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
1
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
2
Crows Feeding on Whelks
Northwestern crow
(Corvus caurinus)
Whelk (Thais lamellosa)
Mollusc
Search intertidal zone
Fly to rocks, Drop prey
Repeat, Shell breaks
3
Crows Feeding on Whelks
Crows choose larger prey
~ Uniform size
At rocks, Fly straight up,
Drop whelk (Re-drop)
Optimal foragers?
“Optimize” H, height?
4
Crows Feeding on Whelks
Number of drops
versus height H
Constraint on problem
Large prey break easier
Kinetic Energy: 𝐾 =
1
𝑚𝑎𝑠𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
2
2
5
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
6
Model: E = kHN
E: Energy cost (Currency)
H: Drop height (Decision)
N(H): No. drops
a = 15.9; b = 1.2
k > 0 constant
Objective Function
7
Deduce Prediction
Derivative
dE/dH = 0
H* = 5.6 m
Minimizes cost
8
Prediction H = 5.6 m
Mean close to H*
Some variation
How? Not issue
Learned?
Issue:
Gain some understanding
of energy efficiency?
9