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Multi-Trophic Level, Pairwise Species Interactions:
Predator-Prey, Parasitoid-Host & Parasite-Host
Relationships
“Nature red in tooth & claw”
Alfred Tennyson (1809 - 1892)
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
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
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
Predation
In the model’s 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.
Equilibrium solution:
For the prey (V) population:
dV/dt = rV - VP
0 = rV - VP
VP = rV
P = r
P = r/
The prey isocline
P^ depends on the ratio of
the growth rate of prey to
the capture efficiency of the
predator
Figure from Gotelli (2001)
dV/dt < 0
dV/dt > 0
Equilibrium solution:
For the predator (P) population:
dP/dt = ßVP - qP
0 = ßVP - qP
ßVP = qP
ßV = q
V = q/ß
The predator isocline
V^ depends on the ratio of the
death rate of predators to the
conversion efficiency of
predators
Figure from Gotelli (2001)
dP/dt < 0
dP/dt > 0
Combined graphical
solution in state space:
The predator and prey
populations cycle because
they reciprocally control one
another’s growth
Figure from Gotelli (2001)
Combined graphical
solution in state space:
The predator and prey
populations cycle because
they reciprocally control one
another’s growth.
Figure from Gotelli (2001)
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 LotkaVolterra 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)
Functional Response Curves
Why might functional responses have these shapes?
Rate of prey capture
Satiation
Host-switching, developing a search image, etc.
Victim abundance (V)
Figure from Gotelli (2001), after Holling (1959)
Predators with either a
Type II or Type III
functional response:
Type II for prey:
dV/dt = rV - [kV / V+D]P
Type III for prey:
dV/dt = rV - [kV2 / V2+D2]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)
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)
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)
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)
Coexistence with stable limit cycles
Coexistence at stable equilibrium
Unstable equilibrium
Figure from Gotelli (2001)
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
Figure from Gotelli (2001)
enriched conditions
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
Figure from Gotelli (2001)
enriched conditions
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
Figure from Gotelli (2001)
enriched conditions
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
This idea also
developed out of a
desire to warn against
indiscriminate use of
resource enrichment to
bolster a population
under management
A
R2
[P]
1
B
2
3
Slope of
consumption
vectors for B
4
5
6
R1 [N]
Imagine what happens
when we fertilize with N
Consumption
vectors
Resource
supply point
Effect of changing the predator isocline
(by changing the numerical response of the predator)
Predator is a
complete
specialist on
the focal prey
Predator’s K depends
on the abundance of
the focal prey
Predator uses
multiple prey, so
predator’s 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)
Effect of prey refuges or immigration (rescue effect)
Tends to stabilize
dynamics
Figure from Gotelli (2001)
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)
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)
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)
Effect of time lags
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…
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)
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
Phenotypic Plasticity & Predation
How might the evolutionary advent of phenotypic plasticity
alter predator-prey dynamics?
Agrawal (2001), Fig. 1
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.
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”)
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 (>0.5 mm)
& small zooplankton (<0.5 mm) together
Large zooplankton were not found with plankton-feeding fish
Size-dependent predation
Crystal Lake, Connecticut
No planktivorous fish
Large plankton
Crystal Lake 22 yr
after introduction of
Alosa aestivalis
(Blueback Herring)
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 (>0.5 mm)
& small zooplankton (<0.5 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
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 smallbodied zooplankton… they eat them (intra-guild predation)!
Brood Parasitism
In some cases brood parasitism represents
“predation” and parasitism combined
Davies 1992, pg. 217
Conceptual models of parasitism
(usually categorized by function rather than taxonomy)
Microparasites – parasites that reproduce within the host, often within the
host’s 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 shortlived; 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
Modeling microparasite-host dynamics
Coupled differential dX/dt = a(X+Y+Z) - bX - βXY + Z
equations, one for dY/dt = βXY - (α+b+v)Y
each type of host dZ/dt = vY - (b+)Z
What is βXY? Combined encounter & infection rate
Birth
a
Susceptible
hosts (X)
a
β
Infected
hosts (Y)
α+b
b
Death

See: Anderson & May (1979); May (1983)
a
v
Immune
hosts (Z)
b
Modeling microparasite-host dynamics
There are many examples of parasites limiting or regulating their host abundances, or
determining distribution patterns. One of the best examples of host populations that
cycle in response to enemies comes from Scotland: Red grouse and their nematode
parasites (Dobson & Hudson 1992).
Grouse:
dH/dt = (b-d-cH)H - (α+)P
Incorporates reduction in survival (α) & reprod. ()
Free-living stages (eggs and larvae) of the worms:
dW/dt = P - W - βWH
Adult worm population (within caecae of grouse):
dP/dt= βWH - (+d+α)P - α(P2/H)(k+1/k)
Final term represents aggregation among hosts
(smaller k  more aggregated)
Parameter values were estimated in the field. For Scotland, the model predicted
the observed 5-yr cycles. For drier sites in England, the model predicted a lack of
cycles owing to higher mortality of free-living stages, and these populations do
indeed lack cycles.
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
Parasite-host interactions & invasive species
molluscs
crustaceans
amphibians & reptiles
fish
birds
mammals
Standardized S of parasites
in introduced range
Parasite species richness (shown below) and parasite
prevalence (% infected hosts) showed similar patterns
1.0
0.5
0
0
Redrawn from Torchin et al. (2003)
1.0
0.5
Standardized S of parasites
in native range
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 Medicine makes good use of these observations
(see G. C. Williams & R. M. Nesse)
Parasite-host interactions through evolutionary time
Co-cladogenesis and other
macro-evolutionary processes…
Cospeciation
Host switch
Duplication
Host
Parasite
Failure to speciate
From J. Weckstein (2003)
Missing the boat
Extinction
Coexistence
Which are most likely under strictly vertical transmission?
All else being equal, will host-switches preferentially
occur onto more common potential hosts?
?
?
All else being equal, will host-switches preferentially
occur onto potential hosts that are more closely
related to the current host?
?
?
What patterns do we expect in communities in which parasites
(predators, parasitoids) have multiple potential “choices”?
?
?
?
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