Metabolic level and size scaling of rates of respiration and growth in unicellular organisms

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1 Functional Ecology 2009, 23, doi: /j x Metabolic level and size scaling of rates of respiration and growth in unicellular organisms Douglas S. Glazier* Department of Biology, Juniata College, Huntingdon, Pennsylvania 16652, USA Summary 1. Metabolic rate is conventionally assumed to scale with body mass to the 3 4-power, independently of the metabolic level of the organisms being considered. However, recent analyses in a variety of animals and plants indicate that the power (log log slope) of this relationship varies significantly with metabolic level, ranging from c.2 3to1. 2. Here I show that the scaling slopes of rates of respiration and growth are related to the metabolic level of a variety of unicellular organisms, as similarly occurs for respiration rates in multicellular organisms. 3. The recently proposed metabolic-level boundaries hypothesis provides insight into these effects of metabolic level. As predicted, the scaling slopes for resting (endogenous) respiration rate in prokaryotes, algae and protozoans are negatively related to metabolic level; and in protozoans, the scaling slope increases with starvation. Also as predicted, the scaling slopes of growth rate in algae and protozoans are negatively related to growth level. Unexpectedly, opposite effects of starvation on the metabolic scaling slopes of unicellular prokaryotes (compared to that of eukaryotes) may be a spurious result of respiration measurements that did not adequately consider the effects of rapid cell multiplication in prokaryotes with extremely short generation times. 4. Analyses of both unicellular and multicellular organisms show that there is no universal metabolic scaling relationship, and that variation in metabolic scaling relationships is systematically and possibly universally related to metabolic level. Key-words: allometric scaling, cell size, growth rate, metabolic rate, unicells Introduction The rates (R) of many biological processes scale with body mass (M) according to the power function R = am b, where a is a normalization constant (antilog of the intercept in a log log plot) and b is the scaling exponent (slope in a log log plot). This power function has been most commonly used to represent the scaling of metabolic rate with body mass, for which it has been conventionally assumed that the scaling slope is 3 4, the so-called 3 4-power law (Kleiber 1961; Peters 1983; Calder 1984; Schmidt-Nielsen 1984; Savage et al. 2004). Furthermore, in a classic, frequently reproduced graph, Hemmingsen (1960) showed that the scaling slope is c. 3 4 in unicellular organisms and in ectothermic and endothermic animals, despite the fact that these groups of organisms have very different metabolic levels (endotherms are about 29 times higher than ectotherms, which are about eight times higher than unicells). Similar relationships have been *Correspondence author. glazier@juniata.edu reported for metabolic rate by Robinson et al. (1983) and Gillooly et al. (2001), and for the intrinsic rate of increase by Fenchel (1974), whereas Phillipson (1981) showed that the metabolic scaling slope varies significantly among unicells [b =0Æ66±0Æ092 (95% confidence limits); N = 21], ectotherms (b = 0Æ88 ± 0Æ00002; N = 470) and endotherms (b = 0Æ69 ± 0Æ0017; N = 71). However, the analysis of Phillipson (1981) has been largely ignored, whereas the analysis of Hemmingsen (1960) has been virtually canonized. As a result, metabolic level has usually been considered to be irrelevant to the scaling slope of metabolic rate, if it is considered at all, especially by proponents of the universality of 3 4-power scaling (Gillooly et al. 2001; Brown et al. 2004). Indeed, Brown et al. (2004) claim that the scaling slope for temperature-adjusted metabolic rate is c. 3 4 in all taxonomic groups of organisms including unicells, plants and animals with metabolic levels exhibiting a 20-fold variation. However, recent analyses have undermined the classic conclusions of Hemmingsen (1960), and have shown strong relationships between the scaling slope and metabolic level. Ó 2009 The Author. Journal compilation Ó 2009 British Ecological Society

