Show that n/n = r - a(n-b)^2 provides an example of the allee effect, if r, a, and b satisfy certain constraints

See the explanation

Explanation:

Let us denote the effective growth rate N/N by R(N).

To find if, and at which N, this effective rate is highest, we evaluate

, under the assumption that r, a, b are all parameters independent of N.

At extremum, the above will vanish, giving  

a(N - b) = 0.

If a ≠ 0, then the extremum occurs at N = b, which is possible if b > 0 (since it represents a population). If this extremum is a maxima, then

, which is possible if a > 0.

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primary succession begins with a bare rock and ends with a forest secondary succession begins after a natural disaster where there is a temporary setback after a forest fire or local destruction, but the surrounding area can fill in

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