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Introduction

Among organisms, metabolic rate does not vary haphazardly but shows highly regular relationships to other organismal properties, in particular to body mass. Although scaling of metabolic rate to body mass has been studied for several decades (e.g., Kleiber 1932; Schmidt‐Nielsen 1984; Brown and West 2000), the allometric coefficients and their theoretical elucidation are still not settled (Brown et al. 2005; Kozłowski and Konarzewski 2005). Currently there exist several explanations, two of which are considered here. The first one was proposed by the group of authors around G. B. West and J. H. Brown, who postulated that metabolism increases, both interspecifically (West et al. 1997) and intraspecifically (West et al. 2001), with body mass at a power of 3/4 (Kleiber's law). The ubiquity of 3/4‐power scaling underlies large‐scale ecological patterns and forms the foundations of the so‐called metabolic theory of ecology (MTE; Brown et al. 2004). West et al. (1997) explained this unitary pattern as a consequence of minimization of dissipative energy during transport of substances within the body through space‐filling fractal‐like networks of branching tubes. For this study, the most important assumption of the model is the size invariance of the terminal capillaries of such networks. Building on this assumption, the proponents of the MTE recently predicted that metabolic rates of size‐invariant cells should decrease with body size (Savage et al. 2007). Conversely, metabolic rates of cells exhibiting body‐size dependence should be cell‐size independent. According to the MTE, the concerted changes in cell sizes, cell numbers, and cell‐specific metabolic rates give rise to the universality of the 3/4 metabolic scaling.

An alternative to West et al.’s (1997) model was proposed by Kozłowski et al. (2003) and, earlier, by Davison (1955, 1956). Kozłowski et al. (2003) question the ubiquity of the 3/4 metabolic scaling and argue that interspecific allometries of metabolic rates are by‐products of diversified patterns of body‐size optimization within taxonomic groups, with different participation by cell size and cell number in the evolution of body size. They based their model on the observation that small cells have higher mass‐specific metabolic rates than do larger cells (Goniakowska 1973; Mongold and Lenski 1996), which could be driven by differences in cell surface‐to‐volume ratio. According to Kozłowski et al. (2003), animal lineages with body‐size changes performed by cell‐number alterations should have a metabolic scaling exponent of 1, while those altering body size solely via cell‐size alterations should have a scaling exponent of 2/3. As they expect that changes in body size in most lineages should encompass changes in both cell size and cell number, the scaling exponent is predicted to range between 2/3 and 1. The change in cell size or, more often, the combination of changes in both cell size and cell number, as a mechanism of evolutionary alteration in body size, is relatively well documented in different lineages of invertebrates (Partridge et al. 1994; Stevenson et al. 1995; Chown et al. 2007) and recently in a vertebrate clade (Starostová et al. 2005).

Surprisingly, the importance of particular cellular mechanisms of interspecific size variation in individual animal lineages and their contributions to metabolic scaling are little known. Kozłowski et al. (2003) tested their own hypothesis interspecifically across mammals and birds, using genome size as a proxy of cell size because cell‐size data for these and other vertebrate groups are lacking or scarce. In other words, they assumed a strong positive relationship between genome size and cell size. However, while the correlation between genome size and cell size (only erythrocytes were broadly tested) holds at the high taxonomic levels, it does not hold at lower levels such as family, genus, and species (Pagel and Johnstone 1992; Starostová et al. 2008). Moreover, cell size is definitely phenotypically plastic within a species—that is, one genome size can correspond to the relatively wide spectrum of cell sizes, depending on temperature (e.g., Van Voorhies 1996)—and within individuals, as different tissues consist of cells differing in size. The theoretical background of Kozłowski et al.'s (2003) hypothesis is based on the relationship between cell size, not genome size, and metabolic rate. The role of cell‐size variation in metabolic scaling suggested by Kozłowski et al.'s (2003) model has been explicitly supported in ants by Chown et al. (2007). In contrast to the original model derivation, the latter article documented the role of cell‐size variation at the intraspecific level.

The aim of this study was to test the validity of the MTE and Kozłowski et al.'s (2003) model by testing their predictions with regard to the significance of the relative contribution of cell size and genome size to scaling of whole‐body metabolic rate within a well‐defined clade. We used eyelid geckos (family Eublepharidae) as a model taxonomic group, and we used their erythrocyte size as a proxy for cell size.

