DEB theory for populations, communities and ecosystems (Background for chapter 9 of DEB3

1. DEB theory for populations, communities and ecosystems (Background for chapter 9 of DEB3 ….. and more) Roger Nisbet April 2015

2. Ecology as basic science • According to Google, ecology is: • The study of how organisms interact with each other and their physical environment. • The study of the relationships between living things and their environment. • The study of the relationship between plants and animals (including humans) and their environment. • The science of the relationships between organisms and their environments.

3. Ecological Application: Ecological Risk Assessment (ERA) Definition1: the process for evaluating how likely it is that the environment may be impacted as a result of exposure to one or more environmental stressors. ERA involves predicting effects of exposure on populations, communities and ecosystems – including “ecosystem services” such as nutrient cycling. Key approach uses process-based, dynamic models of exposure and response to exposure to predict “step-by-step” up levels of organization. • AOP: Adverse outcome pathway • TK-TD: Toxicokinetic-toxico-dynamic • DEB: Dynamic Energy Budget • IBM: Individual-based (population) model 1. http://www.epa.gov/risk_assessment/ecological-risk.htm

4. Stress at different levels of biological organization 1000’s/year few/year 10,000’s/day 100,000’s/day 100’s/year High Throughput Bacterial, Cellular, Yeast, Embryo or Molecular Screening Expensive in vivo testing and ecological experiments Challenge for DEB theorists: to use information from organismal and suborganismal studies to prioritize, guide design, and interpret ecological studies Include those that inform applications such as ERA.

5. Environmental Challenges are Urgent • Climate change effects already occur and will accelerate over decades • Environmental Stress is rapid (e.g. nutrient enrichment, insecticides, water supply, frequency of extreme events) • Technology changes rapidly(e.g. engineered nanomaterials) YET • DEB is over 30 years old and had its origins in ecotoxicology, but only a very few agencies or industries use it, in spite of focused publications (e.g. OECD guidance document) IMPLYING • EITHER: DEB is “too complicated” for practical applications • OR: We (DEB crowd) need to improve communication

6. Meeting the challenges • DEB is “too complicated” for practical applications • Often true (unfortunately) • “Keep it simple”, but NOT stupid • Use both DEB-based and DEB-inspired models • Improving communication • Know intellectual culture of users (e.g. ecology or ecotoxicogy) • Develop useful tools

7. DEB-based population modelS

8. Two approaches to modeling population dynamics • A population is a collection of individual organisms interacting with a shared environment. • Individual-based models (IBMs). Simulate a large number of individuals, each obeying the rules of a DEB model (i-state dynamics). • Structured population models. This involves modeling the distribution of individuals among i-states. A large body of theory has been developed1, and there is a powerful computational approach – the “escalator boxcar train”2.. • See for example many papers by J.A.J. Metz, O. Diekmann, A.M. de Roos • See http://staff.science.uva.nl/~aroos/EBT/index.html

9. Feedbacks via environment • Environment: E-state variables - resources, temperature, toxicants etc. experienced by all organisms. - possible feedback from p-states • Individual Organism: i-state variables - age, size, energy reserves, body burden of toxicant, etc. • Population dynamics: p-state variables - population size, age structure, distribution of i-state variables - derived from i-state and E-state dynamics (book-keeping) Ind Individuals Ind Environment Ind Population Feedback

10. Simplest approach: use ordinary differential equations or delay differential equations for p-state dynamics ODEs can be derived with “ontogenetic symmtery”1 All physiological rates proportional to biomass (in biomass budget models) or to structural volume (in DEB models – V1 morphs) All organisms experience the same per capita risk of mortality (hazard) Include ODEs describing environment (E-state) Resulting equations describe biomass dynamics Delay differential equations (DDEs) follow if assumption 2 is relaxed to2,3: 2a) All organisms in a given life stage experience the same risk of mortality • A.M. de Roos and L.Persson (2013). Population and Community Ecology of Ontogenetic Development. Princeton University Press. See also lectures by de Roos: http://www.science.uva.nl/~aroos/Research/Webinars • R.M. Nisbet. Delay differential equations for structured populations. Pages 89-118 in S. Tuljapurkar, and H. Caswell, editors. Structured Population Models in Marine, Terrrestrial, and Freshwater Systems. Chapman and Hall, New York. • Murdoch, W.W., Briggs, C.J. and Nisbet, R.M. 2003. Consumer-Resource Dynamics. Princeton University Press.

