BIOS 5970: Plant-Herbivore Interactions
Dr. Stephen Malcolm, Department of Biological Sciences
•  D. POPULATION & COMMUNITY DYNAMICS
•  Week 11. Population models 2:
–  Lecture summary:
•  Distribution and abundance - examples
•  Dynamics of predator-prey cycles
–  Lotka-Volterra model
–  Coupled oscillations
–  Density dependence
–  Self limitation
–  Functional responses
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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2. Animal Influences on Plants:
•  Negative or positive impacts.
•  Can influence distribution and abundance of
plant populations.
–  E.g. Seed predation in goldenbush,
Haplopappus squarrosus (Fig. 10-1):
•  Common inland and rare by the coast.
•  Coastal plants:
–  No signs of physiological constraints or suppression of
growth.
–  Produce more flowers per plants and so seed production
and seedling recruitment should be higher (expected).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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3. Seed predation of goldenbush:
•  Svata Louda observed
that flower and seed
predators were present.
•  Experimentally showed
(with insecticide
applications) that
exclusion increased
seedling density most in
coastal populations of
goldenbush (Fig. 10-2).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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4. Wood Rats and Saguaro cacti:
•  Observation 1:
–  Saguaro are widely scattered throughout the Sonoran
desert (probably evenly distributed rather than random).
–  Hypothesis 1:
•  Cacti compete for limited water resources.
•  Observation 2:
–  Massive density independent mortality after fruit eating
birds distribute 40-60 million saguaro seeds/hectare.
–  Only 160-240 thousand germinate.
–  Most seeds killed by freezing and drought.
–  No effect of competition.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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5. Wood Rats and Saguaro cacti:
–  Hypothesis 2:
•  Rodent seed predators influence saguaro distribution.
•  Observation 3:
–  More seedlings survived in the shade under very thorny
plants that may exclude seed & seedling predators such
as rodents & rabbits.
–  Experiment:
•  Caged rodent exclosures showed that more saguaro
seedlings survived when rodent predators were
excluded (see Fig. 10-4):
–  1.9% of 800 caged seedlings survived after 10 years.
–  All uncaged seedlings died.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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6. Giant lobelias, rock hyraxes and
elephants in Kenya:
•  Normally, 2m high lobelias and
senecios on slopes of Mount Kenya
(Fig. 10-5) grow well and suffer little
herbivore-related mortality.
•  Occasionally, elephants forage up to
4000 m altitude and destroy large
numbers of plants.
•  Above that altitude, rock hyraxes
(distant, rabbit-sized relative of
elephants) have minimal impact on
plant populations.
•  But under drought conditions,
hyraxes have a large impact and
selectively kill slow-growing
individuals.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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7. Giant lobelias:
–  During first year of drought:
•  36% of plants with growth rates below population mean
were killed.
•  23% above the growth rate mean were killed.
–  Resulted in high population mortality.
–  Curious result!
•  Contrary to predictions of Growth-Differentiation
Balance (GDB) hypothesis.
•  Contrary to predictions of Resource Availability (RA)
hypothesis.
•  May depend upon the shape of the growth frequency
distribution curve!
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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8. Flower-hummingbird mutualisms:
•  Linhart & Feinsinger (1980) hypothesized that
specialized, flowers with a deep corolla would be
more affected by pollinator limitation on Tobago
than on Trinidad.
Trinidad
Tobago
Hummingbirdpollinated plants
34 spp.
31 spp.
Short-billed
Long-billed
hummingbirds
hummingbirds
--------------- 11 --------------5
0
•  Thus the more specialized flower was affected
negatively by a reduced mutualist assemblage on
Tobago.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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9. Flower-hummingbird
mutualisms:
•  Dye experiments
showed that far less
pollen was moved
among deep-corolla
flowers on Tobago
than on Trinidad
(Fig. 10-6).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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10. Plant influences on animals:
•  Resource Concentration Hypothesis (Root, 1973):
–  Specialist insect herbivores should:
•  “favor high densities of host plants over low densities
because they will find and breed on dense patches
more easily than on patches with few plants.”
•  Enemies Hypothesis:
–  “predicts that parasitoids should control
herbivores more effectively in mixed than in pure
stands of hosts.”
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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11. Tests of hypotheses:
•  Difficult to test and separate.
•  Bach (1980) showed that host plant density had little impact
on density of a specialist beetle herbivore (Fig. 10-7).
•  Parasites also had little influence on herbivores in high or
low host densities (Fig. 10-7).
•  But the presence of other plant species did influence beetle
density with much lower densities on cucumbers mixed with
corn and broccoli (Fig. 10-7).
•  Shading may make cucumbers less palatable in
polycultures:
–  Agrees with both GDB and RA hypotheses.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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12. Population cycles:
•  Famous Hudson's Bay Company data:
–  90 years of snowshoe hare-lynx populations
–  Show approximately 10 year cycles thought to be driven
by lynx (Fig. 10-8) in "top-down" control.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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13. Cycles - cause and effect:
•  Little evidence that lynx cause population
fluctuations in hares.
•  Lynx populations simply influenced by abundance
of all prey and have little impact on prey
populations.
•  Instead, quantity and quality of food have greater
impact on snowshoe hare populations.
•  Compare with the red grouse in Britain:
–  Argument over regulation by food (bottom-up) versus
parasites and fox predation (top-down).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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14. Predation and food shortage hypotheses:
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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15. Snowshoe hare requirements:
•  Each day of winter, need 3000 g of woody browse from
willow, aspen, rose, hazel, saskatoon and scrub birch.
