A measure of genetic distance (D) based on the identity of genes between populations is formulated. It is defined as D = -logeI, where I is the normalized identity of genes between two populations. This genetic distance measures the accumulated allele differences per locus. If the rate of gene substitution per year is constant, it is linearly related to the divergence time between populations under sexual isolation. It is also linearly related to geographical distance or area in some migration models. Since D is a measure of the accumulated number of codon differences per locus, it can also be estimated from data on amino acid sequences in proteins even for a distantly related species. Thus, if enough data are available, genetic distance between any pair of organisms can be measured in terms of D. This measure is applicable to any kind of organism without regard to ploidy or mating scheme.

Genetic distance between populations

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Evolution at two levels in humans and chimpanzees

Hybrid zones are, roughly speaking, narrow regions in which genetically distinct populations meet, mate, and produce hybrids. They are often only a few hundred meters wide and yet may be several hundred kilometers long. They are found in a wide variety of organisms: Tables 1 and 2 list about 150 reasonably clear examples, in which there is a spatial transition between two hybridizing forms. Such a widespread and striking phenomenon requires explanation; more importantly, it offers us several ways of understanding the nature and origin of species. First, hybrid zones pose interesting questions for the taxonomist, for they contrast two views of the species: as a set of populations delimited by genetic barriers to gene exchange; and as a set of populations maintained in a particular stable equilibrium by selection. Second, the wide range of genotypes found in a hybrid zone can be used to analyze the genetic differences and selective forces that separate the taxa involved. This may allow some inferences about the way these differences evolved and, by extrapolation, about the way fully isolated species diverge from each other. Finally, models of parapatric speciation, and of Wright's "shifting balance," involve the formation, move­ ment, and modification of hybrid zones. Hybrid zones must be understood before the plausibility of these models can be judged. After clarifying our terminology, we will summarize the relevant theory and then see how this can be used to make inferences from field data. A notable increase in the number of detailed genetic studies of hybrid zones occurred over

Analysis of Hybrid Zones

The technique of starch gel electrophoresis of enzymes with specific staining for activity in the gel, the so-called zymogram method developed by Hunter and Markert (1957), has found many research applications. Screening studies, comparing relatively large numbers of enzymes among a variety of tissues and organisms, are finding increasing use in research on population genetics, taxonomy, etc. The methods presently available are scattered through the literature. This compilation is published in response to numerous requests from investigators in many fields. Most of the methods outlined here have been used primarily for tissue extracts from mammalian species. A few have been developed only on plants or lower animals, but this is not to say that they will not work on higher organisms. The buffer systems have been for the most part empirically arrived at. All are probably subject to improvement. The techniques of making the gels and carrying out the electrophoresis are not described here. These have been amply presented in a number of publications. The vertical system is essentially that described by Shaw and Koen (1968b). The horizontal system is essentially as described by Beckman and Johnson (1964). The horizontal method has the advantage of employing simpler and less expensive apparatus, and it can be run at room temperature using ice trays to keep the gels cold. For many enzyme systems, it provides as good results as the vertical. Both Connaught starch (Connaught Laboratories, Toronto) and Electrostarch (Otto Hiller Company, Madison, Wisconsin) will give satisfactory results with either technique. Unfortunately, different batches of starch may produce varying results, both in rate of migration and in resolution; also, some batches contain substances

Starch gel electrophoresis of enzymes—A compilation of recipes

It has always been obvious that organisms vary, even to those pre-Darwinian idealists who saw most individual variation as distorted shadows of an ideal. It has been equally apparent, even to those post-Darwinians for whom variation between individuals is the central fact of evolutionary dynamics, that variation is nodal, that individuals fall in clusters in the space of phenotypic description, and that those clusters, which we call demes, or races, or species, are the outcome of an evolutionary process acting on the individual variation. What has changed during the evolution of scientific thought, and is still changing, is our perception of the relative importance and extent of intragroup as opposed to intergroup variation. These changes have been in part a reflection of the uncovering of new biological facts, but only in part. They have also reflected general sociopolitical biases derived from human social experience and carried over into “scientific” realms. I have discussed elsewhere (Lewontin, 1968) long-term trends in evolutionary doctrine as a reflection of long-term changes in socioeconomic relations, but even in the present era of Darwinism there is considerable diversity of opinion about the amount or importance of intragroup variation as opposed to the variation between races and species. Muller, for example (1950), maintained that for sexually reproducing species, man in particular, there was very little genetic variation within populations and that most men were homozygous for wild-type genes at virtually all their loci.

The Apportionment of Human Diversity

A recent survey (Selander and Yang, 1969) of electrophoretically demonstrable genetic variation in proteins in a population of wild house mice (Mus musculus) from Hallowell Farm, Ramona, California, provided a basis for estimating the proportion of polymorphic loci in the total genome. Of 40 loci controlling the 35 enzymes and non-enzymatic proteins studied, 30% were polymorphic, a proportion closely similar to those available for Drosophila pseudoobscura (Lewontin and Hubby, 1966) and for man (Harris et al., 1968; Lewontin, 1967). Because this estimate was based on an analysis of a single population assigned taxonomically to one subspecies (M. m. brevirostris) and derived from ancestral stocks introduced from Europe to North America within historical times (Schwarz and Schwarz, 1943), it seemed desirable to extend the investigation to additional populations and subspecies. In the present paper, we have surveyed electrophoretic protein variation in six samples representing two subspecies of the house mouse, M. m. musculus and M. m. domesticus, occurring in Denmark. Our objectives are to obtain estimates of total genic heterozygosity for comparison with that available for the California population, and to assess the overall degree of genetic difference between the two subspecies, utilizing the loci investigated as a representative sample of the total genome. A genetic comparison of the Danish populations should be of special interest to students of speciation, since M. m. musculus and M. m. domesticus are, in fact, evolutionary semispecies, having acquired many of the attributes of species rank (Mayr, 1963), including conspicuous morphological and behavioral differences. Despite the existence of a zone of allopatric hybridization between the two forms in central Jutland, there appears to be little gene flow between them (Ursin, 1952; and an investigation of protein variation in progress by Hunt). With the Danish material, we have the opportunity to estimate the degree of genetic difference attained by allopatric populations at the critical stage of speciation where coadapted genetic systems are closing and species are forming.

