“Nature red in tooth & claw” Alfred Tennyson (1809 - 1892)

1. Multi-Trophic Level, Pairwise Species Interactions:Predator-Prey, Parasitoid-Host & Parasite-Host Relationships “Nature red in tooth & claw” Alfred Tennyson (1809 - 1892)

2. Predation & Parasitism Why study predation & parasitism? A basic-science answer: All organisms are subject to various sources of mortality, including starvation, disease & predation; to understand population & community structure & dynamics requires knowing something about these processes Photo from Greg Dimijian

3. Predation & Parasitism Why study predation & parasitism? A basic-science answer: All organisms are subject to various sources of mortality, including starvation, disease & predation; to understand population & community structure & dynamics requires knowing something about these processes A utilitarian answer: Understanding how much natural mortality occurs, and why, in populations is critical to managing those that we exploit (e.g., fisheries, game animals, etc.), or wish to control (e.g., weeds, disease organisms or vectors, invasive species, etc.) Photo from Greg Dimijian

4. Predation Modeling predation: Lotka-Volterra model Prey (victims) in the absence of predators: dV/dt = rV Prey in the presence of predators: dV/dt = rV - VP where VPis loss to predators Losses to predators are proportional to VP (probability of random encounters) and  (capture efficiency – effect of a single predator on the per capita growth rate of the prey population) Large  is exemplified by a baleen whale eating krill, small  by a spider catching flies in its web Vis the functional response of the predator (rate of prey capture as a function of prey abundance); in this case linear, i.e., prey capture increases at a constant rate as prey density increases

5. Predation In the model’s simplest form, the predator is specialized on 1 prey species; in the absence of prey the predator pop. declines exponentially: dP/dt = -qP P is the predator pop. size, and q is the per capita death rate Positive population growth occurs when prey are present: dP/dt = ßVP - qP ßis the conversion efficiency – the ability of predators to turn a prey item into per capita growth Large ßis exemplified by a spider catching flies in its web (or wolves preying on moose), small ß by a baleen whale eating krill ßVis the numerical response of the predator population – the per capita growth rate of the predator pop. as a function of the prey pop.

6. The prey isocline P depends on the ratio of the growth rate of prey to the capture efficiency of the predator ^ Equilibrium solution: For the prey (V) population: dV/dt = rV - VP 0 = rV - VP VP= rV P = r P = r/ dV/dt < 0 dV/dt > 0 Figure from Gotelli (2001)

7. Equilibrium solution: For the predator (P) population: dP/dt = ßVP - qP 0 = ßVP - qP ßVP = qP ßV = q V = q/ß dP/dt < 0 dP/dt > 0 The predator isocline V depends on the ratio of the death rate of predators to the conversion efficiency of predators ^ Figure from Gotelli (2001)

8. Combined graphical solution in state space: The predator and prey populations cycle because they reciprocally control one another’s growth Figure from Gotelli (2001)

9. Combined graphical solution in state space: The predator and prey populations cycle because they reciprocally control one another’s growth Figure from Gotelli (2001)

10. Prey limited by both intraspecific competition and predation: dV/dt = rV - VP - cV2 VP  due to predator cV2 due to conspecifics dP/dt = ßVP – qP Now the prey isocline slopes downward, as in the Lotka-Volterra competition models The predator and prey populations reach a stable equilibrium At this point, the prey population is self-limiting, i.e., no predators are required to keep the population from changing in size. What did this point represent in the competition models? Figure from Gotelli (2001)

11. Functional Response Curves Why might functional responses have these shapes? Satiation Rate of prey capture Host-switching, developing a search image, etc. Victim abundance (V) Figure from Gotelli (2001), after Holling (1959)

12. Predators with either a Type II or Type III functional response: Type II for prey: dV/dt = rV - [(kV) / (V+D)]P Type III for prey: dV/dt = rV - [(kV2) / (V2+D2)]P Where k = maximum feeding rate; D = half-saturation constant, i.e., abundance of prey at which feeding rate is half-maximal Predator: dP/dt = ßVP – qP The equilibrium in both cases (Type II & Type III functional responses) is unstable Figure from Gotelli (2001)

