Modelling count data based on weakly dependent spatial covariates using a copula approach: application to rat sightings

Not all environmental processes are observed in a way that allows a straight forward easy modelling. Nevertheless, insights can also be gained by exploring weakly dependent covariates paying attention to details of the distribution. Using the concept of copulas, it is possible to explore the dependence of a multivariate distribution without the distortion of the marginal distribution functions acting on typical correlation measures. Furthermore, copulas turn the attention to the dependence across the entire range of the multivariate distribution and do not only summarise it in a single correlation measure. In our application, we study counts of rat sightings in the city of Madrid. The brown rat lives with mankind and adversely affects public health by transmission of diseases, bites and allergies. Better understanding behavioural and spatial correlation aspects of this species can contribute to its effective management and control. We explore weakly to moderately correlated covariates based on distances to broken sewers, feeding grounds and markets as well as population density. The use of copulas is motivated by the different dependence structures of the four covariates and the asymmetries therein. In order to deal with the discrete zero-inflated counts, we present a new approach that assigns conditional random ranks to discrete data. This way, we mimic an underlying continuous variable easing the vine copula estimation, but do not destroy the dependence as in a uniform randomisation. We show that a 5-dimensional vine copula model is able to capture the dependence in our application.     

Functional ANOVA starting from discrete data: an application to air quality data

A nonparametric functional approach is proposed to compare the mean functions of $k$ k samples of curves. In practice, curves data are usually collected in a discrete form and hence they must be pre-processed to use purely functional techniques. However, in the context of $k$ k -sample tests, the pre-processing step can have effects in terms of power reduction. Hall and Van Keilegom (Stat Sin 17:1511–1531, 2007) proposed a methodology to minimizing these effects in the context of tests for the equality of two distribution functions. Their procedure is here extended to the case of $k$ k -sample hypothesis tests. The asymptotic validity of the procedure is established and its finite sample performance is analyzed through Monte Carlo experiments. As an illustration, the method is applied to air quality data collected from several monitoring stations placed at different geographical locations at the center of Spain.     

Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to show the practical benefits of the unequal allocation in estimating simultaneously the means of more skewed variables through real data. In particular, the allocation rule suggested in the literature for a single skewed distribution may be easily applied when more than one skewed variable are of interest and an auxiliary variable correlated with them is available. This method can lead to substantial gains in precision for all the study variables with respect to the simple random sampling, and to the balanced ranked set sampling too.     

Directing technical change from fossil-fuel to renewable energy innovation: An application using firm-level patent data

In this paper we provide an analysis of directed technical change in the sector of electricity generation. We rely on patent data in fossil-fuel (FF) and renewable energy (REN) technologies for 5471 European firms over the 1978–2006 period. The novelty of our approach is in the focus on firm׳s heterogeneity in driving technological change. We make a distinction between small specialized firms, which innovate in only one type of technology, and large mixed firms, which innovate in both technologies, to analyse how REN patents can replace FF ones at the sector level both through a shift in innovation activities within existing firms and through firms׳ entry and exit. We use zero-inflated count data estimation techniques to identify the factors that affect specialized versus mixed firms׳ patenting behaviour both at the intensive (i.e., levels of innovation) and extensive (i.e., technological entry) margins. We further investigate the implications of our firm-level estimations for reducing the gap between REN and FF innovation at the aggregate level. We establish two key findings: (1) a decrease in the FF-REN technology gap mainly comes about through technological entry of specialized REN firms following an increase in REN market size; (2) increases in FF prices, FF market size, and FF knowledge stocks all increase the technology gap by increasing mixed firms FF innovation rates. An important implication of our results is that policies aimed at increasing REN innovation should focus on helping small firms to start and sustain innovation in the long-run.     

Calculation of the minimum ecological water requirement of an urban river system and its deployment: A case study in Beijing central region

The minimum ecological water requirements of an urban river system and water deployment are key elements in integrated water resources planning and urban ecological construction. Based on a review of ecological water requirement calculation methods and considering the different ecological functions of an urban river system, the ecological function method was used in this paper to calculate the components of the ecological water requirements of an urban river. An envelope curve-based method was proposed for assessing the minimum ecological water requirements of an urban river system. Water resources deployment strategies designed to meet the minimum ecological water requirements were described. Then, the minimum ecological water requirements of the urban river system in Beijing central region, selected as a case study, were investigated. The key parameters for assessing the minimum ecological water requirement in the Beijing urban river system were determined. Based on the ecological objectives and the current status of the different urban river systems within the Beijing central region, the minimum ecological water requirements were calculated. Different types of water sources, including rainwater, upstream water, and reclaimed water, were deployed to meet the ecological water requirements for the urban river system in the Beijing central region.     

