RecapRecap

Species interactionSpecies interactionConsumer-resource interactionsConsumer-resource interactionsParasites and hostParasites and hostHerbivore and plantHerbivore and plant

CompetitionCompetition

MutualismMutualism

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 categoriesTrophic, defensive and dispersal mutualismsTrophic 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

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)

A wonderful story of Acacias plants and ants in Central America, see textbook (298).

Dispersive mutualism:Dispersive mutualism:Birds and mistletoe

BIOL 4120: Principles of EcologyBIOL 4120: Principles of Ecology

Lecture 12: Dynamics of Lecture 12: Dynamics of Consumer-Resource Consumer-Resource

InteractionsInteractions

Dafeng HuiDafeng Hui

Office: Harned Hall 320Office: Harned Hall 320

Phone: 963-5777Phone: 963-5777

Email: dhui@tnstate.eduEmail: 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)Topics (Chapter 15)

15.1 Consumers can limit resource populations15.1 Consumers can limit resource populations15.2 Many predator and prey populations 15.2 Many predator and prey populations

increase and decrease in regular cyclesincrease and decrease in regular cycles15.3 Mathematic models for predator-prey 15.3 Mathematic models for predator-prey

interactioninteraction15.4 Pathogen-host dynamics can be described 15.4 Pathogen-host dynamics can be described

by the S-I-R modelby the S-I-R model15.5 Lotka-Volterra model can be stabilized by 15.5 Lotka-Volterra model can be stabilized by

predator satiationpredator satiation15.6 Factors can reduce oscillation of predator-15.6 Factors can reduce oscillation of predator-

prey modelsprey models15.6 Consumer-Resource system can have more 15.6 Consumer-Resource system can have more

than one stable statethan one stable state

12.1 Consumers can limit resource 12.1 Consumers can limit resource populations populations

Populations of consumer are self-regulatedbecause 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 12.2 Many Predator and Prey populations increase and decrease in regular cyclesincrease and decrease in regular cycles

Cycles of predator and prey populations are commonCycles of predator and prey populations are common The periods of cycles vary from species to speciesThe periods of cycles vary from species to species

Large herbivores (snowshoe hare, muskrat, ruffed Large herbivores (snowshoe hare, muskrat, ruffed grouse) 9-10 yeargrouse) 9-10 year

Small ones (vole, mice, lemming) 4 years cycleSmall ones (vole, mice, lemming) 4 years cycle

Predators feed on large prey have long cycle (red Predators feed on large prey have long cycle (red foxes, lynx, marten, mink)foxes, lynx, marten, mink)

Predators feed on small prey have short cycle (Arctic Predators feed on small prey have short cycle (Arctic fox, hawks, snowy owls)fox, hawks, snowy owls)

Cycles (oscillations) are caused by predator and prey Cycles (oscillations) are caused by predator and prey interaction (predator – prey).interaction (predator – prey).

Time delays and population cyclesTime 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 Physical conditions may change the period of cyclesof 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).

Development of host immunity influences host populationsDevelopment of host immunity influences host populations

Cases of measles reported in London (before vaccine had been developed)

Peaked about every two years

Periodicity in pathogen-host relationshipsPeriodicity in pathogen-host relationships

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 Creating predator-prey cycles in the laboratorylaboratory

Modeling and lab experimentsModeling and lab experiments Studies by GF Gause on protists (1920s)Studies by GF Gause on protists (1920s)

Predator: Ciliated protist, DidiniumPredator: Ciliated protist, Didinium Prey: Protist, ParameciumPrey: Protist, Paramecium Culture medium: test tubeCulture medium: test tube

Difficult to demonstrate the oscillationsDifficult to demonstrate the oscillations Predators eat all prey, then diePredators eat all prey, then die Add refuge (glass wool at bottom of tube), Add refuge (glass wool at bottom of tube),

predators would die and left some prey to survivepredators would die and left some prey to survive Add small number of predators periodicallyAdd small number of predators periodically

oscillations.oscillations.

Huffaker’s mite experimentHuffaker’s mite experiment

C.B. Huffaker, UC Berkeley (1958)

Predator: mite, TyphlodromusPrey: six-potted mite (Eotetranychus), pest of citrus fruitsReproduction: 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 12.3 Mathematical model for predationpredation

Lotka and Volterra equation for predation Lotka and Volterra equation for predation PreyPrey

Where cNWhere cNpredpredNNpreyprey is mortality of prey due to predator. is mortality of prey due to predator. c is per capita capture rate, and Nc is per capita capture rate, and Npred, pred, NNpreyprey are the are the number of predators and prey, respectively. number of predators and prey, respectively.

