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TECHNICAL COMMENT
Ratio Representations of Specific Dynamic Action (Mass-Specific SDA and SDA Coefficient) Do Not Standardize for Body Mass and Meal Size Steven J. Beaupre* Department of Biological Sciences, University of Arkansas, Fayetteville, Arkansas 72701 Accepted 3/10/04
Introduction Specific dynamic action (SDA) is generally defined as the total energy expenditure associated with digestion and assimilation of ingested food and related biosynthesis (Brody 1945; Kleiber 1961). Contributing factors to SDA include secretion of digestive materials into the gastrointestinal tract, energy expended in peristalsis, upregulation and growth of relevant organs, costs of active transport, and energetic cost of intermediary metabolism and growth (Lusk 1931; Wilhelmj et al. 1931; Tandler and Beamish 1979; Wieser 1994; Secor and Diamond 2000; Starck and Beese 2001). Studies of SDA have classically focused on the role of cost of digestion in affecting potential for growth and reproduction (Brody 1945; Kleiber 1961) and on mechanisms producing SDA (Lusk 1931; Wilhemj et al. 1931). More recently, investigators have shifted some attention to the ecological and evolutionary determinants of the magnitude of SDA (Secor and Nagy 1994; Secor and Diamond 1995, 2000; Andrade et al. 1997; Secor 2001; Starck and Beese 2001; Overgaard et al. 2002). Notably, sufficient data now exist for some groups of organisms (e.g., snakes) to investigate specific hypotheses in a phylogenetic context (Secor and Diamond 2000; Secor 2001). Clearly, the present and future value of these studies finds its foundation in the methods used to represent and analyze SDA. SDA manifests itself as an increase in metabolic rate following feeding that, in some species, may last for several days. Researchers have quantified SDA using several variables, including peak metabolic rate following feeding, time to peak metabolic rate, duration of elevated metabolism, factorial scope (peak * E-mail:
[email protected]. Physiological and Biochemical Zoology 78(1):126–131. 2005. 䉷 2005 by The University of Chicago. All rights reserved. 1522-2152/2005/7801-3041$15.00
metabolic rate/baseline metabolic rate), and total SDA (total energy expended above baseline during digestion and assimilation). In this comment, I focus on this latter expression of total SDA because it is the single most relevant measure of the bioenergetic meaning of the SDA response (Kleiber 1961). For the purposes of comparative studies, researchers often find it necessary to extrapolate their SDA data to common body mass or common food mass. Extrapolation to common body mass has been accomplished through the use of massspecific SDA, where total energy (kJ) expended above baseline is divided by body mass, yielding units of kJ kg⫺1 (Secor and Diamond 2000; Secor 2001). Mass-specific SDA has been used as a response variable in phylogenetic comparative analyses (e.g., Secor 2001), has been used to normalize treatments that differ in mean body mass (e.g., in comparing temperature treatments; Toledo et al. 2003), and has been used to extrapolate the SDA response to common body mass (e.g., Secor and Diamond 2000). Extrapolation to common meal size has usually been accomplished through the use of the “SDA coefficient” following Miura et al. (1976), Weatherley (1976), and Jobling and Davies (1980). The SDA coefficient has been defined as the slope of the linear regression relating SDA (kJ) to total ingested or digestible energy (kJ; Jobling and Davies 1980). In some cases, the SDA coefficient refers to the ratio of SDA (kJ) to ingested energy (Overgaard et al. 2002; Robertson et al. 2002). Widespread use of the SDA coefficient probably has its ultimate origin from Kleiber (1961), who strongly recommended the expression of SDA as a percentage of the metabolizable energy content of the meal. Some recent authors attribute the SDA coefficient, at least in part, to Jobling and Davies (1980), who