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Adaptation of marine food webs to environmental change: Theoretical considerations
and comparisons with field data
Albert Gabric
School of Australian Environmental Studies
Griffith University
Nathan, Queensland, 4111
Australia
and
Edward A. Laws
University of Hawaii
Department of Oceanography
1000 Pope Road
Honolulu, HI 96822
USA
Efforts to develop a theoretical understanding of the manner in which
ecosystems adapt to environmental change date from the work of Lotka (1922), who
postulated that natural selection tends to maximize the energy flux through a system, at
least within the constraints to which the system is subject. Odum (1983) expanded on
Lotka’s theory. He argued that natural systems tend to maximize power, and that
theories and corollaries derived from the maximum power principle could explain much
about the structure and processes of these systems. In rationalizing the application of
the maximum power principle to ecosystems, Odum drew analogies between ecosystem
behavior and the laws of thermodynamics. Several authors have challenged the
rationale for the maximum power principle (e.g., Mansson and McGlade, 1993).
Fenchel (1987), for example, has commented that Odum’s approach was appealing
“only because it was sufficiently obscure and incomprehensible to appear profound”.
Nevertheless, a number of authors have explored the application of analogues of
thermodynamic principles to the behavior of natural systems (Jorgensen, 2000;
Jorgensen and Straskraba, 2000), and in many cases these thermodynamic approaches
have met with considerable success in estimating parameters to describe real
ecosystems.
In a recent paper Cropp and Gabric (2001) employed a genetic algorithm to
simulate the evolutionary response of the biota of a model ecosystem. The model
ecosystem consisted of a simple autotroph-herbivore-nutrient (AHN) oceanic mixedlayer. The differential equations describing the dynamics of the system are as follows:
 N 
dA
A  K1AH
  
dt
 N  KS 
(1)
dH
 K1 (1  K 3 )AH  K 2 H
dt
(2)
 N 
dN
A
 K 2 H  K1K 3AH   
dt
 N  KS 
(3)
The total nutrient concentration is No = A + H + N. Given No, the system contains five
adaptive parameters, K1 (herbivore grazing rate), K2 (herbivore mortality rate), K3
(herbivore excretion rate),  (maximum autotroph growth rate), and KS (autotroph halfsaturation nutrient concentration). For a given No, the values of these five parameters
were chosen using a stochastic genetic algorithm that simulated the individual
adaptation in response to selection pressures over evolutionary time scales. A number
of selection pressures were explored, including maximum exergy (Jorgensen, 1992),
maximum ascendancy (Ulanowicz, 1980), entropy production (Schneider, 1998), and
resilience (DeAngelis, 1992). One of the interesting results of the simulations was that
the optimum parameter values proved to be very insensitive to the choice of selection
pressure. In particular, the simulations suggested the hypothesis that within the
constraints of the external environment and the genetic potential of their constituent
biota, ecosystems evolve to the state most resilient to perturbation.
Laws et al. (2000) have applied the hypothesis of maximum resilience to a more
complex food web model of an open-ocean pelagic ecosystem (Fig. 1). The differential
equations describing the population dynamics of this system are similar to those used by
Cropp and Gabric (2001). Most of the parameter values were chosen from information
in the literature or were otherwise constrained in a deterministic manner. Two
parameters, however, were allowed to adapt so as to maximize the resiliency of the
steady state solution. These two adaptive parameters were the relative growth rate
(sensu Goldman, 1980) of the large phytoplankton and the biomass of the filter feeders.
In this case, it was possible to compare the predictions of the model with results of field
studies carried out as a part of the Joint Global Ocean Flux Study and related work.
Some results are shown in Fig. 2-3. Because the system was assumed to be in steady
state, the export ratio equals the f ratio (Eppley and Peterson, 1979) and was designated
the ef ratio. The predicted ef ratios based on the principle of maximum resiliency are in
remarkable agreement with observed ef ratios (Fig 2a), and there is likewise remarkable
agreement between predicted and observed heterotrophic bacterial biomass (Fig. 3).
These comparisons clearly support the assumption that pelagic marine
ecosystems tend to evolve toward a condition of maximum resiliency, as predicted by
the results of the Cropp and Gabric (2001) simulations. In the case of the Laws et al.
(2000) food web, defining the ecological analogue of thermodynamic imperatives such
as entropy and exergy is problematic, but the resiliency of the system is unequivocally
defined through application of perturbation theory (May, 1974). As noted by Patten
(1993), “The admissibility of virtually any system configuration, within given physical
and resource constraints, does not mean the processes of ecosystem organization are
lawless. The challenge is to find the laws.” The extent to which the principle of
maximum resiliency will prove useful in defining the behavior of natural systems in
response to change is unclear. However, the work of Cropp and Gabric (2001) and
Laws et al. (2000) suggest that evolution toward a condition of maximum resiliency
may govern the behavior of a wide variety of pelagic marine communities.
