Slow closure of Earth's carbon cycle

Carbon near the Earth's surface cycles between the production and consumption of organic carbon; the former sequesters carbon dioxide while the latter releases it. Microbes attempt to close the loop, but the longer organic matter survives, the slower microbial degradation becomes. This aging effect leaves observable quantitative signatures: Organic matter decays at rates that are inversely proportional to its age, while microbial populations and concentrations of organic carbon in ocean sediments decrease at distinct powers of age. Yet mechanisms that predict this collective organization remain unknown. Here, I show that these and other observations follow from the assumption that the decay of organic matter is limited by progressively rare extreme fluctuations in the energy available to microbes for decomposition. The theory successfully predicts not only observed scaling exponents but also a previously unobserved scaling regime that emerges when microbes subsist on the minimum energy flux required for survival. The resulting picture suggests that the carbon cycle's age-dependent dynamics are analogous to the slow approach to equilibrium in disordered systems. The impact of these slow dynamics is profound: They preclude complete oxidation of organic carbon in sediments, thereby freeing molecular oxygen to accumulate in the atmosphere.

Modeling of Machine Learning-Based Extreme Value Theory in Stock Investment Risk Prediction: A Systematic Literature Review

The stock market is heavily influenced by global sentiment, which is full of uncertainty and is characterized by extreme values and linear and nonlinear variables. High-frequency data generally refer to data that are collected at a very fast rate based on days, hours, minutes, and even seconds. Stock prices fluctuate rapidly and even at extremes along with changes in the variables that affect stock fluctuations. Research on investment risk estimation in the stock market that can identify extreme values is nonlinear, reliable in multivariate cases, and uses high-frequency data that are very important. The extreme value theory (EVT) approach can detect extreme values. This method is reliable in univariate cases and very complicated in multivariate cases. The purpose of this research was to collect, characterize, and analyze the investment risk estimation literature to identify research gaps. The literature used was selected by applying the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) and sourced from Sciencedirect.com and Scopus databases. A total of 1107 articles were produced from the search at the identification stage, reduced to 236 in the eligibility stage, and 90 articles in the included studies set. The bibliometric networks were visualized using the VOSviewer software, and the main keyword used as the search criteria is "VaR." The visualization showed that EVT, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and historical simulation are models often used to estimate the investment risk; the application of the machine learning (ML)-based investment risk estimation model is low. There has been no research using a combination of EVT and ML to estimate the investment risk. The results showed that the hybrid model produced better Value-at-Risk (VaR) accuracy under uncertainty and nonlinear conditions. Generally, models only use daily return data as model input. Based on research gaps, a hybrid model framework for estimating risk measures is proposed using a combination of EVT and ML, using multivariable and high-frequency data to identify extreme values in the distribution of data. The goal is to produce an accurate and flexible estimated risk value against extreme changes and shocks in the stock market. Mathematics Subject Classification: 60G25; 62M20; 6245; 62P05; 91G70.

Bridging Extremes: The Invertible Bimodal Gumbel Distribution

This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.

Risk modelling of ESG (environmental, social, and governance), healthcare, and financial sectors

Climate change poses enormous ecological, socio-economic, health, and financial challenges. A novel extreme value theory is employed in this study to model the risk to environmental, social, and governance (ESG), healthcare, and financial sectors and assess their downside risk, extreme systemic risk, and extreme spillover risk. We use a rich set of global daily data of exchange-traded funds (ETFs) from 1 July 1999 to 30 June 2022 in the case of healthcare and financial sectors and from 1 July 2007 to 30 June 2022 in the case of ESG sector. We find that the financial sector is the riskiest when we consider the tail index, tail quantile, and tail expected shortfall. However, the ESG sector exhibits the highest tail risk in the extreme environment when we consider a shock in the form of an ETF drop of 25% or 50%. The ESG sector poses the highest extreme systemic risk when a shock comes from China. Finally, we find that ESG and healthcare sectors have lower extreme spillover risk (contagion risk) compared to the financial sector. Our study seeks to provide valuable insights for developing sustainable economic, business, and financial strategies. To achieve this, we conduct a comprehensive risk assessment of the ESG, healthcare, and financial sectors, employing an innovative approach to risk modelling in response to ecological challenges.

