A Multi-Stage Differential-Multifactorial Evolutionary Algorithm for Ingredient Optimization in the Copper Industry

Ingredient optimization plays a pivotal role in the copper industry,for which it is closely related to the concentrate utilization rate,stability of furnace conditions,and the quality of copper production.To acquire a practical ingredient plan,which should exhibit long duration time with sufficient utilization and feeding stability for real applications,an ingredient plan optimization model is proposed in this study to effectively guarantee continuous production and stable furnace conditions.To address the complex challenges posed by this integer programming model,including multiple coupling feeding stages,intricate constraints,and significant non-linearity,a multi-stage differential-multifactorial evolution algorithm is developed.In the proposed algorithm,the differential evolutionary(DE)algorithm is improved in three aspects to efficiently tackle challenges when optimizing the proposed model.First,unlike traditional time-consuming serial approaches,the multifactorial evolutionary algorithm is utilized to optimize multiple complex models contained in the population of evolutionary algorithm caused by the feeding stability in a parallel manner.Second,a repair algorithm is employed to adjust infeasible ingredient lists in a timely manner.In addition,a local search strategy taking feedback from the current optima and considering the different positions of global optimum is developed to avoiding premature convergence of the differential evolutionary algorithm.Finally,the simulation experiments considering different planning horizons using real data from the copper industry in China are conducted,which demonstrates the superiority of the proposed method on feeding duration and stability compared with other commonly deployed approaches.It is practically helpful for reducing material cost as well as increasing production profit for the copper industry.

Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance

To enhance the comprehensive performance of artillery internal ballistics—encompassing power,accuracy,and service life—this study proposed a multi-stage multidisciplinary design optimization(MS-MDO)method.First,the comprehensive artillery internal ballistic dynamics(AIBD)model,based on propellant combustion,rotation band engraving,projectile axial motion,and rifling wear models,was established and validated.This model was systematically decomposed into subsystems from a system engineering perspective.The study then detailed the MS-MDO methodology,which included Stage I(MDO stage)employing an improved collaborative optimization method for consistent design variables,and Stage II(Performance Optimization)focusing on the independent optimization of local design variables and performance metrics.The methodology was applied to the AIBD problem.Results demonstrated that the MS-MDO method in Stage I effectively reduced iteration and evaluation counts,thereby accelerating system-level convergence.Meanwhile,Stage II optimization markedly enhanced overall performance.These comprehensive evaluation results affirmed the effectiveness of the MS-MDO method.

Research on Regulation Method of Energy Storage System Based on Multi-Stage Robust Optimization

To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.

The mechanisms of thermal solidification agent promoting steam diversion in heavy oil reservoirs

At high cycles of steam huff&puff,oil distribution in reservoirs becomes stronger heterogeneity due to steam channeling.Thermal solidification agent can be used to solve this problem.Its solution is a lowviscosity liquid at normal temperature,but it can be solidified above 80℃.The plugging degree is up to 99%at 250℃.The sweep efficiency reaches 59.2%,which is 7.3%higher than pure steam injection.In addition,simultaneous injection of viscosity reducer and/or nitrogen foams can further enhance oil recovery.The mechanism of this technology depends on its strong plugging ability,which changes the flowing pattern of steam to effectively mobilize remaining oil.Viscosity reducer and nitrogen foams further expand the sweep range and extends the effective period.Therefore,thermal solidification agent can plug steam channeling paths and adjust steam flowing direction to significantly enhance oil recovery at high cycles of steam huff&puff.

Fracture propagation law of temporary plugging and diversion fracturing in shale reservoirs under completion experiments of horizontal well with multi-cluster sand jetting perforation

