Article Title: Trophic models and short-term simulations for the coral reefs of Cayos Cochinos and Media
Luna (Honduras): a comparative network analysis, ecosystem development, resilience and fishery
Journal name: Hydrobiologia
Author names: Ignacio Cáceres, Marco Ortiz, Amílcar L. Cupul-Magaña, Fabián A. Rodríguez-Zaragoza*
*Corresponding author: e-mail address: rzf39259@cucba.udg.mx (F.A. Rodríguez-Zaragoza). Laboratorio de
Ecosistemas Marinos y Acuicultura (LEMA), Departamento de Ecología, CUCBA, Universidad de
Guadalajara, Carretera Guadalajara-Nogales, Km. 15.5 Las Agujas de Nextipac, Zapopan 45110, Jalisco,
Mexico. e-mail address: rzf39259@cucba.udg.mx.
Appendix B
Ecopath and Ecosim theoretical frameworks
The energy mass balance of a species or functional group within a network is represented by the following
equation:
𝑃
𝑄
𝐵 𝑖
𝐵 𝑗
𝐵𝑖 ( ) 𝐸𝐸𝑖 − ∑𝑛𝑗=1 𝐵𝑗 ( ) 𝐷𝐶𝑗𝑖 − 𝑌𝑖 − 𝐵𝐴𝑖 − 𝐸𝑖 = 0
(1)
where Bi and Bj are the biomass of prey i and predator j; P/Bi is the productivity of prey i, which is equivalent
to total mortality (Allen, 1971); EEi is the ecotrophic efficiency or the fraction of the total production of a
group or species used in the system; Yi is the fishing production per unit of area and time; Q/Bi is the food
consumption per biomass unit j; DCji is the fraction of prey i in the average diet of predator j; BAi is the
biomass accumulation rate for i; and Ei is the net migration of i. The energy balance of each component of the
model is given by the equation (Christensen et al. 2004):
𝑄 = 𝑃 + 𝑅 + 𝑈𝐴𝐹
(2)
where Q is consumption, P is production, R is respiration, and UAF is unassimilated food for each group or
species of the system. When adding the accumulated biomass BAi and the migration factor Ei in the equation
(1), the focus of Ecopath is based more on energetic continuity than a stable state condition. This situation
allows changes in the network compartments when the mathematical expression is expressed in a dynamic
form.
Ecosim define the consumption (Qij) by next equation equation:
𝑄𝑖𝑗 =
𝑎𝑖𝑗 𝑣𝑖𝑗 𝐵𝑖 𝐵𝑗
2𝑣𝑖𝑗+𝑎𝑖𝑗 𝐵𝑗
(3)
1
where aij represents the instantaneous mortality rate on prey i caused by a single unit of predator j biomass.
Likewise, aij can be understood as the rate of effective search by predator j for prey i. Each aij is estimated
directly from the corresponding Ecopath models by aij = Qi/(BiBj) , where Qi is the total consumption of i. The
vij parameter represent the transference rate between compartment i and j, determining if the flow control
mechanism is bottom-up (v = 1.0), top-down (v = 6.0) o mixed (v = 2.0).
References
Allen, K.R., 1971. Relation between production and biomass. Journal of the Fisheries Research Board of
Canada 28: 1573–1581.
Christensen, V., C. Walters & D. Pauly, 2004. Ecopath with Ecosim: a User’s Guide. Fisheries Centre
Research Reports, vol. 12. University of British Columbia, Vancouver (available online at
http://www.Ecopath.org and http://www.fisheries.ubc.ca).
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