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I've got a silly question, sorry for that. I know, that we probably have no the right answer and the current answer could be "that's evolution, external conditions". I'd like to speculate, why most of mammals (for ex.) and people especially are symmetric? I know, that we are not completely symmetrical, but anyway.
Thanks a lot.
There's really two answers to the question. The first is overall symmetry: mammals, like all tetrapods, are bilaterally symmetric. This comes from a distant common origin with other bilaterally symmetric organisms. Organisms which evolved from this common ancestor often have organs in pairs, probably evolving as a re-use of regulatory genes.
The other answer is the high degree of symmetry in external appearance. While internal organs are roughly symmetric, there is some asymmetry. However the external appearance of most bilaterally symmetric organisms is highly symmetric. This suggests a different force at work. In fact, there is some evidence for sexual selection for bilateral symmetry. Mate choice is driven by indicators of health, and bilateral symmetry is a common indicator of health.
It is, of course, not just mammals, but nearly all animal life is symmetric. Even plants are usually symmetric in some degree. There are exceptions here and there. For example, one interesting exception is that of the fiddler crab which has one claw larger than another. In general, when a single appendage is present on an animal it is nearly always on the center line of the animal. For example, the horn of a rhinocerous or the central horn on a triceratops, or a human's nose.
The symmetry is generally enforced genetically, not environmentally. For example, if you hold a paper up to your face you will find that the left side of the face is different than the right side, or at least that is the way it is for most people. Thus, once conceived, the two sides of the face grow differently, a phenomena that geneticists call genetic "expression". For example, your fingerprints are "expressed" traits, not genetic traits, and for this reason the fingerprint on your left thumb is different than the fingerprint on your right thumb.
Even genetically, however, many parts of the body are not symmetric. For example, the heart is on the left side of the body, but the liver is on the right.
The evolutionary logic for symmetry probably is because it makes locomotion easier and more effective. If an animal is not symmetric, they may have difficulty moving efficiently.
Although not a biologist, Steven Pinker notes that bilateral symmetry evolved in organisms to allow them to move in a straight line. For a bilaterally symmetrical animal to move, they simply alternate movements between one half of their body and the other. This is true for fish, snakes, insects, mammals, etc. There are exceptions, for instance, flying and hopping, but those creatures evolved from ancestors that first locomoted by alternating limbs.
If you look at jellyfish, for example, they are radially symmetric, and their manner of locomotion is to swim in a sort of spiraling shape.
Probably after it arose, bilateral symmetry became a sexual selection criteria, because it is costly to perform during growth, as Pinker goes on to explain.
Radial symmetry describes living and non-living forms these forms can be equally divided into three or more sections that, when rotated through a center of rotation by more than 0° and less than 360°, exactly match each other in orientation and shape. Radial symmetry does not deal with mirror images but near-perfect matches, for example the five equidistant arms of a starfish that circle its central body and are of the same size and shape.
Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension.
Louis Pasteur proposed that biological molecules are asymmetric because the cosmic [i.e. physical] forces that preside over their formation are themselves asymmetric. While at his time, and even now, the symmetry of physical processes are highlighted, it is known that there are fundamental physical asymmetries, starting with time.
Asymmetry in biology Edit
Asymmetry is an important and widespread trait, having evolved numerous times in many organisms and at many levels of organisation (ranging from individual cells, through organs, to entire body-shapes). Benefits of asymmetry sometimes have to do with improved spatial arrangements, such as the left human lung being smaller, and having one fewer lobes than the right lung to make room for the asymmetrical heart. In other examples, division of function between the right and left half may have been beneficial and has driven the asymmetry to become stronger. Such an explanation is usually given for mammal hand or paw preference (Handedness), an asymmetry in skill development in mammals. Training the neural pathways in a skill with one hand (or paw) may take less effort than doing the same with both hands. [ citation needed ]
Nature also provides several examples of handedness in traits that are usually symmetric. The following are examples of animals with obvious left-right asymmetries:
- Most snails, because of torsion during development, show remarkable asymmetry in the shell and in the internal organs. have one big claw and one small claw.
- The narwhal's tusk is a left incisor which can grow up to 10 feet in length and forms a left-handed helix. have evolved to swim with one side upward, and as a result have both eyes on one side of their heads.
- Several species of owls exhibit asymmetries in the size and positioning of their ears, which is thought to help locate prey.
- Many animals (ranging from insects to mammals) have asymmetric male genitalia. The evolutionary cause behind this is, in most cases, still a mystery. 
