Recap
Species interaction
Consumer-resource interactions
Parasites and host
Herbivore and plant
Competition
Mutualism
11.6 Individuals of different species can
collaborate in mutualistic interactions
Mutualism: interaction benefits both species involved.
honeybee and plants
(plants provide honeybee with nectar, bees carry pollen between
plants)
Can be symbiosis: lichens (algae and fungi)
or non-symbiosis: seed dispersal (birds and plants)
Could involve more species
Humans extract honeycombs (for honey)
Birds eat the wax left behind
Bacteria in the guts to digest the wax
Three categories
Trophic, defensive and dispersal mutualisms
Trophic mutualisms: feeding relationship, bacteria in rumens of cows
Defensive mutualism
Food and shelter,
defend partners
against their
consumers
Cleaning fish or shrimp
Clean parasites form
the skins
A wonderful story of Acacias plants and ants in Central America,
see textbook (298).
Some mutualists need their partners to survive and grow. Ants can’t
survive without plants; and plants can’t survive without ants.
Adaptation improved the efficiency of their association: Ants work day
and night to protect plants. Acacias retain leaves all year.
(both unusually)
Dispersive mutualism:
Birds and mistletoe
BIOL 4120: Principles of Ecology
Lecture 12: Dynamics of
Consumer-Resource
Interactions
Dafeng Hui
Office: Harned Hall 320
Phone: 963-5777
Email: dhui@tnstate.edu
Population cycles of predators and
their prey
Data from records
of purchase by
Hudson’s Bay
Company, Canada
MacLuich 1937
Topics (Chapter 15)
15.1 Consumers can limit resource populations
15.2 Many predator and prey populations
increase and decrease in regular cycles
15.3 Mathematic models for predator-prey
interaction
15.4 Pathogen-host dynamics can be described
by the S-I-R model
15.5 Lotka-Volterra model can be stabilized by
predator satiation
15.6 Factors can reduce oscillation of predatorprey models
15.6 Consumer-Resource system can have more
than one stable state
12.1 Consumers can limit resource
populations
Populations of consumer are self-regulated
because of their effects on their resources
And consumers contribute to the regulation of
resource population.
Questions: how large is the rule of consumers?
Predation on cyclamen mites
Cyclamen mite is a
pest of strawberry
in CA
Typhlodromus mite
is a predatory mite
Greenhouse
Experiment
One with predatory
mite and one
without by
applying parathion
Herbivores and Plant Populations
Herbivores can control plant populations
Klamath weed, or St. John’s wort, became a
widely spread pest (poison to cattle and
sheep) following its introduction.
When Chrysolina beetle was introduced, the
Klamath weed was finally under control.
Effects of herbivores on plant production can be
measured using exclosure experiments
12.2 Many Predator and Prey populations
increase and decrease in regular cycles
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Cycles of predator and prey populations are
common
The periods of cycles vary from species to species
 Large herbivores (snowshoe hare, muskrat,
ruffed grouse) 9-10 year
 Small ones (vole, mice, lemming) 4 years cycle
Predators feed on large prey have long cycle (red
foxes, lynx, marten, mink)
Predators feed on small prey have short cycle (Arctic
fox, hawks, snowy owls)
Cycles (oscillations) are caused by predator and
prey interaction (predator – prey).
Time delays and population cycles
Time delays in birth
and death caused
oscillation in
population
Time delays also occur
in predation
Period of population
cycle should be 4 ~ 5
times the time delay
Hare populations
fluctuated less on an
island with few
predators than on the
surrounding mainland.
Physical conditions may change the period
of cycles
4-year cycle in northern Scandinavia, but annually in southern Sweden.
Winter delay in north maintain a long cycle. In the south, owls hunt
voles whole year, create a short cycle. Climate warming may cause the
shift from 4-yr to annual shown in this figure (or multiple prey).
Periodicity in pathogen-host relationships
Cases of measles
reported in
London (before
vaccine had been
developed)
Peaked about
every two years
Development of host immunity influences host populations
Habitat structure can affect population
cycles
Forest tent caterpillar as host
Nuclear polyhedrosis virus as pathogen
In many regions, tent caterpillars
infestations last about 2 years before the
virus brings its host population under
control. In other regions, it may last 9
years
Forest fragmentation plays a role.
Forest edges with more light, inactivate
the virus. Fragmentation prolong the
outbreak.
Habitats has second effects on population
Creating predator-prey cycles in the
laboratory
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Modeling and lab experiments
Studies by GF Gause on protists (1920s)
Predator: Ciliated protist, Didinium
Prey: Protist, Paramecium
Culture medium: test tube
Difficult to demonstrate the oscillations
 Predators eat all prey, then die
 Add refuge (glass wool at bottom of tube),
predators would die and left some prey to survive
 Add small number of predators periodically
oscillations.
Huffaker’s mite experiment
C.B. Huffaker, UC Berkeley
(1958)
Predator: mite, Typhlodromus
Prey: six-potted mite
(Eotetranychus), pest of citrus
fruits
Reproduction: parthenogenesis
Control food resources: number and
dispersion
First study: 40 positions, 4 fruits, 20
prey, after 11 days, reached 5,500 to
8000, added 2 predators, ate all.
A spatial mosaic of habitats allows predators and prey to coexist
6 oranges, 120 positions, grew 200 days with 3 cycles
12.3 Mathematical model for
predation
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Lotka and Volterra equation for predation
Prey dN prey
dt
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
 rN prey  cN prey N pred
Where cNpredNprey is mortality of prey due to predator.
c is per capita capture rate, and Npred, Nprey are the
number of predators and prey, respectively.
Predator
dN pred
dt