2 964 D. S. Glazier The statistics and data selection of Hemmingsen (1960) have been criticized by Prothero (1986), Dodds, Rothman & Weitz (2001), Fenchel (2005) and Makarieva et al. (2005). The scaling analyses of unicellular organisms by both Hemmingsen (1960) and Phillipson (1981) were based on heterogeneous samples of species in undefined metabolic states, including both prokaryotes and eukaryotes, which are very different metabolically. The taxa included in a metabolic scaling analysis significantly affect the scaling slope (Glazier 2005). For example, if bacteria, flagellates and animal zygotes are omitted from the unicellular analysis of Prothero (1986), the slope becomes 0Æ608 ± 0Æ051, which is significantly less than 0Æ75. Dodds et al. (2001) also show that the scaling slopes of birds and mammals are indistinguishable from 2 3, and significantly less than 3 4, a pattern confirmed by numerous other recent analyses (e.g. White & Seymour 2003; McKechnie & Wolf 2004; White et al. 2006; Glazier 2008), including a reanalysis of the data of Gillooly et al. (2001) by Downs et al. (2008). Furthermore, Glazier (2005, 2008, 2009a,c) has shown that much of the variation in the metabolic scaling slopes of various animals and plants can be related to their different metabolic levels. For example, plants, resting turtles, diapausing insects, torpid birds and hibernating mammals that have relatively low metabolic levels all have scaling slopes near 1, whereas resting, non-torpid birds, mammals and winged insects that have relatively high metabolic levels all have scaling slopes near 2 3 (Glazier 2008, 2009a). In addition, in many kinds of animals, high metabolic levels caused by strenuous activity are associated with scaling exponents significantly greater than 3 4 and that approach 1 (Darveau et al. 2002; Weibel et al. 2004; Glazier 2005, 2008, 2009a, 2009b; Niven & Scharlemann 2005). The aim of this study was to explore whether the scaling slopes of rates of respiration and growth in various taxonomic groups of unicellular organisms are also related to metabolic level, as seen for respiration rate in multicellular organisms. If so, this would not only be further evidence against the 3 4-power law, but also demonstrate that metabolic scaling relationships depend critically and perhaps universally on the overall metabolic level of the organisms under consideration. Materials and methods Interspecific scaling of rates of respiration and growth (cell proliferation) with cell volume (lm 3 ) under well-defined physiological conditions were obtained or calculated from data given in the literature, as follows: respiration rates of prokaryotes growing with exogenous substrates and not growing (resting) without exogenous substrates, all adjusted to (Makarieva et al. 2005), respiration rates of algae in the dark at (Tang & Peters 1995), respiration rates of protozoans growing with food and not growing (resting) without food, all adjusted to (Fenchel & Finlay 1983), maximal growth rates of algae under light saturation at 10 C(Sommer 1989)and (Tang 1995), and maximal growth rates of ciliated protozoans at (Taylor & Shuter 1981). These data sets were selected because of their relatively large sample sizes (N 15 species) and broad cell-size ranges (greater than 3 orders of magnitude). Additional experimental data were analysed to examine the effect of light levels on the scaling of growth rate in five species of diatoms and five species of dinoflagellates (Chan 1978). The dark respiration rates of the algae were assumed to represent mostly maintenance metabolism because they were not significantly correlated with previous light history (Tang & Peters 1995), which is expected to influence growth respiration during the dark (e.g. Falkowski et al. 1985; Geider & Osborne 1989). However, growth metabolism and nitrogen assimilation may contribute significantly to dark respiration rates in some species of algae (e.g. Raven 1976; Clark et al. 2002; Needoba & Harrison 2004). In spite of this, the conclusions of this paper are not altered by comparing algal respiratory metabolism in the dark with either state of metabolism observed in the prokaryotes and protozoans, i.e. growth metabolism fuelled by exogenous substrates vs. endogenous (resting) metabolism fuelled by endogenous substrates in the absence of exogenous substrates. In addition, I know of no evidence that variation in the contribution of growth metabolism to dark respiration among species of algae is systematically related to cell size, and thus has caused significant deviations in the metabolic scaling slope. Respiration (metabolic) rates were expressed as nl O 2 h )1, whereas growth rates were calculated as (ln N t ) ln N 0 )day )1, where N t and N 0 are cell densities at the end and beginning of a specific