Transcript Chapter 15: Dynamics of Consumer-Resource

Chapter 15: Dynamics of Consumer-Resource
Interactions
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Population Cycles of Canadian Hare
and Lynx

Charles Elton’s seminal paper focused on fluctuations
of mammals in the Canadian boreal forests.
Elton’s analyses were based on trapping records maintained
by the Hudson’s Bay Company
 of special interest in these records are the regular and
closely linked fluctuations in populations of the lynx and its
principal prey, the snowshoe hare


What causes these cycles?
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Some Fundamental Questions

The basic question of population biology is:
 what
factors influence the size and stability of
populations?

Because most species are both consumers and
resources for other consumers, this basic
question may be refocused:
 are
populations limited primarily by what they eat
or by what eats them?
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More Questions

Do predators reduce the size of prey populations
substantially below the carrying capacity set by
resources for the prey?


this question is prompted by interests in management of
crop pests, game populations, and endangered species
Do the dynamics of predator-prey interactions
cause populations to oscillate?

this question is prompted by observations of predatorprey cycles in nature, such as Elton’s lynx and hare
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Consumers can limit resource
populations.

An example: populations of cyclamen mites, a pest of
strawberry crops in California, can be regulated by a
predatory mite:



cyclamen mites typically invade strawberry crops soon after
planting and build to damaging levels in the second year
predatory mites invade these fields in the second year and keep
cyclamen mites in check
Experimental plots in which predatory mites were
controlled by pesticide had cyclamen mite populations 25
times larger than untreated plots.
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What makes an effective predator?

Predatory mites control populations of cyclamen
mites in strawberry plantings because, like other
effective predators:
 they
have a high reproductive capacity relative to
that of their prey
 they have excellent dispersal powers
 they can switch to alternate food resources when
their primary prey are unavailable
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Consumer Control in Aquatic
Ecosystems
An example: sea urchins exert strong control on
populations of algae in rocky shore communities:
 in
urchin removal experiments, the biomass of algae
quickly increases:
 in
the absence of predation, the composition of the algal
community also shifts:

large brown algae replace coralline and small green algae that
can persist in the presence of predation
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Predator and prey populations often
cycle.

Population cycles observed in Canada are
present in many species:

large herbivores (snowshoe hares, muskrat, ruffed
grouse, ptarmigan) have cycles of 9-10 years:


small herbivores (voles and lemmings) have cycles of 4
years:


predators of these species (red foxes, lynx, marten, mink,
goshawks, owls) have similar cycles
predators of these species (arctic foxes, rough-legged hawks,
snowy owls) also have similar cycles
cycles are longer in forest, shorter in tundra
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Herbivores can control plant
populations

Klamath weed, or St.
John’s wart, became a
widespread pest
following its
introduction into the
western US
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Infestation of Klamath
weed brought under
control by introduced
beetles
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Impact of cattle
grazing
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Many predator and prey populations increase
and decrease in regular cycles
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Why?
Hare populations fluctuated less on an island
with few predators than on the surrounding
mainland
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Other factors…

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
Period and intensity of a cycle also depend on the
physical environment
Owl (predator) and vole (prey) population cycle
dramatically over 4-year periods in northern
Scandinavia – but fluctuate annually in the milder
climate of southern Sweden
Why?
 Prolonged
heavy snow cover protects the voles from the
owls thus creating a delay in the effects…
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Predator-Prey Cycles: A Simple
Explanation

Population cycles of predators lag slightly
behind population cycles of their prey:
 predators
eat prey and reduce their numbers
 predators go hungry and their numbers drop
 with fewer predators, the remaining prey survive
better and prey numbers build
 with increasing numbers of prey, the predator
populations also build, completing the cycle
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Time Lags in Predator-Prey Systems

Delays in responses of births and deaths to an
environmental change produce population cycles:
predator-prey interactions have time lags associated with
the time required to produce offspring
 4-year and 9- or 10-year cycles in Canadian tundra or
forests suggest that time lags should be 1 or 2 years,
respectively:



these could be typical lengths of time between birth and sexual
maturity
the influence of conditions in one year might not be felt until young
born in that year are old enough to reproduce
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Time Lags in Pathogen-Host Systems

Immune responses can create cycles of infection in
certain diseases:

measles produced epidemics with a 2-year cycle in
pre-vaccine human populations:

two years were required for a sufficiently large population of
newly susceptible infants to accumulate
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Time Lags in Pathogen-Host
Systems
other pathogens cycle because they kill sufficient hosts to reduce host
density below the level where the pathogens can spread in the
population:
 such cycling is evident in polyhedrosis virus in tent caterpillars
 In many regions, tent caterpillar infestations last about 2 years
before the virus brings its host population under control
 In other regions, infestations may last up to 9 years
 Forest fragmentation – which creates abundant forest edge –
tends to prolong outbreaks of the tent caterpillar


