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Gábor Holló1 and also Mihály Novák2,3

Gábor Holló

1Institute the Psychology, college of Debrecen, P.O.B. 28, Debrecen, H, 4010, Hungary

Mihály Novák

2Faculty of used Sciences, Campus du Solbosch, bâtiment U, Université Libre de Bruxelles, path F. D. Roosevelt 50, 1050, Brussels, Belgium

3Institute that Nuclear research of the Hungarian Academy of scientific researches (MTA ATOMKI), Debrecen, Hungary

2Faculty of applied Sciences, Campus du Solbosch, bâtiment U, Université Libre de Bruxelles, way F. D. Roosevelt 50, 1050, Brussels, Belgium
Corresponding author.

You are watching: Advantages and disadvantages of radial symmetry

This is one Open accessibility article dispersed under the terms of the an imaginative Commons Attribution license (, which patent unrestricted use, distribution, and also reproduction in any type of medium, detailed the original job-related is correctly cited.


The overwhelming majority of animal types exhibit bilateral symmetry. However, the precise evolutionary prominence of bilateral the opposite is unknown, although elements of the knowledge of the phenomenon have been existing within the scientific ar for decades.

Presentation of the hypothesis

Here us show, through very straightforward physical laws, that locomotion in three-dimensional macro-world room is itself sufficient to explain the maintenance of bilateral the opposite in animal evolution. The capacity to readjust direction, a key element that locomotion, calls for the generation the instantaneous “pushing” surfaces, from which the animal can attain the important force to depart in the brand-new direction. We show that bilateral is the only kind of the contrary that have the right to maximize this force; thus, an proactively locomoting bilateral body have the right to have the maximal manoeuvrability as contrasted to other symmetry types. This confers an obvious selective benefit on the bilateral animal.

Implications of the hypothesis

These considerations imply the watch that pet evolution is a highly channelled process, in i beg your pardon bilateral and radial human body symmetries it seems ~ to be inevitable.


This short article was reviewed by Gáspár Jékely, L. Aravind and also Eugene Koonin.

Keywords: Bilateral symmetry, Radial symmetry, Manoeuvrability, Drag, drag coefficient


Animals display diverse species of symmetry consisting of spherical, cylindrical (also well-known as perfect radial), radial, biradial, bilateral and also asymmetric (for review, see ref. <1>). In this paper, the terms cylindrical and also radial will be offered as synonyms since in the context it provides no an extensive difference. Much more than 99 % that animal types are bilaterally symmetrical. The few exceptions are the amorphous parasitic placozoan Trichoplax, sponges (with asymmetry, spherical symmetry, and also elements that radial the opposite in the skeleton), cnidarians (which include jellyfish, hydras, corals and also sea anemones through radial and biradial symmetry), ctenophores or comb jellies (biradial symmetry), and echinoderms (sea lilies, sea urchins, and sea stars through radial symmetry).

Bilateral symmetry with two human body axes emerged early in animal evolution, more than likely in slow, flat, worm-like organisms locomoting top top a substrate <2>. Hereditary analyses have concluded the the genes responsible because that bilateral symmetry most likely appeared prior come the cnidarian–bilaterian separation <3-6>, in the Precambrian <7,8>. However, also if the slow, cilium-based locomotion on a substrate may describe the generation the bilateral symmetry, it certainly cannot account because that its survival over numerous years of pet evolution. Most recent animal types are bilaterally symmetrical, muscle-based locomoters, either living a pelagic life in water, or locomoting ~ above the land and/or in the air. Why has actually bilaterality, i beg your pardon probably formed in benthic lifestyle, also proved so succesful in free-moving animals?

Presentation of the hypothesis

Now we emphasis on the aquatic environment due to the fact that bilateral symmetry (and animal life, itself) created there, and also had come be preserved there for numerous years, prior to bilaterians conquered the land. Allow us start with the elementary physical fact that to locomote in a fluid, a body needs to overcome traction (the resistance that the tool in i beg your pardon the body moves, exhilaration in opposition to the direction of locomotion).

