1

Lecture 2Lecture 2

Population EcologyPopulation Growth,

Competition and Predation

Population EcologyPopulation Growth,

Competition and Predation

BFLF Biology ConceptsBFLF Biology Concepts

• Population growth• Intraspecfic Competition (Interspecfic)• Predation (Parasitism/Virulence)• Behavior• Evolution?

• Population growth• Intraspecfic Competition (Interspecfic)• Predation (Parasitism/Virulence)• Behavior• Evolution?

2

The Tragedy of the CommonsThe Tragedy of the Commons• Open pasture can support 10 cattle• Currently grazed by 10 herdsmen

each with one

• Open pasture can support 10 cattle• Currently grazed by 10 herdsmen

each with one• One of the herdsmen adds

one more if he can make a profit.

• Adding one more animal = less food for each animal, but since he only has only 1/10 of the herd, he has to pay only 1/10 of the cost.

• One of the herdsmen adds one more if he can make a profit.

• Adding one more animal = less food for each animal, but since he only has only 1/10 of the herd, he has to pay only 1/10 of the cost.

The Tragedy of the CommonsThe Tragedy of the Commons• Shrinking profit margins ⇒

either go out of business or also add more animals.

• Mutual exploitation continues until overgrazing and erosion destroy the pasture system, and all the herdsmen are driven out of business…

• Hardin 1968

• Shrinking profit margins ⇒either go out of business or also add more animals.

• Mutual exploitation continues until overgrazing and erosion destroy the pasture system, and all the herdsmen are driven out of business…

• Hardin 1968

3

St. Matthew Island CollapseSt. Matthew Island Collapse

• Small number of reindeer colonized the island

• Increase rapidly• Use up all of the

resources• Population

collapses

• Small number of reindeer colonized the island

• Increase rapidly• Use up all of the

resources• Population

collapses

Population GrowthPopulation Growth• Exponential Growth• Exponential Growth

Popu

latio

n Si

zePo

pula

tion

Size

TimeTime

Nt = N0ertNNtt = N= N00eertrt

dN/dt = rNdN/dt = rNdN/dt = rN

Nt = popln @ time t

r = growth rate

NNtt = = poplnpopln @ time t@ time t

r = growth rater = growth rate

4

Population GrowthPopulation Growth• Exponential Growth• Exponential Growth

Popu

latio

n Si

zePo

pula

tion

Size

TimeTime

dN/dt = rNdN/dt = rNdN/dt = rNhigh rhigh r

moderate rmoderate r

low rlow r

Population GrowthPopulation Growth• Exponential Growth

– Discrete Time Nt+1 = Nt * R• R = average reproduction

• Exponential Growth– Discrete Time Nt+1 = Nt * R

• R = average reproduction

5

Population GrowthPopulation Growth• Logistic Growth (Malthus)• Intraspecific competition• Logistic Growth (Malthus)• Intraspecific competition

Popu

latio

n Si

zePo

pula

tion

Size

TimeTime

dN/dt = rN(1- N/K)dN/dt = rN(1- N/K)

Carrying Capacity of Environment (K)Carrying Capacity of Environment (K)

Period of Exponential Growth

Period of Exponential Growth

Nt =

N0KN0 + (K−N0)e−r0t

Population Density (N)Population Density (N)

Density-dependent death rate - dDensity-dependent death rate - d

Density-independent birth rate - bDensity-independent birth rate - b

Equilibrium DensityEquilibrium Density

1 dNN dt1 dNN dt

Population Density (N)Population Density (N)

Density-independent death rateDensity-independent death rate

Density-dependent birth rateDensity-dependent birth rate

1 dNN dt1 dNN dt

Population Density (N)Population Density (N)

Density-dependent death rateDensity-dependent death rate

Density-dependent birth rateDensity-dependent birth rate

Density-Dependant Factors Regulate Population SizeDensity-Dependant Factors Regulate Population Size

1 dNN dt1 dNN dt

r = b-d

as N r stabilizing

r = b-d

as N r stabilizing

6

Population GrowthPopulation Growth• Logistic Growth

– Discrete Time Nt+1 = Nt (1+r(1-Nt/K))• R = average reproduction• K = carrying capacity

• Logistic Growth– Discrete Time Nt+1 = Nt (1+r(1-Nt/K))

• R = average reproduction• K = carrying capacity

Which graph of population growth could not be generated by this equation? Nt+1 = Nt (1+r(1-Nt/K))

Which graph of population growth could not be generated by this equation? Nt+1 = Nt (1+r(1-Nt/K))

• A

• B

• A

• B

• C

• D

• C

• D

• E - They could all be generated• F - None could be generated• E - They could all be generated• F - None could be generated

7

Population GrowthPopulation Growth• Logistic Growth

– Discrete Time Nt+1 = Nt (1+r(1-Nt/K))• Limit Cycles• Chaos

• Logistic Growth– Discrete Time Nt+1 = Nt (1+r(1-Nt/K))

