SKELETON WEIGHT ALLOMETRY IN AQUATIC AND TERRESTRIAL VERTEBRATES

William W. REYNOLDS

Department of Biology, The pennsylvania State University, Wilkes-Barre, Pennsylvania 187o8, U .S.A .

Received March 14, 1977

Keywords : allometry, skeleton weight, vertebrates, whales, fishes, bones, evolution .

Abstract

The relation of skeleton weight to body weight with increasingsize is compared for aquatic and terrestrial vertebrates . Due tothe buoyancy of water, the skeleton weights of aquatic vertebrates(fishes and whales) vary in nearly direct proportion (exponent i .o)to body weight ; while the skeletons of terrestrial vertebrates occu-py an increasingly greater proportion of total body weight as sizeincreases (exponent greater than i . i) due to the necessity of sup-porting their weight on land.

Because the strength of a bone (or muscle) is proportionalto its cross-sectional area (a square function), while bodyweight or mass (including that of the skeleton itself) isproportional to volume (a cube function)-assumingequal density-the proportions of terrestrial animals tendto change with increasing size (Galileo, 1638) . Within alimited size range, as for example within felids (Davis,1962) or primates (Schultz, 1962), animals of a similarshape can be scaled up in size, but at larger sizes theseanimals will have a reduced skeletal safety factor (Davis,1962; Currey, 1967; Hill, 1950). Major size increases mayprecede compensating morphological changes predictedby mechanical analysis (Szarski, 1964), but over the longrun of evolution, preservation of shape is not the antici-pated result of an increase in size (Hill, 1950 ; Gould, 1971) .Larger animals must change their shape in order to func-tion as well as smaller animals on land (Galileo, 1638 ;Hill, 1950 ; Gould, 1971) . However, changes in shape havetheir limitations, as there must be an overall increase inthe proportion of the total body weight contributed by

Dr. W. Junk b . v. Publishers - The Hague, The Netherlands

Hydrobiologia vol . 56, 1, pag. 35-37, 1977

the skeleton to compensate for decreasing surface/vol-ume ratios and safety factors, at some point placing anultimate upper limit on the body weight of a terrestrialanimal (Thompson, 1942; Hill, 1950 ; Currey, 1967 ;Schmidt-Nielsen, 1972 ; McMahon, 1973; Reynolds &Karlotski, 1977) . However, aquatic animals are largelyfree of these constraints because of the buoyant effect ofwater (Galileo, 1638 ; Thompson, 1942 ; Reynolds & Kar-lotski, 1977), since gravity is effectively neutralized andthe skeleton does not support the weight of the animal,although it aids in locomotion by providing leverage forthe muscles.

In comparing the overall skeletal allometry of aquaticversus terrestrial vertebrates, it is preferable to use datafrom adults of many species covering as wide a size rangeas possible, as the best basis for broad generalizations .Intraspecific comparisons of young and adult animalsare complicated by considerable ontogenetic allometryresulting from developmental constraints (Donaldson,1919; Gould, 1971) ; while on the other hand, a series ofclosely related species can differ in size with little allo-metry (Davis, 1962) .

Skeletons of bony fishes (Table i ; data from Reynolds& Karlotski, 1977) vary in weight nearly in proportion tothe first power (exponent 1 .0) of body weight (i .e ., directproportionality, with no allometry), according to theequation

WS = 0 .033 Wt'03 or,

l 09 W, = - I .4794 + 1 .029710g W1 ,Where W, = skeleton weight (mass) in g, and W t = totalbody weight in g . The 95%o confidence interval for theslope (± 0.07) includes 1 .0 (Table i). By contrast, theslopes for terrestrial mammals, birds and reptiles exceed

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Table i . Logarithmic equation slope and intercept values, with95% confidence limits, correlation coefficients (r), ranges of bodyweight values (Wt ), and data sources for skeleton weight allo-metry of aquatic and terrestrial vertebrates . The equation is ofthe form log W9 = (intercept) + (slope) log We , where W9 is skele-ton weight (g) and W2 is body weight (g) .

TTh high intercept 0.111. probably ceflede doe difficulty of properly ckmdng whale ekAetone ; the other ekektone were ree0cleared end dried.

•

Intneprcdk data foryerromyaoa rn .Elms; total ark content weight . ' •lnrnay,oBk data for Cyanf11rnd,-,

i . i ( Table i), with 95% confidence limits that do not in-clude 1 .o, a clear indication of the expected allometry(data from Kayser & Heusner, 1964 ; Schmidt-Nielsen,1972; Ultsch, 1974; Prange & Christman, 1976; Reynolds& Karlotski, 1977). This implies that some upper limitmust be reached beyond which the skeleton itself occupiesan unacceptably high percentage of total body weight,weighing too much to be moved by the muscles, andlosing the race between weight (volume) and strength(cross-sectional area) . The y intercepts for these data(Table 1), based on clean, dry skeletal weights relative tofresh (wet) body weights, are about -1 .5 .

Niimi (1974) has presented intraspecific allometricdata for total ash content by weight of three aquatic verte-brates. His slope and intercept data for a soft-rayed (Sal-

mo gairdneri) and a spiny-rayed (Micropterus salmoides)bony fish neatly bracket the interspecific bony fish skele-ton weight data (Reynolds & Karlotski, 1977) in Table 1,indicating that ash content largely reflects dry skeletonweight . Niimi (1974) also gives intraspecific ash weightdata for the sea lamprey Petromyzon marinus, a primi-tive jawless fish with a cartilaginous skeleton . The slopefor the lamprey, as for other fishes, is close to i (Table 1),while the low intercept value (about -2) is a reflection ofthe cartilaginous skeleton .

