Recap

1. Recap Species interaction Consumer-resource interactions Parasites and host Herbivore and plant Competition Mutualism

2. 11.6 Individuals of different species can collaborate in mutualistic interactions Mutualism: interaction benefits both species involved. honeybee and plants (plants provide honeybee with nectar, bees carry pollen between plants) Can be symbiosis: lichens (algae and fungi) or non-symbiosis: seed dispersal (birds and plants) Could involve more species Humans extract honeycombs (for honey) Birds eat the wax left behind Bacteria in the guts to digest the wax Three categories Trophic, defensive and dispersal mutualisms Trophic mutualisms: feeding relationship, bacteria in rumens of cows

3. Defensive mutualism Food and shelter, defend partners against their consumers Cleaning fish or shrimp Clean parasites form the skins

4. A wonderful story of Acacias plants and ants in Central America, see textbook (298). Some mutualists need their partners to survive and grow. Ants can’t survive without plants; and plants can’t survive without ants. Adaptation improved the efficiency of their association: Ants work day and night to protect plants. Acacias retain leaves all year. (both unusually)

5. Dispersive mutualism:Birds and mistletoe

6. BIOL 4120: Principles of Ecology Lecture 12: Dynamics of Consumer-Resource Interactions Dafeng Hui Office: Harned Hall 320 Phone: 963-5777 Email: dhui@tnstate.edu

7. Population cycles of predators and their prey Data from records of purchase by Hudson’s Bay Company, Canada MacLuich 1937

8. Topics (Chapter 15) 15.1 Consumers can limit resource populations 15.2 Many predator and prey populations increase and decrease in regular cycles 15.3 Mathematic models for predator-prey interaction 15.4 Pathogen-host dynamics can be described by the S-I-R model 15.5 Lotka-Volterra model can be stabilized by predator satiation 15.6 Factors can reduce oscillation of predator-prey models 15.6 Consumer-Resource system can have more than one stable state

9. 12.1 Consumers can limit resource populations Populations of consumer are self-regulated because of their effects on their resources And consumers contribute to the regulation of resource population. Questions: how large is the rule of consumers?

10. Predation on cyclamen mites Cyclamen mite is a pest of strawberry in CA Typhlodromus mite is a predatory mite Greenhouse Experiment One with predatory mite and one without by applying parathion

11. Herbivores and Plant Populations Herbivores can control plant populations Klamath weed, or St. John’s wort, became a widely spread pest (poison to cattle and sheep) following its introduction. When Chrysolina beetle was introduced, the Klamath weed was finally under control.

12. Effects of herbivores on plant production can be measured using exclosure experiments

13. 12.2 Many Predator and Prey populations increase and decrease in regular cycles • Cycles of predator and prey populations are common • The periods of cycles vary from species to species • Large herbivores (snowshoe hare, muskrat, ruffed grouse) 9-10 year • Small ones (vole, mice, lemming) 4 years cycle • Predators feed on large prey have long cycle (red foxes, lynx, marten, mink) • Predators feed on small prey have short cycle (Arctic fox, hawks, snowy owls) • Cycles (oscillations) are caused by predator and prey interaction (predator – prey).

14. Time delays and population cycles Time delays in birth and death caused oscillation in population Time delays also occur in predation Period of population cycle should be 4 ~ 5 times the time delay Hare populations fluctuated less on an island with few predators than on the surrounding mainland.

15. Physical conditions may change the period of cycles 4-year cycle in northern Scandinavia, but annually in southern Sweden. Winter delay in north maintain a long cycle. In the south, owls hunt voles whole year, create a short cycle. Climate warming may cause the shift from 4-yr to annual shown in this figure (or multiple prey).

16. Periodicity in pathogen-host relationships Cases of measles reported in London (before vaccine had been developed) Peaked about every two years Development of host immunity influences host populations

17. Habitat structure can affect population cycles Forest tent caterpillar as host Nuclear polyhedrosis virus as pathogen In many regions, tent caterpillars infestations last about 2 years before the virus brings its host population under control. In other regions, it may last 9 years Forest fragmentation plays a role. Forest edges with more light, inactivate the virus. Fragmentation prolong the outbreak. Habitats has second effects on population

18. Creating predator-prey cycles in the laboratory • Modeling and lab experiments • Studies by GF Gause on protists (1920s) • Predator: Ciliated protist, Didinium • Prey: Protist, Paramecium • Culture medium: test tube • Difficult to demonstrate the oscillations • Predators eat all prey, then die • Add refuge (glass wool at bottom of tube), predators would die and left some prey to survive • Add small number of predators periodically oscillations.

