1. Metapopulation and Intertrophic Dynamics From single species population dynamics (and how to harvest them) to complex multi-species (pred-prey) dynamics in time and space.

2. Herons, UK BHT: fig. 10.17 Metapopulation and Intertrophic Dynamics stability fluctuations biotic factors? (density dependence) abiotic factors? (density independence)

3. Metapopulation and Intertrophic Dynamics Density DK SdrJylland Population-level analysis! A B C A+B+C Then again … where is the population-level?

4. Metapopulation and Intertrophic Dynamics Searocket (Cakile edentula) Dispersal – an important population process BHT: fig. 15.19

5. Metapopulation and Intertrophic Dynamics (1) Metapopulations: living in a patchy environment (2) Intertrophic dynamics: squeezed from above and below

6. Metapopulation Dynamics Lawton & Woodroffe 1991 39 sites Slope, vegetation, heterogeneity human disturbance 10 core, 15 peripheral & 14 no-visit water vole Do animals occupy all suitable habitats within their geographic range?

7. Increasing bank angle and structural heterogeneity Increase in % grass Metapopulation Dynamics Lawton & Woodroffe 1991 water vole Do animals occupy all suitable habitats within their geographic range? PCA performed core sites no-visit sites 55% with suitable habitats......30% lack voles because... reduced colonization rates predation Know your species...!

8. Metapopulation Dynamics Hanski & Gilpin 1997...and know your landscape!

9. Metapopulation Dynamics Metapopulation theory Equilibrium “population” of species (extinction - recolonization) The MacArthur-Wilson Equilibrium theory

10. Metapopulation Dynamics Metapopulation theory Mainland-Island model (Single-species version of the M-W multi-species model) Metapopulation

11. Metapopulation Dynamics Metapopulation theory Mainland-Island model (Single-species version of the M-W multi-species model) Metapopulation Levins’s metapopulation model (no mainland; equally large habitat patches)

12. Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : fraction not occupied m : recolonization rate e : extinction rate recolonization – increases with BOTH the no of empty patches (1-P) AND with the no of occupied patches (P). extinction – increases with the no of patches prone to extinction (P). (equal patch size)

13. Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : not occupied m : recolonization rate e : extinction rate

14. Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : not occupied m : recolonization rate e : extinction rate Given that (m – e) > 0, the metapop will grow until equlibrium: dP/dt = 0 => P* = 1 – e/m ( trivial: P* = 0) P time 1-e/m

15. Metapopulation Dynamics Metapopulation theory NOTE: the metapop persists, stably, as a result of the balance between m and e despite unstable local populations! Hanski et al. 1995 Melitaea cinxia local patches the metapop persists: ln(1991) = ln(1993)

16. Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Levins M-I

17. Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Variable patch size

18. Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Variable patch size model Increasing a, the freq of larger patches decreases a = 0 a = 

19. Metapopulation Dynamics Metapopulation theory dP/dt = 0 => P 1 * = 1 – e/m P 2 * = 0 Levins’s model: Melitaea cinxia Hanski et al. 1995 Hanski & Gyllenberg (1993) Two general metapopulation models and the core-satellite species hypothesis. American Naturalist 142, 17-41 across metapops Value of a!

20. Intertrophic Dynamics (2) Intertrophic dynamics: squeezed from above and below (i) Predation on prey are biased BHT: fig. 8.9 Thomson’s Gazelle

21. Intertrophic Dynamics (2) Intertrophic dynamics: squeezed from above and below (ii) Predators AND prey are also ”squeezed from the side” mates territories There is density dependence (crowding), which may influence or be influenced buy predation!

22. Intertrophic Dynamics Demonstrating the effect of predation is NOT straight forward Hokkaido multiannual cyclic seasonal fluctuations Short winter Long winter DD intense DD weak

23. Vito Volterra (1860-1940) Italian mat-phys Alfred J Lotka (1880-1949) American mat-biol % pred fish The Lotka - Volterra model Intertrophic Dynamics

24. Predator (P) Prey (N) q : mortality a' : hunting eff. per predator f : ability to convert food to offspring r : intrinsic rate of increase - a’PN+ fa’PN fa’PN - qP rN - a’PN Intertrophic Dynamics The Lotka-Volterra model

25. isoclines, dN/dt = dP/dt = 0 rN* - a’P*N* = 0 fa’P*N* - qP* = 0fa’P*N* = qP* rN* = a’P*N* => N* = q/fa’ P* = r/a’ predator mortality offpring/prey hunting effeciency prey reproduction Intertrophic Dynamics The Lotka-Volterra model (Predator isocline) (Prey isocline)

26. N* N P P* N* P* N P N* = q/fa’ P* = r/a’ predator mortality offpring/prey hunting effeciency prey reproduction isoclines, dN/dt = dP/dt = 0 Intertrophic Dynamics The Lotka-Volterra model

