Allometry is the study of the relationship of body size to shape,[1] anatomy, physiology and finally 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]

Elephant skeleton
Skeleton of an elephant
Dasyurus maculatus skeleton
Skeleton of a tiger quoll (Dasyurus maculatus).

The proportionately thicker bones in the elephant are an example of allometric scaling


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[6] The relationship between the two measured quantities is often expressed as a power law equation which expresses a remarkable scale symmetry:[7]

or in a logarithmic form:

where is the scaling exponent of the law. Methods for estimating this exponent from data can use type-2 regressions, such as major axis regression or reduced major axis regression, as these account for the variation in both variables, contrary to least squares regression, which does not account for error variance in the independent variable (e.g., log body mass). Other methods include measurement-error models and a particular kind of principal component analysis.

Allometry often studies shape differences in terms of ratios 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 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. Lizards often exhibit allometric changes during their ontogeny.[8]

In addition to studies that focus on growth, allometry also examines shape variation among individuals of a given age (and sex), which is referred to as static allometry.[9] Comparisons of species are used to examine interspecific or evolutionary allometry (see also: Phylogenetic comparative methods).

Isometric scaling and geometric similarity

Scaling range for different organisms[10]
Group Factor Length range
Insects 1000 10-4 to 10-1 m
Fish 1000 10-2 to 10+1 m
Mammals 1000 10-1 to 10+2 m
Vascular plants 10,000 10-2 to 10+2 m
Algae 100,000 10-5 to 100 m

Isometric scaling happens when proportional relationships are preserved as size changes during growth or over evolutionary time. An example is found in frogs — aside from a brief period during the few weeks after metamorphosis, frogs grow isometrically.[11] Therefore, a frog whose legs are as long as its body will retain that relationship throughout its life, even if the frog itself increases in size tremendously.

Isometric scaling is governed by the square-cube law. An organism which doubles in length isometrically will find that the surface area available to it will increase fourfold, while its volume and mass will increase by a factor of eight. This can present problems for organisms. 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. Therefore, this hypothetical organism would experience twice the bone and muscle loads of its smaller version. This mismatch can be avoided either by being "overbuilt" when small or by changing proportions during growth, called allometry.

Isometric scaling is often used as a null hypothesis in scaling studies, with 'deviations from isometry' considered evidence of physiological factors forcing allometric growth.

Allometric scaling

Allometric scaling is any change that deviates from isometry. A classic example discussed by Galileo in his Dialogues Concerning Two New Sciences is the skeleton of mammals. The skeletal structure becomes much stronger and more robust relative to the size of the body as the body size increases.[12] Allometry is often expressed in terms of a scaling exponent based on body mass, or body length (Snout-vent length, total length etc.). A perfectly isometrically scaling organism would see all volume-based properties change proportionally to the body mass, all surface area-based properties change with mass to the power of 2/3, and all length-based properties change with mass to the power of 1/3. 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". One example of positive allometry occurs among species of monitor lizards (family Varanidae), in which the limbs are relatively longer in larger-bodied species.[13] The same is true for some fish, e.g. the muskellunge, the weight of which grows with about the power of 3.325 of its length.[14] A 30-inch (76 cm) muskellunge will weigh about 8 pounds (3.6 kg), while a 40-inch (100 cm) muskellunge will weigh about 18 pounds (8.2 kg), so 33% longer length will more than double the weight.

Determining if a system is scaling with allometry

To determine whether isometry or allometry is present, an expected relationship between variables needs to be determined to compare data to. This is important in determining if the scaling relationship in a dataset deviates from an expected relationship (such as those that follow isometry). The use of tools such as dimensional analysis is very helpful in determining expected slope.[15][16][17] This ‘expected’ slope, as it is known, is essential for detecting allometry because scaling variables are comparisons to other things. Saying that mass scales with a slope of 5 in relation to length doesn’t have much meaning unless knowing the isometric slope is 3, meaning in this case, the mass is increasing extremely fast. For example, different sized frogs should be able to jump the same distance according to the geometric similarity model proposed by Hill 1950[18] and interpreted by Wilson 2000,[19] but in actuality larger frogs do jump longer distances. Dimensional analysis is extremely useful for balancing units in an equation or in this case, determining expected slope.

