Notice that 1 is a power function not an exponential equation the constant d is in the exponent position instead of the variable s. Unlike other applications where we need logarithms to help us solve the equation, here we use logarithms to simplify the allometric equation into a linear equation. We rewrite 1 as a logarithmic equation of the form,.
Therefore, transforming an allometric equation into its logarithmic equivalent gives rise to a linear equation. By rewriting the allometric equation into a logarithmic equation, we can easily calculate the values of the constants c and d from a set of experimental data. If we plot log s on the x -axis and log f on the y -axis, we should see a line with slope equal to d and y- intercept equal to log c.
We call such a plot a log-log plot. Because allometric equations are derived from empirical data, one should be cautious about data scattered around a line of best fit in the xy -plane of a log-log plot. Small deviations from a line of best fit are actually larger than they may appear.
Remember, since the x and y variables are on the logarithmic scale, linear changes in the output variables x and y correspond to exponential changes in the input variables f s and s. Since we are ultimately interested in a relationship between f and s , we need to be concerned with even small deviations from a line of best fit.
Now let's go back to our fiddler crab as a concrete example. If you never thought that sex appeal could be calculated mathematically, think again. Allometric scaling relationships can be described using an allometric equation of the form,.
The variables s and f s represent the two different attributes that we are comparing e. Calder, W. Size, Function and Life History. Cheverud, J. Relationships among ontogenetic, static, and evolutionary allometry. American Journal of Physiological Anthropology 59 , Cooper, S. Gayon, J. History of the concept of allometry. American Zoologist 40 , Gould, S.
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Citation: Shingleton, A. Nature Education Knowledge 3 10 Allometry is the study of how these processes scale with body size and with each other, and the impact this has on ecology and evolution.
Aa Aa Aa. Allometry and Relative Growth. Figure 1: The allometric relationship between chela claw size and body size in growing male fiddler crab Uca pugnax.
The red lines show the measurements made on the crab. Adapted from Moore ; Data from Thompson Broadening the Concept of Allometry. Figure 3: The relationship between ontogenetic, static and evolutionary allometry.
A The relationship between ontogenetic and static allometry. Figure 4: The morphological effects of changing the intercept and slope of a static allometry. Butterflies A through E are hypothetical butterfly species that vary in their wing-body static allometries.
Morphological Allometry and the Evolution of Body Form. Figure 5: The evolutionary allometry between metabolism and body size in marsupials and eutherian mammals. The allometry has the same slope but a different intercept for marsupial compared to eutherian mammals, indicating a generally lower metabolism in the former.
References and Recommended Reading Bonner, J. Kleiber, M. Body size and metabolism. Hilgardia 6 , One common method for predicting human doses is allometric scaling. In allometric scaling, PK data from nonclinical studies in one or more animal species are used to predict human drug exposure for a range of drug doses. This is a rapid method that can inform dosing decisions or determine if it is worthwhile to progress a particular therapeutic compound.
In addition to predicting human exposure from nonclinical studies, allometric scaling can also be used when moving between species as the nonclinical program develops. It can also be used to predict drug doses for pediatric populations by using data from adults. Allometric Scaling Services. Allometric scaling is one of the tools that drug developers use to predict human PK based upon animal data.
This is important information for both drug developers and regulators like the FDA because it provides a data-driven foundation for establishing a safe starting dose in humans.
In biology, the basis of allometric scaling lies in the relationship between metabolic rate defined as the rate of biological life processes and metabolism and the body size of the animal.
The metabolic rate that is used in allometry includes life processes such as number of heart beats or number of breaths in the lifespan of the animal as a function of size. It is critical to understand that as body size increases from one animal species to another, metabolism slows down.
To exploit this, allometric scaling uses mathematical models to describe physiological, anatomical, and biochemical changes in animals as their size changes. Of specific interest for drug development, this approach can predict important PK information for humans using experiments conducted in various animal species. Allometric scaling is frequently used in drug development to inform strategies for first-in-human studies. This includes:. There are several allometric methods that can be used to predict human drug exposure from nonclinical data.
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