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