Self-organized patchiness and catastrophic shifts in ecosystems; The hypothesis

Transcription

1 Self-organized patchiness and catastrophic shifts in ecosystems; The hypothesis Max Rietkerk Copernicus Institute Dept Environmental Sciences Faculty Geosciences Utrecht University

2 Outline lecture 1 The hypothesis Catastrophic shifts Self-organized patchiness Linked by resource concentration Scale-dependent positive feedback

3 Outline lecture 2 Ongoing research and perspectives Local positive feedback (facilitation) and global negative feedback (competition) in arid ecosystems Type I, II and III positive feedback in peatland ecosystems Negative feedback and species coexistence

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5 (Semi-)arid ecosystems Yearly potential evaporation exceeds yearly rainfall Plant growth water limited 40% land surface Main land-use is grazing

6 World distribution arid systems Valentin et al 1999

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8 Desertification Desertification is land degradation in (semi-)arid and dry subhumid areas resulting mainly from adverse human impact (UNCOD 1992) The reduction or spatial reorganization of net primary production in (semi-)arid lands Most desertification happens as runaway phenomena which are irreversible on human time scales Once desertification starts it is hard to stop and almost impossible to remediate in an area

9 Changing environment Increased grazing by domestic lifestock (f.i. Sahelian countries livestock numbers increased 3 fold from 40 million to 120 million between 1950 and 1990) Decreased rainfall (f.i. Sahelian areas from 750 mm/yr in 1950s to 600 mm/yr in 1990s, and severe drought periods in 1970s and 1980s)

10 Infiltration rate increases with vegetation cover Infiltration rate (ml min -1 ) Rietkerk et al 2000 Vegetation cover

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13 A simple model of positive feedback I Losses (e.g. grazing) Plants Rainfall Uptake/ growth + Infiltration Soil water

14 Non-spatial model I P( t) t = [ growth] [ loss] W ( t) t = [ infiltration] [ uptake ] [ evaporation]

15 dp dt dw dt = gw ( ) P ( d+ bp ) = Win( P) c( W) P rww W gw ( ) = g max W k cw ( ) = c max + 1 W W k + 1 W P PPT P + in( )= k W P+ k2 2 0 Rietkerk & Van de Koppel Oikos 1997; Rietkerk et al Oikos 1997

16 A simple model of positive feedback II Losses (e.g. grazing) Plants Nutrient input Uptake/ growth Recycling - Soil nutrients Losses

17 Non-spatial model II P( t) t = [ growth] [ recycling+ loss] N( t) t = [ input] [ uptake recycling ] [ losses]

18 P b d P N g dt dp ) ( ) ( + = N P r P N c N dt dn N in ) ( ) ( = 1 max ) ( k N N g N g + = max max 1 max ) ( g c d k N N c N c + = P k k r P r N N + = 2 2,max ) ( Rietkerk & Van de Koppel Oikos 1997; Rietkerk et al Oikos 1997

19 Catastrophic shifts Equilibrium plant standing crop Rainfall/Nutrient input Rietkerk & Van de Koppel Oikos 1997; Rietkerk et al Oikos 1997

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22 Scheffer et al Nature 2001

23 Catastrophic shifts Are associated with bistability (in the ecological literature this is often called alternative stable states or multiple stable states), Are sometimes called discontinuous transitions (as opposed to continuous transitions), or regime shifts, And in the math literature they are called subcritical bifurcations (as opposed to supercritical bifurcations).

24 Catastrophic shifts Are sudden, abrupt, as compared to gradual environmental change, Show hysteretic loops (difficult to reverse), Have different threshold values associated with this. There are no early warning signals! Result from positive feedback. Challenge Max! Did you ever see one?

25 Until now I have Spatial scale ignored Spatial heterogeneity ignored Spatial processes like run-off ignored What happens if we introduce space?