time interval respectively (Laybourn-Parry 1984). Scaling relationships were determined by least squares regression using log log values. Metabolic and growth levels were estimated as log a, a useful comparative index of the intensity of metabolism or growth at 1-lm 3 cell volume (see also Results). All error terms given for scaling slopes are 95% confidence limits. Significant differences between scaling slopes were tested by determining whether their 95% confidence limits overlapped or by using a t-test (following Zar 1984). Results The interspecific scaling slopes of respiration rate of the five groups of unicells analysed here vary between c.2 3 and over 1, and three of the slopes are significantly different from 3 4 (Fig. 1). Overall, the scaling slope of respiration rate decreases with increasing metabolic level, except for that of growing prokaryotes given exogenous substrates (Fig. 1b). This negative trend is apparent for endogenous respiration rates (in the absence of exogenous substrates), such that low-energy prokaryotes show nearly isometric metabolic scaling with a slope (b =1Æ103 ± 0Æ232; N = 47) not significantly different from 1, whereas higher-energy protists exhibit negatively allometric metabolic scaling with slopes (algae: b = 0Æ880 ± 0Æ063; N =178;protozoans:b =0Æ816 ± 0Æ091; N = 27) significantly lower than 1. In addition, the scaling slope is significantly lower for fed protozoans respiring at relatively high metabolic levels (b = 0Æ681 ± 0Æ085; N = 47), than for fasted protozoans respiring at lower metabolic levels (t = 6Æ59, P < 0Æ001). A significant nutrition-dependent difference in metabolic scaling is also seen when the protozoan data set is restricted to respiration rates that were estimated under fed vs. fasted conditions in a pair-wise fashion in the same species and studies (t =8Æ37, P <0Æ001; fed: b =0Æ563 ± 0Æ138; N = 14; fasted: b =0Æ824 ± 0Æ118; N = 14; data from Fenchel & Finlay 1983). However, this

3 Metabolic scaling in unicells 965 (a) metabolic rate (nl O 2 cell 1 h 1 ) (b) Metabolic scaling slope (b) b = 2/3 b = cell volume (µm 3 ) b = 2/3 b = Metabolic level (log 10 a, nl O 2 h 1 at 1 µm 3 cell volume) Fig. 1. Interspecific scaling of respiration rate at inrelationto cell volume in various groups of unicellular organisms in different physiological states (based on data from Fenchel & Finlay 1983; Tang & Peters 1995; Makarieva et al. 2005). Dotted lines represent scaling in proportion to cell-surface area (b =2 3) and cell volume (b =1). (a) The symbols at the ends of each least squares regression line denote the minimum and maximum cell volumes for each sample (h prokaryotes with and without exogenous substrates: top and bottom dashed lines respectively; s algae without light; d protozoans with and without food: top and bottom solid lines respectively). Scatter plots of the data points for each regression analysis are given in the source references. (b) Metabolic scaling slopes (b ± 95% confidence limits) vs. metabolic level (log a) of the unicells considered above. effect of exogenous food is not seen in prokaryotes whose scaling slope is higher in the presence of exogenous substrates (b = 1Æ331 ± 0Æ191; N = 50) than without, though not significantly so (t =1Æ541, P >0Æ10). The scaling slope of growth rate is also negatively related to the intensity of growth in three groups of unicells (Fig. 2). Relatively slow-growing Antarctic algae, cultured at 0 C, exhibit a scaling slope of nearly 0 (b = )0Æ061 ± 0Æ045, N = 15), thus indicating a weak dependence of growth rate on cell size. However, relatively rapidly growing algae and ciliated protozoans, cultured at, show significantly more negative scaling slopes (b = )0Æ15 ± 0Æ038; N = 126; b = )0Æ247 ± 0Æ102; N = 35 respectively), thus indicating relatively strong effects of cell size on growth rate. The scaling slopes for the algae are also significantly different from )1 4, thus providing further evidence against the universality of the 3 4-power law. Experimental manipulations of algal growth rates reveal additional significant effects of growth level on the scaling of (a) growth rate (day 1 ) (b) Growth scaling slope (b) b = C 0 C b = cell volume (µm 3 ) b = Growth level (log 10 a, day 1 at 1 µm 3 cell volume) b = 1/3 Fig. 2. Interspecific scaling of growth rate in relation to cell volume in algae and ciliated protozoans at the indicated temperatures (data from Taylor & Shuter 1981; Sommer 1989; Tang 1995). (a) The symbols at the ends of each least squares regression line denote the minimum