Why?
Increased forest edge exposes caterpillars to more intense sunlight  inactivates
the virus  thus, habitat manipulation here has secondary effects
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Habitat structure can affect population cycles
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Laboratory Investigations of Predators
and Prey

G.F. Gause conducted simple test-tube experiments
with Paramecium (prey) and Didinium (predator):
in plain test tubes containing nutritive medium, the predator
devoured all prey, then went extinct itself
 in tubes with a glass wool refuge, some prey escaped
predation, and the prey population reexpanded after the
predator went extinct


Gause could maintain predator-prey cycles in such tubes by
periodically adding more predators
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Predator-prey interactions can be modeled by simple
equations.

Lotka and Volterra independently developed
models of predator-prey interactions in the 1920s:
dR/dt = rR - cRP
describes the rate of increase of the prey
population, where:
R is the number of prey
P is the number of predators
r is the prey’s per capita exponential growth rate
c is a constant expressing efficiency of predation
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Lotka-Volterra Predator-Prey Equations

A second equation:
dP/dt = acRP - dP
describes the rate of increase of the predator
population, where:
P is the number of predators
R is the number of prey
a is the efficiency of conversion of food to growth
c is a constant expressing efficiency of predation
d is a constant related to the death rate of predators
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Predictions of Lotka-Volterra Models

Predators and prey both have equilibrium conditions
(equilibrium isoclines or zero growth isoclines):
P = r/c for the predator
 R = d/ac for the prey
 when these values are graphed, there is a single joint
equilibrium point where population sizes of predator and
prey are stable:


when populations stray from joint equilibrium, they cycle with period T
= 2 / rd
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Cycling in Lotka-Volterra Equations

A graph with axes representing sizes of the
predator and prey populations illustrates the cyclic
predictions of Lotka-Volterra predator-prey
equations:
a
population trajectory describes the joint cyclic
changes of P and R counterclockwise through the P
versus R graph
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Factors Changing Equilibrium Isoclines

The prey isocline increases (r/c) if:

Reproductive rate of the prey (r) increases or capture
efficiency of predators (c) decreases, or both:


the prey population would be able to support the burden of a larger
predator population
The predator isocline (d/ac) increases if:

Death rate (d) increases and either reproductive efficiency
of predators (a) or c decreases:

more prey would be required to support the predator population
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Other Lotka-Volterra Predictions

Increasing the predation efficiency (c) alone in the
model reduces isoclines for predators and prey:
fewer prey would be needed to sustain a given capture
rate
 the prey population would be less able to support the more
efficient predator


Increasing the birth rate of the prey (r) should lead to
an increase in the population of predators but not the
prey themselves.
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An increase in the birth rate of prey increases the predator population but not
the prey population.
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Modification of Lotka-Volterra Models for
Predators and Prey

There are various concerns with the Lotka-Volterra
equations:
 the
lack of any forces tending to restore the
populations to the joint equilibrium:
 this
 the
condition is referred to as a neutral equilibrium
lack of any satiation of predators:
 each
predator consumes a constant proportion of the prey
population regardless of its density
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The Functional Response

A more realistic description of predator behavior
incorporates alternative functional responses,
proposed by C.S. Holling:
type I response: rate of consumption per predator is
proportional to prey density (no satiation)
 type II response: number of prey consumed per predator
increases rapidly, then plateaus with increasing prey density
 type III response: like type II, except predator response to
prey is depressed at low prey density

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Welcome back

Yes, exam is on the 23rd of December
 Chapters
7, 8, 10, 14, 15 + cc
 http://www.guardian.co.uk/environment/inter
active/2009/dec/07/copenhagen-climatechange-carbon-emissions
 Exam is in this class room. Promptly at 2 pm
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Oral presentations
I may miss you Friday  (not 100% sure)
Remaining chapters
 Chapters
22, 23, 26, 27 plus ?
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Student Exam questions



submit ?s to me via email that could be used on
the exam. Submit ?s by 21-December (Mon)
The ?s should have the same format as those on
the practice quizzes (i.e., multiple choice with 4
options). You may also email essay questions.
Put "BIOL 207: questions for exam" in the subject
line. For each ? of yours that is used on the
exam, you will receive 1 EC pt. I will limit you to
2 EC ? per exam, but it is in your best interest to
submit several (8-10) ?s.
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Lotka-Volterra model (remember?)


