Biol 208: Lecture 21 - Modelling predator + prey (Lotka-Volterra models of Predation)

What type of species interaction outcome is HETEROTROPHY/Predator prey?

• Mutualism, commensalism, exploitation, neutralism, amensalism + Competition

EXPLOITATION

• Herbivores = Feed on plants but usually don’t kill the entire plant

• Predators = Kill + feed on other animals

What are the 2 types of herbivory?

• What do they normally eat

• Give some examples

• Are the 2 types mutually exclusive?

Grazers:

• Feed on - Low growing, non-woody plants. Often NUTRIENT RICH eg. grasses + herbs

• Ex: Horses, cattle, sheep, bison, elk etc.

Browsers:

• Feed on - High growing, woody plants. NUTRIENT POOR eg. leaves + twigs

• Ex: giraffes, moose, goats, porcupine, elk, mule deer

NOT MUTUALLY Exclusive

• Depends on resource availability

Enclosure experiments

• what are they used to study

• Info dump on the reading assigned about enclosure experiments (Ch 14.1)

  • What was the organism

  • What was the question

  • Methods

  • Results

A tool to study the effects of Herbivory/predation on a species or community by using fences, mesh or an inaccessible position

Ch 14.1 - Herbivorous stream insect + its algal food

Organism = Larval stage of caddisfly = feeds on algae on surface of submerged rocks 

• Characteristics:

  • Builds a portable shelter (sand grains) like snail shell

  • Develop in summer + fall + Benthic

Question: Caddisfly have ability to reduce density of food supply

Methods: Raised One set of tiles above ground = prevent colonization (due to heavy sand made snail shells)

Results: Tiles excluding caddisfly = higher abundance of algae + bacteria

Influence of exploitation is best seen when exploiting organism/factor is removed

3 Things that influence prey populations

1. Food availability

2. Consumptive effects: Direct effects of predators on prey by eating them

3. Non-consumptive effects: Changes to prey that are due to PRESENCE of predators

   • includes shifts in behavior, stress physiology + morphological traits (Predators don’t have to kill prey to impact prey population)

Predators don’t have to kill prey to impact prey population: Info dump on the Non-consumptive effects lynx have on Hare example in class

• Fitness = affected when predation pressure is high

Hares BLOOD CORTISOL levels increase in the years with higher predation rates + in plots with predators present compared to plots with predators excluded

Hares exposed to lynx also have REDUCED REPROD rates

Oscillation predator prey dynamics: Hare populations are couples with their predator

• Talk about the Complementary hypothesis

• Answer the Q - is it food or predation that is the bigger factor in prey population?

Enclosure experiment with hare _ link showed that BOTH FACTORS = important when it comes to affecting Hare populations

• No predator + Lots of food plots had the highest hare density

The Lotka-Volterra models of predation

• What do the subscripts H + P stand for?

• What does the model IGNORE?

• What does every symbol in the equation provided represent?

The model produces reciprocal oscillations/CYCLING of predator + prey populations

• h = PREY (think herbivore cause most of them are)

• p = PREDATOR

dNh/dt = The basic EXPONENTIAL GROWTH of the PREY

• rh = Prey per-capita rate of increase

• Nh = Prey population size

Lotka-Volterra model IGNORES:

• INTRAspecific competition = assumes that predation will control prey population size not resource limitations + intra competition

What does this equation calculate + what does each symbol represent?

Factors predators into PREY population growth

• rh = Prey per-capita rate of increase

• Nh = prey pop. size

• b = CAPTURE EFFICIENCY

• Np = predator pop size

What is Capture efficiency (b)?

• what does b equal if a predator catches 1/50 prey?

Proportion of encounters between predator + prey that results in the predator eating the prey

• AKA. the success rate of the predator

b = 1/50 = 0.02

What does this equation calculate + what do each of the symbol represent?

• why is there no r in this equation?

Calculates the GROWTH of PREDATOR population

• c = CONVERSION FACTOR of prey to predators

• b = capture efficiency

• dp = Per capita DEATH RATE of predators due to natural death

no r because population depends on availability of h (prey)

What is Conversion Factor (c)?

• what does c equal if a predator has to eat5 prey to have enough excess E to prod 1 offspring?

How many prey are required to produce one predator

• how many prey a female needs to consume to make one offspring

c = 1/5 = 0.2

What does this equation represent?

ISOCLINE FOR PREY = Zero prey growth

• the density of predator that would result in ZERO population growth for the prey

When Np = rh/b → prey growth (dNh/dt) = zero

On a STATE SPACE GRAPH

• What is on the X -axis + What is on the Y?

• How would the ISOCLINE FOR PREY be plotted on this graph?

X = Prey density

Y = Predator density

On the state space graph, How does PREY population density change if:

• Np is less than rh/b

• Np is greater than rh/b

What directions do the arrows point?

IF Np = GREATER = Prey population DECREASES

if Np = LESS = Prey population INCREASES

What does this equation represent?

What density of PREY would result in Zero population growth for the predator

ISOCLINE FOR PREDATOR

How would the ISOCLINE FOR PREDATOR be plotted on the state space graph?

• How does PREDATOR population density change if:

  • Nh is less than dp/cb

  • Nh is greater than dp/cb

  What directions do the arrows point?

Nh = LESS = Predator DECREASE

Nh = MORE = Predator INCREASE

If we super impose the graphs we can show the cycling/oscillating predator-prey population dynamics

• What is happening to the Predator vs. Prey populations in each of the quadrants?

Top left = D

• Predator + Prey both Decrease

Top right = C

• Predator increase + Prey Decrease

Bottom Left = A

• Predator Decrease + Prey Increase

Bottom right = B

• Predator + prey both Increase

What is the Joint Equilibrium Point?

The point at which the two isoclines of zero growth intersect (in the middle)

• this is where both populations are balanced + in equilibrium

• No increase or decrease in the population size of either group