 b(cN prey N pred )  dN pred
Where b is efficiency of conversion of prey consumed
(cNpredNprey) and d is death rate of predators
Solving the equations

For prey growth (dN_Prey/dt=0)
• Npred = r/c
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Growth rate of prey population is zero when density
of predators equals per capita growth rate of prey
divided by per capita capture rate of predators.
Any increase in predator density will result in
negative growth in prey population
For predator growth (dN_Pred/dt=0)
• Nprey = d/bc
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Growth rate of predator population is zero when rate
of increase of prey is equal to rate of mortality
divided by the product of b and c.
Thus the two equations interact and this
can be done graphically
Pred
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There is a cyclical
rise and fall in
both the predator
and prey
populations with
time
Density of
predators lags
behind density of
prey
Feast and Famine
scenario
Prey and
predators are
never quite driven
to extinction
Mutual population
regulation
Trajectories of predator and prey
populations and their joint equilibrium point
dP/dt=0 or dv/dt=0
Equilibrium isocline or more
common, zero growth isocline
The change in predator and
prey populations together
follows a closed cycle that
combines the individual
changes in the predator and
prey population, called joint
population trajectory.
Not stable, or neutral stable
(exhibits neutral stability),
as slightly change in either
population will move to next
cycle, rather than return
Another chart to show that Lotka-Volterra model predicts
a regular cycling of predator and prey populations
Period of oscillation:
T=2Pi/sqrt(rd)
If r=2 (200%) and
d=0.5 per year, then
T=6.3
Influence of growth rate on predator and prey
populations
Nprey or V=d/bc is the
minimum requirement
to sustain the growth of
predator populations
Npredator or P=r/c is
the largest number of
predators that the prey
population can sustain.
A surprising prediction
of the model is that
increase in r of prey
growth leads to an
increase in predator
population, not the prey
An increase in the birth rate of prey increases the
predator population, but no the prey population
Bohannan and Lenski,
Michigan State University
Prey: E. coli
Predator: bacteriphage T4
Prey food source: limited
by glucose
Two levels: 0.1 or 0.5 mg
per litter
Add food supply only
increased predator
population.
12.3 Pathogen-host dynamics can
be described by the S-I-R model
Parasites do not remove host from population, but can develop
time delays that lead to population cycling
Course of epidemic depends on Rate of transmission (b) and rate
of recovery (g):
Reproduction ratio: number of secondary cases produced by a
primary case during its period of infectiousness, R0=(b/g)S
R0>1, an epidemic will occur, each infected individual will infect
more than one before it recovers
R0<1, fails to take hold in the population
R0: 5-18 for measles, chicken pox etc. HIV: 2-5; malaria: >100.
The S-I-R model can predict the spread on
epidemic through a host population
Total =100
b=1, g=0.2,
duration of
infectiousness 1/g=5
Beginning,
S=1, R0=b/g*S=5
Assume no births of
S, and no loss of
resistance among
previously infected
individuals.
Influenza virus
Vaccination: remove
individuals from S,
reduce R0.
Case study: The chytrid fungus and the global
decline of amphibians
Pathogenic fungus: Batrachochytrium dendrobatisdis
It kills hosts and persists by infecting alternative species.
Karan Lips, Southern Illinois University, 2006
El Cope: first found in July 2004, rapid spread and caused abrupt drop.
12.5 Lokta-Volterra model can be
stabilized by predator satiation

