Formation of an ant cemetery: swarm intelligence or statistical accident 報告者 : 王敬育

Abstract The model of artificial ants is proposed by Deneubourg in 1991 。 1.pick & drop 2.swarm intelligence A new model with: 1.less intelligence 2.clustering can be explained by a statistical effect 3.the cemetery formation is not a collective phenomenon

Deneubourg ’ s model The key steps are the pick up & lay down phases: the probabilities K 1 ， K 2 are the parameters (K 1 = 0.1 ， K 2 = 0.3 ) f : a fraction representing the number of corpses memorized by the ant along its own path 。 f = N / T N: the numbers of items that encountered in the path T: the last T motion steps (T = 50)

The minimal model Pick up and deposition rule (1)Each time an unloaded ant sees a body on one of its eight neighboring cells ， it loads it with probability 1 。 If there are several bodies ， it chooses one of them 。 (2) After the ant has moved at least one step away ， the corpse is released provided the ant is surrounded by one or more dead bodies in its eight-cell neighborhood 。 If this is the case ， the ant deposits the body in a randomly chosen empty neighboring cell 。

The minimal model (3) Contrarily to Deneubourg ’ s model ， our ants never walk on a corpse 。 (maybe trapped in the cluster) Displacement rule (1)The ants move one cell at a time ， but heading in the same direction for a pre-assigned random number of steps 。 (the steps we call free path) After the number of steps ， the ants select at random a new direction of motion among the eight possible lattice directions and a new length for the next free path 。

The minimal model (2) The free path is chosen uniformly from the set {1,2,3 … L} ， independently for each ant 。 (in this model L = 100) (3) When a corpse lies on the trajectory of the ant ， a new random direction is selected as well as a new free path length 。 (4) To deal with obstacles: an ant which faces a blocking sit chooses a new direction of a new direction of motion and a new free path length 。

Result and comparisons What is the mechanism that biases the dynamics so as to form only one large cluster? In Deneubourg ’ s model: from the intelligence of ants In minimal model: the dynamics is biased towards forming larger clusters ， because : (1) small ones are more likely to disappear under statistical fluctuations (2) clusters cannot build up from nothing

Cemetery formation with heterogeneities

Dynamics of the formation process The process scales as: N( t ) = F(M t ) N( t ) : the number of clusters at time t simulation M: the number of working ants in the simulation F: some unknown universal scaling function depending on the details of the model