Abstract
Energy flow drives the complex systems to evolve. The allometric scaling as the universal energy flow pattern has been found in different scales of ecological systems. It reflects the general power law relationship between flow and store. The underlying mechanisms of energy flow patterns are explained as the branching transportation networks which can be regarded as the result of systematic optimization of a biological target under constraints. Energy flows in the ecological system may be modelled by the food web model and population dynamics on the network. This paper reviews the latest progress on the energy flow patterns, explanatory models for the allometric scaling and modelling approach of flow and network evolution dynamics in ecology. Furthermore, the possibility of generalizing these flow patterns, modelling approaches to other complex systems is discussed.
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References
H. T. Odum, System Ecology: An Introduction, John Wiley Sons Inc, San Francisco, 1983.
S. L. Pimm, Food Webs, University of Chicago Press, Chicago, 2002.
J. H. Brown, Toward a metabolic theory of ecology, Ecology, 2004, 85(7): 1771–1789.
G. B. West, J. H. Brown, and B. J. Enquist, A general model for the origin of allometric scaling laws in biology, Science, 1997, 276: 122–126.
J. R. Banavar, A. Maritan, and A. Rinaldo, Size and form in efficient transportation networks, Nature, 1999, 399: 130–132.
N. Loeuille and M. Loreau, Evolutionary emergence of size-structured food webs, in Proceedings of the National Academy of Sciences of the United States of America, 2005, 102: 5761–5766.
M. E. Moses and J. B. Brown, Allometry of human fertility and energy use, Ecology Letters, 2006, 6: 295–300.
W. Q. Duan, Universal scaling behavior in weighted trade networks, the European Physical Journal B, 2007, 59: 271–276.
C. Kuhnerta, D. Helbinga, and G. B. West, Scaling laws in urban supply networks, Physica A, 2006, 363: 96–103.
T. Gross and B. Blasius, Adaptive coevolutionary networks: A review, Journal of the royal society, 2008, 5: 259–271.
S. E. Jorgensen and H. F. Mejer, A holistic approach to ecological modelling, Ecological Modelling, 1979, 7: 169–189.
M. Kleiber, Body size and metabolism, Hilgardia, 1932, 6: 315–353.
G. B. West and J. H. Brown, The origin of allometric scaling laws in biology from genomes to ecosystems: Towards a quantitative unifying theory of biological structure and organization, Journal of Experimental Biology, 2005, 208(9): 1575–1592.
J. H. Brown, G. B. West, and B. J. Enquist, Scaling in biology: Patterns and processes, causes, and consequences, in Scaling in Biology (ed. by J. H. Bown and G. B. West), Oxford University Press, New York, 2000, 1–24.
J. H. Brown and G. B. West, Scaling in Biology, Oxford University Press, New York, 2000.
P. S. Dodds, D. H. Rothman, and J. S. Weitz, Re-examination of the “3/4-law” of metabolism, Journal of Theoretical Biology, 2001, 209: 9–27.
C. R. White and R. S. Seymour, Mammalian basal metabolic rate is proportional to body mass2/3, in Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(7): 4046–4049.
S. L. Linstedt and W. A. Calder, Body size, physiological time, and longevity of homeothermic animals, the Quarterly Review of Biology, 1981, 56: 1–16.
J. F. Gillooly, E. L. Charnov, G. B. West, V. M. Savage, and J. H. Brown, Effects of size and temperature on developmental time, Nature, 2002, 417: 70–73.
E. L. Charnov, Evolution of mammal life histories, Evolutionary Ecology Research, 2001, 3: 521–535.
K. S. Nielson, Scaling: Why is Animal Size So Important?, Cambridge University Press, Cambridge, 1984.
B. J. Enquist, G. B. West, and J. H. Brown, Quarter-power allometric scaling in vascular plants: Functional basis and ecological consequences, in Scaling in Biology, Oxford University Press, New York, 2000, 167–198.
W. Jetz, C. Carbone, J. Fulford, and J. H. Brown, The scaling of animal space use, Science, 2004, 306: 266–268.
J. Damuth, Population density and body size in mammals, Nature, 1981, 290: 699–700.
S. Nee, A. F. Read, and P. H. Harvey, The relationship between abundance and body size in british birds, Nature, 1991, 351: 312–313.
A. P. Allen, J. H. Brown, and J. F. Gillooly, Global biodiversity, biochemical kinetics, and the energetic-equivalence rule, Science, 2002, 297: 1545–1548.
B. J. Enquist, J. H. Brown, and G. B. West, Allometric scaling of plant energetics and population density, Nature, 1998, 395: 163–165.
