Exploiter-Victim Relationships Host-Parasite: Host death need not occur, and often does not; birth...

Exploiter-Victim Relationships

Host-Parasite: Host death need not occur, and often does not; birth rate of host reduced by parasite

Host-Parasitoid: Host death always occurs

Predator-Prey: Death rate of prey increased by predators

Herbivore-Plant: May resemble predation or parasitism

Parasitoids

Weevils and wasps

Lynx and Snowshoe Hare

Orange Mites, simple universe

Orange Mites, increased patchiness

Orange Mites, complex habitat

Field Studies: Dingoes and kangaroos

Dingoes and Boars

Lamprey and Lake Trout

Fox and Rabbit

Plant-Herbivore

Herbivore-- positive effect?

N-fertilization effects

N-fertilization effects

Big HerbivoresBig Herbivores

Amboseli Elephants

Elephants not excluded

Elephants Excluded

Baobab

Baobab

Baobab, Elephant Damage

Functional ResponseChange in predator’s attack behavior

as prey density increasesBasic forms to consider:

Type I: Linear increase in # attacked with increasing # prey

(insatiable predator)

Type II: Gradual levelling off

As predators become satiated

Type III: Predators satiable as in Type II, but hunt inefficiently at low prey densities

# at

tack

e d/p

red/

tim

e

Prey density

I

II

III

Toxorhynchites

Toxorhynchites brevipalpus

Toxorhynchites Functional Response, sympatric & allopatric

prey:

NC (sympatric)

IL (allopatric)

Fraction killed per predator/timeType I Type II Type III

Prey Density

Type II and III: satiable predators become less effectiveat controlling prey as prey become more abundant.

Lotka-Volterra Predator-Prey Model:

Assume:

1) Random search, producing encounters between prey andpredators (and subsequent attacks) proportional to the product of their densities (attack rate = a’)

2) Exponential prey population growth in absence of predator, with constant growth rate, r

3) Death rate of predator is constant = q

4) Birth rate of predator proportional to #prey consumed

Prey growth equationPrey:

Without predator, dN/dt=rN

If predator searches with attack rate a’, and there are CPredators, then deaths due to predation = a’CN

dN/dt = rN - a’CN

Predator Growth Equation

dC/dt = (birth rate - death rate)C

Death rate assumed constant = qBirth rate: #prey consumed x conversion constant, f

= (#prey consumed)x f

# prey consumed = a’CN (see prey equation)births = a’CNfbirth rate = a’Nf

dC/dt = (a’Nf - q)C

Equilibrium Conditions, Prey

Prey:dN/dt = rN - a’CN = 0

r-a’C = 0C = r/a’

C

N

C = r/a’

Too many predators

Not enough predators

Equilibrium conditions, predatorsdC/dt = (a’Nf - q)C = 0

a’Nf - q = 0

N = q/a’f C

N

N =

q/a’f

More than enough preyN

ot e

noug

h pr

ey

Changes in both species:

C

N

The prey curve has a hump

Humped Prey curves

Rot

ifer

den

sity

Phytoplankton density

Change in phytoplankton density at different combinations of Rotifer density and phytoplankton density

Why the Prey curve has a Hump

1. Resource limits for prey at high densities

(fewer preds needed to keep in check)

2. But, predator is most effective at low prey densities

Effects of a humped prey curve:

Increasing oscillation(unstable)

Damped oscillation(stable point)

Neutralstability

C

N

Effects of a humped prey curve:

Increasing oscillation(unstable)

Damped oscillation(stable point)

Neutralstability

C

N

time