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

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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

predator-prey cycles in nature, such as Elton’s lynx and hare 04/19/23

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: 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

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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…

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 Systemsother 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 - cRPdescribes 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 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

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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 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

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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/

interactive/2009/dec/07/copenhagen-climate-change-carbon-emissions

Exam is in this class room. Promptly at 2 pm

Oral presentations I may miss you Friday (not 100%

sure) Remaining chapters

Chapters 22, 23, 26, 27 plus ?04/19/23

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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 lotka-volterra 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 abundance04/19/23

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:

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

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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

C = equilibrium point; K = carrying capacity04/19/23

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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