Multi-Trophic Level, Pairwise Species Interactions: Predator-Prey, Parasitoid-Host

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Multi-Trophic Level, Pairwise Species
InteractionsPredator-Prey, Parasitoid-Host
Parasite-Host Relationships
Nature red in tooth claw Alfred Tennyson
(1809 - 1892)
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Predation Parasitism
Why study predation parasitism?
A basic-science answer All organisms are
subject to various sources of mortality,
including starvation, disease predation to
understand population community structure
dynamics requires knowing something about these
processes
Photo from Greg Dimijian
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Predation Parasitism
Why study predation parasitism?
A basic-science answer All organisms are
subject to various sources of mortality,
including starvation, disease predation to
understand population community structure
dynamics requires knowing something about these
processes
A utilitarian answer Understanding how much
natural mortality occurs, and why, in populations
is critical to managing those that we exploit
(e.g., fisheries, game animals, etc.), or wish to
control (e.g., weeds, disease organisms or
vectors, invasive species, etc.)
Photo from Greg Dimijian
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Predation
Modeling predation Lotka-Volterra model Prey
(victims) in the absence of predators dV/dt rV
Prey in the presence of predators dV/dt rV -
?VP where ?VP is loss to predators
Losses to predators are proportional to VP
(probability of random encounters) and ? (capture
efficiency effect of a single predator on the
per capita growth rate of the prey
population) Large ? is exemplified by a baleen
whale eating krill, small ? by a spider catching
flies in its web
?V is the functional response of the predator
(rate of prey capture as a function of prey
abundance) in this case linear, i.e., prey
capture increases at a constant rate as prey
density increases
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Predation
In the models simplest form, the predator is
specialized on 1 prey species in the absence of
prey the predator pop. declines
exponentially dP/dt -qP P is the predator
pop. size, and q is the per capita death rate
Positive population growth occurs when prey are
present dP/dt ßVP - qP
ß is the conversion efficiency the ability of
predators to turn a prey item into per capita
growth Large ß is exemplified by a spider
catching flies in its web (or wolves preying on
moose), small ß by a baleen whale eating krill
ßV is the numerical response of the predator
population the per capita growth rate of the
predator pop. as a function of the prey pop.
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Equilibrium solution For the prey (V)
population dV/dt rV - ?VP 0
rV - ?VP ?VP rV ?P r
P r/?
dV/dt lt 0
dV/dt gt 0
Figure from Gotelli (2001)
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Equilibrium solution For the predator (P)
population dP/dt ßVP - qP 0
ßVP - qP ßVP qP ßV q
V q/ß
dP/dt gt 0
dP/dt lt 0
The predator isocline V depends on the ratio of
the death rate of predators to the conversion
efficiency of predators

Figure from Gotelli (2001)
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Combined graphical solution in state space The
predator and prey populations cycle because they
reciprocally control one anothers growth
Figure from Gotelli (2001)
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Combined graphical solution in state space The
predator and prey populations cycle because they
reciprocally control one anothers growth
Figure from Gotelli (2001)
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Prey limited by both intraspecific competition
and predation dV/dt rV - ?VP - cV2 ?VP
? due to predator cV2 ? due to
conspecifics dP/dt ßVP qP Now the prey
isocline slopes downward, as in the
Lotka-Volterra competition models
The predator and prey populations reach a stable
equilibrium
At this point, the prey population is
self-limiting, i.e., no predators are required to
keep the population from changing in size.
What did this point represent in the competition
models?
Figure from Gotelli (2001)
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Functional Response Curves
Why might functional responses have these shapes?
Satiation
Rate of prey capture
Host-switching, developing a search image, etc.