M. Rubner, Ueber den einfluss der körpergrösse auf stoff-und kraftwechsel, Zeitschrift fur Biologie, 1883, 19: 535–562.
G. B. West, J. H. Brown, and B. J. Enquist, The fourth dimension of life: Fractal geometry and allometric scaling of organisms, Science, 1999, 284: 1677–1679.
J. R. Banavar, J. Damuth, A. Maritan, and A. Rinaldo, Supply-demand balance and metabolic scaling, in Proceedings of the National Academy of Sciences of the United States of America, 2002, 99(16): 10506–10509.
P. S. Agutter and D. N. Wheatley, Metabolic scaling: Consensus or controversy? Theoretical Biology and Medical Modelling, 2004, 1(13): 1–13.
A. Bejan, Shape and Structure, from Engineering to Nature, Cambridge University Press, Cambridge, 2001.
A. M. Makarieva and V. G. Gorshkov, Distributive network model of banavar, damuth, maritan and rinaldo (2002): Critique and perspective, Journal of Theoretical Biology, 2006, 239(3): 394–397.
A. M. M., V. G. Gorshkov, and B. L. Li, Revising the distributive networks models of west,brown and enquist (1997) and banavar, maritan and rinaldo (1999): Metabolic inequity of living tissues provides clues for the observed allometric scaling rules, Journal of Theoretical Biology, 2005, 237: 291–301.
J. H. Brown and J. F. Gillooly, Ecological food webs: High-quality data facilitate theoretical unification, in Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(4): 1467–1468.
J. E. Cohen, T. Jonsson, and S. R. Carpenter, Ecological community description using the food web, species abundance, and body size, in Proceedings of the National Academy of Sciences of the United States of America, 2003, 100(4): 1781–1786.
J. E. Cohen, F. Briand, and C. M. Newman, Community Food Webs: Data and Theory (biomathematics vol. 20), Springer-Verlag, Berlin, 1990.
R. J. Williams and N. D. Martinez, Simple rules yield complex foodwebs, Nature, 2000, 404: 180–183.
M. F. Cattin, L. F. Bersier, C. B. Richter, R. Baltensperger, and J. P. Gabriel, Phylogenetic constraints and adaptation explain food-web structure, Nature, 2004, 427: 835–839.
M. C. Emmerson and D. Raffaelli, Predator-prey body size, interaction strength and the stability of a real food web, Journal of Animal Ecology, 2004, 73: 399–409.
S. Jennings and S. Mackinson, Abundance–body mass relationships in size-structured food webs, Ecology Letters, 2003, 6: 971–974.
N. Loeuille and M. Loreau, Evolution of body size in food webs: Does the energetic equivalence rule hold? Ecology Letters, 2006, 9: 171–178.
D. Garlaschelli, G. Caldarelli, and L. Pietronero, Universal scaling relations in food webs, Nature, 2003, 423: 165–168.
S. Allesina and A. Bodini, Food web networks: Scaling relation revisited, Ecological Complexity, 2005, 2: 323–338.
F. J. Frank and D. J. Murrell, A simple explanation for universal scaling relations in food webs, Ecology, 2005, 86(12): 3258–3263.
J. F. Gillooly, A. P. Allen, and J. H. Brown, Food-web structure and dynamics: Reconciling alternative ecological currencies, in Ecological Networks: Linking Structure to Dynamics in Food Webs, Oxford University Press, 2005.
A. J. Lotka, Elements of physical biology, the American Mathematical Monthly, 1926, 33(8): 426–428.
G. Caldarelli, P. G. Higgs, and A. J. McKane, Modelling coevolution in multispecies communities, Journal of Theoretical Biology, 1998, 193: 345–358.
M. Bussenschutt and C. P. Wostl, A discrete, allometric approach to the modeling of ecosystem dynamics, Ecological Modelling, 2000, 126: 33–48.
A. J. McKane, Evolving complex food webs, the European Physical Journal B, 2004, 38: 287–295.
B. Drossel, P. G. Higgs, and A. J. McKane, The influence of predator-prey population dynamics on the long-term evolution of food web structure, Journal of Theoretical Biology, 2001, 208: 91–107.
C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada, 1965, 45: 3–60.
D. L. DeAngelis, Dynamics of Nutrient Cycling and Food Webs, Springer, Berlin, 1991.
L. R. Ginzburg and H. R. Akcakaya, Consequences of ratio-dependent predation for steady-state properties of ecosystems, Ecology, 1992, 73: 1536–1543.