The magnitude of the drag force is:

F = – ½ ρ c A v2

where F is the traction force, ρ is the density of the medium, c is the dimensionless drag coefficient dependence on the human body shape, A is the area of the maximal ar of the human body in the direction that motion, and also v is the body’s velocity <9,10>. The negative sign top top the appropriate side shows that traction is opposite to the direction that motion. The is essential to keep in mind that this equation is precious for cases where the viscous forces are negligible compared to inertial forces, in what is loosely described as the macroscopic world (i.e at high Reynolds numbers). In the microscope world, the pressures are overcame by the viscosity the the liquid rather than by the inertia (i.e. At low Reynolds numbers) <10>, however a discussion of the locomotion in the micro scale world is not the problem of this file (for an in-depth evaluation see ref. <11>).

Given the fact that the tool imposes resistance on the body, if resistance pressures are unequally distributed roughly the body, your resultant pressure will not be zero contrasted to the rectilinear direction (i.e. Motion straight ahead), therefore the body will not relocate on a linear path. This is the situation when a relocating body is asymmetric. Thus, it adheres to that a directionally locomoting pet has to be symmetric in bespeak to prevent this effect. To have the ability to move forward, the animal can have any kind of symmetry, for this reason the strategy outlined below is not adequate to explain the success the bilateral symmetry. Rectilinear movement is, however, not the only aspect of locomotion. One other important aspect is an altering direction, the prominence of which, in this regard, has been largely ignored in the literary works so far. A slim deviation indigenous the directly trajectory can quickly be acquired by flawing one element of symmetry, hence generating asymmetry in the original direction of motion. This have the right to be accomplished by any kind of symmetrical body. However, when a quick changeover is required, the case becomes really different.

In quick transforms in direction, the body has to exercise a pressure in opposing direction to the desired brand-new orientation. This way that it needs to have a “pushing” surface ar in water indigenous which to depart in the brand-new direction. This surface ar is created by the water layer against which the human body is stand in bespeak to push itself away, and it is produced by developing a an excellent instantaneous traction force. Due to the fact that ρ in the equation is unchanged, and also v is diminishing or constant, the pet has to increase the maximal surface ar A and/or the drag coefficient c.

We will now overview the main symmetry varieties in terms of their volume to develop a pushing-off traction force. Provided that a swim body has to minimize the overall drag, that is skin friction <9>, and thus that wetted area, needs to be adequately reduced. Thus, just three key body creates can be considered: spherical (with limitless symmetry planes and also symmetry axes), cylindrical (with countless symmetry planes and also one symmetry axis) and also bilateral (with one aircraft of symmetry). An elongated radial human body that reflects a star-like section is suboptimal due to the fact that it has a very large surface that is much from ideal for swim forwards.

A spherically symmetrical human body cannot create the advertise surface, gift of same shape and drag in every direction. Since the forces – which are various from the one operation in the direction the its movement – acting on this body are all equalized, it will certainly not have the ability to depart in a brand-new direction. It can only rotate roughly itself to deviate to a little extent (as football players bend the ball), yet this is solid an effective changeover and obviously can not guarantee specific manoeuvrability (understood merely as the capacity to carry out quick and also accurate changeovers). In this context we can disregard just how it had the ability to move directly in the very first place.

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A cylindrical (Figure ​(Figure1.A)1.A) or about cylindrical (or radial) human body locomoting with lateral or upright undulation is maybe to boost A, which will certainly be produced by a ar of its body opposed to the direction in i m sorry it desires to move. The area that this surface is given around by the product that the diameter and the size of the body section in question (and of food by that angular orientation to the axis the translation). If that lateral traction coefficient (c) is higher than the frontal, then as soon as the pet turns its body can likewise increase c in the equation. However, regardless of the relationship between the anterior and lateral c, if the product (c A) from the lateral watch is greater than that from the frontal one, this human body will have the ability to move forward and to adjust direction.