Bolzano,Cauchy and the “new analysis” of the early nineteenth century

Summary In this paper I discuss the development of mathematical analysis during the second and third decades of the nineteenth century; and in particular I assert that the well-known correspondence of new ideas to be found in the writings of Bolzano and Cauchy is not a coincidence, but that Cauchy had read one particular paper of Bolzano and drew on its results without acknowledgement. The reasons for this conjecture involve not only the texts in question but also the state of development of mathematical analysis itself, Cauchy both as personality and as mathematician, and the rivalries which were prevalent in Paris at that time.     

Effects of a change in the level of inbreeding on the genetic load

"The effects of inbreeding may not be as noticeable in the first generation as the invigoration immediately apparent after crossing". This statement, published in 1919, has received little attention, and has apparently never been tested empirically, although the reduction of the genetic load of populations by inbreeding is well known in theoretical terms. Because inbreeding increases homozygosity, and hence the effectiveness of selection against recessive or partially recessive detrimental alleles, changes in levels of inbreeding can lead to a reduction in the frequencies of such mutant alleles. This results in equilibration at higher population mean fitness and is referred to as 'purging' populations of their genetic load. Severe inbreeding can also reduce genetic load due to overdominant alleles, provided selection coefficients are not symmetrical at all loci, because alleles giving lower fitness will be reduced in frequency at equilibrium. With either fitness model, however, reduction in genetic load takes time, and the initial effect of an increase in inbreeding is reduced fitness due to homozygosity. There are few data relating to the extent to which fitness is reduced during inbreeding in a set of lines and to how long the reduction lasts before increasing again to the initial level, or higher. Inbreeding experiments involving sib mating in mice and Drosophila subobscura, and successive bottlenecks in house flies have yielded some evidence consistent with the purging hypothesis. Here, we report results of an experiment demonstrating a prolonged time-course of recovery of mean fitness under self-fertilization of a naturally outcrossing plant, and also compare our results with expectations derived by computer calculations. Our results show that the genetic load present in an outcrossing population can be explained only with a high mutation rate to partially recessive deleterious alleles, and that inbreeding purges the population of mutant alleles.     

Gigantecin: A novel antimitotic and cytotoxic acetogenin,with nonadjacent tetrahydrofuran rings,fromGoniothalamus giganteus (Annonaceae)

Summary Gigantecin (I), a novel tetrahydroxy-di-tetrahydrofuran fatty acid -lactone (acetogenin), was isolated from an ethanolic extract of the stem bark ofGoniothalamus giganteus Hook. f., Thomas (Annonaceae), by means of activity-directed fractionation (brine shrimp lethality test). This new compound is extremely cytotoxic to human tumor cells, inhibits crown gall tumors on potato discs, and is active in an assay designed to detect antimitotic agents (9 ASK).