Lecture 12
Chapter 10: Predator Prey interactions
Chapter 11: Plant Herbivore interactions
10.1: Introduction-Historical Perspective
• Aldo Leopold and the “dichotomous view”
• Differences between simplistic models presented a more
modern/recent view:
1) Prey pops at least partially determined by food
resources (bottom up dynamics) in addition to
predators (top down dynamics)
2) Prey pops respond to their entire community of
predators
3) Predator pops are affected by other factors in addition
to their prey pops
10.1: Introduction-Historical Perspective
• Predation Rate
• Numerical response
• Functional response
• Total Response
• Fig. 10.1 Stable limit cycle: Predator - Prey vs. time
• Fig. 10.2 Stable limit cycle: Prey vs. Predator popln
10.1: Introduction-Historical Perspective
• Robert May (1976)
• Various outcomes of stable predator-prey cycles where both go
through regular predictable cycles
Numerical responses range from :
1) Predator spp. extinction and prey spp. survival
2) Extinction of prey followed by extinction of predator
3) Pred-prey poplns oscillate and dampen to stable limit cycle/point
4) Pred-prey go through increasing oscillations leading to extinction of
either or both spp.
5) Immediate stable limit cycle or stable point reached
10.1: Introduction-Historical Perspective
• Fig. 10.3 Pred-prey vs. time: oscillation dampening -> Stable point
• Fig. 10.4 : Prey pop vs. pred. pop: Leads to Stable point
• Fig. 10.5 Prey-predator pops vs. time illustrating dampening
oscillations
• Fig. 10.6 Predator-prey poplns illustrating dampened oscillations
leading to a stable point.
• Fig. 10.7 Predator-prey poplns vs. time with increasing oscillations
leading to extinction of both spp.
• Fig. 10.8 Increasing oscillations of prey popln vs. predator popln
leading to extinction of both spp.
Assumptions vs. reality
1)
2)
3)
4)
5)
Prey usually have a refuge
Predation is almost always not random
Generation times between prey and predator often vary
Predators may be generalist
Predator popln may remain ~ constant independent of
prey popln
6) Predator pop may have a carrying capacity (K)
independent of the prey popln
7) Density-independent mortality
8) Multiple equilibriums can exist between predator-prey
interaction: ex., low density vs. high density
10.2: Lotka-Volterra equation
dN/dt = rnN
Eq. 10.1a
dN/dt = r2N [Kn-N/Kn]
Eq. 10.1b
Where:
Nn = number of individuals of prey spp ~ prey popln size
rn = intrinsic rate of increase for prey spp.
Kn = prey carrying capacity
Without prey the predator popln(P) dies off based on mp =
instantaneous density independent mortality and popln declines as:
dP/dt = -mpP
Eq. 10.2
10.2: Lotka-Volterra equation
And the chance of an encounter between predator and prey is:
ENP
eq. 10.3
E = # < 1, measures predator searching & capturing efficiency
Assumes # prey captured is linear with prey abundance
E is a functional response term based on rate of predation per individual
predator per unit time
xp = constant reflecting efficiency that prey is turned into new predator
individuals ~ Assimilation efficiency of predator
Pop growth for predator = (xp) ENP
10.2: Lotka-Volterra equation
L-V assumes that an encounter leads to death of prey
Therefore prey popln is decreased by term ENP
Prey: dN/dt = rnN-ENP
eq. 10.4a
Predator: dP/dt = xp ENP – mp P
eq. 10.5
At equilibrium:
Predator: P* = rn/E
eq 10.6/7
Prey : N* = mp/xpE
Equilibrium analysis = set both to zero and include carrying capacity (K):
dN/dt = rnN(Kn-N/Kn) – ENP
eq 10.4b
10.3: Early tests of Lotka -Volterra models
Elton (1924) and Elton and Nicholson (1942): snow shoe hare and lynx
Gause (1934): Paramecium spp.
