BIOL 3060 Lecture Notes - Lecture 8: Isocline, Detritivore, Herbivore
Predator -prey
•
Host -parasite
•
Host -parasitoid
•
Herbivore -plant
•
Detritivore -detritus
•
Consumer-Resource Interactions:
Reading: Theory of Consumer-Resource Interactions .cdf (using C-R vs. C-N)
Type I -linear
•
Type II -saturating (curve to plateau)
•
Type III - S-shaped
•
Review: Functional Responses -per consumer ingestion or consumption rate (kg prey/ kg
C vs. Resource density)
Appears, most often show functional responses are Type II
•
Ingestion Rate: a*C*N/(N+N0)
○
'a' -max attack rate
○
N0 -1/2 saturation density
○
Ingestion rate vs. Density
•
Empirical Data:
Consumer population growth rate / consumer = eating rates per consumer (for type I-
III)
•
Numerical responses often are similar to functional responses suggesting population
growth respond as a fraction of what you eat
•
Functional to Numerical Response -"the population grows at a rate proportional to what it
eats"
N -plant biomass (resource)
•
C -herbivore consumer biomass
•
--> fecal loss (f as a fraction): (1-f)a*C*N/(N+N0)
○
--> maintenance cost: mC
○
<-- consumption or intake: a*C*N/(N+N0)
○
C:
•
--> consumption or intake: a*C*N/(N+N0)
○
--> r*N^2 /K
○
<-- rN
○
N:
•
dN/dt = rN(1-N)/K -a*C*N/(N+N0)
•
dC/dt = f*a*CN/(N+N0) -mC
•
A Consumer-Resource Model
= Rosenzweig-MacArthur consumer-resource model (bioenergetics)
Graphical analysis (phaseplane)i)
Consumer cannot persist
○
Stable equilibrium -non-excitable
○
Stabile equilibrium -excitable (oscillatory decay)
○
Cycles (excitable)
○
4 Quantatively Different Dynamical Outcomes from Isoclinesii)
+ relationship to consumer:resource biomass pyramids (e.g. top heavy)
How do the dynamics change as we increase productivity (K)?
○
How do the dynamics change as we increase interaction strength?
○
*interaction strength is related to functional and numerical response
○
Some model experiments:iii)
Some stabilizing factorsiv)
Lab and field resultsv)
Consumer-Resource Theory:
Consumer (C ) vs. Resource (N) Densities (*see slides)
•
i.e. given parameters values (r,K,a), then isocline is the combination of C & N
densities that imply N is not growing (dN/dt =0) --> population is not changing
in respect to time
○
C = 0 at 'K' of Resource (carrying capacity)
○
C = r(1-N/K)(N+N0) / a (red line on graph)
○
Which is dominating (resource or consumer)
!
If consumer is dominating (arrows above graph), resources are
decreasing
!
If resources are dominating (arrows below graph), resources are
increasing
!
Arrows on graph: at given density of C, N is increasing/decreasing
○
N-isocline --> dN/dt = 0
•
i.e. the combination of C & N densities that imply C is not growing
○
N = N0*m / (ea -m)
○
If growth rate = demands, population does not change
○
To the left --> little resources --> C declines (metabolic costs outweigh
resource availability)
○
To the right --> abundant resources --> C increases (a lot of resources for
metabolic costs)
○
C-isocline --> dC/dt = 0
•
Addition of the two isocline vectors
○
Already suggesting a cyclical dynamic
!
At dC/dt = 0 there is no vertical component (left)
!
At dN/dt=0 there is no horizontal component (up)
!
Red dot = equilibrium (arrows follow circular path around dot)
○
C vs Time
!
N vs Time
!
When plotted on same graph, densities oscillate
!
Solutions on the phaseplane can be interpreted as changes through time (time
series -densities vs. time)
○
Phaseplane: understanding the flows around the isoclines start to unfold how C and N
change with time
•
Graphical Analysis: Phaseplane
The consumer density is usually greater than the resource density --> top heavy
arrangement
•
Average biomass density ratio (C:N) >1
•
Cyclic dynamics (excitable/oscillating) -occurs whenever the consumer isocline
(dC/dt=0) lies to the left of the peak on the resource (dN/dt=0) isocline
1)
Overshooting
•
Over time, consumer density becomes lower than resource
•
Moderately top heavy
•
Stable equilibrium dynamics (excitable with oscillatory decay) -occurs whenever
consumer isocline (dC/dt=0) lies to the right of the peak on the resource isocline
(dN/dt=0), but not near N=K
2)
Resource > consumer --> at equilibrium
•
Bottom heavy
•
Stable equilibrium dynamics (non-excitable) -occurs whenever consumer isocline
(dC/dt=0) lies WELL to the right of the peak on the resource isocline (dN/dt=0),
relatively close to N=K
3)
Resource reaches K while consumer density declines over time
•
Bottom heavy (no C)
•
Resource goes to carrying capacity and consumer goes extinct4)
Qualitative Outcomes to this Model:
In each case, increasing the supply of nutrients or energy tends to destroy the steady
state. Thus man must be very careful in attempting to enrich an ecosystem in order to
increase its food yield. There is a real chance that such activity may result in
decimation of the food species that are wanted in greater abundance.”
•
As the system becomes more productive, consumer-resource interactions become less
stable (more excited or oscillatory) and therefore more prone to extinctions
•
Paradox of Enrichment:
Phaseplane shifted to left doesn’t reach dC/dt=0
□
Very low K (similar to low productivity) -consumer cannot exist
!
Phaseplane reaches dC/dt=0
□
Low K -stable equilibrium (non-excitable): consumer and resource
persist and maintain constant densities through time
!
dC/dt=0 is further up the phaseplane
□
Moderate K -stable equilibrium (excitable; oscillatory decay): consumer
and resource persist and maintain constant densities through time
!
High K -unstable equilibrium (excitable; oscillations): cycles/ can reach
low densities periodically
!
Responses:
•
C:N ratio steadily increases --> top heavy
!
Low productivity -prone to "mean driven extinctions"
□
High productivity -prone to "variance instability" or "variance-
driven extinctions"
□
Lambda -declines (below 0) into oscillatory decay and then increases
linearly into oscillations with no return
!
Becomes less and less stable --> overshoot dynamics
!
Overall: Increasing Productivity (K)
•
--> suppression-stability tradeoff
•
How do we expect the dynamics of the system to change as we increase resource
carrying capacity (K)?
