Bi and multilogistic curves
The Component Logistic Model
The Component Logistic Model
There are many ways to visualize logistic growth aside from simple
plotting on a linear scale. It is possible to define a change of
variables that normalizes a logistic curve and renders it as a
straight line (see Figure 2). This view is known as the FisherPry^{3} Transform:

(3) 
Figure 2:
The logistic growth of a bacteria colony plotted using the FisherPry
transform that renders the logistic linear.

Note that

(4) 
so if FP(t) is plotted on a logarithmic scale, the Sshaped logistic is
rendered linear. We observe that the time in which the range is
between 10^{1} and 10^{1} is equal to ,
and the time
at 10^{0} is the point of inflection (t_{m}). Moreover,
because the FisherPry transform normalizes each curve to the carrying
capacity ,
more than one logistic can be plotted on the same
scale for comparison. As we will see, this becomes particularly
useful when we analyze more complex growth behaviors. Figure 2
shows the FisherPry transform of the bacteria example in figure 2. On
the right axis we label the corresponding percent of saturation ( 100 * F) at each
order of magnitude from 10^{}2 to 1^{2} rounded to the nearest percent.
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Perrin S Meyer
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