•  Abundance of these resources influences hare
populations dramatically.
•  Availability of all species also important:
–  Abundance of one species also led to declines in hare
populations.
•  Thus starvation and poisoning must both be important
to snowshoe hares.
•  Plants can also induce chemical defenses and “delayed
induced defense” becomes increasingly important as
hare populations increase.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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16. Population Dynamics of Predation:
•  2 approaches to comparing models with
reality:
–  1. Discrete, difference equations of Nicholson &
Bailey (1935):
•  as in Begon, Mortimer & Thompson (1996).
–  2. Continuous, differential equations of Lotka &
Volterra:
•  as in Begon, Harper & Townsend (1996)
•  Mass action model to which logistic limitation can be
added
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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17. Lotka-Volterra model of prey-predator
dynamics:
•  For prey:
–  dN/dt = rN - consumption rate of prey, or,
–  dN/dt = rN - aPN
•  where N = prey population, P = predator (consumer) population,
and a = attack rate.
•  For predators (consumers):
–  dP/dt = predator birth - qP (death),
–  dP/dt = faPN - qP
•  where q = predator mortality rate (starve exponentially in absence
of prey where dP/dt = -qP) or,
•  (predator birth = consumption rate of prey (aPN) x efficiency f of
turning this into offspring births)
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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18. Zero isoclines for the Lotka-Volterra
model:
–  Prey zero isocline occurs when:
•  dN/dt = 0, or rN = aPN, and so P = r/a
–  Predator (consumer) isocline is at:
•  dP/dt = 0, faPN = qP, or N = q/fa
–  Isoclines are shown together in Fig. 10.2:
•  Begon, Harper & Townsend (1996).
–  Model generates:
•  Coupled oscillations (10.2d) that are unrealistically
'neutrally stable' as opposed to,
•  More realistic set of 'stable limit cycles' with tendency
to return to the original cycle after disturbance.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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19. Prey-predator cycles:
•  Coupled oscillations may or may not be a product of preypredator interactions alone, but may already exist in the
absence of predators (Fig. 10.4).
•  “Bottom-up” (from food) and “Top-down” (from natural
enemies) influences on population cycling in the northern
American community of plants, hares, grouse and predators
(Fig. 10.5).
•  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 it spirals
inwards anticlockwise for damped oscillations.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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20. Self-limitation:
•  Inclusion of intraspecific
competition or mutual
interference in the LotkaVolterra model:
–  This can include a
logistic term in the basic
model!
–  Intraspecific effects will
change the
unrealistically vertical
and horizontal zero
isoclines (Fig. 10.2),
which are densityindependent, to more
realistic, densitydependent shapes as in
Fig. 10.7.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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21. Inclusion of competition:
•  Combined effects of intraspecific competition and predation
are shown in Fig. 10.7:
–  More realistic predator and prey zero isoclines constrained by
intraspecific competition (self limitation).
–  Assume linear functional response (shape of curve of prey eaten as
prey density increases).
–  Oscillations no longer neutrally stable!
•  Strong intraspecific competition can eliminate predator prey
oscillations completely (biii), or weak competition can
dampen oscillations.
•  More efficient predation increases amplitude of oscillations
and interaction is less stable (bi).
•  Higher predator densities generate greater instability.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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22. Effect of efficient predation:
•  Efficient predation with an aggregative response, in
heterogeneous environments, generates stability (Fig. 10.8)
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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23. Type 2 Functional response and the
Lotka-Volterra predation model:
–  Predator functional responses to prey density also
modify Lotka-Volterra model in a similar way:
•  Type 2 functional responses (rising at a decelerating rate to
an asymptote):
–  Prey isocline is humped (Fig. 10.10).
–  At low prey density this can lead to instability and extinction:
»  Unlikely because predator handling times have to be very long.
–  At high prey density this leads to damped oscillations and stability:
»  The “Allee effect”
»  Disproportionately low recruitment at low population density
»  Important in conservation and resource management).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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24. Effect of type 3 functional response:
•  Type 3 functional response (sigmoidal) in which predators
are less efficient at low prey density is shown in Fig. 10.8
(ii), or more efficient at low prey density (i).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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25. Effect of switching:
•  But where predator switches effectively from prey to prey its
abundance may be independent of prey density (Fig. 10.9).
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10-1: Observed and expected frequencies
of goldenbush across a transect.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10-4: Survival of caged and uncaged
saguaro cactus seedlings
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10-7: Striped cucumber beetles on cucumbers in
low- and high-density monocultures & polycultures.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10.2 (Begon et al.
1996): Lotka-Volterra
predator-prey model.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10.4 (Begon et al. 1996): Dynamics of flour mothparasitoid interactions in (a,b) deep medium,
(c,d) shallow medium.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10.5 (Begon
et al. 1996):
Fluctuations in relative
biomass of major wildlife
components in Alberta.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10.6 (Begon et al. 1996): Delayed densitydependence; (a,b,c,d) host-parasitoid model;
(e) field data for pupal predation of winter moths.
BIOS 5970: Plant-Herbivore Interactions - Dr. S. Malcolm. Week 11: Population models 2
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Figure 10.10 (Begon et al. 1996): Effect of a
‘humped’ prey isocline (from type 2 functional
response or an Allee effect).
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