Galton's legacy to research on intelligence

In the 1999 Galton Lecture for the annual conference of The Galton Institute, the author summarizes the main elements of Galton's ideas about human mental ability and the research paradigm they generated, including the concept of 'general' mental ability, its hereditary component, its physical basis, racial differences, and methods for measuring individual differences in general ability. Although the conclusions Galton drew from his empirical studies were seldom compelling for lack of the needed technology and methods of statistical inference in his day, contemporary research has generally borne out most of Galton's original and largely intuitive ideas, which still inspire mainstream scientific research on intelligence.     

A Reconsideration of Galton's Problem (Using a Two-Sex Population)

The main purposes of this paper are to promote and expound the bisexual Galton–Watson branching process as a relevant model for the consideration of Francis Galton's problem regarding the extinction of surnames of “men of note.” A scheme for adapting the bisexual process to consider Galton's problem is introduced. A necessary and sufficient condition for the certain extinction of a male-induced property in a two-sex species is presented. An approach for calculating the extinction of a male-generated characteristic in the two-sex species is proposed. That approach is then used to find the probability of the extinction of surnames in a bisexual population for Alfred Lotka's data based on an United States Census. Finally, these results are then compared with the classic extinction probabilities (from Lotka) associated with the traditional Galton–Watson branching process using asexual reproduction.     

The Development of Francis Galton's Ideas on the Mechanism of Heredity

Galton greeted Darwin's theory of pangenesis with enthusiasm, and tried to test the assumption that the hereditary particles circulate in the blood by transfusion experiments on rabbits. The failure of these experiments led him to reject this assumption, and in the 1870s he developed an alternative theory of heredity, which incorporated those parts of Darwin's theory that did not involve the transportation of hereditary particles throughout the system. He supposed that the fertilized ovum contains a large number of hereditary elements, which he collectively called the “stirp,” a few of which are patent, developing into particular cell types, while the rest remain latent; the latent elements can be transmitted to the next generation, while the patent elements, with rare exceptions, cannot since they have developed into cells. The problem with this theory is that it does not explain the similarity between parent and child unless there is a high correlation between latent and patent elements. Galton probably came to realize this problem during his subsequent statistical work on heredity, and he quietly dropped the idea that patent elements are not transmitted in Natural Inheritance (1889). Galton thought that brothers and sisters had identical stirps, and he attributed differences between them to variability in the choice of patent elements from the stirp, that is to say to developmental variability. He attributed the likeness of monozygotic twins to the similarity of their developmental environment. Galton's twin method was to track the life history changes of twins to see whether twins who were similar at birth diverged in dissimilar environments or whether twins who were dissimilar at birth converged in similar environments. It is quite different from the modern twin method of comparing the similarities between monozygotic and dizygotic twins, on the assumption that monozygotic twins are genetically identical whereas dizygotic twins are not. It has been argued that Galton foreshadowed Weismann's theory of the continuity of the germ-plasm, but this is only true in a weak sense. They both believed that the inheritance of acquired characters was either rare or impossible, but Galton did not forestall the essential part of Weismann's theory, that the germ-plasm of the zygote is doubled, with one part being reserved for the formation of the germ-cells. This revised version was published online in July 2006 with corrections to the Cover Date.     

Optimal approximate conversions of odds ratios and hazard ratios to risk ratios

Odds ratios approximate risk ratios when the outcome under consideration is rare but can diverge substantially from risk ratios when the outcome is common. In this paper, we derive optimal analytic conversions of odds ratios and hazard ratios to risk ratios that are minimax for the bias ratio when outcome probabilities are specified to fall in any fixed interval. The results for hazard ratios are derived under a proportional hazard assumption for the exposure. For outcome probabilities specified to lie in symmetric intervals centered around 0.5, it is shown that the square-root transformation of the odds ratio is the optimal minimax conversion for the risk ratio. General results for any nonsymmetric interval are given both for odds ratio and for hazard ratio conversions. The results are principally useful when odds ratios or hazard ratios are reported in papers, and the reader does not have access to the data or to information about the overall outcome prevalence.     

Sex ratios

Sex ratio theory attempts to explain variation at all levels (species, population, individual, brood) in the proportion of offspring that are male (the sex ratio). In many cases this work has been extremely successful, providing qualitative and even quantitative explanations of sex ratio variation. However, this is not always the situation, and one of the greatest remaining problems is explaining broad taxonomic patterns. Specifically, why do different organisms show so much variation in the amount and precision with which they adjust their offspring sex ratios?     

Activity ratios of ribulose-1,5-bisphosphate carboxylase accurately reflect carbamylation ratios

Activity ratios and carbamylation ratios of ribulose-1,5-bisphosphate carboxylase (RuBPCase) were determined for leaves of Phaseolus vulgaris and Spinacia oleracea exposed to a variety of partial pressures of CO₂ and O₂ and photon flux densities (PFD). It was found that activity ratios accurately predicted carbamylation ratios except in extracts from leaves held in low PFD. In particular, it was confirmed that the loss of RuBPCase activity in low partial pressure of O₂ and high PFD results from reduced carbamylation. Activity ratios of RuBPCase were lower than carbamylation ratios for Phaseolus leaves sampled in low PFD, presumably because of the presence of 2-carboxyarabinitol 1-phosphate. Spinacia leaves sampled in darkness also exhibited lower activity ratios than carbamylation ratios indicating that this species may also have an RuBPCase inhibitor even though carboxyarabinitol 1-phosphate has not been detected in this species in the past.     

Sizing up size ratios

The investigation of the causes of observed size differences between coexisting related animal species requires a knowledge of the statistical distributions of size ratios in randomly constructed guilds. Null models can be useful, but are often subject to constraints that severely limit their applicability. New work on the statistics of size distributions may lead to a better understanding of why animals are the sizes they are.     

A snail with unbiased population sex ratios but highly biased brood sex ratios

Extraordinary sex ratio patterns and the underlying sex-determining mechanisms in various organisms are worth investigating, particularly because they shed light on adaptive sex-ratio adjustment. Here, we report an extremely large variation in the brood sex ratio in the freshwater snail, Pomacea canaliculata. In eight rearing series originating from three wild populations, sex ratios were highly variable among broods, ranging continuously from almost exclusively males to almost exclusively females. However, sex ratios were similar between broods from the same mating pair, indicating that sex ratio is a family trait. Irrespective of the large variations, the average sex ratios in all rearing series were not significantly different from 0.5. We argue that Fisher's adaptive sex-ratio theory can explain the equal average sex ratios, and the results, in turn, directly support Fisher's theory. Polyfactorial sex determination (in which sex is determined by three or more genetic factors) is suggested as the most likely mechanism producing the variable brood sex ratio.