The Aerodynamics of Hovering Insect Flight. II. Morphological Parameters
24 Feb 1984-Philosophical Transactions of the Royal Society B (The Royal Society)-Vol. 305, Iss: 1122, pp 17-40
TL;DR: In this article, the authors presented a set of morphological parameters for a variety of insects that have been filmed in free flight, which can be divided into two distinct groups: gross parameters and shape parameters.
Abstract: Morphological parameters are presented for a variety of insects that have been filmed in free flight. The nature of the parameters is such that they can be divided into two distinct groups: gross parameters and shape parameters. The gross parameters provide a very crude, first-order description of the morphology of a flying animal: its mass, body length, wing length, wing area and wing mass. Another gross parameter of the wings is their virtual mass, or added mass, which is the mass of air accelerated and decelerated together with the wing at either end of the wingbeat. The wing motion during these accelerations is almost perpendicular to the wing surface, and the virtual mass is approximately given by the mass of air contained in an imaginary cylinder around the wing with the chord as its diameter. The virtual mass ranges from 0.3 to 1.3 times the actual wing mass, indicating that the total mass accelerated by the flight muscles can be more than twice the wing mass itself. Over the limited size range of insects in this study, the interspecific variation of non-dimensional forms of the gross parameters is much greater than any systematic allometric variation, and no interspecific correlations can be found. The new shape parameters provide quite a surprise, however: intraspecific coefficients of variation are very low, often only 1%, and interspecific allometric relations are extremely strong. Mechanical aspects of flight depend not only on the magnitude of gross morphological quantities, but also on their distributions. Non-dimensional radii are derived from the non-dimensional moments of the distributions; for example, the first radius of wing mass about the wing base gives the position of the centre of mass, and the second radius corresponds to the radius of gyration. The radii are called \`shape parameters' since they are functions only of the normalized shape of the distributions, and they provide a second-order description of the animal morphology. The various radii of wing area are strongly correlated, as are those of wing mass and of virtual mass: the higher radii for each quantity can all be expressed by allometric functions of the first radius. The overall shape of the distribution of a quantity can therefore be characterized by a single parameter, the position of the centroid of that quantity. The strong relations between the radii of wing area, mass and virtual mass hold for a diverse collection of insects, birds and bats. Thus flying animals adhere to \`laws of shape' regardless of biological differences. Aerodynamic and mechanical considerations are most likely to provide an understanding of these laws of shape, but an explanation has proved elusive so far. The detailed shape of a distribution can be reconstructed from the shape parameters by matching the moments of the observed distribution to those of a suitable analytical function. A Beta distribution is compared with the distribution of wing area, i.e. the shape of the wing, and a very good fit is found. With use of the laws of shape relating the higher radii to the first radius, the Beta distribution can be reduced to a function of only one parameter, thus providing a powerful tool for drawing a close approximation to the entire shape of a wing given only its centroid of area. Quite unexpectedly, the continuous spectrum of wing shapes can then be described in detail by a single parameter of shape.
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TL;DR: The basic physical principles underlying flapping flight in insects, results of recent experiments concerning the aerodynamics of insect flight, as well as the different approaches used to model these phenomena are reviewed.
Abstract: The flight of insects has fascinated physicists and biologists for more than a century. Yet, until recently, researchers were unable to rigorously quantify the complex wing motions of flapping insects or measure the forces and flows around their wings. However, recent developments in high-speed videography and tools for computational and mechanical modeling have allowed researchers to make rapid progress in advancing our understanding of insect flight. These mechanical and computational fluid dynamic models, combined with modern flow visualization techniques, have revealed that the fluid dynamic phenomena underlying flapping flight are different from those of non-flapping, 2-D wings on which most previous models were based. In particular, even at high angles of attack, a prominent leading edge vortex remains stably attached on the insect wing and does not shed into an unsteady wake, as would be expected from non-flapping 2-D wings. Its presence greatly enhances the forces generated by the wing, thus enabling insects to hover or maneuver. In addition, flight forces are further enhanced by other mechanisms acting during changes in angle of attack, especially at stroke reversal, the mutual interaction of the two wings at dorsal stroke reversal or wing-wake interactions following stroke reversal. This progress has enabled the development of simple analytical and empirical models that allow us to calculate the instantaneous forces on flapping insect wings more accurately than was previously possible. It also promises to foster new and exciting multi-disciplinary collaborations between physicists who seek to explain the phenomenology, biologists who seek to understand its relevance to insect physiology and evolution, and engineers who are inspired to build micro-robotic insects using these principles. This review covers the basic physical principles underlying flapping flight in insects, results of recent experiments concerning the aerodynamics of insect flight, as well as the different approaches used to model these phenomena.
