Function Shapes
The Ecosim and Ecospace modules contain forcing functions and mediation functions through which temporal dynamics of the model can be influenced. These functions can be arbitrarily sketched, obtained from external data where known, or derived from a series of predefined mathematical distributions.
The EwE software offers the predefined distributions illustrated in Figures 1 to 10. In addition, efforts are under way to allow users to programmatically add their own distributions via plug-ins.
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- Figure 1 – Original Contours
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- Figure 2 – BetaPDF distribution
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- Figure 3 – Exponential Distribution
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- Figure 4 – Hyperbolic Distribution
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- Figure 5 – Left Shoulder Distribution
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- Figure 6 – Right Shoulder Distribution
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- Figure 7 – Linear Distribution
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- Figure 8 – Normal Distribution
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- Figure 9 – Sigmoid Distribution
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- Figure 10 – Trapezoid Distribution
We illustrate the variables and use of forcing functions shape with an example, see Figure 11.
- X min – Minimum value of the X axis data
- X max – Maximum value of the X axis data
- X mid – Middle of the curve, where the sigmoid function returns 0.5. This does not have to be the mean value of the X axis data.
- X opt – Point on the X axis where the sigmoid function returns 0.998, just short of 1.0 so the function doesn’t have to be completely flatten at this point. Entering this value cause the Steep parameter to be calculated, even if it has been entered. If X opt. is greater than X mid. then the shoulder is increasing to the right. If X opt. is less than X mid. then the shoulder will decrease to the right.
- Steep – Steepness of the curve, high values will make the curve steeper
- Y max – Maximum value on the Y axis. By default this is one. Included as a parameter so the sigmoid function shapes can be used as a forcing function, this allows for sigmoidal growth or decay in a forcing function.
From a user’s perspective it would be good to set the X axis data range (X min. and X max.) in the Functional response to environmental forcing. In this dialogue the response function and the forcing data are both displayed in the Driver histogram & response function plot, there is also UI elements for X min. and X max. and a button to set the Default X axis. Unfortunately, because of the way the Functional response to environmental forcing… dialog has been programmed, it is awkward to use these values to set the default X min. and X max. values.
If X opt. has been entered then Steep parameter will always be calculated, even if it has been entered. To use the Steep parameter instead of X opt., clear the X opt. value and enter only Steep.
Sigmoid functions from older version of EwE are still be included for backwards compatibility. They will appear as Sigmoid_Legacy in the Shape type list
