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Question

Some organisms exhibit a density-dependent mortality from one generation to the next. Let R > 1 be the net reproductive rate (that is, the number of surviving offspring per parent), let x > 0 be the density of parents, and y be the density of surviving offspring. The Beverton-Holt recruitment curve is $y=\frac{R x}{1+\left(\frac{R-1}{K}\right) x}$ where K > 0 is the carrying capacity of the organism’s environment. Show that $\frac{d y}{d x}>0$, and interpret this as a statement about the parents and the offspring.

Solution

VerifiedStep 1

1 of 4### Given Data

The Beverton-Holt recruitment curve is

$y=\dfrac{R x}{1+\left(\dfrac{R-1}{K}\right) x}$

We have to show that $\dfrac{d y}{d x}>0$

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