This study conducted temporary plugging and diversion fracturing(TPDF)experiments using a true triaxial fracturing simulation system within a laboratory setting that replicated a lab-based horizontal well completion with multi-cluster sand jetting perforation.The effects of temporary plugging agent(TPA)particle size,TPA concentration,single-cluster perforation number and cluster number on plugging pressure,multi-fracture diversion pattern and distribution of TPAs were investigated.A combination of TPAs with small particle sizes within the fracture and large particle sizes within the segment is conducive to increasing the plugging pressure and promoting the diversion of multi-fractures.The addition of fibers can quickly achieve ultra-high pressure,but it may lead to longitudinal fractures extending along the wellbore.The temporary plugging peak pressure increases with an increase in the concentration of the TPA,reaching a peak at a certain concentration,and further increases do not significantly improve the temporary plugging peak pressure.The breaking pressure and temporary plugging peak pressure show a decreasing trend with an increase in single-cluster perforation number.A lower number of single-cluster perforations is beneficial for increasing the breaking pressure and temporary plugging peak pressure,and it has a more significant control on the propagation of multi-cluster fractures.A lower number of clusters is not conducive to increasing the total number and complexity of artificial fractures,while a higher number of clusters makes it difficult to achieve effective plugging.The TPAs within the fracture is mainly concentrated in the complex fracture areas,especially at the intersections of fractures.Meanwhile,the TPAs within the segment are primarily distributed near the perforation cluster apertures which initiated complex fractures.

Water hammer protection for diversion systems in front of pumps in long-distance water supply projects

For a water supply system with long-distance diversion pipelines, in addition to the water hammer problems that occur beyond pumps, the safety of the water diversion pipeline in front of pumps also deserves attention. In this study, a water hammer protection scheme combined with an overflow surge tank and a regulating valve was developed. A mathematical model of the overflow surge tank was developed, and an analytical formula for the height of the overflow surge tank was derived. Furthermore, a practical water supply project was used to evaluate the feasibility of the combined protection scheme and analyze the sensitivity of valve regulation rules. The results showed that the combined protection scheme effectively reduced the height of the surge tank, lessened the difficulties related to construction, and reduced the necessary financial investment for the project. The two-stage closing rule articulated as fast first and then slow could minimize the overflow volume of the surge tank when the power failure occurred, while the two-stage opening rule articulated as slow first and then fast could be more conducive to the safety of the water supply system when the pump started up.

Trace Elements of Multi-stage Minerals and Titanite U-Pb Dating for the Gneisses from Liansan Island,Sulu UHPM Belt

Gneisses with anatectic characteristics from the Liansan island in the Sulu UHPM(ultra-high pressure metamorphic)belt were studied for petrography,titanite U-Pb dating and mineral geochemistry.Three origins of garnets are distinguished:metamorphic garnet,peritectic garnet and anatectic garnet,which are formed in the stages of peak metamorphism,retrograde anatexis and melt crystallization,respectively.The euhedral titanite has a high content of REE and high Th/U ratios,which is interpreted as indicating that it was newly-formed from an anatectic melt.The LA-ICP-MS titanite U-Pb dating yields 214-217 Ma ages for the titanite(melt)crystallization.The distribution of trace elements varies in response to the different host minerals at different stages.At the peak metamorphic stage,Y and HREE are mainly hosted by garnet,Ba and Rb by phengite,Sr,Nb,Ta,Pb,Th,U and LREE by allanite and Y,U and HREE by zircon.During partial melting,Y,Pb,Th,U and REE are released into the melt,which causes a dramatic decline of these element contents in the retrograde minerals.Finally,titanite absorbs most of the Nb,U,LREE and HREE from the melt.Therefore,the different stages of metamorphism have different mineral assemblages,which host different trace elements.

Overview of multi-stage charging strategies for Li-ion batteries

To reduce the carbon footprint in the transportation sector and improve overall vehicle efficiency,a large number of electric vehicles are being manufactured.This is due to the fact that environmental concerns and the depletion of fossil fuels have become significant global problems.Lithium-ion batteries(LIBs)have been distinguished themselves from alternative energy storage technologies for electric vehicles(EVs) due to superior qualities like high energy and power density,extended cycle life,and low maintenance cost to a competitive price.However,there are still certain challenges to be solved,like EV fast charging,longer lifetime,and reduced weight.For fast charging,the multi-stage constant current(MSCC) charging technique is an emerging solution to improve charging efficiency,reduce temperature rise during charging,increase charging/discharging capacities,shorten charging time,and extend the cycle life.However,there are large variations in the implementation of the number of stages,stage transition criterion,and C-rate selection for each stage.This paper provides a review of these problems by compiling information from the literature.An overview of the impact of different design parameters(number of stages,stage transition,and C-rate) that the MSCC charging techniques have had on the LIB performance and cycle life is described in detail and analyzed.The impact of design parameters on lifetime,charging efficiency,charging and discharging capacity,charging speed,and rising temperature during charging is presented,and this review provides guidelines for designing advanced fast charging strategies and determining future research gaps.