Environmental control and spatial structure in ecological communities: an example using oribatid mites (Acari,Oribatei)

We have recently proposed to use partial canonical ordinations to partition the variation of species abundance data into four additive components: environmental at a local scale, the spatial component of the environmental influence, pure spatial, and an undetermined fraction. By means of an example, we show how to use the information contained in these fractions to provide better insight into the data. In particular, the interpretation is assisted by separately mapping the various canonical axes and relating them to possible generating processes. We derive a general framework for the causal interpretation of the various fractions of this partition, which includes the environmental and the biotic control models, as well as historical dynamics.Daniel Borcard is research associate in animal ecology at Universite de Neuchâtel, Switzerland. He is interested in soil ecology, and presently working on fundamental and applied projects dealing with peat bog ecology and protection, community succession dynamics, as well as effects of agriculture on mite and insect communities. In order to develop the statistical tools necessary for these projects, he also works in collaboration with Pierre Legendre on modeling the spatial structure of ecological communities. $Pierre Legendre is professor of quantitative biology at Universite de Montreal. He is a former Killam Research Fellow (1989–91), and a member of the Royal Society of Canada since 1992. He is the author of some 100 refereed articles, over 250 papers presented at scientific meetings and research seminars, dealing with numerical ecology, community ecology, environmental assessment and spatial analysis, and textbooks (in French and English) on numerical ecology. During the past 5 years, he served as the Secretary-Treasurer of the International Federation of Classification Societies. *We thank Dr V.M. Behan-Pelletier, of Agriculture Canada, for her help in the identification of the Oribatid mites, and Mrs Lucie Fortin and Dr P. Neumann, Universite de Montreal, for their identifications of the Sphagnum species. This research was carried out during tenure of a Postdoctoral Fellowship of the Swiss National Foundation for Scientific Research by D. Borcard, and of a Killam Research Fellowship of the Canada Council by P. Legendre. It was also supported by NSERC grant No. A7738 to P. Legendre. This is contribution No. 392 of the Groupe d'Écologie des Eaux douccs, Universite de Montreal. The authors wish to dedicate this paper with gratitude to Mr Alain Vaudor, computer analyst in Pierre Legendre's laboratory, who has largely contributed to the planning of this research. Mr Vaudor passed away on October 31, 1991, at age 46. The package for multivariate and spatial data analysis that he has produced during his computer scientist career is available to researchers from P. Legendre.     

Markov regression model for analyzing big data to predict trajectories of repeated categorical outcomes: an application to $$hbox {PM}_{2.5}$$ PM 2.5 air pollution data

Environmental and Ecological Statistics - Fine particulate matter ( $$text{ PM}_{2.5}$$ ), tiny particles in the air, is air contamination that negatively impacts the environment and human health...     

A warning from an ancient oasis: intensive human activities are leading to potential ecological and social catastrophe

The Shiyang River Basin is an inland river basin in the Hexi Corridor, Gansu Province, northwest China. Shiyang is the largest basin in terms of human population density and has the highest exploitation of water resources in the northwest. Serious water shortages constrain social and economic development, and the area has some of the worst ecological and environmental deterioration in China. From historical data and recent observations, we have analysed changes in water systems in the Minqin oasis, at the end of the river basin, and assessed impacts and consequences of a changing climate and intensive human activity. Historically, climate change has been the main cause of changes in the oasis. In the last 50 years, however, a major influence has been intense human activity in the basin. With increasing population (159% in 50 years), the amount of cultivated land has been greatly expanded (by 51%). Many reservoirs have been built by damming rivers and large-scale irrigation has been introduced in the middle reaches of the basin. The introduction of leakage-free canals and more extensive exploitation of underground water have further expanded the irrigated area. Water use by humans has exceeded the carrying capacity of the water resources of the basin, which has led to a dramatic shift in water allocation between the upper and lower reaches and a rapid drop in the water table in the Minqin oasis (by as much as 14 m). The oasis is shrinking, natural vegetation that relies on underground water is disappearing, and desertification is accelerating. An ancient oasis that can be traced back 2000 years is disappearing and this must be a warning sign for future generations.     

Bivariate geostatistical modelling: a review and an application to spatial variation in radon concentrations

We present a comprehensive review of multivariate geostatistical models, focusing on the bivariate case. We compare in detail three approaches, the linear model of coregionalisation, the common component model and the kernel convolution approach, and discuss similarities between them. We demonstrate the merits of the common component class of models as a flexible means for modelling bivariate geostatistical data of the type that frequently arises in environmental applications. In particular, we show how kernel convolution can be used to approximate the common component model, and demonstrate the method using a data-set of calcium and magnesium concentrations in soil samples. We then apply the model to a study of domestic radon concentrations in the city of Winnipeg, Canada, in which exposure was measured at two sites (bedroom and basement) in each residential location. Our analysis demonstrates that in this study the correlation between the two sites within each house dominates the short-range spatial correlation typical of the distribution of radon.     

