Python function for carrying out discrete stochastic simulations of the logistic population model. http://cnr.lwlss.net/DiscreteStochasticLogistic/

simDSLogistic.py

import numpy as np

def simDSLogistic(K,r,N0):
    '''Discrete stochastic logistic model simulation.  Carrying capacity K,
intrinsic growth rate r, initial population size (inoculum) N0.  Returns an
array with a (continuous) time column and a (discrete) population size column.'''
    # Unusually, for this model, we know the number of events a priori
    eventNo=K-N0
    # So we can just generate all required random numbers (quickly) in one go
    unifs=np.random.uniform(size=eventNo)
    # Every event produces one cell and consumes one unit of nutrients
    simres=np.zeros((eventNo+1,2),np.float)
    simres[:,1]=range(N0,K+1)
    # Simulate time between events by generating 
    # exponential random numbers using the inversion method
    dts=-np.log(1-unifs)/(r*simres[1:,1]*(1-simres[1:,1]/K))
    simres[1:,0]=np.cumsum(dts)
    return(simres)

Updated function to avoid slow concatenation of initial conditions onto arrays. Can now simulate a population or culture with a carrying capacity of 1.6M, starting from a single member or cell in 0.37s.

python #logistic #discrete #stochastic