A few dimensional examples follow (M=Mass, L=Length, V=Volume, which is also L cubed because a volume is merely length cubed):

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

To find the expected slope for the relationship between mass and the characteristic length of an animal (see figure), the units of mass (M=L3, because mass is a volume; volumes are lengths cubed) from the Y-axis are divided by the units of the X-axis (in this case, L). The expected slope on a double-logarithmic plot of L3/ L1 in this case is 3 (log10(L3)/log10(L1)=3). This is the slope of a straight line, but most data gathered in science do not fall neatly in a straight line, so data transformations are useful. It is also important to keep in mind what is being compared in the data. Comparing a characteristic such as head length to head width might yield different results from comparing head length to body length. That is, different characteristics may scale differently.[20]

A common way to analyze data such as those collected in scaling is to use log-transformation. There are two reasons for log transformation - a biological reason and a statistical reason. Biologically, log-log transformation places numbers into a geometric domain so that proportional deviations are represented consistently, independent of the scale and units of measurement. In biology this is appropriate because many biological phenomena (e.g. growth, reproduction, metabolism, sensation) are fundamentally multiplicative.[21] Statistically, it is beneficial to transform both axes using logarithms and then perform a linear regression. This will normalize the data set and make it easier to analyze trends using the slope of the line.[22] Before analyzing data though, it is important to have a predicted slope of the line to compare the analysis to.

After data are log-transformed and linearly regressed, comparisons can then use least squares regression with 95% confidence intervals or reduced major axis analysis. Sometimes the two analyses can yield different results, but often they do not. If the expected slope is outside the confidence intervals, then there is allometry present. If mass in this imaginary animal scaled with a slope of 5 and this was a statistically significant value, then mass would scale very fast in this animal versus the expected value. It would scale with positive allometry. If the expected slope were 3 and in reality in a certain organism mass scaled with 1 (assuming this slope is statistically significant), then it would be negatively allometric.

Another example: Force is dependent on the cross-sectional area of muscle (CSA), which is L2. If comparing force to a length, then the expected slope is 2. Alternatively, this analysis may be accomplished with a power regression. Plot the relationship between the data onto a graph. 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. That “number” is the relationship between the data points. The downside, to this form of analysis, is that it makes it a little more difficult to do statistical analyses.

Physiological scaling

Many physiological and biochemical processes (such as heart rate, respiration rate or the maximum reproduction rate) show scaling, mostly associated with the ratio between surface area and mass (or volume) of the animal.[7] The metabolic rate of an individual animal is also subject to scaling.

Metabolic rate and body mass

In plotting an animal's basal metabolic rate (BMR) against the animal's own body mass, a logarithmic straight line is obtained, indicating a power-law dependence. 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. This means that larger-bodied species (e.g., elephants) have lower mass-specific metabolic rates and lower heart rates, as compared with smaller-bodied species (e.g., mice). 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".[23] These relationships of metabolic rates, times, and internal structure have been explained as, "an elephant is approximately a blown-up gorilla, which is itself a blown-up mouse."[24]

Max Kleiber contributed the following allometric equation for relating the BMR to the body mass of an animal.[23] Statistical analysis of the intercept did not vary from 70 and the slope was not varied from 0.75, thus:

(although the universality of this relation has been disputed both empirically and theoretically [25][26])

where is body mass, and metabolic rate is measured in kcal per day.

Consequently, the body mass itself can explain the majority of the variation in the BMR. After the body mass effect, the taxonomy of the animal plays the next most significant role in the scaling of the BMR. The further speculation that environmental conditions play a role in BMR can only be properly investigated once the role of taxonomy is established. 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,[23] the mouse, hamster, and vole type, took into account taxonomy. Results revealed the hamster (warm dry habitat) had lowest BMR and the mouse (warm wet dense habitat) had the highest BMR. Larger organs could explain the high BMR groups, along with their higher daily energy needs. Analyses such as these demonstrate the physiological adaptations to environmental changes that animals undergo.