27. N* = q/fa’ P* = r/a’ N* P* N P BHT: fig. 10.2 Intertrophic Dynamics The Lotka-Volterra model Predator isocline: Prey isocline:

28. Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: N P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators:

29. Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators: Reproduction rate (r ) decreases with increasing N Crowding in prey: N

30. Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators: Reproduction rate (r ) decreases with increasing N Crowding in prey: N KNKN

31. Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: Prey isocline Predator isocline Less effecient predator Predator isocline Prey isocline Combining DD in predator and prey Prey isocline Predator isocline Strong DD in predator BHT: fig. 10.7 The greater the distance from Eq, the quicker the return to Eq!

32. Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey

33. Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey At low N there’s no effect of predator P N (this prey)

34. Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey At low N there’s no effect of predator P N (this prey) Independent of prey (DD still in work) Degree of DD determines level

35. Intertrophic Dynamics Functional response and prey-switching Prey isocline Predator isocline BHT: fig. 10.9 Predator isocline (high DD) Stable pattern with prey density below carrying capacity

36. Intertrophic Dynamics Functional response and prey-switching Many other combinations! Despite initial settings they all become stable! Prey isocline Predator isocline Less effecient predator Predator isocline Prey isocline Combining DD in predator and prey Prey isocline Predator isocline Strong DD in predator BHT: fig. 10.7

37. Intertrophic Dynamics Crowding in practice Heterogeneous media Structural simple media Indian Meal moth BHT: fig. 10.4 time Log density

38. Intertrophic Dynamics Crowding in practice Indian Meal moth Heterogeneous media Structural simple media Intrinsic and extrinsic causes of population cycles (fluctuations)

39. Intertrophic Dynamics Population cycles and their analysis

40. pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots lynx Sunspot + Intertrophic Dynamics Lynx – hare interactions

41. pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots Sunspot lynx - Intertrophic Dynamics Lynx – hare interactions

42. pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots Sunspot lynx + Intertrophic Dynamics Lynx – hare interactions

43. Factorial design large-scale experiment: (1) control blocks (2) ad lib supplemental food blocks (3) predator exclusion blocks (4) 2+3 blocks monitored everything over 15 years (species composition, population dynamics, life histories...) Intertrophic Dynamics Lynx – hare interactions: The Kluane Project

44. Non-additive response 10-fold Increased cycle period... … but neither food addition and predator exclosure prevented hares from cycling - Why? Vegetation-hare-predator year Hare density (-pred, + food) (-pred) (+food) (control) Intertrophic Dynamics Lynx – hare interactions: The Kluane Project

45. Forest/Grassland Closed forest Open forest Atlantic Continental Pacific NAO Intertrophic Dynamics Lynx – hare interactions: A spatial perspective

46. N t = f(N t-1,N t-2,..., N t-11 )!... Kluane indicates that hare- predator interactions are central. lynx hare year density f( N t-1, N t-2 ) decrease N t = f( N t-1, N t-2 ) increase … dynamics non-linear! High dependence (80%) on hare density... Intertrophic Dynamics Lynx – hare interactions: the lynx perspective

47. Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Ottar Bjørnstad Lemmus Clethrionomys Microtus 27 populations Bjørnstad et al. 1995 Hanski et al. 1991 BHT: fig. 15.13 Effect of predators?

48. Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Lemmus Clethrionomys Microtus Bjørnstad et al. 1995 Hanski et al. 1991 Two hypotheses (1)The specialist predator hypothesis (predator numerically linked to prey, that is through reproduction; variations come from variations in predator efficiency) (2)The generalist predator hypothesis (more generalist predators in south than north) delayed effect on prey direct effect on prey Analysis of prey population dynamics: AR(2): N t = f(N t-1,N t-2 ) AR(1): N t = f(N t-1 ) BHT: fig. 15.16 efficiency no of pred

49. Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Lemmus Clethrionomys Microtus Bjørnstad et al. 1995 Ottar analysed 19 time series (>15 years) using autoregression (AR): 17 (89%) time series best described by: AR(2): N t = f(N t-1,N t-2 ) N t-2 N t-1 The generalist predator hypothesis Increasing no of gen pred increases the direct negative effect on prey

50. Metapopulation and Intertrophic Dynamics Combining metapopulation and predator-prey theory BHT section 10.5.5 Comins et al. (1992) The spatial dynamics of host- parasitoid systems. Journal of Animal Ecology 61, 735-748

51. Fagprojekter (1) Harvesting natural populations Niels (2) Cohort variation and life histories Toke (3) Climate and density dependence in population dynamics Mads Max 3-4 pax/groupMax 10-15 pp + figs/tabs