the intrinsic rate of increase of the entire Mendelian population at genetic equilibrium. These Wij values serve as Darwinian fitnesses of the genotypes in determining equilibrium gene frequencies, as in the discrete-generation model: p1=(W12− W22)/(2W12−W11−W22). For a stable genetic polymorphism, r is calculated as the root of the equation (W12−1)2=(W11− 1) (W22−1).
There have been only a few experimental determinations of genotypic life histories to which this basic demographic theory of selection has been applied. Charlesworth (19) cites only the study of genotypes in Tribolium castaneum by Moffa and Costantino (25). We have obtained life history schedules of longevity and fecundity for three sets of genotypes in D. pseudoobscura, and we present below an analysis of selection on them.
Chromosomal variants of D. pseudoobscura were chosen as a realistic and practical genetic system for demographic analysis. Natural populations of this species contain an array of inversions on the third chromosome. These inversions segregate as units, just as if they were alleles at a single locus, because crossing over is effectively suppressed within the inverted regions in heterozygotes for the inversions (2). Indeed, crossing over is nearly eliminated over the entire third chromosome in many combinations. The inversions contain linkage blocks of genes much like those thought on theoretical grounds to be the true units of selection (26). Frequencies of these inversions are regulated by selection in nature, and some of these changes can be reproduced in laboratory populations (2, 11). Selection is often intense, as we should expect for genetic units comprising a 10th of the genome. Differences in selection are consequently easier to measure, and the values obtained are more accurate. Four inversions were used in these experiments: Arrowhead (AR), Chiricahua (CH), Pikes Peak (PP), and Standard (ST).
AR/AR, AR/CH, and CH/CH Under Nearly Optimal Conditions. The first set of data comes from a study by Nickerson and Druger (27). These authors extracted seven AR and seven CH chromosomes from a population cage begun with chromosomes collected at Pinon Flats, Mount San Jacinto, CA. These strains were intercrossed, both within each inversion type and between the two, to yield the AR/AR, AR/CH, and CH/CH flies used in the experiment. For each chromosomal genotype, or karyotype, 10 replicate groups of 5 females and 8 males were placed in glass vials, each of which contained a spoon of blackened, yeasted food. The spoons were replaced, with fresh ones every 24 hr, at which time dead females were counted and removed. The eggs on each spoon were counted, and fecundity was recorded as eggs/female/day. Longevity of preadult life stages was measured as egg-to-adult viability. For each karyotype, 20 groups of 50 eggs were placed in half-pint culture bottles and the number of adults emerging in each bottle was recorded. Longevity of adults was measured on groups of 25 females and 25 males in half-pint culture bottles; at 2-day intervals the flies were transferred to new bottles and the number of dead females were recorded. Twenty replicate bottles were studied for each karyotype. All tests were conducted at 25°C, under nearly optimal conditions. The experiment was continued for 58 days, until all fecundities dropped to zero. Nickerson and Druger did not record the average time spent in preadult life stages, but, fortunately, the development times of karyotypes from cage populations started with the same AR and CH chromosomes from Pinon Flats have been studied by others (6, 7).
AR/AR, AR/PP, and PP/PP Under Nearly Optimal Conditions. Ten strains of AR and 10 of PP from collections at Black Forest, 10 miles north of Colorado Springs, CO, were utilized. Marvin Wasserman isolated these chromosomes in 1970, and we conducted our experiment shortly thereafter, in 1971–1972. Crosses were made among all strains of each chromosomal type and between strains of the two types, so that no fly, whether a homokaryotype or a heterokaryotype, was homozygous for any one ancestral inversion. Longevity and fecundity were measured, as in ref. 7, simultaneously on groups of three females and three males in small, glass creamers, each containing approximately 5 ml of blackened food. A glass chimney plugged with cotton was taped to each creamer, and a drop of yeast solution was added before use. Twenty replicates were set up for each karyotype, and all cultures were kept at 25°C. Every 24 hr each group of flies was transferred to a fresh creamer, the number of dead flies of each sex was recorded, and all eggs in each creamer were counted. Measurements were discontinued after 35 days of adult life, when their effect on the parameters of growth and selection was small. Samples of 50 eggs were cultured in half-pint bottles to estimate development time and preadult viability; 16 replicate cultures were studied for each karyotype.
AR/AR, AR/ST, and ST/ST Under Harsh Conditions. Ten strains of AR and 10 of ST from collections at Mather, CA, in 1959 were employed for measurements of the life history functions l(x) and m(x) under conditions such as those a species might encounter in a harsh environment where population growth was severely restricted. The experiment was conducted exactly as for AR and PP, with two exceptions: five, rather than three, pairs of parents were placed in each creamer, and no yeast was added to the food medium. Thus, the flies suffered greater crowding and they were underfed, if not starved. The daily transfers to new containers did not permit much growth of the yeast and other microorganisms that were transferred on the flies or in their guts. The experiment was continued for 30 days of adult life.
Analysis. The first step is the calculation of rij for each karyotype, because the existence of an equilibrium depends on the relative sizes of these quantities. The rij values are calculated from the life history schedules by numerical solution of the equation . If either a stable or unstable equilibrium is indicated, then the equilibrium equation for age-specific selection can be used to calculate the population growth rate r. This equation does not apply when no genetic equilibrium is indicated, that is, when r12 is intermediate between r11 and r22. In this case the population will ultimately grow at the highest of the genotypic rij values, and substituting this rij into the formulas defining the Wij values provides a useful first approximation to the Darwinian fitnesses (19).
The fitnesses are calculated as for x varying from 1 to G. Here, x=age of adults in days, calculated from eclosion; G=maximal age of organisms in the experiment; and, for genotype AiAj, Dij=mean length of preadult life, lij(x)=probability of survival from zygote to age x, and mij(x)=fecundity as female eggs/female/day. The equilibrium equation is . Beginning with an initial estimate of the population growth rate, r0, an improved estimate r1 is obtained by Newton-Raphson iteration as r1=r0−Z/(dZ/dt). The formula is applied repeatedly to give successively improved estimates, and convergence is rapid. The Darwinian fitnesses are then computed by substituting the final estimate of r into the formulas for the Wij values. The net reproduction, or expected lifetime fecundity of a female zygote, is calculated as Rij=∑x 1ij(x) mij(x), for x varying from 1 to G. Finally, the equilibrium gene frequency, if it exists, is calculated as p1= (W12−W22)/(2W12−W11−W22).
AR/AR, AR/CH, and CH/CH. Nickerson and Druger very kindly made their original data available to us, and it is