Water diversion and agricultural production:Evidence from China

Water diversion can alleviate water shortages caused by the uneven distribution of water resources.China’s Southto-North Water Diversion Project(SNWD)is the largest water diversion project worldwide.Based on the prefecturelevel data of China’s Huang-Huai-Hai Plain from 2000 to 2020,this study employs an empirical strategy of Differencesin-Differences(DID)to analyze the impact of SNWD on agricultural production.The results show that SNWD has significantly increased agricultural production,measured by the agricultural value added.The estimated results of the benchmark model remain robust when the contemporaneous policy is addressed,an alternative outcome is used,subsamples are estimated,and alternative estimation techniques are employed.This study argues that the potential impact mechanism may be that SNWD significantly increases the acreage for cash crops but reduces that for grain crops.Heterogeneity analysis shows that in prefectures with high temperature or land potential,SNWD’s impact on agricultural value added is relatively low.In contrast,in areas with prolonged sunshine or high slopes,SNWD’s impact on agricultural value added is relatively large.Given the low added value of grain crops,the government should consider strengthening food security by subsidizing water supply to sustain grain production.

Comparative assessment of mechanical and chemical fluid diversion techniques during hydraulic fracturing in horizontal wells

The application of fluid diversion during hydraulic fracturing is an evolving technology and has become popular amongst E&P operators over the past few years.The primary objective of the fluid diversion is to improve hydraulic fracturing treatment by increasing stimulated reservoir volume and improving hydrocarbon recovery.This is possible by achieving any of the following objectives:creating uniform distribution of treatment slurry within the target zone;treating unstimulated and under-stimulated zones;or by increasing fracture density by creating a complex fracture network.The fluid diversion application is also helpful in decreasing the number of stages(by increasing stage length)for multi-stage plug-n-perf(PnP)fracturing treatment.It is also applied to prevent fracture-driven interactions between adjacent wells,which is currently a major issue,especially in shale.In addition,for successful refracturing treatment,the diverter application is essential for isolating the existing fractures and redirecting the treatment slurry to the desired unstimulated zones.The diversion methods can be broadly categorized into the mechanical and chemical diversion.Several established mechanical diversion techniques are frac plugs,expandable casing patches,expandable liners,swellable packers,straddle packer assembly,sand plugs,frac sleeves,perforation ball sealers,and limited entry technique.The different chemical diversion techniques are particulates,fibers,gels,surfactants,perforation pods,and composite diverting.This paper describes the current status of established mechanical and chemical diverter technologies and examines their comparative advantages and challenges.Various techniques are suitable for diverter application,but the technique is selected based on the desired objective and conditions of the wellbore and reservoir.The general guidelines for selecting diversion techniques and operational considerations are also provided in the paper.The diagnosis of diversion treatment plays an essential role in diversion technique selection and optimization of selection parameters for the subsequent treatments.Therefore,the application of conventional surface pressure monitoring techniques and advanced diagnostic tools to evaluate diversion effectiveness are briefly described.Presently no standard laboratory testing method is established for the performance evaluation of diverting agents.Therefore,researchers have implemented various laboratory methods,which are briefly summarized in the paper.Significant insight into the diversion technology and guidelines for its selection and successful implementation is provided to help engineers to increase the effectiveness of hydraulic fracturing treatments.The limitations of individual diversion techniques are clarified,which provide the future scope of research for improvement in various diversion technologies.

Resilience effects for household food expenditure and dietary diversity in rural western China

A more resilient livelihood is increasingly recognized as an efficient way to improve vulnerable households’food security and optimize their dietary decisions.This study quantifies rural household resilience in western China,identifies the three pillars(absorptive capacity,adaptive capacity,and transformative capacity)contribution to resilience,and then establishes the estimated Resilience Capacity Index(RCI)linked with food security and dietary diversity supported by the multiple indicator multiple cause(MIMIC)model.Results show that,despite geographical heterogeneity,the RCI consistently increased from 2015 to 2021.Households with a higher RCI inheriting better capacity to deal with risk and shocks are significantly and positively correlated with increasing food expenditure and diversifying food choices.It can be because resilient households will allocate more money to food expenditure instead of saving for livelihood uncertainty.Thus,policymakers can provide more incentives for rural households to adopt more dynamic and effective risk management strategies.This,in turn,could yield positive spillover effects by preventing human capital loss associated with dietary-related chronic diseases and mortality.