Whales are the largest living vertebrates, reaching abody weight of 2 x 1o8 g (Lockyer, 1976). Large dinosaursreached a maximum body weight of about 4 x Io' g(Bakker, 1975), and Romer (1967) questioned whetherthe largest of these could have been fully terrestrial. Hill(1950) notes that grounded whales often break ribs andsuffocate under their own weight . Because whales exceedby approximately an order of magnitude the weight ofthe largest known terrestrial animals, it is reasonable toinfer that they are comparatively free of size constraintsimposed by the necessity of supporting weight on land .

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An additional point of interest is that, although whalesare fully aquatic, they have presumably evolved fromterrestrial mammals . For these reasons, it is particularlyworthwhile to study the skeleton weight allometry ofthese largest of all vertebrates .

Recently Lockyer (1976) has compiled skeletal andbody weights of large whales ranging from 4 .2 x 106 to 1 .9x 10 8 g. Due to the difficulty of properly cleaning theselarge skeletons, the skeleton weights are not for well-cleaned dry skeletons (Lockyer, 1976) as for the other ver-tebrates in Table 1, and this is reflected in the high inter-cept value (- .95) . The slope (1 .0174) for whale skeletons is,however, similar to that for fishes (Table i) . The 95%confidence interval (± 0 .05) includes i .o but not I .1, in-dicating that environmental influences have prevailedover phylogenetic ones, preserving the basic .dichotomyof skeleton weight allometry between terrestrial andaquatic vertebrates, and confirming the effect of waterbuoyancy on skeletal allometry .

References

Bakker, R. T . 1975. Dinosaur renaissance . Sci. Amer. 232 : 58 - 79 .Currey, J . D. 1967 . The failure of exoskeletons and endoskele-

tons . J . Morph. 123 : 1-16 .Davis, D. D. 1962 . Allometric relationships in lions vs . domestic

cats . Evolution 16: 505-514 .Donaldson, H . H . 1919 . Quantitative studies on the growth of the

skeleton in the albino rat . Amer. J. Anat . 26 : 237-314.Galileo, G. L . 1638 . Dialogues concerning two new sciences,

Transl. by H . Crew and A . De Salvio (1933), Macmillan, NewYork . .

Gould, S . J . 1971 . Geometric similarity in allometric growth : acontribution to the problem of scaling in the evolution of size .Amer. Nat . 105 :113-136 .

Hill, A . V. 195o . The dimensions of animals and their musculardynamics . Sci. Progr. 38 : 209-229.

Kayser, C. & Heusner, A. 1964 . Etude comparative du metabo-lisme bnerg6tique dans la sbrie animale . J . Physiol . 56 : 489-524 .

Lockyer, C. 1976 . Body weights of some species of large whales .J . Cons . Int . Explor. Mer 36: 259-273 .

McMahon, T. 1973 . Size and shape in biology . Science 179 : 1201-1204 .

Niimi, A . J . 1974 . Relationship between ash content and bodyweight in lamprey (Petromyzon marinus), trout (Salmogairdneri) and bass (Micropterus salmoides) . Copeia 1974 :794-795 .

Prange, H . D. & Christman, S. P . 1976 . The allometrics ofrattlesnake skeletons. Copeia 1976: 542 - 545 .

Reynolds, W . W. & Karlotski, W . J . 1977 . The allometric re-lationship of skeleton weight to body weight in teleost fishes : apreliminary comparison with birds and mammals . Copeia1977 : 16o-163 .

Anikal Type Intercept 95% c.i. Stop. 95% c .i. r W,(g) 8-

Aquatic.WIWe, -0 .9540• 0.3768 1 .0174 4 .0500 0 .991 101-10' Lockyer(1976)Bent, Other -1 .4797 00.1557 1 .0297 .0 .0689 0 .996 3 .1200 ReyooldeW Keololeki (1977)Iampnye• • -2 .0203 0 .9686 .0 .0176 1-1000 N4mi(1974)

TI-1W.Mummele -1 .5059 0.1496 1 .1230 0.0420 0 .999 6-10• RrynnWe&K01ateki(1977)Bhde -1 .5272 :0.1307 1 .1193 .0.0652 0 .993 3.953 ReymW/&Kenlateki(1977)Snakes•• • -( .699 1 .174 0.993 48-3300 preege&Cluhtman(1976)

Romer, A . S . 1967 . The Vertebrate Story . Univ. Chicago Press,Chicago .

Schmidt-Nielsen, K . 1972. How Animals Work . CambridgeUniv. Press, Cambridge .

Schultz, A . H . 1962 . The relative weights of the skeletal parts inadult primates . Amer . J . Phys . Anthropol ., n .s ., 20: 1-10 .

Szarski, H . 1964 . The structure of respiratory organs in relation tobody size in Amphibia . Evolution 18 : 118-126.

Thompson, D. W. 1942. On Growth and Form . CambridgeUniv. Press, Cambridge .

Ultsch, G . R . 1974. The allometric relationship between meta-bolic rate and body size : role of the skeleton . Amer . Midl . Nat .92 : 500-504.

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