Energy metabolism is subjected to the scaling of an animal and can be overcome by an individual's body design. The metabolic scope for an animal is the ratio of resting and maximum rate of metabolism for that particular species as determined by oxygen consumption. Oxygen consumption VO2 and maximum oxygen consumption VO2 max. Oxygen consumption in species that differ in body size and organ system dimensions show a similarity in their charted VO2 distributions indicating that, despite the complexity of their systems, there is a power law dependence of similarity; therefore, universal patterns are observed in diverse animal taxonomy.[27]

Across a broad range of species, allometric relations are not necessarily linear on a log-log scale. For example, the maximal running speeds of mammals show a complicated relationship with body mass, and the fastest sprinters are of intermediate body size.[28][29]

Allometric muscle characteristics

The muscle characteristics of animals are similar in a wide range of animal sizes, though muscle sizes and shapes can and often do vary depending on environmental constraints placed on them. The muscle tissue itself maintains its contractile characteristics and does not vary depending on the size of the animal. Physiological scaling in muscles affects the number of muscle fibers and their intrinsic speed to determine the maximum power and efficiency of movement in a given animal. The speed of muscle recruitment varies roughly in inverse proportion to the cube root of the animal’s weight (compare the intrinsic frequency of the sparrow’s flight muscle to that of a stork).

For inter-species allometric relations related to such ecological variables as maximal reproduction rate, attempts have been made to explain scaling within the context of dynamic energy budget theory and the metabolic theory of ecology. However, such ideas have been less successful.

Allometry of legged locomotion

Methods of study

Allometry has been used to study patterns in locomotive principles across a broad range of species.[30][31][32][33] Such research has been done in pursuit of a better understanding of animal locomotion, including the factors that different gaits seek to optimize.[33] Allometric trends observed in extant animals have even been combined with evolutionary algorithms to form realistic hypotheses concerning the locomotive patterns of extinct species.[32] These studies have been made possible by the remarkable similarities among disparate species’ locomotive kinematics and dynamics, “despite differences in morphology and size”.[30]

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.[33] Patterns are identified based on dimensionless Froude numbers, which incorporate measures of animals’ leg lengths, speed or stride frequency, and weight.[32][33]

Alexander incorporates Froude-number analysis into his “dynamic similarity hypothesis” of gait patterns. Dynamically similar gaits are those between which there are constant coefficients that can relate linear dimensions, time intervals, and forces. In other words, given a mathematical description of gait A and these three coefficients, one could produce gait B, and vice versa. 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.[33]

It has also been shown that living organisms of all shapes and sizes utilize spring mechanisms in their locomotive systems, probably in order to minimize the energy cost of locomotion.[34] The allometric study of these systems has fostered a better understanding of why spring mechanisms are so common,[34] how limb compliance varies with body size and speed,[30] and how these mechanisms affect general limb kinematics and dynamics.[31]

Principles of legged locomotion identified through allometry

  • Alexander found that animals of different sizes and masses traveling with the same Froude number consistently exhibit similar gait patterns.[33]
  • Duty factors—percentages of a stride during which a foot maintains contact with the ground—remain relatively constant for different animals moving with the same Froude number.[33]
  • The dynamic similarity hypothesis states that "animals of different sizes tend to move in dynamically similar fashion whenever the ratio of their speed allows it".[33]
  • Body mass has even more of an effect than speed on limb dynamics.[31]
  • Leg stiffness, , is proportional to , where is body mass.[31]
  • Peak force experienced throughout a stride is proportional to .[31]
  • The amount by which a leg shortens during a stride (i.e. its peak displacement) is proportional to .[31]
  • The angle swept by a leg during a stride is proportional to .[31]
  • The mass-specific work rate of a limb is proportional to .[31]

Drug dose scaling

The physiological effect of drugs and other substances in many cases scales allometrically.

West, Brown, and Enquist in 1997 derived a hydrodynamic theory to explain the universal fact that metabolic rate scales as the ¾ power with body weight. They also showed why lifespan scales as the +¼ power and heart rate as the -¼ power. Blood flow (+¾) and resistance (-¾) scale in the same way, leading to blood pressure being constant across species.[35]

Hu and Hayton in 2001 discussed whether the basal metabolic rate scale is a ⅔ or ¾ power of body mass. The exponent of ¾ might be used for substances that are eliminated mainly by metabolism, or by metabolism and excretion combined, while ⅔ might apply for drugs that are eliminated mainly by renal excretion.[36]

An online allometric scaler of drug doses based on the above work is available.[37]

The US Food and Drug Administration (FDA) published guidance in 2005 giving a flow chart that presents the decisions and calculations used to generate the maximum recommended starting dose in drug clinical trials from animal data.[38]

Allometric scaling in fluid locomotion

This technical section is not well-written and needs editing.

