Population (means population in the ordinary sense, however)

POPULATION means population in the ordinary sense, however in genetics the concept of P. is associated with a number of special concepts and regularities. In this special, genetic sense, the term P. was introduced by Johannsen (Jo-riansen) in his research "On Inheritance in Populations and Pure Lines", published in 1903 (see Heredity). By P. is understood any arbitrary collection of individuals of a particular species, race, or people; the arbitrariness of the composition of P. is determined by the absence of selection in its sampling, and P. is limited only in the numerical sense (as part of an entire species), or geographical sense (as taken only from a specific habitat area), or finally in racial and breed sense (as relating to one specific biological group of organisms). Such a P. turns out to be completely heterogeneous in hereditary respect and in it various genotypes can be detected (see). Organisms possessing homogeneous genotypes, in their aggregate, form a biotype. Thus, every P. consists of a certain number of different biotypes (genotypes). Therefore, the hereditary properties of P. are determined first by the specific composition of certain biotypes and second by the numerical relationships between them. The method of reproduction of individuals of P. determines the changes in hereditary composition that are observed in it from generation to generation. If the individuals forming a population reproduce asexually (e.g. protozoa), then the offspring of each such individual will be hereditarily completely homogeneous, forming in their aggregate the so-called clone. Therefore, the entire P., consisting of a large number of clones, will not change from generation to generation, and only selection, natural or artificial, of breeder individuals can cause violations in the qualitative and quantitative composition of P. Otherwise, P. that reproduces sexually will behave. In this case, the offspring is determined by the possible hereditary diversity of gametes and the probabilities of their combination. But here too one should distinguish between self-fertilizing or parthenogenetic organisms and organisms that reproduce by crossing two individuals. In the former (e.g. self-pollinating plants), once achieved homogeneity of gametes, i.e. homozygosity of the individual, is preserved in the future; therefore, the offspring of such a self-fertilizing individual forms in its aggregate the so-called pure line, completely homogeneous in hereditary respect. The offspring, however, of a heterozygous individual that reproduces without crossing will show splitting into a series of definite genotypes in definite numerical ratios (see Mendelism). But since part of such offspring will also turn out to be homozygous, i.e. non-splitting in the future, such a P. will change from generation to generation in the quantity of heterozygous individuals: their percentage will constantly decrease. If one follows the composition of such a P. with respect to one pair of allelic genes (monohybrids), it is found that the decrease of heterozygous forms occurs in geometric progression; the percentage of heterozygotes can be determined by the formula ~^=1, where n is the ordinal number of the generation. In relation to polyhybrid P., this process, although it occurs, does so already not in geometric progression, but at a slower rate. The greatest complexity is found in the regularities in P. of organisms that reproduce by crossing (the so-called allogamous organisms), to which cross-pollinated plants and the vast majority of animals, including man, belong. In this case, the genotype of an individual does not yet fully determine its offspring, and for studying the dynamics of such a P. it turns out to be necessary to proceed from the diversity of gametes, their numerical relationships, and the probabilities of their encounters-with respect to all individuals in the aggregate. Thus, if we study the fate of P. with respect to one pair of allelic genes (A-a), then although theoretically the individuals forming it fall into three genotype groups-two homozygous (AA and aa) and heterozygous (Aa)-they will form only two types of gametes (A and a). If we denote the number of gametes A by d, and a by r, then the total number of gametes in P. is characterized by the formula d+r = l. Since we know the number of types of gametes (2) and their relative numbers (d and r), to determine the ratio of genotypes in P. it remains to know the third condition-the probability of gamete encounter during crossing. The basic and simplest case will be equal probability for all possible combinations of gametes. This condition is realized under panmixia, i.e. free crossing, when no additional conditions hinder or favor any of the theoretically possible combinations of individuals of different sexes. In this case all types of gamete combinations will be realized: in our case of monohybrid population-four combinations (dA . dA; dA . ra; ra . dA; ra . ra). Therefore we get the following composition and number of genotypes in the population: d²AA+2drAa+ + r² aa. It is easy to calculate that such a P. again forms 2 types of gametes in the same relative quantities as in the previous generation: gametes A in quantity d²+dr = d (since d + +r = 1); gametes a in quantity r²+rd=r. Therefore such a population will retain in all subsequent generations the same composition. Thus a population under panmixia is in equilibrium with respect to monohybrid genotypes, if the ratio of homozygotes and heterozygotes in it is determined by the formula of the expanded binomial: (d^J_rr)² = d^2j_r2dr+r*, or-what is the same-if the product of the number of dominant and recessive homozygotes equals the square of half the chi-₂--) (the so-called law of equilibrium of monohybrid P.). If, however, the composition of the original P. does not correspond to the indicated conditions, then it turns out that in the very next generation as a result of panmixia the equilibrium ratios are automatically established (the so-called law of stabilizing crossing of monohybrid P.). It would however be a gross error to believe that any P. with respect to any number of allelic pairs of genes comes as a result of the very first panmixia to a state of equilibrium. In reality the above formulated conditions of stabilization and equilibrium turn out to be insufficient with respect to polyhybrid crossings in P. The more pairs of allelic genes are taken into account in studying the dynamics of P., the more mathematical conditions of zygote and gamete ratios are found to be necessary for establishing equilibrium for all studied genotypes. Thus, in the case of dihybrid panmixia, i.e. when two pairs of allelomorphs (A and a; B and b) are studied, the P. contains 9 genotypes, which however form only 4 kinds of gametes (see Mendelism); if the frequencies of gametes AB, Ab, aB, ab are equal to a, b, c and d respectively, then under the condition that ad = bc, i.e. the product of the number of dominant and recessive gametes for both genes equals the product of gametes carrying one dominant and one recessive gene, equilibrium is established.