Multi-Stage Improvement of Marine Predators Algorithm and Its Application

The metaheuristic algorithms are widely used in solving the parameters of the optimization problem.The marine predators algorithm(MPA)is a novel population-based intelligent algorithm.Although MPA has shown a talented foraging strategy,it still needs a balance of exploration and exploitation.Therefore,a multi-stage improvement of marine predators algorithm(MSMPA)is proposed in this paper.The algorithm retains the advantage of multistage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators.Predators further away from the historical optimum are required to move,increasing the exploration capability of the algorithm.In the middle and late stages,the searchmechanism of particle swarmoptimization(PSO)is inserted,which enhances the exploitation capability of the algorithm.This means that the stochasticity is decreased,that is the optimal region where predators jumping out is effectively stifled.At the same time,self-adjusting weight is used to regulate the convergence speed of the algorithm,which can balance the exploration and exploitation capability of the algorithm.The algorithm is applied to different types of CEC2017 benchmark test functions and threemultidimensional nonlinear structure design optimization problems,compared with other recent algorithms.The results show that the convergence speed and accuracy of MSMPA are significantly better than that of the comparison algorithms.

Off-farm employment,agriculture production activities,and household dietary diversity in environmentally and economically vulnerable areas of Asia

Access to off-farm employment has been expected to be a critical approach to ending hunger and all forms of malnutrition,two important targets of achieving Zero Hunger.This study aims to investigate the role of off-farm employment in improving dietary diversity through substitution effect and complementary effect with agricultural production activities and income effect.This study adopts Poisson/Tobit/Probit/OLS regressions and the instrument variable method based on the primary survey data collected among 1,282 households at 12 sites in environmentally and economically vulnerable areas of China,Nepal,Cambodia,Thailand,and Myanmar in 2019.The results show that off-farm employment is positively associated with household dietary diversity and the consumption of flesh meat,fish and other aquatic animals,fruits,and milk and dairy products,which are rich in protein and micronutrients.The results of mechanism analysis show that off-farm employment contributes to household dietary diversity by improving crop diversity,especially for poor households,boosting the probability of livestock raising for households with the middle one-third disposal income,and increasing household income.The positive association between off-farm employment and household dietary diversity is much higher for households with the bottom one-third disposal income,low illiteracy,and from upper-middle income countries.These findings imply that off-farm employment does play a vital role in achieving multiple benefits of poverty alleviation,malnutrition reduction,and agrobiodiversity conservation in environmentally and economically vulnerable areas.However,it may enlarge the gaps in dietary diversity between households with low human capital and from low and lower-middle income countries and those with high human capital and from middle-high countries.

Community structure and species diversity dynamics of a subtropical evergreen broad-leaved forest in China:2005 to 2020

Here,we characterize the temporal and spatial dynamics of forest community structure and species diversity in a subtropical evergreen broad-leaved forest in China.We found that community structure in this forest changed over a 15-year period.Specifically,renewal and death of common species was large,with the renewal of individuals mainly concentrated within a few populations,especially those of Aidia canthioides and Cryptocarya concinna.The numbers of individual deaths for common species were concentrated in the small and mid-diameter level.The spatial distribution of community species diversity fluctuated in each monitoring period,showing a more dispersed diversity after the 15-year study period,and the coefficient of variation on quadrats increased.In 2010,the death and renewal of the community and the spatial variation of species diversity were different compared to other survey years.Extreme weather may have affected species regeneration and community stability in our subtropical monsoon evergreen broad-leaved forests.Our findings suggest that strengthening the monitoring and management of the forest community will help better understand the long-and short-term causes of dynamic fluctuations of community structure and species diversity,and reveal the factors that drive changes in community structure.

