Testing models of biological scaling with mammalian population densities

Two hypotheses have been suggested to explain the form of interspecific scaling of organismal characteristics to body size, such as the well-known increase in total metabolism with body mass. A hypothesis based on simple Euclidean geometry suggests that the scaling of many biological variables to body size should have a scaling exponent of 2/3, or approximate to0.667. On the other hand, according to a hypothesis based on fractal dimensions, the relationship between biological variables and body mass should have a scaling exponent of 0.750. We conducted a power analysis of the predicted exponents of scaling under the Euclidean and fractal hypotheses, using average adult body masses and population densities collected from the published literature on mammalian species. The collected data reflect 987 mammal populations from a broad variety of terrestrial habitats. Using statistical methods we determined the sample sizes required to decide between the values of the scaling exponent of the density-to-mass relationship based on the Euclidean (-0.667) and fractal (-0.750) hypotheses. Non-linearities in the dataset and insufficient power plagued our tests of the predictions. We found that mammalian species weighing less than 100 kg had a linear scaling pattern, sufficient power to reveal a difference between the scaling coefficients -0.667 and -0.750, and an actual scaling coefficient of -0.719 (barely significantly different from -0.667 but not from -0.750). Thus, our results support the fractal hypothesis, though the support was not particularly strong, which suggests that the relationship between body mass and population density should have a scaling exponent of -0.750.PT: J; CR: BANAVAR JR, 1999, NATURE, V399, P130 BLACKBURN TM, 1997, J ANIM ECOL, V66, P233 BROWN JH, 1998, BIOGEOGRAPHY CALDER WA, 1984, SIZE FUNCTION LIFE H COTGREAVE P, 1995, FUNCT ECOL, V9, P285 CURRIE DJ, 1993, OIKOS, V66, P353 CURRIE DJ, 1993, OIKOS, V67, P56 DAMUTH J, 1981, NATURE, V290, P699 DAMUTH J, 1987, BIOL J LINN SOC, V31, P193 DAMUTH J, 1993, NATURE, V365, P748 DOWSETT RJ, 1966, PUKU, V4, P135 DUTOIT JT, 1989, AM NAT, V133, P736 EISENBHERG JF, 1981, MAMMALIAN RAD ANAL T ENQUIST BJ, 1998, NATURE, V395, P163 ENQUIST BJ, 1999, NATURE, V401, P907 GRIFFITHS D, 1987, NATURE, V328, P117 GRIFFITHS D, 1998, J ANIM ECOL, V67, P795 HARVEY PH, 1991, COMP METHOD EVOLUTIO KELT DA, 1999, ECOLOGY, V80, P337 LAWTON JH, 1989, OIKOS, V55, P429 MARQUET PA, 1990, SCIENCE, V250, P1125 MARQUET PA, 1995, J ANIM ECOL, V64, P325 MARQUET PA, 1998, EVOL ECOL, V12, P127 MCMAHON TA, 1976, J THEOR BIOL, V59, P443 MONTFORT A, 1972, TERRE VIE, V26, P216 NIKLAS KJ, 2001, P NATL ACAD SCI USA, V98, P2922 NOWAK RM, 1991, WALKERS MAMMALS WORL, V1 NOWAK RM, 1991, WALKERS MAMMALS WORL, V2 PETERS RH, 1983, ECOLOGICAL IMPLICATI PETERS RH, 1983, OECOLOGIA, V60, P89 PETERS RH, 1984, AM NAT, V124, P498 PIMM SL, 1991, BALANCE NATURE ECOLO POLISHCHUK LV, 1999, OIKOS, V86, P544 ROBINSON JG, 1986, AM NAT, V128, P665 SCHMIDTNIELSON K, 1984, SCALING WHY IS ANIMA SILVA M, 1995, AM NAT, V145, P704 SILVA M, 1995, CRC HDB MAMMALIAN BO SILVA M, 1997, J ANIM ECOL, V66, P327 SILVA M, 2001, GLOBAL ECOL BIOGEOGR, V10, P469 WEST GB, 1997, SCIENCE, V276, P122 WEST GB, 1999, SCIENCE, V284, P1677 WESTOBY M, 1995, J ECOL, V83, P531 WESTOBY M, 1995, J ECOL, V83, P727 WESTOBY M, 1995, J ECOL, V83, P892; NR: 44; TC: 4; J9: CAN J ZOOL; PG: 8; GA: 698CTSource type: Electronic(1