Victim abundance (V)
Figure from Gotelli (2001), after Holling (1959)
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Predators with either a Type II or Type III
functional response Type II for prey dV/dt
rV - (kV) / (VD)P Type III for prey dV/dt
rV - (kV2) / (V2D2)P Where k maximum
feeding rate D half-saturation
constant, i.e., abundance of prey at which
feeding rate is half-maximal
Predator dP/dt ßVP qP
The equilibrium in both cases (Type II Type III
functional responses) is unstable
Figure from Gotelli (2001)
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An even more realistic prey isocline may be a
humped curve In this case, the position of the
predator isocline with respect to the maximum in
the prey isocline determines dynamics
For example, imagine a combination of Allee
effects, decreasing impact of predators with
increases in prey numbers (e.g., Type II or III
functional response), plus increasing impact of
intraspecific competition
Figure from Gotelli (2001)
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An even more realistic prey isocline may be a
humped curve In this case, the position of the
predator isocline with respect to the maximum in
the prey isocline determines dynamics
For example, imagine a combination of Allee
effects, decreasing impact of predators with
increases in prey numbers (e.g., Type II or III
functional response), plus increasing impact of
intraspecific competition
Figure from Gotelli (2001)
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An even more realistic prey isocline may be a
humped curve In this case, the position of the
predator isocline with respect to the maximum in
the prey isocline determines dynamics
For example, imagine a combination of Allee
effects, decreasing impact of predators with
increases in prey numbers (e.g., Type II or III
functional response), plus increasing impact of
intraspecific competition
Figure from Gotelli (2001)
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Coexistence with stable limit cycles
Coexistence at stable equilibrium
Unstable equilibrium
Figure from Gotelli (2001)
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Paradox of enrichment in predator-prey
interactions(Rosenzweig 1971)
This idea developed out of a desire to warn
against indiscriminate use of resource
enrichment to bolster a population under
management
control conditions
enriched conditions
Figure from Gotelli (2001)
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Paradox of enrichment in predator-prey
interactions(Rosenzweig 1971)
This idea developed out of a desire to warn
against indiscriminate use of resource
enrichment to bolster a population under
management
control conditions
enriched conditions
Figure from Gotelli (2001)
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Paradox of enrichment in predator-prey
interactions(Rosenzweig 1971)
But is it only of theoretical interest? See
Abrams Walters 1996 Murdoch et al. 1998,
Persson et al. 2001 In the real world enrichment
generally fails to destabilize dynamics in this
way, perhaps due to nearly ubiquitous occurrence
of some invulnerable prey
control conditions
enriched conditions
Figure from Gotelli (2001)
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Paradox of enrichment in competitive
interactions(Riebesell 1974 Tilman 1982, 1988)
Slope of consumption vectors for A
This is one way in which competitive interactions
can also result in a paradox of enrichment
A
B
Slope of consumption vectors for B
This idea also developed out of a desire to warn
against indiscriminate use of resource enrichment
to bolster a population under management
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R2 P
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R1 N
Imagine what happens when we fertilize with N
Resource supply point
Consumption vectors
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Effect of changing the predator isocline(by
changing the numerical response of the predator)
Predator is a complete specialist on the focal
prey
Predators K depends on the abundance of the
focal prey
Predator uses multiple prey, so predators K is
independent of the focal prey in this case
predator has low K
Where would the predator isocline be if the
predator uses multiple prey and deterministically
drives the focal prey extinct?
