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Adapted by Dann Sklarew, summer 2010, from an original presentation by Amber Pembleton

The “Tru e Blood” Story of How Predators and Prey Modulate Each Others’ Populations (per Lotka-Volterra ). Adapted by Dann Sklarew, summer 2010, from an original presentation by Amber Pembleton BIOL/EVPP607 Spring 2010. Lotka- Volterra ’s Predator -Prey Equation.

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Adapted by Dann Sklarew, summer 2010, from an original presentation by Amber Pembleton

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  1. The “True Blood” Story of How Predators and Prey Modulate Each Others’ Populations (per Lotka-Volterra) Adapted by Dann Sklarew, summer 2010, from an original presentation by Amber Pembleton BIOL/EVPP607 Spring 2010

  2. Lotka-Volterra’sPredator-Prey Equation Where is “r” in these equations? Where is “K?” y represents the biomass or population size for a predator species “Y” while x corresponds to the same for its prey t is time dy/dt and dx/dtrepresent the change of each the population over time α, β, γ and δ parameters which characterize growth and inter-specific interactions.

  3. Predator Equation In this equation, δxy represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey).γyrepresents the loss rate of the predators due to either natural death or emmigration; it leads to an exponential decay in the absence of prey. Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

  4. Prey Equation The prey are assumed to have a non-limiting food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation. With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon

  5. Pattern predicted by the Predator-Prey Model By plotting the implied changes in size for both the predator and prey populations through time, we can see that the two populations continuously cycle out of phase with each other, and the density of predators lags behind prey Why? What does this mean in non-math terms?

  6. References Smith, Thomas M. and Robert Leo Smith. Elements of Ecology. 2009. 7th ed. http://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equation http://3.bp.blogspot.com/_zsPzrOdGfpY/SufsrMKlIKI/AAAAAAAAAbc/XYhcOl7fVLA/s400/true-blood-season-two-teaser-poster.jpg

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