1. Chapter 18: Dynamics of Predation Robert E. Ricklefs The Economy of Nature, Fifth Edition (c) 2001 by W. H. Freeman and Company

2. Population Cycles of Canadian Hare and Lynx zCharles Elton’s seminal paper focused on fluctuations of mammals in the Canadian boreal forests. yElton’s analyses were based on trapping records maintained by the Hudson’s Bay Company yof special interest in these records are the regular and closely linked fluctuations in populations of the lynx and its principal prey, the snowshoe hare zWhat causes these cycles?

4. (c) 2001 by W. H. Freeman and Company Some Fundamental Questions zThe basic question of population biology is: ywhat factors influence the size and stability of populations? zBecause most species are both consumers and resources for other consumers, this basic question may be refocused: yare populations limited primarily by what they eat or by what eats them?

5. (c) 2001 by W. H. Freeman and Company More Questions zDo predators reduce the size of prey populations substantially below the carrying capacity set by resources for the prey? ythis question is prompted by interests in management of crop pests, game populations, and endangered species zDo the dynamics of predator-prey interactions cause populations to oscillate? ythis question is prompted by observations of predator-prey cycles in nature, such as Elton’s lynx and hare

6. (c) 2001 by W. H. Freeman and Company Consumers can limit resource populations. zAn example: populations of cyclamen mites, a pest of strawberry crops in California, can be regulated by a predatory mite: ycyclamen mites typically invade strawberry crops soon after planting and build to damaging levels in the second year ypredatory mites invade these fields in the second year and keep cyclamen mites in check zExperimental plots in which predatory mites were controlled by pesticide had cyclamen mite populations 25 times larger than untreated plots.

8. (c) 2001 by W. H. Freeman and Company What makes an effective predator? zPredatory mites control populations of cyclamen mites in strawberry plantings because, like other effective predators: ythey have a high reproductive capacity relative to that of their prey ythey have excellent dispersal powers ythey can switch to alternate food resources when their primary prey are unavailable

9. (c) 2001 by W. H. Freeman and Company Consumer Control in Aquatic Ecosystems zAn example: sea urchins exert strong control on populations of algae in rocky shore communities: yin urchin removal experiments, the biomass of algae quickly increases: xin the absence of predation, the composition of the algal community also shifts: large brown algae replace coralline and small green algae that can persist in the presence of predation

10. (c) 2001 by W. H. Freeman and Company Predator and prey populations often cycle. zPopulation cycles observed in Canada are present in many species: ylarge herbivores (snowshoe hares, muskrat, ruffed grouse, ptarmigan) have cycles of 9-10 years: xpredators of these species (red foxes, lynx, marten, mink, goshawks, owls) have similar cycles ysmall herbivores (voles and lemmings) have cycles of 4 years: xpredators of these species (arctic foxes, rough-legged hawks, snowy owls) also have similar cycles ycycles are longer in forest, shorter in tundra

14. (c) 2001 by W. H. Freeman and Company Predator-Prey Cycles: A Simple Explanation zPopulation cycles of predators lag slightly behind population cycles of their prey: ypredators eat prey and reduce their numbers ypredators go hungry and their numbers drop ywith fewer predators, the remaining prey survive better and prey numbers build ywith increasing numbers of prey, the predator populations also build, completing the cycle

15. (c) 2001 by W. H. Freeman and Company Time Lags in Predator-Prey Systems zDelays in responses of births and deaths to an environmental change produce population cycles: ypredator-prey interactions have time lags associated with the time required to produce offspring y4-year and 9- or 10-year cycles in Canadian tundra or forests suggest that time lags should be 1 or 2 years, respectively: xthese could be typical lengths of time between birth and sexual maturity xthe influence of conditions in one year might not be felt until young born in that year are old enough to reproduce

16. (c) 2001 by W. H. Freeman and Company Time Lags in Pathogen- Host Systems zImmune responses can create cycles of infection in certain diseases: ymeasles produced epidemics with a 2-year cycle in pre-vaccine human populations: xtwo years were required for a sufficiently large population of newly susceptible infants to accumulate

