Confidence intervals for the mean of the delta-lognormal distribution

Data that are skewed and contain a relatively high proportion of zeros can often be modelled using a delta-lognormal distribution. We consider three methods of calculating a 95% confidence interval for the mean of this distribution, and use simulation to compare the methods, across a range of realistic scenarios. The best method, in terms of coverage, is that based on the profile-likelihood. This gives error rates that are within 1% (lower limit) or 3% (upper limit) of the nominal level, unless the sample size is small and the level of skewness is moderate to high. Our results will also apply to the delta-lognormal linear model, when we wish to calculate a confidence interval for the expected value of the response variable, given the value of one or more explanatory variables. We illustrate the three methods using data on red cod densities, taken from a fisheries trawl survey in New Zealand.

Analysis and prediction of $$\mathrm{PM}_{10}$$ concentration levels in Tunisia using statistical learning approaches

Over the past years, the health impact of airborne particulate matter \(\mathrm{PM}_{10}\) has become a very topical subject. Thereby, a lot of research effort in the environmental sciences goes towards the modeling and the prediction of ambient \(\mathrm{PM}_{10}\) concentrations. In this paper, we are interested in the statistical classification of the daily mean \(\mathrm{PM}_{10}\) concentration in Tunisia according to the authority regulation. We consider two monitoring stations: a big industrial station and a traffic station. The main goal of this work is to determine the pertinent predictors of \(\mathrm{PM}_{10}\) concentration within a nonlinear multiclass framework. To do this, we used two popular statistical learning methods; the support vector machines (SVM) and the random forests (RF). The statistical results obtained on the real datasets, show that RF outperform SVM for the purpose of variable selection even with a reduced number of observations compared to the number of explicative variables. It was also demonstrated that the \(\mathrm{PM}_{10}\) concentration measured yesterday is the most relevant predictor of its present-day value. Moreover, we found that the more delayed values of \(\mathrm{PM}_{10}\) concentration may be crucial to get an accurate prediction.     

Rarefaction and nonrandom spatial dispersion patterns

Rarefaction estimates how many species are expected in a random sample of individuals from a larger collection and allows meaningful comparisons among collections of different sizes. It assumes random spatial dispersion. However, two common dispersion patterns, within-species clumping and segregation among species, can cause rarefaction to overestimate the species richness of a smaller continuous area. We use field studies and computer simulations to determine (1) how robust rarefaction is to nonrandom spatial dispersion and (2) whether simple measures of spatial autocorrelation can predict the bias in rarefaction estimates. Rarefaction does not estimate species richness accurately for many communities, especially at small sample sizes. Measures of spatial autocorrelation of the more abundant species do not reliably predict amount of bias. Survey sites should be standardized to equal-sized areas before sampling. When sites are of equal area but differ in number of individuals sampled, rarefaction can standardize collections. When communities are sampled from different-sized areas, the mean and confidence intervals of species accumulation curves allow more meaningful comparisons among sites. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Partitioning of \alpha and \beta diversity using hierarchical Bayesian modeling of species distribution and abundance

Diversity partitioning is becoming widely used to decompose the total number of species recorded in an area or region \((\gamma )\) into the average number of species within samples \((\alpha )\) and the average difference in species composition \((\beta )\) among samples. Single-value metrics of \(\alpha \) and \(\beta \) diversity are popular because they may be applied at multiple scales and because of their ease in computation and interpretation. Studies thus far, however, have emphasized observed diversity components or comparisons to randomized, null distributions. In addition, prediction of \(\alpha \) and \(\beta \) components using environmental or spatial variables has been limited to more extensive data sets because multiple samples are required to estimate single \(\alpha \) and \(\beta \) components. Lastly, observed diversity components do not incorporate variation in detection probabilities among species or samples. In this study, we used hierarchical Bayesian models of species abundances to provide predictions of \(\alpha \) and \(\beta \) components in species richness and composition using environmental and spatial variables. We illustrate our approach using butterfly data collected from 26 grassland remnants to predict spatially nested patterns of \(\alpha \) and \(\beta \) based on the predicted counts of butterflies. Diversity partitioning using a Bayesian hierarchical model incorporated variation in detection probabilities by butterfly species and habitat patches, and provided prediction intervals for \(\alpha \) and \(\beta \) components using environmental and spatial variables.     

