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Outbreak 5.
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Let's go back to that last pink love sphere
animation (bottom of page). Let's suppose you set B = 13. The plot of
DP / Dt
(vertical axis) verses P and B is shown at left. Along the line B = 13 I've
indicated values of DP / Dt
at four different points (vertical yellow arrows). The first arrow is at B = 13, P = 36,
and DP / Dt = 7.87.
This is a moderate growth rate, so as we click through 80 generations in the animation
below with B = 13, we expect a moderately steep slope to the growth curve once we get through
the necessarily slow start (why?). Then we enter a small region of slow growth where the second arrow is
indicated (B = 13, P = 112,
DP / Dt = 2.95).
Between P = 100 and P = 140 the value of
DP / Dt averages
something less than 4, so it takes more than (140-100)/4 = 10 generations to get out
of this slow growth region (shallow slope to the growth curve).
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The next arrow is at B = 13, P = 381,
DP / Dt = 23.76.
This is very fast growth and the growth curve will be steep at this point. And finally we get into the
area of the fourth arrow, with growth rapidly approaching zero. As it does the population
curve will flatten out and asymptotically approach the limiting value P = 583. So, with B = 13 all the way through we expect the population curve to take some time to get growing (flattish slope), followed by a short stretch of medium slope, and medium stretch of flattish slope, a medium stretch with steep slope, followed by an asymptotic tailing off to a flat slope. Play it through. Then play around. Let the population get up to around 480, then change B to 18 and watch the population get decimated. If you've got something against pink love spheres (some traumatic childhood experience?), then this should prove enjoyable. The point of all this, however, is to understand the relationship between the plot of DP / Dt verses B and P (or N) and what actually happens in a "real" population (it should be stated - which may already be clear - that the way I programmed pink love sphere reproduction has an element of randomness to it, just like real life, and who's to say these pink love spheres aren't real life (does the Prime Directive apply here?)). One final note: it's obviously not very natural to have the value of B set by some alien entity (namely, you). In Nature the efficacy of the predator population often fluctuates on its own in response to what's happening to the prey population. And that will be our next step. |
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