C. Models 1. Pathogens R = (b/g)S b = rate of transmission g = recovery time (inverse of infectious period)
C. Models 2. Lotka-Volterra Models Goal - create a model system in which there are oscillations of predator and prey populations that are out-of-phase with one another. Basic Equations: a. Prey Equation: dV/dt = rV - cVP where rV defines the maximal, geometric rate c = predator foraging efficiency: % eaten P = number of predators V= number of prey, so PV = number of encounters and cPV = number of prey killed (consumed) So, the formula describes the maximal growth rate, minus the number of prey individuals lost by predation.
C. Models 2. Lotka-Volterra Models b. Predator The Equation: dP/dt = a(cPV) - dP where CPV equals the number of prey consumed, and a = the rate at which food energy is converted to offspring. So, a(cVP) = number of predator offspring produced. d = mortality rate, and P = # of predators, so dP = number of carnivores dying. So, the equation boils down to the birth rate (determined by energy "in" and conversion rate to offspring) minus the death rate.
V. Dynamics of Consumer-Resource Interactions A. Predators can limit the growth of prey populations B. Oscillations are a Common Pattern C. Models D. Lab Experiments 1. Gause P. caudatum (prey) and Didinium nasutum (predator)
In initial experiments, Paramecium populations would increase, followed by a pulse of Didinium, and then they would crash.
P. caudatum (prey) and Didinium nasutum (predator) In initial experiments, Paramecium populations would increase, followed by a pulse of Didinium, and then they would crash. He added glass wool to the bottom, creating a REFUGE that the predator did not enter.
He induced oscillations by adding Paramecium as 'immigrants'
D. Laboratory Experiments 1. Gause 2. Huffaker six-spotted mite (Eotetranychus sexmaculatus) was prey - SSM Predatory mite (Typhlodromus occidentalis) was predator - PM