asserted that the relationship between total SDA and ingested energy was linear. Jobling and Davies (1980) in turn attribute the SDA coefficient to Weatherley (1976), who also assumes linearity, citing Kerr (1971) and Beamish (1974). In both cases (mass-specific SDA and SDA coefficient), raw data are converted to a ratio. The use of ratios to standardize physiological variables, and especially the use of mass-specific ratios, has been criticized in the literature (Atchley et al. 1976; Atchley 1978; Packard and Boardman 1988, 1999; Raubenheimer and Simpson 1992; Beaupre and Dunham 1995; Raubenheimer 1995). Fundamentally, the use of ratios implicitly assumes isometric scaling (linear,
Technical Comment 127 with intercept p 0) between numerator and denominator. Departures from isometry (i.e., allometry) are known to result in estimation errors, statistical errors, and spurious correlations (Atchley et al. 1976; Atchley 1978; Packard and Boardman 1988, 1999; Raubenheimer and Simpson 1992; Beaupre and Dunham 1995; Raubenheimer 1995). Packard and Boardman (1988, 1999) have presented particularly cogent reviews of the range of problems associated with the analysis of ratios. My purpose in this technical comment is to critically examine the scaling relationships that underlie the SDA coefficient and mass-specific SDA. By reanalyzing data from two early and influential publications (Kerr 1971; Jobling and Davies 1980) and considering my own work on SDA, I demonstrate that these relationships are actually allometric. Using allometric relationships of SDA in the timber rattlesnake (Crotalus horridus; Zaidan and Beaupre 2003), I investigated the potential for estimation errors when utilizing ratios to scale to common body mass or common food mass. Material and Methods Mass-Specific SDA In studies of the SDA response of the timber rattlesnake (Crotalus horridus), a regression equation was developed that predicted SDA (mL CO2) as an exponential function of snake body mass and ingested prey mass (Zaidan and Beaupre 2003). In that study, we quantified SDA in response to body size (70– 1,000 g), meal size (10%, 30%, and 50% of snake body weight), fast duration (1 and 5 mo), and temperature (25⬚C and 30⬚C). A simple two-variable allometric relationship (SDA [mL CO2 ] p 12.158[SW]0.160[PW]1.030, where SW is snake weight [g] and PW is prey weight [g]) explained 97% of the variance in our data set. We also considered several alternative regression models, including one that was linear with prey mass but resulted in a significant decrease in explained variance (from 97% to 84%). In addition, I tested an allometric model that included an intercept term (SDA p a ⫹ b[SW]c[PW]d) using nonlinear regression (SAS, PROC NLIN), which established that the intercept (a) was very close to, and not significantly different from, 0. Therefore, for the purposes of this technical comment, I consider the exponential regression relationship reported by Zaidan and Beaupre (2003) to be the best estimate of the true effects of snake body size and prey size on SDA in timber rattlesnakes. I note that our regression expresses prey size as weight (g) and SDA as milliliters CO2 produced instead of energy equivalents. Because diets employed by Zaidan and Beaupre (2003) were relatively uniform (adult mice purchased at one time from a commercial supplier), values of SDA and PW can easily be converted to kilojoule equivalents using simple conversion factors. To compare the true regression-based relationship and data generated by mass-specific extrapolation, I calculated mean mass-specific SDA for C. horridus fed 10% of their body weight
