Ecosystem Modeling Workshop
Co-Sponsored by CaRA, GCOOS, GOMA, & SECOORA
October 14-16, 2009, St. Petersburg, FL
A History and Evolution of Ecosystems Models
Claire B. Paris
Assistant Professor
Rosenstiel School of Marine & Atmospheric Science
University of Miami
Nasseer Idrisi
Assistant Professor, CaRA Subregional Coordinator
US Virgin Islands
Center for Marine and Environmental Studies
University of The Virgin Islands
Outline
1.
2.
3.
4.
5.
what is an ecosystem model
how are they developed
where we were
where we are
where we want to be
1. what is an ecosystem model?
Definition: A simplified representation of complex ecosystems
(e.g. foodweb), aimed at characterizing their major dynamics and
predicting their behavior
- forced from the outside at the boundaries with input from data or other
models
- interact dynamically through coupling with physical models
Forcing:
-Temperature
-Interacting chemicals
-Currents
-PAR
-etc….
P
N
Z
D
2. how are ecosystem models developed?
•
Holistic or reductionist approaches (bottomup, POM)
•
Predictive approach (hypothesis in terms of
expected results)
•
Inferential, deduct mechanism (hypothesis in
terms of processes)
•
Mechanistic or empirical methods deductive
reasoning
•
hypothesis generating (experimental
modeling)
Each has its own strengths and weaknesses. The development of a model,
the type of model, the approach and method used, and the final analysis and
synthesis should be suited to the study (e.g., start with a specific question,
what observed patterns characterize the system dynamic, Grim 2005)
3. Where we were
Raymond Pearl (1920s): described population growth through
mathematical representation using the logistic equation (Verhulst:
1845, 1847)) to forecast human population growth. Pearl also laid the
foundations for developing empirically-derived models of demography
that include information on fecundity and birth rates, death rates,
immigration and emigration that statistically describe the dynamics of
a population.
dN =
dt
rN(K-N)
K
r and K are specific to a
species and environment
conditions, but can change
depending on species and
conditions
3. Where we were
Alfred Lotka (1924) and Vito Volterra (1926) independently developed a system
of coupled ordinary differential equations that describe predator-prey
interactions over time. These are exponential in nature and the populations at
different trophic levels are constrained by their coupled nature. The
competitive model system, also attributed to Lotka and Volterra describe the
interactions between two species through coupled logistic equations where
each population is constrained by the other and a carrying capacity term in
each
where x and y are prey and
predator,
α, is the prey’s growth rate
β, is an interaction parameter
(predation of Y on X)
γ, the assimilation efficiency of Y
δ is the mortality rate of the predator
3. Where we were:
NPZ 3 compartments system
The next major step in ecosystem modeling came with Gordon Riley (1946)
with a 3-level system of coupled ordinary differential equations that
describes a planktonic marine ecosystem. These models increased in
sophistication with John Steele (1974) and Steele and Frost (1977) that
accommodate better means for parameterization, and more robust with
regards to assumptions and constraints.
Franks and Chen (1996) coupled a Nutrient-Phytoplankton-Zooplankton
(NPZ) model into a primitive equation model and applied it to examine the
summertime plankton dynamics on GB. That was the first modeling effort
to study the biological process under the “realistic” physical environment
in the GoM/GB region.
From Francisco Werner’s 1999 tutorial at
UNC
3. Where we were
NPZ 3 compartments system
Franks and Chen (2000) carried out numerical experiments for 2-D and 3-D
cases on Georges Bank:
The 2-D experiments were conducted on a south-north transect across the
center of GB. The model is driven by tidal forcing only with an assumption that
the cross-bank distribution of temperature, phytoplankton and nutrients on GB
is mainly related closely to the tidal mixing front.
The 3-D experiments were conducted with emphasis on the role of tidal mixing
and advection in the spatial and temporal distributions of temperature,
phytoplankton, zooplankton, and nutrients on GB. Similar to the 2-D case, the
initial fields of temperature and biological variables are specified to be uniform
in the horizontal with assumption that the spatial and temporal variations of
physical and biological variables are caused by tidal mixing and advection.
The model-predicted distribution of tidal mixing front is in excellent agreement with previous observations.
3. Where we were
Model formulations and assumptions: Up to this point, it is understood that the
models used to represent ecosystems require many assumptions regarding
the model boundaries and how these systems are forced and the nature of
the behavior of the modeled components to forcing from outside the system
and from within the system. How do we constrain a model variable and how
do we constrain the variable’s behavior? These are important questions that
need to be asked when developing the model system for a particular study.
3. Where we were
Population modeling: At the base of ecosystem models is the population, and
throughout the 20th century, population model development evolved with the
Leslie Matrix Model (P.H. Leslie, 1945) that uses demographics, information
that Pearl used to describe human populations. Beverton and Holt (1957)
developed models for fisheries to hindcast fish cohorts to understand fish
population growth, and this evolved into Virtual Population and Multispecies
Virtual Population Analysis that are used for fisheries management.
