Among patients in a trauma registry who were hypotensive on arrival in the ED and had major injuries isolated to the abdomen requiring emergency laparotomy, the probability of death showed a relationship to both the extent of hypotension and the length of time in the ED for patients who were in the ED for 90 minutes or less. The probability of death increased approximately 1% for each 3 minutes in the ED.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. International Biometric Society is collaborating with JSTOR to digitize, preserve and extend access to Biometrics. INTRODUCTION AND THEORYIn classical genetics many genes are known to have manifold effects, i.e., the gene seems to affect unrelated characters. An example of such a gene is the "vestigial gene" in Drosophila which affects not only the bristles and wings but also fecundity. Examples of similar genes in other organisms abound in the literature. When a gene has manifold effects, its action is called pleiotropic.In quantitative genetics, just as in qualitative genetics, it is easy to conceive of a gene affecting many characteristics. We shall therefore consider a random mating population with respect to one segregating locus at which there is an arbitrary number of alleles and suppose two characters X and Y are observed. If the genes act pleiotropically, to any genotype, A A , there correspond two genotypic values Xi i and Yi , one for the character X and one for the character Y.Let the genotypic values Xi; and Yii be deviations from their respective means. Then if pi and pi represent the frequencies of genes Ai and Ai in the population, the X's and Y's satisfy the conditions Eii pipiXii = Eii pipiYii = 0, where summation extends over all alleles. We now make the following set of definitions. The additive effects of genes with respect to the characters in question are defined as oa*-Xi. = E pjXi , a*-X.; = E piXiiY i i ai Yi. = Piii X a= Y.; = pi5ii 1 518 This content downloaded from 150.108.161.71 on Tue

Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k = 1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97–1.38). When less dispersed with k = 2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity.

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