Modeling the evolution of ant foraging strategies with genetic algorithms. Kenneth Letendre CS 365 September 4, 2012

Transcription

1 Modeling the evolution of ant foraging strategies with genetic algorithms Kenneth Letendre CS 365 September 4, 2012

2 Harvester Ants Genus Pogonomyrmex A model organism for study of central place foraging Ants are a model of distributed decision making (Ant colony optimization) Questions: How does territory size scale with colony size? How does foraging behavior and recruitment scale?

3 Agent-Based Model of Ant Colony Foraging Model behaviors based on literature and our own observations Why an ABM? Some behaviors depend on parameters likely vary with colony size or food distribution We used genetic algorithms to select parameters We compared behavior of these optimized models ant colonies in the field

4 Pheromone Recruitment and Collective Problem-Solving Foraging ants search for food Successful foragers lay pheromone trails on the return trip to the nest Foragers leaving the nest follow trails Ants arriving at sites where more food is to be found have reduced search time, reinforce trails Pheromones evaporate over time The colony converges its foraging effort on high quality sites that maximize food collection rate (lowest travel time and lowest search time) (Detrain & Deneubourg, 2008) Convergence is at the heart of distributed decision-making by insect colonies, and by ACO. Model 1

5 Parameters Parameter α ω γ δ Function Determines the probability each time step that an ant walking from the nest will stop walking and begin to search. Searching ants moving in a correlated random walk. ω determines the baseline degree of deviation in the direction an ant will move from one time step to the next. Determines the additional degree of deviation in turning early on in an ant's search Exponent determines how quickly turning behavior approaches the baseline turning behavior as time spent searching t s increases. SD = ω + γ / t s δ ε η For ants following a pheromone trail, determines the probability each time step that an ant will abandon the trail and begin searching before reaching its end. Determines the rate at which pheromones evaporate.

6 Optimization by Genetic Algorithm Want to ensure model performs the foraging task optimally So we can compare apples to apples when looking at differences in model behavior in different situations Parameters are floating point numbers. Assuming discretization to two digits, the search space of all parameters is > (10 2 ) 6 = We used genetic algorithms (GAs) to search this space Population of parameter sets initialized with random values Each colony in each generation evaluated on 8 standard grids Selection for total number of seeds collected Parameters inherited subject to crossover and mutation

7 Optimization by Genetic Algorithm Ten Ants 1000 Ants Fitness Curves for Optimization on Piled Foods

8 Recruitment: Comparison to Field Data Field Simple Recruitment Flanagan et al, 2012 Model 2 Model 3 Model 4 Model 5

9 Recruitment: Comparison to Field Data Simple Recruitment Field Density-Dependent

10 Parameters cont.: Site Fidelity and Recruitment Ants use two mechanisms to exploit information: site fidelity (ants' individual memory of foraging sites) recruitment (information shared via pheromone trails) Model ants take a count C of food available in the neighboring 8 cells Successful foragers decide to recruit with probability p r = λ r + C / μ r Decide to return to the last successful site with probability p f = λ f + C / μ f Decide to follow pheromone trails from the nest with probability p t = λ t - C / μ t Thus the GA can find an optimal balance between reliance on private vs. shared information Model 6

11 Optimization by Genetic Algorithms We optimized models to forage on: Using: site fidelity alone recruitment alone Both methods neither foraging method

12 Foraging Success and Search Times Variation in search times accounts for 51% of variation in foraging success.

13 Empirical Comparison to Field Data Rate of collection of piled seeds normalized by rate of collection of random seeds

14 Scaling of Colony Territory in vivo and in silico Field (Moses, 2005) Model 4.40x 0.59 Number of Foragers

15 Conclusions Modeling allows us to test hypotheses about ant foraging behavior Under controlled conditions not possible in the field We can experiment with foraging strategies impossible to isolate in real ants Common models of pheromone recruitment (ants lay pheromone trails each return trip) do not work well for all problem types Convergence may happen eventually on piles of seeds, but perhaps not before the piles have been collected Decisions about recruitment based on local information markedly improve the value/information content of pheromone trails We investigated site fidelity as a foraging strategy Site fidelity works better for every every food distribution we tested Both site fidelity and recruitment produce fit to field data Both strategies together work better together than either alone