INTERACTIONS AMONG POPULATIONS

1
INTERACTIONS AMONG POPULATIONS I. COMPETITION
A. Modeling Competition B. Empirical Tests of
Competition C. The Nature of Competitive
Interactions D. Problems with L-V
Models
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2
INTERACTIONS AMONG POPULATIONS I. COMPETITION
A. Modeling Competition B. Empirical Tests of
Competition C. The Nature of Competitive
Interactions D. Problems with L-V Models 1.
Have to conduct pairwise competition experiments
to quantify competition coefficients
)  
   
 
3
INTERACTIONS AMONG POPULATIONS I. COMPETITION
A. Modeling Competition B. Empirical Tests of
Competition C. The Nature of Competitive
Interactions D. Problems with L-V Models 1.
Have to conduct pairwise competition experiments
to quantify competition coefficients 2. The
nature of the competition is undefined... is it
contest or scramble? What resource is
limiting?
)  
   
 
4
INTERACTIONS AMONG POPULATIONS I. COMPETITION
A. Modeling Competition B. Empirical Tests of
Competition C. The Nature of Competitive
Interactions D. Problems with L-V Models E.
Solution - Tilman's Resource Models
(1982) ....... get ready ......
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E. Solution - Tilman's Resource Models
(1982)
Isoclines graph population growth relative to
resource ratios (2 resources, R1, R2) Consumption
rate of Species A(Ca).
)  
   
 
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E. Solution - Tilman's Resource Models
(1982)
Isoclines graph population growth relative to
resource ratios (2 resources, R1, R2) Consumption
rate of Species A(Ca). Resource limitation can
occur in different environments with different
initial resource concentrations (S1, S2).
)  
   
 
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E. Solution - Tilman's Resource Models
(1982)
Species B requires more of both resources than
species A.
   
 
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E. Solution - Tilman's Resource Models
(1982)
Species B requires more of both resources than
species A. So, no matter the environment and no
matter the consumptions curves (lines from S),
the isocline for species B will be "hit" first.
So, Species B will stop growing, but Species A
can continue to grow and use up resources....
this drops resources below B's isocline, and B
will decline.
   
 
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E. Solution - Tilman's Resource Models
(1982)
Species B requires more of both resources than
species A. So, no matter the environment and no
matter the consumptions curves (lines from S),
the isocline for species B will be "hit" first.
So, Species B will stop growing, but Species A
can continue to grow and use up resources....
this drops resources below B's isocline, and B
will decline. So, if one isocline is completely
within the other, then one species will always
win.
   
 
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E. Solution - Tilman's Resource Models
(1982)
If the isoclines intersect, coexistence is
possible (there are densities where both species
are equilibrating at values gt 1).
   
 
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E. Solution - Tilman's Resource Models
(1982)
If the isoclines intersect, coexistence is
possible (there are densities where both species
are equilibrating at values gt 1). Whether this is
a stable coexistence or not depends on the
consumption curves. Consider Species B. It
requires more of resource 1, but less of resource
2, than species A. Yet, it also consumes more of
resource 1 than resource 2 - it is a "steep"
consumption curve. So, species B will limit its
own growth more than it will limit species A.
   
 
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E. Solution - Tilman's Resource Models
(1982)
If the isoclines intersect, coexistence is
possible (there are densities where both species
are equilibrating at values gt 1). Whether this is
a stable coexistence or not depends on the
consumption curves. Consider Species B. It
requires more of resource 1, but less of resource
2, than species A. Yet, it also consumes more of
resource 1 than resource 2 - it is a "steep"
consumption curve. So, species B will limit its
own growth more than it will limit species A.
This will be a stable coexistence for
environments with initial conditions between the
consumption curves (S3). If the consumption
curves were reversed, there would be an unstable
coexistence in this region.
   
 
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E. Solution - Tilman's Resource Models (1982) -
Benefits 1. The competition for resources is
defined
   
 
14
E. Solution - Tilman's Resource Models (1982) -
Benefits 1. The competition for resources is
defined 2. The model has been tested in plants
and planton and confirmed
   
 
15
E. Solution - Tilman's Resource Models (1982) -
Benefits 1. The competition for resources is
defined 2. The model has been tested in plankton
and confirmed
   
Cyclotella wins
 
Cyclotella
Stable Coexistence
Asterionella wins
PO4 (uM)
Asterionella
SiO2 (uM)
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E. Solution - Tilman's Resource Models (1982) -
Benefits 1. The competition for resources is
defined 2. The model has been tested in plants
and planton and confirmed 3. Also explains an
unusual pattern called the "paradox of
enrichment"
   
 
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E. Solution - Tilman's Resource Models (1982) -
Benefits 1. The competition for resources is
defined 2. The model has been tested in plants
and planton and confirmed 3. Also explains an
unusual pattern called the "paradox of
enrichment" If you add nutrients, sometimes the
diversity in a system drops... and one species
comes to dominate. (Fertilize your lawn so that
grasses will dominate... huh?)
   
