chapter 18: dynamics of predation

Chapter 18: Dynamics of PredationRobert E. RicklefsThe Economy of Nature, Fifth Edition

(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?


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?


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


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.


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


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


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


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


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


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


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


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


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


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


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


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


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


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.


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


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


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


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


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


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


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


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


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


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


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


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


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.


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.


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.

chapter 18: dynamics of predation

Documents

populations of algae

size of prey populations

game populations

resource populations

stability of populations

cyclamen mite populations

prey cycles

yearpredatory mites