Answer:
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
[tex]\frac{d}{dN} R=-2a(N-b)[/tex] , 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
[tex]\frac{d^{2} }{dN^{2} } R=-2a<0[/tex] , which is possible if a > 0.
Hope this helps!
The allele effect is the interaction and the relation between the average of the individual fitness of a species and the population size of the area. It is a biological phenomenon that occurs due to genetic drift or natural selection.
Let the effective growth rate [tex](\dfrac{N}{N})[/tex] be given as [tex]\rm R(N)[/tex].
Evaluate at what value of N will be the effective rate the highest under the parameters r, a and b:
[tex]\dfrac{d}{dN} \rm R= -2a (N-b)[/tex]
From the above, it can be stated that the values are independent of N.
When at extreme conditions the above equation will be given as,
[tex]\rm a(N-b)=0[/tex]
If in this case [tex]a\neq 0[/tex], then the values of the [tex]\rm N=b[/tex] that is possible in the case of [tex]\rm b>0[/tex]. Now the equation will be:
[tex]\dfrac{d^{2}}{dN^{2}}\rm R=-2a<0[/tex]
Therefore, it is possible to have this value only when the [tex]\rm a>0[/tex].
Learn more about allele effect here:
https://brainly.com/question/15392786