PredatorPredator

Where b is efficiency of conversion of prey consumed Where b is efficiency of conversion of prey consumed (cN(cNpredpredNNpreyprey) and d is death rate of predators) and d is death rate of predators

predpreypreyprey NcNrNdt

dN

predpredpreypred dNNcNbdt

dN )(

Solving the equationsSolving the equations For prey growth (dN_Prey/dt=0)For prey growth (dN_Prey/dt=0)

• NNpredpred = r/c = r/c Growth rate of prey population is zero when density Growth rate of prey population is zero when density

of predators equals per capita growth rate of prey of predators equals per capita growth rate of prey divided by per capita capture rate of predators.divided by per capita capture rate of predators.

Any increase in predator density will result in Any increase in predator density will result in negative growth in prey populationnegative growth in prey population

For predator growth (dN_Pred/dt=0)For predator growth (dN_Pred/dt=0)• NNpreyprey = d/bc = d/bc

Growth rate of predator population is zero when rate Growth rate of predator population is zero when rate of increase of prey is equal to rate of mortality of increase of prey is equal to rate of mortality divided by the product of b and c.divided by the product of b and c.

Thus the two equations interact and this Thus the two equations interact and this can be done graphicallycan be done graphically

There is a cyclical There is a cyclical rise and fall in rise and fall in both the predator both the predator and prey and prey populations with populations with timetime

Density of Density of predators lags predators lags behind density of behind density of preyprey

Feast and Famine Feast and Famine scenarioscenario

Prey and Prey and predators are predators are never quite driven never quite driven to extinctionto extinction

Mutual population Mutual population regulationregulation

Pred

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. coliPredator: 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 12.3 Pathogen-host dynamics can be described by the S-I-R modelbe 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)SR0>1, an epidemic will occur, each infected individual will infect more than one before it recoversR0<1, fails to take hold in the populationR0: 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 =100b=1, g=0.2, duration of infectiousness 1/g=5Beginning, S=1, R0=b/g*S=5

Assume no births of S, and no loss of resistance among previously infected individuals.

Influenza virusVaccination: remove individuals from S, reduce R0.

Case study: The chytrid fungus and the global decline of amphibians

Pathogenic fungus: Batrachochytrium dendrobatisdisIt kills hosts and persists by infecting alternative species.

Karan Lips, Southern Illinois University, 2006El Cope: first found in July 2004, rapid spread and caused abrupt drop.

The Lotka–Volterra model is criticized for The Lotka–Volterra model is criticized for overemphasizing the mutual regulation of overemphasizing the mutual regulation of predator and prey populationspredator and prey populations• Differential equations, no time delayDifferential equations, no time delay

(Difference equations, add time delay)(Difference equations, add time delay)• No internal forces act to restore the No internal forces act to restore the

populations to the joint equilibrium point, populations to the joint equilibrium point, random perturbations could increase random perturbations could increase oscillations to a point that V=0 or P=0oscillations to a point that V=0 or P=0

• cNpreyNpredator: at a given Npred, the rate at cNpreyNpredator: at a given Npred, the rate at which prey are captured increases with Nprey. which prey are captured increases with Nprey. This is not true. There is predator satiation.This is not true. There is predator satiation.

12.5 Lokta-Volterra model can be stabilized by 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).

The The functional responsefunctional response is the is the relationship between the per capita relationship between the per capita predation rate (number of prey consumed predation rate (number of prey consumed per unit time) and prey population sizeper unit time) and prey population size• This idea was introduced by M.E. This idea was introduced by M.E.

Solomon in 1949Solomon in 1949 Three types of functional response (I, II, Three types of functional response (I, II,

and III)and III)• Developed by C.S. HollingDeveloped by C.S. Holling

Functional Responses Relate Prey Consumed Functional Responses Relate Prey Consumed to Prey Densityto Prey Density

Functional responseFunctional response• NNe: per capita rate of predation, i.e., # of e: per capita rate of predation, i.e., # of

prey eaten during a given period of search prey eaten during a given period of search time.time.

• Type I functional responseType I functional response• Ne=cT Nprey Ne=cT Nprey • Passive predator such as spider or the prey Passive predator such as spider or the prey

is less sufficiently abundant (e.g., kestrels is less sufficiently abundant (e.g., kestrels and voles)and voles)

• All time (T) allocated to feeding is All time (T) allocated to feeding is searching.searching.

• LinearLinear• Ne/Nprey=cT constantNe/Nprey=cT constant

Type II responseType II response• Ne increase with Nprey rapidly, but level off at Ne increase with Nprey rapidly, but level off at

high prey density.high prey density.

Type III functional responseType III functional response

• Sigmoid (S-shaped) responseSigmoid (S-shaped) response• At high prey density, the response is the same as At high prey density, the response is the same as

type II response; however, the rate of prey type II response; however, the rate of prey consumed is low when the prey density is low at consumed is low when the prey density is low at first, increasing in a S-shaped fashion.first, increasing in a S-shaped fashion.

