DEB theory for ecosystems
Roger Nisbet
May 2017
DEB as “pivot” linking suborganismal to ecological
processes?
Communities
+
Ecosystems
Populations
DEB theory
Individuals
Ecological models
Organs
Cells
Molecules
Pivot
Laure’s slide on DEB Fantasy World
Forcing
variables
Environmental
data
Ordinary differential
Equations
State variables
Initial values
Auxiliary
Equations
State
variables
Primary
Parameter
values
Observables
Organism
data
Auxiliary
parameter
values
Fantasy world
Real world
‘Mainstream’ theoretical ecologists’ fantasy world
Forcing
variables
Environmental
data
Ordinary differential
Equations
State variables
Initial values
State variables = Observables
Organism
data
Primary
Parameter
values
Structured pop. Model fantasy world
Real world
ABSTRACTIONS IN THREE FANTASY WORLDS
DEB theory
Structure
Reserve
Homestasis
Maturity
Theoretical Ecology
Density dependence
Storage effect
Niche
Neutrality
ESS
Environmental
Chemistry
Organic nitrogen
Inoragnic nitrogen
Reactive phosphorus
ABSTRACTIONS IN THREE FANTASY WORLDS
DEB theory
Structure
Reserve
Homestasis
Maturity
Theoretical Ecology
Density dependence
Storage effect
Niche
Neutrality
ESS
Environmental
Chemistry
Organic nitrogen
Inoragnic nitrogen
Reactive phosphorus
Modeling ecosystems requires coupling ideas from these three worlds
Key to connecting with DEB – theory on material fluxes (page 8 of course notes)
“Textbook” fantasy of carbon flow and phosphorus cycling in a lake
Nisbet et al, Theor. Pop. Biol 1991
Nitrogen flows in a fjord
Gurney and Nisbet 1998
Simplest DEB (DAB) model – “canonical community”
(Kooijman 2010 – 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)
May still require some added
specificity in mineral fluxes
POTENTIAL AREA FOR
FUTURE RESEARCH WITH
MANY APPLICATIONS
How to proceed meanwhile?
Use “DEB-inspired” models
1) Recognize key components of DEB theory
- Strict mass balance for elemental matter
- Strong homeostasis
- Some organisms need two state variables
- Uses dynamic equations relating environment to
functional group performance and to metabolic
products
2) Simplify DEB representation of individuals
3) Exploit 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
Green = Producers
Blue = Consumers
TIME
TIME
Populations without rapid recycling don’t cycle
IMPLYING
Dynamics of remineralization is important
McCauley et al. Nature, 402:653-656, 1999
Slow remineralization approximation
(P inputs from decoupled “junk” pool)
• Low consumer populations with 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)
Muller et al. 2001
Muller et al. 2001
Muller et al. 2001
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
DEB theory and community ecology
Possible mechanisms for species coexistence
Kooijman 2010, page 337
Bas’s List in bigger print
(1) mutual syntrophy, where the fate of one species is
directly linked to that of another
(2) nutritional `details': The number of substrates is
actually large, even if the number of species is small
(3) social interaction, which means that feeding rate is
no longer a function of food availability only
(4) spatial structure: extinction is typically local only and
followed by immigration from neighbouring patches;
(5) temporal structure
Bas’s List in bigger print
(1) mutual syntrophy, where the fate of one species is
directly linked to that of another
(2) nutritional `details': The number of substrates is
actually large, even if the number of species is small
(3) social interaction, which means that feeding rate is
no longer a function of food availability only
(4) spatial structure: extinction is typically local only and
followed by immigration from neighbouring patches;
(5) temporal structure
DEB theory can contribute new theory on mutualism
SYNTROPHIC SYMBIOSIS
MUTUAL EXCHANGE OF PRODUCTS
CORALS
FREE LIVING
INTEGRATION
FULLY MERGED
Erik Muller slide
FREE LIVING HOST
Erik Muller slide
FREE LIVING SYMBIONT
Erik Muller slide
SHARING THE SURPLUS
ENDOSYMBIOSIS
• HOST RECEIVES PHOTOSYNTHATE SYMBIONT CANNOT USE
• SYMBIONT RECEIVES NITROGEN HOST CANNOT USE
Erik Muller slide
Model predictions
• Stable host;symbiont ratio at level consistent with data synthesis from 126
papers describing 37 genera, and at least 73 species
• Dark respiration rates broadly consistent with data
E.B. Muller et al. JTB 2009. ; P. Edmunds et al. Oecologia, 2011; Y. Eynaud et al Ecological Modelling 2011.
Priorities for research in community/ecosystem dynamics
• Modifying and testing the canonical community
representation with explicit recognition of chemical
transformations in the environment
• Wider use of DEB inspired models – a powerful
toolbox
• Modeling community dynamics with mutualism