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homology(hōmŏl`əjē), in biology, the correspondence between structures of different species that is attributable to their evolutionary descent from a common ancestor. For example, the forelimbs of vertebrates, such as the wing of bird or bat, and the foreleg of an amphibian, are homologous; there is an almost identical number of bones in the limbs, and the pattern construction is identical. Homologous structures do not necessarily have to have the same function; the wings of birds and forelegs of a horse are homologous through they clearly serve different functions. Analogyanalogy,
in biology, the similarities in function, but differences in evolutionary origin, of body structures in different organisms. For example, the wing of a bird is analogous to the wing of an insect, since both are used for flight.
..... Click the link for more information. is the functional similarity between structures that do not have a common origin; for example, the wings of birds and those of insects are analogous.
in biology, a similarity of organs constructed in the same way and developing from identical embryonic rudiments in different animals and plants; such homologous organs may be dissimilar in appearance and perform different functions.
The determination of homology and its juxtaposition to analogy were proposed by the English scientist R. Owen (1843), who distinguished specific homology from serial homology. He defined specific homology as the correspondence of an organ in one animal to an organ in another, in terms of position and relationship with other parts of the body (for example, the human arm, the cetacean flipper, and the avian wing). Serial homology, or homodynamy, he understood to be correspondence in the same animal of body parts located along the same longitudinal axis (for example, the human arm and leg). The commonality of origin of organisms was first given as the natural-historical explanation for homology by C. Darwin (1859). The German anatomist C. Gegenbaur (1898) distinguished complete and incomplete homology. In complete homology the similarity of organs according to their position and connections with other organs is not disrupted by variations in form and size; in incomplete homology certain parts of organs may disappear through evolution (defective homology), or new parts may appear (augmentative homology). The combination of loss of some parts of the body and the new formation of others is called imitative homology (German biologist M. Fürbringer).
The morphological criteria for homology are similar position and structure of the organs and the presence of transitional forms. The ontogenetic criterion of homology is the development of organs from similar embryonic rudiments. An example of homology in plants is that of leaves that have been modified due to the results of various functions and converted into flower petals, stamens, or one of several kinds of thorns. Specific instances of homology are homodynamy, homonomy, and homotypy.
REFERENCESShmal’gauzen, I. I. Osnovy sravnitel’noi anatomii pozvonochnykh zhivotnykh, 2nd ed. Moscow, 1935.
Darwin, C. Proiskhozhdenie vidov putem estestvennogo otbora: Soch., vol. 3. Moscow-Leningrad, 1939.
Bliakher, L. la. “Analogiia i gomologiia.” In the collection Ideia razvitiia v biologii. Moscow, 1965.
Haeckel, E. Generelle Morphologie der Organismen, vols. 1–2. Berlin, 1866.
Gegenbaur, C. Vergleichende Anatomie der Wirbelthiere. Leipzig, 1898.
Owen, R. On the Archetype and Homologies of the Vertebrate Skeleton. London, 1847.
L. IA. BLIAKHER
(in mathematics). (1) In projective geometry, a one-to-one transformation of a projective plane onto itself, in which the linear distribution of points is preserved and all points of a given straight line—the axis of homology—remain fixed.
(2) A concept of topology. In the simplest case homology refers to the property by which a closed curve on a given surface is the boundary of a certain part of the surface. For example, the curve l on the surface of a torus is the boundary of a part 5 of this surface; it is said to be homologous to zero. The curve λ is not homologous to zero since it is not a boundary of any part of the surface; a cut along it will not result in a piece of the torus falling out (see Figure 1).