Midterm 3: Lecture 16 - predation concepts

Lotka-Volterra predator prey equations

Start with assumption of exponential growth

• N = prey population size

• P = predator population size

In absence of predators:

• In absence of predators: dN/dt = rN

• In absence of prey: dP/dt = -mP

  • For predators, m = mortality rate of predator, replaces r

Key assumptions of equation

• Prey is only limited by its predator

• Predator is a specialist - eats only one prey species

• Predator population can eat an unlimited # or prey

Equation for prey

Prey

• dN/dt = [exponential growth] - [consumption by predators]

• dN/dt = rN - cNP

New terms:

• c = capture efficiency of prey

Equation for predator

Predator

• dP/dt = [ability to reproduce due to consumption of prey] - [deaths]

• dP/dt = acNP - mP

New terms:

• c = capture efficiency of prey

• a = rate at which predator converts prey to offspring

Graphical approach: prey

Prey

Step 1: Solve Lotka-Volterra equations - one species at a time for solutions at equilibrium (when population size isn’t changing)

dN/dt = rN - cNP = 0

r = cP

P = r/c

*For Prey, dN/dt = 0 when P = r/c

Graphical approach: predators

Predators

Step 1: Solve Lotka-Volterra equations - one species at a time for solutions at equilibrium (when population size isn’t changing)

dP/dt = acNP - mP = 0

acN = m

N = m/ac

The equations predict this dynamic of predator and prey populations

Our key assumptions are unrealistic

• Remove assumption 1 (prey is only limited by its predator):

  • Prey controlled by predator and by other density-dependent factors (like limits on)

  • Implications: no oscillations

• Remove Assumption 2 (predator is a specialist - eats only one prey species):

  • In addition to last slide, prey population growth limited at low prey population sizes

    • Might be hard to find mates

  • Implications: Fluctuations in population sizes depend on predator efficiency.

    • If they are efficient, then predators will hunt prey to extinction

• Remove Assumption 3 (Predators can’t consume an unlimited number of prey. Functional response of predators to prey density):

  • Predators can’t consume an unlimited number of prey. Functional response of predators to prey density

  • Implications: If predators switch prey or reach carrying capacity, population sizes of predator and prey don’t fluctuate

Functional response of predators to prey abundance

Example of type III functional response

Habitat edges can:

• Increase abundance of wildlife like deer, quail, and turkeys

• Increase abundance of harmful invasive species

• Be managed to reduce harmful effects on native species

• All of the above

Ro = (b/g)S, 6 years ago, MSU closed to attempt to reduce R0 by reducing which variable in this equation?

S