Food web modeling: The following step was to extend to food web modeling
(Robert May, Joel Cohen, Robert Ulanowicz, Neo Martinez, and many more)
with increased complexity with regards to populations and communities within
ecosystems.
Individual-Based Models: Other than food webs, population models also became
more sophisticated with the increase in computer power. This advancement in
computational power has led to the development of individual-based and
agent-based models (IBMs) of populations and communities.
From Francisco Werner’s 1999 tutorial at
UNC
spatially-explicit Lagrangian models
4. Where we are now:
Biophysical coupled ecosystem models (e.g., P. Franks, C. Miller) include what
are termed NPZ/NPZD ecosystem models that simulate interactions among
pelagic state variables of nutrients, phytoplankton, zooplankton and detritus
in the Eulerian field. These Eulerian models are coupled to IBMs that are
modeled as Lagrangian particles.
It has been argued that advances in coupled NPZ models have not moved
forward as much as they should (Franks, in press), the reason has been
attributed to a fact that many of these studies are not hypothesis-driven, or if
they are, the study design does not allow for the rejection of the main
hypothesis in favor of an alternative hypothesis. Rather, model parameters
are tweaked endlessly until the model output fits the data and the desired
outcome is achieved.
5. Where we are now
3D OGCM-7 compartments NP
Tsiaras and Kourafalou (2006)explored the main physical and biological
processes that control the seasonal cycle of the plankton dynamics over the
Western Black Sea by means of a 3-D, 7-compartment, on-line coupled
biophysical model - high frequency forcing indicated that seasonal production
was linked to the Danube river’s discharge.
4. Where we are now
Coupled physical-biological Lagrangian particle models have followed a more
productive path than NPZ models as evidenced by the nature and quality of
publications produced over the past several years.
coupling NPZD with
spatially-explicit
Lagrangian models
Idrisi et al. (2004) use the physiologicallyexplicit NPZD model and a simple
behavior for the Lagrangian model that is
also physiologically constrained to
simulate emergence from diapause of an
Arabian Sea copepod species.2.71% of
individuals were physically upwelled into
favorable conditions and 23.4% of
individuals swam into bloom conditions.
5. Where we are now
Olascoaga et al. (2005) coupled an NPZD to MICOM for the Arabian Sea using
a growth function that is temperature dependent and parameterized from
JGOFS data from the 1995-1996 Arabian Sea Expedition
Physiologically-explicit temperature-dependent growth can be global and applicable
across latitudes
Coupling to ocean circulation:
Coupling an NPZD to
ocean circulation
4. Where we are now: static ecological model
Ecopath, a static mass-balance system, ecosim – time-dynamic simulation, and
ecospace – spatially explicit simulation (Christensen and Walters).
Ecopath introduces prey behavior with the predator-prey transfer functions of a
Holling type II or III equation. The system has been criticized such as – that
the general predictions on predator declines can be understood from basic
life-history information, and that all energy is cycled within the system and the
species diet is inflexible. The authors of ecopath make valid counterarguments, but it is yet to be seen as to the success of this system.
3 Components:
▪
Ecopath – a static, mass-balanced
snapshot of the system
▪
Ecosim – a time dynamic simulation module
for policy exploration
▪
Ecospace – a spatial and temporal dynamic
module primarily designed for exploring impact
and placement of protected areas
5. Where we want to be
The path forward is to reflect on the past – triumphs and failures, evaluate past
mistakes and apply corrective measures. An ecosystem model should be
treated as an hypothesis, and should be rejected if the results do not
represent the phenomenon being tested.
How then will we know if, given a certain scenario, a Michaelis-Menton function
is adequate to represent phytoplankton growth, or do we need a temperaturedependent growth function, or PAR absorption function, or maybe something
else?
Good models use experiments and field data to develop parameters, modeling
studies need to work hand in hand with laboratory/field experiments and field
data collection, and to take advantage of advances in assimilation
techniques. These advances are necessary, especially in the context of this
workshop for IOOS, whose mission is to develop operational models for use
by managers, policy makers, and other product users. We cannot provide an
operational ecosystem model if we cannot get the science of the ecosystem
Field observations &
model correct.
Lab experiments
Data Assimilation
5. Where we want to be
deYound, Heath, Werner, Chai, Megrey, Monfray (2004 Science) Relationship
between trophic level and functional complexity within marine ecosystem
models. The rhomboids indicate the conceptual characteristics for models
with different species and differing areas of primary focus.
Key Modeling Aspects & Challenges
•
physical model in which the biological
representation is embedded should have
appropriate resolution & complexity
•
modeling with uncertainties: probabilistic vs
deterministic simulations (endemic lack of
knowledge of processes & structures at those
scales), i.e. ensemble forecast, iterative
stochastic approach - less precise but more
accurate!
