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| ATTN: anymouse, and function geeks. |
by Esteis |
2006-11-19 12:55:59 |
Re: my post of tuesday on saturation curves. My teacher has since informed me that the most commonly used function to model saturation is the so-called Hill function, which takes the form
f(x) = x / (x + h).
It's nifty properties are as follows:
- In the positive domain, it returns values between 0 and 1, which makes it suitable as a scaling factor.
- It has just the one parameter, namely h. The definition of h is elegant, too: it's the value of x at which y = 0.5. E.g. the number of empty patches which yields a growth speed that is 50% of the max.
- If you square it, you get a neatly S-shaped curve, similar to the logistic function. The half-max point remains at x = h; at 0 and towards infinity, the slope approaches 0.
- You can write 1 - f(x) to get a function which shows decrease as x increases, from 1 down to 0. Ditto for 1 - f(x)2.
My teacher told me this function is one of the workhorses of population modelling, especially in the simple stages. The other commonly used function for asymptotic decrease is the exponential function g(x) = e-x/h.
Gentle reader, I hope you found this somewhat interesting. anymouse and MatthewDBA, thanks for your replies, yesterday.
If anybody wants to know more, you can download the reader for the course --- it's the one called Modeling Population Dynamics: a graphical approach. A ton of interesting stuff, clearly explained. |
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[ Reply ] |
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thanks for the reply | by anymouse | 2006-09-07 02:06:33 |
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[whispers] (No, it was tuesday.) (n/t) | by Esteis | 2006-09-07 02:53:52 |
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