Investigating the complex relationship between in situ Southern Ocean pCO_{2} and its ocean physics and biogeochemical drivers using a nonparametric regression approach

The objective in this paper is to investigate the use of a non-parametric approach to model the relationship between oceanic carbon dioxide \((pCO_2)\) and a range of ocean physics and biogeochemical in situ variables in the Southern Ocean, which influence its in situ variability. The need for this stems from the need to obtain reliable estimates of carbon dioxide concentrations in the Southern Ocean which plays an important role in the global carbon flux cycle. The main challenge involved in this objective is the spatial limitation and seasonal bias of the in situ data. Moreover, studies have also reported that the relationship between \(pCO_2\) and its drivers is complex. As such, in this paper, we use the non-parametric kernel regression approach since it is able to accurately capture the complex relationships between the response and predictor variables. In this analysis we use the in situ data obtained from the SANAE49 return leg journey between Antarctic to Cape Town. To the best of our knowledge, this is the first time this data set has been subjected to such analysis. The model variants were developed on a training data subset, and the ‘goodness’ of the models were assessed on an “unseen” test data subset. Results indicate that the nonparametric approach consistently captures the relationship more accurately in terms of mean square error, root mean square error and mean absolute error, over a standard parametric approach (multiple linear regression). These results provide a platform for using the developed nonparametric regression model based on in situ measurements to predict \(pCO_2\) for a larger spatial region in the Southern Ocean based on satellite biogeochemical measurements of predictor variables, given that satellites do not measure \(pCO_2\) .     

Modeling binomial amphibian roadkill data in distance sampling while accounting for zero-inflation,serial correlation and varying cluster sizes simultaneously

Roadkill is of ecological importance so that there is increasing academic research to understand the causes and patterns of roadkills and their impact on ecosystems. This work is motivated by the study on roadkills of endangered Bufo calamita (B. calamita) (The natterjack toad) out of amphibian roadkills. The status of B. calamita is regarded as unfavorable due to large population declines. In the mentioned study, B. calamita and total amphibian roadkills were recorded via distance sampling on a National Road of Southern Portugal between March 1995 and March 1997. The traditional binomial modeling of these data are challenged by three issues. First, the zeros in B. calamita counts far exceeded its nominal level. Second, there is likely serial correlation among observations along the road. Finally, there is varying number of total amphibian roadkills at each sampling location; therefore, there is likely randomness in the number of total amphibian roadkills. All these features may contribute to overdispersion in the binomial observations. These three issues are routinely addressed one at a time separately, the first through zero-inflated binomial models, the second, for example, by means of random effects models for serially correlated binomial data and the third by models for binomial data with random cluster sizes. Therefore the data cannot be adequately modeled by any of these separate models. In this paper, we propose a new model to tackle these three issues simultaneously in the binomial analysis of B. calamita roadkills out of amphibian roadkills. Our approach is generally applicable to other binomial data with these three features.     

Description and sensitivity analysis for the LESV model: Water quality variables and the balance of organisms in a fjordic region of restricted exchange

In this paper we describe a new ecological model for Regions of Restricted Exchange (RRE), such as fjords, estuaries, rias and lagoons. The model is intended to simulate the impact of external nutrient input on microplankton (phytoplankton plus pelagic microheterotrophs) in RREs. We have implemented the model with the practical purpose of finding a safe limit to the capacities of RRE to assimilate fish-farm waste. Sea-cage farming of fish is increasing in fjords in northern and southern hemispheres, and its external nutrient input can lead to environmental problems such as eutrophication and deoxygenation. The model includes a physical system of three layers with exchanges driven by tidal movement, freshwater input, wind stirring. The biological part includes two microplankton compartments, each parameterizing a microbial loop and each containing chlorophyll. The first compartment represents diatoms and associated heterotrophs, and the second compartment represents flagellates and associated heterotrophs. As well as the balance of these organisms, the model simulates concentrations of nutrient N, P, and Si, dissolved oxygen, and water transparency. Chlorophyll and nutrient change are linked by yields (q  ). Losses of microplankton to grazing by mesozooplankton or benthos are simulated by a temperature-dependent grazing pressure acting on a mean loss (_L0)$(L_0)$. The model also includes the ability to simulate point source inputs of nutrients or organic matter and a generic tracer with first order decay. Sea-cage fish-farms exemplify such point sources. In order to explore model behaviour, we included inputs from a 1500 tonnes salmon farm multiplied by a factor (γ)$(\gamma )$. We carried out sensitivity analysis to identify the most influential model parameters and forcing variables in the case of the shallow Scottish fjord, Loch Creran, in 1975 before the introduction of salmon farming. We tested the model fit to this pristine state (γ=0)$(\gamma =0)$, using Major Axis Regression of simulated variables on observed variables. The model successfully follows the seasonal cycles of chlorophyll (summer over both microplanktons) and the limiting nutrients (P, N). The sensitivity analysis identified three sets of key parameters: (γ)$(\gamma )$ and other fish-farm coefficients, which control farm waste effects on an RRE; (_L0)$(L_0)$ parameters for each microplankton, which link these to the rest of the ecosystem and which have implications for future inclusion of shellfish farming in the model and, chlorophyll yields from nutrients (q), which are crucial for the predication of eutrophication and the ecological understanding of the model.     