Figure from Gotelli (2001)
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Effect of prey refuges or immigration (rescue
effect)
Tends to stabilize dynamics
Figure from Gotelli (2001)
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Experiment demonstrating the stabilizing
influence of refuges Six-spotted mite feeds on
oranges and disperses among oranges by foot or by
ballooning on silk strands Predatory mite
disperses by foot
See Huffaker (1958)
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Experiment demonstrating the stabilizing
influence of refuges Six-spotted mite feeds on
oranges and disperses among oranges by foot or by
ballooning on silk strands Predatory mite
disperses by foot
In experimental arrays, predators drove prey
extinct in the absence of prey refuges predator
pop. then crashed In large arrays with refuges
(see fig.) predators prey coexisted with
coupled oscillations
See Huffaker (1958)
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Effect of time lags
So far we have assumed that responses of
predators to prey (and vice versa) are
instantaneous
Time lags (the time required for consumed prey to
be transformed into new predators, or for
predators to die from starvation) add realism
Incorporating time lags into models generally has
a destabilizing effect, leading to
larger-amplitude oscillations
Harrison (1995) incorporated time lags into the
numerical response of Didinium consuming
Paramecium prey This greatly improved fits of
models to actual population fluctuations of
predator prey described by Luckinbill (1973)
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Additional biological complexity
Coexistence at stable equilibria, after damped
oscillation cycles, or within stable limit
cycles, or instability lack of
coexistence, depending especially on the biology
of the interacting species
Functional response of predators to prey
(generally destabilizing if non-linear)
Carrying capacity of predators and prey in the
absence of the other (often stabilizing)
Refuges for the prey (often stabilizing)
Specificity of the predator to the prey
(destabilizing if the switch occurs at a very low
prey density, but stabilizing if the switch
occurs at a higher prey density) Etc
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Lynx hare
Canada Lynx Snowshoe Hare exhibit synchronized
oscillatory dynamics in nature (Elton Nicholson
1942)
Hare pops. cycle with peak abundance every 10
yr Lynx pops. track hare pops., with 1 - 2 yr
time lag
Figure from Gotelli (2001)
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Lynx hare
Simple Lotka-Volterra model is not a complete
explanation e.g., cycles are broadly
synchronized, even on some Canadian islands w/o
lynx
Hare populations are co-limited by food
availability predation (e.g., Keith 1983)
hares rapidly deplete food quantity (principally
buds young stems of shrubs saplings)
quality (hares stimulate induced defenses of food
plants) Low food availability increases
susceptibility to predation (lynx, weasels,
foxes, coyotes, goshawks, owls etc.)
Sun spot cycles and their influence on climate
food plants are also implicated (e.g., Krebs et
al. 2001) At any rate, the lynx-hare cycle is
more complex than suggested by the superficial
resemblance to Lotka-Volterra models
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Phenotypic Plasticity Predation

• How might the evolutionary advent of phenotypic
  plasticityalter predator-prey dynamics?

Agrawal (2001), Fig. 1
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Escape through predator satiation(as may occur
in Type II III functional responses)
Plant examples Janzen (1976) suggested that
seed predation is a major selective force
favoring masting (massive supra-annual seed
production). Bamboos are the most dramatic mast
fruiters, with many species fruiting at 30-50 yr
intervals and some much longer, e.g.,
Phyllostachys bambusoides fruits at 120 year
intervals! Other masters Dipterocarpaceae,
oaks, beech, many conifers, and possibly the
majority of tropical trees.
Animal examples Williams et al. (1983)
provided evidence that Magicicada spp. emerge
once every 13 or 17 yrs to avoid similarly
cycling predators. These emerge at densities of
up to 4 million/ha 4 tons of cicadas/ha ? the
highest biomass of a natural population of
terrestrial animals ever recorded.
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Size-dependent predation
Mean-field assumption all prey are the same
(size, etc.)
Large prey may escape consumption owing to
mechanical constraints on feeding, e.g., Paine
(1966) found that the gastropod Muricanthus
becomes too large for Heliaster starfish to handle
Small prey may escape detection, or resources
expended in capturing and handling them may
exceed resources obtained by their consumption
(the celery bind)
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Size-dependent predation
Brooks and Dodson (1965) proposed that
size-dependent predation by fish determines the
size structure of freshwater zooplankton
Observations Lakes seldom contained
abundant large zooplankton (gt0.5 mm)
small zooplankton (lt0.5 mm) together Large
zooplankton were not found with plankton-feeding
fish
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Size-dependent predation
Crystal Lake, Connecticut No planktivorous
fish Large plankton
Crystal Lake 22 yr after introduction of Alosa
aestivalis (Blueback Herring)
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Size-dependent predation
Brooks and Dodson (1965) proposed that
size-dependent predation by fish determines the
size structure of freshwater zooplankton
Observations Lakes seldom contained
abundant large zooplankton (gt0.5 mm) small
zooplankton (lt0.5 mm) together Large
zooplankton were not found with plankton-feeding
fish
Hypotheses Large zooplankton are superior
competitors for food (phytoplankton)
because of greater filtering efficiency
Planktivorous fish selectively consume
large-bodied, competitively superior
plankton
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Size-dependent predation
Detailed analyses of the mechanisms of change
showed that Fish do indeed selectively
remove large-bodied zooplankton But,
large-bodied zooplankton do not competitively
exclude small- bodied zooplankton they
eat them (intra-guild predation)!
