Phenotypic Gambit Predict Focal Individual’s Behavior:

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Presentation transcript:

Phenotypic Gambit Predict Focal Individual’s Behavior: Does Behavior of Other Individual (s) Matter? NO: “Standard Optimization;” Find Maximal Currency of Fitness YES: Game Theory; Social Interaction Find Evolutionary Stable Strategy

Individual Behavior Crows Feeding on Whelks: references R. Zach (1978) Selection and dropping of whelks by Northwestern crows, Behaviour, 67, 134 - 147 R. Zach (1979) Shell dropping: Decision-Making and optimal foraging in Northwestern crows, Behaviour, 68, 106 – 117 http://www-rohan.sdsu.edu/~jmahaffy/courses/f00/math122/lectures/optimization

Crows Feeding on Whelks Northwestern crow (Corvus caurinus) Whelk (Thais lamellosa) Mollusc Search intertidal zone Fly to rocks, Drop prey Repeat, Shell breaks

Crows Feeding on Whelks Crows choose larger prey ~ Uniform size At rocks, Fly straight up, Drop whelk (Re-drop) Optimal foragers? “Optimize” H, height?

Crows Feeding on Whelks Number of drops versus height H Constraint on problem Large prey break easier Kinetic Energy: 𝐾= 1 2 𝑚𝑎𝑠𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2

Outline Model Hypothesis: Selection favors dropping whelk from height minimizing energetic cost to forager Individual Behavior: No Social Interaction Translate Height [H] into currency of fitness [Cost] Find H* where Cost minimal

Model: E = kHN E: Energy cost (Currency) H: Drop height (Decision) N(H): No. drops k > 0 constant Objective Function a = 15.9; b = 1.2

Deduce Prediction Derivative dE/dH = 0 H* = 5.6 m Minimizes cost

Prediction H = 5.6 m Mean close to H* Some variation How? Not issue Learned? Issue: Gain some understanding of energy efficiency?