Lecture 12. Chapter 10: Predator Prey interactions Chapter 11: Plant Herbivore interactions

Transcription

1 Lecture 12 Chapter 10: Predator Prey interactions Chapter 11: Plant Herbivore interactions

2 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

3 10.1: Introduction-Historical Perspective Predation Rate Numerical response Functional response Total Response Fig Stable limit cycle: Predator - Prey vs. time Fig Stable limit cycle: Prey vs. Predator popln

4 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

5 10.1: Introduction-Historical Perspective Fig Pred-prey vs. time: oscillation dampening -> Stable point Fig : Prey pop vs. pred. pop: Leads to Stable point Fig Prey-predator pops vs. time illustrating dampening oscillations Fig Predator-prey poplns illustrating dampened oscillations leading to a stable point. Fig Predator-prey poplns vs. time with increasing oscillations leading to extinction of both spp. Fig Increasing oscillations of prey popln vs. predator popln leading to extinction of both spp.

6 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

7 10.2: Lotka-Volterra equation dn/dt = r n N Eq. 10.1a dn/dt = r 2 N [K n -N / K n ] Eq. 10.1b Where: N n = number of individuals of prey spp ~ prey popln size r n = intrinsic rate of increase for prey spp. K n = prey carrying capacity Without prey the predator popln(p) dies off based on m p = instantaneous density independent mortality and popln declines as: dp/dt = -m p P Eq. 10.2

8 10.2: Lotka-Volterra equation And the chance of an encounter between predator and prey is: ENP eq 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 x p = constant reflecting efficiency that prey is turned into new predator individuals ~ Assimilation efficiency of predator Pop growth for predator = (x p ) ENP

9 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 = r n N-ENP eq. 10.4a Predator: dp/dt = x p ENP m p P eq At equilibrium: Predator: P* = r n /E Prey : N* = m p /x p E eq 10.6/7 Equilibrium analysis = set both to zero and include carrying capacity (K): dn/dt = r n N(K n -N/K n ) ENP eq 10.4b

10 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

11 10.4: Predation functional responses Type I Type II Type III - Fig Daphnia major ingestion of algae exhibiting Type I functional response curve Fig Damsel fly larvae Type II functional response curve while feeding on Daphnia major Fig Three Lemming predators Type III functional response curves

12 10.5: Addition of prey density with Type II and III functional response modes Fig Predator-prey interaction following Lotka-Volterra equations with a Type I functional response -> mutual extinction Fig Predator-prey interaction with a Type II functional response -> both become stable Fig Predator-prey interaction with a Type III functional response with threshold -> both become stable

13 10.6: Rosenzweig and MacArthur Fig Prey and predator isoclines overview Fig Prey isocline with Allee effect, MVP, and K Fig Predator-prey isoclines with inefficient predator -> decreasing oscillations to stable point, S, where 2 isoclines meet Fig Predator-prey isoclines for moderately efficient predator -> stable limit cycle

14 10.6: Rosenzweig and MacArthur Fig Highly efficient predator, increasing isolations with extinction of both spp. Fig Predator-prey interaction with predator growth limited by an additional factor (not prey) -> stable point, S, is reached Fig Effect of paradox of enrichment on predator-prey interaction -> mutual extinction Fig Predator-prey interaction when prey have a refuge -> stable cycle Context Dependent!

15 OMIT: 10.7: Half-saturation constant use in predatorprey interactions dp/dt = [brp/k R +R] m p P eq revised from two competing species Where: P = predator population m p = death rate b = max rate of conversion of prey resource into predators R = prey population K R = 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.

16 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 Density Independent host-parasitoid -> unstable Fig Density Dependent host-parasitoid with K -> stable Fig Density Independent host-parasitoid -> mutual extinction

17 10.8: Parasitoid-host interactions & Nicholson-Bailey models Fig Stable limit cycle of host-parasitoid relationship Fig Host-parasitoid poplns over time, a = > Stable point Fig Host-Parasitoid polns interactions, search efficiency, a = > stable point

18 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

19 10.10: Trophic cascades Definition: Estes et al = Progression of indirect effects by predators across successively lower trophic levels 10.11: Dangers of predatory lifestyle Solitary Predator:

20 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

21 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

22 Chapter 11: Plant-Herbivore Interactions

23 11.1: Introduction-Historical Perspective Relationship between herbivore-plant relationships and 2 nd compounds was discovered by Fraenkel (1959) Initially thought of as wastes from metabolism without a function Ehrlich and Raven (1964) argued that 2 nd 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

24 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

25 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 2 nd compounds is metabolically expensive!

26 11.2 Classes of chemical defenses Nitrogen based 2 nd compounds: Alkaloids Deadly night shade-> Coca plant (cocaine) ->

27 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)

28 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 ex., Apiaceae (carrot family) Terpenoids

29 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

30 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

31 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 Revisit hare and the lynx story

32 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:

33 11.8 Detoxification of plant compounds by herbivores Stage 1 Stage 2

34 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

35 11.10 Soil fertility & chemical defense Optimal defense theory

36 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

37 11.12 Modeling plant-herbivore popln dynamics Density independent growth = r v V with r v = ~ intrinsic rate of growth V = plant abundance or biomass Density dependent growth with logistic equation dv/dt = r v V (K v -V/K v ) K v = 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?

38 11.12 Modeling plant-herbivore popln dynamics Type II Functional Response ~ non-linear response FNV/ (1 + Fh 2 V) h = handling time component Type III Functional Response ~ threshold response FNV 2 / (1+ Fh 3 V 2 )

39 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.

40 11.12 Modeling plant-herbivore popln dynamics Now plant growth response becomes: dv/dt = r v V(K v -V/K v ) fnv/b+v eq 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 dv/dt = u 0 (1-V/K v ) eq u 0 = plant growth rate with V close to 0, and V = only above ground biomass called Linear re-growth model

41 OMIT: Modeling plant-herbivore popln dynamics Herbivore popln can be modeled with Positive Numerical Response Density independent Density dependent Following Lotka-Volterra numerical response = X h fnv f = maximum grazing rate X h = herbivore s assimilation rate X h f = max rate plant material is turned into new herbivores Can follow similar logic used in predator-prey models (Chapter 10)

42 OMIT: Modeling plant-herbivore popln dynamics Herbivore death rate is density independent constant m h OR add coefficient θ = density independent when equals 1 but also increases herbivore death rate at high densities if θ>1 dn/dt = X h FNV/(b+V) m h N θ eq If rework considering amount of food/herbivore instead of amt. food/area: Ratio dependent (also similar to pred-prey) dn/dt = X h FN (V/N) m h N eq If both stop growing then reach equilibrium where dn/dt =0

43 OMIT: 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* = m h N*/X h f eq N* = X h fv*/m h eq Replace logistic with linear re-growth and achieve stability (no time lag): dv/dt = u 0 (1-V/K v ) fnv/(b+v) eq dn/dt = X h N [fv/b+v) μ h ] eq. 11.8

44 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 effects- Keystone species -

45 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

46 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?