resource competition among >2 species one resource –species with lowest r * excludes all others...
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Resource competition among >2 species
• One resource– species with lowest R* excludes all others
– example: species 1 excludes all others
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Resource competition among >2 species
• Two resources, essential• Constant, homogeneous environment• Two resources - two coexisting species
at equilibrium– which two species depends on resource
ratios– each species is best competitor for a
particular ratio of resources
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R1
R2 sp.1
sp.2
sp.3
sp.4
1 & 21
2
3
2 & 3
3& 4
4
12
23
43
Resource competition, >2 species
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New effect: spatial variation
• Suppose resource ratios vary locally– natural heterogeneity in soil nutrients– consequences for coexistence?
• When there is local spatial variation in resource ratios, >2 species can coexist – with local spatial segregation (patchiness)– More species than resources
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R1
R2 sp.1
sp.2
sp.3
sp.4
12
23
43
1, 2, 3, & 4
Variation in resource ratios
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Spatial variation• Local variation fosters diversity• More species than resources possible• Dependent on extent of variation• Plant communities
– often 100’s or 1000’s species– only about 12 essential resources– often patchy
• Variance in Resource Ratios Hypothesis (VRR)
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What is the effect of nutrient enrichment?
• Relationship of diversity & productivity• Unimodal vs. Monotonic• Mechanisms producing relationships
– Unimodal– particularly decrease in diversity with
productivity
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R1
R2sp.1
sp.2
sp.3
sp.4
12
23
43
1, 2, 3, & 4
2 & 3
4 only1 only
Enrichment and coexistence
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Nutrient enrichment• Increase all resources uniformly
– local variation in resource ratios allows coexistence of fewer species
• Increase one resource– necessarily makes resource ratios more extreme– raises, then lowers number of coexisting species
• Assumes resources increase without increasing variation
• “Paradox of enrichment” – enrichment = reduced diversity
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Switching resources• Does VRR predict coexistence of many
species on 2 switching resources?– species don’t specialize on ratios– each species consumes one resource or the other
only
• At equilibrium there are 2 species, each consuming and limited by one resourse – Fundamental difference between animal and plant
communities
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R1
R2
sp.1
sp.2
sp.3
1
4
1 & 4sp.4
Switching resources
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Plants vs. Animals• Plants use essential resources• VRR predicts high species:resources
ratio• Animals use switching resources• Theory predicts species:resources ratio
= 1
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Coexistence and evolution• Competitive coevolution
– 2 spp. competing for 1 resource cannot coexist– if individuals vary in resource use– if that variation is heritable– competition creates selection
• May select for increasing efficiency– selection for better resource use (lower R* )– a “race” to be most efficient– end result is still exclusion
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Coexistence and evolution• Competition may select for divergence in
resource use– individuals exploiting an alternative resource
favored (not affected by competition)– alternative resources could be different spatially,
temporally, in size– for substitutable or switching resources– evolution of divergence may avoid exclusion
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Example: Divergence in prey size
size of prey
freq
. of
use
size of prey
freq
. of
use
selection against
time
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Evolution of divergence in resource use
R1
R2
sp. 1
sp. 2
unstable
sp. 2
sp. 1
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Evolution of divergence in resource
use
R1
R2 sp. 1
sp. 2
unstable
R2 sp. 1
sp. 2
stable
R2 sp. 1
sp. 2
stable
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Competitive character displacement
• Competition selects for divergence in a morphological feature– presumably results in divergence of
resource use– often held to be the best evidence for the
importance of competition– Example: Sitta nuthatches
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Nuthatches
– Example: Sitta nuthatches– Asia & Europe– Ranges include regions of allopatry (no
contact)– also regions of sympatry (co-occur)– Sitta neurenmayer (Europe)– Sitta tephronata (Asia)– Sympatry in Iran
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Nuthatches
• Bill size– related to prey size– data suggest character displacement on bill
size• S. neurenmeyer S.