References
Cropp, R. and A. Gabric. 2001. Ecosystem adaptation: Do ecosystems maximize
resilience? Ecology (in press)
DeAngelis, D. L. 1992. Dynamics aof Nutrient Cycling and Foodwebs. Chapman and
Hall, London.
Eppley, R. W. and B. J. Peterson. 1979. Particulate organic matter flux and planktonic
new production in the deep ocean. Nature 282: 677-680.
Fenchel, T. 1987. Ecology – Potentials and Limitations. Ecology Institute,
Oldendorf/Luhe, Germany.
Goldman, J. C. 1980. Physiological processes, nutrient availability, and the concept of
relative growth rate in marine phytoplankton ecology, pp. 179-194 in P. G.
Falkowski (ed.) Primary Productivity in the Sea. Plenum, New York.
Jorgensen, S. E. 1992. Development of models able to account for changes in species
composition. Ecological Modeling 62: 195-208.
Jorgensen, S. E. 2000. A general outline of thermodynamic approaches to ecosystem
theory. In Jorgensen, S. E. and F. Muller (eds.) Handbook of Ecosystem
Theories and Management. CRC Press, Boca Raton, Florida.
Jorgensen, S. E. and M. Straskraba. 2000. Ecosystems as cybernetic systems. In
Jorgensen, S. E. and F. Muller (eds.) Handbook of Ecosystem Theories and
Management. CRC Press, Boca Raton, Florida.
Laws, E. A., P. G. Falkowski, W. O. Smith, H. Ducklow, and J. J. McCarthy. 2000.
Temperature effects on export production in the open ocean. Global
Biogeochem. Cycles 14: 1231-1246.
Lotka, A. J. 1922. Contribution to the energetics of evolution. Proc. Natl. Acad. Sci. 8:
147-150.
Mansson, B. A., and J. M. McGlade. 1993. Ecollgy, thermodynamics and H. T. Odum’s
conjectures. Oecologia 93: 582-596.
May, R. M. 1974. Stability and Complexity in Model Ecosystems. 2nd ed. Princeton
Univ. Press, Princeton, NJ, 265 pp.
Odum, H. T. 1983. Systems Ecology: An Introduction. Wiley, New York.
Patten, B. C. 1993. Toward a more holistic ecology, and science: the contribution of H.
T. Odum. Oecologia 93: 597-602.
Schneider, E. D. 1988. Thermodynamics, ecological succession and natural selection: a
common thread. Pages 107-138 in Weber, B. H., D. J. Depew, and J. D. Smith
(eds.) Entropy, Information and Evolution. MIT Press, Cambridge, MA, USA.
Ulanowicz, R. E. 1980. An hypothesis on the development of natural communities. J.
Theor. Biol. 85: 223-245.
f6
Carnivores
X6
Filter
feeders
X5
External
nutrient
f5
Loading
rate = L
Detrital
POM
Large
phytoplankton
X2L
Export
f2L
Ciliates
X4
f4
Inorganic
nutrient X1
Flagellates
X3
Bacteria
f3
Small
phytoplankton X2S
DOM
Figure 1. Feeding and excretion relationships in a model pelagic food web in which
photosynthetic production is partitioned between small and large phytoplankton cells.
0.7
a
0.7
b
Ross Sea
Ross Sea
0.6
0.6
Greenland polynya
Observed ef ratio
0.5
Greenland polynya
North Atlantic Bloom
0.5
Station P
Peru-normal
Station P
0.4
Peru-normal
0.4
0.3
0.3
Peru-El Nino
0.2
Peru-El Nino
0.2
Arabian
Sea
HOT
Arabian Sea
EqPac-normal
HOT
EqPac-normal
0.1
0
North Atlantic Bloom
0.1
BATS
EqPac-El Nino
0
0.1
0.2
0.3
0.4
0.5
Model ef ratio
0.6
0.7
0
BATS
EqPac-El Nino
0
200
400
600
800
Total primary production (mg N m -2 d-1)
1000
Figure 2. (a) Model ef ratios versus observed ef ratios as reported by Laws et al. (2000). The
straight line is the 1:1 line. (b) Total primary production versus observed ef ratios at the
same locations.
Peru-upwelling
2
Heterotrophic bacterial biomass from model (mg C m -3)
10
NABE
Arabian Sea
EqPac-normal
1
10
Ross Sea
Station P
EqPac-El Nino
BATS
HOT
Greenland
1
10
2
10
Heterotrophic bacterial biomass from field data (mg C m -3)
Figure 3. Relationship between estimates of heterotrophic bacterial carbon from the Laws et al.
(2000) model and from field data. The straight line is the 1:1 line.