• Limit Cycles• Chaos

Real Population GrowthReal Population Growth

8

• Human population growth

• Human population growth

9

Human Population Age Distribution

More Developed Countries

Human Population Age Distribution

More Developed Countries

Age IntervalAge Interval

Number of people (Millions)Number of people (Millions) FemalesFemalesMalesMales

80 - 9070 - 8060 - 7050 - 6040 - 5030 - 4020 - 3010 - 200 -10

80 - 9070 - 8060 - 7050 - 6040 - 5030 - 4020 - 3010 - 200 -10

Long periods of no net growth lead to even distribution

Long periods of no net growth lead to even distribution

Population Summary for the USPopulation Summary for the US

2000

2025

2050

http://blue.census.gov/

10

Population Age Distribution

Less Developed Countries

Population Age Distribution

Less Developed CountriesAgeAge

300300300300Number of people (Millions)Number of people (Millions) FemalesFemales

MalesMales

Population Summary for UgandaPopulation Summary for Uganda

2000

2025

2050

http://blue.census.gov/

Very high reproductive rate

11

Human Population GrowthHuman Population Growth

YearYear

Pop

ulat

ion

(Bill

ions

)P

opul

atio

n (B

illio

ns)

11

22

33

44

55

66

Agriculture & domestification of animals

Agriculture & domestification of animals

4 million4 million 7 million7 million

Hunter GatherersHunter Gatherers

Adapted from: Cohen, “How Many People Can the Earth Support”Adapted from: Cohen, “How Many People Can the Earth Support”

10,000 BC10,000 BC 8,000 BC8,000 BC 2,000 AD2,000 AD004,000 BC4,000 BC

Bubonic PlagueBubonic Plague

Industrial RevolutionIndustrial Revolution

(1400)(1400)

(1800)(1800)

Modern Medicine (reduced mortality)Modern Medicine (reduced mortality)

(1900)(1900)

Fossil FuelFossil Fuel

6,289,870,258*

(4/30/2003)

http://www.census.gov/main/www/popclock.htmlhttp://www.census.gov/main/www/popclock.html

6,363,174,549(4/28/2004)

6,432,150,287(4/22/05)

Now projected to reach 9 Billion

and level off

6 Billion (1999)6 Billion (1999)

http://www.census.gov/ipc/prod/wp02/wp02-1.pdf

12

Demographic TransitionDemographic Transition

Stage 1

High birth rateHigh, but fluctuating

death rate

Stage 1

High birth rateHigh, but fluctuating

death rate

Stage 2

Declining death ratesContinuing high birth

rates

Stage 2

Declining death ratesContinuing high birth

rates

Stage 3

Declining birth and death rates

Stage 3

Declining birth and death rates

Stage 4

Low death rateLow, but fluctuating

birth rate

Stage 4

Low death rateLow, but fluctuating

birth rate

What do you think is the human carrying capacity of earth?What do you think is the human carrying capacity of earth?

• A - 6 billion• B - 9 billion• C - 12 billion• D - 15 billion

• A - 6 billion• B - 9 billion• C - 12 billion• D - 15 billion

13

Human Population Growth and BiodiversityHuman Population Growth and Biodiversity• Human Influences on Biodiversity

– Immigration into new places– Destruction of habitat and species– Fragmentation of habitat– Introduction of non-native species– Competition with agriculture

• Human Influences on Biodiversity– Immigration into new places– Destruction of habitat and species– Fragmentation of habitat– Introduction of non-native species– Competition with agriculture

The Fundamental Ecological Niche: “An n-dimensional hyper-volume every point on which a species can survive and reproduce indefinitely in the absence of other species” (Hutchinson)

The Fundamental Ecological Niche: “An n-dimensional hyper-volume every point on which a species can survive and reproduce indefinitely in the absence of other species” (Hutchinson)

Food size

Food sizetemperature

temperature

hum

idity

hum

idity

14

Interspecific CompetitionInterspecific Competition

Food size

Food sizetemperature

temperature

hum

idity

hum

idity

niche overlap leads to competition

The Realized Ecological Niche:the niche actually occupied in the presence of other speciesThe Realized Ecological Niche:the niche actually occupied in the presence of other species

Food size

Food sizetemperature

temperature

hum

idity

hum

idity

15

One species eats seeds of one size rangeN

umbe

r con

sum

edN

umbe

r con

sum

ed

Seed size (one niche dimension)

Partial niche overlap can lead to Niche Partitioning and Competitive Coexistence

Species 1

Species 2

Num

ber c

onsu

med

Num

ber c

onsu

med

Seed size

16

Complete niche overlap

Species 1: Strong competitorSpecies 1: Strong competitor

Species 2: Weak competitor,driven to extinctionSpecies 2: Weak competitor,driven to extinction

Num

ber c

onsu

med

Seed size

Strong niche overlap can lead to Competitive Exclusion

Observed Distributions: Is this due to competition? Or differential tolerance of desiccation?

