1. DEB theory for poopulatins, communities and ecosystems - lecture III (Background for sections 9.1 and 9.4 of DEB3) Roger Nisbet April 2015

2. Remember my pet

3. Carbon flow and phosphorus cycling in a lake

4. Simplest DEB (DAB) model – “canonical community” (DEB3 – section 9.4) Producers: get energy from light and use nutrients to make biomass Consumers: feed on producers and decomposers Detritus: products and corpses from producers and consumers Decomposers: remineralize nutrients from detritus, but also utilize nutrients

5. Chemical transformations in canonical community

6. Mass balance equations for canonical community Consumer and decomposer (4): each has reserve and structure Producer (3): 2 reserves plus structure Detritus (4): consumer + producer feces; dead decomposers / consumers Minerals (4): H, C, O, N. No. of equations reduced slightly by mass balance (C and N conserved)

7. Mass balance equations for canonical community Consumer and decomposer (4): each has reserve and structure Producer (3): 2 reserves plus structure Detritus (4): consumer + producer feces; dead decomposers / consumers Minerals (4): H, C, O, N. No. of equations reduced slightly by mass balance (C and N conserved)

8. Precursor – book chapter In: Jorgensen, S. E. 2000 Thermodynamics and ecological modelling. CRC Publ., Boca Raton, FL,USA, pages 19{60

9. Precursor – book chapter In: Jorgensen, S. E. 2000 Thermodynamics and ecological modelling. CRC Publ., Boca Raton, FL,USA, pages 19{60

10. How to KISS? DEB-inspired and DEB-related models 1) Recognize key strengths of DEB theory - Strict mass balance for elemental matter - Strong homeostasis - Some organisms need two state variables - Use “nonlinear mechanistic regression” relating environment to performance and products 2)Simplify DEB representation of individuals 2)Plagiarize key ideas from DEB theory - Products from weighted sum of fluxes - Synthesizing unit (SU) 4) Choose simplifications matching modeling objectives

11. Model Simplification for C and P flows in a lake

12. Fast remineralization/uptake approximation (Andersen 1998; Loladze et al., 2000; Muller et al 2001; Andersen et al 2004;

13.  Large amp. Cycles  No cycles (consistent with other studies) Classic consumer-resource cycles may occur McCauley et al. Nature, 402:653-656, 1999 Lab populations (with rapid P recycling) may cycle MAGNITUDE OF REMINERALIZATION RATES MATTERS

14. Slow remineralization approximation (P inputs from decoupled “junk” pool) Low populations, stable equilibrium, “donor control” from junk pool. Most P resides in junk pool

15. DEB view of mass flow in V1 consumer Animal Growth Development Reproduction Survival Food (X) Metabolic Products

16. * * E.B. Muller, R.M. Nisbet, S.A.L.M. Kooijman, J.J. Elser, E. McCauley, Ecology Letters 4: 519-529 (2001)

17. Option 1  Rosenzweig-MacArthur model Add food (producer) dynamics Per capita growth rate of phytoplankton = where Q = Phosphorus quota (units mol P/mgC) 1.Let T = total phosphorus in system and assume all bound in food Then with K = T/k q 2. Take account of P bound in consumer 

18. Muller et al. 2001

23. Nelson, W.A., McCauley, E & Wrona, F.J. (2001). Multiple dynamics in a single predator– prey system: experimental effects of food quality. Proc. R. Soc. Lond. B, 268, 1223–1230. Discussed by: Andersen, T., Elser, J.J. and Hessen, D. (2004)Stoichiometry and population dynamics. Ecology Letters 7: 884–900 Evidence for multiple attractors * ? (“HBD” = Herbivore biomass dynamics)

24. BIODIVERSITY AND ECOSYSTEM FUNCTION A challenge for DEBologists

25. 25 Species- abundance distributions Plots of abundance of species in collections as frequency distributions have charcteristic form commonly well described by log-normal distribution

26. 26 Why Lognormal-like Distribution? May (1975) proposed a purely statistical explanation, and lognormal distribution is the product of many random variables acting on the population of many species. Sugihara suggested lognormal distribution is a consequence of the species within a community subdividing niche space. Hubbell and others recently developed neutral theory. Differences between species are irrelevant. All individuals of all species have same birth and death probabilities (Controversial – see special feature in Ecology June 2006).

27. 27 Neutral theory “tested”? (21457 trees from 224 species) Source: J. Harte: Nature 424: 1006-7 (2003)

28. 28 Adding niches * Carroll, I.T., Cardinale, B.J. and Nisbet, R.M. (2011). Niche and fitness differences relate the maintenance of diversity to ecosystem function, Ecology, 92: 1157-1165. With simple (non-DEB) bioenergetic model: Defined niche differences (ND) and relative fitness differences (RFD) in terms of invasibility (related to Chesson’s stabilizing and equalizing mechanisms) Show that high ND promotes coexistence and high RFD promotes competitve exclusion Calculated the relative yield total,’a measure of diversity’s effect on the biomass of competitors.

29. 29 Relative yield – 2 species model Analytic Numerical

30. 30 Relative yield – 3 and 4 species

31. 31 Define a neutral community in DEB Use DEB to explore biodiversity- ecosystem function relations CHALLENGES