•
ISCN = -a / (N+N0)
!
ISNC = +fa / (N+N0)
!
Interaction strength: rate of flow of biomass (energy) per unit consumer per
unit of resource between consumer and resource
•
Very low attack rate (a) --> very weak IS (consumer does not exist)
!
Low C:N (only changes consumer isocline)
□
Low attack rate (a) --> low IS (stable equilibrium; non-excitable)
!
Moderate C:N
□
Moderate attack rate (a) --> moderate IS (stable equilibrium; oscillatory
decay)
!
High C:N (inverted biomass pyramid)
□
High attack rates (a) --> strong IS (cyclic dynamics)
!
Responses: (high growth rate + lag = instability)
•
As consumer-resource interaction strength increases, consumer-
resource interactions tend to become more top heavy (high C:N)
and less stable (more oscillatory) and therefore more prone to
extinction
□
As energy flow increases between consumer and its resource, the
interaction becomes more oscillatory (drives "runaway
consumption" or overshoot dynamics)
□
Given excitable dynamics then,
!
Principle of Interaction Strength:
•
dC/dt=0 at smaller densities of N
□
*see slide
□
Adding energy --> top heavy (C>N) --> instable
□
Increasing energy flux (K or a):
!
Summary: the influence of increased energy flux/interaction strength/resource
productivity -& the paradox of enrichment
•
How do we expect the dynamics of the system to change as we increase interaction
strength?
•
Some Model Experiments:
If high energy flow between a consumer and its resource tends to destabilize the
consumer resource interaction (excitable)
•
Then, anything that inhibits energy flow, by reducing resource productivity that is
accessible to C, or weakening C's interaction acts to stabilize the interaction against
runaway consumption
•
A Corollary to Consumer-Resource Interaction
Refugia (spatial heterogenity) --> when resource densities are low, resources
become inaccessible (type III functional response)
1)
Consumer interference --> as consumers attain higher densities (prey tend to be
at low densities) interference between consumers lowers attack rates
2)
Donor control --> consumers are given the "doomed surplus" but do not eat
healthy resources/prey (remove feedback; consumers are eating resource that
are not viable)
3)
All stabilizing features involve a reduction in energy flow to the consumer (prevents
too much consumer biomass) or weakens the consumers influence on the resource
•
Stabilizing Mechanisms in Consumer-Resource Theory:
Experiments and Field Results
http://www.youtube.com/watch?v=rZ7wv2LhynM
!
Subject: paramecium --> didinium (reduced medium and thereby changed
nutrient amounts)
○
K is ~1000
!
Oscillations cause extinction
!
Control:
○
K is reduced to 400
!
Reduced attack rates with methyl cellulose which made the water more
vicious and slowed interaction rates
!
Manipulation:
○
Excitable dynamics are stabilized (increased persistence) by weakening IS and
reducing K
○
Principle of Interaction Strength & Paradox of Enrichment (Luckinbill 1973)
•
Flow-through experiment
○
Subject: Algae --> rotifers
○
Increased resource productivity --> increase C (inflation)
○
C extinction
!
Stable dynamics
!
Oscillations
!
Collapse due to oscillations
!
Production moved through all 4 dynamic predictions:
○
*C density increased relative to N as predicted (top heavy)
○
Productivity & Stability (Fussmmann et al. Nature, 2000)
•
Homogenous case: rapid extinction due to strong overshoot and cycle
that collapses
!
Predatory mite were feeding on 6-spotted mite (that consumed oranges)
○
Heterogenous case (refuge): predator-prey interaction persisted longer
!
Still cyclic but now persisted
!
Reduced 'a' and 'K'
!
With patchy environment and reduced movement of predatory mite relative to
prey mites with vaseline and a fan (some oranges were covered) -->reduced
interaction rates or strength
○
As you add energy to a lag, you get an overshoot
!
Note: predator increases after prey increase (=lag)
○
Huffaker's mites: Spatial Lab Mirocosm
•
Experiments:
= resource concentration hypothesis (by entomological researchers)
!
Monocultures and insect outbreaks (e.g. Budworm on Balsam Fir cycles tend
to be greater in Balsam Fir monocultures) --> greater productivity of firs, K,
per unit area
○
Lynx are extremely mobile with high attack rates and hares are very
productive for their size, large cycles occur in this system
!
Interaction strength and productivity in nature:
○
Some examples:
•
Therefore, aquatic ecosystems have higher resource productivity and
interaction strength
!
Aquatic -small, more edible, high growth, high consumption rate
○
More variable (high CV) --> less stable in aquatic ecosystems
!
Therefore, aquatic ecosystems are more top heavy with more variable
dynamics
!
Herbivore: Plant Biomass -higher in aquatic than terrestrial
○
Aquatic vs. Terrestrial
•
Field Results: Principles of Interaction Strength/ Energy Flux or Paradox of Enrichment
Reading: Mittelbach, Ch.7 (pg. 125-126, 132-136, 145-146)
Interference Competition -when one species restricts another species access to
a limiting resource (aggression, territorial defense, occupying space)
1)
Exploitative Competition -when 2 species consumer the same resource base 2)
Two qualitative types:
•
Note: R is the resource (R* theory vs. N)
!
Food web flow diagram -details energy flow and quantity
○
C declines if R<R* (loss>growth) and increases if R>R* where R is the
realized resource density (R* is where dC/dt=0)
!
dC/dt = growth rate -loss rate = {faR/(R+R0) -m}C
!
Recall: Rosenweig-MacArthur Consumer-Resource
○
The best competitors reduces the resource to the lowest level (lowest R*)
and the other competitior (with higher R*) decreases at this level to
extinction
!
In other words, the best competitor has the lowest R* (the R* rule)
!
Coexistence could only occur under a common resource if they
had identical R*
□
Therefore, complete competitors cannot coexist
!
Tilman's R* equilibrium competition theory:
○
Tilman's R* Rule: Exploitative Competition Theory
•
Examine population growth rates in isolation of potential competitor (along;
determine R*s -make a prediction of winner) VS. population growth with
competitor (together)
○
Synedra (Rs* -nutrient level)
□
Asterionella (Ra* -nutrient level)
!
*Synedra has a lower Rs* -more efficient consumer
!
When placed in environment together, Synedra is the better competitior
(drives Asterionella to extinction via competitive exclusion)
!
