es100: community ecology
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ES100:
Community Ecology
8/22/07
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
Types of Interactions
Competition
Predator-Prey
Mutualism
Commensalism
Competition
Natural Selection minimizes competition!
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
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
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
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
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
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
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
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.
Predator-prey
Predator-Prey Relationships
• Prey defenses: avoid conflict!• coevolution
• as predator evolves, prey evolves to evade it
• warning coloration and mimicry• Camouflage
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
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
•Bottom-up vs. Top-Down control•Predators can promote diversity by keeping competition in check
Predator-Prey Relationships
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
Mutualism
Both species benefit
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
Commensalism One species benefits, the other is unaffected
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
Assumptions of Lotka-Volterra Models
All assumptions of logistic growth model… plus:
Interaction coefficients, carrying capacities, and intrinsic growth rates are constant.
Summary of Interaction Equations:
Competition: (- , -)
Predator/Prey: (+, -)
Mutualism: (+, +)
Commensalism: (+, 0)
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
1
2121111
1 ?
K
NaNKNr
dt
dN⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
2
1212222
2 ?
K
NaNKNr
dt
dN
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
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
1. Separate Births and Deaths
= Births - Deaths
Births = b*N
Deaths = d*N
dN dt
Births and deaths may be density dependent
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
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
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
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!
Community Dynamics
Community: a group of populations (both plants and animals) that live together in a defined region.
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
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
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?
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?
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?
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
Food Web doesn’t account for Keystone Species
Kelp provides otter habitat
Sea urchins eat kelp
Otters eat sea urchins
Summary
Modeling Species Interactions Competition Predator-prey
Mutualism Commensalism
Community Dynamics Food Webs
Keystone Species
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