Extreme value modelling of SARS-CoV-2 community transmission using discrete generalized Pareto distributions

Superspreading has been suggested to be a major driver of overall transmission in the case of SARS-CoV-2. It is, therefore, important to statistically investigate the tail features of superspreading events (SSEs) to better understand virus propagation and control. Our extreme value analysis of different sources of secondary case data indicates that case numbers of SSEs associated with SARS-CoV-2 may be fat-tailed, although substantially less so than predicted recently in the literature, but also less important relative to SSEs associated with SARS-CoV. The results caution against pooling data from both coronaviruses. This could provide policy- and decision-makers with a more reliable assessment of the tail exposure to SARS-CoV-2 contamination. Going further, we consider the broader problem of large community transmission. We study the tail behaviour of SARS-CoV-2 cluster cases documented both in official reports and in the media. Our results suggest that the observed cluster sizes have been fat-tailed in the vast majority of surveyed countries. We also give estimates and confidence intervals of the extreme potential risk for those countries. A key component of our methodology is up-to-date discrete generalized Pareto models which allow for maximum likelihood-based inference of data with a high degree of discreteness.

S-duct flow distortion with non-uniform inlet conditions

Convoluted aero-engine intakes are often required to enable closer integration between engine and airframe. Although the majority of previous research focused on the distortion of S-duct intakes with undistorted inlet conditions, there is a need to investigate the impact of more challenging inlet conditions at which the intake duct is expected to operate. The impact of inlet vortices and total pressure profiles on the inherent unsteady flow distortion of an S-duct intake was assessed with stereo particle image velocimetry. Inlet vortices disrupted the characteristic flow switching mode but had a modest impact on the peak levels and unsteady fluctuations. Non-uniform inlet total pressure profiles increased the peak swirl intensity and its unsteadiness. The frequency of swirl angle fluctuations was sensitive to the azimuthal orientation of the non-uniform total pressure distribution. The modelling of peak distortion with the extreme value theory revealed that although for some inlet configurations the measured peak swirl intensity was similar, the growth rate of the peak values beyond the experimental observations was substantially different and it was related with the measured flow unsteadiness. This highlights the need of unsteady swirl distortion measurements and the use of statistical models to assess the time-invariant peak distortion levels. Overall, the work shows it is vital to include the effect of the inlet flow conditions as it substantially alters the characteristics of the complex intake flow distortion.

Spatial Methods for Inferring Extremes in Dengue Outbreak Risk in Singapore

Dengue is a major vector-borne disease worldwide. Here, we examined the spatial distribution of extreme weekly dengue outbreak risk in Singapore from 2007 to 2020. We divided Singapore into equal-sized hexagons with a circumradius of 165 m and obtained the weekly number of dengue cases and the surface characteristics of each hexagon. We accounted for spatial heterogeneity using max-stable processes. The 5-, 10-, 20-, and 30-year return levels, or the weekly dengue case counts expected to be exceeded once every 5, 10, 20, and 30 years, respectively, were determined for each hexagon conditional on their surface characteristics remaining constant over time. The return levels were higher in the country's east, with the maximum weekly dengue cases per hexagon expected to exceed 51 at least once in 30 years in many areas. The surface characteristics with the largest impact on outbreak risk were the age of public apartments and the percentage of impervious surfaces, where a 3-year and 10% increase in each characteristic resulted in a 3.8% and 3.3% increase in risk, respectively. Vector control efforts should be prioritized in older residential estates and places with large contiguous masses of built-up environments. Our findings indicate the likely scale of outbreaks in the long term.

A leader cell triggers end of lag phase in populations of Pseudomonas fluorescens

The relationship between the number of cells colonizing a new environment and time for resumption of growth is a subject of long-standing interest. In microbiology this is known as the "inoculum effect." Its mechanistic basis is unclear with possible explanations ranging from the independent actions of individual cells, to collective actions of populations of cells. Here, we use a millifluidic droplet device in which the growth dynamics of hundreds of populations founded by controlled numbers of Pseudomonas fluorescens cells, ranging from a single cell, to one thousand cells, were followed in real time. Our data show that lag phase decreases with inoculum size. The decrease of average lag time and its variance across droplets, as well as lag time distribution shapes, follow predictions of extreme value theory, where the inoculum lag time is determined by the minimum value sampled from the single-cell distribution. Our experimental results show that exit from lag phase depends on strong interactions among cells, consistent with a "leader cell" triggering end of lag phase for the entire population.