26 A simple spatial model Losses (e.g. grazing) Plants Rainfall Surface water Uptake + Infiltration Soil water

27 Spatial model O( x r, t) t = [ rainfall ] [ infiltration] ± [ overland flow] W ( x v, t) t = [ infiltration] [ uptake ] [ evaporation] ± [ water movement] P( x,t r ) t = [ growth] [ loss] ± [ dispersal]

28 P D p P d P k W W g c t P + + = 1 max W D w W r w P k W W g k P W k P O t W = 1 max α O D o k P W k P O R t O = α Hillerislambers et al Ecology 2001; Rietkerk et al AmNat 2002

29 Grid approach x-direction y-direction

30 Model simulations Increased grazing or decreased rainfall gaps labyrints spots 400 m grid size = 2 x 2 m Rietkerk et al AmNat 2002

31 Self-organized patchiness! Outcome of internal dynamics only, starting from random initialization As a result of plant-soil characteristics Concentration of soil water under vegetated patches This is due to the fact that higher biomass leads to higher infiltration rates outbalancing higher transpiration rates Can you see this? Yes!

32 Aerial pictures Increased grazing or decreased rainfall? 800 m 650 m Courtesy S Prince Univ of Maryland

33 Self-organized patchiness at multiple scales 1 m Northern Negev (Israel) (200 mm annual rainfall) Soil water transport due to differences in evapotranspiration (Von Hardenberg et al 2001) 650 m Niger ( mm annual rainfall) Surface water movement due to differences in infiltration (Rietkerk et al 2002)

34 from: Aguiar & Sala

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37 Model simulation Slope (top on right hand side) grid size = 2 x 2 m 400 m Rietkerk et al AmNat 2002

38 This is of course all very nice (isn t it?), but Where are the catastrophic shifts? For this: one-dimensional numerical analysis in the next slides

39 Spatial bifurcation plant density (g m -2 ) herbivory (d -1 )

40 Productivity plant density (g m -2 ) homogeneous mean field spatial maximum spatial average herbivory (d -1 )

41 Region of spatial patterns spots (hysteresis) Extinction herbivory (d -1 ) gaps labyrints Homogeneous plant cover rainfall (mm d -1 )

42 So, what do we have here? 1) Turing patterns! (No homogeneous solutions possible). 2) Non-Turing patterns, associated with bistability, and either homogeneous or patterned outcome dependent on initial conditions. 3) Certain patterning arising depending on direction of change. Are there more ecosystems behaving in similar ways?

43 Rietkerk et al AmNat 2004 Northern peatlands

44 db/dt = growth mortality +/- dispersal dh/dt = rainfall transpiration evaporation +/- ground water flow dn/dt = nutrient input uptake + recycling loss +/- movement through ground water flow +/- diffusion

45 ) ( )) ( ( ] [ y B x B B D bb db H h Bf N g t B + + = )} ( ) ( { f(h(h)) f(h(h)) y H H y x H H x k e tv B p t H + Θ + Θ Θ Θ = )} ] ([ ) ] ([ { ) 2 ] [ 2 2 ] [ 2 ( ] [ f(h(h)) ] [ ] [ y H N y x H N x k y N x N N D H t H N rn B g u d B N u in N t N + Θ Θ Θ + =

46 Peatland patterns Peatland patterns can be explained by spatial exchange of nutrients Rietkerk et al AmNat 2004

47 Spatial bifurcation 1000 LP 1 B (gb m -2 ) LP 2 LP 1 LP N in (g N m -2 y -1 ) T

48 Nutrient-limited savannas m Lejeune et al Phys Rev E 2002

49 Equilibrium density of ecosystem engineer Catastrophic shift from selforganized patchy to homogeneous state Catastrophic shift from homogeneous to self-organized patchy state Resource input Rietkerk et al Science 2004 Region of global bistability

50 So what I suggest is that All ecosystems with self-organised patchiness resulting from a resource concentration mechanism also exhibit catastrophic shifts.

51 This is because Ecosystem engineers at low densities may be unable to harvest resources from their surroundings. The positive feedback does not operate!

52 Scale-dependent feedback Feedback effect + - distance Rietkerk et al Science 2004

53 Mussel beds Patterns in mussel beds Courtesy N Dankers Van de Koppel et al AmNat 2005

54 Coral reefs Mistr and Bercovici Ecosystems 2003

55 Tidal flats Van de Koppel et al Ecology 2001

56 Sea grass Courtesy HHT Prins Just a vague idea...

57 Acknowledgements Maarten Boerlijst (neat simulations!) (UvA) Andre de Roos (UvA) Stefan Dekker (UU) Johan van de Koppel (NIOO)... And many others! (from all over)

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