Invasive species often display a wave of advance as they colonize new areas. Mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the function f(r)=2Dr, where r is the reproductive rate of individuals and D is a parameter quantifying dispersal. Calculate the derivative of the wave speed with respect to the reproductive rate r and explain its meaning.

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insonsipthinye · Accepted Answer

As r (the reproductive rate) increases, advances gained from it by the invasive species become less pronounced.RESULT (A faster reproductive rate (r) is advantageous, but the benefit gained by the invasive species from pushing this rate higher and higher will become less and less, as r increases.)f′(r)=DDr

Math models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the fun f(r)=2\sqrt{Dr}

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