The mass and density of an organism have a large effect on the organism's locomotion through a fluid. For example, a tiny organisms uses flagella and can effectively move through a fluid it is suspended in. Then on the other scale a blue whale that is much more massive and dense in comparison with the viscosity of the fluid, compared to a bacterium in the same medium. The way in which the fluid interacts with the external boundaries of the organism is important with locomotion through the fluid. For streamlined swimmers the resistance or drag determines the performance of the organism. This drag or resistance can be seen in two distinct flow patterns. There is Laminar Flow where the fluid is relatively uninterrupted after the organism moves through it. Turbulent flow is the opposite, where the fluid moves roughly around an organisms that creates vortices that absorb energy from the propulsion or momentum of the organism. Scaling also affects locomotion through a fluid because of the energy needed to propel an organism and to keep up velocity through momentum. The rate of oxygen consumption per gram body size decreases consistently with increasing body size.[39] (Knut Schmidt-Nielson 2004)

In general, smaller, more streamlined organisms create laminar flow (R < 0.5x106), whereas larger, less streamlined organisms produce turbulent flow (R > 2.0×106).[18] Also, increase in velocity (V) increases turbulence, which can be proved using the Reynolds equation. In nature however, organisms such as a 6‘-6” dolphin moving at 15 knots does not have the appropriate Reynolds numbers for laminar flow R = 107, but exhibit it in nature. Mr. 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. The factors that contribute are:

  • Surface area of the organism and its effect on the fluid in which the organism lives is very important in determining the parameters of locomotion.
  • The Velocity of an organism through fluid changes the dynamic of the flow around that organism and as velocity increases the shape of the organism becomes more important for laminar flow.
  • Density and viscosity of fluid.
  • Length of the organism is factored into the equation because the surface area of just the front 2/3 of the organism has an effect on the drag

The resistance to the motion of an approximately stream-lined solid through a fluid can be expressed by the formula: C(total surface)V2/2 [18]
V = velocity

ρ = density of fluid
Cf = 1.33R − 1 (laminar flow) R = Reynolds number
Reynolds number [R] = VL/ν
V = velocity
L = axial length of organism
ν = kinematic viscosity (viscosity/density)

Notable Reynolds numbers:

R < 0.5x106 = laminar flow threshold
R > 2.0x106 = turbulent flow threshold

Scaling also has an effect on the performance of organisms in fluid. This is extremely important for marine mammals and other marine organisms that rely on atmospheric oxygen to survive and carry out respiration. This can affect how fast an organism can propel itself efficiently and more importantly how long it can dive, or how long and how deep an organism can stay underwater. Heart mass and lung volume are important in determining how scaling can affect metabolic function and efficiency. Aquatic mammals, like other mammals, have the same size heart proportional to their bodies.

Mammals have a heart that is about 0.6% of the total body mass across the board from a small mouse to a large Blue Whale. It can be expressed as: Heart Weight = 0.006Mb1.0, where Mb is the body mass of the individual.[39] Lung volume is also directly related to body mass in mammals (slope = 1.02). The lung has a volume of 63 ml for every kg of body mass. In addition, the tidal volume at rest in an individual is 1/10 the lung volume. Also respiration costs with respect to oxygen consumption is scaled in the order of Mb.75.[39] This shows that mammals, regardless of size, have the same size respiratory and cardiovascular systems and it turn have the same amount of blood: About 5.5% of body mass. This means that for a similarly designed marine mammals, the larger the individual the more efficiently they can travel compared to a smaller individual. It takes the same effort to move one body length whether the individual is one meter or ten meters. This can explain why large whales can migrate far distance in the oceans and not stop for rest. It is metabolically less expensive to be larger in body size.[39] This goes for terrestrial and flying animals as well. In fact, for an organism to move any distance, regardless of type from elephants to centipedes, smaller animals consume more oxygen per unit body mass than larger ones. This metabolic advantage that larger animals have makes it possible for larger marine mammals to dive for longer durations of time than their smaller counterparts. That the heart rate is lower means that larger animals can carry more blood, which carries more oxygen. Then in conjuncture with the fact that mammals reparation costs scales in the order of Mb.75 shows how an advantage can be had in having a larger body mass. More simply, a larger whale can hold more oxygen and at the same time demand less metabolically than a smaller whale.