Example: Tilman's Diatoms
○
Competition Experiments:
•
Argues that consumers are better competitors on different resources (e.g.
nitrogen and phosphorous) and differential ability to exploit different
resources could allow consumers to coexist
!
Resource Niche Differentiation
○
Another solution to competitive exclusion appears to be that species
differentiate the way they use resource, can be better at exploiting a
resource in specific space/habitats
!
Spatial Niche Differentiation
○
Tilman's R* Theory: How do you get coexistence?
•
*see slide
○
Large resource overlap -strong interspecific competition
○
Argument: competition drives divergence --> character displacement
!
Example of niche differentiation: organisms have adapted to specialize
on different aspects of their world. This type of divergence can create
rapid diversification (adaptive radiation), especially in isolated areas
!
Little resource overlap -weak interspecific competiton
○
Ex. Adaptive Radiation and Character Displacement in Darwin's finches (bill
depth)
○
Graphic Interpretation of Competition: Resource Utilization Curves
•
Interspecific Competition -the interaction between two species where the increased
abundance of any one species causes the population growth of the other species to decrease
A large number of phytoplankton use a limited number of nutrients and undergo
photosynthesis in a relatively unstructured environment
•
Water is often deficient in nutrients, competition ought to be strong
•
Hutchinson suggested that they may coexist because the environment is so variable in
time that competitive exclusion doesn’t have time to occur (=coexistence in time;
non-equilibrium idea)
•
C2 has lower R* so would win at equilibrium
○
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
Nearly neutral species are highly competitive (similar traits)
•
Temporal Niche Differentiation -The Paradox of the Plankton
Species with the lowest R* outcompetes the other species as it cannot survive on that
low level of resources
•
Tilman's R* Rule: Exploitative Competition Theory -An Equilibrium Perspective
With nearly neutral species (similar traits/ parameters but not identical)
•
The consumer (ex. C2) with the lower R* will win at equilibrium (can consume
resource to the lowest density)
•
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
So, although C2 has a lower R* (win at equilibrium), if R varied (fluctuated or
cycled) it can drive coexistence
○
Variations of R:
•
Armstrong & McGehee's Non-equilibrium coexistence:
There are pulses of strong mast every 2-5 years
○
Deer Mice (less active) and White Footed Mice (very active) consume oak mast
•
Metabolically slow
○
Low cost lifestyle
○
Can survive at low resource densities
○
Deer Mice:
•
Metabolically fast
○
High cost lifestyle
○
Has high growth rates at high resource densities
○
More reproductive input
○
White-footed Mice:
•
Metabolic cost vs. Body Size --> positive correlation
○
*Production -strong interactors
□
Also includes hare and lynx
□
White-footed --> very mobile, higher consumption rates
!
*Tolerance -weak interactors
□
Also includes hedgehogs
□
Deer mice --> slow moving, lower consumption rates, flexible (torpor)
!
Mice both have same body size with varying metabolic costs
○
Correlated traits drive this continuum: metabolic cost, movement, consumption
rates, metabolic flexibility
○
*Mammals: The Slow-Fast Metabolic Continuum (Production-Tolerance trade-off
continuum)
•
Weak mast years -Deer Mice win (much more stable)
○
Strong mast years -White-footed Mice win (much more variable)
○
Coexistence in Time:
•
Ex. Coexistence in Time: Sister Species and Trade-offs
There is no superorganism --> trade-offs
•
There are costs and benefits to adaptations
•
Variability in resources/conditions (space or time)1)
Species differentiation such that every species must be the best competitor on
some spatial or temporal scale
2)
To coexist:
•
*the role of trade-offs mediates the balancing of species
What enables coexistence?
Highly dispersive gets a "good" resource habitat first
!
Competitive species get there slower but win in long-term
!
E.g. colonizing plant species vs. competitive
!
Dispersal-Competition Trade-off
○
Highly productive animal takes advantage of good conditions/times
!
Tolerance animal does better during harsh times (climate, resources,
predators)
!
Production-Tolerance Trade-off
○
Specialist has higher attack rates on one species
!
Generalist has more prey
!
Specialist-Generalist Trade-off
○
Some trade-offs that can maintain diversity:
•
Competition, Trade-offs & Maintaining Diversity
Functional response
Numerical response
Consumer-Resource Interactions
Friday,*February*10,*2017
9:54*AM
Predator -prey
•
Host -parasite
•
Host -parasitoid
•
Herbivore -plant
•
Detritivore -detritus
•
Consumer-Resource Interactions:
Reading: Theory of Consumer-Resource Interactions .cdf (using C-R vs. C-N)
Type I -linear
•
Type II -saturating (curve to plateau)
•
Type III - S-shaped
•
Review: Functional Responses -per consumer ingestion or consumption rate (kg prey/ kg
C vs. Resource density)
Appears, most often show functional responses are Type II
•
Ingestion Rate: a*C*N/(N+N0)
○
'a' -max attack rate
○
N0 -1/2 saturation density
○
Ingestion rate vs. Density
•
Empirical Data:
Consumer population growth rate / consumer = eating rates per consumer (for type I-
III)
•
Numerical responses often are similar to functional responses suggesting population
growth respond as a fraction of what you eat
•
Functional to Numerical Response -"the population grows at a rate proportional to what it
eats"
N -plant biomass (resource)
•
C -herbivore consumer biomass
•
--> fecal loss (f as a fraction): (1-f)a*C*N/(N+N0)
○
--> maintenance cost: mC
○
<-- consumption or intake: a*C*N/(N+N0)
○
C:
•
--> consumption or intake: a*C*N/(N+N0)
○
--> r*N^2 /K
○
<-- rN
○
N:
•
dN/dt = rN(1-N)/K -a*C*N/(N+N0)
•
dC/dt = f*a*CN/(N+N0) -mC
•
A Consumer-Resource Model
= Rosenzweig-MacArthur consumer-resource model (bioenergetics)
Graphical analysis (phaseplane)i)
Consumer cannot persist
○
Stable equilibrium -non-excitable
○
Stabile equilibrium -excitable (oscillatory decay)
○
Cycles (excitable)
○
4 Quantatively Different Dynamical Outcomes from Isoclinesii)
+ relationship to consumer:resource biomass pyramids (e.g. top heavy)
How do the dynamics change as we increase productivity (K)?
○
How do the dynamics change as we increase interaction strength?
