We used nondisruptive, whole-stream methods to measure hydraulic characteristics, ecosystem metabolism, and phosphorus cycling in the west fork of Walker Branch (WB), Tennessee and in Hugh White Creek (HWC), North Carolina. Although similar in many of their hydrological and chemical characteristics, transient storage zone volume in HWC was relatively large (-1.5 times that of the flowing water zone), whereas transient storage zone volume in WB was small (-0.1 times that of the flowing water zone). Both streams were highly heterotrophic (gross primary production : total respiration ratios

Summary Despite considerable progress in understanding tumour development. the law of growth for human tumours is still a matter of some dispute. In this study, we used large-scale mammography screening trial data to deduce the growth law of primary breast cancer. We compared the empirical tumour population size distributions of primary breast cancer inferred from these data to the distributions that correspond to various possible theoretical growth functions. From this. we showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth (exponent = 0.5). This law indicates unbounded growth but with slowing mass-specific growth rate and doubling time. In the clinical size ranges, it implies a greater decline in the mass-specific growth rate than would be predicted by the Gompertz law using the accepted parameters. This suggests that large tumours would be less sensitive to cycle-specific therapies. and be better treated first by non-cell cycle-specific agents. We discussed the use of our study to estimate the sensitivity of mammography for the detection of small tumours. For example, we estimated that mammography is about 30% less sensitive in the detection of tumours in the 1 to Flehinger. 1991 and Xu and Prorok. 1997 for theoretical discussions). Nex ertheless. the benefit of screening. especiall in youncer women (< 50 Xyears). still remains somew-hat controv-ersial (Fletcher et al. 1993: Tabar et al. 1995 In the present w-ork. we employed extensive clinical data from large mammogaraphv screening trials that should be representatiVe of the general population. Usinc mathematical tools. we extracted from these data useful information about breast cancer growth.

An age-structured model is developed for analyzing the effects of marine reserves and other long-term closures on fishery yield, assuming larvae are well-mixed and that exchange of adults between the open and closed areas is negligible. A number of analytic results are derived, including a formula for the gradient of yield with respect to fishing mortality and closure fraction. Increasing the closure fraction at equilibrium spawning stock biomass (SSB), B, will increase yield if and only if s′(B) > 1/b0(0), where s′(B) is the slope of the stock–recruitment curve at B and b0(0) is SSB per recruit at zero fishing mortality. Conditions for the level of closure required to prevent stock collapse are also derived. Applications of the theory to canary rockfish (Sebastes pinniger) and Georges Bank sea scallop (Placopecten magellanicus) illustrate that long-term closures increase yield only at low SSB associated with fishing mortalities greater than FMSY and with low closure fractions. The theory presented here gives simple analytic and graphical techniques for predicting the effects of long-term closures on yield and stock persistence.

The effect of periphyton biomass on hydraulic characteristics and nutrient cycling was studied in laboratory streams with and without snail herbivores. Hydraulic characteristics, such as average water velocity, dispersion coefficients, and relative volume of transient storage zones (zones of stationary water), were quantified by performing short-term injections of a conservative tracer and fitting an advection-dispersion model to the conservative tracer concentration profile downstream from the injection site. Nutrient cycling was quantified by measuring two indices: (1) uptake rate of phosphorus from stream water normalized to gross primary production (GPP), a surrogate measure of total P demand, and (2) turnover rate of phosphorus in the periphyton matrix. These measures indicate the importance of internal cycling (within the periphyton matrix) in meeting the P demands of periphyton. Dense growths of filamentous diatoms and blue-green algae accumulated in the streams with no snails (high-biomass streams), whereas the periphyton communities in streams with snails consisted almost entirely of a thin layer of basal cells of Stigeoclonium sp. (low-biomass streams). Dispersion coefficients were significantly greater and transient storage zones were significantly larger in the high-biomass streams compared to the low-biomass streams. Rates of GPP-normalized P uptake from water and rates of P turnover in periphyton were significantly lower in high biomass than in low biomass periphyton communities, suggesting that a greater fraction of the P demand was met by recycling in the high biomass communities. Increases in streamwater P concentration significantly increased GPP-normalized P uptake in high biomass communities, suggesting diffusion limitation of nutrient transfer from stream water to algal cells in these communities. Our results demonstrate that accumulations of periphyton biomass can alter the hydraulic characteristics of streams, particularly by increasing transient storage zones, and can increase internal nutrient cycling. They suggest a close coupling of hydraulic characteristics and nutrient cycling processes in stream ecosystems.

A stochastic model for solute transport in streams with transient storage zones is presented. This model has an analytic solution in terms of a rapidly converging infinite series. Besides being computationally efficient, this solution is of interest because the terms of the series can be interpreted physically. Simple methods for roughly estimating storage zone parameters directly from tracer injection data are introduced. These methods give quick estimates of these parameters without requiring solutions to the model equations.