As an indicator of unfitness Edit
- Certain disturbances during the development of the organism, resulting in birth defects.
- Injuries after cell division that cannot be biologically repaired, such as a lost limb from an accident.
Since birth defects and injuries are likely to indicate poor health of the organism, defects resulting in asymmetry often put an animal at a disadvantage when it comes to finding a mate. For example, a greater degree of facial symmetry is seen as more attractive in humans, especially in the context of mate selection. In general, there is a correlation between symmetry and fitness-related traits such as growth rate, fecundity and survivability for many species. This means that, through sexual selection, individuals with greater symmetry (and therefore fitness) tend to be preferred as mates, as they are more likely to produce healthy offspring. 
Pre-modern architectural styles tended to place an emphasis on symmetry, except where extreme site conditions or historical developments lead away from this classical ideal. To the contrary, modernist and postmodern architects became much more free to use asymmetry as a design element.
While most bridges employ a symmetrical form due to intrinsic simplicities of design, analysis and fabrication and economical use of materials, a number of modern bridges have deliberately departed from this, either in response to site-specific considerations or to create a dramatic design statement.
Some asymmetrical structures
In fire protection Edit
In fire-resistance rated wall assemblies, used in passive fire protection, including, but not limited to, high-voltage transformer fire barriers, asymmetry is a crucial aspect of design. When designing a facility, it is not always certain, that in the event of fire, which side a fire may come from. Therefore, many building codes and fire test standards outline, that a symmetrical assembly, need only be tested from one side, because both sides are the same. However, as soon as an assembly is asymmetrical, both sides must be tested and the test report is required to state the results for each side. In practical use, the lowest result achieved is the one that turns up in certification listings. Neither the test sponsor, nor the laboratory can go by an opinion or deduction as to which side was in more peril as a result of contemplated testing and then test only one side. Both must be tested in order to be compliant with test standards and building codes.
There are no a and b such that a < b and b < a.  This form of asymmetry is an asymmetrical relation.
Certain molecules are chiral that is, they cannot be superposed upon their mirror image. Chemically identical molecules with different chirality are called enantiomers this difference in orientation can lead to different properties in the way they react with biological systems.
Asymmetry arises in physics in a number of different realms.
The original non-statistical formulation of thermodynamics was asymmetrical in time: it claimed that the entropy in a closed system can only increase with time. This was derived from the Second Law (any of the two, Clausius' or Lord Kelvin's statement can be used since they are equivalent) and using the Clausius' Theorem (see Kerson Huang ISBN 978-0471815181). The later theory of statistical mechanics, however, is symmetric in time. Although it states that a system significantly below maximum entropy is very likely to evolve towards higher entropy, it also states that such a system is very likely to have evolved from higher entropy.
Particle physics Edit
Symmetry is one of the most powerful tools in particle physics, because it has become evident that practically all laws of nature originate in symmetries. Violations of symmetry therefore present theoretical and experimental puzzles that lead to a deeper understanding of nature. Asymmetries in experimental measurements also provide powerful handles that are often relatively free from background or systematic uncertainties.
Parity violation Edit
Until the 1950s, it was believed that fundamental physics was left-right symmetric i.e., that interactions were invariant under parity. Although parity is conserved in electromagnetism, strong interactions and gravity, it turns out to be violated in weak interactions. The Standard Model incorporates parity violation by expressing the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model. A consequence of parity violation in particle physics is that neutrinos have only been observed as left-handed particles (and antineutrinos as right-handed particles).
In 1956-1957 Chien-Shiung Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson found a clear violation of parity conservation in the beta decay of cobalt-60. [ citation needed ] Simultaneously, R. L. Garwin, Leon Lederman, and R. Weinrich modified an existing cyclotron experiment and immediately verified parity violation. [ citation needed ]
CP violation Edit
After the discovery of the violation of parity in 1956–57, it was believed that the combined symmetry of parity (P) and simultaneous charge conjugation (C), called CP, was preserved. For example, CP transforms a left-handed neutrino into a right-handed antineutrino. In 1964, however, James Cronin and Val Fitch provided clear evidence that CP symmetry was also violated in an experiment with neutral kaons.
CP violation is one of the necessary conditions for the generation of a baryon asymmetry in the early universe.
Combining the CP symmetry with simultaneous time reversal (T) produces a combined symmetry called CPT symmetry. CPT symmetry must be preserved in any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian. As of 2006, no violations of CPT symmetry have been observed.