○
*interaction strength is related to functional and numerical response
○
Some model experiments:iii)
Some stabilizing factorsiv)
Lab and field resultsv)
Consumer-Resource Theory:
Consumer (C ) vs. Resource (N) Densities (*see slides)
•
i.e. given parameters values (r,K,a), then isocline is the combination of C & N
densities that imply N is not growing (dN/dt =0) --> population is not changing
in respect to time
○
C = 0 at 'K' of Resource (carrying capacity)
○
C = r(1-N/K)(N+N0) / a (red line on graph)
○
Which is dominating (resource or consumer)
!
If consumer is dominating (arrows above graph), resources are
decreasing
!
If resources are dominating (arrows below graph), resources are
increasing
!
Arrows on graph: at given density of C, N is increasing/decreasing
○
N-isocline --> dN/dt = 0
•
i.e. the combination of C & N densities that imply C is not growing
○
N = N0*m / (ea -m)
○
If growth rate = demands, population does not change
○
To the left --> little resources --> C declines (metabolic costs outweigh
resource availability)
○
To the right --> abundant resources --> C increases (a lot of resources for
metabolic costs)
○
C-isocline --> dC/dt = 0
•
Addition of the two isocline vectors
○
Already suggesting a cyclical dynamic
!
At dC/dt = 0 there is no vertical component (left)
!
At dN/dt=0 there is no horizontal component (up)
!
Red dot = equilibrium (arrows follow circular path around dot)
○
C vs Time
!
N vs Time
!
When plotted on same graph, densities oscillate
!
Solutions on the phaseplane can be interpreted as changes through time (time
series -densities vs. time)
○
Phaseplane: understanding the flows around the isoclines start to unfold how C and N
change with time
•
Graphical Analysis: Phaseplane
The consumer density is usually greater than the resource density --> top heavy
arrangement
•
Average biomass density ratio (C:N) >1
•
Cyclic dynamics (excitable/oscillating) -occurs whenever the consumer isocline
(dC/dt=0) lies to the left of the peak on the resource (dN/dt=0) isocline
1)
Overshooting
•
Over time, consumer density becomes lower than resource
•
Moderately top heavy
•
Stable equilibrium dynamics (excitable with oscillatory decay) -occurs whenever
consumer isocline (dC/dt=0) lies to the right of the peak on the resource isocline
(dN/dt=0), but not near N=K
2)
Resource > consumer --> at equilibrium
•
Bottom heavy
•
Stable equilibrium dynamics (non-excitable) -occurs whenever consumer isocline
(dC/dt=0) lies WELL to the right of the peak on the resource isocline (dN/dt=0),
relatively close to N=K
3)
Resource reaches K while consumer density declines over time
•
Bottom heavy (no C)
•
Resource goes to carrying capacity and consumer goes extinct4)
Qualitative Outcomes to this Model:
In each case, increasing the supply of nutrients or energy tends to destroy the steady
state. Thus man must be very careful in attempting to enrich an ecosystem in order to
increase its food yield. There is a real chance that such activity may result in
decimation of the food species that are wanted in greater abundance.”
•
As the system becomes more productive, consumer-resource interactions become less
stable (more excited or oscillatory) and therefore more prone to extinctions
•
Paradox of Enrichment:
Phaseplane shifted to left doesn’t reach dC/dt=0
□
Very low K (similar to low productivity) -consumer cannot exist
!
Phaseplane reaches dC/dt=0
□
Low K -stable equilibrium (non-excitable): consumer and resource
persist and maintain constant densities through time
!
dC/dt=0 is further up the phaseplane
□
Moderate K -stable equilibrium (excitable; oscillatory decay): consumer
and resource persist and maintain constant densities through time
!
High K -unstable equilibrium (excitable; oscillations): cycles/ can reach
low densities periodically
!
Responses:
•
C:N ratio steadily increases --> top heavy
!
Low productivity -prone to "mean driven extinctions"
□
High productivity -prone to "variance instability" or "variance-
driven extinctions"
□
Lambda -declines (below 0) into oscillatory decay and then increases
linearly into oscillations with no return
!
Becomes less and less stable --> overshoot dynamics
!
Overall: Increasing Productivity (K)
•
--> suppression-stability tradeoff
•
How do we expect the dynamics of the system to change as we increase resource
carrying capacity (K)?
•
ISCN = -a / (N+N0)
!
ISNC = +fa / (N+N0)
!
Interaction strength: rate of flow of biomass (energy) per unit consumer per
unit of resource between consumer and resource
•
Very low attack rate (a) --> very weak IS (consumer does not exist)
!
Low C:N (only changes consumer isocline)
□
Low attack rate (a) --> low IS (stable equilibrium; non-excitable)
!
Moderate C:N
□
Moderate attack rate (a) --> moderate IS (stable equilibrium; oscillatory
decay)
!
High C:N (inverted biomass pyramid)
□
High attack rates (a) --> strong IS (cyclic dynamics)
!
Responses: (high growth rate + lag = instability)
•
As consumer-resource interaction strength increases, consumer-
resource interactions tend to become more top heavy (high C:N)
and less stable (more oscillatory) and therefore more prone to
extinction
□
As energy flow increases between consumer and its resource, the
interaction becomes more oscillatory (drives "runaway
consumption" or overshoot dynamics)
□
Given excitable dynamics then,
!
Principle of Interaction Strength:
•
dC/dt=0 at smaller densities of N
□
*see slide
□
Adding energy --> top heavy (C>N) --> instable
□
Increasing energy flux (K or a):
!
Summary: the influence of increased energy flux/interaction strength/resource
productivity -& the paradox of enrichment
•
How do we expect the dynamics of the system to change as we increase interaction
strength?
•
Some Model Experiments:
If high energy flow between a consumer and its resource tends to destabilize the
consumer resource interaction (excitable)
•
Then, anything that inhibits energy flow, by reducing resource productivity that is
accessible to C, or weakening C's interaction acts to stabilize the interaction against
runaway consumption
•
A Corollary to Consumer-Resource Interaction
Refugia (spatial heterogenity) --> when resource densities are low, resources
become inaccessible (type III functional response)
1)
Consumer interference --> as consumers attain higher densities (prey tend to be
at low densities) interference between consumers lowers attack rates
2)
Donor control --> consumers are given the "doomed surplus" but do not eat
healthy resources/prey (remove feedback; consumers are eating resource that
are not viable)
3)
All stabilizing features involve a reduction in energy flow to the consumer (prevents
too much consumer biomass) or weakens the consumers influence on the resource
•
Stabilizing Mechanisms in Consumer-Resource Theory:
Experiments and Field Results
http://www.youtube.com/watch?v=rZ7wv2LhynM
!