and maximum cell volumes for each sample (d ciliates; s algae). Dotted lines represent scaling that is independent of cell volume (b = 0) or related to cell-surface area (b = )1 3). Scatter plots of the data points for each regression analysis are given in the source references. (b) Growth scaling slopes (b ± 95% confidence limits) vs. growth level (log a) of the unicells considered above. Dotted lines represent the scaling slopes expected from the metabolic scaling of algae (b =0Æ88) and protozoans with food (b =0Æ681) shown in Fig. 1. growth rate with cell size. In both diatoms and dinoflagellates, increasing growth level (associated with increasing irradiance) results in decreasing scaling slopes (Fig. 3). Although the confidence limits of these scaling slopes are large and overlapping, presumably because of small sample sizes (N =5 species within each group) and relatively small cell-size ranges (<3 and <2 orders of magnitude in the diatoms and dinoflagellates respectively), the scaling slopes are highly significantly negatively correlated with growth level (log a) within each of these algal groups. Parenthetically, it should be emphasized that the relationships reported here between the scaling slope (b) and metabolic level (intercept, log a) cannot be explained as being merely the result of a statistical autocorrelation between these two parameters (see also Glazier 2005, 2008, 2009a). Closely proximate, crossing regression lines may show

4 966 D. S. Glazier Growth scaling slope (b) correlations between b and log a, purely for statistical reasons (cf. Peters 1983), but most of the regressions analysed here have distinctly different elevations and do not cross (see Figs 1 and 2). Therefore, relationships between b and metabolic level exist regardless of what common cell size is used to compare metabolic levels. Furthermore, the relationships observed here between b and metabolic level remain essentially the same, even if another estimate of metabolic level is used that shows no autocorrelation with b whatsoever (i.e. the mass-specific metabolic rate at the midpoint of each regression line). Discussion b = 1/3 b = Growth level (log 10 a, cell divisions day 1 at 1 mm 3 cell volume) Fig. 3. Interspecific scaling exponents (b ±95% confidence limits) for growth rate in relation to growth level (log a) of five species of diatoms (d) and five species of dinoflagellates (s) cultured at 21 C under six levels of irradiance (8, 16, 32, 80, 160 and 256 le m )2 s )1 ). These scaling parameters are based on least squares linear regressions of log 10 cell divisions day )1 vs. log 10 cell volume (lm 3 ) (data from Chan 1978). The solid and dashed curved lines are the polynomial regressions for b vs. log a in diatoms [b = )0Æ Æ498 (log a) ) 0Æ661 (log a) 2 ; r =0Æ985; P =0Æ005] and dinoflagellates [b = )0Æ Æ185 (log a) ) 0Æ263 (log a) 2 ; r = 0Æ992, P = 0Æ002] respectively. Dotted lines represent scaling that is independent of cell volume (b = 0) or related to cell-surface area (b = )1 3). This study provides further support for the deconstruction of the classic Hemmingsen (1960) pattern of universal 3 4-power scaling of metabolic rate in unicells and ectothermic and endothermic animals. Other studies have already shown that many ectothermic animals have scaling slopes significantly greater than 3 4 (Phillipson 1981; Glazier 2005, 2009a; White et al. 2006), whereas endothermic animals typically have scaling slopes significantly less than 3 4 (Phillipson 1981; Dodds et al. 2001; Glazier 2005, 2008, 2009a; White et al. 2006; Downs et al. 2007). As shown here and elsewhere, unicellular organisms often have metabolic scaling slopes significantly different from 3 4, as well (Fig. 1; Phillipson 1981; Prothero 1986; Tang & Peters 1995; Glazier 2005; Makarieva et al. 2005). Furthermore, as already shown for respiration rates in multicellular organisms (Glazier 2005, 2008, 2009a,c; Killen et al. 2008), much of the variation in the scaling slope for rates of respiration and growth in unicellular organisms is related to metabolic level (Fig. 1b), as predicted by the metaboliclevel boundaries (MLB) hypothesis (Glazier 2005, 2008, 2009a). According to the MLB hypothesis, when maintenance costs are high, the scaling of resting metabolic rates should be predominantly influenced by surface-dependent fluxes of nutrients, wastes and (or) and heat (scaling as M 2 3 ), whereas when maintenance costs are low and amply accommodated by surface-dependent processes, metabolic scaling should be predominantly a function