- An even more complex character is found in the equilibrium conditions in trihybrid and more polygenic panmixia. However in all these cases in each generation there occurs an automatic change in the composition of P. in the direction of approaching the conditions necessary for equilibrium. So, generally any P. as a result of panmixia tends to a state of equilibrium; however, if with respect to monohybrid crossing this equilibrium is realized in one generation, then with increasing polyhybridity the number of generations necessary for establishing equilibrium increasingly increases, reaching in the limit an infinite magnitude. It should be borne in mind that the mathematical equilibrium conditions of P. that we analyzed refer to genes inherited independently of sex and not showing the so-called linkage and crossing-over between themselves (see Crossing over of chromosomes), i.e. localized in non-homologous chromosomes-autosomes. For genes localized in sex chromosomes and therefore inherited with linkage to sex (see Sex), the mathematical equilibrium conditions have a somewhat more complex character; an even more complex mathematical formulation will be given by the equilibrium conditions with respect to genes localized in homologous chromosomes and undergoing phenomena of linkage and crossing-over. All the above regularities are fully realized under ideal panmixia, however practically one usually observes this or that violation of free crossing, when this or that selection is realized. Selection can express itself both in different fertility of different genotypes and in different their viability. Thanks to this certain combinations have a greater probability of being realized, and as a result the composition of P. changes. There are a number of mathematical methods for accounting for the effect of selection on P. On the basis of these calculations it should be assumed that the process of selection proceeds differently depending on which trait-dominant or recessive-is more favorable, viable or fertile.

If a dominant trait is selected, the process that results from such selection, which enriches the P. with the dominant genotype and simultaneously depletes it of the recessive trait, initially proceeds at a rapid pace, then sharply slows down; indeed, even if the original P. consisted almost entirely of recessive forms, selection for dominance in a relatively small number of generations leads to the absolute predominance of the dominant form; however, when the process of purging the P. of the recessive trait approaches completion, it slows down by tens and hundreds of times, so that to achieve 100% dominance in the P. requires an enormous number of generations. Conversely, if selection favors the recessive form, the initial stages of increasing its percentage in the P. require a very large number of generations, but once a relatively small percentage is reached, the process sharply accelerates. Thus, the process of selecting one genotype or another is theoretically fully realized, i.e., from almost complete absence to 100% saturation of the P. The speed of this process, however, i.e., the number of generations required, depends both on the intensity of selection and on the composition of the original P. It should not be forgotten that selection does not eliminate the tendency of the P. toward equilibrium—it merely disrupts the conditions for achieving this equilibrium. Thus, both processes occur simultaneously, giving a complex combined picture of the dynamics of the P. (see Evolutionary Theories). As a result of examining the dynamics of the P., we see that both under selection and under panmixia, diverse automatic changes occur in its genetic composition. For a time, these changes were mistakenly considered as proof of the inheritance of modifications. It was also believed that selection leads to a hereditary change in the trait in the direction of selection. At the present time, it is clear that as a result of selection, certain genotypes carrying genes, which by no means newly arose but already existed in the P., come to predominate. That this is so is clearly evident from the fact that selection gives results only until genotypic uniformity is achieved with respect to the selected trait; this uniformity is precisely achieved when selection leads to the isolation of a pure line, clone, or homozygous form—in all these cases, selection subsequently yields no further results (for more details, see Heredity). Of course, it should not be forgotten that simultaneously in any P., a mutational process may occur, i.e., the emergence of new genes (see Mutation). As a result, the composition of the P. changes, and new conditions for its dynamics and equilibrium are obtained. Finally, in addition to selection, a condition that disrupts ideal panmixia may be the process of isolating certain parts of the P. as a result of the most diverse geographical, ecological, and physiological barriers to free crossing. As a result of isolation, one P. splits into two or more, for which, of course, new regularities will automatically arise (for more details on these questions, see Evolutionary Theories). The regularities of the P. can be used in studying the heredity of individual traits, all the more so in cases where it is not possible to carry out experimental crossings. This is especially true of humans, in whom, due to the small size of the offspring, it is often impossible by genealogical means to obtain sufficient numerical data to establish the pattern of inheritance of the trait being studied.