The temptation to apply statistical procedures to the data must be tempered by the fact that one cannot make a "random sample" of vertebrate species. We must work with the data available, and such data tend to come to a great extent from domesticated animals, laboratory animals, and higher primates. Data for other vertebrates are available for only a few species. Instead of trying to obtain a random sample, we have tried to obtain data from all the vertebrate classes and from animals that lie at the extremes of the various parameters under consideration. Thus, we have obtained data for fish, amphibia, reptiles, birds, and mammals. Among fish we have a weight range from a 9-g goldfish to a 4,200-g shark, and among mammals we have animals ranging from the shrew and mouse to the elephant and whale. As weight and taxonomic differences would be expected to increase the variance of our data, one may claim that our procedure is a conservative one, If anything, we should end up with more variance than would be expected if it were possible to do a random sampling procedure, and, therefore, our ability to generalize to the vertebrates as a whole should be, if anything, enhanced.
We are also unable to obtain a random sample of data from individuals within each species. Instead, we have limited our data to healthy adults and have, whenever data must be combined from several individuals, used data from individuals of similar body weight. This procedure would be expected to reduce the variance in the data obtained. There are changes in the various relevant parameters over the course of ontogeny that are quite complex and variable from species to species. The human infant, on the one hand, uses a very high proportion of total metabolism for the central nervous system as evidenced by the fact that the brain-to-body weight ratio is much higher than that of an adult (18), and the metabolic rate of the brain is greater as well (49). The rat or dog pup, on the other hand, does not use a significantly greater proportion of metabolism for the central nervous system (CNS) than does an adult; although the brain-to-body weight ratio is greater for an infant, the metabolic rate of brain tissue is correspondingly lower (38, 83). Comparable data are not available for other vertebrate infants. In old age, the metabolic rate of brain tissue (and consequently, the ratio of CNS to body metabolism) decreases slightly in both humans (49) and rats (64). Similarly, health could be a factor in the data, since an emaciated animal might have a lowered body metabolism, but still require the normal brain metabolism. Therefore, to eliminate these sources of variance as much as possible from the data, we have limited our sample to healthy adults.
There are good theoretical reasons to exclude data of very young, very old, and unhealthy individuals from our sample. The metabolic activity of a very young bird or mammal should not be considered without regard to the metabolism of the parents and siblings. In a sense, from an evolutionary perspective, the family unit might be considered as the appropriate unit of analysis; in some cases the parents may "sacrifice" a considerable proportion of their own body metabolism in order to make possible the development of the offspring. For example, it may be the prolonged feeding of the human infant by the mother that makes possible the fact that it can devote such a large proportion of its metabolism to the developing brain. Very old and emaciated animals may be eliminated in order to concentrate on metabolic ratios of those types of individuals (i.e., healthy but not very old individuals) that have most likely made the major contribution to the evolution of the species, i.e., contributed to the gene pool that determines the relationships under consideration.
The reliability of data on brain and body weights and resting metabolism is well established in most cases. Figures that show the relationship between brain and body weight and between resting metabolism and body weight for healthy adults of various species usually have remarkably low variance (8, 18). There are two species, however, in which the resting metabolic rates may be called into question: the shrew and the whale. Although one source on whale metabolism suggests that the body metabolic rate of the finback whale is half that of a dolphin (42) another reference suggests that is may be considerably less, perhaps only 1/5 or 1/7 the metabolism of the dolphin (46). The latter figure is more consonant with predictions from other mammalian data (41) and will be used here. In the shrew, there is the problem that the animal is never really at rest (70), and therefore the quoted values or "resting metabolism" may be more the equivalent of an active metabolic rate in other species.