of tissue (cell) demand, which is directly proportional to tissue (cell) mass or volume (scaling as M 1 ). Therefore, the scaling slope for resting metabolic rate should be a negative function of metabolic level. The MLB hypothesis should apply to the scaling of metabolic and growth rates observed in this study, as long as cell surface area scales to the 2 3-power of cell volume and cell volume scales proportionately to cell mass. Deviations from scaling relationships expected by the MLB hypothesis may occur if cell shape changes with cell size, or if cells contain vacuolar spaces that scale allometrically with cell volume (as may occur in diatoms: see Strathmann 1967; Hitchcock 1983; and also later discussion on the allometry of cell-carbon content in algae). In any case, as predicted by the MLB hypothesis, the scaling of resting (endogenous) metabolic rates is essentially isometric in low-energy prokaryotes, but negatively allometric in higher-energy protists. Effects of energy deprivation further reveal the effects of metabolic level on metabolic scaling. Protozoans without food have a lower metabolic level and steeper scaling slope than those with food (Fig. 1). Similar effects of food deprivation on metabolic scaling have been observed in several animal species (Glazier 2005). However, prokaryotes show an apparently opposite effect: those without exogenous substrates exhibit both a lower metabolic level and a lower scaling exponent than those with exogenous substrates, though the difference in slopes is not significant (Fig. 1). This apparent difference in nutritional effects on prokaryotic vs. eukaryotic unicells is likely a spurious result of technical difficulties in estimating the respiration rates of extremely small prokaryotes, which out of necessity must be measured with large numbers of cells in a respirometry chamber. Consequently, estimates of respiration rate are substantially more variable in prokaryotes than in protists. The 95% confidence limits of the metabolic scaling slopes for prokaryotes are more than twice as large as those of the larger protists (Fig. 1b). Furthermore, reproduction during respiration rate measurements is a significant confounding factor for prokaryotes, which have very short generation times (often <0Æ5 h under optimal conditions: Bonner 1965). The generation time of many prokaryotes is often less than that of the duration of a respirometry experiment, whereas the generation time of protists is usually greater (usually > 6 h: Bonner 1965; Laybourn-Parry 1984, 1992). Thus the number of cells involved in respiration measurements is much more uncertain for studies of growing prokaryotes than for studies of growing protists. As a result, the effects of resource availability on

5 Metabolic scaling in unicells 967 metabolic scaling in prokaryotes are much more difficult to estimate reliably compared with protists. Other factors that make it difficult to obtain uniform metabolic data in tiny freeliving cells are discussed by Fenchel & Finlay (1983), Laybourn-Parry (1984), Fenchel (2005) and Beardall et al. (2009). The MLB hypothesis further predicts that the scaling of biological processes dependent on metabolic energy should vary with metabolic level, as does the scaling of metabolic rate itself (Glazier 2009a). As predicted, the scaling of growth rate in unicellular organisms varies significantly with metabolic (growth) level. Relatively rapidly growing ciliated protozoans exhibit steeper scaling slopes than slower growing algae (Fig. 2). Furthermore, the scaling slopes for growth rate in algae and ciliates cultured at are not significantly different from those expected from the metabolic scaling slopes of these taxa cultured at the same temperature (Fig 2b). As the metabolic rate of algae scales as M 0Æ88, the scaling of growth rate should scale as M )0Æ12, which is within the 95% confidence limits of that observed (M )0Æ15±0Æ04 ). Similarly, as the metabolic rate of protozoans with food scales as M 0Æ68,the scaling of growth rate should scale as M )0Æ32, which is again within the 95% confidence limits of that observed (M )0Æ25±0Æ10 ). Parallel scaling has been observed for carbon production rates in algae (b = 0Æ90 = least squares regression slope, calculated as the reduced major axis slope, 0Æ91, multiplied by the correlation coefficient, 0Æ99, given by Maran o n 2008) and for generation time in protozoans (b = 0Æ243 0Æ362: Finlay 1977; Baldock et al. 1980). In other studies with more limited sample sizes, the scaling slopes of growth rate