13. An even more realistic prey isocline may be a humped curve: In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition Figure from Gotelli (2001)

14. An even more realistic prey isocline may be a humped curve: In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition Figure from Gotelli (2001)

15. An even more realistic prey isocline may be a humped curve: In this case, the position of the predator isocline with respect to the maximum in the prey isocline determines dynamics For example, imagine a combination of Allee effects, decreasing impact of predators with increases in prey numbers (e.g., Type II or III functional response), plus increasing impact of intraspecific competition Figure from Gotelli (2001)

16. Coexistence with stable limit cycles Coexistence at stable equilibrium Unstable equilibrium Figure from Gotelli (2001)

17. Paradox of enrichment in predator-prey interactions(Rosenzweig 1971) This idea developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management “control” conditions enriched conditions Figure from Gotelli (2001)

18. Paradox of enrichment in predator-prey interactions(Rosenzweig 1971) This idea developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management “control” conditions enriched conditions Figure from Gotelli (2001)

19. Paradox of enrichment in predator-prey interactions(Rosenzweig 1971) But is it only of theoretical interest? See: Abrams & Walters 1996; Murdoch et al. 1998, Persson et al. 2001 In the real world enrichment generally fails to destabilize dynamics in this way, perhaps due to nearly ubiquitous occurrence of some invulnerable prey “control” conditions enriched conditions Figure from Gotelli (2001)

20. Paradox of enrichment in competitive interactions(Riebesell 1974; Tilman 1982, 1988) Slope of consumption vectors for A This is one way in which competitive interactions can also result in a paradox of enrichment A B Slope of consumption vectors for B This idea also developed out of a desire to warn against indiscriminate use of resource enrichment to bolster a population under management 1 3 2 R2 [P] 4 5 6 R1 [N] Imagine what happens when we fertilize with N Consumption vectors Resource supply point

21. Effect of changing the predator isocline(by changing the numerical response of the predator) Predator is a complete specialist on the focal prey Predator’s K depends on the abundance of the focal prey Predator uses multiple prey, so predator’s K is independent of the focal prey; in this case predator has low K Where would the predator isocline be if the predator uses multiple prey and deterministically drives the focal prey extinct? Figure from Gotelli (2001)

22. Effect of prey refuges or immigration (rescue effect) Tends to stabilize dynamics Figure from Gotelli (2001)

23. Experiment demonstrating the stabilizing influence of refuges Six-spotted mite feeds on oranges and disperses among oranges by foot or by ballooning on silk strands Predatory mite disperses by foot See Huffaker (1958)

24. Experiment demonstrating the stabilizing influence of refuges Six-spotted mite feeds on oranges and disperses among oranges by foot or by ballooning on silk strands Predatory mite disperses by foot In experimental arrays, predators drove prey extinct in the absence of prey refuges; predator pop. then crashed In large arrays with refuges (see fig.) predators & prey coexisted with coupled oscillations See Huffaker (1958)

25. Effect of time lags So far we have assumed that responses of predators to prey (and vice versa) are instantaneous Time lags (the time required for consumed prey to be transformed into new predators, or for predators to die from starvation) add realism Incorporating time lags into models generally has a destabilizing effect, leading to larger-amplitude oscillations Harrison (1995) incorporated time lags into the numerical response of Didinium consuming Paramecium prey This greatly improved fits of models to actual population fluctuations of predator & prey described by Luckinbill (1973)

26. Additional biological complexity Coexistence at stable equilibria, after damped oscillation cycles, or within stable limit cycles, or instability & lack of coexistence, depending especially on the biology of the interacting species: Functional response of predators to prey (generally destabilizing if non-linear) Carrying capacity of predators and prey in the absence of the other (often stabilizing) Refuges for the prey (often stabilizing) Specificity of the predator to the prey (destabilizing if the switch occurs at a very low prey density, but stabilizing if the switch occurs at a higher prey density) Etc…

