Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

The ancient Britons: groundwater fauna survived extreme climate change over tens of millions of years across NW Europe

Global climate changes during the Cenozoic (65.5–0 Ma) caused major biological range shifts and extinctions. In northern Europe, for example, a pattern of few endemics and the dominance of wide-ranging species is thought to have been determined by the Pleistocene (2.59–0.01 Ma) glaciations. This study, in contrast, reveals an ancient subsurface fauna endemic to Britain and Ireland. Using a Bayesian phylogenetic approach, we found that two species of stygobitic invertebrates (genus Niphargus) have not only survived the entire Pleistocene in refugia but have persisted for at least 19.5 million years. Other Niphargus species form distinct cryptic taxa that diverged from their nearest continental relative between 5.6 and 1.0 Ma. The study also reveals an unusual biogeographical pattern in the Niphargus genus. It originated in north-west Europe approximately 87 Ma and underwent a gradual range expansion. Phylogenetic diversity and species age are highest in north-west Europe, suggesting resilience to extreme climate change and strongly contrasting the patterns seen in surface fauna. However, species diversity is highest in south-east Europe, indicating that once the genus spread to these areas (approximately 25 Ma), geomorphological and climatic conditions enabled much higher diversification. Our study highlights that groundwater ecosystems provide an important contribution to biodiversity and offers insight into the interactions between biological and climatic processes.

Remote sensing of intertidal morphological change in Morecambe Bay, U.K., between 1991 and 2007

Tidal Flats are important examples of extensive areas of natural environment that remain relatively unaffected by man. Monitoring of tidal flats is required for a variety of purposes. Remote sensing has become an established technique for the measurement of topography over tidal flats. A further requirement is to measure topographic changes in order to measure sediment budgets. To date there have been few attempts to make quantitative estimates of morphological change over tidal flat areas. This paper illustrates the use of remote sensing to measure quantitative and qualitative changes in the tidal flats of Morecambe Bay during the relatively long period 1991–2007. An understanding of the patterns of sediment transport within the Bay is of considerable interest for coastal management and defence purposes. Tidal asymmetry is considered to be the dominant cause of morphological change in the Bay, with the higher currents associated with the flood tide being the main agency moulding the channel system. Quantitative changes were measured by comparing a Digital Elevation Model (DEM) of the intertidal zone formed using the waterline technique applied to satellite Synthetic Aperture Radar (SAR) images from 1991–1994, to a second DEM constructed from airborne laser altimetry data acquired in 2005. Qualitative changes were studied using additional SAR images acquired since 2003. A significant movement of sediment from below Mean Sea Level (MSL) to above MSL was detected by comparing the two Digital Elevation Models, though the proportion of this change that could be ascribed to seasonal effects was not clear. Between 1991 and 2004 there was a migration of the Ulverston channel of the river Leven north-east by about 5 km, followed by the development of a straighter channel to the west, leaving the previous channel decoupled from the river. This is thought to be due to independent tidal and fluvial forcing mechanisms acting on the channel. The results demonstrate the effectiveness of remote sensing for measurement of long-term morphological change in tidal flat areas. An alternative use of waterlines as partial bathymetry for assimilation into a morphodynamic model of the coastal zone is also discussed.

Estimating oceanic heat content change using isotherms

This paper presents a new analysis of ocean heat content changes over the last 50 yr using isotherms by calculating the mean temperature above the 148C isotherm and the depth of the 148C isotherm as separate variables. A new quantity called the ‘‘relative heat content’’ (‘‘RHC’’) is introduced, which represents the minimum local heat content change over time, relative to a fixed isotherm. It is shown how mean temperature and isotherm depth changes make separable and additive contributions to changes in RHC. Maps of RHC change between 1970 and 2000 show similar spatial patterns to a traditional fixed-depth ocean heat content change to 220 m. However, the separate contributions to RHC suggest a more spatially uniform contribution from warming above the isotherm, while isotherm depth changes show wind-driven signals, of which some are identifiable as being related to the North Atlantic Oscillation. The time series show that the warming contribution to RHC dominates the global trend, while the depth contribution only dominates on the basin scale in the North Atlantic. The RHC shows minima associated with the major volcanic eruptions (particularly in the Indian Ocean), and these are entirely contributed by mean temperature changes rather than isotherm depth changes. The depth change contributions to RHC are strongly affected by the recently reported XBT fall-rate bias, whereas the mean temperature contributions are not. Therefore, only the isotherm depth change contributions toRHCwill need to be reassessed as fall-rate-corrected data become available.

Past, present and future change in the Atlantic meridional overturning circulation

Observations and numerical modelling experiments provide evidence for links between variability in the Atlantic Meridional Overturning Circulation (AMOC) and global climate patterns. Reduction in the strength of the overturning circulation is thought to have played a key role in rapid climate change in the past and may have the potential to significantly influence climate change in the future, as noted in the last two IPCC assessment reports (2001, 2007). Both IPCC reports also highlighted the significant uncertainties that exist regarding the future behaviour of the AMOC under global warming. Model results suggest that changes in the AMOC can impact surface air temperature, precipitation patterns and sea level, particularly in areas bordering the North Atlantic, thus affecting human populations. Here current understanding of past, present and future change in the AMOC and the effects of such changes on climate are reviewed. The focus is on observations of the AMOC, how the AMOC influences climate and in what way the AMOC is likely to change over the next few decades and the 21st 34 century. The potential for decadal prediction of the AMOC is also discussed. Finally, the outstanding challenges and possible future directions for AMOC research are outlined.