1,182 citations
TL;DR: Design characteristics of insect-based flying machines are presented, along with estimates of the mass supported, the mechanical power requirement and maximum flight speeds over a wide range of sizes and frequencies.
Abstract: The wing motion in free flight has been described for insects ranging from 1 to 100 mm in wingspan. To support the body weight, the wings typically produce 2–3 times more lift than can be accounted for by conventional aerodynamics. Some insects use the fling mechanism: the wings are clapped together and then flung open before the start of the downstroke, creating a lift-enhancing vortex around each wing. Most insects, however, rely on a leading-edge vortex (LEV) created by dynamic stall during flapping; a strong spanwise flow is also generated by the pressure gradients on the flapping wing, causing the LEV to spiral out to the wingtip. Technical applications of the fling are limited by the mechanical damage that accompanies repeated clapping of the wings, but the spiral LEV can be used to augment the lift production of propellers, rotors and micro-air vehicles (MAVs). Design characteristics of insect-based flying machines are presented, along with estimates of the mass supported, the mechanical power requirement and maximum flight speeds over a wide range of sizes and frequencies. To support a given mass, larger machines need less power, but smaller ones operating at higher frequencies will reach faster speeds.
764 citations
Cites background or methods from "The Aerodynamics of Hovering Insect..."
...They scale with Reynolds number as (Ellington, 1984c): CD,pro = 7Re −1/2 , (9) where Re is given by equation 1....
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...The other tiny insects that have been filmed to date rely on the fling mechanism for enhanced lift production: the greenhouse white-fly Trialeurodes vaporariorum (Weis-Fogh, 1975b) and thrips (Ellington, 1984b)....
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...Changes in angle of attack have been observed to initiate accelerations at low speeds (Ellington, 1984b)....
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...The mean lift coefficient CL in hovering and slow flight, with and without loads, is usually 2–3 or less (e.g. Ellington, 1984c; Ennos, 1989; Dudley and Ellington, 1990b; Cooper, 1993; Dudley, 1995; Willmott and Ellington, 1997b); a value of 2 will be used as a conservative upper limit....
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...The wings must therefore produce a compensatory nose-down pitching moment about their bases, and this is accomplished by locating the centre of lift aft of the body; the mean flapping angle of the wings in the stroke plane is typically directed 20–30 ° backwards during hovering (Ellington, 1984b)....
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TL;DR: A standard quasi-steady model of insect flight is modified to include rotational forces, translational forces and the added mass inertia, and the revised model predicts the time course of force generation for several different patterns of flapping kinematics more accurately than a model based solely on translational force coefficients.
Abstract: We used a dynamically scaled model insect to measure the rotational forces produced by a flapping insect wing. A steadily translating wing was rotated at a range of constant angular velocities, and the resulting aerodynamic forces were measured using a sensor attached to the base of the wing. These instantaneous forces were compared with quasi-steady estimates based on translational force coefficients. Because translational and rotational velocities were constant, the wing inertia was negligible, and any difference between measured forces and estimates based on translational force coefficients could be attributed to the aerodynamic effects of wing rotation. By factoring out the geometry and kinematics of the wings from the rotational forces, we determined rotational force coefficients for a range of angular velocities and different axes of rotation. The measured coefficients were compared with a mathematical model developed for two-dimensional motions in inviscid fluids, which we adapted to the three-dimensional case using blade element theory. As predicted by theory, the rotational coefficient varied linearly with the position of the rotational axis for all angular velocities measured. The coefficient also, however, varied with angular velocity, in contrast to theoretical predictions. Using the measured rotational coefficients, we modified a standard quasi-steady model of insect flight to include rotational forces, translational forces and the added mass inertia. The revised model predicts the time course of force generation for several different patterns of flapping kinematics more accurately than a model based solely on translational force coefficients. By subtracting the improved quasi-steady estimates from the measured forces, we isolated the aerodynamic forces due to wake capture.