Traveling long distances and deep dives are a combination of good stamina and also moving an efficient speed and in an efficient way to create laminar flow, reducing drag and turbulence. In sea water as the fluid, it traveling long distances in large mammals, such as whales, is facilitated by their neutral buoyancy and have their mass completely supported by the density of the sea water. On land, animals have to expend a portion of their energy during locomotion to fight the effects of gravity.

Flying organisms such as birds are also considered moving through a fluid. In scaling birds of similar shape, it has also been seen that larger individuals have less metabolic cost per kg than smaller species, which would be expected because it holds true for every other form of animal. Birds also have a variance in wing beat frequency. Even with the compensation of larger wings per unit body mass, larger birds also have a slower wing beat frequency, which allows larger birds to fly at higher altitudes, longer distances, and faster absolute speeds than smaller birds. Because of the dynamics of lift-based locomotion and the fluid dynamics, birds have a U-shaped curve for metabolic cost and velocity. Because flight, in air as the fluid, is metabolically more costly at the lowest and the highest velocities. On the other end, small organisms such as insects can make gain advantage from the viscosity of the fluid (air) that they are moving in. A wing-beat timed perfectly can effectively uptake energy from the previous stroke. (Dickinson 2000) This form of wake capture allows an organism to recycle energy from the fluid or vortices within that fluid created by the organism itself. This same sort of wake capture occurs in aquatic organisms as well, and for organisms of all sizes. This dynamic of fluid locomotion allows smaller organisms to gain advantage because the effect on them from the fluid is much greater because of their relatively smaller size.[39] [40]

Allometric engineering

Allometric engineering is a method for manipulating allometric relationships within or among groups.[41]

In characteristics of a city

Arguing that there are a number of analogous concepts and mechanisms between cities and biological entities, Bettencourt et al. showed a number of scaling relationships between observable properties of a city and the city size. GDP, "supercreative" employment, number of inventors, crime, spread of disease,[24] and even pedestrian walking speeds[42] scale with city population.


Some examples of allometric laws:

  • Kleiber's law, metabolic rate is proportional to body mass raised to the power:
  • breathing and heart rate are both inversely proportional to body mass raised to the power:
  • mass transfer contact area and body mass :
  • the proportionality between the optimal cruising speed of flying bodies (insects, birds, airplanes) and body mass raised to the power :

Determinants of size in different species

Many factors go into the determination of body mass and size for a given animal. These factors often affect body size on an evolutionary scale, but conditions such as availability of food and habitat size can act much more quickly on a species. Other examples include the following:

  • Physiological design
Basic physiological design plays a role in the size of a given species. For example, animals with a closed circulatory system are larger than animals with open or no circulatory systems.[23]
  • Mechanical design
Mechanical design can also determine the maximum allowable size for a species. Animals with tubular endoskeletons tend to be larger than animals with exoskeletons or hydrostatic skeletons.[23]
  • Habitat
An animal’s habitat throughout its evolution is one of the largest determining factors in its size. On land, there is a positive correlation between body mass of the top species in the area and available land area.[43] However, there are a much greater number of “small” species in any given area. This is most likely determined by ecological conditions, evolutionary factors, and the availability of food; a small population of large predators depend on a much greater population of small prey to survive. In an aquatic environment, the largest animals can grow to have a much greater body mass than land animals where gravitational weight constraints are a factor.[18]

See also


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Further reading

External links

Allometric engineering

Allometric engineering is the process of experimentally shifting the scaling relationships, for body size or shape, in a population of organisms. More specifically, the process of experimentally breaking the tight covariance evident among component traits of a complex phenotype by altering the variance of one trait relative to another. Typically, body size is one of the two traits. The measurements of the two traits are plotted against each other and the scaling relationship can be represented as: . Manipulations of this sort alter the scaling relationships either by shifting the intercept (b), slope (m) or both to create novel variants (see: Allometry, for more details). These novel variants can then be tested for differences in performance or fitness. Through careful testing, one could sequentially test each component of a trait suite to determine how each part contributes to the function of the entire complex phenotype, and ultimately the fitness of the organism. This technique allows for comparison within or among biological groups differing in size by adjusting morphology to match one another and comparing their performances.


Bacterivores are free-living, generally heterotrophic organisms, exclusively microscopic, which obtain energy and nutrients primarily or entirely from the consumption of bacteria. Many species of amoeba are bacterivores, as well as other types of protozoans. Commonly, all species of bacteria will be prey, but spores of some species, such as Clostridium perfringens, will never be prey, because of their cellular attributes.

