shiba
Island Biogeography functions

## Survival function

We use the logarithm function as the basic survival function for an island with area :

We standardize this by using proportions of total land area:

The curve can be forced through (0,0) and (1,1):

Increasingly steeper a (0,0) are and

Generalizing, the basic survival curve is:

Finally, a further parameter, sets the survival for :

Survival probability

In the input data, is set with probSurvA and shape parameter is set with probSurvB. Values of ‘1.0’ for probSurvA and ‘2.0’ for probSurvB are appropriate starting values. You can view the shape of the curve with the ‘-l’ flag.

## Dispersal function

For dispersal, we use a negative power function dependent on the distance between two places ( ), standardized by maximum distance between any two places ( ):

The concavity of the curve (steepness at (0,1)) can best be adjusted with a parameter (as opposed to varying the ‘base,’ i.e. 10):

Finally, a further parameter, sets the dispersal probability for distance zero, i.e., when landmasses are touching.

Dispersal probability

In the input data, is set with probDispA and shape parameter is set with probDispB. Values of ‘1.0’ for probDispA and ‘2.0’ for probDispB are appropriate starting values. You can view the shape of the curve with the ‘-l’ flag.