Subject: paramecium --> didinium (reduced medium and thereby changed
nutrient amounts)
○
K is ~1000
!
Oscillations cause extinction
!
Control:
○
K is reduced to 400
!
Reduced attack rates with methyl cellulose which made the water more
vicious and slowed interaction rates
!
Manipulation:
○
Excitable dynamics are stabilized (increased persistence) by weakening IS and
reducing K
○
Principle of Interaction Strength & Paradox of Enrichment (Luckinbill 1973)
•
Flow-through experiment
○
Subject: Algae --> rotifers
○
Increased resource productivity --> increase C (inflation)
○
C extinction
!
Stable dynamics
!
Oscillations
!
Collapse due to oscillations
!
Production moved through all 4 dynamic predictions:
○
*C density increased relative to N as predicted (top heavy)
○
Productivity & Stability (Fussmmann et al. Nature, 2000)
•
Homogenous case: rapid extinction due to strong overshoot and cycle
that collapses
!
Predatory mite were feeding on 6-spotted mite (that consumed oranges)
○
Heterogenous case (refuge): predator-prey interaction persisted longer
!
Still cyclic but now persisted
!
Reduced 'a' and 'K'
!
With patchy environment and reduced movement of predatory mite relative to
prey mites with vaseline and a fan (some oranges were covered) -->reduced
interaction rates or strength
○
As you add energy to a lag, you get an overshoot
!
Note: predator increases after prey increase (=lag)
○
Huffaker's mites: Spatial Lab Mirocosm
•
Experiments:
= resource concentration hypothesis (by entomological researchers)
!
Monocultures and insect outbreaks (e.g. Budworm on Balsam Fir cycles tend
to be greater in Balsam Fir monocultures) --> greater productivity of firs, K,
per unit area
○
Lynx are extremely mobile with high attack rates and hares are very
productive for their size, large cycles occur in this system
!
Interaction strength and productivity in nature:
○
Some examples:
•
Therefore, aquatic ecosystems have higher resource productivity and
interaction strength
!
Aquatic -small, more edible, high growth, high consumption rate
○
More variable (high CV) --> less stable in aquatic ecosystems
!
Therefore, aquatic ecosystems are more top heavy with more variable
dynamics
!
Herbivore: Plant Biomass -higher in aquatic than terrestrial
○
Aquatic vs. Terrestrial
•
Field Results: Principles of Interaction Strength/ Energy Flux or Paradox of Enrichment
Reading: Mittelbach, Ch.7 (pg. 125-126, 132-136, 145-146)
Interference Competition -when one species restricts another species access to
a limiting resource (aggression, territorial defense, occupying space)
1)
Exploitative Competition -when 2 species consumer the same resource base 2)
Two qualitative types:
•
Note: R is the resource (R* theory vs. N)
!
Food web flow diagram -details energy flow and quantity
○
C declines if R<R* (loss>growth) and increases if R>R* where R is the
realized resource density (R* is where dC/dt=0)
!
dC/dt = growth rate -loss rate = {faR/(R+R0) -m}C
!
Recall: Rosenweig-MacArthur Consumer-Resource
○
The best competitors reduces the resource to the lowest level (lowest R*)
and the other competitior (with higher R*) decreases at this level to
extinction
!
In other words, the best competitor has the lowest R* (the R* rule)
!
Coexistence could only occur under a common resource if they
had identical R*
□
Therefore, complete competitors cannot coexist
!
Tilman's R* equilibrium competition theory:
○
Tilman's R* Rule: Exploitative Competition Theory
•
Examine population growth rates in isolation of potential competitor (along;
determine R*s -make a prediction of winner) VS. population growth with
competitor (together)
○
Synedra (Rs* -nutrient level)
□
Asterionella (Ra* -nutrient level)
!
*Synedra has a lower Rs* -more efficient consumer
!
When placed in environment together, Synedra is the better competitior
(drives Asterionella to extinction via competitive exclusion)
!
Example: Tilman's Diatoms
○
Competition Experiments:
•
Argues that consumers are better competitors on different resources (e.g.
nitrogen and phosphorous) and differential ability to exploit different
resources could allow consumers to coexist
!
Resource Niche Differentiation
○
Another solution to competitive exclusion appears to be that species
differentiate the way they use resource, can be better at exploiting a
resource in specific space/habitats
!
Spatial Niche Differentiation
○
Tilman's R* Theory: How do you get coexistence?
•
*see slide
○
Large resource overlap -strong interspecific competition
○
Argument: competition drives divergence --> character displacement
!
Example of niche differentiation: organisms have adapted to specialize
on different aspects of their world. This type of divergence can create
rapid diversification (adaptive radiation), especially in isolated areas
!
Little resource overlap -weak interspecific competiton
○
Ex. Adaptive Radiation and Character Displacement in Darwin's finches (bill
depth)
○
Graphic Interpretation of Competition: Resource Utilization Curves
•
Interspecific Competition -the interaction between two species where the increased
abundance of any one species causes the population growth of the other species to decrease
A large number of phytoplankton use a limited number of nutrients and undergo
photosynthesis in a relatively unstructured environment
•
Water is often deficient in nutrients, competition ought to be strong
•
Hutchinson suggested that they may coexist because the environment is so variable in
time that competitive exclusion doesn’t have time to occur (=coexistence in time;
non-equilibrium idea)
•
C2 has lower R* so would win at equilibrium
○
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
Nearly neutral species are highly competitive (similar traits)
•
Temporal Niche Differentiation -The Paradox of the Plankton
Species with the lowest R* outcompetes the other species as it cannot survive on that
low level of resources
•
Tilman's R* Rule: Exploitative Competition Theory -An Equilibrium Perspective
With nearly neutral species (similar traits/ parameters but not identical)
•
The consumer (ex. C2) with the lower R* will win at equilibrium (can consume
resource to the lowest density)
•
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
So, although C2 has a lower R* (win at equilibrium), if R varied (fluctuated or
cycled) it can drive coexistence
○
Variations of R:
•
Armstrong & McGehee's Non-equilibrium coexistence:
There are pulses of strong mast every 2-5 years
○
Deer Mice (less active) and White Footed Mice (very active) consume oak mast
•
Metabolically slow
○
Low cost lifestyle
○
Can survive at low resource densities
○
Deer Mice:
•
Metabolically fast
○
High cost lifestyle
○
Has high growth rates at high resource densities
○
More reproductive input
○
White-footed Mice:
•
Metabolic cost vs. Body Size --> positive correlation
○
*Production -strong interactors
□
Also includes hare and lynx
□
White-footed --> very mobile, higher consumption rates
!