tephronta• Allopat. 25 mm 25
mm• Sympat. 22 mm 28 mm
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Prediction of character displacementbi
ll le
ngth
(m
m)
site (longitude)
S. tephronata
S. neurenmayer
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Actual pattern (Grant 1972)bi
ll le
ngth
(m
m)
site (longitude)
S. tephronata
S. neurenmayer
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Nuthatches
• No shift in cline of bill size when region of sympatry is reached
• Bill sizes vary geographically in a continuous fashion
• Not much evidence for character displacement
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Hydrobia snails
• intertidal mud snails– particle feeders (diatoms, sediment)
• Allopatry– H. ventricosa mean length = 3.1 mm– H. ulvae mean length = 3.3 mm
• Sympatry– H. ventricosa mean length = 2.8 mm– H. ulvae mean length = 4.5 mm
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Hydrobia snailsQuestions
• Character displacement?• Competition for food particles?• Levinton - does particle size affect
growth?– larger species does best on larger
particles?• Result: No difference in growth for
different particle sizes
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Hydrobia snails: More questions
• H. ulvae & H. ventricosa sympatric in lagoons• H. ulvae alone in intertidal• Lagoon H. ulvae
– alone … 1.2 X larger than intertidal H. ulvae– w/ H. ventricosa … 1.4 X larger than intertidal H.
ulvae
• size difference due to physical environment?• lagoons: low reproduction, high growth
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Character displacement• Classic cases of character displacement now
questioned• Probably not a widespread phenomenon• Morphology (size) presumed related to resource
use• Competition presumed to be the driving force• Examples of size differences reducing
competition?
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Caribbean AnolisPacala & Roughgarden 1985
• St. Maarten• A. gingivinus
– SVL = 41 mm• A. wattsi
– SVL = 38 mm
• St. Eustatius• A. bimaculatus
– SVL = 53 mm• A. wattsi
– SVL = 40 mm
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Caribbean Anolis
• Predict less competition on St. Eustatius
• Note: size strongly correlated with prey size
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Experiment
60 Ag100 Aw
60 Ag100 Aw
60 Ag 60 Ab100 Aw
60 Ab100 Aw
60 Ab
60 Ag 60 Ab
St. Maarten St. Eustatius
12 X 12 m enclosures; fenced 1.5 m; clear lizards
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Caribbean Anolis
• St. Maarten• A. gingivinus + A. wattsi
– less food in stomach– lower growth rate (0.5X)– perch height higher (2X)
• compared to A. gingivinus alone
• Interspecific effect strong
• St. Eustatius• A. bimaculatus + A. wattsi
– same amount in stomach– same growth rate– same perch height
• compared to A. bimaculatus alone
• Interspecific effect absent
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Alternative interpretation• Suppose competition is absent on St. Eustatius
– large resource base, abundant food– predators reduce density
• A. bimaculatus enclosures– escapes occurred over time– density: 60 45 30 lizards– 1 mo 2 mo– as density drops growth increases; competition
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Conclusion
• Size difference reduced competition• One case, but it shows this effect is possible• Authors do NOT claim size difference evolved
due to competition• Has not established that size would evolve in
response to competition
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Morphological evolution & competition (Schluter 1994)
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Sticklebacks
• species complex• extreme body forms
– limnetic - feed on plankton (e.g., Daphnia)– benthic - feed on benthic invertebrates
Representative limnetic (top) and benthic (bottom) stickleback from Lake Enos in British Columbia, Canada. Click to enlarge. Posted with permission from Paul J. B. Hart and Andrew B. Gill, "Evolution of Foraging Behaviour int the threespine stickleback," in The Evolutionary Biology of the Threespine Stickleback, eds. Michael A. Bell and Susan A. Foster, (Oxford: Oxford University Press), 1994, p. 211. © Oxford University Press
see also Robinson & Wilson 1994
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Sticklebacks
• Morphological intermediates exist• 1 sp. in a lake -- typically intermediate
morph• 2 spp. in a lake -- typically 2 morphs• Morphology is related to feeding
efficiency and growth• Hypothesis: evolved morphological
divergence due to competition (Character displacement)
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Experiment• 23 X 23 m ponds• Target species intermediate in morphology• produced by hybridization
