FISHERY BULLETIN: VOL. 70, NO. 4 



and is equivalent to a specific growth rate of 

 about 1.1 doubling-s/day. Such a value would 

 be appropriate for temperate waters, but prob- 

 ably not for polar or eutrophic tropical waters. 

 But to make Pmax a function of temperature 

 would probably add unnecessary complexity for 

 modeling purposes, although it would add real- 

 ism. However, the use of constant values makes 

 the model restrictive geographically (see, for 

 example. Parsons and Anderson's, 1970, use of 

 the model of Steele and Menzel, 1962, for the 

 subarctic North Pacific). 



A plant physiologist would perhaps prefer to 

 approach modeling phytoplankton growth in the 

 sea in as physiologically realistic way as possible 

 and to let the computer handle the complexity. 

 But it is questionable how realistically this can 

 now be accomplished or what insight would 

 thereby result. 



Equation (1) of this paper can be considered 

 a model of sorts and its apparent universality is 

 appealing. Comparing its predictions as to 

 growth rate and assimilation number with data 

 from natural phytoplankton shows, moreover, 

 the magnitude of diflference between potential 

 plant growth and reality, as it is now best esti- 

 mated. The gulf between real and maximum ex- 

 pected values shows how significant are the other 

 environmental factors which affect phytoplank- 

 ton: radiant energy, nutrient concentrations, 

 grazing, and mixing processes. All of these 

 parameters have been successfully treated in 

 models since the 1940's (see Patten's summary 

 review, 1968 ; Parsons, Giovando, and LeBras- 

 seur, 1966; Dugdale and Goering, 1967). 



A physiologically realistic model might begin 

 with a relation between temperature and max- 

 imum expected growth rate, as in Eppley and 

 Sloan (1966). In that paper the variations in 

 growth rate among species were rationalized by 

 including the chlorophyll concentration per unit 

 cell volume (a parameter not readily measur- 

 able in assemblages of mixed species, but sus- 

 ceptible to averaging) . This parameter seemed 

 also to compensate for the sun-shade alterations 

 of phytoplankton photosynthesis when used to 

 calculate radiant energy absorbed by a cell's pig- 

 ments. However, the problem of daylength 

 could not be adequately handled for species 



which grow faster with a few hours darkness 

 each day than in continuous light. 



None of the models proposed for primary 

 productivity simulation has attempted to treat 

 diel periodicity in the metabolic processes of 

 phytoplankton. Nor is the alteration of chem- 

 ical composition attendant to growth with lim- 

 iting concentrations of nutrients or to variations 

 with irradiance or temperature treated. 



One suspects that the simple models now 

 available can be satisfactory for describing the 

 major features of regional phytoplankton pro- 

 duction. Realistic physiological models will 

 probably remain in the "special purpose" cate- 

 gory for the insight of those familiar enough 

 with the subject to use them as guide to their 

 own research. Nevertheless, it is admitted, giv- 

 en the current popularity of modeling, that 

 neither the reader nor the author may be able 

 to resist for long the temptation to combine 

 Equation (1) with a realistic function for nu- 

 trient assimilation rate vs. ambient concentra- 

 tion, a function for the dependence of ix and 

 assimilation number upon light, and a suitable 

 function for describing eflTects of mixing, in line 

 with critical depth theory, and to try it with 

 his favorite set of oceanic data. 



ACKNOWLEDGMENTS 



I am grateful to Mrs. Elizabeth Stewart for 

 computer calculations and graphs, to Mrs. Vir- 

 ginia Moore for drawing the inked figures, and 

 to Ms. Janice Walker for typing the manuscript. 

 I thank my colleagues Dr. 0. Holm-Hansen, 

 David Checkley, and Dr. James T. McCarthy for 

 use of unpublished data, and E. H. Renger and 

 Mrs. Gail Hirota for expert analytical services. 

 This study was supported by the U.S. Atomic 

 Energy Commission Contract No. AT (11-1) 

 GEN 10, P.A. 20. 



LITERATURE CITED 



Antia, N. J., C. D. McAllister, T. R. Parsons, 

 K. Stephens, and J. D. H. Strickland. 



1963. Further measurements of primary produc- 

 tion using a large-volume plastic sphere. Limnol. 

 Oceanogr. 8:166-183. 



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