Sample Size Determination for Grouped Exponential Observations: A Cost Function Approach

Calculating the required sample size for a desired power at a given type I error level, we often assume that we know the exact time of all subject responses whenever they occur during our study period. It is very common, however, in practice that we only monitor subjects periodically and, therefore, we know only whether responses occur or not during an interval. This paper includes a quantitative discussion of the effect resulting from data grouping or interval censoring on the required sample size when we have two treatment groups. Furthermore, with the goal of exploring the optimum in the number of subjects, the number of examinations per subject for test responses, and the total length of a study time period, this paper also provides a general guideline about how to determine these to minimize the total cost of a study for a desired power at a given α-level. A specified linear cost function that incorporates the costs of obtaining subjects, periodic examinations for test responses of subjects, and the total length of a study period, is assumed, primarily for illustrative purpose.     

Deposition of BaSO4 in the tight junctions of amphibian epithelia causes their opening; apical Ca2+ reverses this effect

Selective deposition of BaSO₄ in the tight junctions (TJs) of frog skins led to profound and reversible functional alterations of these structures, as revealed by changes of tissue conductance (G), clamping current (I), and fluxes of extracellular markers (sulfate (J^SO ₄) and sucrose (J^SUC)). Experiments were performed with nominally Ca²⁺ -free simple salt solutions on the apical side (usually KCl) and Na₂SO₄-Ringer on the inner side of skins. The deposition of BaSO₄ in the TJs was obtained by diffusion and/or migration through the paracellular path of Ba²⁺ from the apical solution and SO ₄ ^2– from the inner solution. A brief presence (2 to 6 min) of apical Ba²⁺ (Ba²⁺ pulse) is followed (i.e., when Ba²⁺ is removed from the apical fluid) by a large increase of G, I, J^SO ₄ and J^SUC, above pre-Ba²⁺ levels. These attain a steady state within 15 to 30 min (overshoot phase), characterizing a conspicuous increase of the paracellular permeability. During the overshoot phase, a second Ba²⁺ pulse blocks the paracellular route while apical Ba²⁺ is present, leading to a new and larger overshoot when the Ba²⁺ pulse is terminated. Addition of apical Ca²⁺ triggers the resealing of the TJs, resulting in a full recovery of G, I, J^SO ₄ and J^SUC. This Ca²⁺ -induced recovery persists when apical Ca²⁺ is removed. The presence of a normal Ca²⁺ concentration in the inner bathing Ringer does not induce the recovery process. Tissues remain viable after being submitted to the Ba²⁺ treatment and the subsequent overshoot. Experiments performed in the urinary bladder of Rana catesbeiana and skins and urinary bladders of Bufo marinus indicate that Ba²⁺ effect can also be elicited in these tissues. The above results seem to report general properties of the TJs. Incidentally, they warn about the use of Ba²⁺ as an ion channel blocker in epithelial membranes in association with SO ₄ ^2– -containing solutions on the contralateral side.This project was supported by grants from Fundação de Amparo à Pesquisa do Estado de São Paulo (91/0293-7 to F.L.V., and 90/1788-1 to A.S.), and Conselho Nacional de Desenvolvimento Científico e Tecnológico (410068/90-0 and 303633-85/BF to F.L.V.). J.A.C. received a doctoral fellowship from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/Fundação Universidade do Rio Grande. We thank Dr. Alice T. Ferreira for help in the measurements of free Ca²⁺ concentration.     

The potential for and constraints on the evolution of compensatory ability in Asclepias syriaca

To investigate the potential for and constraints on the evolution of compensatory ability, we performed a greenhouse experiment using Asclepias syriaca in which foliar damage and soil nutrient concentration were manipulated. Under low nutrient conditions, significant genetic variation was detected for allocation patterns and for compensatory ability. Furthermore, resource allocation to storage was positively, genetically correlated both with compensatory ability and biomass when damaged, the last two being positively, genetically correlated with each other. Thus, in the low nutrient environment, compensatory ability via resource allocation to storage provided greater biomass when damaged. A negative genetic correlation between compensatory ability and plant biomass when undamaged suggests that this mechanism entailed an allocation cost, which would constrain the evolution of greater compensatory ability when nutrients are limited. Under high nutrient conditions, neither compensatory ability nor allocation patterns predicted biomass when damaged, even though genetic variation in compensatory ability existed. Instead, plant biomass when undamaged predicted biomass when damaged. The differences in outcomes between the two nutrient treatments highlight the importance of considering the possible range of environmental conditions that a genotype may experience. Furthermore, traits that conferred compensatory ability did not necessarily contribute to biomass when damaged, demonstrating that it is critical to examine both compensatory ability and biomass when damaged to determine whether selection by herbivores can favor the evolution of increased compensation. Received: 2 April 1999 / Accepted: 21 September 1999     

The effect of costs associated with toxin production in a competitive system

In this paper, we study a two-species competitive system where both the species produce toxin against each other at some cost to their growth rates. A much wider set of outcomes is possible for our system. These outcomes are important contrasts to competitive exclusion or bistable attractors that are often the outcomes for competitive systems. We show that toxin helps to gain an advantage in competition for toxic species whenever the cost of toxin production remains within some moderate value; otherwise it may result in the extinction of the species itself.