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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
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