Protein polymorphism and genic heterozygosity in two european subspecies of the house mouse.

PROTEIN polymorphisms demonstrable by zone electrophoresis are finding increasing use in studies of the population genetics, systematics, and ecology of rodents. For wild populations of the house mouse (Mus musculus), studies to date have dealt largely with esterases and hemoglobin (PETRAS 1967; SELANDER and YANG 1969; SELANDER, YANG and HUNT 1969), although genetically determined variation in a variety of other proteins has been described in laboratory strains and may be expected to occur in wild mice from which the domestic forms were derived. In an effort to increase the number of protein types available for studies of wild populations, and to assess the extent of genic polymorphism in wild populations of this species for comparison with estimates available for Drosophila and other organisms, we have examined electrophoretic variation in 35 enzymes and nonenzymatic proteins in samples of mice taken in several barns at a farm in southern California.

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Protein polymorphism and genic heterozygosity in a wild population of the house mouse (Mus musculus).

To many early evolutionists, particularly those of the mutationist school, the existence of evolutionarily stable forms ("living fossils" or phylogenetic "relics") posed a difficult problem, and, even among contemporary biologists, the feeling that "a long-standing stability of organization seems antithetical to the concept of evolution" may persist (Volpe, 1967:140). In the early part of this century, it was popularly believed that stable or slowly evolving (bradytelic) lines lacked the genetic variation necessary for more rapid evolution as a result of having abnormally low mutation rates; as Mayr (1963) puts it, a lack of variation in time and space was interpreted as a reflection of genotypic stability. Largely because of the influence of Simpson (1944), Stebbins (1944), Schmalhausen (1949), and Dobzhansky (1951), the mutationists' interpretation of bradytely has now been all but abandoned by evolutionists in favor of the view that the principal factors controlling rates of evolution are to be found in the organism-environment relationship. Additionally, Mayr (1963 :304) has suggested that phenotypic "uniformity in space and time is due to a highly perfected 'buffering system,' in other words, to genetic homeostasis." The ecological hypothesis is well expressed in Simpson's (1944:141) conclusions that "the final and probably the most fundamental factor in the relationship is that bradytelic groups are so well adapted to a particular, continuously available environment that almost any mutation occurring in them must be disadvantageous" and that "bradytely results from the equilibrium of large breeding populations of animals specifically adapted to a continuously available environment that is relatively invariable . . . ." Yet, as Mayr (1963) notes, there is no evidence to refute (or to support) the hypothesis that bradytely results from loss of mutability. The recent development of electrophoretic techniques for demonstrating allelic variation at loci controlling enzymes and other proteins in natural populations (Hubby and Lewontin, 1966; Lewontin and Hubby, 1966) permits a test of the mutationists' thesis. The purpose of this study is to compare degrees of protein polymorphism and underlying genic heterozygosity in a classic phylogenetic "relic," the horseshoe or king crab (Limulus polyphemus), and in several representatives of horotelic lines (those evolving at standard rates) for which data are already available. Evidence of a level of genetic variation in Limulus similar to that in horotelic forms will support the modern ecological and homeostatic interpretations of bradytely. But if the mutationists' thesis is valid, Limulus should show an unusually low degree of polymorphism at its genetic loci. Limulus polyphemus is one of five living species of the Subclass Xiphosura, a group of marine arthropods usually placed with the Subclass Eurypterida (extinct giant water scorpions) in the Class Merostomata of the Subphylum Chelicerata. Following a period of adaptive radiation in the early and middle Paleozoic, the Merostomata became much less prominent after the Permian. Several Mesozoic forms are known in the Family Mesolimulidae, but by the Tertiary the fossil record is all but absent. There are presently three living genera, all belonging to the Family Limulidae, only one of which, Tachypleus, is known from the fossil record (Stormer,

Genetic variation in the horseshoe crab (limulus polyphemus), a phylogenetic "relic".

Hybridization in the grackle Quiscalus quiscula in Louisiana.

Fourteen population samples of Drosophila pavani were obtained from a number of localities in Chile. The populations sampled were dispersed over 7 degrees of latitude and 1800 meters of elevation, and were drawn at three different times. Sixteen electrophoretic loci were assayed for each population; eight of the loci were analyzed statistically for geographic variation; the other eight were essentially monomorphic. For all eight variable loci, variation in allelic frequencies among populations was highly significant. In all cases, a significant portion of the variation among populations was associated with variation in gross environmental variables (latitude, elevation, month of collection). The implications of the evidence were discussed, and the authors concluded that there was suggestive evidence for selection.

Suh Y. Yang

Papers

Protein polymorphism and genic heterozygosity in two european subspecies of the house mouse.

Protein polymorphism and genic heterozygosity in a wild population of the house mouse (Mus musculus).

Genetic variation in the horseshoe crab (limulus polyphemus), a phylogenetic "relic".

Hybridization in the grackle Quiscalus quiscula in Louisiana.

Isozyme frequency patterns in drosophila pavani associated with geographical and seasonal variables