Characterization of Inclusion Size Distributions in Steel Wire Rods

The control of inclusions in steel components is essential to guarantee strong performance. The reliable characterization of inclusion populations is essential not only to evaluate the quality of the components but also to allow the use of analytical procedures for the comparison and discrimination of inclusion populations. In this work, inclusion size distributions in wire rod specimens from six plant-scale heats were measured and analyzed. For the measurements, the metallographic procedure specified in the ASTM E2283 standard was used. The population density function (PDF) approach and the extreme value statistical procedure specified in the ASTM E2283 standard were used to analyze the whole size distribution and the upper tail of the size distribution, respectively. The PDF approach allowed us to identify differences among inclusion size distributions and showed that new inclusions were not formed after the liquid steel treatment process. The extreme value statistical procedure led to the prediction of the maximum inclusion length for each heat, which was used for the statistical discrimination of heats. Furthermore, the estimation of the probability of finding an inclusion larger than a given inclusion size using the extreme value theory allowed us to order the heats for different critical inclusion sizes.

Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

Crash Diagnosis and Price Rebound Prediction in NYSE Composite Index Based on Visibility Graph and Time-Evolving Stock Correlation Network

This study proposes a framework to diagnose stock market crashes and predict the subsequent price rebounds. Based on the observation of anomalous changes in stock correlation networks during market crashes, we extend the log-periodic power-law model with a metric that is proposed to measure network anomalies. To calculate this metric, we design a prediction-guided anomaly detection algorithm based on the extreme value theory. Finally, we proposed a hybrid indicator to predict price rebounds of the stock index by combining the network anomaly metric and the visibility graph-based log-periodic power-law model. Experiments are conducted based on the New York Stock Exchange Composite Index from 4 January 1991 to 7 May 2021. It is shown that our proposed method outperforms the benchmark log-periodic power-law model on detecting the 12 major crashes and predicting the subsequent price rebounds by reducing the false alarm rate. This study sheds light on combining stock network analysis and financial time series modeling and highlights that anomalous changes of a stock network can be important criteria for detecting crashes and predicting recoveries of the stock market.

On Max-Semistable Laws and Extremes for Dynamical Systems

Suppose (f,X,μ) is a measure preserving dynamical system and ϕ:X→R a measurable observable. Let Xi=ϕ∘fi-1 denote the time series of observations on the system, and consider the maxima process Mn:=max{X1,…,Xn}. Under linear scaling of Mn, its asymptotic statistics are usually captured by a three-parameter generalised extreme value distribution. This assumes certain regularity conditions on the measure density and the observable. We explore an alternative parametric distribution that can be used to model the extreme behaviour when the observables (or measure density) lack certain regular variation assumptions. The relevant distribution we study arises naturally as the limit for max-semistable processes. For piecewise uniformly expanding dynamical systems, we show that a max-semistable limit holds for the (linear) scaled maxima process.

Human mortality at extreme age

We use a combination of extreme value statistics, survival analysis and computer-intensive methods to analyse the mortality of Italian and French semi-supercentenarians. After accounting for the effects of the sampling frame, extreme-value modelling leads to the conclusion that constant force of mortality beyond 108 years describes the data well and there is no evidence of differences between countries and cohorts. These findings are consistent with use of a Gompertz model and with previous analysis of the International Database on Longevity and suggest that any physical upper bound for the human lifespan is so large that it is unlikely to be approached. Power calculations make it implausible that there is an upper bound below 130 years. There is no evidence of differences in survival between women and men after age 108 in the Italian data and the International Database on Longevity, but survival is lower for men in the French data.

Extreme Value Theory for Hurwitz Complex Continued Fractions

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.