Huffacker (1958): mites and oranges
10.4: Predation functional responses
Type I –
Type II –
Type III • Fig. 10.9 Daphnia major ingestion of algae exhibiting Type I
functional response curve
• Fig. 10.10 Damsel fly larvae Type II functional response curve while
feeding on Daphnia major
• Fig. 10.11 Three Lemming predators Type III functional response
curves
10.5: Addition of prey density with Type II and III
functional response modes
• Fig. 10.12 Predator-prey interaction following Lotka-Volterra
equations with a Type I functional response -> mutual extinction
• Fig. 10.13 Predator-prey interaction with a Type II functional
response -> both become stable
• Fig. 10.14 Predator-prey interaction with a Type III functional
response with threshold -> both become stable
10.6: Rosenzweig and MacArthur
• Fig. 10.15 Prey and predator isoclines overview
• Fig. 10.16 Prey isocline with Allee effect, MVP, and K
• Fig. 10.17 Predator-prey isoclines with inefficient predator ->
decreasing oscillations to stable point, S, where 2 isoclines meet
• Fig. 10.18 Predator-prey isoclines for moderately efficient predator
-> stable limit cycle
10.6: Rosenzweig and MacArthur
• Fig. 10.19 Highly efficient predator, increasing isolations with
extinction of both spp.
• Fig. 10.20 Predator-prey interaction with predator growth limited by
an additional factor (not prey) -> stable point, S, is reached
• Fig. 10.21 Effect of paradox of enrichment on predator-prey
interaction -> mutual extinction
• Fig. 10.22 Predator-prey interaction when prey have a refuge ->
stable cycle
• Context Dependent!
OMIT: 10.7: Half-saturation constant use in predatorprey interactions
• dP/dt = [bRP/KR+R] – mpP
eq. 7.20 revised
from two
competing species
Where:
• P = predator population
• mp = death rate
• b = max rate of conversion of prey resource into predators
• R = prey population
• KR = half-saturation constant
 Results in a General Mechanistic Equation for both competitive
interactions and predator-prey interactions for the growth rate of
the consuming population.
10.8: Parasitoid-host interactions & Nicholson-Bailey
models
• Assumptions of N-B models:
1) Number of encounters between parasitoids and a host or prey
species is proportional to the host density
2) Encounters are randomly distributed among hosts.
• Fig. 10.23 Density Independent host-parasitoid -> unstable
• Fig. 10.24 Density Dependent host-parasitoid with K -> stable
• Fig. 10.25 Density Independent host-parasitoid -> mutual extinction
10.8: Parasitoid-host interactions & Nicholson-Bailey
models
• Fig. 10.26 Stable limit cycle of host-parasitoid relationship
• Fig. 10.27 Host-parasitoid poplns over time, a = 0.03 -> Stable point
• Fig. 10.28 Host-Parasitoid polns interactions, search efficiency, a =
0.03 -> stable point
10.9: Field studies of predator-prey interactions – on
your own
• Swedish fox- prey interactions:
Are population cycles caused by predation alone?
• Snowshoe hare cycles:
• Moose-wolf interactions:
• Predator-prey relationships in Africa
1) Predation sensitive food hypothesis
2) Predator regulation hypothesis
3) The surplus predation hypothesis
10.10: Trophic cascades
Definition: Estes et al. 2001 = “Progression of indirect effects by
predators across successively lower trophic levels”
10.11: Dangers of predatory lifestyle
Solitary Predator:
10.12: Escape from predation – on your own
1) Escape in time
2) Escape in space
3) Behavior
4) Physical mechanisms
5) Chemical mechanisms
6) Coloration:
i. Cryptic
ii. Confusing
iii. Startle
iv. Flash
v. Aposematic
7) Mimicry: Batesian vs. Muellerian
Highlights: Predator-Prey Interactions
•
•
•
•
•
•
•
•
•
The Lotka–Volterra equations
Functional responses
Functional responses and the Lotka–Volterra equations
Graphical analyses
The half-saturation constant in predator–prey
interactions
Nicholson–Bailey models
Field studies of predator–prey interactions
Trophic cascades
Types of escape from predation
Chapter 11: Plant-Herbivore Interactions
11.1: Introduction-Historical Perspective
Relationship between herbivore-plant relationships and 2nd
compounds was discovered by Fraenkel (1959)
Initially thought of as wastes from metabolism without a function
Ehrlich and Raven (1964) argued that 2nd compounds were a product
of the plants coevolutionary history with herbivores
-provided foundation for ecological approach to plant herbivore
interactions.