746 citations
TL;DR: A dynamically scaled mechanical model of the fruit fly Drosophila melanogaster is used to study how changes in wing kinematics influence the production of unsteady aerodynamic forces in insect flight, finding no evidence that stroke deviation can augment lift, but it nevertheless may be used to modulate forces on the two wings.
Abstract: We used a dynamically scaled mechanical model of the fruit fly Drosophila melanogaster to study how changes in wing kinematics influence the production of unsteady aerodynamic forces in insect flight. We examined 191 separate sets of kinematic patterns that differed with respect to stroke amplitude, angle of attack, flip timing, flip duration and the shape and magnitude of stroke deviation. Instantaneous aerodynamic forces were measured using a two-dimensional force sensor mounted at the base of the wing. The influence of unsteady rotational effects was assessed by comparing the time course of measured forces with that of corresponding translational quasi-steady estimates. For each pattern, we also calculated mean stroke-averaged values of the force coefficients and an estimate of profile power. The results of this analysis may be divided into four main points.
(i) For a short, symmetrical wing flip, mean lift was optimized by a stroke amplitude of 180° and an angle of attack of 50°. At all stroke amplitudes, mean drag increased monotonically with increasing angle of attack. Translational quasi-steady predictions better matched the measured values at high stroke amplitude than at low stroke amplitude. This discrepancy was due to the increasing importance of rotational mechanisms in kinematic patterns with low stroke amplitude.
(ii) For a 180° stroke amplitude and a 45° angle of attack, lift was maximized by short-duration flips occurring just slightly in advance of stroke reversal. Symmetrical rotations produced similarly high performance. Wing rotation that occurred after stroke reversal, however, produced very low mean lift.
(iii) The production of aerodynamic forces was sensitive to changes in the magnitude of the wing’s deviation from the mean stroke plane (stroke deviation) as well as to the actual shape of the wing tip trajectory. However, in all examples, stroke deviation lowered aerodynamic performance relative to the no deviation case. This attenuation was due, in part, to a trade-off between lift and a radially directed component of total aerodynamic force. Thus, while we found no evidence that stroke deviation can augment lift, it nevertheless may be used to modulate forces on the two wings. Thus, insects might use such changes in wing kinematics during steering maneuvers to generate appropriate force moments.
(iv) While quasi-steady estimates failed to capture the time course of measured lift for nearly all kinematic patterns, they did predict with reasonable accuracy stroke-averaged values for the mean lift coefficient. However, quasi-steady estimates grossly underestimated the magnitude of the mean drag coefficient under all conditions. This discrepancy was due to the contribution of rotational effects that steady-state estimates do not capture. This result suggests that many prior estimates of mechanical power based on wing kinematics may have been grossly underestimated.
726 citations
Cites background or methods or result from "The Aerodynamics of Hovering Insect..."
...To obtain the correct range of Reynolds numbers, we used an isometrically enlarged wing planform of an actual D. melanogaster wing to ensure that the shape parameters (Ellington, 1984a) were identical to those of D. melanogaster....
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...…the fluid density, R is the wing length, c – is the mean chord length, r ˆ and c ˆ(r ˆ) are the non-dimensional radial position along the wing and non-dimensional chord length, respectively (for nomenclature, see Ellington, 1984a), φ is the angular position of the wing and α is the angle of attack....
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...…2 ν −1 AR −1 , where Φ is stroke amplitude, n is wingbeat frequency, R is wing length, ν is kinematic viscosity, aspect ratio AR is 4R 2 S −1 and S is the surface area of a wing pair; Ellington, 1984c) and the reduced frequency parameter (body velocity/wing velocity) constant (Spedding, 1993)....
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...It is worth noting that the range of CD – values is much higher than has been previously reported for Drosophila virilis wings under steady-state conditions (Vogel, 1967) or estimated on the basis of Reynolds number (CD≈0.7; Ellington, 1984c)....
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...From the forces on each wing, we calculated the corresponding mean force coefficients using an equation derived from blade element theory (Ellington, 1984c; Dickinson et al., 1999): where F – is the magnitude of a specific force component (lift, drag, radial, total) averaged over the stroke, Φ is…...
