Brander-Taylor Model

Model Description

This is the original Brander-Taylor Easter Island model. Brander and Taylor (1998) describes the model as the following: "The paper presents a general equilibrium model of renewable resource and population dynamics related to the Lotka-Volterra predator-prey model, with man as the predator and the resource base as the prey. We apply the model to the rise and fall of Easter Island, showing that plausible parameter values generate a 'feast  and famine" pattern of cyclical adjustment in population and resource stocks. Near-monotonic adjustment arises for higher values of a resource regeneration parameter, as might apply elsewhere in Polynesia. We also describe other civilizations that might have declined because of population over-shooting and endogenous resource degradation".

Default Dynamics

(Please describe default dynamics for this model.)

$\frac{dS}{dt} = rS\left(1-\frac{S}{K}\right)-\alpha\beta LS$
Brander-Taylor resource stock change: resource stock grows logistically and is harvested.
$\frac{dL}{dt} = L\left(\phi\alpha\beta S - \sigma\right)$
Brander-Taylor population change: population growth is proportional to the difference between their resource consumption level and death rate. 
#parameters
#from original: sig=d-b

par alpha=1e-5, beta=0.4, sigma=0.1, phi=4, r=0.04, K=12000

#Initial conditions
init S=12000, L=40
gwth=r*S*(1-S/K)
harv=alpha*beta*L*S
aux growth=gwth
aux harvest=harv

S'=gwth-harv
L'=L*( phi*alpha*beta*S - sigma )

@ dt=0.1, total=500, xplot=S,yplot=L,axes=2d
@ xmin=0,xmax=15000,ymin=0,ymax=15000
@ xlo=0,ylo=0,xhi=15000,yhi=15000
@ maxstor=200000
@ bounds=100000

done

Anderies JM,  Arizona State University. 

Bozicevic M,  Arizona State University. 

You can adjust total time of simulation below.
This model has two state variables. You can set their initial values below.
This model has six parameters. You can set their values below.
Enter the axes to be plotted for this model.