# 异速生长

$y = kx^{a} \,\!$ 或是寫成對數形式： $\log y = a \log x + \log k\,\!$

$a$为公式的标度幂指数。估计此指数可从类型2回归，如主轴回归压轴回归分析来解释两变量的变化，与最小二乘法回归相反，它不解释自变量（如对数体重）的误差方差。其他方法包括测量误差模型和特别类型的主成分分析法

## 如何判定异速生长

Allometric relations show as straight lines when plotted on double-logarithmic axes

## 生理尺度生长

### 代谢率与体重

Max Kleiber 提出了下列异速生长方程来表述基础代谢率与动物体重间关系[14]，统计分析中其截距为70而斜率为0.75：

$\mathrm{Metabolic\ Rate} = 70 M^{0.75}$

$M$为体重，代谢率以千卡/天计。

• 生理因素影响

• 肌体机械因素影响

• 生境因素影响

## 参考资料

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2. ^ Damuth J. Scaling of growth: plants and animals are not so different. Proc. Natl. Acad. Sci. U.S.A. February 2001, 98 (5): 2113–4. Bibcode:2001PNAS...98.2113D. doi:10.1073/pnas.051011198. PMC 33381. PMID 11226197.
3. ^ Otto Snell. Die Abhängigkeit des Hirngewichts von dem Körpergewicht und den geistigen Fähigkeiten. Arch. Psychiatr. 1892, 23 (2): 436–446. doi:10.1007/BF01843462.
4. ^ Thompson, D'Arcy W. On Growth and Form Canto. Cambridge University Press. 1992. ISBN 978-0-521-43776-9.
5. ^ Huxley, Julian S. Problems of Relative Growth 2nd. New York: Dover. 1972. ISBN 0-486-61114-0.
6. ^ Emerson SB. Allometry and Jumping in Frogs: Helping the Twain to Meet. Evolution. September 1978, 32 (3): 551–564. JSTOR 2407721.
7. ^ Schmidt-Nielsen 1984
8. ^ Christian, A.; Garland, T., Jr.. Scaling of limb proportions in monitor lizards (Squamata: Varanidae) (PDF). Journal of Herpetology. 1996, 30 (2): 219–230. JSTOR 1565513.
9. ^ Pennycuick, Colin J. Newton Rules Biology. Oxford University Press. 1992: 111. ISBN 0-19-854021-3.
10. ^ Schmidt-Nielsen 1984，第237页
11. ^ Gibbings, J.C. Dimensional Analysis. Springer. 2011. ISBN 978-1-84996-317-6.
12. ^ 12.0 12.1 Hill, A.V. The dimensions of animals and their muscular dynamics. Science Progress. April 1950, 150 (4176): 820. Bibcode:1949Natur.164R.820. doi:10.1038/164820b0.
13. ^ Wilson RS, Franklin CE, James RS. Allometric scaling relationships of jumping performance in the striped marsh frog Limnodynastes peronii. J. Exp. Biol. June 2000, 203 (Pt 12): 1937–46. PMID 10821750.
14. ^ 14.0 14.1 14.2 Willmer, Pat. Environmental Physiology of Animals. Wiley-Blackwell. 2009.
15. ^ Burness, G. P.; Diamond, Jared; Flannery, Timothy. Dinosaurs, dragons, and dwarfs: The evolution of maximal body size. Proc. Natl. Acad. Sci. U.S.A. 2001, 98 (25): 14518–23. Bibcode:2001PNAS...9814518B. doi:10.1073/pnas.251548698. PMC 64714. PMID 11724953.