Allometric scaling of maximal photosynthetic growth rate to surface/volume ratio

Values for maximum growth rates (p,,,,,) (d-l) at 15”-20°C and surface area/volume ratios (SA/V) (m* m-‘) for aquatic angiosperms (n = 14), macroalgae (n = 34), and microalgae (n = 44) were derived from our own experimental work and from the literature. A significant linear relationship (R* = 0.86) was found between log CL max and log SA/V with the slope 0.66 (95% C.I.: 0.61-0.72) and the intercept -3.80[95% C.I.: (-3.59X-4.00)].Onegeneralallometricexpression can therefore describe the scaling of maximal growth rate as a function of organism size over a 1,700-fold range of SA/V ratios spanning small unicellular algae as well as multicellular aquatic angiosperms. The size dependence of maximal growth rate for aquatic photosynthetic organisms is close to that expected from the well-known “3/4 law,” governing the size dependence of metabolic rates in animals. The general relationship that exists between organism size and metabolic rates is described by the allometric equation: rate = a(body size)b (Hemmingsen 1950; Zeuthen 1953; von Bertalan@ 1957). For sizespecific metabolic rates the equation takes the form: rate/body size = a(body size)‘when c = b 1. For unicells and animals, the value of b is well established to be about Acknowledgments We thank T. Fenchel, G. Ring, J. Sorensen, and three anonymous reviewers for comments on the manuscript. S.L.N. was supported by a grant from the Danish Research Academy. 0.75 and thus c takes the value of about -0.25. This metabolic relationship seems to hold for terrestrial higher plants as well (Hemmingsen 1950; Prothero 1979). Likewise, the maximal growth rate scales with size of animals and unicells with a c value of about -0.25 (Fenchel 1974; reviewed by Peters 1983). In contrast, Banse (1982) found only a weak size dependence of growth in diatoms and dinoflagellates and so questioned the applicability of the above socalled 3/4 law of allometry for planktonic algae. The possibility that allometric relationships describe rates for a wide range of metabolic processes and over a wide range of organism sizes and types has important ecological implications. Knowledge of the relationship between organism size and such important characteristics as respiration and maximal growth rate will make it possible to predict the potential productivity of individual plant populations and the energy budget of an ecosystem under optimal conditions if the present size spectrum of organisms is known. Comparison with observed values will indicate to what extent the system is limited by environmental factors, and what would be the possible effect of, for example, nutrient enrichment. Quantitative description of the size dependence of aquatic plant growth will also help in