tians or whether adult H. zapus range further north. 

 Acknowledgments 



We thank Jean R. Dunn and Arthur W. Kendall, 

 Jr. (Northwest and Alaska Fisheries Center) for 

 helpful discussions and review of the manuscript. 

 Alex E. Peden (British Columbia Provincial 

 Museum) kindly assisted in the identification of 

 Hemilepidotus zaipus postflexion larvae. 



Literature Cited 



DiNGERKUS, G., AND L. D. UHLER. 



1977. Enzyme clearing of alcian blue stained whole small 

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GORBUNOVA, N. N. 



1964. Razmnozhenie i razvitie polucheshuinykh bychkov 

 (Cottidae, Pisces) (Breeding and development of hemilepido- 

 tine sculpins (Cottidae, Pisces)). [In. Russ.) Tr. Inst. 

 OkeanoL, Akad. Nauk SSSR 73:235-251. (Transl. by Isr. 

 Program Sci. Transl., 1966; in T. S. Rass (editor), Fishes of 

 the Pacific and Indian Oceans, biology and distribution, p. 

 249-266; available U.S. Dep. Commer., Natl. Tech. Inf. Serv., 

 Springfield, Va., as TT 65-50120.) 

 Hattori, S. 



1964. Studies on fish larvae in the Kuroshio and adjacent 

 waters. [In Jpn., Engl, synop.) Bull. Tokai Reg. Fish. Res. 

 Lab. 40, 158 p. 

 Kendall, A. W., Jr., and B. Vinter. 



1984. Development of hexagrammids (Pisces: Scorpaeni- 

 formes) in the Northeastern Pacific Ocean. U.S. Dep. 

 Commer., NOAA Tech. Rep. NMFS 2, 44 p. 

 Matarese, a. C, S. L. Richardson, and J. R. Dunn. 



1981. Larval development of the Pacific tomcod, Microgadus 

 proximus, in the Northeast Pacific Ocean with comparative 

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 and Pacific cod, Gadus macrocepkalus (Gadidae). Fish. Bull. , 

 U.S. 78:923-940. 

 Peden, A. E. 



1978. A systematic revision of the hemilepidotine fishes 

 (Cottidae). Syesis 11:11-49. 



Richardson, S. L., and W. A. Laroche. 



1979. Development and occurrence of larvae and juveniles of 

 the rockfishes Sehastes crameri, Sebastes pinniger, and 

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Richardson, S. L., and B. B. Washington. 



1980. Guide to identification of some sculpin (Cottidae) larvae 

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Ann C. Matarese 

 Beverly M. Vinter 



NOAA, Natwnal Marine Fisheries Service 

 Northwest and A laska Fisheries Center 

 2725 Montlake BouLeniard East 

 Seattle, WA 98112-2097 



AN APPROACH TO ESTIMATING 

 AN ECOSYSTEM BOX MODEL 



Recent trends in ecosystem modeling have produced 

 complex simulation models which are very data in- 

 tensive (Andersen and Ursin 1977; Laevastu and 

 Larkins 1981). However, in many situations the con- 

 struction of a biomass budget for a box model of an 

 ecosystem is relatively simple and can provide impor- 

 tant information about the ecosystem standing stock 

 and energy flow (Walsh 1981; Pauly 1982; Polovina 

 1984). 



The ECOPATH model is an analytical procedure 

 to estimate a biomass budget for a box model of an 

 ecosystem given inputs which specify the com- 

 ponents of the ecosystem, together with their mor- 

 tality, diet, and energetics value. A computer pro- 

 gram for ECOPATH has been written in BASIC-80, 

 version 5.21, by Microsofti (CP/M version). A listing 

 of the ECOPATH computer program and a user's 

 manual are available from the author. 



The ECOPATH model produces estimates of mean 

 annual biomass, annual biomass production, and an- 

 nual biomass consumption for each of the user 

 specified species-groups. The species-groups repre- 

 sent aggregations of species with similar diet and life 

 history characteristics and which have a common 

 physical habitat. The ECOPATH model is not a 

 simulation model with a time component as are some 

 more complex ecosystem models. It estimates a 

 biomass budget for the marine ecosystem in a static 

 situation under the assumption that the ecosystem is 

 at equilibrium conditions. 



Equilibrium conditions are defined to exist when 

 the mean annual biomass for each species-group does 

 not change from year to year. This condition results 

 in a system of biomass budget equations which, for 

 species-group i, can be expressed as 



Production of biomass for species i - all 

 predation on species i - nonpredatory 

 biomass mortality for species i - fishery catch 

 for species i = for all i. (1) 



The ECOPATH model expresses each term in the 

 budget equation as a linear function of the unknown 

 mean annual biomasses {B,'s) so the resulting 

 biomass budget equations become a system of simul- 

 taneous equations linear in the B-s. The mean annual 

 biomass estimates are obtained by solving the 

 system of simultaneous linear equations. 



'Reference to trade names does not imply endorsement by the Na- 

 tional Marine Fisheries Service, NOAA. 



FISHERY BULLETIN: VOL. 83, NO. 3, 1985. 



457 



