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Unformatted text preview: 1 Length of any side = 1L Area of any face = A A = L 2 Volume = V V = L 3 A = V 2/3 = L 2 Length of any side = 3L Area of any face = A = 9L 2 Volume = V = 27L 3 A = V 2/3 = 9L 2 In general: A In general: A ∝ L 2 , V , V ∝ L 3 , , and and A A ∝ V 2/3 2/3 Allometry is nothing more than a detailed analysis of the effects of scale, or size. L A = L 2 3L A = 9L 2 Allometry is nothing more than a detailed analysis of the effects of scale, or size. Allometric relationships are expressed as power functions, where a variable of interest, such as metabolic rate, is expressed as a power function of body size. Power functions are of the form: Y = aX b , where X is raised to the power b. Power functions are nonlinear and can be hard to visualize and manipulate. Log transformation is used to linearize power functions. From: Y = aX b To: log Y = log a + b(log x). The logtransformed equation describes a straight line. 2 y = x 2 R 2 = 1 50 100 150 200 250 300 350 400 5 10 15 20 Length Area y = x 3 R 2 = 1 1000 2000 3000 4000 5000 6000 7000 8000 5 10 15 20 Length Volume 1000 2000 3000 4000 5000 6000 7000 8000 5 10 15 20 Length Area or Volume y = 2x + 0 R 2 = 1 0.5 1 1.5 2 2.5 3 0.2 0.4 0.6 0.8 1 1.2 1.4 Log Length Log Area y = 3x + 0 R 2 = 1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.2 0.4 0.6 0.8 1 1.2 1.4 Log Length Log Volume 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.2 0.4 0.6 0.8 1 1.2 1.4 Log Length Log Area or Log Volume y = y = aX aX b log y = log a + b log X log y = log a + b log X log transformation J equation of a straight line Area = a ● (Length) 2 Log (Area) = Log (a) + 2 ● Log (Length) Volume = a ● (Length) 3 Log (Volume) = Log (a) + 3 ● Log (Length) y = x 2 R 2 = 1 50 100 150 200 250 300 350 400 5 10 15 20 Length Area y = x 3 R 2 = 1 1000 2000 3000 4000 5000 6000 7000 8000 5 10 15 20 Length Volume 1000 2000 3000 4000 5000 6000 7000 8000 5 10 15 20 Length Area or Volume...
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This note was uploaded on 08/18/2011 for the course ECOLOGY 351 taught by Professor Staff during the Spring '11 term at Rutgers.
 Spring '11
 Staff
 Ecology

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