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Brood Parasitism

• In some cases brood parasitism represents
• predation and parasitism combined

Davies 1992, pg. 217
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Conceptual models of parasitism(usually
categorized by function rather than taxonomy)
Microparasites parasites that reproduce within
the host, often within the hosts cells, and are
generally small in size and have short lifespans
relative to their hosts hosts that recover often
have an immune period after infection (sometimes
for life) infections are often transient
examples include bacterial, viral, fungal
infectious agents, as well as many protozoans
Macroparasites parasites that grow, but have no
direct reproduction within the host (they produce
infective stages that must colonize new hosts)
typically much larger and have longer generation
times than microparasites immune response in
hosts is typically absent or very short-lived
infections are often chronic as hosts are
continually reinfected examples include
helminths and arthropods
Parasitoids insects whose larvae develop by
feeding on a single arthropod host and
invariably kill that host e.g., Nicholson-Bailey
models
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Modeling microparasite-host dynamics
What is ßXY?
Combined encounter infection rate
Birth
a
a
a
Susceptible hosts (X)
Infected hosts (Y)
Immune hosts (Z)
ß
v
b
a b
b
Death
?
See Anderson May (1979) May (1983)
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Modeling macroparasite-host dynamics
Red grouse (U.K.) and their nematode parasites
(Dobson Hudson 1992)
Grouse dH/dt (b-d-cH)H - (a?)P
Incorporates reduction in survival (a) reprod.
(?) Free-living stages (eggs and larvae) of the
worms dW/dt ?P - ?W - ßWH Adult worm
population (within caecae of grouse) dP/dt
ßWH - (?da)P - a(P2/H)(k1/k) Final
term represents aggregation among hosts
(smaller k ? more aggregated)
Parameter values estimated in the field
Scotland (wetter) model predicted observed
5-yr cycles England (drier) model predicted
observed lack of cycles (possibly owing to
higher mortality of free-living stages)
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Parasitism
The same rich variety of dynamics observed for
predators and their prey arise in various kinds
of parasite-host and parasitoid-host models,
including all possibilities from stable
coexistence, to unstable exclusion, to cycles and
chaos
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Parasite-host interactions invasive species
Parasite species richness (shown below) and
parasite prevalence ( infected hosts) showed
similar patterns
1.0
1-to-1 line
molluscs
crustaceans
Standardized S of parasites in introduced range
amphibians reptiles
0.5
fish
birds
mammals
0
0
1.0
0.5
Standardized S of parasites in native range
Redrawn from Torchin et al. (2003)
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Parasite-host interactions through evolutionary
time
Evolutionary trajectories of virulence
Some key results Horizontal vs.
vertical transmission (see Ewald 1994)
Horizontal transmission generally leads to
greater virulence than
vertical transmission Greater virulence usually
results from higher transmission
rates in general
Degree of alignment of reprod. interests
(see Herre et al. 1999) The tighter
the dependence of parasite reproduction on host
reproduction, the less
virulent parasites tend to become
Darwinian Agriculture Medicine make
good use of these observations (see R. F.
Denison G. C. Williams R. M. Nesse)
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Parasite-host interactions through evolutionary
time
Co-cladogenesis and other macro-evolutionary
processes
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Cospeciation
Which are most likely under strictly vertical
transmission?
From J. Weckstein (2003)
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All else being equal, will host-switches
preferentially occur onto more common potential
hosts?
?
?
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All else being equal, will host-switches
preferentially occur onto potential hosts that
are more closely related to the current host?
?
?
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What patterns do we expect in communities in
which parasites (predators, parasitoids) have
multiple potential choices?
?
?
?
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Ghosts of Predation Past
North American Cheetah (Miracinonyx) went extinct
11,000 yr ago even so the Pronghorn Antelope
remains the fastest land animal in N. Am.
Miracinonyx was similar to extant Acinonyx jubatus
Photos from http//www.hoothollow.com