11. Population dynamics and bioenergetics – two bodies of coherent theory Coming soon – de Roos keynote! DEB Biomass –based models

12. DEB-based IBMs* * B.T. Martin, E.I. Zimmer, V. Grimm and T. Jager (2012). Methods in Ecology and Evolution 3: 445-449

13. DEB-IBM • Implemented in Netlogo(Free) • Computes population dynamics in simple environments with minimal programming • User manual with examples * B.T. Martin, E.I. Zimmer, V.Grimm and T. Jager (2012). Methods in Ecology and Evolution 3: 445-449

14. Population model tests* Low food (0.5mgC d-1) * B.T. Martin, T. Jager, R.M. Nisbet, T.G. Preuss, V. Grimm(2013). Predicting population dynamics from the properties of individuals: a cross-level test of Dynamic Energy Budget theory. American Naturalist, 181:506-519.

15. Refining the model • Martin et al. tested 3 size selective food-dependent submodels • Juveniles more sensitive • Adults more sensitive • Neutral sensitivity • Fit submodels to low food level compare GoF at all food levels Theory Data

16. Best model Low food High food Abundance Days Days

17. Futher test: Daphnia populations in large lab systems with dynamic food * Maturity time LA cycle Large amplitude cycles Small amplitude cycles Cycle period Maturity time SA cycle * McCauley, E., Nelson, W.A. and Nisbet, R.M. 2008. Small amplitude prey-predator cycles emerge from stage structured interactions in Daphnia-algal systems. Nature, 455: 1240-1243.

18. DEB-IBM dynamics Population density Maturation time

19. Effects of a contaminant on Daphnia populations Feeding Somatic maintenance Maturity maintenance 3,4- dichloranaline x Maturation Reproduction Growth Data from T.G. Preuss et al. J. Environmental Monitoring 12: 2070-2079 (2010) Modeling from B.T. Martin et al. Ecotoxicology, DOI 10.1007/s10646-013-1049-x (2013)

20. Generalization: relating physiological mode of action of toxicants to demography of populations near equilibrium1 1. Martin, B., Jager, T., Nisbet, R.M., Preuss, T.G., and Grimm, V. (2014). Ecological Applications, 24:1972-1983.

21. Simplification – consider DEBkiss*? Likelihood profiles g v *Jager, T., B. T. Martin, and E. I. Zimmer. 2013. DEBkiss or the quest for the simplest generic model of animal life history. Journal of Theoretical Biology 328:9-18.

22. DEB-INSPIRED MODEL OF feedbacks involving metabolic products

23. Bathch cultures of microalgae* • Citrate coated silver NPs were added to batch cultures of Chlamydomonas reinhardtii after 1, 6 and 13 days of population growth. • Response depended on culture history • Experiments showed that environment (not cells) changed between treatments • dynamic model included: algal growth, nanoparticle dissolution, bioaccumulation , DOC production, DOC-mediated inactivation of nanoparticles and of ionic silver. • Model fits (red lines) * L. M. Stevenson, H. Dickson, T. Klanjscek, A. A. Keller, E. McCauley & R. M. Nisbet (2013). Plos ONE DOI 10.1371/journal.pone.0074456

24. Batch cultures of microalgae* 88888 • Citrate coated silver NPs were added to batch cultures of Chlamydomonas reinhardtii after 1, 6 and 13 days of population growth. • Response depended on culture history • Experiments showed that environment (not cells) changed between treatments • dynamic model included: algal growth, nanoparticle dissolution, bioaccumulation , DOC production, DOC-mediated inactivation of nanoparticles and of ionic silver. • Model fits (red lines) * L. M. Stevenson, H. Dickson, T. Klanjscek, A. A. Keller, E. McCauley & R. M. Nisbet (2013). Plos ONE DOI 10.1371/journal.pone.0074456

25. Dynamic Energy Budget (DEB) Perspective DEB model equations characterize an organisms as a “reactor” that converts resources into products Algal mass (M) Growth Development Division Metabolic Products (DOC, N or P waste) Resources (CO2, light, nutrients) Rate of product (DOC) production

26. So, what’s going on? Stationary Slowing Nano Nano Fast Nano Chl below detectable limit

27. So, what’s going on? Stationary Slowing Nano+Ionic Nano Nano Nano+Ionic Fast Nano Chl below detectable limit

28. Environmental Implication Can algal-produced organic material protect other aquatic species? Daphnia 48-hr survival Red = standard medium; Blue = water from late algal cultures Control 1 μg/L 10 μg/L 100 μg/L

30. DEB theory for communities

31. Communities and Ecosystems • Community:collection of interacting species • Ecosystem: Focus on energy and material flows among groups of species (e.g. trophic levels). • Overarching challenge – understanding biodiversity • Community dynamics involves much more than bioenergetic processes . • No consensus on whether “biology matters” – neutral theory • Is DEB relevant?

