lecture 12 - science.umd.edu ecology sprin… · pop growth for predator = (x p) enp . 10.2:...

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


• 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


• 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


• 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) Prey usually have a refuge

2) Predation is almost always not random

3) Generation times between prey and predator often vary

4) Predators may be generalist

5) 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 Prey : N* = mp/xpE eq 10.6/7

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 predator-prey 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

10.11: Dangers of predatory lifestyle

Solitary Predator:

Definition: Estes et al. 2001 = “Progression of indirect effects by predators across successively lower trophic levels”

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


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


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) ->


Nitrogen based secondary compounds:

Glycosides – biologically active forms

of steroids

Cardiac glycosides ->

Found in 11 plant families including:

Apocynanaceae, Asclepiadaceae, Scrophulariaceae

(from terpenoids)


Carbon based secondary compounds:

Phenolic compounds

Flavanoids (provide color to flowers/fruits)

Hydrolyzable tannins

Non-hydrozlyable or Condensed tannins

Furanocoumarins ex., Apiaceae (carrot family)

Terpenoids

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


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 with N = #herbivores

EQUAL TO?


Type II Functional Response ~ non-linear response

FNV/ (1 + Fh2V)

h = handling time component

Type III Functional Response ~ threshold response

FNV2/ (1+ Fh3V2)


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….


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)


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


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


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 effects-

Keystone 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?

lecture 12 - science.umd.edu ecology sprin… · pop growth for predator = (x p) enp . 10.2:...

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