*Tolerance -weak interactors
□
Also includes hedgehogs
□
Deer mice --> slow moving, lower consumption rates, flexible (torpor)
!
Mice both have same body size with varying metabolic costs
○
Correlated traits drive this continuum: metabolic cost, movement, consumption
rates, metabolic flexibility
○
*Mammals: The Slow-Fast Metabolic Continuum (Production-Tolerance trade-off
continuum)
•
Weak mast years -Deer Mice win (much more stable)
○
Strong mast years -White-footed Mice win (much more variable)
○
Coexistence in Time:
•
Ex. Coexistence in Time: Sister Species and Trade-offs
There is no superorganism --> trade-offs
•
There are costs and benefits to adaptations
•
Variability in resources/conditions (space or time)1)
Species differentiation such that every species must be the best competitor on
some spatial or temporal scale
2)
To coexist:
•
*the role of trade-offs mediates the balancing of species
What enables coexistence?
Highly dispersive gets a "good" resource habitat first
!
Competitive species get there slower but win in long-term
!
E.g. colonizing plant species vs. competitive
!
Dispersal-Competition Trade-off
○
Highly productive animal takes advantage of good conditions/times
!
Tolerance animal does better during harsh times (climate, resources,
predators)
!
Production-Tolerance Trade-off
○
Specialist has higher attack rates on one species
!
Generalist has more prey
!
Specialist-Generalist Trade-off
○
Some trade-offs that can maintain diversity:
•
Competition, Trade-offs & Maintaining Diversity
Functional response
Numerical response
Consumer-Resource Interactions
Friday,*February*10,*2017 9:54*AM
Predator -prey
•
Host -parasite
•
Host -parasitoid
•
Herbivore -plant
•
Detritivore -detritus
•
Consumer-Resource Interactions:
Reading: Theory of Consumer-Resource Interactions .cdf (using C-R vs. C-N)
Type I -linear
•
Type II -saturating (curve to plateau)
•
Type III - S-shaped
•
Review: Functional Responses -per consumer ingestion or consumption rate (kg prey/ kg
C vs. Resource density)
Appears, most often show functional responses are Type II
•
Ingestion Rate: a*C*N/(N+N0)
○
'a' -max attack rate
○
N0 -1/2 saturation density
○
Ingestion rate vs. Density
•
Empirical Data:
Consumer population growth rate / consumer = eating rates per consumer (for type I-
III)
•
Numerical responses often are similar to functional responses suggesting population
growth respond as a fraction of what you eat
•
Functional to Numerical Response -"the population grows at a rate proportional to what it
eats"
N -plant biomass (resource)
•
C -herbivore consumer biomass
•
--> fecal loss (f as a fraction): (1-f)a*C*N/(N+N0)
○
--> maintenance cost: mC
○
<-- consumption or intake: a*C*N/(N+N0)
○
C:
•
--> consumption or intake: a*C*N/(N+N0)
○
--> r*N^2 /K
○
<-- rN
○
N:
•
dN/dt = rN(1-N)/K -a*C*N/(N+N0)
•
dC/dt = f*a*CN/(N+N0) -mC
•
A Consumer-Resource Model
= Rosenzweig-MacArthur consumer-resource model (bioenergetics)
Graphical analysis (phaseplane)
i)
Consumer cannot persist
○
Stable equilibrium -non-excitable
○
Stabile equilibrium -excitable (oscillatory decay)
○
Cycles (excitable)
○
4 Quantatively Different Dynamical Outcomes from Isoclines
ii)
+ relationship to consumer:resource biomass pyramids (e.g. top heavy)
How do the dynamics change as we increase productivity (K)?
○
How do the dynamics change as we increase interaction strength?
○
*interaction strength is related to functional and numerical response
○
Some model experiments:
iii)
Some stabilizing factors
iv)
Lab and field results
v)
Consumer-Resource Theory:
Consumer (C ) vs. Resource (N) Densities (*see slides)
•
i.e. given parameters values (r,K,a), then isocline is the combination of C & N
densities that imply N is not growing (dN/dt =0) --> population is not changing
in respect to time
○
C = 0 at 'K' of Resource (carrying capacity)
○
C = r(1-N/K)(N+N0) / a (red line on graph)
○
Which is dominating (resource or consumer)
!
If consumer is dominating (arrows above graph), resources are
decreasing
!
If resources are dominating (arrows below graph), resources are
increasing
!
Arrows on graph: at given density of C, N is increasing/decreasing
○
N-isocline --> dN/dt = 0
•
i.e. the combination of C & N densities that imply C is not growing
○
N = N0*m / (ea -m)
○
If growth rate = demands, population does not change
○
To the left --> little resources --> C declines (metabolic costs outweigh
resource availability)
○
To the right --> abundant resources --> C increases (a lot of resources for
metabolic costs)
○
C-isocline --> dC/dt = 0
•
Addition of the two isocline vectors
○
Already suggesting a cyclical dynamic
!
At dC/dt = 0 there is no vertical component (left)
!
At dN/dt=0 there is no horizontal component (up)
!
Red dot = equilibrium (arrows follow circular path around dot)
○
C vs Time
!
N vs Time
!
When plotted on same graph, densities oscillate
!
