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Allometry

 

 
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Allometry
 
 
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Allometry is the study of the relationship between size
Size

The word size may refer to how big something is. In particular:* Measurement* Dimensions: length, width, height, diameter, perimeter, area, volume...
 and shape
Shape

The shape of an object located in some space is the part of that space occupied by the object, as determined by its external boundary ? abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties ....
,, first outlined by Otto Snell in 1892 and Julian Huxley
Julian Huxley

Sir Julian Sorell Huxley Fellow of the Royal Society was an English evolutionary biologist, Humanist and Internationalism . He was a proponent of natural selection, and a leading figure in the mid-twentieth century evolutionary synthesis....
 in 1932. Allometry is a well-known study, particularly in statistical shape analysis
Statistical shape analysis

Statistical shape analysis is a geometry analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathology bone shapes, etc....
 for its theoretical developments, as well as in biology
Biology

Biology is a branch of the natural sciences concerned with the study of living organisms and their interaction with each other and their environment ....
 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
Insect

Insects are the biggest class of arthropods and the only ones with wings. They are the most diverse group of animals on the planet. They are most diverse at the equator and their diversity declines toward the poles....
 species (e.g., the Hercules Beetle
Hercules beetle

The Hercules beetle is the most famous of the rhinoceros beetles. Native to the rainforests of central America and South America, they also can be found in coastal regions of North Carolina....
), 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.

Allometry studies shape differences in terms of ratio
Ratio

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....
s of the objects' dimensions.






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Allometry is the study of the relationship between size
Size

The word size may refer to how big something is. In particular:* Measurement* Dimensions: length, width, height, diameter, perimeter, area, volume...
 and shape
Shape

The shape of an object located in some space is the part of that space occupied by the object, as determined by its external boundary ? abstracting from other properties such as colour, content, and material composition, as well as from the object's other spatial properties ....
,, first outlined by Otto Snell in 1892 and Julian Huxley
Julian Huxley

Sir Julian Sorell Huxley Fellow of the Royal Society was an English evolutionary biologist, Humanist and Internationalism . He was a proponent of natural selection, and a leading figure in the mid-twentieth century evolutionary synthesis....
 in 1932. Allometry is a well-known study, particularly in statistical shape analysis
Statistical shape analysis

Statistical shape analysis is a geometry analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathology bone shapes, etc....
 for its theoretical developments, as well as in biology
Biology

Biology is a branch of the natural sciences concerned with the study of living organisms and their interaction with each other and their environment ....
 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
Insect

Insects are the biggest class of arthropods and the only ones with wings. They are the most diverse group of animals on the planet. They are most diverse at the equator and their diversity declines toward the poles....
 species (e.g., the Hercules Beetle
Hercules beetle

The Hercules beetle is the most famous of the rhinoceros beetles. Native to the rainforests of central America and South America, they also can be found in coastal regions of North Carolina....
), 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.

Allometry studies shape differences in terms of ratio
Ratio

A ratio is an expression which compares quantities relative to each other. The most common examples involve two quantities, but in theory any number of quantities can be compared....
s of the objects' dimensions. Two objects of different size but common shape will have their dimensions in the same ratio. Take, for example, a biological object that grows as it matures. Its size changes with age but the shapes are similar. Studies of ontogenetic allometry often use lizards or snakes as model organisms because they lack parental care after birth
Birth

Birth is the act or process of bearing or bringing forth offspring . The offspring is brought forth from the mother. Different forms of birth are oviparity, vivipary or Ovoviviparity....
 or hatching
Hatching

Hatching is an artistic technique used to create tonal or shading effects by drawing closely spaced parallel lines. When lines are placed at an angle to one another, it is called cross-hatching....
 and because they exhibit a large range of body size between the juvenile
Juvenile

Juvenile may refer to:*Juvenile or minor*Juvenile , American musician*Juvenile *Juvenile , a Japanese movie*"The Juvenile", a song by Jonas Berggren...
 and adult
Adult

The term adult has at least three distinct meanings. It can indicate a biologically grown or mature person. It may also mean a plant, animal, or person who has reached full growth or alternatively is capable of reproduction, or a person who has attained the legally fixed age of majority; as opposed to a minor....
 stage. Lizards often exhibit allometric changes during their ontogeny.