J. Zhang, Energy flows and maximum power on an evolutionary ecological network model, in Advances in Artificial Life: 9th European Conference, ECAL 2007, Springer, 2007, 113–122.
S. Jain and S. Krishna, Large extinctions in an evolutionary model: The role of innovation and keystone species, PNAS, 2002, 99: 2055–2060.
A. J. McKane and B. Drossel, Models of food web evolution, in Ecological Networks: Linking Structure to Dynamics in Food Webs, Oxford University Press, New York, 2005.
M. Doebeli and U. Dieckmann, Evolutionary branching and sympatric speciation caused by different types of ecological interactions, the American Naturalist, 2000, 156: 77–101.
U. Dieckmann and M. Doebeli, On the origin of species by sympatric speciation, Nature, 1999, 400(22): 354–357.
C. I. Hiroshi and T. Ikegami, Food-web formation with recursive evolutionary branching, Journal of Theoretical Biology, 2006, 238: 1–10.
H. T. Odum and R. C. Pinkerton, Time’s speed regulator: The optimum efficiency for maximum power output in physical and biological systems, American Scientist, 1955, 43: 331–343.
J. D. Farmer, S. A. Kauffman, and N. H. Packard, Autocatalytic replication of polymers, Physica D, 1986, 22: 50–67.
R. J. Bagley, D. J. Farmer, and W. Fontana, Evolution of a metabolism, in Artificial Life II (ed. by C. G. Angton, C. Taylor, J. D. Farmer, and Rasmussen), Addison-Wesley, Los-Alamos, 1991.
S. Jain and S. Krishna, A model for the emergence of cooperation, interdependence, and structure in evolving networks, PNAS, 2001, 98: 543–547.
A. J. Lotka, Contribution to the energetics of evolution, in Proceedings of the National Academy of Sciences of the United States of America, 1922, 8(6): 147–151.
A. S. Charles, Maximum Power: The Ideas and Applications of H. T. Odum, CO: University Press of Colorado, Niwot, 1995.
E. H. Decker, S. Elliott, F. A. Smith, D. R. Blake, and F. S. Rowland, Energy and material flow through the urban ecosystem, Annual Review of Energy and the Environment, 2000, 25: 685–740.
T. E. Graedel and B. R. Allenby, Industrial Ecology, Prentice Hall, Upper Saddle River, 2002.
R. U. Ayers and A. V. Kneese, Production, consumption, and externalities, the American Economic Review, 1969, 59(3): 282–297.
P. H. Brunner and H. Rechberger, Practical Handbook of Material Flow Analysis, CRC, 2003.
R. Axtell, Zipf distribution of U.S. firm sizes, Science, 2001, 293: 1818–1820.
T. S. Ray, An approach to the synthesis of life, in Artificial Life II: Proceedings of an Interdisciplinary Workshop on the Synthesis and Simulation of Living Systems (Santa Fe Institute Studies in the Sciences of Complexity, Vol. 10) (ed. by C. G. Langton et al.), Addison-Wesley, 1992, 371–408.
B. A. Huberman and T. Hogg, The emergence of computational ecologies, in 1992 Lectures in Complex Systems, Addison-Wesley, 1993, 185–205.
C. Ofria and C. O. Wilke, Avida: A software platform for research in computational evolutionary biology, Artificial Life, 2004, 10: 191–229.
G. Nicolis and I. Prigogine, Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order Through Fluctuations, John Wiley Sons, San Francisco, 1977.
P. Bak, How Nature Works: The Science of Self-Organized Criticality, Springer, New York, 1999.
L. M. Martyusheva and V. D. Seleznevb, Maximum entropy production principle in physics, chemistry and biology, Physics Reports, 2006, 426: 1–45.
R. Dewar, Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states, Journal of Physics A: Mathematical and General, 2003, 36: 631–641.
R. C. Dewar, Maximum entropy production and the fluctuation theorem, Journal of Physics A: Mathematical and General, 2005, 38: L371–L381.
L. H. Chai, A theoretical analysis of bubble interaction in boiling systems, International Journal of Thermal Sciences, 2004, 43: 1067–1073.
J. Whitfield, Survival of the Likeliest, PLoS Biology, 2007, 5: e142.
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This research is supported by Guozhi Xu Post Doctoral Research Foundation and the National Natural Science Foundation of China under Grant No. 60574068.
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Zhang, J. Energy flows in complex ecological systems: a review. J Syst Sci Complex 22, 345–359 (2009). https://doi.org/10.1007/s11424-009-9169-3
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DOI: https://doi.org/10.1007/s11424-009-9169-3