[the rate of change in the prey
population ] = [the intrinsic growth rate
of the prey population] – [the removal
of prey individuals by predators]
Equilibrium isocline
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Pathogen-host dynamics
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Individuals in a host populations are initially
susceptible to a new pathogen  become infected
(and can infect others)  recover and become
resistant
Predator satiation and lotkavolterra model
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The Functional Response

A more realistic description of predator behavior
incorporates alternative functional responses,
proposed by C.S. Holling:
type I response: rate of consumption per predator is
proportional to prey density (no satiation)
 type II response: number of prey consumed per predator
increases rapidly, then plateaus with increasing prey density
 type III response: like type II, except predator response to
prey is depressed at low prey density

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The Holling Type III Response

What would cause the type III functional response?
 heterogeneous
habitat, which provides a limited
number of safe hiding places for prey
 lack of reinforcement of learned searching behavior
due to a low rate of prey encounter
 switching by predator to alternative food sources
when prey density is low
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switching


When the predatory water bug (N. glauca) was
presented with 2 types of prey in the lab, it
consumed the more abundant prey species,
whichever it was, in a proportion greater than its
percentage of occurrence.
The switching depended on a variation in the
success of attacks on prey as a function of their
relative density
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Variation in prey availability does not always lead to
switching
Some predators will switch prey only when the
availability of their principal prey is extremely low
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% of snowshoe hares, squirrels and small mammals in diets of lynx
and coyote
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Predator population
have a numerical
response to changes in
prey density. What
does that mean?
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The Numerical Response


Individual predators can increase their consumption of
prey only to the point of satiation
If individual predators exhibit satiation (type II or III
functional responses), continued predator response to
prey must come from:

increase in predator population through local population
growth or immigration from elsewhere

this increase is referred to as a numerical response
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Several factors reduce predator-prey
oscillations.

All of the following tend to stabilize predator and
prey numbers (in the sense of maintaining nonvarying
equilibrium population sizes):
predator inefficiency
 density-dependent limitation of either predator or prey by
external factors
 alternative food sources for the predator
 refuges from predation at low prey densities
 reduced time delays in predator responses to changes in
prey abundance

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Destabilizing Influences

The presence of predator-prey cycles indicates
destabilizing influences:

such influences are typically time delays in predator-prey
interactions:




developmental period
time required for numerical responses by predators
time course for immune responses in animals and induced defenses in
plants
when destabilizing influences outweigh stabilizing ones,
population cycles may arise
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Predator-prey systems can have more than one stable
state.

Prey are limited both by their food supply and the
effects of predators:
 some
populations may have two or more stable
equilibrium points, or multiple stable states:
 such


a situation arises when:
prey exhibits a typical pattern of density-dependence (reduced
growth as carrying capacity is reached)
predator exhibits a type III functional response
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Three Equilibria

The model of predator and prey responses to prey
density results in three stable or equilibrium states:

a stable point A (low prey density) where:


an unstable point B (intermediate prey density) where:


any increase in prey population is more than offset by increasingly
efficient prey capture by predator
control of prey shifts from predation to resource limitation
a stable point C where:

prey escapes control by predator and is regulated near its carrying
capacity by resource scarcity
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Multiple states in predator-prey system (type III functional response)
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Implications of Multiple Stable States
Predators may control prey at a low level (point A in
model), but can lose the potential to regulate prey at
this level if prey density increases above point B in the
model:

a predator controlling an agricultural pest can lose control of
that pest if the predator is suppressed by another factors for
a time:


once the pest population exceeds point B, it will increase to a high level
at point C, regardless of predator activity
at this point, pest population will remain high until some other factor
reduces the pest population below point B in the model
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Intensity of predation relative to prey recruitment determines the number of stable
predator-prey equilibrium points
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Effects of Different Levels of Predation




Inefficient predators cannot maintain prey at low
levels (prey primarily limited by resources).
Increased predator efficiency adds a second stable
point at low prey density.
Further increases in predator functional and numerical
responses may eliminate a stable point at high prey
density
Intense predation at all prey levels can drive the prey
to extinction
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When can predators drive prey to
extinction?

It is clearly possible for predators to drive their
prey to extinction when:
 predators
and prey are maintained in simple
laboratory systems
 predators are maintained at high density by
availability of alternative, less preferred prey:
 biological
control may be enhanced by providing alternative
prey to parasites and predators
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What equilibria are likely?

Models of predator and prey suggest that:
 prey
are more likely to be held at relatively low or
relatively high equilibria (or perhaps both)
 equilibria at intermediate prey densities are highly
unlikely
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YES! PAGE 324! MAXIMUM
SUSTAINABLE YIELD
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