•
The response of marine food webs to
environmental changes cannot be based on
the predictions of static models whose
parameters are chosen based on the
goodness of fit of model output to currently
observed phenomena. The reason is that
communities of organisms are adaptive. In
order to understand how biological
communities adapt, it is first necessary to
understand the principles that drive the
organization of those communities.
5. Where we want to be
The European Regional Seas Ecosystem Model (ERSEM, Baretta et al., 1995)
consists of five modules (conceptual units): Primary producer module; Microbial
loop module; Mesozooplankton module; Benthic nutrients module and Benthic
biology module.
5. Where we want to be
Chen (UMass) and Beardsley (WHOI), have developed an integrated model system for the Gulf of
Maine (GoM)/Georges Bank (GB)/New England shelf (NES) region. The major components of this
system include:
1) the modified fifth-generation community mesoscale atmospheric model (MM5);
2) the unstructured grid Finite-Volume Coastal Ocean circulation Model (FVCOM);
3) a 3-D suspended sediment transport model;
4) a generalized lower trophic level food web model [called Flexible Biological Module (FBM)],
5) a multi-stage zooplankton models (developed by Cabell Davis at WHOI).
4. Where we want to be: Multi-scale modeling
Srinivasan and Paris (RSMAS) have developed a coupled physical-biological
IBM, the Connectivity Modeling System (CMS) with particle swimming
behavior and trophic levels interactions (NPZ), featuring 1) on-the-fly access
of ocean model data using OPeNDAP, 2) the Earth Modeling System
Framework (EMSF) that channels multi-scale data from model and
observation, 3) statistical interpolation of observations, 4) Lagrangian and
Eulerian data assimilation, 5) nesting capabilities, 6) a flexible biological
module, a 7) a GIS-based habitat module, and 8) a genetic matrix-based
module. Partners providing high-resolution ocean models for the CMS are
Kourafalou (SoFL-HYCOM, FLKey-HYCOM) and Cherubin (ROMS).
1. Raymond Pearl human population growth models (logistic).
Summary
2.
Lotka-Volterra predator-prey and competition models.
3. Wiegert predator-prey models.
4. Leslie matrix population models.
5. Virtual Population Analysis of commercially important fish populations.
6. Multi-virtual population analysis of commercially important fish communities.
7. Nutrient-phytoplankton-zooplankton-detritus numerical difference models.
8. Food web models: networks, links, and energy flows.
9. Individual-based models.
10. Agent-based models.
11. Ecopath.
12. Coupled biophysical NPZD and higher complexity models in the Eulerian
field.
13. Coupled biophysical individual-based models in the Lagrangian field.
The first three models (1-3) are either individual or a set of coupled differential
equations. Models 4-9 and 12-13 are individual or sets of coupled linear
difference equations. Models 12 and 13 are coupled to a physical model and
be spatially explicit, rather than being a ‘box’ model as earlier models were,
and the earlier models considered space implicitly. Models 10 and 11 are
Discussion
What type of ecosystem models we want for the region?
Objectives of Ecosystem Modeling for CaRA, GCOOS, GOMA, & SECOORA:
-Identify existing weaknesses, theoretical constraints, and needed advances in
ecosystem modeling
-what are the issues/problems that ecosystem models are expected to address?
-review ecosystem modeling activities underway in the Gulf of Mexico, Caribbean
Sea, and southeastern U.S. coastal waters, including estuaries and bays
-Unified, coordinated program of ecosystem modeling for the region
Ecosystem Modeling Workshop
14-16 October 2009
St. Petersburg, FL
5. Where we want to be
Conceptual Model: hypothesis testing
From Idrisi et al. (2001) Impact of an invasive grazer on pelagic lower food web
(N-P-Z).
Factors
Zebra mussel invasion=> Phosph
Phyto
Zoopl
Hypothesized
InorganicP
ParticulateP
Reality
Biomass
Production
Biomass
Production
Contrary to the hypothesized decrease in primary production, increase in water
clarity
led to the system maintaining constant productivity levels that led to an increase
in
Lagrangian particle tracking algorithm
Adlandsvik et al. (WAKMF
2006)
Advantages with particle tracking
• Good numerical properties:
Avoids numerical diffusion and dispersion
Permit longer time steps and offline tracking
• Individual based (IBM): Physical basis for individual based biological models
• Relatively easy to implement
Scientific status for particle tracking
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•
•
Theoretical basis known for at least 20 years
Good algorithms are available
Some details regarding vertical boundary conditions are not understood (Ross and Sharples 2004)
Turbulence parameterization beyond eddy diffusivity – random walk formulation
Practical issues with particle tracking
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Numerical method
Euler forward
Higher order (e.g. RK4, adaptative)
Random number generator
Quality of Rn generator
shape of distribution (Hunter et al. 1993, Ross & Sharples 2004)
Land boundaries
Important practial problem, not discussed, no good solution
Artificial 2D convergence
Spatially varying diffusivity
‘naïve’ RW does not work, but never addressed in larval transport
Need correction velocity from low to high diffusivity (Visser 1997)