vs. cell volume have all been reported to be less in algae (b = )0Æ11 to )0Æ22) than in ciliated protozoans (Banse 1982a; Blasco et al. 1982; Mizuno 1991; Finkel 2001), as predicted by the MLB hypothesis. This is also true for the scaling exponent (b = )0Æ13) described for diatoms based on several different studies (Sarthou et al. 2005). An apparent exception (b = )0Æ320 ± 0Æ089) was reported by Schlesinger et al. (1981) who compared growth rate to cell carbon content, rather than to cell volume as is the case here. This unexpectedly higher slope may have arisen because cell carbon content appears to vary allometrically with cell volume in algae (Mullin et al. 1966; Strathmann 1967; Verity et al. 1992). However, it is unknown whether the allometry of cell carbon content is a result or contributing cause of metabolic scaling in algae (Blasco et al. 1982). Furthermore, other algal studies have shown little difference between b values based on cell volume vs. cell carbon content (growth scaling: b = )0Æ066 vs. )0Æ082; Sommer 1989; b = )0Æ15 vs. )0Æ21; Tang 1995; metabolic scaling: b =0Æ88 vs. 0Æ93; Tang & Peters 1995). Experimental manipulations of algal growth rates additionally show that metabolic (growth) level affects the scaling slope, as predicted by the MLB hypothesis. Higher growth rates, induced by increased irradiance, are associated with lower scaling slopes (Fig. 3; Chan 1978). Schlesinger et al. (1981) reported similar experimental effects of irradiance on b (but see Finkel et al. 2004). And in a comparison of four separate studies of the scaling of algal growth rates, Banse (1976) showed that the scaling slope increased as growth conditions became less optimal. Furthermore, colonial algae, which have relatively low growth rates, exhibit less negative scaling slopes for growth rate (in relation to total colony size) than do unicellular algae with higher growth rates (Nielsen 2006; cf. Beardall et al. 2009), again as predicted by the MLB hypothesis. However, the effects of temperature on metabolic scaling in unicells both support and contradict the MLB hypothesis. Slow-growing Antarctic algae cultured at 0 C exhibit a significantly less negative scaling slope for growth rate than do faster growing algae cultured at, as predicted (Fig. 2). However, temperature appears to have little effect on the scaling of growth rate in ciliates (Finlay 1977) and amoebae (Baldock et al. 1980). The effects of temperature on metabolic scaling slopes in animals are mixed, as well (Banse 1982b; Glazier 2005). These heterogeneous results among studies may be the result of various methodological differences, and (or) taxonomic differences in adaptive strategies, thermal histories, or size-specific thermal sensitivities (cf. Glazier 2005). In conclusion, this study demonstrates that the scaling slopes of rates of respiration and growth in unicellular organisms are generally related to metabolic level, as has been shown elsewhere for multicellular organisms (Glazier 2005, 2008, 2009a,b,c; Killen et al. 2008). This systematic variation in the scaling slope (ranging widely from c. 2 3to1)is uniquely predicted by the MLB hypothesis, which focuses on variation in metabolic scaling between physical boundary limits, rather than on average tendencies, as many other models do (e.g. West et al. 1997; Banavar et al. 1999; cf. Glazier 2005, 2009a). These postulated limits involve surface- and volume-related constraints whose relative influence depends on metabolic level, thereby linking the two major parameters of allometric power functions, the slope (b) and the intercept (log a). Metabolic level is, in turn, likely affected by various factors related to the ecology and lifestyle of specific taxa of organisms (Killen et al. 2008; Glazier 2009a). Acknowledgements I thank two anonymous reviewers for helpful comments on a previous version of this paper and for alerting me to relevant literature. References Baldock, B.M., Baker, J.H. & Sleigh, M.A. (1980) Laboratory growth rates of six species of freshwater Gymnamoebia. Oecologia, 47, Banavar, J.R., Maritan, A. & Rinaldo, A. (1999) Size and form in efficient transport networks. Nature, 399, Banse, K. (1976) Rates of growth, respiration and photosynthesis of unicellular algae as related to cell size a review. Journal of Phycology, 12, Banse, K. (1982a) Cell volumes, maximal growth rates of unicellular algae and ciliates, and the role of ciliates in the marine pelagial. Limnology and Oceanography, 27, Banse, K. (1982b) Mass-scaled rates of respiration and intrinsic growth in very small invertebrates. Marine Ecology Progress Series, 9, Beardall, J., Allen, D., Bragg, J., Finkel, Z.V., Flynn, K.J., Quigg, A., Rees, T.A.V., Richardson, A. & Raven, J.A. (2009) Allometry and stoichiometry of unicellular, colonial and multicellular phytoplankton. New Phytologist, 181, Blasco, D., Packard, T.T. & Garfield, P.C. (1982) Size dependence of growth rate, respiratory electron transport system activity, and chemical

