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Question

Question
We are using Lotka-Volterra dynamics as a descriptor of host-parasite population dynamics. Here, dH//dt=rH-aHP dP//dt=caHP-dP where H= host biomass and P= parasite biomass At equilibrium, both dH//dt and dP//dt=0 . What is the equilibrium biomass of hosts? a. r//alpha b. ca c. HOert d. r-d e. d//c alpha

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Willie

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Answer

a. r/a

Explanation

To find the equilibrium biomass of hosts, we need to set the rates of change of host and parasite biomass to zero, as given by the Lotka-Volterra equations. At equilibrium, we have:dH/dt = 0dP/dt = 0The equations for the rates of change are:dH/dt = rH - aHPdP/dt = caHP - dPSetting dH/dt to zero gives us:0 = rH - aHPThis equation can be solved for H by factoring out H:H(r - aP) = 0This gives us two possible solutions: H = 0 or r - aP = 0. Since H cannot be zero (as it represents biomass), we must have:r - aP = 0Solving for P gives us:P = r/aNow, we need to find the equilibrium biomass of hosts, which is H. We can use the second equation for the rates of change of parasites:dP/dt = caHP - dP = 0Substituting P = r/a into the equation gives us:0 = caH(r/a) - d(r/a)Simplifying, we get:0 = crH - dr/aNow, we can solve for H:H = dr/acrH = r/a