Allometry
Allometry (Ancient Greek ἄλλος állos "other", μέτρον métron "measurement") is the study of the relationship of body size to shape,[1] anatomy, physiology and behaviour,[2] first outlined by Otto Snell in 1892,[3] by D'Arcy Thompson in 1917 in On Growth and Form[4] and by Julian Huxley in 1932.
[5] Allometry is a well-known study, particularly in statistical shape analysis for its theoretical developments, as well as in biology for practical applications to the differential growth rates of the parts of a living organism's body.
One application is in the study of various insect species (e.g., Hercules beetles), where a small change in overall body size can lead to an enormous and disproportionate increase in the dimensions of appendages such as legs, antennae, or horns.
Studies of ontogenetic allometry often use lizards or snakes as model organisms both because they lack parental care after birth or hatching and because they exhibit a large range of body sizes between the juvenile and adult stage.
In the case of above, the animal now has eight times the biologically active tissue to support, but the surface area of its respiratory organs has only increased fourfold, creating a mismatch between scaling and physical demands.
Similarly, the organism in the above example now has eight times the mass to support on its legs, but the strength of its bones and muscles is dependent upon their cross-sectional area, which has only increased fourfold.
If, after statistical analyses, for example, a volume-based property was found to scale to mass to the 0.9th power, then this would be called "negative allometry", as the values are smaller than predicted by isometry.
Conversely, if a surface area-based property scales to mass to the 0.8th power, the values are higher than predicted by isometry and the organism is said to show "positive allometry".
Log-log transformation places numbers into a geometric domain so that proportional deviations are represented consistently, independent of the scale and units of measurement.
Fit this to a power curve (depending on the stats program, this can be done multiple ways), and it will give an equation with the form: y=Zxn, where n is the number.
Overall metabolic rate in animals is generally accepted to show negative allometry, scaling to mass to a power of ≈ 0.75, known as Kleiber's law, 1932.
The straight line generated from a double logarithmic scale of metabolic rate in relation to body mass is known as the "mouse-to-elephant curve".
"[25] Max Kleiber contributed the following allometric equation for relating the BMR to the body mass of an animal.
The challenge with this lies in the fact that a shared environment also indicates a common evolutionary history and thus a close taxonomic relationship.
There are strides currently in research to overcome these hurdles; for example, an analysis in muroid rodents,[24] the mouse, hamster, and vole type, took into account taxonomy.
[31][32][33][34] Such research has been done in pursuit of a better understanding of animal locomotion, including the factors that different gaits seek to optimize.
[34] Allometric trends observed in extant animals have even been combined with evolutionary algorithms to form realistic hypotheses concerning the locomotive patterns of extinct species.
[33] These studies have been made possible by the remarkable similarities among disparate species' locomotive kinematics and dynamics, "despite differences in morphology and size".
[31] Allometric study of locomotion involves the analysis of the relative sizes, masses, and limb structures of similarly shaped animals and how these features affect their movements at different speeds.
[34] Patterns are identified based on dimensionless Froude numbers, which incorporate measures of animals' leg lengths, speed or stride frequency, and weight.
Dynamically similar gaits are those between which there are constant coefficients that can relate linear dimensions, time intervals, and forces.
The hypothesis itself is as follows: "animals of different sizes tend to move in dynamically similar fashion whenever the ratio of their speed allows it."
While the dynamic similarity hypothesis may not be a truly unifying principle of animal gait patterns, it is a remarkably accurate heuristic.
For example, plasma concentration of carotenoids scales to the three-quarter power of mass in nine predatory and scavenger raptor species.
[36] West, Brown, and Enquist in 1997 derived a hydrodynamic theory to explain the universal fact that metabolic rate scales as the 3⁄4 power with body weight.
G. A. Steven observed and documented dolphins moving at 15 knots alongside his ship leaving a single trail of light when phosphorescent activity in the sea was high.
[41] This shows that mammals, regardless of size, have similarly scaled respiratory and cardiovascular systems and the same relative amount of blood: about 5.5% of body mass.
This means that for similarly designed marine mammals, a larger individual can travel more efficiently, as it takes the same effort to move one body length.
GDP, "supercreative" employment, number of inventors, crime, spread of disease,[25] and even pedestrian walking speeds[44] scale with city population.
Bettencourt’s model suggests that superlinear scaling arises from the quadratic growth of social interactions with population size under budget constraints.
