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Brander-Taylor Model

Model Type
SES Library XPP model

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.)

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Name Initial Value Description
\(S\) - Renewable resource stock (e.g., fish, trees, soil fertility).
\(L\) - Population in a society that is dependdent on a renewable resource base.
Name Default Value Description
\(\alpha\) - Productivity of harvest labor, measured as the proportion of total stock harvested in a time period.
\(\beta\) - Proportion of total labor spent on harvesting.
\(\sigma\) - Default death rate in absence of harvest (d-b in the original paper), in population units per time.
\(\phi\) - Fertility of the population due to harvesting, in population units per resource unit per time.
\(r\) - Growth rate of the resource, in resource units per time.
\(K\) - Carrying capacity of the resource in resource units.
$$\frac{dS}{dt} = rS\left(1-\frac{S}{K}\right)-\alpha\beta LS$$
$$\frac{dL}{dt} = L\left(\phi\alpha\beta S - \sigma\right)$$
brander-taylor_model.ode
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