The Lotka–Volterra model is criticized for
overemphasizing the mutual regulation of
predator and prey populations
• Differential equations, no time delay
(Difference equations, add time delay)
• No internal forces act to restore the
populations to the joint equilibrium point,
random perturbations could increase
oscillations to a point that V=0 or P=0
• cNpreyNpredator: at a given Npred, the rate at
which prey are captured increases with Nprey.
This is not true. There is predator satiation.
Functional and numerical
responses

cN_preyN_pred (cVP):
• For prey population, this term serves to
regulate population growth through mortality
• For predator population, it serves to regulate
population growth through two distinct
responses:
Predator’s Functional responses: the great the number
of prey, the more the predator eats. The relationship
between per capita rate of consumption and the
number of prey (cNpreyNpred).
Predator’s Numerical response: an increase in
consumption of prey results in an increase in
predator reproduction (b(cNpreyNpred).
Functional Responses Relate Prey Consumed
to Prey Density
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The functional response is the
relationship between the per capita
predation rate (number of prey consumed
per unit time) and prey population size
• This idea was introduced by M.E.
Solomon in 1949
Three types of functional response (I, II,
and III)
• Developed by C.S. Holling

Functional response
• Ne: per capita rate of predation, i.e., # of
prey eaten during a given period of search
time.
• Type I functional response
• Ne=cT Nprey
• Passive predator such as spider or the prey
is less sufficiently abundant (e.g., kestrels
and voles)
• All time (T) allocated to feeding is
searching.
• Linear
• Ne/Nprey=cT constant

Type II response
• Ne increase with Nprey rapidly, but level off at
high prey density.

Type III functional response
• Sigmoid (S-shaped) response
• At high prey density, the response is the same as
type II response; however, the rate of prey
consumed is low when the prey density is low at
first, increasing in a S-shaped fashion.
•
•
•
•
Factors caused the S-shape response
1. availability of cover to escape the predators
2. predator’s search image
3. Prey switching. Switch to other preys (more
abundant)
Functional responses related prey consumed to prey
density

Functional response
• As prey increases,
predators take more prey
• But how
 Linear
• Rate of predation is
constant
 Decreasing rate to
maximum
• Rate of predation
decline
 Sigmoidal
• Decrease at low
density as well as
high, increase to
maximum then
declines
(Right panel is predation rate,
# prey consumed divided by
prey density)
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Linear Type 1 (European kestrel to vole)
 Mortality of prey simply density
dependent
 No limits on system
Decreasing Type 2 (weasel on rodent)
 Predators can only eat so much –
satiation
 Time needed to kill and eat prey
becomes limiting
Sigmoid Type 3 (warbler on budworm
larvae)
 Capture rate is density dependent
 Availability of cover
 Alternative prey when preferred is
rare (prey switching)
 Prey not part of predators search
image, not a desirable food source
Model of prey switching

Prey switching
(water bug)
• Palatable versus
less palatable
• Better return per
kill
• Less energy
needed to find
and kill an
abundant prey
Predators respond numerically to changing
prey density

Aggregative response in the
redshank
Numerical response
• Predators reproduce
more
 However
reproduction
usually slower than
prey
• Movement into high
prey density areas
 This aggregative
response is very
important as it
rapidly increases
predator density

Other numerical response as increased reproductive effort
•
•
•
•
Weasels as predators
Rodents as prey
Predators followed prey in reproduction
Increase of rodent was due to good harvest in 1990
Predator population exhibits a
numerical response to change
in prey density
Most of the increase was due
to local population growth
rather than immigration from
else where
After hare density fell to a
low level, red squirrels and
other small mammals were
eaten by lynx.
Numerical response of a predator population
lags behind changes in prey density following
counterclockwise joint population trajectory
predicted by the Lotka-Volterra model
12.5 Factors that reduce
oscillations in predator-prey models
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Stability: achievement of an unvarying
equilibrium size, often the carrying capacity
Predator-prey: oscillations, but several factors
could stabilize, move to stable equilibrium:
• Predator inefficiency (c decrease)
• Density-dependent limitations of prey or
predator by other external factors
• Alternative food resource for predator
• Refuges for prey at low prey density
• Reduced time delays in predator responses to
changes in prey abundance
12.6 Consumer-resource system can
have more than one stable state
Population size is determined by: abundance of its
resources and of its consumers
One Extreme: resource population is only limited by
its own food supply
Another: resource population is depressed below its
carrying capacity
Balances between these factors create multiple
equilibrium points: alternative state states
Consumer-imposed equilibrium:
At low density, prey can seek refuge, avoid
predators
At low density, prey grows faster than predators
Low stable equilibrium point well below its
carrying capacity
Resource-imposed equilibrium
in some cases, prey population can move up from
the consumer-imposed equilibrium, due to the
limited number of predators, predator satiation,
or other factors that keep predators in check
(nest limitation), reach equilibrium set by its
carrying capacity.
Population could have two stable states and
sometime move between these two (crop and
forest pests, diseases).
The End
Recap
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Dynamics of resource and consumer
populations
Lab experiment
Math model
Lotka and Volterra equation for predation
dN prey
dt
dN pred
dt
 rN prey  cN prey N pred
 b(cN prey N pred )  dN pred