7. Match the predator-prey isoclines (on the next page) with a biological mechanism that could explain them (put the letter of the appropriate graph next to its description below). Some graphs will be used more than once and some descriptions fit more than one graph. (16 points) Graph(s): A. the prey has a refuge from predators at low prey densities: ______________ B. the prey experiences an Allee Effect at low prey densities: ______________ C. the predator is limited by cover rather than prey at ______________ high predator densities: D. the predator experiences mild interference from other predators at high predator densities: ______________ E. all predators in the population can efficiently track the availability of patchy prey through space, finding and exploiting the most _____________ available at any given time F. the prey population becomes self limited at low predator densities _____________ G. the predator is efficient at low prey density, (e.g. it can sustaining itself on very low food intake) _____________ H. the prey population grows exponentially in the absence of predation _____________ over the range of densities shown in the phase diagram

Predator-Prey Isoclines: (for problem 7) NOTE!

A predator isocline is labeled: dpdt

= 0 A prey isocline is labeled: dndt

= 0

(a) (b) (c)

dpdt

= 0 dndt

= 0 dpdt

= 0

Prey density (n) Prey density (n) Prey density (n) (d) (e) (f)

dpdt

= 0 dndt

= 0 dpdt

= 0

Prey density (n) Prey density (n) Prey density (n) (g) (h)

dndt

= 0 dndt

= 0

Prey density (n) Prey density (n)

Predator density (p)

Predator density (p)

Predator density (p)

bhc

d

a,f

b,e,h

a

g

Taxon

2 species

Food chainStrong interactions

Dynamics (e.g. stability) in food webs: driven by attributes of the system or of web members??

• Older (Elton 1927, MacArthur 1972) and current (Tilman, Naeem) view: diversity stabilizes communities– Eggs in many baskets, redundant rivets, parallel vs series

circuits– Backup resources or control paths, etc.– Monocultures less stable– Islands less stable than mainland communities– Lab less stable field predator-prey systems– Temperate zone population dynamics less stable than tropical

Resilience

Resistance

Glob

al

High

Low

Low HighLocal

Stability properties

Resilience: rate of recovery by system to previous state following perturbation

Resistance: degree of perturbation system can withstand without changing

• Community: co-occurring organisms

• Food (interaction) web: depiction of feeding (or any significant) relationships in a community (arbitrarily resolved and delimited)

• System characteristics1. Diversity, S (number of

spp)2. Connectance, number of

links (realized / possible interactions)

Interaction webs,food webs, food chains

3. Average interaction strength, β

System: group of entities united by interaction or interdependence to form or act as an entire unit

May 1973: overturned, for a while, this intuition with computer models showing that communities more likely to return to equilibrium after perturbation if

β [ S C ] 0.5 < 1•System characteristics1.Diversity, S (number of

species)2.Connectance, C/ S2

(C = number of actual interactions, S2 = number of possible interactions) (or S (S-1) if no cannibalism)

C/S2 = 9/16

βij =[ δ (dNi/dt)] / δj

Interaction strength

Paine 1988 re-interpreted these results as ‘pruning’ (simply reflecting a tradeoff in investigator effort).

•System characteristics1.Diversity, S (number of spp)2.Connectance, C/ S2 (C = number of actual interactions, S2 = number of possible interactions)

S

C

Pimm, Lawton, Cohen, and others combed literature and found hyperbolic relationships between S and C, which they interpreted as support for prediction that diverse, highly connected webs with strong interactions are dynamically more fragile.

Other objections to descriptive (S,C) food web theory (Polis 1991)

• Web arbitrarily delimited: graphs plot Artic Ocean and carrion fauna on dead toad as equivalent points

• Diversity (S) inconsistently measured: higher trophic levels much more resolved than lower ones

• Theorists asserted omnivory and loops (A eats B eats C eats A) were rare (because they destabilized their models), but they’re actually rampant in nature– Intraguild predation (size dependence)– Omnivory

• Life history• Generalist feeders

scorpion

spider

cricket

Polis and Holt 1989

?

• Trophic level: functional grouping of organisms according to their primary food source– Bottom up level: number of

energy transfers from fixation of organic carbon) to reach that level

– Top down level: number of lower levels that are alternatively released and suppressed when this level and those higher are removed.

Food chain: simplified caricature-Aggregate (community level trophic cascades), orfind strong interactors (large β)?

Food chain length determines limiting factors for plants:

One trophic level: plants are not limited by consumers, and increase until they are limited by resources like light or nutrients.

With odd food chain lengths, the world should look green;with even lengths, it should look barren.

Two trophic levels: grazers suppress plants, so adding light or nutrients increases grazer biomass, not plant biomass.

Three trophic levels: predators protect plants from grazers, so plants are resource limited.

Four trophic levels: predators of predators release grazers, so plants are grazer, not resource limited.