Baryon asymmetry of the universe Edit
The baryons (i.e., the protons and neutrons and the atoms that they comprise) observed so far in the universe are overwhelmingly matter as opposed to anti-matter. This asymmetry is called the baryon asymmetry of the universe.
Isospin violation Edit
Isospin is the symmetry transformation of the weak interactions. The concept was first introduced by Werner Heisenberg in nuclear physics based on the observations that the masses of the neutron and the proton are almost identical and that the strength of the strong interaction between any pair of nucleons is the same, independent of whether they are protons or neutrons. This symmetry arises at a more fundamental level as a symmetry between up-type and down-type quarks. Isospin symmetry in the strong interactions can be considered as a subset of a larger flavor symmetry group, in which the strong interactions are invariant under interchange of different types of quarks. Including the strange quark in this scheme gives rise to the Eightfold Way scheme for classifying mesons and baryons.
Isospin is violated by the fact that the masses of the up and down quarks are different, as well as by their different electric charges. Because this violation is only a small effect in most processes that involve the strong interactions, isospin symmetry remains a useful calculational tool, and its violation introduces corrections to the isospin-symmetric results.
In collider experiments Edit
Because the weak interactions violate parity, collider processes that can involve the weak interactions typically exhibit asymmetries in the distributions of the final-state particles. These asymmetries are typically sensitive to the difference in the interaction between particles and antiparticles, or between left-handed and right-handed particles. They can thus be used as a sensitive measurement of differences in interaction strength and/or to distinguish a small asymmetric signal from a large but symmetric background.
- A forward-backward asymmetry is defined as AFB=(NF-NB)/(NF+NB), where NF is the number of events in which some particular final-state particle is moving "forward" with respect to some chosen direction (e.g., a final-state electron moving in the same direction as the initial-state electron beam in electron-positron collisions), while NB is the number of events with the final-state particle moving "backward". Forward-backward asymmetries were used by the LEP experiments to measure the difference in the interaction strength of the Z boson between left-handed and right-handed fermions, which provides a precision measurement of the weak mixing angle.
- A left-right asymmetry is defined as ALR=(NL-NR)/(NL+NR), where NL is the number of events in which some initial- or final-state particle is left-polarized, while NR is the corresponding number of right-polarized events. Left-right asymmetries in Z boson production and decay were measured at the Stanford Linear Collider using the event rates obtained with left-polarized versus right-polarized initial electron beams. Left-right asymmetries can also be defined as asymmetries in the polarization of final-state particles whose polarizations can be measured e.g., tau leptons.
- A charge asymmetry or particle-antiparticle asymmetry is defined in a similar way. This type of asymmetry has been used to constrain the parton distribution functions of protons at the Tevatron from events in which a produced W boson decays to a charged lepton. The asymmetry between positively and negatively charged leptons as a function of the direction of the W boson relative to the proton beam provides information on the relative distributions of up and down quarks in the proton. Particle-antiparticle asymmetries are also used to extract measurements of CP violation from B meson and anti-B meson production at the BaBar and Belle experiments.
Asymmetry is also relevant to grammar and linguistics, especially in the contexts of lexical analysis and transformational grammar.
Enumeration example: In English, there are grammatical rules for specifying coordinate items in an enumeration or series. Similar rules exist for programming languages and mathematical notation. These rules vary, and some require lexical asymmetry to be considered grammatically correct.
Cryo-EM reveals new species-specific proteins and symmetry elements in the Legionella pneumophila Dot/Icm T4SS
Legionella pneumophila is an opportunistic pathogen that causes the potentially fatal pneumonia known as Legionnaires’ Disease. The pathology associated with infection depends on bacterial delivery of effector proteins into the host via the membrane spanning Dot/Icm type IV secretion system (T4SS). We have determined sub-3.0 Å resolution maps of the Dot/Icm T4SS core complex by single particle cryo-EM. The high-resolution structural analysis has allowed us to identify proteins encoded outside the Dot/Icm genetic locus that contribute to the core T4SS structure. We can also now define two distinct areas of symmetry mismatch, one that connects the C18 periplasmic ring (PR) and the C13 outer membrane cap (OMC) and one that connects the C13 OMC with a 16-fold symmetric dome. Unexpectedly the connection between the PR and OMC is DotH, with five copies sandwiched between the OMC and PR to accommodate the symmetry mismatch. Finally, we observe multiple conformations in the reconstructions that indicate flexibility within the structure. We hypothesize this conformational flexibility is likely to facilitate the Dot/Icm T4SS’s ability to translocate a remarkably large set of
300 putative substrates across the inner and outer membranes of the bacterial cell.
