# Allometry definition, equations and examples

2786
Simon Doyle

The allometry, Also called allometric growth, it refers to the differential growth rate in various parts or dimensions of organisms during the processes involved in ontogeny. Likewise, it can be understood in phylogenetic, intra and interspecific contexts..

These changes in the differential growth of the structures are considered local heterochronies and play a fundamental role in evolution. The phenomenon is widely distributed in nature, both in animals and plants.

Article index

• 1 Fundamentals of growth
• 2 Definitions of allometry
• 3 Equations
• 3.1 Graphic representation
• 3.2 Interpretation of the equation
• 4 Examples
• 4.1 The claw of the fiddler crab
• 4.2 The wings of bats
• 4.3 Limbs and head in humans
• 5 References

## Growth fundamentals

Before establishing the definitions and implications of allometric growth, it is necessary to remember key concepts of the geometry of three-dimensional objects..

Let's imagine we have a cube of edges L. Thus, the surface of the figure will be 6Ltwo, while the volume will be L3. If we have a cube where the edges are twice those of the previous case, (in notation it would be 2L) the area will increase by a factor of 4, and the volume by a factor of 8.

If we repeat this logical approach with a sphere, we will obtain the same relationships. We can conclude that the volume grows twice the area. In this way, if we have that the length increases 10 times, the volume will have increased 10 times more than the surface.

This phenomenon allows us to observe that when we increase the size of an object - whether it is alive or not - its properties are modified, since the surface will vary differently than the volume..

The relationship between surface and volume is stated in the principle of similarity: "similar geometric figures, the surface is proportional to the square of the linear dimension, and the volume is proportional to the cube of it".

## Definitions of allometry

The word "allometry" was proposed by Huxley, in 1936. Since that time a series of definitions have been developed, focused from different points of view. The term comes from griella roots allos that they mean another, and metron what does measure mean.

The famous biologist and paleontologist Stephen Jay Gould defined allometry as "the study of changes in proportions correlated with variations in size".

Allometry can be understood in terms of ontogeny - when relative growth occurs at the level of the individual. Similarly, when differential growth takes place in several lineages, allometry is defined from a phylogenetic perspective.

Likewise, the phenomenon can occur in populations (at the intraspecific level) or, between related species (at the interspecific level)..

## Equations

Several equations have been proposed to evaluate the allometric growth of the different structures of the body..

The most popular equation in the literature to express allometries is:

y = bxto

In the expression, x Y and and are two measurements of the body, for example, weight and height or the length of a member and the length of the body.

In fact, in most studies, x it is a measure related to body size, such as weight. Thus, it seeks to show that the structure or measure in question has changes disproportionate to the total size of the organism.

The variable to It is known in the literature as an allometric coefficient, and it describes the relative growth rates. This parameter can take different values.

If it is equal to 1, the growth is isometric. This means that both structures or dimensions evaluated in the equation grow at the same rate.

In case the value assigned to the variable Y has a growth greater than that of x, the allometric coefficient is greater than 1, and it is said that there is positive allometry.

In contrast, when the above relationship is opposite, the allometry is negative and the value of to takes values ​​less than 1.

### Graphic representation

If we take the previous equation to a representation in the plane, we will obtain a curvilinear relationship between the variables. If we want to obtain a graph with a linear trend we must apply a logarithm in both greetings of the equation.

With the aforementioned mathematical treatment, we will obtain a line with the following equation: log y = log b + a log x.

### Interpretation of the equation

Suppose we are evaluating an ancestral form. The variable x represents the body size of the organism, while the variable Y represents the size or height of some characteristic that we want to evaluate, whose development begins at age to and stop growing in b.

The processes related to heterochronies, both pedomorphosis and peramorphosis result from evolutionary changes in any of the two parameters mentioned, either in the rate of development or in the duration of development due to changes in the parameters defined as to or b.

## Examples

### The claw of the fiddler crab

Allometry is a widely distributed phenomenon in nature. The classic example of positive allometry is the fiddler crab. These are a group of decapod crustaceans belonging to the genus Uca, being the most popular species Uca pugnax.

In young males, the claws correspond to 2% of the animal's body. As the individual grows, the caliper grows disproportionately in relation to the overall size. Eventually the clamp can reach up to 70% of body weight.

### The wings of bats

The same positive allometry event occurs in the phalanges of bats. The forelimbs of these flying vertebrates are homologous to our upper limbs. Thus, in bats, the phalanges are disproportionately long.

To achieve a structure of this category, the growth rate of the phalanges had to increase in the evolutionary evolution of the bats..

### Limbs and head in humans

In us humans, there are also allometries. Let's think about a newborn baby and how parts of the body will vary in terms of growth. The limbs lengthen more during development than other structures, such as the head and trunk.

As we see in all the examples, allometric growth significantly alters the proportions of bodies during development. When these rates are modified, the shape of the adult changes substantially.

## References

1. Alberch, P., Gould, S. J., Oster, G. F., & Wake, D. B. (1979). Size and shape in ontogeny and phylogeny. Paleobiology5(3), 296-317.
2. Audesirk, T., & Audesirk, G. (2003). Biology 3: evolution and ecology. Pearson.
3. Curtis, H., & Barnes, N. S. (1994). Invitation to biology. Macmillan.
4. Hickman, C. P., Roberts, L. S., Larson, A., Ober, W. C., & Garrison, C. (2001). Integrated principles of zoology. McGraw-Hill.
5. Kardong, K. V. (2006). Vertebrates: comparative anatomy, function, evolution. McGraw-Hill.
6. McKinney, M. L., & McNamara, K. J. (2013). Heterochrony: the evolution of ontogeny. Springer Science & Business Media.

Chemistry
3481
Basil Manning