Fretwell and others predicted that food chains should lengthen across a gradient of environmental productivity

P = plants, H = herbivores, C = carnivoresS = secondary carnivores

(eat carnivores)

PredatorDensity, P

Prey density, N

Predator functional response (aN) depends only on prey density (Lotka Volterra)

dN/dt = 0

K highK low

Predator experiences interference from other predators, so functional response (a (N,P)) decreases with predator density

Self limiting prey in rich and poor environments

P

N

dP/dt = 0

dN/dt = 0

K highK low

Environmental ProductivityLow High

Efficient predator

Inefficient predator

Pred

ator

or

Prey

Biom

ass

Prey versus Ratio (Prey/predator) dependent functional responses (efficient vs inefficient tracking by predators, respectively)

Simple Lotka Volterra models with efficient predators

Models with predator functional responses that reflect interference

Odd number of levels: green (plants resource limited)

Even number of levels: barren (plants grazer limited)

Characteristics of organisms that imply that food chain theory shouldn’t work:

1. Green could be inedible (world is one trophic level) (Feeney)

2. consumers are co-limited by predators and food (or other factors) (Sih, Sinclair, Power)

3. Omnivory blurs trophic levels (Polis, Peters)

4. Factors other than consumers or food limit populations (Andrewartha and Birch)

1

Food Webs and Food Chains 10/24/06 Recommended readings Barabasi, A. N. 2002. Linked. The new science of networks. Perseus, Cambridge, MA. Berlow, E. L., S. A. Navarrete, C. J. Briggs, M. E. Power, and B. A. Menge. 1999. Quantifying

variation in the strengths of species interactions. Ecology (Washington D C) 80:2206-2224.

Carpenter, S. R., J. F. Kitchell, and J. R. Hodgson. 1985. Cascading trophic interactions and lake productivity. BioScience 35:634-649.

Croll, D. A., J. L. Maron, J. A. Estes, E. M. Danner, and G. V. Byrd. 2005. Introduced predators transform subarctic islands from grassland to tundra. Science 307:1959-1961.

Duggins, D. O. 1980. Kelp beds and sea otters: an experimental approach. Ecology 61:447-453. Elton, C. 1927. Animal Ecology. Sidgwick and Jackson, London. Estes, J. A., M. T. Tinker, T. M. Williams, and D. F. D.F. Doak. 1998. Killer whale predation

on sea otters linking oceanic and nearshore ecosystems. Science 282:473-476. Estes, J. A., and J. F. Palmisano. 1974. Sea otters: their role in structuring nearshore

communities. Science 185:1058-1060. MacArthur, R. H. 1972. Geographical Ecology. Harper and Row, New York. MacArthur, R. H. 1972. Strong, or weak, interactions? Transactions, The Connecticut Academy of

Arts and Sciences 44:177-188. Paine, R. T. 1966. Food web complexity and species diversity. American Naturalist 100:65-

75. Paine, R. T. 1980. Food webs: linkage, interaction strength and community infrastructure.

Journal of Animal Ecology 49:667-685. Paine, R. T. 1992. Food web analysis: field measurements of per capita interaction strength.

Nature. Polis, G. A. 1991. Complex trophic interactions in deserts: an empirical critique of food web

theory. American Naturalist 138:123-155. Power, M. E., W. J. Matthews, and A. J. Stewart. 1985. Grazing minnows [Campostoma

anomalum] piscivorous bass, and stream algae: Dynamics of a strong interaction. Ecology (Tempe) 66:1448-1456.

Power, M. E., D. Tilman, J. Estes, B. A. Menge, L. S. Mills, W. J. Bond, G. Daily, J. Lubchenco, J. C. Castilla, and R. T. Paine. 1996. Challenges in the quest for keystones. BioScience 46:609-628.

Power, M. E., T. L. Dudley, and S. D. Cooper. 1989. Grazing catfish, fishing birds, and attached algae in a Panamanian stream. Environmental Biology of Fishes 26:285-294.

Scheffer, M., S. Carpenter, J. A. Foley, C. Folkes, and B. Walker. 2001. Catastrophic shifts in ecosystems. Nature 413:591-596.

Simenstad, C. A., J. A. Estes, and K. W. Kenyon. 1978. Aleuts, sea otters, and alternate stable-state communities. Science 200:403-411.

Springer, A.M., J.A. Estes, G.B. van Vliet, T.M. Williams, D.F. Doak, E.M. Danner, K.A. Forney, and B. Pfister. Sequential megafaunal collapse in the North Pacific Ocean: an ongoing legacy of industrial whaling? In press, Proc. Nat. Acad. Sci.

Steinberg, P. D., J. A. Estes, and F. C. Winter. 1995. Evolutionary consequences of food chain length in kelp forest communities. Proc. Natl. Acad. Sci. 92:8145-8148.