Biology Chapter 17
adds to the body's flexibility and it enormously increases the potential for the development of specialized body parts.
Body Structure: hollow, porous bodies that are typically asymmetrical, some have radial symmetry
outer layer of flattened sells
inner layer flagellated "collar cells"
Feeding: filter feeders. movement of flagella on the collar cells produces a current of water which flows through the body wall
support & movement Protein fibers and sharp slivers of silica or calcium carbonate provide support
can move very slow
considered sessile "they remain ancored to their substrate
Reproduction: hermaphrodites, each releases sperm into water currents and retains eggs . zygote develops into blastula which is released and may drift for some time before settling in a new habitat. reproduce asexually by budding or fragmentation
Body Structure: radially symmetrical
Polyp - sessile stalk with tentacles on one end
Meduse - Free Swimming, bell shaped body form typical of jelly fishes
Cnidocytes: Stinging cells embedded into the tentacles of cnidarians that contain tiny harpoons
Diversity: Corals and sea anemones belong to a clade of cnidarians that exist exclusively as sessile polyps. Second clade contains hydras and the jellyfishes.
Feeding: Carnivores that use theri tentacles to grab and sting passing prey
Support & movement
Body wall acts as a hydrostatic skeleton. Swim with tentacles, never and muscle cells.
Reproduction: sexually and asexually
Habitat: Free living, usually aquatic or parasitic on other animals
Body Structure: lack coelom. Each cell can exchange materials with the environment. Bilateral symmetry
3 germ layers
Diversity: Pylum includes free living flatworms (marine flatworm and planarian, flukes and tapeworms
Feeding: free living flatworms usually predators or scavengers
Fluke: fees on blood and other host tissues
Tapeworm: lacks a mouth and digestive system, it attaches to the hosts intestine and absorbs food through its body wall
Circulation and respiration: Flatworms lack specialized circulatory and respiratory systems. Diffuse through the body wall
Excretion: specialized structures maintain internal water balance and excrete nitrogenous wastes through pores on the body surface
Nervous system: flatworms have nerve cords and clusters of nerve cells at the head end, forming a simple brain, others have nerve net
Support and movement: flatworms have a hydrostatic skeleton and may creep or swim by contracting muscles in a rolling motion
Reproduction: flatworms reporduce asexually. free living species
tapeworms: posterior end of a tapeworms body consists of repeated reproductive organs. Portions containing fertilized eggs break off and leave the host in feces. When a new host swallows the reproductive structures in contaminated water, the eggs hatch into larvae and colonize and mature in the host's body.
Defense: inside the host, parasitic flatworms are safe from predators. free living forms secrete a protective mucus.
Habitat: Terestrial, marine and freshwater
Mantle: A fold of tissue that secretes a shell in most species.
Foot: provides movement
Visceral mass: contains the digestive and reproductive organs
Radula: tongue-like strap with teeth made of chitin, scrape food into their mouths.
Chitons marine animals w/8 flat shells that overlap like shingles
Bivalves: clams and scallops 2 part, hinged shells
Gastropods: stomach-foot - include snails and slugs
Cephalopods: head-foot are marine animals such as octopuses and squids
Feeding: Chitons scrape algae off rocks, bivalves filter food particles out of water.
most gastropods are herbivores:
Cephalopods are predators
Circulatory system: most mollusks have an open circulatory system in which a heart pumps blood to tissues throughout the body cavity instead of within vessels.
Cephalopods have closed circulatory system with blood confined to vessels
Respiratory system: Aquatic mollusks have gills terrestrial snails and slugs have a lung derived from a space called the mantle cavity.
Excretory system: organ filters blood and produces urine
Nervous system: simple and ladder-like to complex and cephalized. octopus nervous system includes a brain, visual system and sense of touch.
Reproduction: fertilization may be external or internal
Defense: hard shells of bivalves
snails protect against many predators
cephalopods - other defenses, squirt ink
Squids & octopuses can change their color and shape to match their background
Symmetry of species - Biology
The key kinds of symmetry relevant in the study of organismal biology are radial and bilateral symmetry. In studying the evolutionary development of symmetry in plants and animals, one fascinating element that emerges is that symmetry is not easily broken in natural selection. Evidence of this comes primarily from genetic tests conducted with the fruit fly (Drosophila). For more specific information about these experiments, click here. Some scientists believe that the recorded prevalence of bilateral symmetry in organisms is simply a default result of the fact that most cells do not possess any "symmetry breaking" information. Consequently, the study of asymmet ry in organisms is intriguing, but it is a field of study that is relatively hazy due to the lack of information on cellular differentiation or coordinates of differentiation. Two examples of asymmetrical development in animals are revealed in the lobster claw, which is randomly asymmetrical, and in the coiling pattern of snails, which possess fixed asymmetry. The sponge, which is a fascinating organism in just about every aspect, actually possesses no symmetry at all and no formulaic pattern of asymmetry. For more detailed information, a very technical essay entitled, "From symmetry to asymmetry: Phylogenetic patterns of asymmetry variation in a nimals and their evolutionary significance," is available from the Biology department of the University of Alberta.
