Color attractions for Macrosiphon euphorbae were investigated by observing apterous aphids in an arena containing competitions between pairs of 16 distinct commercial paints. Relative attractiveness of these paints was found to be transitive in this population of aphids and attractiveness coefficients were assigned via a version of the Bradley–Terry model for paired comparisons. Reflected energy spectra, adjusted for illumination at the arena floor, were determined for the same paints. Alternative monostimulus, distimulus, and tristimulus explanations for relationships between attractiveness and spectral features were examined. The existence of two receptors in the visible spectrum, one sensitive to light at 590–595 nm and one at 425–460 nm, is inferred. A distimulus ratio of energies reflected at 595 nm and at 425 nm is found to be an effective predictor of attractiveness in this sample of paints.

The authors examine tests of structural change in m linear models of arbitrary rank. They find that the null hypothesis implicit in these tests is broader than the hypothesis of coefficient equality and that it depends on the ranks of the design matrices constituting the models. As a consequence, these tests have no power against a region of the parameter space that includes nonequality of coefficient vectors. However, these tests possess a UMP property and imposing those restrictions implicit when the null hypothesis is not rejected does produce the conventional pooled estimator. The authors also provide various interpretations of the tests. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Predictive forms of the Chow test are used in investigating structural change when the number of predictors exceeds the number of observations. This test has been argued to be more powerful than the more widely used analysis of covariance test even when the number of predictors does not exceed the number of observations. In that circumstance we show that either the hypothesis claimed is not testable or the test is not uniformly most powerful excepting a fortuitous coincidence between the number of predictors and the number of observations. We suggest an alternative test for structural change conditional on a prior specification test adapted from McAleer and Tse (1988).

Strategies are analyzed for maximizing the ultimate limit to truncation selection for a quantitative trait in finite populations. By using a formulation of Kimura and Crow [Kimura, M. & Crow, J. F. (1978) Proc. Natl. Acad. Sci. USA 75, 6168-6171], it is shown that the limit is maximized by truncating at the mode with the highest ordinate of the phenotypic distribution. This implies 50% selection for the normal or any unimodal symmetric distribution and, for skewed distributions, selection of more than one-half if desired phenotypes are in the long tail of the distribution, less than one-half if in the short tail. For dioecious populations, the optimal procedure requires, in addition, equal numbers recorded and selected of each sex. For monoecious populations the limit can be improved by using the best individuals mated to the next-best individuals. Limitations of the results are discussed.

Exact distributions of times to fixation are derived for neutral alleles in a discrete generation, constant census model that accommodates specified variations in gametic contributions per parent. This enables an evaluation of the performance of the effective number concept, and of diffusion equation approximations, used to characterize the time scale of drift events. Following simultaneous comparisons of modes, medians, means and standard deviations of exact and approximate distributions of times to fixation, it is concluded that diffusion equation methods, in conjunction with the appropriate effective number, do produce accurate results.

A general model which accommodates different fitness values of an individual in association with each other type of individual is studied. The model in conjunction with population composition, in which individuals are assumed to be dispersed at random, determines the relative fitness values of individuals. Expressions for the change in gene frequency and for the mean are derived for one locus with two alleles in a random mating population. Equilibrium and max/min mean compositions generally require solving third-degree equations, but explicit expressions are found for models with general levels of dominance and some of their variants. Protected polymorphisms, genetic loads, inbreeding depressions, and the cost of a gene substitution are also considered. Many additional features of the statics and dynamics of populations are introduced with the effects of population composition on fitnesses. A single globally stable equilibrium can exist without any dominance. There may be multiple equilibria, up to three, with various stability characteristics, some of which are protected polymorphisms. There need not be any correspondence between compositions for max/min means and those for equilibria. Inbreeding depressions may be curvilinear, and even stable equilibrium populations may show negative inbreeding depressions. Very different models may give the same genetic load. The number of genetic deaths required for a gene substitution may be as few as twice the population size. One appeal of the model is that it encompasses several classes of models, including those with constant fitness values, and thus provides a basis for determining the appropriate model. After considering alternative experiments and measures of discrimination, we conclude that only survival values of the genotypes for several population compositions would be sufficient to discriminate between certain models.

General procedures are developed for finding equilibrium and maximum/minimum mean compositions for a population of autogenous components competing in a pairwise manner among individuals. The procedures, involving elementary matrix techniques, are easy to apply for any specific competitive model. Necessary and sufficient conditions are developed for the mean to be a maximum and for the equilibrium composition to be stable. The problem of a maximum mean reduces to that of evaluating a quadratic form which must be negative definite, and is easily accomplished for a specific competitive model. Stability of equilibrium depends on the eigenvalues of a first-order transition matrix relating deviations of component frequencies from their equilibrium frequencies in successive generations. For stability, all of the eigenvalues must vanish in time. These conditions, sometimes difficult to find, are illustrated for a three- and four-component model. The eigenvalues also provide considerable information about the dynamics of the population. They determine the rate of divergence from, or convergence to, equilibrium composition. Often some of them are complex, which accounts for the oscillating behavior of component frequencies. In such cases they provide estimates of the periodicity. Through them the effect of the relative magnitudes of competitive effects upon periodicity and on rate of divergence or convergence can be evaluated. Amplitudes of oscillations, when these occur, are primarily determined by initial frequencies and can be approximated by harmonic expressions derived from the transition matrix. Competitive effects are measured as the deviation of a component's competitive performance from the competitor's performance in competition with itself, a definition different from the prevalent one. Equilibria and stability are entirely a function of these competitive effects. Although the details are complicated, a general conclusion is that a preponderance of positive competitive effects is required for stable equilibria. Some models with three or more components have a multiplicity of equilibria compositions. In these cases and under certain conditions, the population moves to the equilibrium nearest to the initiating composition. Consequently, the equilibrium reached depends on the initial frequencies.