Morphology
intermediate X benthic
intermediate X intermediate
intermediate X limnetic
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Hypothesis• Competition with a limnetic will have greatest
effect on survival and growth of forms morphologically similar to limnetic
Morphology
LimneticTarget
Morphology
LimneticTarget
time
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Experiment• Hybrids add variation on which selection
can work
Morphology
intermediate X benthic
intermediate X intermediate
intermediate X limnetic
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Implication
• If hypothesis is supported, selection for character divergence is occurring via competition
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Experiment
Experimental1800 target1200 limnetic
Control1800 target X 2 ponds
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Data collection• 3 months• Collect fish, measure Target• Growth rate reduced by density
– competition occurs• Regression of growth vs. morphology• Slope = growth differential between
more benthic and more limnetic
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Results
I x B I x I I x L
Gro
wth Control
Competitor
morphology
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Results• Growth differential
– significant for 1 experimental group– nearly so for a 2nd experimental group– clearly not significant for both controls
• Survival differential– some evidence for an effect in 1 pond
• Target individuals with limnetic morphology fare worst
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Conclusions• Experimental evidence for character
displacement• Caveats:
– pseudoreplication – statistical weakness
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Lake whitefish Coregonus lavaretus
dwarf, limnetic
benthic
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Null models in community ecology
• Experiments– show that a process occurs– may show it can cause effects on distribution,
abundance, fitness of a limited set of species– Does that process structure the community as a
whole?– experiments rarely can test that
• If interspecific competition is important, what patterns would be predicted for communities?
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Community patterns
• Competition favors differences in resource use among co-occurring species
• Predict: co-occurring species should be more different in resource use than expected if species were placed together randomly.
• Should be present across similar species within a community
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G. E. Hutchinson • Co-occurring European Corixids• Body lengths – ratio of larger to
smaller tended to be >1.3• Morphology as a surrogate for
resource use• Origin of idea of limiting
similarity
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Morphological pattern
• Predict: co-occurring species should be more different in morphology than expected if species were placed together randomly.
• "Community-wide character displacement"• How do you tell?• Null models or Neutral models of communities• Morin 98-103; Chase & Leibold 117-122
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Statistical Null hypotheses• Hypothesis of only chance affecting outcome• e.g., c2 for mendelian assortment
– coat color… Red White Roan– RR rr Rr
• Cross two Roan: Rr x Rr• Expect: RR = 0.25; Rr = 0.50; rr = 0.25• observe: RR = 0.26; Rr = 0.38; rr = 0.36• c2 = 7.76, P<0.05 … significant departure from
(null) expectation
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Statistical Null hypotheses• Expected: assumption of random sampling of
alleles• P<0.05: results deviating as far (or farther) than
observed expected <5% of the times if only random processes are involved
• conclude: some non-random process is structuring alleles at this locus
• Same general pattern in community ecology, but the model and math are more complex
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Example – Dytiscid beetles(Juliano & Lawton 1990)
• 28 species, Northern England• 9 different sites have 8 to 16 species• interspecific variation in size and shape• Are co-occurring species more different in
morphology than expected?
Hygrotus inaequalis
Hyphydrus ovatus
Hydroporus planus
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Issues for null models• What is the character of interest?
– Resource use– Morphology
• one variable• many variables• correlation of variables
– Co-occurrence (do pairs of species co-occur less often than expected … “forbidden combinations”)
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Issues for null models• What is the source pool of species?
