Thresholds, non-linearity and prediction in freshwater ecosystems

1. Thresholds, non-linearity and prediction in freshwater ecosystems Walter K. Dodds Division of Biology Kansas State University

2. Acknowledgements Collaborators- Michelle Evans-White, Keith Gido, Jonathon Aguilar, David Chandler, Xiaoying Yang, Don Huggins, Debbie Baker Funding- NSF EPSCoR Ecological Forecasting, EPA STAR- Thresholds

3. The talk • Why does it matter? • Defining thresholds and non-linearity • Abiotic patterns • Biotic patterns • Conclusions

4. Why does it matter? • Many ecological responses are not linear • We are entering a no-analog world that may push us into new areas where we have not been before • Fox. 2007. Science 316:823-825 • Milly et al.2008. Science 319:573-574 • Some thresholds may be very difficult to come back from- total management headaches

5. Thresholds and non-linearity • Threshold is formally a mathematical concept that is a state change to a new one that is locally stable • Breakpoint is a change in type of functional relationship, but this does not necessarily mean a threshold • Non-linearity can be a breakpoint (more than one function) or take any of many types of functions (e.g. exponential, saturating)

6. Defining breakpoints and non-linearity • Non-linearity and breakpoints can be defined statistically or empirically • Spatial and temporal scales are important • Understanding thresholds generally requires a mechanistic approach • A practical example- extinction • No statistics necessary • Not a reversible state

7. Some methods for non-linear and breakpoint characterization • Non-linear regression • Breakpoint regression • Logistic regression/ change point analyses • Two dimensional Kolmogorov-Smirnov (non parametric)

8. NH4+ uptake by Flathead Lake phytoplankton community V = Vmax* [NH4+ ] (Ks + [NH4+ ])

9. Examples of abiotic patterns • Anoxic hypoxia and reversing eutrophication • Stream flow under the Ogallala Aquifer

10. Dissociation of iron phosphate FePO4 Fe3++ PO43- Oxic FePO4 PO43- Fe2+ Anoxic

11. Anoxic Hypoxia • Lakes will be pushed to a eutrophic state if fertilized to the point that oxygen disappears from hypolimnion • Recycling of PO43- from anoxic bottom waters in fall mixing stimulates algal production • Understanding these processes necessary for controlling eutrophication (Carpenter et al. 1999 Ecol. Appl. 9:751-771)

12. Stream flow andthe Ogallala • Large scale change in hydrology • Driven by agriculture irrigation • Intensified with recent increases in grain prices allowing fuel costs for deep pumping to be offset

13. Areas in red dropped more than 10 m between 1980 and 1995, in orange 5 m, in yellow 2 m

14. An example of long-term ecological impacts of humans on the Great Plains

15. Arikaree River, Kansas(courtesy of KDWP) 1980’s 1996 2006

16. Groundwater recharge in 1965

17. Groundwater recharge in 2005

18. Groundwater recharge in 2020

19. Threshold? • Streams have entered a new state (dry) • Will they ever recover? • Over thousands of years, yes • Is this a threshold or just a non-linearity? • Depends upon time scale

20. Biotic examples • Extinction • Nutrients, stoichiometry and aquatic biodiversity • Ecosystem goods and services

21. Extinctions • 1/3 of European freshwater fish face extinction (IUCN) • 2/5 of North American fishes are imperiled (61 extinct, 280 endangered) Jelks, H.L. Fisheries 33:372-407 • Unionid mussels, same story, substantial extinction debt (Poole, K. E. and J. A. Downing. 2004. JNABS 23:114-125) • We have pushed our freshwaters across a major biological break point and threshold

22. Nutrients in Midwest streams Macroinvertebrate and nutrient data compiled for Midwest streams

23. Methodology • Quantify statistical threshold points in richness variation across nutrients using nonparametric changepoint analysis (King & Richardson 2003) • Regression tree analysis • Bootstrap simulation (Efron &Tibshirani 1993) • Cumulative probability of changepoint (5, 50, 95%) • 5% = 5% of the bootstrap simulations resulted in a changepoint < x

24. Thresholds common with diversity and total phosphorus in water column 5% = 0.040 50% = 0.051 95% = 0.091

25. Primary consumers more strongly influenced

26. Ecosystem goods and servicesA few examples • Possible threshold of watershed area above which sediment input increases drastically • Species area relationships are non-linear • A saturating logarithmic relationship between area and richness • Restoration or conservation of very rare habitat will yield greater increases in diversity values conserved

27. Fish in lakes Decreasing lake area… from 50 to 10 hectares as opposed to 2-10 hectares

28. Ecosystem goods and servicesA few more examples Toxins with a minimum toxicity Ecoestrogens that are only active at very low concentrations N saturation of denitrification rates

29. Mulholland et al Nature 2008

30. Conclusions An equilibrium approach is an approximation in a no-analog world Linear models are not universal Several approaches have been taken to identify non-linear conditions and potential breakpoints in relationships

31. Conclusions- continued • Identification of breakpoints can be important for predicting responses in aquatic environments • Biotic and abiotic systems exhibit breakpoints • Ecosystem goods and services of value to humanity can vary in non-linear ways; there is practical value in considering non-linear responses

32. The end- a breakpoint in your attention span