Do an Experiment!

Chthamalusin upperintertidal zone

Chthamalusin upperintertidal zone

Mean tidal levelMean tidal level

Balanusin lowerintertidal zone

Balanusin lowerintertidal zone

17

Spring high tideSpring high tide

Neap high tideNeap high tide

Mean tidal levelMean tidal level

Neap low tideNeap low tide

Could not become adults

due to competition

Could not become adults

due to competition

Larval Settlement

Zone

Larval Settlement

ZoneAdult

DistributionAdult

DistributionRealized

NicheRealized

Niche

Barnacles subject to desiccation

Barnacles subject to desiccation

Spring low tideSpring low tide

Larval Settlement

Zone

Larval Settlement

ZoneAdult

DistributionAdult

Distribution

Distribution of Two Barnacle Species – Balanus and ChthamalusDistribution of Two Barnacle Species – Balanus and Chthamalus

BalanusBalanus

ChthamalusChthamalus

FundamentalNiche

FundamentalNiche

Lotka-VolterraInterspecific CompetitionLotka-VolterraInterspecific Competition• dN1/dt = r1*N1 ((K1 – N1 – (a *N2))/ K1)• dN2/dt = r2*N2 (K2 – N2 - (b *N1))/ K2)

– Two logistic growth models– Two species N1 and N2

– a : impact of species 2 on species 1– b : impact of species 1 on species 2

• dN1/dt = r1*N1 ((K1 – N1 – (a *N2))/ K1)• dN2/dt = r2*N2 (K2 – N2 - (b *N1))/ K2)

– Two logistic growth models– Two species N1 and N2

– a : impact of species 2 on species 1– b : impact of species 1 on species 2

18

Lotka-Volterra CompetitionLotka-Volterra Competition

PredationPredation• Hare and Lynx Cycles

• Trapping data described by equations by Lotka (1925) and Volterra (1926)

• Hare and Lynx Cycles

• Trapping data described by equations by Lotka (1925) and Volterra (1926)

19

What drives the oscillation?What drives the oscillation?

Snowshoe Hare and Lynx Population Population Cycles Snowshoe Hare and Lynx Population Population Cycles

18401840 19301930

11 years11 years

18701870 19001900

Num

ber o

f Pel

ts (t

hous

ands

)N

umbe

r of P

elts

(tho

usan

ds)

150150

5050

100100

Hudson Bay Company Trapping Records

(1840 –1940)

Hudson Bay Company Trapping Records

(1840 –1940)HareHare

LynxLynx

PredationPredation

Lotka-VolterraPredator-Prey EquationsLotka-VolterraPredator-Prey Equations

• dx/dt = Ax - Bxy• dy/dt = -Cy + Dxy

– x : number of prey– y : number of predators– xy : encounter rate of predator and prey– A : growth rate of prey– B : efficiency of predator– C : density dependent death of predators– D : conversion of prey to predator

• dx/dt = Ax - Bxy• dy/dt = -Cy + Dxy

– x : number of prey– y : number of predators– xy : encounter rate of predator and prey– A : growth rate of prey– B : efficiency of predator– C : density dependent death of predators– D : conversion of prey to predator

20

Lotka-Volterra OscillationsLotka-Volterra Oscillations• Periodic Cycling• Prey Leads Predator• Periodic Cycling• Prey Leads Predator

Predator-Prey ModelsPredator-Prey Models

• Agent-based Predator-Prey– Grass

• Spreads out from other grass– Rabbits

• Walk around randomly and use energy• If they land on grass they eat it• If they eat enough they reproduce• If they run out of energy they die

• Agent-based Predator-Prey– Grass

• Spreads out from other grass– Rabbits

• Walk around randomly and use energy• If they land on grass they eat it• If they eat enough they reproduce• If they run out of energy they die

21

Predator-Prey ModelsPredator-Prey Models

Evolution and SelectionEvolution and Selection

• In the absence of selection if we start with 16 different colors of rabbits (in the previous model), how many of those colors will persist in the long run?– A - 16– B - 10-15– C - 8-10– D - 1-2

• In the absence of selection if we start with 16 different colors of rabbits (in the previous model), how many of those colors will persist in the long run?– A - 16– B - 10-15– C - 8-10– D - 1-2

22

Rabbits and Grass with ColorRabbits and Grass with Color

• Evolution?• Selection?• Evolution?• Selection?

What is happening?What is happening?

• Evolution?• Selection?• Evolution?• Selection?

23

EvolutionEvolution

• Descent with modification• Change in gene frequency in a

population over time– Mutation– Migration– Selection– Genetic Drift

• Descent with modification• Change in gene frequency in a

population over time– Mutation– Migration– Selection– Genetic Drift– Genetic Drift– Genetic Drift