Competitive exclusion principle

In ecology, the competitive exclusion principle, sometimes referred to as Gause's law, is a proposition named for Georgy Gause that two species competing for the same limiting resource cannot coexist at constant population values. When one species has even the slightest advantage over another, the one with the advantage will dominate in the long term. This leads either to the extinction of the weaker competitor or to an evolutionary or behavioral shift toward a different ecological niche. The principle has been paraphrased in the maxim "complete competitors can not coexist".

Cranial evolutionary allometry

Cranial evolutionary allometry (CREA) is a scientific theory regarding trends in the shape of mammalian skulls during the course of evolution in accordance with body size (i.e., allometry). Specifically, the theory posits that there is a propensity among closely related mammalian groups for the skulls of the smaller species to be short and those of the larger species to be long. This propensity appears to hold true for placental as well as non-placental mammals, and is highly robust. Examples of groups which exhibit this characteristic include antelopes, fruit bats, mongooses, squirrels and kangaroos as well as felids.It is believed that the reason for this trend has to do with size-related constraints on the formation and development of the mammalian skull. Facial length is one of the best known examples of heterochrony.

Diameter tape

A diameter tape (D-tape) is a measuring tape used to estimate the diameter of a cylinder object, typically the stem of a tree or pipe. A diameter tape has either metric or imperial measurements reduced by the value of π. This means the tape measures the diameter of the object. It is assumed that the cylinder object is a perfect circle. The diameter tape provides an approximation of diameter; most commonly used in dendrometry.Diameter tapes are usually made of cloth or metal, and on one side of the tape have diameter measurements and on the other standard measurements (not reduced by π).

Dominance (ecology)

Ecological dominance is the degree to which a taxon is more numerous than its competitors in an ecological community, or makes up more of the biomass.

Most ecological communities are defined by their dominant species.

In many examples of wet woodland in western Europe, the dominant tree is alder (Alnus glutinosa).

In temperate bogs, the dominant vegetation is usually species of Sphagnum moss.

Tidal swamps in the tropics are usually dominated by species of mangrove (Rhizophoraceae)

Some sea floor communities are dominated by brittle stars.

Exposed rocky shorelines are dominated by sessile organisms such as barnacles and limpets.

Feeding frenzy

In ecology, a feeding frenzy occurs when predators are overwhelmed by the amount of prey available. For example, a large school of fish can cause nearby sharks, such as the lemon shark, to enter into a feeding frenzy. This can cause the sharks to go wild, biting anything that moves, including each other or anything else within biting range. Another functional explanation for feeding frenzy is competition amongst predators. This term is most often used when referring to sharks or piranhas. It has also been used as a term within journalism.

Harrison's rule

Harrison's rule is an observation in evolutionary biology by Launcelot Harrison which states that in comparisons across closely related species, host and parasite body sizes tend to covary positively.


The term isometric comes from the Greek for "having equal measurement".

isometric may mean:

Isometric projection (or "isometric perspective"), a method for the visual representation of three-dimensional objects in two dimensions; a form of orthographic projection, or more specifically, an axonometric projection.

Isometric graphics in video games and pixel art, a near-isometric parallel projection used in computer art.

Isometry and isometric embeddings in mathematics, a distance-preserving representation of one metric space as a subset of another. Like congruence in geometry.

Isometric exercise, a form of resistance exercise in which one's muscles are used in opposition with other muscle groups, to increase strength, for bodybuilding, physical fitness, or strength training.

Isometre, a rhythmic technique in music.

Isometric joystick, a type of pointing stick, a computer input option

Isometric process, a thermodynamic process at constant volume (also isovolumetric)

Cubic crystal system, also called isometric crystal system

Isometric platform game, a video game sub-genre.

Isometric scaling, the opposite of allometry, which occurs when changes in size (during growth or over evolutionary time) do not lead to changes in proportion.

"Isometric (Intro)", a song by Madeon from the album, Adventure

Jacob Weiner

Jacob Weiner (born Robert Milton Weiner; 1947 in Brooklyn, New York) is an American plant ecologist at the University of Copenhagen. Weiner has made contributions to several areas of plant ecology, including competition, allocation, allometry and application of ecological knowledge to agricultural production.