Theoretical Framework and Specific Predictions

The MTE and the model by Kozłowski et al. (2003) make contrasting predictions with respect to the contribution of cell metabolism to whole‐body metabolic rates. Savage et al. (2007) reasoned that cell metabolic rate and cell size within multicellular organisms should roughly conform to two strategies dictated by the ubiquitous optimized 3/4‐scaling of total metabolic rate: metabolic rate of short‐lived, quickly dividing cells, such as erythroblasts and consequently derived erythrocytes, should be body‐size dependent, whereas their size should be body‐size invariant. Conversely, cell volume of slowly dividing cells is expected to be body‐size dependent, whereas cell metabolism should be roughly invariant with body size. Thus, a null hypothesis for the MTE is that erythrocyte size is independent of body mass.

In contrast to the MTE, the model by Kozłowski et al. (2003) assumes that per volume cell metabolic rate decreases as cell size increases. For a group of species composed of cells of the same size, metabolic rate should be directly proportional to body mass (isometry), which is mathematically equivalent to (1) size independence of mass‐specific metabolic rate (MS‐SMR), (2) allometry with an exponent equal to 1, and (3) linear regression of the metabolic rate with respect to body mass through the origin (because of the proportionality and the assumption that an organism with a size equal to 0 should have a metabolism equal to 0). We use (1) to test the isometry of the metabolic rate, which we adopt as a null hypothesis. If the isometry is rejected, there should exist a negative association between MS‐SMR and cell size. There should also exist a negative relationship between MS‐SMR and genome size if genome size affects metabolic rate scaling directly or if genome size unequivocally determines cell size.

Material and Methods

Eyelid geckos are a monophyletic group sharing similar morphology but exhibiting large variations in body, cell, and genome sizes (Kratochvíl and Frynta 2002; Starostová et al. 2005, 2008), thereby making them a very suitable subject of studies of mechanisms underlying standard metabolic rate (SMR) variation. The range of body sizes of the geckos in our study was 3.06–100.10 g. Animals used in this study were bred in our laboratory (Charles University, Prague), or they originated from the pet trade. Erythrocyte size and metabolic rate in representatives of 14 geographically and phenotypically distant populations and/or species of eyelid geckos were measured (see fig. 1 for the list of species and sample sizes). SMR measurements were performed on adult individuals at 25°C (which is very close to the temperature in breeding facilities [mean temperature, ∼26°C]) during the light phase. Animals were fasted for 2 days before trials. SMR was measured as O₂ consumption in an open‐flow respirometry system (Sable Systems, Las Vegas, NV) that was calibrated with a bubble flow meter (Optiflow 420, Supelco, Bellefonte, PA). To achieve the greatest measurement precision, air flow (range, 5–45 mL min⁻¹) and metabolic chamber volume (range, 50–300 cm³) were adjusted to the body mass of an individual animal. We defined SMR as the lowest 10 min recorded during a 180‐min trial, calculated according to equation (4a) of Withers (1977) and converted to standard (stpd) conditions. The animals were weighed to the nearest 0.01 g before each metabolic trial was performed.

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Figure 1: Relationship between mean mass‐specific standard metabolic rate (SMR) and mean erythrocyte area (a) and median genome size (b). AF = Aeluroscalabotes felinus (Günther, 1864), ; CE = Coleonyx elegans Gray, 1845, ; CM = Coleonyx mitratus (Peters, 1845), ; CV = Coleonyx variegatus (Baird, 1858), ; EAI = Iranian population of Eublepharis angramainyu Anderson and Leviton, 1966, ; EAS = Syrian population of Eublepharis angramainyu, ; EF = Eublepharis cf. fuscus Börner, 1981, ; EM = Eublepharis macularius Blyth, 1854, ; GA = Goniurosaurus araneus Grismer, Viets, and Boyle, 1999, ; GLI = Goniurosaurus lichtenfelderi (Mocquard, 1897), ; GLU = Goniurosaurus luii Grismer, Viets, and Boyle, 1999, ; GS = Goniurosaurus splendens Nakamura and Uéno, 1959, ; HC = Hemitheconyx caudicinctus (Duméril, 1851), ; HA = Holodactylus africanus Boettger, 1893, . Sample sizes (n) indicate numbers of individuals with successfully measured SMR.

