Dynamics (e.g. stability) in food webs: driven by attributes of the system or of web members?? May 1973: overturned, for a while, this intuition with computer models showing that communities more likely to return to equilOther objections to descriptive (S,C) food web theory (Polis 1991)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) bhcda,fb,e,hagTaxon2 speciesFood chainStrong interactionsDynamics (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 tropicalResilienceResistanceGlobal High LowLow HighLocalStability propertiesResilience: rate of recovery by system to previous state following perturbationResistance: 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 chains3. Average interaction strength, βSystem: group of entities united by interaction or interdependence to form or act as an entire unitMay 1973: overturned, for a while, this intuition with computer models showing that communities more likely to return to equilibrium after perturbation ifβ [ 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= 9/16βij=[ δ (dNi/dt)] / δjInteraction strengthPaine 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)SCPimm, 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 feedersscorpionspidercricketPolis and Holt 1989?•Trophiclevel: 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 productivityP = plants, H = herbivores, C = carnivoresS = secondary carnivores (eat carnivores)PredatorDensity, PPrey density, NPredator functional response (aN) depends only on prey density (Lotka Volterra)dN/dt = 0K highK lowPredator experiences interference from other predators, so functional response (a (N,P)) decreases with