Solutions on the phaseplane can be interpreted as changes through time (time
series -densities vs. time)
○
Phaseplane: understanding the flows around the isoclines start to unfold how C and N
change with time
•
Graphical Analysis: Phaseplane
The consumer density is usually greater than the resource density --> top heavy
arrangement
•
Average biomass density ratio (C:N) >1
•
Cyclic dynamics (excitable/oscillating) -occurs whenever the consumer isocline
(dC/dt=0) lies to the left of the peak on the resource (dN/dt=0) isocline
1)
Overshooting
•
Over time, consumer density becomes lower than resource
•
Moderately top heavy
•
Stable equilibrium dynamics (excitable with oscillatory decay) -occurs whenever
consumer isocline (dC/dt=0) lies to the right of the peak on the resource isocline
(dN/dt=0), but not near N=K
2)
Resource > consumer --> at equilibrium
•
Bottom heavy
•
Stable equilibrium dynamics (non-excitable) -occurs whenever consumer isocline
(dC/dt=0) lies WELL to the right of the peak on the resource isocline (dN/dt=0),
relatively close to N=K
3)
Resource reaches K while consumer density declines over time
•
Bottom heavy (no C)
•
Resource goes to carrying capacity and consumer goes extinct4)
Qualitative Outcomes to this Model:
In each case, increasing the supply of nutrients or energy tends to destroy the steady
state. Thus man must be very careful in attempting to enrich an ecosystem in order to
increase its food yield. There is a real chance that such activity may result in
decimation of the food species that are wanted in greater abundance.”
•
As the system becomes more productive, consumer-resource interactions become less
stable (more excited or oscillatory) and therefore more prone to extinctions
•
Paradox of Enrichment:
Phaseplane shifted to left doesn’t reach dC/dt=0
□
Very low K (similar to low productivity) -consumer cannot exist
!
Phaseplane reaches dC/dt=0
□
Low K -stable equilibrium (non-excitable): consumer and resource
persist and maintain constant densities through time
!
dC/dt=0 is further up the phaseplane
□
Moderate K -stable equilibrium (excitable; oscillatory decay): consumer
and resource persist and maintain constant densities through time
!
High K -unstable equilibrium (excitable; oscillations): cycles/ can reach
low densities periodically
!
Responses:
•
C:N ratio steadily increases --> top heavy
!
Low productivity -prone to "mean driven extinctions"
□
High productivity -prone to "variance instability" or "variance-
driven extinctions"
□
Lambda -declines (below 0) into oscillatory decay and then increases
linearly into oscillations with no return
!
Becomes less and less stable --> overshoot dynamics
!
Overall: Increasing Productivity (K)
•
--> suppression-stability tradeoff
•
How do we expect the dynamics of the system to change as we increase resource
carrying capacity (K)?
•
ISCN = -a / (N+N0)
!
ISNC = +fa / (N+N0)
!
Interaction strength: rate of flow of biomass (energy) per unit consumer per
unit of resource between consumer and resource
•
Very low attack rate (a) --> very weak IS (consumer does not exist)
!
Low C:N (only changes consumer isocline)
□
Low attack rate (a) --> low IS (stable equilibrium; non-excitable)
!
Moderate C:N
□
Moderate attack rate (a) --> moderate IS (stable equilibrium; oscillatory
decay)
!
High C:N (inverted biomass pyramid)
□
High attack rates (a) --> strong IS (cyclic dynamics)
!
Responses: (high growth rate + lag = instability)
•
As consumer-resource interaction strength increases, consumer-
resource interactions tend to become more top heavy (high C:N)
and less stable (more oscillatory) and therefore more prone to
extinction
□
As energy flow increases between consumer and its resource, the
interaction becomes more oscillatory (drives "runaway
consumption" or overshoot dynamics)
□
Given excitable dynamics then,
!
Principle of Interaction Strength:
•
dC/dt=0 at smaller densities of N
□
*see slide
□
Adding energy --> top heavy (C>N) --> instable
□
Increasing energy flux (K or a):
!
Summary: the influence of increased energy flux/interaction strength/resource
productivity -& the paradox of enrichment
•
How do we expect the dynamics of the system to change as we increase interaction
strength?
•
Some Model Experiments:
If high energy flow between a consumer and its resource tends to destabilize the
consumer resource interaction (excitable)
•
Then, anything that inhibits energy flow, by reducing resource productivity that is
accessible to C, or weakening C's interaction acts to stabilize the interaction against
runaway consumption
•
A Corollary to Consumer-Resource Interaction
Refugia (spatial heterogenity) --> when resource densities are low, resources
become inaccessible (type III functional response)
1)
Consumer interference --> as consumers attain higher densities (prey tend to be
at low densities) interference between consumers lowers attack rates
2)
Donor control --> consumers are given the "doomed surplus" but do not eat
healthy resources/prey (remove feedback; consumers are eating resource that
are not viable)
3)
All stabilizing features involve a reduction in energy flow to the consumer (prevents
too much consumer biomass) or weakens the consumers influence on the resource
•
Stabilizing Mechanisms in Consumer-Resource Theory:
Experiments and Field Results
http://www.youtube.com/watch?v=rZ7wv2LhynM
!
Subject: paramecium --> didinium (reduced medium and thereby changed
nutrient amounts)
○
K is ~1000
!
Oscillations cause extinction
!
Control:
○
K is reduced to 400
!
Reduced attack rates with methyl cellulose which made the water more
vicious and slowed interaction rates
!
Manipulation:
○
Excitable dynamics are stabilized (increased persistence) by weakening IS and
reducing K
○
Principle of Interaction Strength & Paradox of Enrichment (Luckinbill 1973)
•
Flow-through experiment
○
Subject: Algae --> rotifers
○
Increased resource productivity --> increase C (inflation)
○
C extinction
!
Stable dynamics
!
Oscillations
!
Collapse due to oscillations
!
Production moved through all 4 dynamic predictions:
○
*C density increased relative to N as predicted (top heavy)
○
Productivity & Stability (Fussmmann et al. Nature, 2000)
•
Homogenous case: rapid extinction due to strong overshoot and cycle
that collapses
!
Predatory mite were feeding on 6-spotted mite (that consumed oranges)
○
Heterogenous case (refuge): predator-prey interaction persisted longer
!
Still cyclic but now persisted
!
Reduced 'a' and 'K'
!
With patchy environment and reduced movement of predatory mite relative to
prey mites with vaseline and a fan (some oranges were covered) -->reduced
interaction rates or strength
○
As you add energy to a lag, you get an overshoot
!
Note: predator increases after prey increase (=lag)
○
Huffaker's mites: Spatial Lab Mirocosm
•
Experiments:
= resource concentration hypothesis (by entomological researchers)
!
Monocultures and insect outbreaks (e.g. Budworm on Balsam Fir cycles tend
to be greater in Balsam Fir monocultures) --> greater productivity of firs, K,
per unit area
○
Lynx are extremely mobile with high attack rates and hares are very
productive for their size, large cycles occur in this system
!
Interaction strength and productivity in nature:
○
Some examples:
•
Therefore, aquatic ecosystems have higher resource productivity and
interaction strength
!