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Book•
01 Oct 2007TL;DR: In this paper, the authors introduce fixed, rigid, flexible, and flapping wing aerodynamic models for fixed and flexible wing aerodynamics, and propose a flexible wing model for flapping aerodynamics.
Abstract: 1. Introduction 2. Fixed, rigid wing aerodynamics 3. Flexible wing aerodynamics 4. Flapping wing aerodynamics.
580 citations
References
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Book•
01 Jan 1976
TL;DR: This book reviews biological structural materials and systems and their mechanically important features and demonstrates that function at any particular level of biological integration is permitted and controlled by structure at lower levels of integration.
Abstract: This book deals with an interface between mechanical engineering and biology. Available for the first time in paperback, it reviews biological structural materials and systems and their mechanically important features and demonstrates that function at any particular level of biological integration is permitted and controlled by structure at lower levels of integration. Five chapters discuss the properties of materials in general and those of biomaterials in particular. The authors examine the design of skeletal elements and discuss animal and plant systems in terms of mechanical design. In a concluding chapter they investigate organisms in their environments and the insights gained from study of the mechanical aspects of their lives.
1,407 citations
TL;DR: In this article, the average lift coefficient, Reynolds number, the aerodynamic power, the moment of inertia of the wing mass and the dynamic efficiency in animals which perform normal hovering with horizontally beating wings are derived.
Abstract: 1. On the assumption that steady-state aerodynamics applies, simple analytical expressions are derived for the average lift coefficient, Reynolds number, the aerodynamic power, the moment of inertia of the wing mass and the dynamic efficiency in animals which perform normal hovering with horizontally beating wings. 2. The majority of hovering animals, including large lamellicorn beetles and sphingid moths, depend mainly on normal aerofoil action. However, in some groups with wing loading less than 10 N m -2 (1 kgf m -2 ), non-steady aerodynamics must play a major role, namely in very small insects at low Reynolds number, in true hover-flies (Syrphinae), in large dragonflies (Odonata) and in many butterflies (Lepidoptera Rhopalocera). 3. The specific aerodynamic power ranges between 1.3 and 4.7 WN -1 (11-40 cal h -1 gf -1 ) but power output does not vary systematically with size, inter alia because the lift/drag ratio deteriorates at low Reynolds number. 4. Comparisons between metabolic rate, aerodynamic power and dynamic efficiency show that the majority of insects require and depend upon an effective elastic system in the thorax which counteracts the bending moments caused by wing inertia. 5. The free flight of a very small chalcid wasp Encarsia formosa has been analysed by means of slow-motion films. At this low Reynolds number (10-20), the high lift co-efficient of 2 or 3 is not possible with steady-state aerodynamics and the wasp must depend almost entirely on non-steady flow patterns. 6. The wings of Encarsia are moved almost horizontally during hovering, the body being vertical, and there are three unusual phases in the wing stroke: the clap , the fling and the flip . In the clap the wings are brought together at the top of the morphological upstroke. In the fling, which is a pronation at the beginning of the morphological downstroke, the opposed wings are flung open like a book, hinging about their posterior margins. In the flip, which is a supination at the beginning of the morphological upstroke, the wings are rapidly twisted through about 180°. 7. The fling is a hitherto undescribed mechanism for creating lift and for setting up the appropriate circulation over the wing in anticipation of the downstroke. In the case of Encarsia the calculated and observed wing velocities at which lift equals body weight are in agreement, and lift is produced almost instantaneously from the beginning of the downstroke and without any Wagner effect. The fling mechanism seems to be involved in the normal flight of butterflies and possibly of Drosophila and other small insects. Dimensional and other considerations show that it could be a useful mechanism in birds and bats during take-off and in emergencies. 8. The flip is also believed to be a means of setting up an appropriate circulation around the wing, which has hitherto escaped attention; but its operation is less well understood. It is not confined to Encarsia but operates in other insects, not only at the beginning of the upstroke (supination) but also at the beginning of the downstroke where a flip (pronation) replaces the clap and fling of Encarsia . A study of freely flying hover-flies strongly indicates that the Syrphinae (and Odonata) depend almost entirely upon the flip mechanism when hovering. In the case of these insects a transient circulation is presumed to be set up before the translation of the wing through the air, by the rapid pronation (or supination) which affects the stiff anterior margin before the soft posterior portions of the wing. In the flip mechanism vortices of opposite sense must be shed, and a Wagner effect must be present. 9. In some hovering insects the wing twistings occur so rapidly that the speed of propagation of the elastic torsional wave from base to tip plays a significant role and appears to introduce beneficial effects. 10. Non-steady periods, particularly flip effects, are present in all flapping animals and they will modify and become superimposed upon the steady-state pattern as described by the mathematical model presented here. However, the accumulated evidence indicates that the majority of hovering animals conform reasonably well with that model. 11. Many new types of analysis are indicated in the text and are now open for future theoretical and experimental research.
