The occurrence of natural selection demands (i) that there exists genetical heterogeneity, and (2) that unlike genotypes leave different average numbers of progeny. It is now known that both of these conditions are fulfilled, and all the available facts of evolution are in accord with the genetical theory of variation and selection.

Species must, on this view, differ in the same way as, but to a greater extent than, varieties or individuals of the same species.

The application of this criterion leads us to the conclusion that species differences are polygenic, i.e. depend on quantitative characters whose variation is controlled by many genes. These genes have individual effects which are both similar to one another and small when compared with non-heritable fluctuation. Other kinds of heritable difference are ancillary to polygenic variation in speciation.

Each individual polygene is inherited in the same way as the familiar major mutants of the laboratory. As, however, there are many polygenes affecting a given character, the aggregate type of inheritance is distinct from that of the major mutants. Polygenically controlled differences are quantitative rather than qualitative and do not lead to the sharp segregation shown by the more familiar genetical differences. Polygenic characters, such as stature in man, can show any degree of expression between wide limits. Many genotypes may have the same phenotype. Thus polygenic theory relates continuous phenotypical variation to discontinuous genotypical variation, the biometrical to the genetical.

These special properties of polygenic behaviour lead us to a new and clearer understanding of the action of natural selection in producing adaptive and evolutionary changes.

Very fine adaptation of the phenotype to environment is made possible by the existence of such a wide range of phenotypic expression. The frequency distribution of the individual phenotypes found in a population may approximate to a normal curve. It may, however, also be skew, to an extent determined by the dominance and interaction relations of the polygenes and by the scale on which the character is measured. The central, most frequent, phenotype must closely approximate to the optimum for the prevailing environment. Departure from this central type will thus mean poorer adaptation and loss of fitness.

The phenotype is produced by the genotype acting as a whole. Since polygenes have effects similar to one another, a given phenotype may correspond to various genotypes some containing one and some another allelomorph of a given polygene. As a consequence neither allelomorph will have an unconditional advantage over the other, in the way that major mutants do. Rather the advantage of any allelomorph of a polygene will be conditioned by the other polygenes present. Fisher's theory of dominance then leads us to expect that, in wild populations, equal numbers of polygenes will show dominance of the allelomorphs leading to increased and decreased expression of the character. Artificial selection disturbs this equality. The existing evidence is in keeping with these expectations.

The existence of polygenic variation free in the phenotype must lead to some individuals departing from the optimum and so showing reduced fitness. Variation is to this extent disadvantageous, but it is also essential for prospective adaptive and evolutionary change. The polygenic variability necessary for prospective change need not, however, exist as free phenotypic variation which will affect fitness. It may be hidden in the genotype under the cloak of phenotypic constancy, when it will have no effect in lowering fitness. Such hidden, or potential, variability is released, and shown freely by the phenotype, as a result of segregation from heterozygotes. Free variability may pass into the potential state by means of crossing between unlike individuals. Some potential variability will exist as differences between homozygous individuals. Such homozygotic variability can be freed by segregation only after intercrossing has rendered it hetero-zygotic.

If most of the variability in a population is potential, high current fitness can be combined with the possibility of great, though slow, change under selection. In such cases the response of the organism to selection will largely depend on the fixation of variability as it passes from the undetectable potential to the detectable free state. Thus selection may superficially appear to create its own free directional variability.

The frequency of recombination between polygenes affecting a character will control the rate of variability release. Consequently the effective recombination frequency is itself an adaptive character and will be subject to selective action. The evolution of genetic systems is largely the history of this selective control of effective recombination.

Control of recombination is almost wholly achieved within chromosomes, so that the storage of variability must depend on intrachromosome adjustment. Natural selection will tend to build up balanced combinations of polygenes within each of the chromosomes. These combinations will have the properties of close adaptation to the optimum, great variability storage and slow variability release.

Combinations are characterized by two kinds of balance, that of the individual combination, as shown in homozygotes (internal balance), and that of pairs of combinations when working together in heterozygotes (relational balance). Dominance permits the adjustment of these balances independently of one another. The theory of polygenic balance shows how polymorphism and clines can be maintained.

Heterosis is due to a particular kind of poor relational balance brought about by artificial selection. The concept of heterosis is now extended to include all types of such unbalance, natural and artificial. Poor relational balance encourages isolation, and so heterosis, in this broad sense, stimulates the rise of isolation mechanisms and hybrid sterility.

The store of polygenic variability, steadily depleted by random fluctuations in allelomorph frequency and by response to selection, is replenished by new mutations. Since all polygenes affecting a given character have much the same effect, the phenotypical properties of a population may be stable or nearly so even though the genotype is fluid. Fixation, mutation, segregation and recombination cause a genotypic flux to exist under the cloak of a phenotypic stability, itself maintained by the action of the same natural selection, which, under new conditions, would lead to new adaptation.

The mechanical relations of unlike combinations, whose constituent polygenes are intermingled along the same chromosome, are sufficient to account for the degeneration of unused organs.

The breeding, or mating, system of a species determines the frequency of heterozygosity, upon which the rate of release of potential variability depends. Inbreeding gives homozygosity and high immediate fitness; but it freezes potential variability in the homozygotic state and so reduces the chance of prospective adaptation. Outbreeding has the reverse effect and sacrifices some fitness to flexibility.

The breeding system is thus an adaptive character. It will be subject to selective change towards more closely controlled inbreeding or outbreeding. A controlled compromise between inbreeding and outbreeding may also occur. The strength and direction of control is probably polygenically determined, though the actual controlling mechanism may depend upon a major switch gene for its direct action.

A change from outbreeding to inbreeding increases local adaptation and so leads to heterosis and isolation. It also freezes potential variability and lowers the chance of prospective adaptation. Thus a species which shows such a change to inbreeding will break up into a swarm of small, locally fit, but inflexible, new species. As a consequence of their inflexibility, most of these must perish when environmental changes set in.