– Islands• Mainland fauna• All species on similar islands
–Limits of source pool• Taxonomic• Geographic• Trophic
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Issues for null models
• What is the source pool of species?–Real species (discrete values)
• Randomization tests–Statistical distributions (continuous)
• Monte Carlo methods; simulations
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Issues for null models• Identifying the assemblage present
–presence/absence–abundance
• rare species may transients, not integrated into the community
• rarity may be a result of inappropriate morphology or resource use
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Issues for null models• Test statistic – measure of differences
– Size ratios (Univariate only)– Morphological nearest neighbor distance– Minimum spanning tree
• Mean vs. Variation– predict mean difference larger than expected– predict variation of difference smaller than
expected (regularity of species spacing)– combination
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Issues for null models
• Constraints on randomization– Stratify by other factors, e.g., genera within
families– Overall distribution – widespread species more
likely to be included– Dispersal ability – good dispersers more likely
to be included
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Source pool : The narcissus effect• Colwell & Winkler 1984• What if assemblages at all locations are affected
by competition– morphologies are more distinct than expected– randomly draw real species … that effect is
incorporated into randomly drawn assemblages– real assemblages do not differ from randomly drawn
because both include the effect of competition on morphology
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Source pool issues: The narcissus effect• Solution?• Synthetic species (unlike any real species, but
within the range of variation)• Draw from continuous distributions of
morphological variables (match discrete distributions)
size
# s
pe
cie
s
size
# s
pe
cie
s
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Dytiscid morphology• length, width, depth, head width
– correlated in real species
• for real species, choose at random, and allocate to community– each species brings correlated morphological
measurements
• Cannot simply choose length, width, depth, head– omits correlation structure
• Canonical discriminant function– produces uncorrelated variables (up to 4)– choose canonical variates
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Dytiscid beetles
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Test: randomization• real community with S species
– calculate nearest neighbor distance (NND) in morphological space for
all species– get mean NND and SD NND
• draw S species from pool– calculate NND in morphological space for all species– get mean NND and SD NND
• Repeat many (500 or 1000) times• Test stat [Mean NND – SD NND] =D• Is real D large compared to those drawn at random?
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Test: Monte Carlo
• real community with S species– calculate nearest neighbor distance (NND) in morphological
space for all species– get mean NND and SD NND
• draw S species from distributions of Canonical functions– calculate NND in morphological space for all species– get mean NND and SD NND
• Repeat many (500 or 1000) times• Test stat [Mean NND – SD NND] =D• Is real D large compared to those drawn at random?
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Test statistic• Reject H0 if observed >95% of all others• Result …For one site, there was a significant pattern
of large mean NND and large D, but not of small SD NND
• Species at one site are more dissimilar than expected by chance– and given average dissimilarity, the are less variable than
expected by chance (D)• using synthetic species (vs. real) null hypothesis is
rejected slightly more frequently (narcissus effect)
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Null distribution and real
communties
Real species
Synthetic species
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Other results
• Significant– Hawks (Accipter spp.)– Middle eastern cats– Some tiger beetle (Carabidae) assemblages– Desert Rodents
• Not significant– Birds (Tres Marias & Channel Islands)– Most tiger beetle assemblages– Multiple passerine bird assemblages
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What does it show?
• A significant result establishes that there is a pattern, consistent with prediction.
• Does not establish what the mechanism is.• Experiments to test mechanisms where patterns
exist– e.g., experiments like Pacala & Roughgarden
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Exploitation mostly predation
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Exploitation mostly predation
• Predator: kills and eats victim• Parasite: lives intimately with victim and
usually does not necessarily kill victim• Herbivore/Carnivore distinction not that
important for dynamics
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Exploitation
• How does the presence / absence of a predator affect:– species populations– assemblages of prey species– evolution of prey
• Does predation contribute to community patterns?