-proposed Evolutionary Arms Race = The process of evolution and
counter-evolution of chemical defenses between plants and
herbivores
11.1: Introduction-Historical Perspective
Evolutionary Arms Race = The process of evolution and
counter-evolution of chemical defenses between plants and
herbivores
Assumptions:
1) Herbivore activity is harmful to plants
2) Plants are able to evolve defenses that deter herbivores
3) Herbivore life activities guided by ability of plants to defend
themselves
4) Herbivores appear as generalists but exhibit preference
5) Majority of herbivores are specialists
11.2 Classes of plant chemical defenses
> 40,000 chemical compounds
Referred to as allelochemicals
Three main types:
1) terpenoids
2) phenolics
3) nitrogen-based ~ such as alkaloids
Production of 2nd compounds is metabolically expensive!
11.2 Classes of chemical defenses
Nitrogen based 2nd compounds:
Alkaloids
Deadly night shade->
Coca plant (cocaine) ->
11.2 Classes of chemical defenses
Nitrogen based secondary compounds:
Glycosides – biologically active forms
of steroids
Cardiac glycosides ->
Found in 11 plant families including:
Apocynanaceae, Asclepiadaceae, Scrophulariaceae
(from terpenoids)
11.2 Classes of chemical defenses
Carbon based secondary compounds:
Phenolic compounds
Flavanoids (provide color to flowers/fruits)
Hydrolyzable tannins
Non-hydrozlyable or Condensed tannins
Furanocoumarins
Terpenoids
ex., Apiaceae (carrot family)
11.3 Constitutive vs. Induced defenses
Constitutive defense =
Induced defense =
To qualify as an induced defense (or resistance), the response
must result in a decrease in herbivore or predatory damage
AND an increase in fitness must be observed in the non-induced
controls.
Conditions necessary for evolution of inducible defense:
1) selective pressures variable and unpredictable
2) reliable cue needed to activate defense
3) defense must be effective
4) inducible defense must save energy compared to constitutive
defense or no defense
11.4 Plant communication
Damage of one plant promotes induction of chemical defense from
surrounding plants.
Plants that share same air space may chemically communicate with
one another
When plants are damaged volatile chemical cues may be sent to
herbivores, and by the predators and parasites of the herbivores
to locate plants
11.5 Plant–parasitoid communication
When herbivore ~ caterpillar begins to eat a leaf, the plant releases a
volatile chemical that attracts parasitoids
Natural history of this interaction….
11.6 Revisit hare and the lynx story
11.7 Novel defense/herbivore response
Fig. 1. Squirt-gun defense of (A) Bursera
trimera, (B) Bursera rzedowski, and (C) Bursera
schlechtendalii.
Becerra J X et al. Amer. Zool. 2001;41:865-876
11.8 Detoxification of plant compounds by
herbivores
Stage 1
Stage 2
11.9 Plant apparency & chemical defense
A general theory, Feeny (1976) to predict the type and amount of
defense a plant has evolved:
1) Apparent species
2) Unapparent species
3) Developmental variation within a plant
11.10 Soil fertility & chemical defense
11.11 Optimal defense theory
11.12 Modeling plant-herbivore popln dynamics
Most common approach:
Most models based on grazers of vegetation and assume that plant
quality does not vary and ONLY examine the effect of quantity
consumed by grazers.
Second approach:
Assume that quality can vary but a set quantity is consumed by
grazer.