32. RESOURCE COMPETITION

33. A little demography

34. A little demography

35. A little demography

36. A little population ecology • Ultimate fate of a closed population that does not influence its environment is unbounded growth or extinction. • Without feedback, the long-term average pattern of growth or decline of populations is exponential – even in fluctuating environments • The long term rate of exponential growth, r, is obtained as the solution of the equation • (Note similarity to equation for R0 )

37. A little population ecology • Ultimate fate of a closed population that does not influence its environment is unbounded growth or extinction. • Without feedback, the long-term average pattern of growth or decline of populations is exponential – even in fluctuating environments • The long term rate of exponential growth, r, is obtained as the solution of the “Euler-Lotka” equation1 • (Note similarity to equation for R0 ) • Feedback from organisms in focal population to the environment may lead to an equilibrium population (R0 = 1) or to more exotic population dynamics such as cycles. 1. A.M. de Roos (Ecology Letters 11: 1-15, 2009) contains a computational approach (with sample code) for solving this equation when b(a) and S(a) come from a DEB model.

38. Resource competition Consider two species competing for a single food resource, X. For each species, R0 is a function of X., and at equilibrium, R0=1. Thus equilibrium coexistence is unlikely. Idea behind competitive exclusion principle

39. Resource competition Consider two species competing for a single food resource, X. For each species, R0 is a function of X., and at equilibrium, R0=1. Thus equilibrium coexistence is unlikely. Idea behind competitive exclusion principle (CEP) Coexistence at equilibrium of N species requires N resources

40. Theory behind CEP is sound • David Tilman (1977) Resource Competition between Plankton Algae: An Experimental and Theoretical Approach. Ecology, 58, 338-348. • 2 algal species, 2 substrates (P and Si); • Described by Droop model (evolutionary ancestor of DEB) • Chemostat dynamics + labe experiments • Field data from Lake Michigan LAB LAKE

41. Possible mechanisms for species coexistence DEB3 page 337

42. Bas’s List in bigger print mutual syntrophy, where the fate of one species is directly linked to that of another nutritional `details': The number of substrates is actually large, even if the number of species is small social interaction, which means that feeding rate is no longer a function of food availability only spatial structure: extinction is typically local only and followed by immigration from neighbouring patches; (5) temporal structure

43. SYNTROPHIC SYMBIOSIS MUTUAL EXCHANGE OF PRODUCTS FREE LIVING INTEGRATION FULLY MERGED CORALS

44. FREE LIVING HOST

45. FREE LIVING SYMBIONT

46. SHARING THE SURPLUS • HOST RECEIVES PHOTOSYNTHATE SYMBIONT CANNOT USE • SYMBIONT RECEIVES NITROGEN HOST CANNOT USE ENDOSYMBIOSIS

47. Model predictions E.B. Muller et al. (2009)JTB , 259: 44–57. ; P. Edmunds et al. Oecologia, in review; Y. Eynaud et al. (2011) Ecological Modelling, 222: 1315-1322. • Stable host;symbiont ratio at level consistent with data synthesis from 126 papers describing 37 genera, and at least 73 species • Dark respiration rates also consistenT with data

48. Bas’s List in bigger print mutual syntrophy, where the fate of one species is directly linked to that of another nutritional `details': The number of substrates is actually large, even if the number of species is small social interaction, which means that feeding rate is no longer a function of food availability only spatial structure: extinction is typically local only and followed by immigration from neighbouring patches; (5) temporal structure

49. Example of (6) Temporal structure Daphnia galeata competing with Bosminalongirostris • Experiments by Goulden et al. (1982). • Low-food, 2-day transfers: Bosmina dominated • High-food, 4-day transfers: Daphnia dominated • Note: experiments only ran for ~70 days, • so long-term coexistence not known • BUT CEP--> outcome of competition independent of enrichment. • EXPLANATION: Temporal variability due to experimenter!

50. Competition between Daphniaand Bosmina Fine line, Daphnia; bold line, Bosmina NOTE SMALL COEXISTENCE REGION – CONSISTENT WITH ASSERTION IN DEB3 IS THIS GENERAL?