(for methodological details, see Zaidan and Beaupre 2003). I then estimated SDA (mL CO2) for a meal size of 10% of body mass and range of body sizes (from 100 to 4,000 g) using both the exponential regression and the mass-specific ratio. The two curves were plotted, and I expressed the mass-specific SDA estimate as a percentage of regression-based SDA estimate. As another demonstration, I calculated SDA (mL CO2 based on the above scaling relationship) for animals of differing size, all ingesting a meal at 10% of their body mass. I then expressed this calculated SDA in mass-specific form. SDA Coefficient Consideration of the SDA coefficient was based on both a reanalysis of foundational data that has led to the widespread use of this ratio and on simulation using the regression-based estimates from Zaidan and Beaupre (2003) described above. Most studies that utilize the SDA coefficient cite Jobling and Davies (1980) as the source of this ratio, although Jobling and Davies (1980) attribute the ratio to others (Miura et al. 1976; Weatherley 1976), who in turn attribute the ratio to others (Kerr 1971; Beamish 1974). Of these early articles, only Kerr (1971) and Jobling and Davies (1980) present raw data in a form that can be extracted and reanalyzed. Jobling and Davies (1980) plotted 22 data points (their Fig. 2) relating SDA (kJ) to ingested energy (kJ). Likewise, Kerr (1971) plotted 28 data points (his Fig. 1) relating SDA (kJ) to ingested energy (kJ). Both authors asserted that the relationship between these variables was linear and presented linear regression equations relating them. Using a metric caliper (accurate to Ⳳ0.001 cm), I extracted the original data from both publications and reconstructed the original data sets. I ran a linear regression and compared it to their results to check the accuracy of my data extraction. Then, I log transformed both variables (SDA and ingested energy) and fitted an exponential model for both data sets. The overall fit of the exponential and linear models was assessed by examination of explained variance. Use of the SDA coefficient to compare different animals on a per-ingested energy basis implicitly assumes isometric scaling between SDA and ingested energy. I examined this assumption by comparing linear and exponential models for the relationship between SDA and ingested energy. Furthermore, use of the SDA coefficient assumes that body mass is unimportant in determining SDA (there is no concept of body mass in the ratio of SDA [kJ] to ingested energy). If the SDA coefficient is unaffected by body mass, then a plot of coefficient versus body mass should yield no relationship. I investigated the validity of this assumption by calculating the SDA coefficient for an identical meal (50 g) over a range of body masses (from 100 to 4,000 g). Assuming a wet mass energy density of 8 kJ g⫺1 (Secor and Diamond 2000), a 50-g meal would correspond to 400 kJ. I used the scaling relationship from Zaidan and Beaupre (2003) to estimate SDA (mL CO2) for a 50-g meal over the range of
128 S. J. Beaupre snakes fed 10% of body weight observed by Zaidan and Beaupre (2003) was 3.62 mL CO2 g⫺1 (SD p 0.75, n p 26). Large errors are apparent in a comparison of mass-specific estimates to regression estimates of SDA (Fig. 1). The mass-specific estimates ranged from 132% of regression-based estimates at low body mass to 66% of regression-based estimates at high body mass. For Crotalus horridus, it appears that the mass-specific ratios overestimate SDA when extrapolating to smaller body masses and underestimate SDA when extrapolating to larger body masses. Furthermore, mass-specific SDA as calculated for snakes of differing sizes consuming a meal of 10% body mass (Table 1) was highly variable, despite the fact that the same underlying scaling relationship was used to generate SDA values. Table 1 demonstrates that mass-specific values are not constant, or even similar, across a range of body and prey weights.
SDA Coefficient
Figure 1. Comparison of specific dynamic action (SDA) based on the scaling relationship from Zaidan and Beaupre (2003) with estimates of SDA based on mass-specific SDA as a function of body mass. Percentages on the plot are percent difference, calculated by (mass-specific estimate)/(regression estimate)# 100. Lower plot provides resolution for low body mass range.