Difference in structural symmetry is one of the guiding elements behind animal diversification and the vertebrate/invertebrate split during an animal's evolutionary history. In tracing the history of biological diversity, biologists have now almost unive rsally agreed on the fact that the animal kingdom is monophyletic, meaning that if one could trace the entire evolutionary tree of animals all the way back to the Precambrian era, all of the branches would converge on one single protistan ancestor.
From that single ancestor, one of the earliest branching points in the hypothetical phylogeny of animals is the place at which multicellular beings with true tissues (eumetazoa) split into those possessing radial symmetry and those possessing bilateral sy mmetry.
Radial Symmetry: A radial animal has a top and a bottom (or an oral and aboral side), but has no head end or rear end and no left or right. Examples of animals possessing radial symmetry are: jellyfishes, corals, anemones, and ctenophora.
Bilateral Symmetry: Bilateral (two-sided) symmetry is the most common form of symmetry possible, and it is found throughout the biological and non-biological world. Animals possessing bilateral symmetry have a dorsal (top) side, a ventral (bottom ) side, an anterior (head) end, a posterior (tail) end, and a distinct left and right side. Associated with bilateral symmetry is the phenomenon of cephalization, which is the evolutionary trend towards the concentration of sensory equipment on the anter ior end this means that such organisms are directionally sensitive and mobile. Generally the anterior, or cephalized, end is the first to encounter food, danger, or other stimuli. Before bipedal development (common in humans and apes), cephalization wa s an adaptation for movement such as crawling, burrowing, or swimming. Examples of animals that possess bilateral symmetry are: flatworms, common worms ("ribbon worms"), clams, snails, octopuses, crustaceans, insects, spiders, brachiopods, sea stars, sea urchins, and vertebrates.
The symmetry of an animal generally fits its lifestyle. For example, many radial animals are sessile forms or plankton and their symmetry equips them to meet their environment equally well from all sides. More active animals are generally bilateral. Th e two forms of symmetry, however, are not absolutely separate. A great deal of radial symmetry is proven to emerge secondarily from a bilateral condition (frequently it emerges from animals adapting to a more sedentary lifestyle). Some animals, such as t he sea urchin, are radially symmetrical, but their embryonic development and internal anatomy show that they arose from a bilaterally symmetrical ancestor.
Images of symmetry in the animal kingdom (according to phyla>:
- (no symmetry) (radial) (bilateral)
- Arthropoda: Dragonfly | Crayfish (bilateral)
- An example of the "midplane" in bilateral symmetry.
Bilateral and radial symmetry are also found in the Plant kingdom symmetry in ggeneral, however, is less significant here that among animals. These forms of symmetry have the most significance in the structure of flowers, which are the points of fertili zation for angiosperms. Unlike the animal kingdom in which organisms with radial symmetry developed out of a nascent bilateral structure, the opposite is true for plants. Many plant phyla have gradually evolved from having radial symmetry to having bila teral symmetry. Much of this is a result of form following function: plants possessing bilateral symmetry are capable of signaling a particular pollinator in the direction of the flowers fertilizing organs. A good way to judge floral symmetry is to plac e flowers in the following categories: 1) fused petals - radial symmetry, 2) free petals, fully open, most often radial symmetry, 3) free petals, closed, most often bilateral.
More Images of Symmetry in Flowers:
Other Biological Implications of Symmetry
Symmetry is a pivotal concept in many other areas of biology, particularly in the study of molecular biology. Molecular biology is ultimately more complex than organismal biology, but if you want to learn more, here are some excellent links to molecular biology pages regarding symmetry:
For a comprehensive list of links to articles and analyses about macromolecular symmetry (primarily proteins) click here.
For an interesting article on dihedral symmetry in cancer cells (warning, this is very technical), go here.
For a great article on the symmetry of the largest macromolecule ever discovered, go here.