Biodiversity metrics on ecological networks: Demonstrated with animal gastrointestinal microbiomes

Biodiversity has become a terminology familiar to virtually every citizen in modern societies.It is said that ecology studies the economy of nature,and economy studies the ecology of humans;then measuring biodiversity should be similar with measuring national wealth.Indeed,there have been many parallels between ecology and economics,actually beyond analogies.For example,arguably the second most widely used biodiversity metric,Simpson(1949)’s diversity index,is a function of familiar Gini-index in economics.One of the biggest challenges has been the high“diversity”of diversity indexes due to their excessive“speciation”-there are so many indexes,similar to each country’s sovereign currency-leaving confused diversity practitioners in dilemma.In 1973,Hill introduced the concept of“numbers equivalent”,which is based on Renyi entropy and originated in economics,but possibly due to his abstruse interpretation of the concept,his message was not widely received by ecologists until nearly four decades later.What Hill suggested was similar to link the US dollar to gold at the rate of$35 per ounce under the Bretton Woods system.The Hill numbers now are considered most appropriate biodiversity metrics system,unifying Shannon,Simpson and other diversity indexes.Here,we approach to another paradigmatic shift-measuring biodiversity on ecological networks-demonstrated with animal gastrointestinal microbiomes representing four major invertebrate classes and all six vertebrate classes.The network diversity can reveal the diversity of species interactions,which is a necessary step for understanding the spatial and temporal structures and dynamics of biodiversity across environmental gradients.

Contemporary outcomes of patients undergoing robotic-assisted radical cystectomy:A comparative analysis between intracorporeal ileal conduit and neobladder urinary diversions

Objective We aimed to compare perioperative and oncologic outcomes for patients undergoing robotic-assisted radical cystectomy(RARC)with intracorporeal ileal conduit(IC)and neobladder(NB)urinary diversion.Methods Patients undergoing RARC with intracorporeal urinary diversion between January 2017 and January 2022 at the Icahn School of Medicine at Mount Sinai,New York,NY,USA were indexed.Baseline demographics,clinical characteristics,perioperative,and oncologic outcomes were analyzed.Survival was estimated with Kaplan-Meier plots.Results Of 261 patients(206[78.9%]male),190(72.8%)received IC while 71(27.2%)received NB diversion.Median age was greater in the IC group(71[interquartile range,IQR 65-78]years vs.64[IQR 59-67]years,p<0.001)and BMI was 26.6(IQR 23.2-30.4)kg/m^(2).IC group was more likely to have prior abdominal or pelvic radiation(15.8%vs.2.8%,p=0.014).American Association of Anesthesiologists scores were comparable between groups.The IC group had a higher proportion of patients with pathological tumor stage 2(pT2)tumors(34[17.9%]vs.10[14.1%],p=0.008)and pathological node stages pN2-N3(28[14.7%]vs.3[4.2%],p<0.001).The IC group had less median operative time(272[IQR 246-306]min vs.341[IQR 303-378]min,p<0.001)and estimated blood loss(250[150-500]mL vs.325[200-575]mL,p=0.002).Thirty-and 90-day complication rates were 44.4%and 50.2%,respectively,and comparable between groups.Clavien-Dindo grades 3-5 complications occurred in 27(10.3%)and 34(13.0%)patients within 30 and 90 days,respectively,with comparable rates between groups.Median follow-up was 324(IQR 167-552)days,and comparable between groups.Kaplan-Meier estimate for overall survival at 24 months was 89%for the IC cohort and 93%for the NB cohort(hazard ratio 1.23,95%confidence interval 1.05-2.42,p=0.02).Kaplan-Meier estimate for recurrence-free survival at 24 months was 74%for IC and 87%for NB(hazard ratio 1.81,95%confidence interval 0.82-4.04,p=0.10).Conclusion Patients undergoing intracorporeal IC urinary diversion had higher postoperative cancer stage,increased nodal involvement,similar complications outcomes,decreased overall survival,and similar recurrence-free survival compared to patients undergoing RARC with intracorporeal NB urinary diversion.