Karl J. Niklas

Karl Joseph Niklas (born 1948) is the Liberty Hyde Bailey Professor emeritus in the Section of Plant Biology, School of Integrative Plant Science, at Cornell University. He is best known for his work on plant biomechanics, allometry, and functional morphology, and for his long-standing contributions to understanding plant evolutionary biology, particularly early land plant evolutionary diversification patterns and morphospaces.

Kleiber's law

Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the ¾ power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M the animal's mass, then Kleiber's law states that q0 ~ M¾. Thus, over the same timespan, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses.

The exact value of the exponent in Kleiber's law is unclear, in part because there is currently no completely satisfactory theoretical explanation for the law.

Len R. Troncale

Lenard Raphael Troncale (born 1943) is an American biologist, Professor of Cellular and Molecular Biology, and former Director of the Institute for Advanced Systems Studies at the California State Polytechnic University.


Ontogeny (also ontogenesis or morphogenesis) is the origination and development of an organism, usually from the time of fertilization of the egg to the organism's mature form—although the term can be used to refer to the study of the entirety of an organism's lifespan.

Ontogeny is the developmental history of an organism within its own lifetime, as distinct from phylogeny, which refers to the evolutionary history of a species. In practice, writers on evolution often speak of species as "developing" traits or characteristics. This can be misleading. While developmental (i.e., ontogenetic) processes can influence subsequent evolutionary (e.g., phylogenetic) processes (see evolutionary developmental biology), individual organisms develop (ontogeny), while species evolve (phylogeny).

Ontogeny, embryology and developmental biology are closely related studies and those terms are sometimes used interchangeably. The term ontogeny has also been used in cell biology to describe the development of various cell types within an organism.Ontogeny is a useful field of study in many disciplines, including developmental biology, developmental psychology, developmental cognitive neuroscience, and developmental psychobiology.

Ontogeny is also a concept used in anthropology as "the process through which each of us embodies the history of our own making".

Recruitment (biology)

In biology, especially marine biology, recruitment occurs when a juvenile organism joins a population, whether by birth or immigration, usually at a stage whereby the organisms are settled and able to be detected by an observer.There are two types of recruitment: closed and open.In the study of fisheries, recruitment is "the number of fish surviving to enter the fishery or to some life history stage such as settlement or maturity".

Relative abundance distribution

In the field of ecology, the relative abundance distribution (RAD) or species abundance distribution describes the relationship between the number of species observed in a field study as a function of their observed abundance. The graphs obtained in this manner are typically fitted to a Zipf–Mandelbrot law, the exponent of which serves as an index of biodiversity in the ecosystem under study.

Stag beetle

Stag beetles are a group of about 1,200 species of beetles in the family Lucanidae, presently classified in four subfamilies. Some species grow to over 12 cm (4.7 in), but most are about 5 cm (2.0 in).

Tree allometry

Tree allometry establishes quantitative relations between some key characteristic dimensions of trees (usually fairly easy to measure) and other properties (often more difficult to assess). To the extent these statistical relations, established on the basis of detailed measurements on a small sample of typical trees, hold for other individuals, they permit extrapolations and estimations of a host of dendrometric quantities on the basis of a single (or at most a few) measurements.

The study of allometry is extremely important in dealing with measurements and data analysis in the practice of forestry. Allometry studies the relative size of organs or parts of organisms. Tree allometry narrows the definition to applications involving measurements of the growth or size of trees. Allometric relationships often are used to estimate difficult tree measurements, such as volume, from an easily measured attribute such as diameter at breast height (DBH).

The use of allometry is widespread in forestry and forest ecology. In order to develop an allometric relationship there must be a strong relationship and an ability to quantify this relationship between the parts of the subject measured and the other quantities of interest. Also when developing this equation one must play in factors which affect tree growth such as age, species, site location, etc. Once all these guidelines are met, one may attempt to develop an allometric equation.

William J. Sanders

William J. Sanders is a vertebrate paleontologist and Research Scientist/Preparator at the University of Michigan. He has written a number of papers on fossil elephants.EDUCATION

Ph.D. Department of Anthropology, New York University. Dissertation Title: "Function, Allometry, and Evolution of the Australopithecine Lower Precaudal Spine." 1995.

M.Phil. Department of Anthropology, New York University. 1990.

B.A. Department of Anthropology, The University of Chicago. 1979.

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