## FUND 3.5 species model

Eli has a post up on Richard Tol’s FUND model, examining its treatment of species extinction in section 5.6 Ecosystems. The model is meant to run from 1950 to the year 3000 in time steps of 1 year.

The number of species at time step t is given in equation E.2:
$B_{t}=max\{\frac{B_{0}}{100};B_{t-1}(1-\rho - \gamma \frac{\Delta T^{2}}{\tau^{2}})\}$
where $\rho=0.003$ and $\gamma=0.001$ are “expert guesses”, $\tau=0.025^{\circ} C$ is a scaling parameter and $\Delta T$ is the temperature change with regard to the previous year.

A brief examination of the formula lets one guess, that the exponential decay given by the $\rho$ parameter will dominate the evolution of species numbers, but let’s have a look. I have assumed a simplistic temperature model: temperature change after 2000 follows an arcus tangens function with an initial slope of 2°C/century and levels off at various $T_{max}$. Here’s the result.

As expected, the exponential decay dominates the behaviour of all curves, $T_{max}$ has rather little influence. By the year 3000 the model rates the number of species at 4% to 5% of todays level. I expect this result to be robust with regard to changes in the temperature model.