Aquatic -small, more edible, high growth, high consumption rate
○
More variable (high CV) --> less stable in aquatic ecosystems
!
Therefore, aquatic ecosystems are more top heavy with more variable
dynamics
!
Herbivore: Plant Biomass -higher in aquatic than terrestrial
○
Aquatic vs. Terrestrial
•
Field Results: Principles of Interaction Strength/ Energy Flux or Paradox of Enrichment
Reading: Mittelbach, Ch.7 (pg. 125-126, 132-136, 145-146)
Interference Competition -when one species restricts another species access to
a limiting resource (aggression, territorial defense, occupying space)
1)
Exploitative Competition -when 2 species consumer the same resource base 2)
Two qualitative types:
•
Note: R is the resource (R* theory vs. N)
!
Food web flow diagram -details energy flow and quantity
○
C declines if R<R* (loss>growth) and increases if R>R* where R is the
realized resource density (R* is where dC/dt=0)
!
dC/dt = growth rate -loss rate = {faR/(R+R0) -m}C
!
Recall: Rosenweig-MacArthur Consumer-Resource
○
The best competitors reduces the resource to the lowest level (lowest R*)
and the other competitior (with higher R*) decreases at this level to
extinction
!
In other words, the best competitor has the lowest R* (the R* rule)
!
Coexistence could only occur under a common resource if they
had identical R*
□
Therefore, complete competitors cannot coexist
!
Tilman's R* equilibrium competition theory:
○
Tilman's R* Rule: Exploitative Competition Theory
•
Examine population growth rates in isolation of potential competitor (along;
determine R*s -make a prediction of winner) VS. population growth with
competitor (together)
○
Synedra (Rs* -nutrient level)
□
Asterionella (Ra* -nutrient level)
!
*Synedra has a lower Rs* -more efficient consumer
!
When placed in environment together, Synedra is the better competitior
(drives Asterionella to extinction via competitive exclusion)
!
Example: Tilman's Diatoms
○
Competition Experiments:
•
Argues that consumers are better competitors on different resources (e.g.
nitrogen and phosphorous) and differential ability to exploit different
resources could allow consumers to coexist
!
Resource Niche Differentiation
○
Another solution to competitive exclusion appears to be that species
differentiate the way they use resource, can be better at exploiting a
resource in specific space/habitats
!
Spatial Niche Differentiation
○
Tilman's R* Theory: How do you get coexistence?
•
*see slide
○
Large resource overlap -strong interspecific competition
○
Argument: competition drives divergence --> character displacement
!
Example of niche differentiation: organisms have adapted to specialize
on different aspects of their world. This type of divergence can create
rapid diversification (adaptive radiation), especially in isolated areas
!
Little resource overlap -weak interspecific competiton
○
Ex. Adaptive Radiation and Character Displacement in Darwin's finches (bill
depth)
○
Graphic Interpretation of Competition: Resource Utilization Curves
•
Interspecific Competition -the interaction between two species where the increased
abundance of any one species causes the population growth of the other species to decrease
A large number of phytoplankton use a limited number of nutrients and undergo
photosynthesis in a relatively unstructured environment
•
Water is often deficient in nutrients, competition ought to be strong
•
Hutchinson suggested that they may coexist because the environment is so variable in
time that competitive exclusion doesn’t have time to occur (=coexistence in time;
non-equilibrium idea)
•
C2 has lower R* so would win at equilibrium
○
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
Nearly neutral species are highly competitive (similar traits)
•
Temporal Niche Differentiation -The Paradox of the Plankton
Species with the lowest R* outcompetes the other species as it cannot survive on that
low level of resources
•
Tilman's R* Rule: Exploitative Competition Theory -An Equilibrium Perspective
With nearly neutral species (similar traits/ parameters but not identical)
•
The consumer (ex. C2) with the lower R* will win at equilibrium (can consume
resource to the lowest density)
•
At low R, C1 decreases less
○
At high R, C2 increases more
○
Each has a relative advantage at some point in time and this can drive
coexistence in a fluctuating environment
○
So, although C2 has a lower R* (win at equilibrium), if R varied (fluctuated or
cycled) it can drive coexistence
○
Variations of R:
•
Armstrong & McGehee's Non-equilibrium coexistence:
There are pulses of strong mast every 2-5 years
○
Deer Mice (less active) and White Footed Mice (very active) consume oak mast
•
Metabolically slow
○
Low cost lifestyle
○
Can survive at low resource densities
○
Deer Mice:
•
Metabolically fast
○
High cost lifestyle
○
Has high growth rates at high resource densities
○
More reproductive input
○
White-footed Mice:
•
Metabolic cost vs. Body Size --> positive correlation
○
*Production -strong interactors
□
Also includes hare and lynx
□
White-footed --> very mobile, higher consumption rates
!
*Tolerance -weak interactors
□
Also includes hedgehogs
□
Deer mice --> slow moving, lower consumption rates, flexible (torpor)
!
Mice both have same body size with varying metabolic costs
○
Correlated traits drive this continuum: metabolic cost, movement, consumption
rates, metabolic flexibility
○
*Mammals: The Slow-Fast Metabolic Continuum (Production-Tolerance trade-off
continuum)
•
Weak mast years -Deer Mice win (much more stable)
○
Strong mast years -White-footed Mice win (much more variable)
○
Coexistence in Time:
•
Ex. Coexistence in Time: Sister Species and Trade-offs
There is no superorganism --> trade-offs
•
There are costs and benefits to adaptations
•
Variability in resources/conditions (space or time)1)
Species differentiation such that every species must be the best competitor on
some spatial or temporal scale
2)
To coexist:
•
*the role of trade-offs mediates the balancing of species
What enables coexistence?
Highly dispersive gets a "good" resource habitat first
!
Competitive species get there slower but win in long-term
!
E.g. colonizing plant species vs. competitive
!
Dispersal-Competition Trade-off
○
Highly productive animal takes advantage of good conditions/times
!
Tolerance animal does better during harsh times (climate, resources,
predators)
!
Production-Tolerance Trade-off
○
Specialist has higher attack rates on one species
!
Generalist has more prey
!
Specialist-Generalist Trade-off
○
Some trade-offs that can maintain diversity:
•
Competition, Trade-offs & Maintaining Diversity
Functional response
Numerical response
Consumer-Resource Interactions
Friday,*February*10,*2017 9:54*AM