Borrow from predator-prey models and our dependable Lotka-Volterra
models
11.12 Modeling plant-herbivore popln dynamics
Density independent growth = rvV
with rv = ~ intrinsic rate of growth
V = plant abundance or biomass
Density dependent growth with logistic equation
dV/dt = rvV (Kv-V/Kv)
Kv = carrying capacity for plant reproduction
F = efficiency of herbivore’s removal of plant tissue
(similar to E = predator efficiency)
Herbivore Functional response = FNV = Type 1
EQUAL TO?
with N = #herbivores
11.12 Modeling plant-herbivore popln dynamics
Type II Functional Response ~ non-linear response
FNV/ (1 + Fh2V)
h = handling time component
Type III Functional Response ~ threshold response
FNV2/ (1+ Fh3V2)
11.12 Modeling plant-herbivore popln dynamics
Half-saturation constant for herbivore-plant interaction:
fNV/(b+V)
f = maximum consumption or grazing rate
b = half of the maximum consumption rate
V = plant biomass or abundance
N = number of herbivores
Using the functional response with a half-saturation constant, the plant
growth equation becomes….
11.12 Modeling plant-herbivore popln dynamics
Now plant growth response becomes:
dV/dt = rvV(Kv-V/Kv) – fNV/b+V
eq. 11. 1
Using logistic growth of V assumes as gets close to K growth slows. This
is reasonable for annuals (seed to seed within one year)
However, many plants are long-lived and store resources underground,
so growth may follow a linear and not a logistic growth curve Fig.
11.1
dV/dt = u0(1-V/Kv)
eq. 11.2
u0 = plant growth rate with V close to 0, and V = only above ground
biomass called Linear re-growth model
OMIT: 11.12 Modeling plant-herbivore popln
dynamics
Herbivore popln can be modeled with Positive Numerical Response
Density independent
Density dependent
Following Lotka-Volterra numerical response = XhfNV
f = maximum grazing rate
Xh = herbivore’s assimilation rate
Xhf = max rate plant material is turned into new herbivores
Can follow similar logic used in predator-prey models (Chapter 10)
OMIT: 11.12 Modeling plant-herbivore popln
dynamics
Herbivore death rate is density independent constant mh
OR add coefficient θ = density independent when equals 1 but also
increases herbivore death rate at high densities if θ>1
dN/dt = XhFNV/(b+V) –mhNθ
eq. 11.3
If rework considering amount of food/herbivore instead of amt.
food/area: Ratio dependent (also similar to pred-prey)
dN/dt = XhFN (V/N) –mhN
eq. 11.4
If both stop growing then reach equilibrium where dN/dt =0
OMIT: 11.12 Modeling plant-herbivore popln
dynamics
If both stop growing then reach equilibrium* where dN/dt =0
Leads to paradox of enrichment, unstable with vegetation abundant
(owing to built in time lag):
V* = mhN*/Xhf
eq. 11.5
N* = XhfV*/mh
eq. 11.6
Replace logistic with linear re-growth and achieve stability (no time
lag):
dV/dt = u0(1-V/Kv) – fNV/(b+V)
eq. 11.7
dN/dt = XhN [fV/b+V) – μh]
eq. 11.8
11.12 Modeling plant-herbivore popln dynamics
Presence of a refuge to protect plant biomass is key (and again similar
to prey having a refuge to hide)
Models can also incorporate -up to now only dealt with quantity of
veg.
Quality of vegetation modeling ex., Larch budworm interaction
Tritrophic interactions Overcompensation –
Community level effectsKeystone species -
Highlights: Plant-Hebivore Interactions
• Classes of chemical defenses
• Constitutive versus induced defense
• Plant communication and plant–parasitoid
communication
• Novel defenses/herbivore responses
• Detoxification of plant compounds by herbivores
• Plant apparency, soil fertility, and chemical defense
• The optimal defense theory
• Modeling plant–herbivore population dynamics
• The complexities of plant–herbivore interactions
Highlights of plant-herbivore & predator-prey systems
1) Addition of self-limitation terms adds stability to both relationships
2) Modeling producers with linear re-growth rather than logistic growth
also produces a more stable outcome
3) Multi-tropic models do a better job of explaining nature – surprised?
Questions?