Historical biogeography and evolutionary diversification of Lilium(Liliaceae): New insights from plastome phylogenomics

Here, we infer the historical biogeography and evolutionary diversification of the genus Lilium. For this purpose, we used the complete plastomes of 64 currently accepted species in the genus Lilium(14plastomes were newly sequenced) to recover the phylogenetic backbone of the genus and a timecalibrated phylogenetic framework to estimate biogeographical history scenarios and evolutionary diversification rates of Lilium. Our results suggest that ancient climatic changes and geological tectonic activities jointly shaped the distribution range and drove evolutionary radiation of Lilium, including the Middle Miocene Climate Optimum(MMCO), the late Miocene global cooling, as well as the successive uplift of the Qinghai-Tibet Plateau(QTP) and the strengthening of the monsoon climate in East Asia during the late Miocene and the Pliocene. This case study suggests that the unique geological and climatic events in the Neogene of East Asia, in particular the uplift of QTP and the enhancement of monsoonal climate, may have played an essential role in formation of uneven distribution of plant diversity in the Northern Hemisphere.

Effectiveness of groundwater extraction in Beijing since the ingauration of the first phase of the South-to-North Water Diversion Project, China

This study assess the effectiveness of groundwater pressure extraction in Beijing since the opening of the first phase of the South-to-North Water Diversion Project,using survey and evaluation methods.Firstly,an analysis of water consumption structure and the usage of diverted river water in Beijing in recent years was conducted.Secondly,the volume of groundwater pressure extraction in Beijing after the 33 project's inauguration was examined,revealing a decrease from 1.96 billion m^(3) in 2014 to 1.35 billion m^(3) in 2020.The proportion of water supply reduced from 52.3%in 2014 to 33.3%in 2020,leading to an optimized water supply structure.By the end of 2020,groundwater pressure extraction in Beijing is estimated at 446 million m3,with a substantial reduction in over-exploitation of groundwater.Groundwater resources have been effectively replenished,and the strategic reserve capacity has been enhanced.Furthermore,this study evaluates the change in groundwater levels as an indicator of the effectiveness of pressure extraction.The declining trend of groundwater levels in Beijing has been effectively mitigated,and there has been a consistent rebound in groundwater levels over the past five years.

Biodiversity responses to insular fragmentation in Amazonia: Two decades of research in the Balbina Hydroelectric Reservoir

As hydropower development expands across lowland tropical forests,flooding and concomitant insular fragmentation have become important threats to biodiversity.Newly created insular landscapes serve as natural laboratories to investigate biodiversity responses to fragmentation.One of these most iconic landscapes is the Balbina Hydroelectric Reservoir in Brazilian Amazonia,occupying>400000 ha and comprising>3500 forest islands.Here,we synthesise the current knowledge on responses of a wide range of biological groups to insular fragmentation at Balbina.Sampling has largely concentrated on a set of 22 islands and three mainland sites.In total,39 studies were conducted over nearly two decades,covering 17 vertebrate,invertebrate,and plant taxa.Although species responses varied according to taxonomic group,island area was consistently included and played a pivotal role in 66.7%of all studies examining patterns of species diversity.Species persistence was further affected by species traits,mostly related to species capacity to use/traverse the aquatic matrix or tolerate habitat degradation,as noted for species of vertebrates and orchid bees.Further research is needed to improve our understanding of such effects on wider ecosystem functioning.Environmental Impact Assessments must account for changes in both the remaining habitat amount and configuration,and subsequent long-term species losses.

Strong evidence for latitudinal diversity gradient in mosses across the world

Species richness generally decreases with increasing latitude,a biodiversity gradient that has long been considered as one of the few laws in ecology.This latitudinal diversity gradient has been observed in many major groups of organisms.In plants,the latitudinal diversity gradient has been observed in vascular plants,angiosperms,ferns,and liverworts.However,a conspicuous latitudinal diversity gradient in mosses at a global or continental scale has not been observed until now.Here,we analyze a comprehensive data set including moss species in each band of 20° in latitude worldwide.Our results show that moss species richness decreases strongly with increasing latitude,regardless of whether the globe is considered as a whole or different longitudinal segments(e.g.,Old World versus New World) are considered separately.This result holds when variation in area size among latitudinal bands is taken into account.Pearson's correlation coefficient between latitude and species richness is-0.99 for both the Northern and Southern Hemispheres.Because bryophytes are an extant lineage of early land plants and because mosses not only include most of extant species of bryophytes but also are important constituents of most terrestrial ecosystems,understanding geographic patterns of mosses is particularly important The finding of our study fills a critical knowledge gap.