• Factors caused the S-shape responseFactors caused the S-shape response• 1. availability of cover to escape the predators1. availability of cover to escape the predators• 2. predator’s 2. predator’s search imagesearch image• 3. 3. Prey switching.Prey switching. Switch to other preys (more Switch to other preys (more

abundant)abundant)

Functional responseFunctional response• As prey increases, As prey increases,

predators take more preypredators take more prey• But howBut how

LinearLinear• Rate of predation is Rate of predation is

constantconstant Decreasing rate to Decreasing rate to

maximummaximum• Rate of predation Rate of predation

declinedecline SigmoidalSigmoidal

• Decrease at low Decrease at low density as well as density as well as high, increase to high, increase to maximum then maximum then declinesdeclines

Functional responses related prey consumed to prey density

(Right panel is predation rate, (Right panel is predation rate, # prey consumed divided by # prey consumed divided by prey density)prey density)

Linear Type 1 (European kestrel to vole)Linear Type 1 (European kestrel to vole) Mortality of prey simply density Mortality of prey simply density

dependentdependent No limits on systemNo limits on system

Decreasing Type 2 (weasel on rodent)Decreasing Type 2 (weasel on rodent) Predators can only eat so much – Predators can only eat so much –

satiationsatiation Time needed to kill and eat prey Time needed to kill and eat prey

becomes limitingbecomes limiting Sigmoid Type 3 (warbler on budworm Sigmoid Type 3 (warbler on budworm

larvae)larvae) Capture rate is density dependentCapture rate is density dependent Availability of coverAvailability of cover Alternative prey when preferred is Alternative prey when preferred is

rare (prey switching)rare (prey switching) Prey not part of predators search Prey not part of predators search

image, not a desirable food sourceimage, not a desirable food source

Prey switching Prey switching (water bug)(water bug)• Palatable versus Palatable versus

less palatableless palatable• Better return per Better return per

killkill• Less energy Less energy

needed to find needed to find and kill an and kill an abundant preyabundant prey

Model of prey switching

Numerical responseNumerical response• Predators reproduce Predators reproduce

moremore However However

reproduction reproduction usually slower than usually slower than prey prey

• Movement into high Movement into high prey density areasprey density areas

This This aggregative aggregative responseresponse is very is very important as it important as it rapidly increases rapidly increases predator densitypredator density

Predators respond numerically to changing prey density

Aggregative response in the redshank

Other numerical response as increased Other numerical response as increased reproductivereproductive effort effort• Weasels as predatorsWeasels as predators• Rodents as preyRodents as prey• Predators followed prey in reproductionPredators followed prey in reproduction• Increase of rodent was due to good harvest in 1990Increase 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

Stability: achievement of an unvarying Stability: achievement of an unvarying equilibrium size, often the carrying capacityequilibrium size, often the carrying capacity

Predator-prey: oscillations, but several factors Predator-prey: oscillations, but several factors could stabilize, move to stable equilibrium:could stabilize, move to stable equilibrium:• Predator inefficiency (c decrease)Predator inefficiency (c decrease)• Density-dependent limitations of prey or Density-dependent limitations of prey or

predator by other external factorspredator by other external factors• Alternative food resource for predatorAlternative food resource for predator• Refuges for prey at low prey densityRefuges for prey at low prey density• Reduced time delays in predator responses to Reduced time delays in predator responses to

changes in prey abundancechanges in prey abundance

12.5 Factors that reduce oscillations in predator-prey models

Population size is determined by: abundance of its Population size is determined by: abundance of its resources and of its consumersresources and of its consumers

One Extreme: resource population is only limited by One Extreme: resource population is only limited by its own food supplyits own food supply

Another: resource population is depressed below its Another: resource population is depressed below its carrying capacitycarrying capacity

Balances between these factors create multiple Balances between these factors create multiple equilibrium points: alternative state statesequilibrium points: alternative state states

12.6 Consumer-resource system can have more than one stable state

Consumer-imposed equilibrium:Consumer-imposed equilibrium:

At low density, prey can seek refuge, avoid At low density, prey can seek refuge, avoid predatorspredators

At low density, prey grows faster than predatorsAt low density, prey grows faster than predators

Low stable equilibrium point well below its Low stable equilibrium point well below its carrying capacitycarrying capacity

Resource-imposed equilibriumResource-imposed equilibrium

in some cases, prey population can move up from in some cases, prey population can move up from the consumer-imposed equilibrium, due to the the consumer-imposed equilibrium, due to the limited number of predators, predator satiation, limited number of predators, predator satiation, or other factors that keep predators in check or other factors that keep predators in check (nest limitation), reach equilibrium set by its (nest limitation), reach equilibrium set by its carrying capacity.carrying capacity.

Population could have two stable states and Population could have two stable states and sometime move between these two (crop and sometime move between these two (crop and forest pests, diseases).forest pests, diseases).

The EndThe End

RecapRecap Dynamics of resource and consumer Dynamics of resource and consumer

populationspopulations Lab experimentLab experiment Math modelMath model Lotka and Volterra equation for predation Lotka and Volterra equation for predation

predpreypreyprey NcNrNdt

dN

predpredpreypred dNNcNbdt

dN )(