What if we have an excess of the predators relative to prey (e.g. The "equilibrium" predator-prey ratio is 1:10 using the parameters in Fig. Interspecific predator/prey ratio effect. That "crowding" effect would pull the right-hand side of the red isocline in Fig. What would a density-dependent (logistic-based) prey isocline look like? Most obviously perhaps, we'd expect the prey growth rate to decline at high levels of its own population, V. Again, the vector-sum method will be a very useful tool. Our approach will be graphical - that is, rather than try to solve increasingly complex equations, we will make inferences aboutthe system's behavior based on examination of graphs for a variety of shapes and placements of the isoclines. We will include density -dependence for the prey. Let's see what would happen to the system if we made one reasonableimprovement in the predator-prey model. We would like our model to be a little more robust (less sensitive to initial conditions and less sensitive to reasonable changes in the assumptions).įirst "improvement" - logistic prey growth. That means that if we tweak parameters a little (e.g., by changing the starting population sizes, which we call the "initial conditions") then we get very different outcomes. The basic model makes some rather unrealistic simplifying assumptions.Ĭan we do better? The Lotka-Volterra predator-prey model is what is called "structurally unstable". Last time I introduced the classic Lotka-Volterra equations for jointly analyzing predator and prey dynamics. Return to Main Index page Go back to notes for Lecture 23, 13-Mar Go forward to lecture 25, 27-Mar-13 PopEcol Lect 24 Lecture notes for ZOO 4400/5400 Population Ecology
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