body sizes and then converted these values to energy equivalents, assuming a respiratory quotient of 0.72 and corresponding energy conversion factor of 27.42 J mL⫺1 CO2 (Gessaman and Nagy 1988). SDA coefficients at each body mass were calculated by dividing estimated SDA (kJ) by ingested energy (400 kJ). The resulting coefficients were plotted against body mass to look for a relationship. Results Mass-Specific Increment When simultaneously considered with prey weight, the scaling exponent for the effect of timber rattlesnake body mass on the SDA increment was small (SW0.16; Zaidan and Beaupre 2003) and represents a significant deviation from the scaling exponent of 1.0 required for isometry. The mean mass-specific SDA for
Twenty-two data points were extracted from Jobling and Davies (1980; Fig. 2). Results of a linear regression (SDA [kJ] p 0.156[ingested kJ] ⫹ 0.09; R 2 p 0.74, P ! 0.0001) compared favorably, within rounding and estimation error, to the original reported results (SDA [kJ] p 0.161[ingested kJ] ⫹ 0.08; Jobling and Davies 1980). However, the exponential model (SDA [kJ] p 0.2134[ingested kJ]0.87; R 2 p 0.82, P ! 0.0001) exhibited a substantial increase in explained variance. Twenty-eight data points were extracted from Kerr (1971; Fig. 1). Again, a linear regression produced similar results (SDA [cal] p 0.278 # ingested energy [cal]; R 2 p 0.88, P ! 0.0001) to the original report (SDA [cal] p 0.288 # ingested energy [cal]). However, again the exponential model (SDA [cal] p 0.352[ingested cal]0.93; R 2 p 0.93, P ! 0.0001) exhibited a substantial increase in explained variance. Thus, it appears that the data from both Jobling and Davies (1980) and Kerr (1971) are best described by allometric scaling between SDA and ingested energy rather than a linear scaling as they originally asserted. I note that for C. horridus, SDA cannot be accurately predicted without knowledge of both snake body mass and prey Table 1: Calculations of specific dynamic action Body Mass (g) 100 500 1,000 2,000
10% Meal Size
SDA (mL CO2)
M-S SDA (mL CO2 g⫺1)
10 50 100 200
272.2 1,847.7 4,215.6 9,618.1
2.72 3.70 4.22 4.81
Note. Calculations based on the scaling relationship derived by Zaidan and Beaupre (2003) for timber rattlesnakes of varying body mass ingesting a meal at 10% of body mass. Note that mass-specific (M-S) specific dynamic action (SDA) is highly variable, despite the SDA data having been derived by the same scaling relationship.
Technical Comment 129
Figure 2. Specific dynamic action (SDA) coefficient (SDA expressed as percentage of ingested energy) for a 50-g (400 kJ) meal for timber rattlesnakes of differing body mass. Note the strong dependency of the SDA coefficient on body mass.
mass, and the relationship is allometric in both variables (Zaidan and Beaupre 2003). Because of allometric contributions from body mass in C. horridus, an exponential model (SDA [mL CO2 ] p 19.54[ingested g]1.15; n p 36, R 2 p 0.96, P ! 0.0001) better describes the relationship between SDA and ingested energy than a linear model (SDA [mL CO2 ] p 39.3[ingested g] ⫺ 138.9; n p 36, R 2 p 0.93, P ! 0.0001) because it explains slightly more of the variance. The SDA coefficient is clearly sensitive to body mass (Fig. 2), ranging from 9.7% to 17.7% over the mass range of 100–4,000 g. Therefore, for the data sets examined, the relationship between SDA and ingested mass or energy appears to be allometric, and the SDA coefficient is not unaffected by body mass. Discussion The relationship between SDA and body mass is allometric (with exponent !11.0 and/or intercept !10). Therefore, the use of mass-specific SDA to adjust to common body mass will result in potentially large errors in estimation. As demonstrated in Figure 1, errors will tend toward overestimation when extrapolating to smaller size and underestimation when extrapolating to larger size. Although some studies report mass scaling exponents that do not differ significantly from 1.0 (Secor and Diamond 1997a), isometry also requires intercept equal to 0, a condition not demonstrated by any study to date. Secor and Diamond report a mass scaling relationship (their Table 2) of SDA (kJ) p ⫺0.25W1.01Ⳳ0.02. The relationship was generated for meal sizes of 25% snake body weight only, however, because snake body weights are variable, the actual meal weight is variable, and there is significant variation in prey weight that is exactly correlated with snake weight (bigger snakes have bigger