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Predation & population dynamics
• Predators eat prey; prey die due to predation• How does this affect population dynamics?• Lotka-Volterra predator-prey model• Starting point• N = number in prey population• P = number in predator populatio
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Lotka-Volterra predator-prey• Without predation, prey grow exponentially
dN / dt = r1 N • Predation is an increasing function of N & P• Effect of predation on prey population = C1 NP
• C1 is the capture efficiency
• So, with predation…
dN / dt = r1 N - C1 NP
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Lotka-Volterra predator-prey• Without prey, predators starve to death
exponentially
dP / dt = - r2 P• Predation is an increasing function of N & P• Effect of predation on predator population=C2 NP
• C2 = product of capture & conversion efficiencies
• So, with prey …
dP / dt = C2 NP - r2 P
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Lotka-Volterra predator-prey:Equilibrium predictions
• At equilibrium• dN / dt = 0 and dP / dt =0• there is a specific, constant density of
predators, above which prey cannot increase• there is a specific, constant density of prey,
below which predator cannot increase
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Lotka-Volterra predator-prey isoclines
Pre
dato
r (P
)
Prey (N)
dN / dt < 0
dN / dt > 0
dN / dt = 0
PREY ISOCLINE
Pre
dato
r (P
)Prey (N)
dP / dt < 0
dP / dt > 0
dP / dt =
0PREDATOR ISOCLINE
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Lotka-Volterra predator-prey isoclines
dN / dt = 0
Pre
dato
r (P
)
Prey (N)
dP / dt =
0
equilibrium
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Lotka-Volterra predator-prey isoclines
dN / dt = 0
Pre
dato
r (P
)
Prey (N)
dP / dt = 0
START HERE
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Lotka-Volterra predator-prey dynamics
Time (t )
Den
sity
(N
or
P
)
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Predator-prey cycles in real data• Hare & Lynx• What assumptions are
built into Lotka-Volterra predator-prey models?
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Simplifying Assumptions
• Simplifying Environmental– Constant in time– Uniform or random in space
• Simplifying Biological– Individuals are identical & constant in time– Exponential prey growth– Prey limited only by predation– Predator growth dependent only on predation
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Explanatory Assumption• Predators and prey encounter each other at
random, like bimolecular collisions– Frequency of encounter proportional to product of
densities
• Individual predator feeding rate increases linearly as N increases– No limit on increase in feeding rate
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Unrealistic elements• No limits on prey except predation
– expect real prey may be limited by food, space, etc. when abundant
– upper limit ( K ) for prey even with no predators
• Predators do not saturate with prey– expect real predators to hit a maximum number eaten– expect an upper limit for predators with maximal food (KP )
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Gause’s predator-prey experiments
Didinium
Paramecium
ParameciumPrey
Didinium Predatory ciliate
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Didinium - Paramecium predator-prey experiment
Time (t )
Den
sity
(N
or
P
)
Paramecium
Didinium
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Gause’s Predator-Prey experiments
• Predator and prey in a simple environment• No cycles (stable or otherwise)• Predator exterminates prey• Predator dies out shortly after• Inconsistent with Lotka-Volterra predator-prey
models
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Gause’s Modified Predator-Prey experiments
• Regular immigration of Paramecium• Produces cycles of predator & prey• Consistent with Lotka-Volterra predator-prey
models?• No
– violates simplifying assumptions– prey population now not soley governed by
exponential growth and predation
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Huffaker’sPredator-Prey experiments
• Mites– predator Typhlodromus– prey Eotetranychus
• on oranges• With oranges evenly
spread on a tray– no cycles– prey extinction, then
predator extinction
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Huffaker’s modifiedPredator-Prey experiments
• Add barriers to dispersal• rubber balls, vaseline
– cycles
• Confirms Lotka-Volterra prediction?
• NO– violates simplifying
environmental assumption
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Predator-Prey models & experiments: Conclusions
• Lotka-Volterra models are largely inadequate• lab systems meeting assumptions -- no cycles• Stable oscillations when system is “fixed”• Conceptual error:
– Design experiments to meet assumptions, then test predictions
– Don’t manipulate experiments until they confirm theory
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Improved Predator-Prey models • Self limitation of prey and predators• Asymptotic prey consumption by
predators• Spatial refuges for prey• graphical approach
– Rosezweig & MacArthur (1963)• mathematical approach
– Williams (1980) Grover (1997)– Gilpin & Ayala (1973) Populus 5.4