6 968 D. S. Glazier composition in marine diatoms in the laboratory. Journal of Phycology, 18, Bonner, J.T. (1965) Size and Cycle: An Essay on the Structure of Biology. Princeton University Press, Princeton, NJ. Brown, J.H., Gillooly, J.F., Allen, A.P., Savage, V.M. & West, G.B. (2004) Toward a metabolic theory of ecology. Ecology, 85, Calder, W.A. (1984) Size, Function, and Life History. Harvard University Press, Cambridge, MA. Chan, A.T. (1978) Comparative physiological study of marine diatoms and dinoflagellates in relation to irradiance and cell size. 1. Growth under continuous light. Journal of Phycology, 14, Clark, D.R., Flynn, K.J. & Owens, N.J.P. (2002) The large capacity for dark nitrate-assimilation in diatoms may overcome nitrate limitation of growth. New Phytologist, 155, Darveau, C.-A., Suarez, R.K., Andrews, R.D. & Hochachka, P.W. (2002) Allometric cascade as a unifying principle of body mass effects on metabolism. Nature, 417, Dodds, P.S., Rothman, D.H. & Weitz, J.S. (2001) Re-examination of the 3 4- law of metabolism. Journal of Theoretical Biology, 209, Downs, C.J., Hayes, J.P. & Tracy, C.R. (2008) Scaling metabolic rate with body mass and inverse body temperature: a test of the Arrhenius fractal supply model. Functional Ecology, 22, Falkowski, P.G., Dubinsky, Z. & Wyman, K. (1985) Growth irradiance relationships in phytoplankton. Limnology and Oceanography, 30, Fenchel, T. (1974) Intrinsic rate of increase: the relationship with body size. Oecologia, 14, Fenchel, T. (2005) Respiration in aquatic protists. Respiration in Aquatic Ecosystems (eds P. A. del Giorgio & P. J. le B. Williams), pp Oxford University Press, Oxford. Fenchel, T. & Finlay, B.J. (1983) Respiration rates in heterotrophic, free-living protozoa. Microbial Ecology, 9, Finkel, Z.V. (2001) Light absorption and size scaling of light-limited metabolism in marine diatoms. Limnology and Oceanography, 46, Finkel, Z.V., Irwin, A.J. & Schofield, O. (2004) Resource limitation alters the 3 4 size scaling of metabolic rates in phytoplankton. Marine Ecology Progress Series, 273, Finlay, B.J. (1977) The dependence of reproductive rate on cell size and temperature in freshwater ciliated protozoa. Oecologia, 30, Geider, R.J. & Osborne, B.A. (1989) Respiration and microalgal growth: a review of the quantitative relationship between dark respiration and growth. New Phytologist, 112, Gillooly, J.F., Brown, J.H., West, G.B., Savage, V.B. & Charnov, E.L. (2001) Effects of size and temperature on metabolic rate. Science, 293, Glazier, D.S. (2005) Beyond the 3 4-power law : variation in the intra- and interspecific scaling of metabolic rate in animals. Biological Reviews of the Cambridge Philosophical Society, 80, Glazier, D.S. (2008) Effects of metabolic level on the body-size scaling of metabolic rate in birds and mammals. Proceedings of the Royal Society of London. Series B, Biological Sciences, 275, Glazier, D.S. (2009a) A unifying explanation for diverse metabolic scaling in animals and plants. Biological Reviews of the Cambridge Philosophical Society (in press). Glazier, D.S. (2009b) Activity affects intraspecific body-size scaling of metabolic rate in ectothermic animals. Journal of Comparative Physiology B, in press. DOI: s Glazier, D.S. (2009c) Ontogenetic body-mass scaling of resting metabolic rate covaries with species-specific metabolic level and body size in spiders and snakes. Comparative Biochemistry and Physiology A, in press. DOI: j.cbpa Hemmingsen, A.M. (1960) Energy metabolism as related to body size and respiratory surfaces, and its evolution. Reports of the Steno Memorial Hospital and Nordisk Insulin Laboratorium, 9, Hitchcock, G.L. (1983) An examination of diatom area: volume ratios and their influence on estimates of plasma volume. Journal of Plankton Research, 5, Killen, S.S., Atkinson, D. & Glazier, D.S. (2008) Ecological factors contributing to variation in the scaling of metabolic rate with body mass in fishes. Comparative Biochemistry and Physiology, Part A, 150, S111. Kleiber, M. (1961) The Fire of Life. Wiley, New York. Laybourn-Parry, J. (1984) A Functional Biology of Free-Living Protozoa. University of California Press, Berkeley, CA. Laybourn-Parry, J. (1992) Protozoan Plankton Ecology. Chapman & Hall, London. Makarieva, A.M., Gorshkov, V.G. & Li, B.