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:

where and are *“expert guesses”*, is a scaling parameter and 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 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 . Here’s the result.

As expected, the exponential decay dominates the behaviour of all curves, 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.

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