Island Biogeography functions

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.

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.

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