-L. (2005) Energetics of the smallest: do bacteria breathe at the same rate as whales? Proceedings of the Royal Society of London. Series B, Biological Sciences, 272, Maraño n, E. (2008) Inter-specific scaling of phytoplankton production and cell size in the field. Journal of Plankton Research, 30, McKechnie, A.E. & Wolf, B.O. (2004) The allometry of avian basal metabolic rate: good predictions need good data. Physiological and Biochemical Zoology, 77, Mizuno, M. (1991) Influence of cell volume on the growth and size reductions of marine and estuarine diatoms. Journal of Phycology, 27, Mullin, M.M., Sloan, P.R. & Eppley, R.W. (1966) Relationship between carbon content, cell volume, and area in phytoplankton. Limnology and Oceanography, 11, Needoba, J.A. & Harrison, P.J. (2004) Influence of low light and a light:dark cycle on NO 3 ) uptake, intracellular NO 3 ), and nitrogen isotope fractionation by marine phytoplankton. Journal of Phycology, 40, Nielsen, S.L. (2006) Size-dependent growth rates in eukaryotic and prokaryotic algae exemplified by green algae and cyanobacteria: comparisons between unicells and colonial growth forms. Journal of Plankton Research, 28, Niven, J.E. & Scharlemann, J.P. (2005) Do insect metabolic rates at rest and during flight scale with body mass? Biology Letters, 1, Peters, R.H. (1983) The Ecological Implications of Body Size. Cambridge University Press, Cambridge. Phillipson, J. (1981) Bioenergetic options and phylogeny. Physiological Ecology: An Evolutionary Approach to Resource Use (eds C. R. Townsend & P. Calow), pp Sinauer Associates, Sunderland, MA. Prothero, J. (1986) Scaling of energy metabolism in unicellular organisms: a reanalysis. Comparative Biochemistry and Physiology, 83A, Raven, J.A. (1976) The quantitative role of dark respiratory processes in heterotrophic and photolithotrophic plant growth. Annals of Botany, 40, Robinson, W.R., Peters, R.H. & Zimmerman, J. (1983) The effect of body size and temperature on metabolic rate of organisms. Canadian Journal of Zoology, 61, Sarthou, G., Timmermans, K.R., Blain, S. & Tréguer, P. (2005) Growth physiology and fate of diatoms in the ocean: a review. Journal of Sea Research, 53, Savage, V.M., Gillooly, J.F., Woodruff, W.H., West, G.B., Allen, A.P., Enquist, B.J. & Brown, J.H. (2004) The predominance of quarter-power scaling in biology. Functional Ecology, 18, Schlesinger, D.A., Molot, L.A. & Shuter, B.J. (1981) Specific growth rates of freshwater algae in relation to cell size and light intensity. Canadian Journal of Fisheries and Aquatic Science, 38, Schmidt-Nielsen, K. (1984) Scaling: Why Is Animal Size So Important? Cambridge University Press, New York. Sommer, U. (1989) Maximal growth rates of Antarctic phytoplankton: only weak dependence on cell size. Limnology and Oceanography, 34, Strathmann, R.R. (1967) Estimating the organic carbon content of phytoplankton from cell volume or plasma volume. Limnology and Oceanography, 12, Tang, E.P.Y. (1995) The allometry of algal growth rates. Journal of Plankton Research, 17, Tang, E.P.Y. & Peters, R.H. (1995) The allometry of algal respiration. Journal of Plankton Research, 17, Taylor, W.D. & Shuter, B.J. (1981) Body size, genome size, and intrinsic rate of increase in ciliated protozoa. The American Naturalist, 118, Verity, P.G., Robertson, C.Y., Tronzo, C.R., Andrews, M.G., Nelson, J.R. & Sieracki, M.E. (1992) Relationships between cell volume and the carbon and nitrogen content of marine photosynthetic nanoplankton. Limnology and Oceanography, 37, Weibel, E.R., Bacigalupe, L.D., Schmitt, B. & Hoppeler, H. (2004) Allometric scaling of maximal metabolic rate in mammals: muscle aerobic capacity as determinant factor. Respiratory Physiology & Neurobiology, 140, West, G.B., Brown, J.H. & Enquist, B.J. (1997) A general model for the origin of allometric scaling laws in biology. Science, 276, White, C.R. & Seymour, R.S. (2003) Mammalian basal metabolic rate is proportional to body mass 2 3. Proceedings of the National Academy of Sciences of the United States of America, 100, White, C.R., Phillips, N.F. & Seymour, R.S. (2006) The scaling and temperature dependence of vertebrate metabolism. Biology Letters, 2, Zar, J.H. (1984) Biostatistical Analysis. Prentice-Hall, Englewood Cliffs, NJ. Received 15 January 2009; accepted 21 April 2009 Handling Editor: Andrew Clarke