C. Models
1. Pathogens
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.
Number of Prey (V)
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.
Basic Equations:
1. Prey
2. Predator
3. Dynamics
1.
4.
1.
2.
3.
2. 3.
4.
1.
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)
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
D. Laboratory Experiments
1. Gause
2. Huffaker
3. Holyoak and Lawler-1996
Holyoak and Lawler-1996
Used a bacteriovore ciliate, Colpidium striatum as the prey and our old friend
Didinium nasutum as the predator.
3. Holyoak and Lawler-1996
Set up replicate 30mL bottles, linked together by tubes, and single flask
systems.
D. Complexities and Applications
2. Multiple State States
Consider a Type III functional response, where the predation rate is
highest at intermediate prey densities.
Birth rate
Predation Rate
V
D. Complexities and Applications
2. Multiple State States
Consider a Type III functional response, where the predation rate is
highest at intermediate prey densities.
Birth rate
Predation Rate
V