Modelling seasonal dynamics of biomasses and nitrogen contents in a seagrass meadow (Zostera noltii Hornem.): application to the Thau lagoon (French Mediterranean coast)

Anumerical deterministic model for a seagrass ecosystem (Zostera noltii meadows) has been developed for the Thau lagoon. It involves both above- and belowground seagrass biomasses, nitrogen quotas and epiphytes. Driving variables are light intensity, wind speed, rain data and water temperature. This seagrass model has been coupled to another biological model in order to simulate the relative contributions of each primary producer to: (i) the total ecosystem production, (ii) the impact on inorganic nitrogen and (iii) the fluxes towards the detritus compartment. As a first step in the modelling of seagrass beds in the Thau lagoon, the model has a vertical structure based on four boxes (a water box on top of three sediment boxes) and the horizontal variability is neglected until now. This simple box structure is nevertheless representative for the shallow depth Z. noltii meadows, spread over large areas at the lagoon periphery.After calibration, simulation results have been compared with in situ measurements and have shown that the model is able to reproduce the general pattern of biomasses and nitrogen contents seasonal dynamics. Moreover, results show that, in such shallow ecosystems, seagrasses remain the most productive compartment when compared with epiphytes or phytoplankton productions, and that seagrasses, probably due to their ability in taking nutrients in the sediment, have a lower impact on nutrient concentration in the water column than the phytoplankton. Furthermore, in spite of active mechanisms of internal nitrogen redistribution and reclamation, the occurrence of a nitrogen limitation of the seagrass growth during summer, already mentioned in the literature, have also been pointed out by the model. Finally, simulations seems to point out that epiphytes and phytoplankton could compete for nitrogen in the water column, while a competition for light resources seems to be more likely between epiphytes and seagrasses.     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.     

Lip-reading in remote subjects: an attempt to quantify and separate ingestion, breathing and vocalisation in free-living animals using penguins as a model

A new mandibular sensor is presented here based on the use of a Hall sensor, attached to one mandible, opposite a magnet, attached to the other mandible. Changes in sensor voltage, proportional to magnetic field strength, and thus inter-mandibular angle, are recorded in a logger. This system was tested on seven captive Adélie penguins (Pygoscelis adeliae) and three gentoo penguins (Pygoscelis papua) during: (1) feeding trials on land, where birds were given known quantities and types of food; and (2) trials in water where birds were allowed to swim and dive freely. In addition, six free-living Magellanic penguins (Spheniscus magellanicus) were equipped with the system for single foraging trips. Angular signatures were looked for in instances when both captive and free-living birds might open their beaks, and it was discovered that five major behaviours could be identified: ingestion, breathing, calling, head shaking and preening. Captive feeding trials showed that prey mass could be determined with reasonable accuracy (r²=0.92), and there was some indication that prey type could be resolved if recording frequency were high enough. Vocalisations in Adélie penguins (arc calls) took <0.7 s for mean maximum beak angles of 4.2° (SD 1.3), and were distinguished by their relatively gradual change in beak angle and by their high degree of symmetry. Beak shakings were distinguishable by their short duration (multiple peaks of <0.5 s) and minimal maximum angle (<0.5°). Preening behaviour was apparent due to multiple decreasing peaks (angles <8°). Breathing could be subdivided into that during porpoising, where a characteristic double peak in beak angle was recorded, and that during normal surface rests between dives. During porpoising, only the primary peak (mean maximum beak angle 25.1°, SD 4.7) occurred when the bird was out of the water (mean maximum for second peak 5.9°, SD 4.1). During normal surface rests in free-living birds, breaths could be distinguished as a series of beak openings and closures, showing variation in amplitude and frequency according to an apparent recovery from the previous dive and preparation for the subsequent dive to come. The mandibular measuring system presented shows considerable promise for elucidating many hitherto intractable aspects of the behaviour of free-living animals.     

Feasibility of using an automated colorimetric procedure for the determination of seawater nitrate in the 0 to 100 nM range: Examples from field and culture

An automatic colorimetric procedure for measuring nanomolar quantities of nitrate and nitrite in seawater has been improved in sensitivity. Application of this method toin situ investigations in the North Atlantic Ocean in January 1989 and algal culture (Skeletonema costatum) experiments in the laboratory demonstrated that one can record concentrations in the 0 to 100 nM range using classical Technicon AutoAnalyzer equipment. In this working range highest precision obtained was ±2.87 and ±1.24 nM for nitrate and nitrite, respectively.     

Preparation of molten salt-type (meth)acrylic monomers and their application as catalysts in the synthesis of benzyl phenyl sulfide: an alternative to the usual toxic sulfides synthesis

The synthesis of new ionic liquids and their potential catalysis activity in the preparation of benzylphenylsulfide are described.