Optimality of Ant Foraging Jason Green Supervisor: Bernd Meyer Is it really optimal, and how do we find that out?

Context Field Studies Laboratory Studies Mathematical Models Simulations

Pheromone trails

Y - Bridge ● At a fork in the trail, more ants go towards the better food source

Y - Bridge ● The probability of an ant going a certain direction is:

Y - Bridge ● The probability of an ant going a certain direction is:

Simulating the model ● The mathematical model generalised for a grid structure

Context Field Studies Laboratory Studies Mathematical Models Simulations

Mathematical Model vs Simulations ● Mathematical models allow us to solve the problem in a closed system – Eg. Determining when the colony will converge on a single food source ● Mathematical models allow us to determine if a certain behaviour holds over a range of values – Eg. Convergence occurs irrespective of the amount of pheromone deposited ● Mathematical Models alone get too complicated – The more parameters involved make it harder to solve ● Simulations allows us to see what is actually happening – Easier to recognise patterns – Easier to assess behaviour

Existing Simulations ● Only made for proof of concept ● Lack of resolution ● Only simple behaviour Not good enough!

My Solution ● Improve the resolution ● Add extra behaviours – Crowding – True random walk – Any more? ● Fully customisable ● Gather statistical data ● Automatic Optimisation

What I have done so far ● Created a Heirarchical grid data strucutre – Only allocates memory to nodes that are in use

What I have done so far ● Created a Heirarchical grid data strucutre – Pointers to neighbouring cells for faster navigation

My Solution ● Improve the resolution ● Add extra behaviours – Crowding – True random walk – Any more? ● Fully customisable ● Gather statistical data ● Automatic Optimisation