Download - ES100: Community Ecology
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ES100:
Community Ecology
8/22/07
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What Controls Population Size and Growth Rate (dN/dt)?
• Density-dependent factors:• Intra-specific competition
• food• Space
• contagious disease• waste production• Interspecific competition• Other species interactions!
• Density-independent factors:• disturbance, environmental conditions
• hurricane• flood• colder than normal winter
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Types of Interactions
Competition
Predator-Prey
Mutualism
Commensalism
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Competition
Natural Selection minimizes competition!
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Species Interactions
• How do we model them?• Start with logistic growth
= r * N (1 – )= r * N (1 – )N K
dN dt
= r * N ( - )= r * N ( - )N K
dN dt
K K
= r * N ( )= r * N ( )dN dt
K-N K
Use this equation for 2 different species
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Species Interactions• Population 1 N1
• Population 2 N2
• But the growth of one population should have an effect the size of the other population
= r= r11 * N * N11 ( ) ( )dN
1 dt
K1-N1 K1
= r= r22 * N * N22 ( ) ( )dN
2 dt
K2-N2 K2
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Species Interactions
• New term for interactions
a12 effect of population 2 on population 1
a21 effect of population 1 on population 2
• Multiply new term by population sizethe larger population 2 is, the larger its effect on
population 1 (and vice versa)
a12 * N2 a21 * N1
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Competition: Lotka-Volterra Model If two species are competing, the growth of one
population should reduce the size of the other
Population 1 N1
Population 2 N2
= r= r11 * N * N11 dN
1 dt
K1 - N1 - a12 N2 K1
= r= r22 * N * N22 dN
2 dt
K2 - N2 - a21 N1 K2
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Competition If two species are competing, the growth of one
population should reduce the size of the other
Population 1 N1
Population 2 N2
= r= r11 * N * N11 dN
1 dt
K1 - N1 - a12 N2 K1
= r= r22 * N * N22 dN
2 dt
K2 - N2 - a21 N1 K2
Because this is a negative term, K is reduced
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Blue Area = Bluejay’s Carrying Capacity
It takes 1squirrel to use the portion of the carrying capacity occupied by 4 bluejays.
aBS = 4
Interspecific competition regulates bluejay population
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=
B
SBBBB
B
K
NNKNr
dt
dN 4
COMPETITION
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Green Area = Squirrel’s Carrying Capacity
It takes 4 bluejays to use the portion of the carrying capacity occupied by 1 squirrel.
aSB =.25 Intraspecific competition regulates squirrel population
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=
s
Bssss
S
K
NNKNr
dt
dN 25.
COMPETITION
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Outcomes of Competition Model Many possible outcomes, depends on the balance of:
r1 vs r2
K1 vs K2
a21 vs a12
a12 > 1 Interspecific competition dominates population size of species 1
a12 < 1 Intraspecific competition dominates population size of species 1
a12 is the per capita effect of species 2 on the the pop’n growthrate of species 1, measured relative to the effect of species 1.
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Predator-prey
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Predator-Prey Relationships
• Prey defenses: avoid conflict!• coevolution
• as predator evolves, prey evolves to evade it
• warning coloration and mimicry• Camouflage
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Red = Fox’s Carrying Capacity
It takes 10 rabbits to support 1 fox
aFR =.10
⎟⎟⎠
⎞⎜⎜⎝
⎛ +−=
F
RFFFF
F
K
NNKNr
dt
dN 10.
Predator-PreyPredator-Prey
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Yellow = Rabbits Carrying Capacity
It takes 10 rabbits to support 1 fox
aRF = 10
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=
R
FRRRR
R
K
NNKNr
dt
dN 10
Predator-PreyPredator-Prey
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•Bottom-up vs. Top-Down control•Predators can promote diversity by keeping competition in check
Predator-Prey Relationships
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Predatory-Prey If it is a predator-prey relationship, then the two
populations have opposite effects on one another
Prey (N1)
Predator (N2)
= r= r11 * N * N11 dN
1 dt
K1 - N1 - a12 N2 K1
= r= r22 * N * N22 dN
2 dt
K2 - N2 + a21 N1 K2
Because this is a negative term, K is reduced
Because this is a positive term, K is increased
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Mutualism
Both species benefit
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Mutualism If it is a mutually beneficial relationship, then the two
populations increase each other’s size
Population 1 N1
ti
Population 2 N2
= r= r11 * N * N11 dN
1 dt
K1 - N1 + a12 N2 K1
= r= r22 * N * N22 dN
2 dt
K2 - N2 + a21 N1 K2
Because this is a positive term, K is increased
Because this is a positive term, K is increased
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Commensalism One species benefits, the other is unaffected
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Commensalism
If the relationship is commensalistic, one species benefits (the commensal) and the other is unaffected
Population 1 N1
Population 2 N2
= r= r11 * N * N11 dN
1 dt
K1 - N1 + a12 N2 K1
= r= r22 * N * N22 dN
2 dt
K2 - N2
K2
Because this is a positive term, K is increased
Because there is no a21 term, K is unchanged
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Assumptions of Lotka-Volterra Models
All assumptions of logistic growth model… plus:
Interaction coefficients, carrying capacities, and intrinsic growth rates are constant.