1,279 citations
TL;DR: It is argued that the tilt of the stroke plane relative to the horizontal is an adaptation to the geometrically unfavourable induced wind and to the relatively large lift/drag ratio seen in many insects.
Abstract: 1. Expressions have been derived for an estimate of the average coefficient of lift, for the variation in bending moment or torque caused by wind forces and by inertia forces, and for the power output during hovering flight on one spot when the wings move according to a horizontal figure-of-eight. 2. In both hummingbirds and Drosophila the flight is consistent with steady-state aerodynamics, the average lift coefficient being 1.8 in the hummingbird and 0.8 in Drosophila. 3. The aerodynamic or hydraulic efficiency is 0.5 in the hummingbird and 0.3 in Drosophila, and in both types the aerodynamic power output is 22-24 cal/g body weight/h. 4. The total mechanical power output is 39 cal g-1 h-1 in the hummingbird because of the extra energy needed to accelerate the wing-mass. It is 24 cal g-1 h-1 in Drosophila in which the inertia term is negligible because the wing-stroke frequency is reduced to the lowest possible value for sustained flight. 5. In both animals the mechanical efficiency of the flight muscles is 0.2. 6. It is argued that the tilt of the stroke plane relative to the horizontal is an adaptation to the geometrically unfavourable induced wind and to the relatively large lift/drag ratio seen in many insects. The vertical movements at the extreme ends may serve to reduce the interaction between the shed ‘stopping’ vortex and the new bound vortex of opposite sense which has to be built up during the early part of the return stroke. 7. Two additional non-steady flow situations may exist at either end of the stroke, delayed stall and delayed build-up of circulation (Wagner effect), but since they have opposite effects it is probable that the resultant force is of about the same magnitude as that estimated for a steady-state situation. 8. Most insects have an effective elastic system to counteract the adverse effect of wing-inertia, but small fast-moving vertebrates have not. It is argued that the only material available for this purpose in this group is elastin and that it is unsuited at the rates of deformation required because recent measurements have shown that the damping is relatively high, probably due to molecular factors.
349 citations
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TL;DR: In this paper, it is shown that birds operate with an essentially unstable physical system, and therefore that stable flight is only possible with continuous control, and that birds can only fly by continuous flapping of their wings.
Abstract: Summary
Bird flight can be studied neither as a problem in physics nor from the standpoint of biology alone. Both points of view are necessary and complementary.
It is convenient to consider separately those birds which habitually glide or soar in air currents and those which normally fly by continuous flapping of their wings.
The gliding and soaring types all obtain energy to maintain flight from air movements of various kinds. The terrestrial birds soar by making use of masses of warm air (‘thermals’) which rise from ground heated by the sun. These birds typically have large wing surfaces and fly slowly. In contrast, the gliding sea birds usually obtain energy either from air deflected upwards by cliffs or by an oceanic swell, or else they can make use of the incresea of wind velocity with height, which tends to be uniform over an unobstructed water surface. Such birds usually have long narrow wings and can glide at high speed with a small angle of descent.
Within the flapping species we can distinguish four types of wing movement with different properties. First, there is the symmetrical wing flappingof the hummingbirds, which can remain stationary with the body axis vertical. Associated with this flight there are unique adaptations of both the skeleton and musculature. Secondly, there is the flapping cycle typical of the small passerine birds, where the upstroke is only a recovery stroke and takes place with the wings folded. Here, as might be expected, the elevator muscles are relatively much smaller than those of the humming birds. Thirdly, there is the flight with complex movements as seen in the pigeon, where a propulsive upstroke occurs in slow flight at take off-and landing, but is reduced and finally disappears as the forward speed increases. Here again the relative muscle weights show adaptation, the elevators being relatively larger than those of the passerines but not as large as those found in humming birds. The fourth type, typical of large birds, shows only a simple powered downstroke and sustaining upstroke. These birds are incapable of slow flight and have small elevator muscles.
