Mathematical model describing the decision-making process of a swarm of honeybees for selecting one nest-site among many
N.F. Britton, N.R. Franks, S.C. Pratt, T.D. Seeley, Deciding on a new home: how do honeybees agree ?, Proceedings of the Royal Society of London. Series B: Biological Sciences 269 (1498), 1383-1388 (2002) [Link]
Description
The population of the honeybees is divided in three main groups: X are the bees that are neutral (or unbelievers) in the decision, Y is the class of the bees that believes either in one site (Y1) or in another site (Y2) and they are actively spreading their beliefs (called evangelical bees) to the other bees, Z is the class of the bees that believes either in one site (Z1) or in the other site (Z2) but they do not spread (called not-evangelical bees) their beliefs to the others.
Probabilistic Program Computing the Bees Model (Source Code)
x = Normal(475, 5)
y1 = Uniform(350, 400)
y2 = Uniform(100, 150)
z1 = Normal(35, 1.5)
z2 = Normal(35, 1.5)
#dt = 0.1
#beta = 0.001 - We assume that beta = beta1 = beta2
#gamma = 0.3
#delta_beta = 0.0005 - delta * beta
#alpha_beta = 0.0007 - alpha * beta
while true:
x, y1, y2, z1, z2 = x + dt*((-beta)*x*y1 - beta*x*y2), y1 + dt*(beta*x*y1 - gamma*y1 + delta_beta *y1*z1 + alpha_beta*y1*z2), y2 + dt*(beta*x*y2 - gamma*y2 + delta_beta*y2*z2 + alpha_beta*y2*z1), z1 + dt*(gamma*y1 - delta_beta*y1*z1 - alpha_beta*y2*z1), z2 + dt*(gamma*y2 - delta_beta*y2*z2 - alpha_beta*y1*z2)
end
Program features | Value | Dependency Graph |
---|---|---|
if statements | Yes | (L) Linear (NL) nonlinear ![]() |
State space | Infinite, continuous | |
Circular Dependency | Yes | |
Symbolic Constants | Yes | |
Effective Variables | No | |
Defective Variables | Yes (x, y1, y2, z1, z2) |
Probabilistic Program Simulation:
Parameter | Current Value | Tuning |
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Number of program executions: | ||
Number of loop iterations (n): | ||
Integration step (dt): | ||
Parameter (beta): | ||
Parameter (gamma): | ||
Parameter (delta): | ||
Parameter (alpha): |