18. (c) 2001 by W. H. Freeman and Company Time Lags in Pathogen- Host Systems zother pathogens cycle because they kill sufficient hosts to reduce host density below the level where the pathogens can spread in the population: ysuch cycling is evident in polyhedrosis virus in tent caterpillars yIn many regions, tent caterpillar infestations last about 2 years before the virus brings its host population under control yIn other regions, infestations may last up to 9 years yForest fragmentation – which creates abundant forest edge – tends to prolong outbreaks of the tent caterpillar xWhy? xIncreased forest edge exposes caterpillars to more intense sunlight  inactivates the virus  thus, habitat manipulation here has secondary effects

22. (c) 2001 by W. H. Freeman and Company Laboratory Investigations of Predators and Prey zG.F. Gause conducted simple test-tube experiments with Paramecium (prey) and Didinium (predator): yin plain test tubes containing nutritive medium, the predator devoured all prey, then went extinct itself yin tubes with a glass wool refuge, some prey escaped predation, and the prey population reexpanded after the predator went extinct xGause could maintain predator-prey cycles in such tubes by periodically adding more predators

23. (c) 2001 by W. H. Freeman and Company Predator-prey interactions can be modeled by simple equations. zLotka and Volterra independently developed models of predator-prey interactions in the 1920s: dR/dt = rR - cRP describes the rate of increase of the prey population, where: R is the number of prey P is the number of predators r is the prey’s per capita exponential growth rate c is a constant expressing efficiency of predation

24. (c) 2001 by W. H. Freeman and Company Lotka-Volterra Predator- Prey Equations zA second equation: dP/dt = acRP - dP describes the rate of increase of the predator population, where: P is the number of predators R is the number of prey a is the efficiency of conversion of food to growth c is a constant expressing efficiency of predation d is a constant related to the death rate of predators

25. (c) 2001 by W. H. Freeman and Company Predictions of Lotka- Volterra Models zPredators and prey both have equilibrium conditions (equilibrium isoclines or zero growth isoclines): yP = r/c for the predator yR = d/ac for the prey ywhen these values are graphed, there is a single joint equilibrium point where population sizes of predator and prey are stable: xwhen populations stray from joint equilibrium, they cycle with period T = 2  /  rd

26. (c) 2001 by W. H. Freeman and Company Cycling in Lotka-Volterra Equations zA graph with axes representing sizes of the predator and prey populations illustrates the cyclic predictions of Lotka- Volterra predator-prey equations: ya population trajectory describes the joint cyclic changes of P and R counterclockwise through the P versus R graph

27. (c) 2001 by W. H. Freeman and Company Factors Changing Equilibrium Isoclines zThe prey isocline increases if: yr increases or c decreases, or both: xthe prey population would be able to support the burden of a larger predator population zThe predator isocline increases if: yd increases and either a or c decreases: xmore prey would be required to support the predator population

28. (c) 2001 by W. H. Freeman and Company Other Lotka-Volterra Predictions zIncreasing the predation efficiency (c) alone in the model reduces isoclines for predators and prey: yfewer prey would be needed to sustain a given capture rate ythe prey population would be less able to support the more efficient predator zIncreasing the birth rate of the prey (r) should lead to an increase in the population of predators but not the prey themselves.

29. (c) 2001 by W. H. Freeman and Company Modification of Lotka-Volterra Models for Predators and Prey zThere are various concerns with the Lotka-Volterra equations: ythe lack of any forces tending to restore the populations to the joint equilibrium: xthis condition is referred to as a neutral equilibrium ythe lack of any satiation of predators: xeach predator consumes a constant proportion of the prey population regardless of its density

30. (c) 2001 by W. H. Freeman and Company The Functional Response zA more realistic description of predator behavior incorporates alternative functional responses, proposed by C.S. Holling: ytype I response: rate of consumption per predator is proportional to prey density (no satiation) ytype II response: number of prey consumed per predator increases rapidly, then plateaus with increasing prey density ytype III response: like type II, except predator response to prey is depressed at low prey density

31. (c) 2001 by W. H. Freeman and Company The Holling Type III Response zWhat would cause the type III functional response? yheterogeneous habitat, which provides a limited number of safe hiding places for prey ylack of reinforcement of learned searching behavior due to a low rate of prey encounter yswitching by predator to alternative food sources when prey density is low