Return Period Evaluation of the Largest Possible Earthquake Magnitudes in Mainland China Based on Extreme Value Theory

The largest possible earthquake magnitude based on geographical characteristics for a selected return period is required in earthquake engineering, disaster management, and insurance. Ground-based observations combined with statistical analyses may offer new insights into earthquake prediction. In this study, to investigate the seismic characteristics of different geographical regions in detail, clustering was used to provide earthquake zoning for Mainland China based on the geographical features of earthquake events. In combination with geospatial methods, statistical extreme value models and the right-truncated Gutenberg–Richter model were used to analyze the earthquake magnitudes of Mainland China under both clustering and non-clustering. The results demonstrate that the right-truncated peaks-over-threshold model is the relatively optimal statistical model compared with classical extreme value theory models, the estimated return level of which is very close to that of the geographical-based right-truncated Gutenberg–Richter model. Such statistical models can provide a quantitative analysis of the probability of future earthquake risks in China, and geographical information can be integrated to locate the earthquake risk accurately.

Portfolio Tail Risk: A Multivariate Extreme Value Theory Approach

This paper develops a method for assessing portfolio tail risk based on extreme value theory. The technique applies separate estimations of univariate series and allows for closed-form expressions for Value at Risk and Expected Shortfall. Its forecasting ability is tested on a portfolio of U.S. stocks. The in-sample goodness-of-fit tests indicate that the proposed approach is better suited for portfolio risk modeling under extreme market movements than comparable multivariate parametric methods. Backtesting across multiple quantiles demonstrates that the model cannot be rejected at any reasonable level of significance, even when periods of stress are included. Numerical simulations corroborate the empirical results.

Evidence that coronavirus superspreading is fat-tailed

Superspreaders, infected individuals who result in an outsized number of secondary cases, are believed to underlie a significant fraction of total SARS-CoV-2 transmission. Here, we combine empirical observations of SARS-CoV and SARS-CoV-2 transmission and extreme value statistics to show that the distribution of secondary cases is consistent with being fat-tailed, implying that large superspreading events are extremal, yet probable, occurrences. We integrate these results with interaction-based network models of disease transmission and show that superspreading, when it is fat-tailed, leads to pronounced transmission by increasing dispersion. Our findings indicate that large superspreading events should be the targets of interventions that minimize tail exposure.

Introducing the GEV Activation Function for Highly Unbalanced Data to Develop COVID-19 Diagnostic Models

Fast and accurate diagnosis is essential for the efficient and effective control of the COVID-19 pandemic that is currently disrupting the whole world. Despite the prevalence of the COVID-19 outbreak, relatively few diagnostic images are openly available to develop automatic diagnosis algorithms. Traditional deep learning methods often struggle when data is highly unbalanced with many cases in one class and only a few cases in another; new methods must be developed to overcome this challenge. We propose a novel activation function based on the generalized extreme value (GEV) distribution from extreme value theory, which improves performance over the traditional sigmoid activation function when one class significantly outweighs the other. We demonstrate the proposed activation function on a publicly available dataset and externally validate on a dataset consisting of 1,909 healthy chest X-rays and 84 COVID-19 X-rays. The proposed method achieves an improved area under the receiver operating characteristic (DeLong's p-value < 0.05) compared to the sigmoid activation. Our method is also demonstrated on a dataset of healthy and pneumonia vs. COVID-19 X-rays and a set of computerized tomography images, achieving improved sensitivity. The proposed GEV activation function significantly improves upon the previously used sigmoid activation for binary classification. This new paradigm is expected to play a significant role in the fight against COVID-19 and other diseases, with relatively few training cases available.

An unethical optimization principle

If an artificial intelligence aims to maximize risk-adjusted return, then under mild conditions it is disproportionately likely to pick an unethical strategy unless the objective function allows sufficiently for this risk. Even if the proportion η of available unethical strategies is small, the probability p _U of picking an unethical strategy can become large; indeed, unless returns are fat-tailed p _U tends to unity as the strategy space becomes large. We define an unethical odds ratio, Υ (capital upsilon), that allows us to calculate p _U from η, and we derive a simple formula for the limit of Υ as the strategy space becomes large. We discuss the estimation of Υ and p _U in finite cases and how to deal with infinite strategy spaces. We show how the principle can be used to help detect unethical strategies and to estimate η. Finally we sketch some policy implications of this work.

Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder

In this paper, we study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the strength of the synaptic connections are randomly generated from known, generally arbitrary, probability distributions. We derived semi-analytical expressions of the occurrence probability of the stationary states and the mean multistability diagram of the model, in terms of the distribution of the synaptic connections and of the external stimuli to the network. Our calculations rely on the probability distribution of the bifurcation points of the stationary states with respect to the external stimuli, calculated in terms of the permanent of special matrices using extreme value theory. While our semi-analytical expressions are exact for any size of the network and for any distribution of the synaptic connections, we focus our study on networks made of several populations, that we term "statistically homogeneous" to indicate that the probability distribution of their connections depends only on the pre- and post-synaptic population indexes, and not on the individual synaptic pair indexes. In this specific case, we calculated analytically the permanent, obtaining a compact formula that outperforms of several orders of magnitude the Balasubramanian-Bax-Franklin-Glynn algorithm. To conclude, by applying the Fisher-Tippett-Gnedenko theorem, we derived asymptotic expressions of the stationary-state statistics of multi-population networks in the large-network-size limit, in terms of the Gumbel (double exponential) distribution. We also provide a Python implementation of our formulas and some examples of the results generated by the code.

Developing a Hierarchical Model for the Spatial Analysis of PM10 Pollution Extremes in the Mexico City Metropolitan Area

We implemented a spatial model for analysing PM10 maxima across the Mexico City metropolitan area during the period 1995–2016. We assumed that these maxima follow a non-identical generalized extreme value (GEV) distribution and modeled the trend by introducing multivariate smoothing spline functions into the probability GEV distribution. A flexible, three-stage hierarchical Bayesian approach was developed to analyse the distribution of the PM10 maxima in space and time. We evaluated the statistical model’s performance by using a simulation study. The results showed strong evidence of a positive correlation between the PM10 maxima and the longitude and latitude. The relationship between time and the PM10 maxima was negative, indicating a decreasing trend over time. Finally, a high risk of PM10 maxima presenting levels above 1000 μg/m3 (return period: 25 yr) was observed in the northwestern region of the study area.

Rateless Lossy Compression via the Extremes

We begin by presenting a simple lossy compressor operating at near-zero rate: The encoder merely describes the indices of the few maximal source components, while the decoder's reconstruction is a natural estimate of the source components based on this information. This scheme turns out to be near optimal for the memoryless Gaussian source in the sense of achieving the zero-rate slope of its distortion-rate function. Motivated by this finding, we then propose a scheme comprised of iterating the above lossy compressor on an appropriately transformed version of the difference between the source and its reconstruction from the previous iteration. The proposed scheme achieves the rate distortion function of the Gaussian memoryless source (under squared error distortion) when employed on any finite-variance ergodic source. It further possesses desirable properties, and we, respectively, refer to as infinitesimal successive refinability, ratelessness, and complete separability. Its storage and computation requirements are of order no more than (n2)/(log β n) per source symbol for β > 0 at both the encoder and the decoder. Though the details of its derivation, construction, and analysis differ considerably, we discuss similarities between the proposed scheme and the recently introduced Sparse Regression Codes of Venkataramanan et al.

Index for Predicting Insurance Claims from Wind Storms with an Application in France

For insurance companies, wind storms represent a main source of volatility, leading to potentially huge aggregated claim amounts. In this article, we compare different constructions of a storm index allowing us to assess the economic impact of storms on an insurance portfolio by exploiting information from historical wind speed data. Contrary to historical insurance portfolio data, meteorological variables show fewer nonstationarities between years and are easily available with long observation records; hence, they represent a valuable source of additional information for insurers if the relation between observations of claims and wind speeds can be revealed. Since standard correlation measures between raw wind speeds and insurance claims are weak, a storm index focusing on high wind speeds can afford better information. A storm index approach has been applied to yearly aggregated claim amounts in Germany with promising results. Using historical meteorological and insurance data, we assess the consistency of the proposed index constructions with respect to various parameters and weights. Moreover, we are able to place the major insurance events since 1998 on a broader horizon beyond 40 years. Our approach provides a meteorological justification for calculating the return periods of extreme-storm-related insurance events whose magnitude has rarely been reached.

