Summary 1The influence of botanical composition on annual phytomass production of a semiarid grassland in response to precipitation was tested with a 19-year experiment. Three compositional states reflecting good, medium and poor rangeland condition, whose basal cover increased from poor through to good, were created in 1978.2 Multiple regression models were developed for assessing whether phytomass was influenced by precipitation, composition, phytomass of the previous year, basal cover, abundance of individual species, or diversity. Composition and precipitation accounted for 66% of the variation in phytomass, but a separate model of basal cover by precipitation was equally successful. The linear effect of rainfall on phytomass was enhanced as composition improved from poor (0.076 g m -2 mm ) to good (0.277 g m -2 mm -1 ). Phytomass increased for low precipitation if it had been high the preceding year. Phytomass was more variable over time with deteriorating condition. 3 Species' complementarity ensured greater and more stable production. Setaria sphacelata , Eragrostis chloromelas and Digitaria eriantha increased phytomass on the good or medium condition grasslands during drier years, whereas Themeda triandra had this effect during wetter years. 4 Precipitation-use efficiency (PUE) was influenced mostly by composition and a linear and quadratic effect of precipitation (63% of variance). Optimum PUE of 0.308, 0.203 and 0.096 g m -2 mm -1 for the good, medium and poor condition grasslands, respectively, occurred at intermediate amounts ( ± 680 mm) of precipitation. PUE was increased if phytomass had been high the previous year. 5 Species' complementarity of PUE in response to precipitation was evident for all compositional states. Ten, mostly uncommon, species and their interaction with precipitation explained an extra 21-42% of the variance. Stability of production was related to PUE for medium and poor condition grassland. Uncommon species therefore ensured growth efficiency and stabilized production as condition deteriorated. 6 Diversity had no influence on phytomass or PUE except for a small to moderate effect, respectively, for the medium condition grassland. 7 Vegetation structure, through limiting runoff and promoting infiltration, is an important control on the amount and efficiency of plant production under variable precipitation, whilst composition further influences the amount and stability of production.

Phase I clinical trials are typically small, uncontrolled studies designed to determine a maximum tolerated dose of a drug which will be used in further testing. Two divergent schools have developed in designing phase I clinical trials. The first defines the maximum tolerated dose as a statistic computed from data, and hence it is identified, rather than estimated. The second defines the maximum tolerated dose as a parameter of a monotonic dose-response curve, and hence is estimated. We review techniques from both philosophies. The goal is to present these methods in a single package, to compare them from philosophical and statistical grounds, to hopefully clear up some common misconceptions, and to make a few recommendations. This paper is not a review of simulation studies of these designs, nor does it present any new simulations comparing these designs.

A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low. Results relating to these constrained designs for log doses on the real line are described and the associated equivalence theorem is given. The ideas are extended to more practical situations, specifically to those involving discrete doses. In particular, a Bayesian sequential optimal design scheme comprising a pilot study on a small number of patients followed by the allocation of patients to doses one at a time is developed and its properties explored by simulation.

The unimodal, right-skewed distribution, most frequently identified in contemporary descriptions of placental mammal body size distributions, masks an underlying multidistribution structure; a long-term evolutionary process that has generated a concatenation of two or three frequency distributions specific to locomotory modes (plantigrade, digitigrade and unguligrade). The Afrotropical assemblages are bimodal, with a tendency towards trimodality, whereas the Nearctic assemblage is unimodal. However, mixtures of two and three normal distributions fitted the Nearctic data well, suggesting a multidistribution structure masked by disproportionate species numbers within locomotory modes. Differences in proportional species numbers within modes between assemblages may reflect the evolutionary history of form and function. However, common interassemblage predictions of such proportions in contemporary distributions may be disguised by the relative severity of the Pleistocene megafaunal extinction (patterns supported by the fossil record), geographical scale, and taxonomic composition. A species gap occurs at body sizes around 1 kg at the interface between the largest plantigrade mammals and the smallest digitigrade mammals, coincident with the minimum interspecific variance of basal metabolic rate. In terms of the evolution of the optimal body size in the trade-off between mortality and production, there may be good historical and evolutionary reasons why we should not expect optimization to produce the same results in different zoogeographical assemblages. Moreover, the evolution of diverse mammalian forms and functions, especially with respect to predator-prey interactions and diet, render a single body size optimum untenable in the search for an energetic definition of fitness.

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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.This article reports the application of the annealing algorithm to the construction of exact D-, I-, and G-optimal designs for polynomial regression of degree 5 on the interval [-1, 1] and for the second-order model in two factors on the design space [-1, 1] x [-1, 1]. Details of the perturbation scheme and the annealing schedules used are given, and the method of implementation is illustrated by means of a simple example. The algorithm is assessed by comparing its performance, in terms of computer time and efficiency, with the modified Fedorov procedure, and it is shown to be particularly effective in finding G-optimal designs. The salient features of the exact designs constructed in this study are also summarized.

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