The wing shape of birds is generally correlated with their type of flight, which in turn can be shown to be adapted to their habitat and mode of life. In particular, the emargination of the primary feathers may, when extensive, be either a means of improving the slow speed performance and control of land-soaring birds, or a method of increasing the efficiency of the short broad wings of birds such as the partridge, which takes off from thickets.
There have been many attempts to estimate the energy used in flight. Estimates can be made from measurements of the metabolism of the animals and also by theoretical studies of tentative aerodynamic parameters. No direct measurements of the properties of the flapping system have yet been possible. All the estimates so far made suggest both an energy output from the muscles higher than that found in non-flying animals and also a very efficient aerodynamic system with little air resistance.
The maintenance of stability in flight can be examined theoretically and it is clear that birds operate with an essentially unstable physical system, and therefore that stable flight is only possible with continuous control. This type of system is advantageous in that it permits great manoeuvrability with little expenditure of energy.
Two possible lines of the early evolution of the flight mechanism have been proposed, one from a terrestrial cursorial ancestor and the other from an arboreal form. For physical reasons the cursorial ancestor is difficult to justify. Development from an arboreal form allows one to postulate a line of evolution with feathers arising primarily as heat insulators in association with a homoiothermal physiology, later becoming adapted for flight. This theory overcomes the difficulty that feathers used for flight can have no selective advantage for this purpose at an early stage of their evolution.
344 citations
TL;DR: The expectations and variances of coefficients of variation under the assumption of normality are reviewed and the effects of appreciable departures from this assumption are examined.
Abstract: Sokal, R. R., and C. A. Braumann (Department of Ecology and Evolution, State University of New York at Stony Brook, Stony Brook, New York 11794) 1980. Significance tests for coefficients of variation and variability profiles. Syst. Zool. 29:50-66.-The distribution of sample estimates of the coefficient of variation is studied analytically and by Monte Carlo simulation. Derivations are given for the expected value of a coefficient of variation and for its standard error. Various proposed standard errors for coefficients of variation are evaluated. Standard errors are derived for differences between coefficients of variation for samples of independent and correlated characters. Methods are proposed for testing the homogeneity of sets of independent and correlated coefficients of variation. Tests of homogeneity of variability profiles as well as for parallelism of such profiles are furnished. [Coefficients of variation, variability profiles.] The employment of coefficients of variation in systematic research is of long standing. Various evolutionary hypotheses require for their examination the establishment of differences in the amounts by which characters vary in populations. Such differences can be examined for the same character across several populations of the same species or of different species, or the comparison may be within the same population but among different characters. Such comparisons of the amounts of variation are generally adjusted for differences in magnitude of the character means, hence the employment of the coefficient of variation, V. A recent renewal of interest in the coefficient of variation is due to two developments. Various studies, collectively called population phenetics, have probed the effects of evolutionary processes on variability patterns in animal and plant populations and have tried to establish the converse-the drawing of inferences about evolutionary processes from observed variability patterns. Studies such as those of Soule (1967), Soule and Stewart (1970), Rothstein (1973), Lande (1977), or Sokal (1976) come to mind readily. A second reason for an increased interest in coefficients of variation is the stimulating book by Yablokov (1974) introducing the study of variability profiles in mammalian populations. Variability profiles are graphs in which the amount of variation expressed as a variance or coefficient of variation is plotted against a horizontal axis representing the suite of characters under study. Examination of variability profiles within and among populations leads to inferences about the amount of developmental (and ultimately evolutionary) control of variability for different characters in the same population and among populations. There is a need for appropriate methods to examine the types of comparisons being considered. In this paper we shall briefly review the expectations and variances of coefficients of variation under the assumption of normality and examine the effects of appreciable departures from this assumption. We shall then turn to the comparison of two or more coefficients of variation for the same character from different populations. This account will be followed by a discussion of tests applicable to a single variability profile, which in turn will lead to the comparison of several profiles. These can be considered for the same hierarchic level, as in local population samples of the same species, or the comparison may be between different hierarchic levels representing natural sampling units, such as variability within local populations versus variability across populations. Analytical work on the expectations
315 citations