32. (c) 2001 by W. H. Freeman and Company The Numerical Response zIf individual predators exhibit satiation (type II or III functional responses), continued predator response to prey must come from: yincrease in predator population through local population growth or immigration from elsewhere xthis increase is referred to as a numerical response

33. (c) 2001 by W. H. Freeman and Company Several factors reduce predator-prey oscillations. zAll of the following tend to stabilize predator and prey numbers (in the sense of maintaining nonvarying equilibrium population sizes): ypredator inefficiency ydensity-dependent limitation of either predator or prey by external factors yalternative food sources for the predator yrefuges from predation at low prey densities yreduced time delays in predator responses to changes in prey abundance

34. (c) 2001 by W. H. Freeman and Company Destabilizing Influences zThe presence of predator-prey cycles indicates destabilizing influences: ysuch influences are typically time delays in predator- prey interactions: xdevelopmental period xtime required for numerical responses by predators xtime course for immune responses in animals and induced defenses in plants ywhen destabilizing influences outweigh stabilizing ones, population cycles may arise

35. (c) 2001 by W. H. Freeman and Company Predator-prey systems can have more than one stable state. zPrey are limited both by their food supply and the effects of predators: ysome populations may have two or more stable equilibrium points, or multiple stable states: xsuch a situation arises when: prey exhibits a typical pattern of density-dependence (reduced growth as carrying capacity is reached) predator exhibits a type III functional response

36. (c) 2001 by W. H. Freeman and Company Three Equilibria zThe model of predator and prey responses to prey density results in three stable or equilibrium states: ya stable point A (low prey density) where: xany increase in prey population is more than offset by increasingly efficient prey capture by predator yan unstable point B (intermediate prey density) where: xcontrol of prey shifts from predation to resource limitation ya stable point C where: xprey escapes control by predator and is regulated near its carrying capacity by resource scarcity

37. (c) 2001 by W. H. Freeman and Company Implications of Multiple Stable States zPredators may control prey at a low level (point A in model), but can lose the potential to regulate prey at this level if prey density increases above point B in the model: ya predator controlling an agricultural pest can lose control of that pest if the predator is suppressed by another factors for a time: xonce the pest population exceeds point B, it will increase to a high level at point C, regardless of predator activity xat this point, pest population will remain high until some other factor reduces the pest population below point B in the model

38. (c) 2001 by W. H. Freeman and Company Effects of Different Levels of Predation zInefficient predators cannot maintain prey at low levels (prey primarily limited by resources). zIncreased predator efficiency adds a second stable point at low prey density. zFurther increases in predator functional and numerical responses may eliminate a stable point at high prey density zIntense predation at all prey levels can drive the prey to extinction

39. (c) 2001 by W. H. Freeman and Company When can predators drive prey to extinction? zIt is clearly possible for predators to drive their prey to extinction when: ypredators and prey are maintained in simple laboratory systems ypredators are maintained at high density by availability of alternative, less preferred prey: xbiological control may be enhanced by providing alternative prey to parasites and predators

40. (c) 2001 by W. H. Freeman and Company What equilibria are likely? zModels of predator and prey suggest that: yprey are more likely to be held at relatively low or relatively high equilibria (or perhaps both) yequilibria at intermediate prey densities are highly unlikely

41. (c) 2001 by W. H. Freeman and Company Summary 1 zPredators can, in some cases, reduce prey populations far below their carrying capacities. zPredators and prey often exhibit regular cycles, typically with cycle lengths of 4 years or 9-10 years. zLotka and Volterra proposed simple mathematical models of predator and prey that predicted population cycles.

42. (c) 2001 by W. H. Freeman and Company Summary 2 zIncreased productivity of the prey should increase the predator’s population but not the prey’s. zFunctional responses describe the relationship between the rate at which an individual predator consumes prey and the density of prey. zThe Lotka-Volterra models incorporate a type I functional response, which is inherently unstable. zType III functional responses can result in stable regulation of prey populations at low densities.

43. (c) 2001 by W. H. Freeman and Company Summary 3 zType III functional responses can result from switching. zNumerical responses describe responses of predators to prey density through local population growth and immigration. zSeveral factors tend to stabilize predator-prey interactions, but time lags tend to destabilize them. zPredator-prey systems may have multiple stable points.