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# Consider an ecosystem consisting of a prey and a predator.If H is the density of prey,p is the density of predator r in the intrinsic rate of prey population increases and q is the predation rate coefficient.Which of the following correctly represents change in prey population density with time?

$\begin{array}{1 1}(a)\;\large\frac{dH}{dt}=\normalsize rH+qp\\ (b)\;\large\frac{dH}{dt}=\normalsize rH-qp\\(c)\;\large\frac{dH}{dt}=\normalsize rH-qHp \\(d)\;\large\frac{dH}{dt}=\normalsize qH+rHp\end{array}$

$rH\rightarrow$ Biotic potential $\times$ Population $\rightarrow$ Natality-Natural mortality
$qHp\rightarrow (q\times H\times p\rightarrow$Predator population
$\large\frac{dH}{dt}$=Natality-Deaths(natural+predated)
$\Rightarrow$ (Natality-natural)-predated
$\large\frac{dH}{dt}=\normalsize rH-qHp$
Hence (c) is the correct answer.