meals if meals are fixed at 25% snake weight). The confounding of meal size with body size in this case calls into question the validity of Secor and Diamond’s (1997a) estimated mass scaling relationship. Reanalyzed data from two foundational articles (Kerr 1971; Jobling and Davies 1980) and from more recent work (Zaidan and Beaupre 2003) suggest that the relationship between SDA and ingested energy is allometric. Therefore, use of the SDA coefficient to standardize observations to a common meal size will result in estimation errors of varying magnitude. Such errors are unpredictable without knowledge of the true allometric relationships relating SDA to ingested energy. Because of allometric contributions of body mass to SDA, the SDA coefficient is affected by body mass (also demonstrated in Beamish 1974). Therefore, the SDA coefficient should not be used to standardize SDA observations for groups of organisms that differ in body size. Variation in body size produced changes in the SDA coefficient from 9.7% to 17.7% (Fig. 2), a range that spans approximately 30% of the total range of variation in the SDA coefficient among reptiles measured (from approximately 4% to 33% of ingested energy as reported in Secor 2001). Unfortunately, the use of mass-specific SDA and the SDA coefficient are deeply embedded in the SDA literature. A brief sample of recent important articles reveals the use and analysis of mass-specific SDA in phylogenetic comparative studies (Secor and Diamond 2000; Secor 2001) and the common use of the SDA coefficient (Costa and Kooyman 1984; Andrade et al. 1997; Secor and Diamond 1997b, 2000; Secor 2001; McCue and Lillywhite 2002; Overgaard et al. 2002; Robertson et al. 2002; Wang et al. 2002; Toledo et al. 2003). The consequences of analysis of these ratios are difficult to predict because the degree of error incurred will be dependent on the characteristics of the allometry that underlies the ratio components, which may well vary among species and diet types. In some cases, the SDA coefficient is used in statistical procedures that have been demonstrated to produce spurious correlation in other contexts. For example, Robertson et al. (2002) regress the SDA coefficient on food consumption (their Fig. 3) and find a significant negative relationship. Such statistically significant relationships have been observed previously when a ratio is regressed against its denominator (or variables that are correlated with it) and are best considered as spurious correlations with little or no biological meaning (see Raubenheimer 1995). Physiological diversity and specific allometry of SDA results from complex and interacting contributions of a variety of factors including costs of digestive secretions, peristalsis, upregulation and growth of relevant organs, active transport, and intermediary metabolism and growth (Lusk 1931; Wilhelmj et al. 1931; Tandler and Beamish 1979; Wieser 1994; Secor and Diamond 2000; Starck and Beese 2001). The relative importance of these contributing factors certainly varies over diverse ecological, phylogenetic, and dietary scales. The use of simple
130 S. J. Beaupre ratios to represent this complexity relegates the potentially rich physiological diversity of the SDA response into obscurity. In my opinion, the use of multivariable allometric models is one option for revealing physiological diversity in response to ecological, phylogenetic, and dietary contexts. I recommend the abandonment of mass-specific SDA and the SDA coefficient in favor of more robust statistical techniques that analyze the raw data. Data sets should be reanalyzed to produce scaling relationships that reflect the simultaneous allometric contributions of animal body mass and food mass to SDA. Such scaling relationships can be used to extrapolate SDA data to common body size and/or meal size for comparative studies (however, in general, extrapolation of values beyond the range of data used to derive the scaling relationship is not recommended). Furthermore, as suggested previously by numerous authors (Packard and Boardman 1988, 1999; Raubenheimer and Simpson 1992; Beaupre and Dunham 1995; Raubenheimer 1995), ANCOVA is an indispensable tool for comparing groups that vary with respect to one or more continuous covariates (e.g., body mass and meal size).
Acknowledgments Early drafts of the manuscript benefited from comments and contributions by C. Montgomery, P. Petraitis, and F. Zaidan. All described animal procedures employed in this and related studies were approved under the University of Arkansas Institutional Animal Care and Use Committee Protocol 99003. The work was supported by funds from the University of Arkansas Research Incentive Fund, the Arkansas Science and Technology Authority (grant 97-B-06), and the National Science Foundation (grant IBN-9728470) to S.J.B.
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