Allometric scaling

Allometric scaling's key equation for all of life equates Metabolic Rate P, to body mass W, raised to a power (4µ - 1)/4µ, where µ is percentage of capture by mass W of energy from oxidation reactions, for storage or expenditure. The equation models the rate at which electrical power needs to be captured, given the limitations of organic chemistry, by a biological system, in order to sustain itself for a duration. With metabolic rate expressed in calories/second, or watts (Joules/second), an extremely high metabolic rate, like that seen for masses less than one milligram at µ less than 15%, translates to many seconds, and long life for cells if the energy is available.

This scaling equation, when graphed for a range of values from e-13 to e+8 grams, and from -22 to 141% metabolic efficiency µ, clearly models the evolution of life to the extent that it was driven by metabolic considerations, that is, terms of bioenergetics
Bioenergetics

Bioenergetics is the subject of a field of biochemistry that concerns energy flow through living systems. This is an active area of Biology research that includes the study of thousands of different Cell processes such as cellular respiration and the many other metabolism processes that can lead to production and utilization of energy in for...
. This model clearly depicts how energy fluctuations were equilibrated by biological systems in such a way as to drive evolution. This model explains the difference between cancerous cells and stem cells in terms of proliferation and metabolic efficiency, how the former can be triggered to apoptosis
Apoptosis

Apoptosis is the process of programmed cell death that may occur in multicellular organisms. Programmed Cell death involves a series of biochemical events leading to a characteristic cell Morphology and death, in more specific terms, a series of biochemical events that lead to a variety of morphological changes, including Bleb , changes...
, and the proliferation of the latter can be extended, through the application of electrochemistry acting upon µ.

This equation models the mass increase of fat cells, and illustrates, in terms of metabolism and bioenergetics, how fat cells are related to the evolution of mammals by making prolonged in utero development possible. This equation clearly depicts why resort to dieting to reduce fat cell mass is a bad strategy, why increased activity levels is a good strategy, and how to increase muscle mass independently of muscle use.

This equation is not well understood even by its major proponents who, on the one hand, hint it might hold the secret to the aging process, and, on the other, believe that all metabolism is mass dependent, operates at 1000% µ, is the result of respiration, and is not anaerobic, or electrochemical. These beliefs have no variable in the equation to represent them, and even conflict with its terms. The denominator of µ is expressed in amperes. P is expressed in watts. W is expressed in grams mass, and the numerator of µ is the rate at which anabolic organic reactions are triggered by available amperes. The value for W is a reflection of the size and duration of working of the numerator, appearing as either growth or division.

In contrast, one refers to isometric scaling when growth does not lead to a change in geometry of an organism.

Further reading

  • Calder, W. A. 1984. Size, function and life history. Harvard University Press, Cambridge, Mass. 431 pp.
  • McMahon, T. A. and J. T. Bonner. 1983. On Size and Life. Scientific American
  • Niklas, K. J. 1994. Plant allometry: The scaling of form and process. University of Chicago Press, Chicago. 395 pp.
  • Peters, R. H. 1983. The ecological implications of body size. Cambridge University Press, Cambridge. 329 pp.
  • Reiss, M. J. 1991. The allometry of growth and reproduction. Cambridge University Press, Cambridge.182 pp.
  • Schmidt-Nielsen, K. 1984. Scaling: why is animal size so important? Cambridge University Press, Cambridge. 241 pp.


See also

  • Allometric law
    Allometric law

    An allometric law describes the relationship between two attributes of living organisms, and is usually expressed as a power-law:where is the scaling exponent of the law....
  • Constructal theory
    Constructal theory

    The constructal theory is the mental viewing that the generation of design in nature is a physics phenomenon that unites all animate and inanimate systems, and that this phenomenon is covered by the Constructal Law stated by Adrian Bejan in 1996:...
  • Evolutionary physiology
    Evolutionary physiology

    Evolutionary physiology is the study of physiological evolution, which is to say, the manner in which the functional characteristics of individuals in a population of organisms have responded to selection across multiple generations during the history of the population....
  • Metabolic theory of ecology
    Metabolic theory of ecology

    The metabolic theory of ecology is a theory that claims to explain the relationships between body mass and metabolic rate in organisms from unicellular microbes to plants and animals over 27 orders of magnitude, based on the physics and geometry of supply networks....
  • Phylogenetic comparative methods
    Phylogenetic comparative methods

    Phylogenetic comparative methods use information on the evolutionary relationships of organisms to compare species #Reference-Harvey-and-Pagel-1991 ....
  • Power law
    Power law

    A power law is a special kind of mathematical relationship between two quantities. If one quantity is the frequency of an event, the relationship is a power-law distribution, and the frequencies decrease very slowly as the size of the event increases....
     (also know as a scaling law)