 
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If you add nutrients, sometimes the diversity in
a system drops... and one species comes to
dominate.
Change from an initial stable coexistence
scenario (S1) to a scenario where species A
dominates (S2).
   
 
19
I. Competition II. Predation
   
 
20
I. Competition II. Predation A. Lotka-Volterra
Models Goal - create a model system in which
there are oscillations of predator and prey
populations that are out-of-phase with one
another.
   
 
21
I. Competition II. Predation A. Lotka-Volterra
Models Goal - create a model system in which
there are oscillations of predator and prey
populations that are out-of-phase with one
another. Basic Equations
   
 
22
I. Competition II. Predation A. Lotka-Volterra
Models Goal - create a model system in which
there are oscillations of predator and prey
populations that are out-of-phase with one
another. Basic Equations 1. Prey

   
 
23
I. Competition II. Predation A. Lotka-Volterra
Models Goal - create a model system in which
there are oscillations of predator and prey
populations that are out-of-phase with one
another. Basic Equations 1. Prey
a. Equation dH/dt rH - pPH where rH
defines the maximal, geometric rate p
predator foraging efficiency eaten P
number of predators H number of prey, so PH
number of encounters and pPH number of prey
killed (consumed) So, the formula describes the
maximal growth rate, minus the number of prey
individuals lost by predation.
   
 
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b. The Prey Isocline dH/dt 0 when rH
pPH when P r/p. Curious dynamic. There is a
particular number of predators that can limit
prey growth below this number of predators,
REGARDLESS OF THE NUMBER OF PREY, prey increase.
Greater than this number of predators, REGARDLESS
OF THE NUMBER OF PREY, and the prey declines.
Prey's rate of growth is independent of its own
density (rather unrealistic).
   
 
25
I. Competition II. Predation A. Lotka-Volterra
Models Goal - create a model system in which
there are oscillations of predator and prey
populations that are out-of-phase with one
another. Basic Equations 1. Prey
2. Predator a. The Equation dP/dt a(pPH)
- mP where pPH equals the number of prey
consumed, and a the rate at which food
energy is converted to offspring. So, a(pPH)
number of predator offspring produced. m
mortality rate, and P of predators, so mP
number of carnivores dying. So, the equation
boils down to the birth rate (determined by
energy "in" and conversion rate to offspring)
minus the death rate.
   
 
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b. The Predator's Isocline dP/dt 0 when
mP a(pPH) or when H m/ap Again, Predator's
growth is independent of its own density there is
a critical number of prey which can support a
predator population of any size below this
number, the predator population declines - above
this number and the population can increase.

   
 
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Basic Equations 1. Prey 2. Predator 3.
Dynamics
   
 
1.
4.
1.
2.
3.
4.
1.
2.
3.
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I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models
   
 
29
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models 1. Constant Predation Rate is
Unrealistic
   
 
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I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models 1. Constant Predation Rate is
Unrealistic a. L-V rate called a Type I
functional response captured is a constantly
function () of of prey available or of
predators.
L-V
   
 
Prey Captured
Prey Density
31
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models 1. Constant Predation Rate is
Unrealistic a. L-V rate called a Type I
functional response captured is a constantly
function () of of prey available or of
predators. b. Nicholson-Bailey (1935) success
rate declines at higher prey density or predator
density either as a result of interference among
predators or as a result of handling
time/satiation limit. Type II functional response

L-V
   
 
Prey Captured
Prey Density
32
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models 1. Constant Predation Rate is
Unrealistic a. L-V rate called a Type I
functional response captured is a constantly
function () of of prey available or of
predators. b. Nicholson-Bailey (1935) success
rate declines at higher prey density or predator
density either as a result of interference among
predators or as a result of handling
time/satiation limit. Type II functional response
c. Hollings (1959) At low densities of prey,
the predator does poorly because they do not
develop a good search image or an efficient
strategy. Sigmoidal, with maximum L-V rate only
at intermediate prey densities. Type III
functional response. - b and c result in
curved isoclines for predator
L-V
   
 
Prey Captured
Prey Density
33
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models C. Multiple State States 1. Consider a
Type III functional response, where the predation
rate is highest at intermediate prey densities.

   
 
H
34
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models C. Multiple State States 1. Consider a
Type III functional response, where the predation
rate is highest at intermediate prey densities.
2. Also consider a prey population limited by
its own density.
   
 
H
35
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models C. Multiple State States 1. Consider a
Type III functional response, where the predation
rate is highest at intermediate prey densities.
2. Also consider a prey population limited by
its own density. 3. Consider the relative rates
of recruitment and predation the rates at which
prey are added (by recruitment) or lost (by
pred).
   
 
H
36
I. Competition II. Predation A. Lotka-Volterra
Models B. Major Criticisms and Modified
Models C. Multiple State States 1. Consider a
Type III functional response, where the predation
rate is highest at intermediate prey densities.
2. Also consider a prey population limited by
its own density. 3. Consider the relative rates
of recruitment and predation the rates at which
prey are added (by recruitment) or lost (by
pred). 4. Based on the efficiency of the
predator, multiple stable states are possible.

   
 
H