).

16 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

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

18 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

19 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

20 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?

21 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

22 Another example – Honey bee – Apis mellifera

23 Number of flowers visited (= number of loads) Interflower time (= increase in carrying effort)

24 Sarcophaga on cow dung

25 Sarcophaga mating behaviour % eggs fertilized Time in copula

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

27 Economics of food type Shore crabs – choice of different sized mussels Size of mussel Profitability Percentage of diet

28 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?

29 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) E1h1E1h1 E2h2E2h2 > - Large prey are more profitable

30 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 1 S 1 + h 1 E2h2E2h2 > or E 1 h 2 E 2 S1S1 > - h 1 Choice of prey 2 (less profitable) depends on the abundance of prey 1(as expressed by S 1 )

31 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

32 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

33 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.

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

35 IDEAL FREE DISTRIBUTION Two experiments Sticklebacks DaphniaDaphnia x 2 End AEnd B

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

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

38 IDEAL FREE DISTRIBUTION Mating in Sarcophaga

39 Expectation Relative numbers of males at each patch  Expected number of arriving females Time after pat deposition Number of males on pat Staying time Male mating success

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