chapter 18: dynamics of predation
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Chapter 18: Dynamics of Predation. Robert E. Ricklefs The Economy of Nature, Fifth Edition. Population Cycles of Canadian Hare and Lynx. Charles Elton’s seminal paper focused on fluctuations of mammals in the Canadian boreal forests. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 18: Dynamics of PredationRobert E. RicklefsThe Economy of Nature, Fifth Edition
(c) 2001 by W. H. Freeman and Company
(c) 2001 by W. H. Freeman and Company
Population Cycles of Canadian Hare and LynxCharles 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?
(c) 2001 by W. H. Freeman and Company
Some Fundamental QuestionsThe 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?
(c) 2001 by W. H. Freeman and Company
More QuestionsDo 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
predator-prey cycles in nature, such as Elton’s lynx and hare
(c) 2001 by W. H. Freeman and Company
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.
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Consumer Control in Aquatic EcosystemsAn 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
(c) 2001 by W. H. Freeman and Company
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:predators of these species (red foxes, lynx, marten,
mink, goshawks, owls) have similar cycles small herbivores (voles and lemmings) have
cycles of 4 years:predators of these species (arctic foxes, rough-legged
hawks, snowy owls) also have similar cycles cycles are longer in forest, shorter in tundra
(c) 2001 by W. H. Freeman and Company
Predator-Prey Cycles: A Simple ExplanationPopulation 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
(c) 2001 by W. H. Freeman and Company
Time Lags in Predator-Prey SystemsDelays 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
(c) 2001 by W. H. Freeman and Company
Time Lags in Pathogen-Host SystemsImmune 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
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Laboratory Investigations of Predators and PreyG.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
(c) 2001 by W. H. Freeman and Company
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 - cRPdescribes the rate of increase of the prey population, where:R is the number of prey P is the number of predatorsr is the prey’s per capita exponential growth ratec is a constant expressing efficiency of predation
(c) 2001 by W. H. Freeman and Company
Lotka-Volterra Predator-Prey EquationsA second equation:
dP/dt = acRP - dPdescribes the rate of increase of the predator population, where:P is the number of predatorsR is the number of preya is the efficiency of conversion of food to growthc is a constant expressing efficiency of predation
d is a constant related to the death rate of predators
(c) 2001 by W. H. Freeman and Company
Predictions of Lotka-Volterra ModelsPredators 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
(c) 2001 by W. H. Freeman and Company
Cycling in Lotka-Volterra EquationsA 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
(c) 2001 by W. H. Freeman and Company
Factors Changing Equilibrium IsoclinesThe prey isocline increases if:
r increases or c decreases, or both:the prey population would be able to support
the burden of a larger predator populationThe predator isocline increases if:
d increases and either a or c decreases:more prey would be required to support the
predator population
(c) 2001 by W. H. Freeman and Company
Other Lotka-Volterra PredictionsIncreasing 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 predatorIncreasing the birth rate of the prey (r)
should lead to an increase in the population of predators but not the prey themselves.
(c) 2001 by W. H. Freeman and Company
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 condition is referred to as a neutral
equilibrium the lack of any satiation of predators:
each predator consumes a constant proportion of the prey population regardless of its density
(c) 2001 by W. H. Freeman and Company
The Functional ResponseA 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
(c) 2001 by W. H. Freeman and Company
The Holling Type III ResponseWhat 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
(c) 2001 by W. H. Freeman and Company
The Numerical ResponseIf 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 elsewherethis increase is referred to as a numerical
response
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Destabilizing InfluencesThe presence of predator-prey cycles
indicates destabilizing influences: such influences are typically time delays in
predator-prey interactions:developmental periodtime required for numerical responses by predatorstime course for immune responses in animals and
induced defenses in plants when destabilizing influences outweigh
stabilizing ones, population cycles may arise
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Three EquilibriaThe model of predator and prey responses to
prey density results in three stable or equilibrium states: a stable point A (low prey density) where:
any increase in prey population is more than offset by increasingly efficient prey capture by predator
an unstable point B (intermediate prey density) where: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
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Effects of Different Levels of PredationInefficient 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
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
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
(c) 2001 by W. H. Freeman and Company
Summary 1Predators can, in some cases, reduce prey
populations far below their carrying capacities.
Predators and prey often exhibit regular cycles, typically with cycle lengths of 4 years or 9-10 years.
Lotka and Volterra proposed simple mathematical models of predator and prey that predicted population cycles.
(c) 2001 by W. H. Freeman and Company
Summary 2Increased productivity of the prey should
increase the predator’s population but not the prey’s.
Functional responses describe the relationship between the rate at which an individual predator consumes prey and the density of prey.
The Lotka-Volterra models incorporate a type I functional response, which is inherently unstable.
Type III functional responses can result in stable regulation of prey populations at low densities.
(c) 2001 by W. H. Freeman and Company
Summary 3Type III functional responses can result from
switching.Numerical responses describe responses of
predators to prey density through local population growth and immigration.
Several factors tend to stabilize predator-prey interactions, but time lags tend to destabilize them.
Predator-prey systems may have multiple stable points.