27. Lynx & hare Canada Lynx & Snowshoe Hare exhibit synchronized oscillatory dynamics in nature (Elton & Nicholson 1942) Hare pops. cycle with peak abundance ~ every 10 yr; Lynx pops. track hare pops., with ~ 1 - 2 yr time lag Figure from Gotelli (2001)

28. Lynx & hare Simple Lotka-Volterra model is not a complete explanation; e.g., cycles are broadly synchronized, even on some Canadian islands w/o lynx Hare populations are co-limited by food availability & predation (e.g., Keith 1983); hares rapidly deplete food quantity (principally buds & young stems of shrubs & saplings) & quality (hares stimulate induced defenses of food plants) Low food availability increases susceptibility to predation (lynx, weasels, foxes, coyotes, goshawks, owls & etc.) Sun spot cycles and their influence on climate & food plants are also implicated (e.g., Krebs et al. 2001) At any rate, the lynx-hare cycle is more complex than suggested by the superficial resemblance to Lotka-Volterra models

29. Phenotypic Plasticity & Predation How might the evolutionary advent of phenotypic plasticityalter predator-prey dynamics? Agrawal (2001), Fig. 1

30. Escape through predator satiation(as may occur in Type II & III functional responses) Plant examples: Janzen (1976) suggested that seed predation is a major selective force favoring “masting” (massive supra-annual seed production). Bamboos are the most dramatic mast fruiters, with many species fruiting at 30-50 yr intervals and some much longer, e.g., Phyllostachysbambusoides fruits at 120 year intervals! Other masters: Dipterocarpaceae, oaks, beech, many conifers, and possibly the majority of tropical trees. Animal examples: Williams et al. (1983) provided evidence that Magicicada spp. emerge once every 13 or 17 yrs to avoid similarly cycling predators. These emerge at densities of up to 4 million/ha = 4 tons of cicadas/ha  the highest biomass of a natural population of terrestrial animals ever recorded.

31. Size-dependent predation Mean-field assumption: all prey are the same (size, etc.) Large prey may escape consumption owing to mechanical constraints on feeding, e.g., Paine (1966) found that the gastropod Muricanthus becomes too large for Heliaster starfish to handle Small prey may escape detection, or resources expended in capturing and handling them may exceed resources obtained by their consumption (the “celery bind”)

32. Size-dependent predation Brooks and Dodson (1965) proposed that size-dependent predation by fish determines the size structure of freshwater zooplankton Observations: Lakes seldom contained abundant large zooplankton (>0.5 mm) & small zooplankton (<0.5 mm) together Large zooplankton were not found with plankton-feeding fish

33. Size-dependent predation Crystal Lake, Connecticut No planktivorous fish Large plankton Crystal Lake 22 yr after introduction of Alosa aestivalis (Blueback Herring)

34. Size-dependent predation Brooks and Dodson (1965) proposed that size-dependent predation by fish determines the size structure of freshwater zooplankton Observations: Lakes seldom contained abundant large zooplankton (>0.5 mm) & small zooplankton (<0.5 mm) together Large zooplankton were not found with plankton-feeding fish Hypotheses: Large zooplankton are superior competitors for food (phytoplankton) because of greater filtering efficiency Planktivorous fish selectively consume large-bodied, competitively superior plankton

35. Size-dependent predation Detailed analyses of the mechanisms of change showed that: Fish do indeed selectively remove large-bodied zooplankton But, large-bodied zooplankton do not competitively exclude small- bodied zooplankton… they eat them (intra-guild predation)!

