Simulating the Evolution of Ant Behaviour in Evaluating Nest Sites James Marshall, Tim Kovacs, Anna Dornhaus and Nigel Franks

Purpose of Work Use an Evolutionary Algorithm to study evolution of behaviour in real ants Note: we use EA to optimise our simulation, not to simulate real evolution Why did ants evolve this way? Are other behaviours just as good / better? What algorithms do ants use to self-organise?

Evolutionary Trajectory of Ants Two approaches to simulation of evolution: simulate evolution in detail (hard!) compare specific alternative behaviours (easier)

Nest Size Evaluation Leptothorax albipennis appears to measure nest volume using an algorithm called Buffon’s needle Each ant makes 2 visits to potential nest: - Visit 1: lay pheromone trail - Visit 2: assess pheromone density Between visits ant returns to old nest site

Movement of a Real Ant Figure from: Mallon, E.B. and Franks, N.R. Ants Estimate Area Using Buffon’s Needle. Proc. R. Soc. Lond. B 267(2000) 765-770.

1-pass vs 2-pass Evaluation of Nest Size Why visit potential nest twice? Nest relocation often occurs in response to attacks and is time-critical Why not do both steps during same visit?

Experiments Simulate nest size evaluation and compare 1-pass and 2-pass strategies. Most importantly: does 1-pass work? i.e. can we implement Buffon’s needle with it? Also: which classifies nest size more reliably? which requires less time in nest?

Experimental Details Assumptions: Ant movement is a constrained random walk Ants measure pheromone density using an arousal level increase level when trail crossed decrease level on all time steps

Experimental Details 3 sizes of square nest used Half of ants use 1-pass and half use 2-pass Ants evolve the following characteristics: total time spent in nest t arousal decay rate classification divisor d

Experimental Details Ant converts arousal level at end of visit to size classification e using e = (c-1) -min[int(r/d), c-1] where c is number of size categories (3), r is arousal level and d is classification divisor

Fitness Calculation An ant’s fitness is given by: f = -q |e - s| - t where q = 1000 provides selective pressure towards assessment quality s is actual nest size and t is time spent in nest

Evolutionary Algorithm Rank population by fitness cull least fit 1/3 of population replace with offspring from fittest 2/3 Generate offspring: Apply uniform crossover to adjacently ranked pairs of ants with probability 10% Mutate with probability 1%: change value uniformly at random by up to 10%

Results No significant difference between 1 and 2- pass in: number of trials which reached 100% accuracy number of generations needed to reach it total time spent in nest Conclusion: Buffon’s needle can be implemented with 1-pass But 1-pass spent no less time in nest Perhaps our simulation didn’t capture something important

Discussion Note that 2-pass requires time to make an extra trip to potential nest, so 1-pass is faster Why do ants use 2-pass? Evolutionary accident? Maybe ants can’t lay and detect pheromones simultaneously We’ve shown 2-pass isn’t necessary algorithmically