For everything you could ever want to know about molecular and structural biology, visit the Nature Magazine Structural Biology site. You will have to logon with a user name, but it's free and seems to have no strings attached.
Chordates (Chordata) are a group of animals that includes vertebrates, tunicates, lancelets. Of these, the vertebrates—lampreys, mammals, birds, amphibians, reptiles, and fishes—are the most familiar and are the group to which humans belong.
Chordates are bilaterally symmetrical, which means there is a line of symmetry that divides their body into halves that are roughly mirror images of each other. Bilateral symmetry is not unique to chordates. Other groups of animals—arthropods, segmented worms, and echinoderms—exhibit bilateral symmetry (although in the case of echinoderms, they are bilaterally symmetrical only during the larval stage of their life cycle as adults they exhibit pentaradial symmetry).
All chordates have a notochord that is present during some or all of their life cycle. A notochord is a semi-flexible rod that provides structural support and serves as an anchor for the animal's large body muscles. The notochord consists of a core of semi-fluid cells enclosed in a fibrous sheath. The notochord extends the length of the animal's body. In vertebrates, the notochord is only present during the embryonic stage of development, and is later replaced when vertebrae develop around the notochord to form the backbone. In tunicates, the notochord remains present throughout the animal's entire life cycle.
Chordates have a single, tubular nerve cord that runs along the back (dorsal) surface of the animal which, in most species, forms a brain at the front (anterior) end of the animal. They also have pharyngeal pouches that are present at some stage in their life cycle. In vertebrates, pharyngeal pouches develop into various different structures such as the middle ear cavity, the tonsils, and the parathyroid glands. In aquatic chordates, the pharyngeal pouches develop into pharyngeal slits which serve as openings between the pharyngeal cavity and the external environment.
Another characteristic of chordates is a structure called the endostyle, a ciliated groove on the ventral wall of the pharynx that secretes mucus and traps small food particles that enter the pharyngeal cavity. The endostyle is present in tunicates and lancelets. In vertebrates, the endostyle is replaced by the thyroid, an endocrine gland located in the neck.
Special Issue Editor
The lack of symmetry within the shapes of cell nuclei has long been a reliable criterion for diagnosing cancerous cells, but the reasons remain entirely mysterious. This is an extreme example of a general pattern of biological symmetry-breaking being discovered in particular instances, but the causal principles being left unexplained.
One phenomenon that actually has been intensively studied is the causation of right-left asymmetry of vertebrate hearts and abdominal organs. This turns out to be controlled by the submicroscopic rotation symmetry of flagella. Another well-studied phenomenon is the causation of planes of right-left reflection symmetry by the (random) locations where sperm fuse with egg cells.
To explain the breaking of displacement symmetry, such as segmentation of the spine, alternative possible mechanisms have been invented by Turing and by Zeeman. Surgical juxtaposition of tissues with oppositely-oriented axes can stimulate formation of doubled, tripled, or even quadrupled reflection symmetry.
A tantalizing example of dilation symmetry is the ability of some embryos to form normally-proportioned anatomy over as much as 8 to 1 variations of volume. Hans Driesch&rsquos discovery of this unexpected ability of embryos &ldquoto scale&rdquo drove him to despair of mechanistic causes, and has motivated Wolpert&rsquos influential &ldquoFrench Flag&rdquo hypothesis. Opportunities remain which will likely prove as revolutionary as any application of symmetry to physics.
Prof. Dr. Albert K. Harris
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The implicit assumption of symmetry and the species abundance distribution
Species abundance distributions (SADs) have played a historical role in the development of community ecology. They summarize information about the number and the relative abundance of the species encountered in a sample from a given community. For years ecologists have developed theory to characterize species abundance patterns, and the study of these patterns has received special attention in recent years. In particular, ecologists have developed statistical sampling theories to predict the SAD expected in a sample taken from a region. Here, we emphasize an important limitation of all current sampling theories: they ignore species identity. We present an alternative formulation of statistical sampling theory that incorporates species asymmetries in sampling and dynamics, and relate, in a general way, the community-level SAD to the distribution of population abundances of the species integrating the community. We illustrate the theory on a stochastic community model that can accommodate species asymmetry. Finally, we discuss the potentially important role of species asymmetries in shaping recently observed multi-humped SADs and in comparisons of the relative success of niche and neutral theories at predicting SADs.
Appendix S1 Ensamble formulas for SADs.
Appendix S2 Differences in species sampling detectability.
Appendix S3 The logseries and the multinomial likelihood.
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