36. Brood Parasitism In some cases brood parasitism represents “predation” and parasitism combined Davies 1992, pg. 217

37. Conceptual models of parasitism(usually categorized by function rather than taxonomy) Microparasites – parasites that reproduce within the host, often within the host’s cells, and are generally small in size and have short lifespans relative to their hosts; hosts that recover often have an immune period after infection (sometimes for life); infections are often transient; examples include: bacterial, viral, fungal infectious agents, as well as many protozoans Macroparasites – parasites that grow, but have no direct reproduction within the host (they produce infective stages that must colonize new hosts); typically much larger and have longer generation times than microparasites; immune response in hosts is typically absent or very short-lived; infections are often chronic as hosts are continually reinfected; examples include: helminths and arthropods Parasitoids – insects whose larvae develop by feeding on a single arthropod host and invariably kill that host; e.g., Nicholson-Bailey models

38. dX/dt = a(X+Y+Z) - bX - βXY + Z dY/dt = βXY - (α+b+v)Y dZ/dt = vY - (b+)Z Coupled differential equations, one for each type of host Modeling microparasite-host dynamics What is βXY? Combined encounter & infection rate Birth a a a Susceptible hosts (X) Infected hosts (Y) Immune hosts (Z) β v α + b b b Death  See: Anderson & May (1979); May (1983)

39. Modeling macroparasite-host dynamics There are many examples of parasites limiting or regulating their host abundances, or determining distribution patterns. One of the best examples of host populations that cycle in response to enemies comes from Scotland: Red grouse and their nematode parasites (Dobson & Hudson 1992). Grouse: dH/dt = (b-d-cH)H - (α+)P Incorporates reduction in survival (α) & reprod. () Free-living stages (eggs and larvae) of the worms: dW/dt = P - W - βWH Adult worm population (within caecae of grouse): dP/dt= βWH - (+d+α)P - α(P2/H)(k+1/k) Final term represents aggregation among hosts (smaller k  more aggregated) Parameter values were estimated in the field. For Scotland, the model predicted the observed 5-yr cycles. For drier sites in England, the model predicted a lack of cycles owing to higher mortality of free-living stages, and these populations do indeed lack cycles.

40. Parasitism The same rich variety of dynamics observed for predators and their prey arise in various kinds of parasite-host and parasitoid-host models, including all possibilities from stable coexistence, to unstable exclusion, to cycles and chaos

41. Parasite-host interactions & invasive species Parasite species richness (shown below) and parasite prevalence (% infected hosts) showed similar patterns 1.0 1-to-1 line molluscs crustaceans Standardized S of parasites in introduced range amphibians & reptiles 0.5 fish birds mammals 0 1.0 0 0.5 Standardized S of parasites in native range Redrawn from Torchin et al. (2003)

42. Parasite-host interactions through evolutionary time Evolutionary trajectories of virulence… Some key results: Horizontal vs. vertical transmission (see Ewald 1994) Horizontal transmission generally leads to greater virulence than vertical transmission Greater virulence usually results from higher transmission rates in general Degree of alignment of reprod. interests (see Herre et al. 1999) The tighter the dependence of parasite reproduction on host reproduction, the less virulent parasites tend to become Darwinian Medicine makes good use of these observations (see G. C. Williams & R. M. Nesse)

43. Parasite-host interactions through evolutionary time Co-cladogenesis and other macro-evolutionary processes…

44. Hostswitch Duplication Host Parasite Failure to speciate Missing the boat Extinction Coexistence Cospeciation Which are most likely under strictly vertical transmission? From J. Weckstein (2003)

45. All else being equal, will host-switches preferentially occur onto more common potential hosts? ? ?

46. All else being equal, will host-switches preferentially occur onto potential hosts that are more closely related to the current host? ? ?

47. What patterns do we expect in communities in which parasites (predators, parasitoids) have multiple potential “choices”? ? ? ?

48. Ghosts of Predation Past North American Cheetah (Miracinonyx) went extinct ~11,000 yr ago; even so the Pronghorn Antelope remains the fastest land animal in N. Am. Miracinonyx was similar to extant Acinonyx jubatus Photos from: http://www.hoothollow.com