DEB theory for poopulatins, communities and ecosystems -

lecture III

(Background for sections 9.1 and 9.4 of DEB3)

Roger Nisbet

April 2015

Remember my pet

Carbon flow and phosphorus cycling in a lake

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

Chemical transformations in canonical community

Mass balance equations for canonical communityConsumer and decomposer (4): each has reserve and structureProducer (3): 2 reserves plus structureDetritus (4): consumer + producer feces; dead decomposers / consumersMinerals (4): H, C, O, N.No. of equations reduced slightly by mass balance (C and N conserved)

Mass balance equations for canonical communityConsumer and decomposer (4): each has reserve and structureProducer (3): 2 reserves plus structureDetritus (4): consumer + producer feces; dead decomposers / consumersMinerals (4): H, C, O, N.No. of equations reduced slightly by mass balance (C and N conserved)

Precursor – book chapter

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

Precursor – book chapter

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

How to KISS? DEB-inspired and DEB-related

models1) 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

3) Plagiarize key ideas from DEB theory- Products from weighted sum of fluxes- Synthesizing unit (SU)

4) Choose simplifications matching modeling objectives

Model Simplification for C and P flows in a lake

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

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

Slow remineralization approximation(P inputs from decoupled “junk” pool)

Low populations, stable equilibrium, “donor control” from junk pool. Most P resides in junk pool

DEB view of mass flow in V1 consumer

AnimalGrowth

DevelopmentReproduction

Survival

Food (X) Metabolic Products

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)1(

QQ

QQCaa

*

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

Option 1 Rosenzweig-MacArthur model

Add food (producer) dynamics

hFF

FCI

K

FrF

dt

dF

max1

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/kq

2. Take account of P bound in consumer

1 Qkr

Q

qk

CqTK

Muller et al. 2001

Muller et al. 2001

Muller et al. 2001

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)

BIODIVERSITY AND ECOSYSTEM FUNCTION

A challenge for DEBologists

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Species- abundance distributions

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

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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).

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Neutral theory “tested”?(21457 trees from 224 species)

Source: J. Harte: Nature 424: 1006-7 (2003)

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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.

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Relative yield – 2 species model

Analytic Numerical

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Relative yield – 3 and 4 species

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• Define a neutral community in DEB

• Use DEB to explore biodiversity-ecosystem function relations

CHALLENGES