Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 1 : The model /Maury, Olivier /Faugeras, Blaise /Shin, Yunne-Jai Poggiale, J. C. /Ben Ari, Tamara /Marsac, Francis size spectrum mathematical model predation Bioenergetics dynamic energy budget DEB theory energy flow This paper presents an original size-structured mathematical model of the energy flow through marine ecosystems, based on established ecological and physiological processes and mass conservation principles. The model is based on a nonlocal partial differential equation which represents the transfer of energy in both time and body weight (size) in marine ecosystems. The processes taken into account include size-based opportunistic trophic interactions, competition for food, allocation of energy between growth and reproduction, somatic and maturity maintenance, predatory and starvation mortality. All the physiological rates are temperature-dependent. The physiological bases of the model are derived from the dynamic energy budget theory. The model outputs the dynamic size-spectrum of marine ecosystems in term of energy content per weight class as well as many other size-dependent diagnostic variables such as growth rate, egg production or predation mortality. In stable environmental conditions and using a reference set of parameters derived from empirical studies, the model converges toward a stationary linear log-log size-spectrum with a slope equal to -1.06, which is consistent with the values reported in empirical studies. In some cases, the distribution of the largest sizes departs from the stationary linear solution and is slightly curved downward. A sensitivity analysis to the parameters is conducted systematically. It shows that the stationary size-spectrum is not very sensitive to the parameters of the model. Numerical simulations of the effects of temperature and primary production variability on marine ecosystems size-spectra are provided in a companion paper [Maury, O., Shin, Y.J., Faugeras, B., Ben Ari, T., Marsac, F., 2007. Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 2: simulations. Progress in Oceanography, doi:10.1016/j.pocean.2007.05.001]. 2007 text https://www.documentation.ird.fr/hor/fdi:010040825 fdi:010040825 Maury Olivier, Faugeras Blaise, Shin Yunne-Jai, Poggiale J. C., Ben Ari Tamara, Marsac Francis. Modeling environmental effects on the size-structured energy flow through marine ecosystems. Part 1 : The model. 2007, 74 (4), 479-499 EN