GRECA talk
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The talk I gave to the GRECA at UQAM in 2008. My first talk of the PhD.
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GRECA talk
- 1. The story so far... Steven Hamblin
- 2. The Hero of our story...
- 3. Act I
- 6. Producer
- 9. Other forms of scrounging.
- 19. Rules
- 20. Rules • Relative payoff sum
- 21. Rules • Relative payoff sum • Perfect Memory
- 22. Rules • Relative payoff sum • Perfect Memory • Linear Operator
- 23. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) where 0 < x < 1 is a memory factor, ri > 0 is the residual value associated with alternative i, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 24. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) where 0 < x < 1 is a memory factor, ri > 0 is the residual value associated with alternative i, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 25. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) where 0 < x < 1 is a memory factor, ri > 0 is the residual value associated with alternative i, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 26. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) where 0 < x < 1 is a memory factor, ri > 0 is the residual value associated with alternative i, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 27. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) where 0 < x < 1 is a memory factor, ri > 0 is the residual value associated with alternative i, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 28. Perfect Memory Si (t) = + Ri (t)/(⇥ + Ni (t)) where Ri (t) is the cumulative payo s from alternative i to time t, Ni (t) is the number of time periods from the beginning in which the option was selected, and ⇥ are parameters.
- 29. Perfect Memory Si (t) = + Ri (t)/(⇥ + Ni (t)) where Ri (t) is the cumulative payo s from alternative i to time t, Ni (t) is the number of time periods from the beginning in which the option was selected, and ⇥ are parameters.
- 30. Perfect Memory Si (t) = + Ri (t)/(⇥ + Ni (t)) where Ri (t) is the cumulative payo s from alternative i to time t, Ni (t) is the number of time periods from the beginning in which the option was selected, and ⇥ are parameters.
- 31. Perfect Memory Si (t) = + Ri (t)/(⇥ + Ni (t)) where Ri (t) is the cumulative payo s from alternative i to time t, Ni (t) is the number of time periods from the beginning in which the option was selected, and ⇥ are parameters.
- 32. Linear Operator Si (t) = xSi (t 1) + (1 x)Pi (t) where 0 < x < 1 is a memory factor, Pi (t) is the payo to alternative i at time t, and Si (t) is the value that the animal places on the behavioural alternative i at time t.
- 34. Bird Start At a patch with food? Yes Feed NO Produce or scrounge? Scrounge Produce Move randomly No Any conspecifics feeding? Move to closest Yes There yet? Yes No Closest still feeding? No
- 35. • 5 or 10 birds. Bird Start At a patch with food? Yes • Foraging grid is Feed NO a regular 10x10 grid, with movement in the 4 cardinal directions. Produce or scrounge? Scrounge Produce Move randomly No Any conspecifics feeding? Move to closest Yes There yet? • 20 patches on Yes No Closest still feeding? No the grid, with 10 or 20 food items in each.
- 37. Relative Payoff Sum? Si (t) = xSi (t 1) + (1 Perfect Memory? Si (t) = Linear Operator? Si (t) = xSi (t x)ri + Pi (t) + Ri (t)/(⇥ + Ni (t)) 1) + (1 x)Pi (t)
- 38. Relative Payoff Sum? Si (t) = xSi (t 1) + (1 Perfect Memory? Si (t) = Linear Operator? Si (t) = xSi (t x)ri + Pi (t) + Ri (t)/(⇥ + Ni (t)) 1) + (1 x)Pi (t)
- 39. Relative Payoff Sum? Si (t) = xSi (t 1) + (1 Perfect Memory? Si (t) = Linear Operator? Si (t) = xSi (t x)ri + Pi (t) + Ri (t)/(⇥ + Ni (t)) 1) + (1 x)Pi (t) Multiple stable rules with multiple parameters?
- 40. Genetic Algorithms • Algorithms that simulate evolution to solve optimization problems.
- 41. Initial population Measure fitness > n generations Select for reproduction Mutation Exit
- 42. Genetic algorithm to optimize parameters and simulate population dynamics. Foraging / Learning rule simulation.
- 43. Results to date
- 47. Relative Payoff Sum Si (t) = xSi (t 1) + (1 x)ri + Pi (t) rp >> rs for large population sizes. 5 4 Value assigned to 3 behaviour 2 Producer residual 1 Scrounger residual -1 0 1 2 3 4 5 Time without payo! to behaviour 6 7 8
- 49. • Under the assumptions of this model, the Relative Payoff Sum rule is optimal. • Whether RPS is favored depends on payoff variance: • low variance = more attractive power. • Differences in residuals gives a prediction for empirical tests.
- 50. Next steps?
- 51. Other games...
- 52. Genetic algorithm to optimize parameters and simulate population dynamics. Foraging / Learning rule simulation.
- 53. Genetic programming to optimize rule structure. Genetic algorithm to optimize parameters and simulate population dynamics. Foraging / Learning rule simulation.
- 54. Act II
- 61. +
- 62. Foraging / Learning rule simulation.
- 63. Foraging / Learning rule simulation. Swappable grids (Moore / VN / Hex / Dirichlet)
- 64. Genetic algorithm to optimize parameters and simulate population dynamics. Foraging / Learning rule simulation. Swappable grids (Moore / VN / Hex / Dirichlet)
- 65. Results to date
- 66. Act III
- 67. +
- 72. One field, a few names... • Graph theory.... • Social network analysis.... • Network theory...
- 77. Graph measures... • Degree • Centrality
- 78. Graph measures... • Degree • Centrality • Clustering
- 79. Graph measures... • Degree • Centrality • Clustering • Path length
- 80. Graph measures... • Degree • Centrality • Clustering • Path length • Etc...
- 81. Six degrees...
- 83. • Small world network: • High clustering, low path length.
- 85. Birds # of connections to other foragers
- 86. Most birds have few connections Birds # of connections to other foragers
- 87. Most birds have few connections Birds A few birds have many connections # of connections to other foragers
- 92. =
- 93. =
- 94. Small world network analysis Foraging / Learning rule simulation.
- 95. The end of the story.