Simulation of late-twenty-first-century changes in wintertime atmospheric circulation over Europe due to anthropogenic causes

Evidence is presented, based on an ensemble of climate change scenarios performed with a global general circulation model of the atmosphere with high horizontal resolution over Europe, to suggest that the end-of-century anthropogenic climate change over the North Atlantic--European region strongly projects onto the positive phase of the North Atlantic Oscillation during wintertime. It is reflected in a doubling of the residence frequency of the climate system in the associated circulation regime, in agreement with the nonlinear climate perspective. The strong increase in the amplitude of the response, compared to coarse-resolution coupled model studies, suggests that improved model representation of regional climate is needed to achieve more reliable projections of anthropogenic climate change on European climate.

Options for support to agriculture and food security under climate change

Agriculture and food security are key sectors for intervention under climate change. Agricultural production is highly vulnerable even to 2C (low-end) predictions for global mean temperatures in 2100, with major implications for rural poverty and for both rural and urban food security. Agriculture also presents untapped opportunities for mitigation, given the large land area under crops and rangeland, and the additional mitigation potential of aquaculture. This paper presents a summary of current knowledge on options to support farmers, particularly smallholder farmers, in achieving food security through agriculture under climate change. Actions towards adaptation fall into two broad overlapping areas: (1) accelerated adaptation to progressive climate change over decadal time scales, for example integrated packages of technology, agronomy and policy options for farmers and food systems, and (2) better management of agricultural risks associated with increasing climate variability and extreme events, for example improved climate information services and safety nets. Maximization of agriculture’s mitigation potential will require investments in technological innovation and agricultural intensification linked to increased efficiency of inputs, and creation of incentives and monitoring systems that are inclusive of smallholder farmers. Food systems faced with climate change need urgent, broad-based action in spite of uncertainties.

Flood risk and climate change: global and regional perspectives

A holistic perspective on changing rainfall-driven flood risk is provided for the late 20th and early 21st centuries. Economic losses from floods have greatly increased, principally driven by the expanding exposure of assets at risk. It has not been possible to attribute rain-generated peak streamflow trends to anthropogenic climate change over the past several decades. Projected increases in the frequency and intensity of heavy rainfall, based on climate models, should contribute to increases in precipitation-generated local flooding (e.g. flash flooding and urban flooding). This article assesses the literature included in the IPCC SREX report and new literature published since, and includes an assessment of changes in flood risk in seven of the regions considered in the recent IPCC SREX report—Africa, Asia, Central and South America, Europe, North America, Oceania and Polar regions. Also considering newer publications, this article is consistent with the recent IPCC SREX assessment finding that the impacts of climate change on flood characteristics are highly sensitive to the detailed nature of those changes and that presently we have only low confidence1 in numerical projections of changes in flood magnitude or frequency resulting from climate change.

Climate change

This chapter presents a broad overview of understanding of climate change over the past century or so, together with a discussion of some of the uncertainties. It provides a background to the developments in understanding of climate change, presents evidence that climate has changed and assesses the mechanisms that cause climate change, with a particular emphasis on those due to human activity. The concepts underlying climate modelling are introduced and results are then presented that strongly support the view that human activity has played a major role in the observed climate change over the past 50 years. Possible changes in climate over the coming century are then discussed.

Understanding El Niño in ocean-atmosphere general circulation models: progress and challenges

Determining how El Niño and its impacts may change over the next 10 to 100 years remains a difficult scientific challenge. Ocean–atmosphere coupled general circulation models (CGCMs) are routinely used both to analyze El Niño mechanisms and teleconnections and to predict its evolution on a broad range of time scales, from seasonal to centennial. The ability to simulate El Niño as an emergent property of these models has largely improved over the last few years. Nevertheless, the diversity of model simulations of present-day El Niño indicates current limitations in our ability to model this climate phenomenon and to anticipate changes in its characteristics. A review of the several factors that contribute to this diversity, as well as potential means to improve the simulation of El Niño, is presented.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Ancient lakes of the Sahara

As a result of climate change over the past 5000 years the Sahara changed from savannah to a desert landscape. The beds of ancient lakes are home to snail shells and the petrified roots of trees and shrubs. Examples of human occupation can also be seen in the form of fireplaces and discarded tools. Examination of the geological history of these sites can give a clearer picture of how the climate changed and how humans coped with these changes.

The Representative Soil Sampling Scheme of England and Wales: a statistical analysis of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme of England and Wales has recorded information on the soil of agricultural land in England and Wales since 1969. It is a valuable source of information about the soil in the context of monitoring for sustainable agricultural development. Changes in soil nutrient status and pH were examined over the period 1971-2001. Several methods of statistical analysis were applied to data from the surveys during this period. The main focus here is on the data for 1971, 1981, 1991 and 2001. The results of examining change over time in general show that levels of potassium in the soil have increased, those of magnesium have remained fairly constant, those of phosphorus have declined and pH has changed little. Future sampling needs have been assessed in the context of monitoring, to determine the mean at a given level of confidence and tolerable error and to detect change in the mean over time at these same levels over periods of 5 and 10 years. The results of a non-hierarchical multivariate classification suggest that England and Wales could be stratified to optimize future sampling and analysis. To monitor soil quality and health more generally than for agriculture, more of the country should be sampled and a wider range of properties recorded.