Nine populations of Juniperus virginiana were sampled at approximately 150-mile intervals along a 1500-mile transect from northeastern Texas to Washington, D.C. Individual plants were examined for terpenoids by gas liquid chromatography and the resulting data analyzed by numerical classification methods using characters weighted according to their estimated variance in the natural populations. The results of the analysis show that these populations of J. virginiana cluster clinally from northeast to southwest, the more homogeneous populations occurring in the Appalachian region of North America; the more divergent populations found in progressively more distant regions, as measured along the transect from the northeast toward the southwest. No biochemical evidence could be found to support the hypothesis that hybridization with J. ashei might be causing this variability, as had been widely supposed previously.

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The opposing requirements in an evolving population for a rapid rate of multiple gene substitution and for the maintenance of normal population size can be reconciled in a variety of ways. The ways out of the impasse suggested here invoke deviations from the usual assumption of a large continuous population with constant numbers. In a colonial population system there may be significant random fluctuations in the accidental mortality rate between different colonies; and those colonies with reduced numbers of accidental deaths could tolerate the larger number of selective deaths that go hand in hand with rapid evolution. In new daughter colonies founded by one or a few colonizing individuals from a large polymorphic ancestral population, some genes may reach complete fixation in one or a few generations, without the usual concomitant selective cost. Or, in the same setup, the favored alleles may change by chance from rare to moderately common, but not to complete fixation, during the founding of some daughter colonies; and this raises the allele frequencies above the low range, where the cost of selection is greatest, so that the cost of further selective changes is bearable.

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Gas chromatographic analyses of the nut oils of 155 samples, representing 15 taxa of Carya, confirm the basic uniformity of fatty‐acid composition within the walnut family. All taxa contain small amounts of the saturated fatty acids—palmitic and stearic—and variable amounts of the unsaturated oleic and linoleic acids, and at least trace amounts of linolenic. Quantitative differences in the relative amounts of the five fatty acids support the morphologic recognition of two sections within the genus. Members of the section Carya are characterized by higher linoleic and lower oleic acid percentages than are those of section Apocarya. It is also true, however, that tetraploids of section Carya tend to have higher linoleic and lower oleic acid percentages than diploids within the same section. Numerical analyses of the oil data reveal close similarities between certain members of the more “primitive” section Apocarya and the diploid members of section Carya. The highly heterogeneous assemblage within section Apocarya could be split into three groups on the basis of oil data. It is equally obvious, however, that the American taxa of the genus Carya have had a long and reticulate phylogeny and that recognition of additional categories above the species level would not result in natural assemblages.

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It is shown for a continuous haploid model that the common standard assumptions usedin calculating the cost of gene substitution, namely, large constant population size and small constant selective value, are unnecessary. Population size may fluctuate during the course of substitution without affecting the calculated total cost. The selective intensity does not need to be small and constant to give the standard result for substitution cost. Diploid models with multiple alleles are analyzed and contrasted with standard two-allele models in respect to calculation of substitution cost. The influence of population structure on the probability of occurrence of complete gene substitution is discussed on the basis of a numerical example. The robust nature of the cost-of-selection concept is examined in the light of a conservation principle.The original model of Haldane (1, 2) for the cost of selection and more recent standard models (3) assume constant large population size and constant small selective value. Using continuous deterministic models, both haploid and diploid, we have arrived at a more general formulation that does not require these assumptions. A number of other models have been analyzed in recent papers (see ref. 4 for references), but none of the deterministic models previously considered encompass the same generality as that presented here. In addition, we consider the cost-of-selection concept in terms of population structure and a general conservation principle. HAPLOID MODELThe cost of selection in the haploid or asexual case is first discussed for a discrete generation model, and then for a continuous model with random births and deaths. The calculation of cost for the discrete model follows the analysis of Crow and Kimura (3) closely, except that the presentation here begins explicitly with the difference equations describing the dynamic behavior of the number of individuals of each type in the population. The derivation for the continuous model is analogous to the discrete model argument. However, in the continuous case few restrictive assumptions or approximations are required. In particular, the latter approach for computing cost is valid for quite general population models, including those containing density-dependent fitness. In addition, the common assumptions of weak selection and stable population size during the process of the substitution are not required.Discrete Generation Model. We shall adopt the following customary notation for the fitnesses, frequencies, and numerical strength of the two competing types:The number of individuals of each type in successive generations is described by a pair of difference equations: