1. 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

2. Individual Behavior Crows Feeding on Whelks: references
R. Zach (1978) Selection and dropping of whelks by Northwestern crows, Behaviour, 67,
R. Zach (1979) Shell dropping: Decision-Making and optimal foraging in Northwestern crows, Behaviour, 68, 106 – 117

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

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

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

6. 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

7. 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

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

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