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ABOUT BODY WEIGHT VERSUS BRAIN WEIGHT OF MAMMALS

Biometrics is the quantitative analysis of ontogenetic ("of or relating to life cycle or development") parameters such as height, weight, shape, morphology, age, etc. Biometrics is one key to understanding growth of individuals with time. Biometrics can also be applied to groups of organisms (such as a population of Douglas fir trees, or all butterflies, or all mammals) to gain insights into fundamental principles of growth or behavior in those groups.

Allison and Cicchetti (1976) provide data on body weight (in kilograms) and corresponding brain weight (in grams) for 62 different terrestrial mammals (no whales). Students should question the meaning of these pairs of numbers immediately. For example, there is only one pair of numbers for humans. Is this a single datum of a single human? Is this the mean of many measurements? Old or young, male or female, well fed or malnourished? The "human" in the table weighs 62 kilograms or 136 pounds; is this representative? In addition, these data were not collected by a single investigator, nor were they collected in the same manner, perhaps adding complexity.

The values of body weight range over 6 orders of magnitude. To represent data with such a wide range of values on a single graph requires logarithms. The plot of log body weight versus log brain weight shows a strong positive correlation, as to be expected.

A linear regression through the log-log data has a fairly high correlation coefficient, suggesting a good fit of a power law to the original ("unlogged") data. The slope of this line is less than 1, indicating a variable ratio of body to brain weight as a function of size of the mammal. The exponent less than 1 indicates that small mammals have relatively large brains compared to body size, probably because they have relatively large heads.

Despite taking the log of both variables, a large amount of scatter remains. Thus the best fit power law to these data will not have much predictive value; one would not use this empirical relationship to predict brain weight of a mammal for which only body weight was known. Your prediction might be off by an order of magnitude or more.

Mammals that plot above the best fit line have relatively large brains for their body size; monkeys, chimps, babboons and humans all plot well above the line. And in case you're feeling smug, so do ground squirrels. The opossum falls well below the line.

It would be interesting to see data for a single species, such as coyotes or rabbits.

Reference: Allison, T. and Cicchetti, D. V. (1976), Sleep in mammals: ecological and constitutional correlates; Science, v. 194, pp. 732-734.

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 Allison et al (1976), mammals brain and body weight body wt kg brain wt g log body log brain 6654.000 5712.00 3.82 3.76 1.000 6.60 0.00 0.82 3.385 44.50 0.53 1.65 0.920 5.70 -0.04 0.76 2547.000 4603.00 3.41 3.66 10.550 179.50 1.02 2.25 0.023 0.30 -1.64 -0.52 160.000 169.00 2.20 2.23 3.300 25.60 0.52 1.41 52.160 440.00 1.72 2.64 0.425 6.40 -0.37 0.81 465.000 423.00 2.67 2.63 0.550 2.40 -0.26 0.38 187.100 419.00 2.27 2.62 0.075 1.20 -1.12 0.08 3.000 25.00 0.48 1.40 0.785 3.50 -0.11 0.54 0.200 5.00 -0.70 0.70 1.410 17.50 0.15 1.24 60.000 81.00 1.78 1.91 529.000 680.00 2.72 2.83 27.660 115.00 1.44 2.06 0.120 1.00 -0.92 0.00 207.000 406.00 2.32 2.61 85.000 325.00 1.93 2.51 36.330 119.50 1.56 2.08 0.101 4.00 -1.00 0.60 1.040 5.50 0.02 0.74 521.000 655.00 2.72 2.82 100.000 157.00 2.00 2.20 35.000 56.00 1.54 1.75 0.005 0.14 -2.30 -0.85 0.010 0.25 -2.00 -0.60 62.000 1320.00 1.79 3.12 0.122 3.00 -0.91 0.48 1.350 8.10 0.13 0.91 0.023 0.40 -1.64 -0.40 0.048 0.33 -1.32 -0.48 1.700 6.30 0.23 0.80 3.500 10.80 0.54 1.03 250.000 490.00 2.40 2.69 0.480 15.50 -0.32 1.19 10.000 115.00 1.00 2.06 1.620 11.40 0.21 1.06 192.000 180.00 2.28 2.26 2.500 12.10 0.40 1.08 4.288 39.20 0.63 1.59 0.280 1.90 -0.55 0.28 4.235 50.40 0.63 1.70 6.800 179.00 0.83 2.25 0.750 12.30 -0.12 1.09 3.600 21.00 0.56 1.32 83.000 98.20 1.92 1.99 55.500 175.00 1.74 2.24 1.400 12.50 0.15 1.10 0.060 1.00 -1.22 0.00 0.900 2.60 -0.05 0.41 2.000 12.30 0.30 1.09 0.104 2.50 -0.98 0.40 4.190 58.00 0.62 1.76 3.500 3.90 0.54 0.59 4.050 17.00 0.61 1.23

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