19. Huffaker’s mite experiment C.B. Huffaker, UC Berkeley (1958) Predator: mite, Typhlodromus Prey: six-potted mite (Eotetranychus), pest of citrus fruits Reproduction: parthenogenesis Control food resources: number and dispersion First study: 40 positions, 4 fruits, 20 prey, after 11 days, reached 5,500 to 8000, added 2 predators, ate all.

20. A spatial mosaic of habitats allows predators and prey to coexist 6 oranges, 120 positions, grew 200 days with 3 cycles

21. 12.3 Mathematical model for predation • Lotka and Volterra equation for predation • Prey • Where cNpredNprey is mortality of prey due to predator. c is per capita capture rate, and Npred, Nprey are the number of predators and prey, respectively. • Predator • Where b is efficiency of conversion of prey consumed (cNpredNprey) and d is death rate of predators

22. Solving the equations • For prey growth (dN_Prey/dt=0) • Npred = r/c • Growth rate of prey population is zero when density of predators equals per capita growth rate of prey divided by per capita capture rate of predators. • Any increase in predator density will result in negative growth in prey population • For predator growth (dN_Pred/dt=0) • Nprey = d/bc • Growth rate of predator population is zero when rate of increase of prey is equal to rate of mortality divided by the product of b and c. • Thus the two equations interact and this can be done graphically

24. Pred • There is a cyclical rise and fall in both the predator and prey populations with time • Density of predators lags behind density of prey • Feast and Famine scenario • Prey and predators are never quite driven to extinction • Mutual population regulation

25. Trajectories of predator and prey populations and their joint equilibrium point dP/dt=0 or dv/dt=0 Equilibrium isocline or more common, zero growth isocline The change in predator and prey populations together follows a closed cycle that combines the individual changes in the predator and prey population, called joint population trajectory. Not stable, or neutral stable (exhibits neutral stability), as slightly change in either population will move to next cycle, rather than return

26. Another chart to show that Lotka-Volterra model predicts a regular cycling of predator and prey populations Period of oscillation: T=2Pi/sqrt(rd) If r=2 (200%) and d=0.5 per year, then T=6.3

27. Influence of growth rate on predator and prey populations Nprey or V=d/bc is the minimum requirement to sustain the growth of predator populations Npredator or P=r/c is the largest number of predators that the prey population can sustain. A surprising prediction of the model is that increase in r of prey growth leads to an increase in predator population, not the prey

28. An increase in the birth rate of prey increases the predator population, but no the prey population Bohannan and Lenski, Michigan State University Prey: E. coli Predator: bacteriphage T4 Prey food source: limited by glucose Two levels: 0.1 or 0.5 mg per litter Add food supply only increased predator population.

29. 12.3 Pathogen-host dynamics can be described by the S-I-R model Parasites do not remove host from population, but can develop time delays that lead to population cycling Course of epidemic depends on Rate of transmission (b) and rate of recovery (g): Reproduction ratio: number of secondary cases produced by a primary case during its period of infectiousness, R0=(b/g)S R0>1, an epidemic will occur, each infected individual will infect more than one before it recovers R0<1, fails to take hold in the population R0: 5-18 for measles, chicken pox etc. HIV: 2-5; malaria: >100.

30. The S-I-R model can predict the spread on epidemic through a host population Total =100 b=1, g=0.2, duration of infectiousness 1/g=5 Beginning, S=1, R0=b/g*S=5 Assume no births of S, and no loss of resistance among previously infected individuals. Influenza virus Vaccination: remove individuals from S, reduce R0.

31. Case study: The chytrid fungus and the global decline of amphibians Pathogenic fungus: Batrachochytrium dendrobatisdis It kills hosts and persists by infecting alternative species. Karan Lips, Southern Illinois University, 2006 El Cope: first found in July 2004, rapid spread and caused abrupt drop.

32. 12.5 Lokta-Volterra model can be stabilized by predator satiation • The Lotka–Volterra model is criticized for overemphasizing the mutual regulation of predator and prey populations • Differential equations, no time delay (Difference equations, add time delay) • No internal forces act to restore the populations to the joint equilibrium point, random perturbations could increase oscillations to a point that V=0 or P=0 • cNpreyNpredator: at a given Npred, the rate at which prey are captured increases with Nprey. This is not true. There is predator satiation.