The reliability of data on spinal cord weights is probably less than that of brain weight. Because of the scarcity of data in the literature, we have been forced to make some extrapolations across species, in two cases (whale and alligator) make estimates from planimetry, and in one case (elephant) make an overall estimate for spinal cord metabolism without regard to its weight. However, since spinal metabolism in most of these animals accounts for 10% or less of the metabolism of the CNS, one may assume that errors deriving from such extrapolations would not have a very great effect on the final data; i.e., a 30% error in spinal cord weight would change the overall ratio of CNS to body metabolism by only 3%.
The greatest problem in data reliability concerns the estimates of brain and spinal cord metabolism. The two functions that we have plotted in Figs. 1 and 2 are derived from the only direct data that are available, and these data are not as numerous as one would like. However, there are considerable indirect data that support these functions. We have relied upon in vivo measurements, but there are also many in vitro measurements that can be compared. As a general rule, in vivo measurements of tissue metabolism are twice as great as the equivalent in vitro measurements of sliced tissue (i.e., tissue with the cell structure still intact) according to McIlwain (66) and in vitro measurements from sliced tissue are 2.2 times greater than measurements from homogenized tissue with the cells broken down (25, 71). Also, one can make comparisons between metabolic rates of whole brain and isolated cerebral cortex in mammals on the basis of the fact that cortex metabolism is 40% greater than whole-brain metabolism (23, 25, 66).
The function for brain metabolism in warm-blooded vertebrates is supported by both in vitro measurements and by in vivo cortical measurements. The function for metabolism of cortex in vivo can be calculated from data supplied for the rat (23)) rhesus monkey (9), and human (66). A regression equation fitted to these data is
log y = 1.04 - 0.13 log x (6)where y is brain metabolic rate in cm3 O2 · 100 g-1 · min-1 and x is brain weight in grams. Reducing this equation by a factor of l/1.4 in order to make it equivalent to whole brain rather than cortex, as noted above, one obtains the equation
log y = 0.89 - 0.13 log x (7)and this question can be taken as confirmation of Eq. 1. Similarly, one can obtain a function from the in vitro determinations of slices of cortical tissue from the mouse, rat, cat, and cow, as obtained by Eliot and Henderson (25). A regression equation fitted to their data is the following
log y = 0.76 - 0.15 log x (8)where y and x represent the same parameters as in previous equations. To convert this to an equivalent whole-brain in vivo measure, one must multiply by a factor of two (whole brain-to-slice metabolic ratio) and then reduce it by a factor of l/1.4 (whole brain-to-cortex metabolic ratio). When this is done, one obtains the following equation which also corresponds well to Eq. 1
log y = 0.91 - 0.15 log x (9)
The function for brain metabolism in cold-blooded vertebrates is also supported by data from in vitro measurements. Data for homogenized brain tissue in vitro has been obtained for the bass (29), bullfrog (74), turtle (63), salmon (71), and goldfish (27) at approximately 20°C. The obtained data are as follows, expressed in cm3 O2 · 100 g-1 · min-1 and multiplied by 4.4 to convert from homogenized to in vivo equivalents. They may be compared to expected values predicted by Eq. 3 derived from the Q10 equation. Bass, obtained value 1.8 and predicted 2.1; bullfrog, obtained value 1.5 and predicted 2.4; salmon, obtained value 2.6 and predicted 2.7; turtle, obtained value 1.8 and predicted 2.5; and goldfish, obtained value 2.2 and predicted 2.8.
Independent and theoretical support for the form of Eq. 4 for spinal metabolic rate may be obtained from a consideration of the proportion of the spinal cord that is made up of gray matter. Because gray matter has a much higher metabolic rate than white matter (24) one can explain the lower proportional metabolism of large spinal cords in terms of their lower gray matter content. We have calculated a function for the proportion of spinal cord made up of gray matter as a function of spinal cord weight in a variety of vertebrates, using data from Hovy (39) and Lassek and Rasmussen (55). The resulting function has approximately the same slope as that of Eq. 4
log y = 0.52 - 0.17 log SW (10)where y is the percent of the spinal cord consisting of gray matter and SW is the spinal cord weight in grams.
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