BIOS 6150: Ecology
Dr. Stephen Malcolm, Department of Biological Sciences
•  Week 7: Dynamics of Predation.
•  Lecture summary:
•  Categories of predation.
•  Linked prey-predator
cycles.
•  Lotka-Volterra model.
•  Density-dependence.
•  Interference.
•  Functional response.
•  Aggregation of risk.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
Click on picture
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2. Categories of Predation:
•  Predators:
•  Kill & completely consume many prey items during their life.
•  Parasitoids:
•  Free-living adult insects that lay eggs in or on their single host
(“prey”) in which the larva (or larvae) develops into a new freeliving adult. The host is always killed.
•  Parasites:
•  Most of their life is spent in close association in or on a single
host and usually do not kill the host.
•  Herbivores:
•  Most only partially consume individual plants, but they include
a range of plant feeders that act like:
•  true parasites (e.g. aphids)
•  parasitoids (e.g. fig wasps)
•  predators (e.g. mice and seed beetles).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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3. Prey - predator cycles:
•  Dynamics of change in
numbers through time:
•  Prey-predator, hostparasitoid and plantherbivore interactions
(Fig. 10.1).
•  “Coupled oscillations”
•  How do we describe
these dynamics?
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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4. Snowshoe hare - lynx cycles:
•  Snowshoe hare-lynx cycling is a famous
example (Fig. 10.1c [10.1a, 4th ed.]).
•  But is it the interaction, or other factors such
as prey food availability, and induced
defense, that generates the cycles?
•  Hare-plant interactions appear to generate a
time-lag that in turn generates the cycles
that are simply tracked by the predatory
lynx and not generated by lynx.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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5. Other factors can influence apparently
coupled oscillations:
•  Other interactions may
influence the dynamics of
trophic and competitive
interactions among plants,
hares, grouse and
predators (Fig. 10.5, 3rd
ed.).
•  A system much like that for
the snowshoe hare-lynx
interaction of Fig. 10.1c.
•  Here lynx may “fine-tune”
the cycles.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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6. Population Dynamics of Predation
•  Two modeling approaches:
•  (1) Based on the discrete, difference equations
of Nicholson & Bailey (1935):
•  As in Begon, Mortimer & Thompson (1996).
•  (2) Based on the continuous, differential
equations of Lotka (1932) & Volterra (1926):
•  As in Begon, Townsend & Harper (2006).
•  Without logistic limitation of prey or predators.
•  This is a mass action model to which logistic
limitation can be added.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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7. The Lotka-Volterra model of
prey-predator dynamics:
•  For prey,
dN =rN -consumption rate of prey, or,
dt
dN = rN - aPN
dt
Where N = prey population, P = predator population, and a = attack rate.
•  For predators (consumers),
dP =predator births-qp(deaths), or,
dt
dP = faPN - qP
dt
Where q = predator mortality rate (starve exponentially in absence of
prey, so dP/dt = -qP). Predator birth = consumption rate of prey (aPN) x
efficiency f of turning this into offspring births).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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8. Zero isoclines for the Lotka-Volterra model:
•  The prey zero isocline occurs when:
dN =0, or rN =aPN , and so P = r
a
dt
•  The predator (consumer) isocline is at:
dP =0, or faPN =qP , or N = q
dt
fa
•  These isoclines are shown together in Fig.10.2:
•  Model generates coupled oscillations (10.2d) that are
unrealistically 'neutrally stable' as opposed to a more
realistic set of 'stable limit cycles' with a tendency to
return to the original cycle after disturbance.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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9. Prey-predator cycles:
•  Coupled oscillations (Fig. 10.18) may or may not be a product of preypredator interactions alone, but may already exist in absence of predators
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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10. Bottom-up & top
down influences:
•  “Bottom-up” (from
food) and “topdown” (from natural
enemies) influences
on population cycling
in the North American
community of plants,
hares, grouse and
predators (Fig. 10.5,
3rd ed.).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
Trophic
level
1
2
2
3
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11. Delayed density-dependence:
•  Cycles can also show delayed density dependent
mortality (Fig. 10.6) in which mortality appears to be
density independent.
•  But when plotted as a time series (k-value against
log host density) spirals inwards for damped
oscillations.