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After completing metabolic trials, a drop of blood taken from the humeral vessel was used to prepare blood smears. Dry area (projection area) of 50 dry erythrocytes from three males and three females per species (or distinct populations—possibly even different species—in the case of Eublepharis angramainyu) were measured, and the means of these values were used in subsequent analyses. For Coleonyx brevis Stejneger, 1893, only a single individual was available, and for Goniurosaurus araneus Grismer, Viets, and Boyle, 1999, and Holodactylus africanus Boettger, 1893, four individuals were available for erythrocyte size measurements. Cell size was measured using light microscopy and subsequent image analysis (analySIS 1.10, Soft Imaging System). For details on slide preparation and staining, see Starostová et al. (2005).

Genome size (GS) was measured for two additional species not considered by Starostová et al. (2008; Aeluroscalabotes felinus (Günther, 1864), ; and Goniurosaurus splendens Nakamura and Uéno, 1959, ) with flow cytometry using 4′‐6‐diamidino‐2‐phenylindole fluorochrome (DAPI). For detailed description of sample preparation and measurements, see Starostová et al. (2008).

Because species data are not independent, we performed the phylogenetically adjusted analysis using the phylogenetic generalized least squares (PGLS) approach (Martins and Hansen 1997). We computed the phylogenetic comparative analyses using COMPARE, version 4.6b (Martins 2004), employing the phylogenetic tree of the eyelid geckos that is based on figure 4 in Joanniaux and Kumazawa (2008). We replenished this tree by adding two additional species (E. angramainyu populations from Syria and Iran and Eublepharus cf. fuscus) according to the topology presented earlier (Starostová et al. 2005). Study populations of E. angramainyu live in allopatry, which allows us to treat them as independent evolutionary units. For the phylogenetically adjusted analysis, we set all branch lengths as equal. Statistical analyses were performed using STATISTICA (StatSoft 2001) software.

Results

Among the eyelid geckos we studied, SMR increased with body mass more slowly than isometrically (log SMR = −0.628 + 0.565 log mass), which means that mass‐specific SMR decreased with body mass. Confidence interval (95% CI) of the scaling exponent ranged from 0.389 to 0.742 and excluded both the values of 1 ( ) and 0.75 ( ). Erythrocyte area also significantly increased with body mass ( ), albeit with an extremely low exponent of 0.07 (95% CI, 0.04–0.10).

We found a strong negative correlation between MS‐SMR and erythrocyte area ( , ; fig. 1a), even stronger than the correlation between MS‐SMR and body mass ( , ). Likewise, erythrocyte area very strongly correlated with body mass ( , ). These three correlations support Kozłowski et al.'s (2003) model unless there exists an unknown common cause for correlation of MS‐SMR and erythrocyte size with body mass. The support for the model by Kozłowski et al. (2003) would be even stronger if MS‐SMR correlated negatively with mass‐corrected erythrocyte size (expressed as residuals from regression of erythrocyte area on body mass). It is not surprising, however, that such correlation is not significant ( , ), taking into account the low number of data points and the small portion of the expected variation in erythrocyte size remaining after mass correction.

The correlation between GS and MS‐SMR was not significant ( , ; fig. 1b). Similar to our previous study, the correlation between genome size and erythrocyte size was also not significant ( , ; for illustration, see fig. 2 in Starostová et al. 2008).

Phylogenetically adjusted analyses confirmed these conclusions. The PGLS analysis showed that the effect of phylogeny is minimal: the PGLS correlation coefficient between MS‐SMR and erythrocyte area is −0.725, which is very close to that based on raw data (estimated indicates low evolutionary constraint). The phylogenetic analyses confirmed a nonsignificant relationship between genome size and MS‐SMR.