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Summary of Interaction Equations:
Competition: (- , -)
Predator/Prey: (+, -)
Mutualism: (+, +)
Commensalism: (+, 0)
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
1
2121111
1 ?
K
NaNKNr
dt
dN⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
2
1212222
2 ?
K
NaNKNr
dt
dN
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Test you knowledge!What type of relationship– what equation to use?
A coati eats tree fruit.
Your dog has a flea
You use a fast bicyclist to “draft” off of
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Problems with Simple Logistic Growth
1. Births and deaths not separated-you might want to look at these processes separately
-predation may have no effect on birth rate
2. Carrying capacity is an arbitrary, set value
3. No age structure
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1. Separate Births and Deaths
= Births - Deaths
Births = b*N
Deaths = d*N
dN dt
Births and deaths may be density dependent
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1. Separate Births and Deaths
= Births - Deaths
Births = b*N
Deaths = d*N
dN dt
Births rate may be density dependentDeath rate may be dominated by predator effects
Example:Births = b*N(1- N )
KDeaths = db+a21N2
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2. Refine Carrying Capacity
If the population is a herbivore, K may depend on the population of plants
= r= rHH * N * NHH (1 – ) (1 – )dNH
dtNH NP
Kherbivore= Nplant
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Remaining Problems
Age Structure
Space: animals rely on different parts of landscape for different parts of their life cycle
Individuality: Populations are collections of individuals, not lumped pools
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General Notes on Using Models
How complex should model be? K.I.S.S. Identify research needs:
Build model structureTest model to see what it is most sensitive toDo research to find values of unknown parameters
If build a model that accurately predicts dynamics,it can be used as a management tool.Look critically at assumptions!
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Community Dynamics
Community: a group of populations (both plants and animals) that live together in a defined region.
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Trophic Cascade
Eagles
Foxes
Mice
Plants 1st trophic level
2nd trophic level
3rd trophic level
4th trophic level
autotroph/ primary producer
herbivore/ primary
consumer
predator/ secondary consumer
predator/ tertiary consumer
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How would we Model the Fox Population?
Why not include the effect of the plant population?
What if foxes had a competitor?
⎟⎟⎠
⎞⎜⎜⎝
⎛ −+−=
F
EFEMFMFFFF
F
K
NaNaNKNr
dt
dN
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Trophic Cascade
Eagles
Foxes
Mice
Plants 1st trophic level
2nd trophic level
3rd trophic level
4th trophic level
if eagles go extinct, what could happen to…
foxes?
mice?
plants?
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Trophic Cascade
Eagles
Foxes
Mice
Plants 1st trophic level
2nd trophic level
3rd trophic level
4th trophic levelIf a new
predator on mice is introduced, what could happen to…
mice?
plants?
foxes?
eagles?
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Trophic Cascade
Eagles
Foxes
Mice
Plants 1st trophic level
2nd trophic level
3rd trophic level
4th trophic levelIf drought
caused a dip in plant production, what would happen to…
mice?
foxes?
eagles?
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Simplified Temperate Forest Food Web
What happens to when it’s a WEB instead of a CHAIN?
Oak seedling
Deer
Wolf
Fox
Rabbit
Grasses Herbs
Caterpillars
Shrews
Eagle
In long term, balance is restored
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Food Web doesn’t account for Keystone Species
Kelp provides otter habitat
Sea urchins eat kelp
Otters eat sea urchins
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Summary
Modeling Species Interactions Competition Predator-prey
Mutualism Commensalism
Community Dynamics Food Webs
Keystone Species
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