Summarising censored survival data using the mean residual life function

The mean residual life function provides a clear and simple summary of the effect of a treatment or a risk factor in units of time, avoiding hazard ratios or probability scales, which require careful interpretation. Estimation of the mean residual life is complicated by the upper tail of the survival distribution not being observed as, for example, patients may still be alive at the end of the follow-up period. Various approaches have been developed to estimate the mean residual life in the presence of such right censoring. In this work, a novel semi-parametric method that combines existing non-parametric methods and an extreme value tail model is presented, where the limited sample information in the tail (prior to study termination) is used to estimate the upper tail behaviour. This approach will be demonstrated with simulated and real-life examples.

A simulation-based assessment and an illustration to the surveillance of Salmonella

We propose a new method that could be part of a warning system for the early detection of time clusters applied to public health surveillance data. This method is based on the extreme value theory (EVT). To any new count of a particular infection reported to a surveillance system, we associate a return period that corresponds to the time that we expect to be able to see again such a level. If such a level is reached, an alarm is generated. Although standard EVT is only defined in the context of continuous observations, our approach allows to handle the case of discrete observations occurring in the public health surveillance framework. Moreover, it applies without any assumption on the underlying unknown distribution function. The performance of our method is assessed on an extensive simulation study and is illustrated on real data from Salmonella surveillance in France.

Generative models versus underlying symmetries to explain biological pattern

Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative models confirm the plausibility of an explanation and make testable hypotheses for further experiments. However, studies rarely consider the broad family of alternative models that match the same observed pattern. The symmetries that define the broad class of matching models are in fact the only aspects of information truly revealed by observed pattern. Commonly observed patterns derive from simple underlying symmetries. This article illustrates the problem by showing the symmetry associated with the observed rate of increase in fitness in a constant environment. That underlying symmetry reveals how each particular generative model defines a single example within the broad class of matching models. Further progress on the relation between pattern and process requires deeper consideration of the underlying symmetries.

Adaptive walks and distribution of beneficial fitness effects

We study the adaptation dynamics of a maladapted asexual population on rugged fitness landscapes with many local fitness peaks. The distribution of beneficial fitness effects is assumed to belong to one of the three extreme value domains, viz. Weibull, Gumbel, and Fréchet. We work in the strong selection-weak mutation regime in which beneficial mutations fix sequentially, and the population performs an uphill walk on the fitness landscape until a local fitness peak is reached. A striking prediction of our analysis is that the fitness difference between successive steps follows a pattern of diminishing returns in the Weibull domain and accelerating returns in the Fréchet domain, as the initial fitness of the population is increased. These trends are found to be robust with respect to fitness correlations. We believe that this result can be exploited in experiments to determine the extreme value domain of the distribution of beneficial fitness effects. Our work here differs significantly from the previous ones that assume the selection coefficient to be small. On taking large effect mutations into account, we find that the length of the walk shows different qualitative trends from those derived using small selection coefficient approximation.

The population genetics of beneficial mutations

The population genetic study of advantageous mutations has lagged behind that of deleterious and neutral mutations. But over the past two decades, a number of significant developments, both theoretical and empirical, have occurred. Here, I review two of these developments: the attempt to determine the distribution of fitness effects among beneficial mutations and the attempt to determine their average dominance. Considering both theory and data, I conclude that, while considerable theoretical progress has been made, we still lack sufficient data to draw confident conclusions about the distribution of effects or the dominance of beneficial mutations.

Getting the Most From Your Extreme Wind Data: A Step by Step Guide

Models for extremes of environmental processes have been studied extensively in recent years. The particular problems arising when attempting to estimate return levels from sequences of measurements on the appropriate variables have been considered in some detail. In particular, the aspects of seasonal variation and short-range dependence have received a great deal of attention. In this paper we present a case study based on 10 years of hourly wind speed measurements collected at a U.K. site, elucidating the most successful procedure emerging from an extensive study of this data. The basic model (in which an extreme value distribution is fitted to cluster peak excesses over a high threshold) is standard. However the emphasis is on a number of practical problems which will arise when such models are fitted to wind speeds, but which have received little consideration. These include: model selection and assessment of model adequacy when the threshold, and some or all of the parameters, are allowed to vary seasonally; the choice of the best combination of threshold and cluster identification procedure; and the choice of a measure of precision for return level estimates. The aim is to suggest an algorithm which can be generally applied to the problem of gust return level estimation at individual sites.