Transcript Consumers
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 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)
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)
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 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
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;
Lab populations (with rapid P recycling) may cycle
Classic consumer-resource cycles may occur
McCauley et al. Nature, 402:653-656, 1999
Large amp. Cycles
No cycles
(consistent with other studies)
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
Animal
Food (X)
Growth
Development
Reproduction
Survival
Metabolic
Products
*
Q(1 Q)
a aC
2
1 Q Q
* E.B.
Muller, R.M. Nisbet, S.A.L.M. Kooijman, J.J. Elser, E. McCauley, Ecology Letters 4: 519-529 (2001)
Add food (producer) dynamics
kQ
Per capita growth rate of phytoplankton = r 1
Q
where Q = Phosphorus quota (units mol P/mgC)
1. Let T = total phosphorus in system and assume all bound in food
Then
dF
F I max FC
rF 1
dt
K F Fh
with
2. Take account of P bound in consumer
K = T/kq
T Cq
K
kq
Option 1 Rosenzweig-MacArthur model
Muller et al. 2001
Muller et al. 2001
Muller et al. 2001
Evidence for multiple attractors*?
(“HBD” = Herbivore biomass dynamics)
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
BIODIVERSITY AND
ECOSYSTEM FUNCTION
A challenge for DEBologists
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
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.
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.
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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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CHALLENGES
• Define a neutral community in DEB
• Use DEB to explore biodiversityecosystem function relations
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