•  If plotted against log host density-t then gives
straight line relationship.
•  This regulates a host-parasitoid model with different
degrees of density dependence:
•  under- (b<1), exactly- (b=1), or over-compensating (b>1).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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12. Self-limitation: Inclusion of intraspecific competition
or mutual interference in the Lotka-Volterra model:
•  Can include a logistic term in the basic model!
•  Intraspecific effects change the unrealistically
vertical and horizontal zero isoclines of Fig. 10.2,
which are density-independent, to more realistic,
density-dependent shapes (Fig. 10.7).
•  These prey and predator isoclines are constrained
by intraspecific competition (self limitation),
assuming a linear functional response*:
•  Shape of curve of prey eaten as prey density increases.
•  Oscillations are no longer neutrally stable!
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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13. Change in predator efficiency:
•  Decrease in predator efficiency dampens oscillations,
decreases predator abundance & increases prey abundance
•  E.g. Fig. 10.7d (i) & (ii).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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14. Strong predator self-limitation:
•  Strong intraspecific competition can eliminate
predator-prey oscillations completely.
•  E.g. Fig. 10.7d (iii).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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15. Functional responses and the
Lotka-Volterra predation model:
•  Predator functional responses to prey density also modify the model.
•  Type 3 functional response (sigmoidal):
•  Predators inefficient at low prey density stabilizes interaction (Fig. 10.11ai), but
decrease in efficiency (e.g. interference) increases oscillations (Fig. 10.11aii).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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16. Effect of switching:
•  If a predator switches effectively from prey to prey then its
abundance may be independent of prey density (Fig. 10.11b).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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17. Effect of a type 2 functional response
or an Allee effect:
•  For type 2 functional responses (decelerating rise to
asymptote) the prey isocline is humped (Fig. 10.12).
•  At low prey density this can lead to instability and
extinction (unlikely because predator handling times
have to be very long).
•  But at high prey density this leads to damped
oscillations and stability.
•  “Allee effect”
•  Disproportionately low rate of recruitment at low population
density also generates a humped prey isocline.
•  Important in conservation and resource management.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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18. Effect of predator efficiency combined
with environmental heterogeneity:
•  Efficient predation with an aggregative response in heterogeneous environments can generate stability as in Fig. 10.11.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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19. Spatial heterogeneity:
•  Aggregated prey, or prey occurring in
crevices or other refuges, show spatial
heterogeneity (clumped distributions):
•  E.g. prey mites in Huffaker’s orange experiment.
•  The prey isoclines can look like those in Fig.
10.11 which tends to generate stable equilibria
quickly.
•  Hence the coexistence of the prey and predator
mites.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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20. “Pseudo-interference:
•  Also generates an aggregation of risk among hosts
of parasites because at high parasitoid density,
attacked hosts are more likely to have been
parasitized already (like Fig 10.7d iii).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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21. Aggregation of risk:
•  Aggregative
responses of
parasitoids to hosts
can either be the
same at all host
densities
(Fig. 10.14a) or,
•  Density
dependent (Fig.
10.14 b & c) or,
•  Density
independent
(Fig. 10.14d).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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21. The CV2>1 rule:
•  Such aggregations of risk led Pacala,
Hassell and May to generate the CV2>1 rule:
•  If the coefficient of variation (standard deviation/
mean) of the risk of being parasitized is greater
than 1 then the interaction is more likely to be
stable.
•  Especially when aggregated risk is host density
independent (as in Fig. 10.14d).
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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Prey isocline
Predator isocline
Figure 10.2:
Lotka-Volterra
predator-prey model:
(a) Prey and (b)
predator zero
isoclines; (c) cycling,
(d) neutral stability
through time, and (e)
effect of disturbance.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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Figure 10.6 (3rd ed.): Delayed density dependence in (a) hostparasitoid model, (b, c, d) plots of k mortality against log
density to show delayed density dependence, and (e) field data.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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Figure 10.7:
Influence on both
(a) predator, and
(b) prey, zero
isoclines subject
to crowding and
(c) effects on
stability.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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Figure 10.12: Influence of a humped prey isocline on stability
for (i) efficient predator, and (ii) inefficient predator.
BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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BIOS 6150: Ecology - Dr. S. Malcolm. Week 7: Dynamics of predation
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