Discussion

The whole‐organism metabolic rate is the sum of energy expenditures of individual cells building various tissues (see Darveau et al. 2002). Surprisingly, this fundamental fact has not become the center of discussion on the legitimacy of models put forward for the explanation of metabolic scaling. Although it was not clearly stated in the formulation of the mathematical model that was suggested to explain Kleiber's law (West et al. 1997; Brown et al. 2004), the model by West et al. (1997) is based on the assumption of the cell‐size invariance, at least with respect to erythrocyte size. According to the derivation in West et al.’s (1997) model, dimensions of the terminal capillaries of the supply systems (i.e., blood systems in the case of vertebrates) should be strictly independent of body size. It is therefore logical to predict that capillary‐size invariance forces the size invariance of erythrocytes, whose narrowest dimensions must tightly match the cross‐sectional area of capillaries to ensure efficient gas exchange (Snyder and Sheafor 1999; Jeong et al. 2006).

The results of our earlier study (Starostová et al. 2005) clearly contradict the above prediction, since the dry erythrocyte area varies by about 36% in concert with the variation in body size within the eyelid geckos, our model organisms. These results corroborate other analyses documenting a substantial variation in erythrocyte size in other major vertebrate taxa. For example, Promislow (1991) demonstrated a significant positive correlation between erythrocyte volume and body mass in mammals, and he used the exact same data set that was recently used by Savage et al. (2007) in their analysis supporting erythrocyte size invariance. The dramatically different conclusions of these two studies that were undertaken using the same data set could result from the fact that Savage et al. (2007) neglected the phylogenetic adjustments. More importantly, we demonstrated that MS‐SMR correlates negatively with cell size, which suggests that the variation in cell size thus significantly contributes to interspecific differences in SMR. We are not the first to detect the correlation between erythrocyte size and metabolic rate. For example, Gregory (2002) demonstrated an inverse correlation between mass‐independent erythrocyte size and mass‐independent resting metabolic rates (RMRs) in birds. However, unlike Gregory (2002), we did not correct the erythrocyte size for body mass before we analyzed its effect on metabolic rate. According to the theoretical framework, such a correction is erroneous because adjusting for body mass before analyses are performed potentially removes part of the variation that we aim to explain; there is no a priori reason for positive correlation between body mass and erythrocyte size, and according to the MTE, such a correlation should not exist.

Differences in cell size cannot be the only reason for the deviation of SMR from strict proportionality to body mass. According to Kozłowski et al. (2003), a slope of 2/3 is expected if body mass in a lineage changes exclusively through cell‐size changes, which seems to not be the case in our geckos. Thus, variation in cell size should produce the slope for SMR allometry somewhere between 0.67 and 1. The additional flattening of the SMR–body mass dependence can be attributed to differences in organ size (Konarzewski and Diamond 1995; Książek et al. 2004; Brzęk et al. 2007) and body composition, that is, the increasing proportion of metabolically inert tissues such as bones or fat with size. Size‐dependent differences in membrane permeability may constitute another important source of SMR variability (Hulbert 2007). If decrease of membrane permeability with body mass and not the surface‐to‐volume ratio of cells was a primary reason for size dependence of MS‐SMR, it would remain to be explained why permeability correlates so strongly with cell sizes.

The notion of a significant effect of erythrocyte size on metabolic rate is based on the assumption that erythrocyte size can be used as a proxy of the cell size of other cell types. This is supported by the results of studies by Nitecki (1972, 1973). Using these data, we have found tight correlations between the sizes of erythrocytes and the sizes of other cells in different tissues in passerine birds (J. Kozłowski, A. François‐Krassowska, S. Maciak, and T. Pis, unpublished data). However, it is necessary to demonstrate such correlations in geckos in further studies.

Vinogradov (1995, 1997) and Gregory (2002) studied the relationships between metabolic rate and GS in birds and mammals. As well, Kozłowski et al. (2003) used genome size as a proxy for cell size. Our results warn that such correlations cannot be presumed, especially at the low systematic level. In the case of the geckos in our study, there is a lack of correlation between GS and cell size; more precisely, two species (Coleonyx variegatus and Coleonyx brevis) escaped from such a relationship, possibly as a result of tighter DNA packing (Starostová et al. 2008).

In conclusion, we have demonstrated that allometric scaling of SMR in a uniform taxonomic group of eyelid geckos significantly deviates from the alleged 3/4 metabolic scaling rule and that this deviation can be partially explained by cell‐size variation. We suggest that similar studies performed within other clades can significantly contribute toward the understanding of already well‐established (e.g., Glazier 2005; White et al. 2007) between‐taxa diversification of allometric exponents of metabolic rates.