[R-sig-dyn-mod] Solved. (Was: Re: Failed attempt to use modFit- part 2)

[Thomas Petzoldt]

Hi,

thanks for your extensive summary. Please note that emails containing 
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The 2 equation approach seems to be frequently used in the literature 
but is quite obvious:

dy1/dt = -a * y1 + (b1-d1) * y1
dy2/dt =  a * y1 + (b2-d2) * y2

For micro-organisms it may be assumed that sub-population y1 adapts to 
the medium and only y2 is growing.

One may also assume that birth (b) and death (d) rates of population y1 
are balanced (b1 - d1 = 0), so that its net growth rate r1 = 0 and can 
be omitted, while in population y2: r2 = (b2 - d2) > 0. The latter can 
now be replaced by a resource limitation term, extended by further 
stages, or simply be "cut off" with a logistic term:

dy1/dt = -a * y1
dy2/dt =  a * y1 + rmax * (1 - y2/K) * y2


A demographic interpretation may be found in Wikipedia:

http://en.wikipedia.org/wiki/Demographic_transition

... but it is surely much more complex in reality - especially the 
mechanisms, and the value of K. So be careful with your interpretation.

Thomas P.