poopulatins communities and ecosystems lecture III Background for sections 91 and 94 of DEB3 Roger Nisbet April 2015 Remember my pet Carbon flow and phosphorus cycling in a lake Simplest DEB DAB model canonical community ID: 263512
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Slide1
DEB theory for
poopulatins
, communities
and ecosystems - lecture III
(Background for sections 9.1 and 9.4 of DEB3)
Roger Nisbet
April
2015Slide2
Remember my petSlide3
Carbon flow and phosphorus cycling in a lakeSlide4
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 nutrientsSlide5
Chemical transformations in canonical communitySlide6
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)Slide7
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)Slide8
Precursor – book chapter
In:
J
o
rgensen
, S. E. 2000 Thermodynamics and ecological
modelling
. CRC Publ., Boca Raton,
FL,USA
, pages 19{60Slide9
Precursor – book chapter
In:
J
o
rgensen
, S. E. 2000 Thermodynamics and ecological
modelling
. CRC Publ., Boca Raton,
FL,USA
, pages 19{60Slide10
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
Simplify DEB representation of individuals
Plagiarize key ideas from DEB theory
- Products from weighted sum of fluxes
- Synthesizing unit (SU)
4)
Choose simplifications matching modeling objectivesSlide11
Model Simplification for C and P flows in
a lakeSlide12
Fast remineralization/uptake approximation
(Andersen 1998; Loladze et al., 2000; Muller et al 2001; Andersen et al 2004; Slide13
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 MATTERSSlide14
Slow remineralization approximation
(P inputs from decoupled “junk” pool)
Low populations, stable equilibrium, “donor control” from junk pool. Most P resides in junk poolSlide15
DEB view of mass flow in V1 consumer
Animal
Growth
Development
Reproduction
Survival
Food (X)
Metabolic
ProductsSlide16
*
*
E.B. Muller, R.M. Nisbet, S.A.L.M.
Kooijman
, J.J.
Elser
, E. McCauley,
Ecology Letters
4
:
519-529 (2001)Slide17
Option 1
Rosenzweig-MacArthur model
Add food (producer) dynamics
Per capita growth rate of phytoplankton =
where
Q
= Phosphorus
quota
(units mol P/mgC)
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
Slide18
Muller et al. 2001Slide19
Muller et al. 2001Slide20
Muller et al. 2001Slide21Slide22Slide23
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)Slide24
BIODIVERSITY AND ECOSYSTEM FUNCTION
A challenge for DEBologistsSlide25
Species- abundance distributions
Plots of abundance of species in collections as frequency distributions have charcteristic form commonly well described by
log-normal distributionSlide26
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
). Slide27
Neutral theory “tested”?
(21457 trees from 224 species)
Source: J. Harte:
Nature
424: 1006-7 (2003)Slide28
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.Slide29
Relative yield – 2 species model
Analytic NumericalSlide30
Relative yield – 3 and 4 speciesSlide31
Define a neutral community in DEB
Use DEB to explore biodiversity-ecosystem function relations
CHALLENGES