33. Functional and numerical responses • cN_preyN_pred (cVP): • For prey population, this term serves to regulate population growth through mortality • For predator population, it serves to regulate population growth through two distinct responses: Predator’s Functional responses: the great the number of prey, the more the predator eats. The relationship between per capita rate of consumption and the number of prey (cNpreyNpred). Predator’s Numerical response: an increase in consumption of prey results in an increase in predator reproduction (b(cNpreyNpred).

34. Functional Responses Relate Prey Consumed to Prey Density • The functional response is the relationship between the per capita predation rate (number of prey consumed per unit time) and prey population size • This idea was introduced by M.E. Solomon in 1949 • Three types of functional response (I, II, and III) • Developed by C.S. Holling

35. Functional response • Ne: per capita rate of predation, i.e., # of prey eaten during a given period of search time. • Type I functional response • Ne=cT Nprey • Passive predator such as spider or the prey is less sufficiently abundant (e.g., kestrels and voles) • All time (T) allocated to feeding is searching. • Linear • Ne/Nprey=cT constant

36. Type II response Ne increase with Nprey rapidly, but level off at high prey density.

37. Type III functional response Sigmoid (S-shaped) response At high prey density, the response is the same as type II response; however, the rate of prey consumed is low when the prey density is low at first, increasing in a S-shaped fashion. Factors caused the S-shape response 1. availability of cover to escape the predators 2. predator’s search image 3. Prey switching. Switch to other preys (more abundant)

38. Functional response As prey increases, predators take more prey But how Linear Rate of predation is constant Decreasing rate to maximum Rate of predation decline Sigmoidal Decrease at low density as well as high, increase to maximum then declines Functional responses related prey consumed to prey density • (Right panel is predation rate, # prey consumed divided by prey density)

40. Linear Type 1 (European kestrel to vole) • Mortality of prey simply density dependent • No limits on system • Decreasing Type 2 (weasel on rodent) • Predators can only eat so much – satiation • Time needed to kill and eat prey becomes limiting • Sigmoid Type 3 (warbler on budworm larvae) • Capture rate is density dependent • Availability of cover • Alternative prey when preferred is rare (prey switching) • Prey not part of predators search image, not a desirable food source

41. Model of prey switching • Prey switching (water bug) • Palatable versus less palatable • Better return per kill • Less energy needed to find and kill an abundant prey

42. Numerical response Predators reproduce more However reproduction usually slower than prey Movement into high prey density areas This aggregative response is very important as it rapidly increases predator density Predators respond numerically to changing prey density Aggregative response in the redshank

43. Other numerical response as increased reproductive effort • Weasels as predators • Rodents as prey • Predators followed prey in reproduction • Increase of rodent was due to good harvest in 1990

44. Predator population exhibits a numerical response to change in prey density Most of the increase was due to local population growth rather than immigration from else where After hare density fell to a low level, red squirrels and other small mammals were eaten by lynx.

45. Numerical response of a predator population lags behind changes in prey density following counterclockwise joint population trajectory predicted by the Lotka-Volterra model

46. 12.5 Factors that reduce oscillations in predator-prey models • Stability: achievement of an unvarying equilibrium size, often the carrying capacity • Predator-prey: oscillations, but several factors could stabilize, move to stable equilibrium: • Predator inefficiency (c decrease) • Density-dependent limitations of prey or predator by other external factors • Alternative food resource for predator • Refuges for prey at low prey density • Reduced time delays in predator responses to changes in prey abundance

47. 12.6 Consumer-resource system can have more than one stable state Population size is determined by: abundance of its resources and of its consumers One Extreme: resource population is only limited by its own food supply Another: resource population is depressed below its carrying capacity Balances between these factors create multiple equilibrium points: alternative state states

48. Consumer-imposed equilibrium: At low density, prey can seek refuge, avoid predators At low density, prey grows faster than predators Low stable equilibrium point well below its carrying capacity Resource-imposed equilibrium in some cases, prey population can move up from the consumer-imposed equilibrium, due to the limited number of predators, predator satiation, or other factors that keep predators in check (nest limitation), reach equilibrium set by its carrying capacity. Population could have two stable states and sometime move between these two (crop and forest pests, diseases).

49. The End

50. Recap • Dynamics of resource and consumer populations • Lab experiment • Math model • Lotka and Volterra equation for predation