Lévy walk patterns in the foraging movements of spider monkeys (<Emphasis Type="Italic">Ateles geoffroyi</Emphasis>)

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other, nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns closely resemble what physicists know as Lévy walks. First, the length of a trajectorys constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Lévy walk model to be an optimal strategy to search for scarce resources distributed at random. Second, the frequency distribution of the duration of stops or waiting times also approximates to a power-law function. Finally, the mean square displacement during the monkeys first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Lévy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own and when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.Communicated by D. Watts     

Flexible hierarchical mark-recapture modeling for open populations using WinBUGS

Hierarchical mark-recapture models offer three advantages over classical mark-recapture models: (i) they allow expression of complicated models in terms of simple components; (ii) they provide a convenient way of modeling missing data and latent variables in a way that allows expression of relationships involving latent variables in the model; (iii) they provide a convenient way of introducing parsimony into models involving many nuisance parameters. Expressing models using the complete data likelihood we show how many of the standard mark-recapture models for open populations can be readily fitted using the software WinBUGS. We include examples that illustrate fitting the Cormack–Jolly–Seber model, multi-state and multi-event models, models including auxiliary data, and models including density dependence.

Modelling skewed data with many zeros: A simple approach combining ordinary and logistic regression

We discuss a method for analyzing data that are positively skewed and contain a substantial proportion of zeros. Such data commonly arise in ecological applications, when the focus is on the abundance of a species. The form of the distribution is then due to the patchy nature of the environment and/or the inherent heterogeneity of the species. The method can be used whenever we wish to model the data as a response variable in terms of one or more explanatory variables. The analysis consists of three stages. The first involves creating two sets of data from the original: one shows whether or not the species is present; the other indicates the logarithm of the abundance when it is present. These are referred to as the presence data and the log-abundance data, respectively. The second stage involves modelling the presence data using logistic regression, and separately modelling the log-abundance data using ordinary regression. Finally, the third stage involves combining the two models in order to estimate the expected abundance for a specific set of values of the explanatory variables. A common approach to analyzing this sort of data is to use a ln (y+c) transformation, where c is some constant (usually one). The method we use here avoids the need for an arbitrary choice of the value of c, and allows the modelling to be carried out in a natural and straightforward manner, using well-known regression techniques. The approach we put forward is not original, having been used in both conservation biology and fisheries. Our objectives in this paper are to (a) promote the application of this approach in a wide range of settings and (b) suggest that parametric bootstrapping be used to provide confidence limits for the estimate of expected abundance.     

Spatial smoothing techniques for the assessment of habitat suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of observations is often violated in practice since the points at which the observations are collected are spatially aligned. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.

Dance dialects and foraging range in three Asian honey bee species

Summary We measured the distance dialects in the dance languages of three honey bee species in Thailand (Apis florea, A. cerana, and A. dorsata), and used these dialects to examine the hypothesis that a colony's dialect is adaptively tuned to enhance efficiency of communication over the distances that its foragers typically fly. in contrast to previous interspecific comparisons in Sri Lanka (Lindauer 1956; Punchihewa et al. 1985), we found no striking dialect differences among the Asian bees in Thailand. The adaptive tuning hypothesis predicts that the foraging ranges of the three species should also be similar, but comparisons of colonial foraging range using the forage mapping technique (Visscher and Seeley 1982) actually revealed marked differences. This raises the possibility that the link between ecology and distance code is more subtle than previously supposed, if a link exists at all. Offprint requests to: F.C. Dyer     

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.     

Prospective evaluation of designs for analysis of variance without knowledge of effect sizes

Estimation of design power requires knowledge of treatment effect size and error variance, which are often unavailable for ecological studies. In the absence of prior information on these parameters, investigators can compare an alternative to a reference design for the same treatment(s) in terms of its precision at equal sensitivity. This measure of relative performance calculates the fractional error variance allowed of the alternative for it to just match the power of the reference. Although first suggested as a design tool in the 1950s, it has received little analysis and no uptake by environmental scientists or ecologists. We calibrate relative performance against the better known criterion of relative efficiency, in order to reveal its unique advantage in controlling sensitivity when considering the precision of estimates. The two measures differ strongly for designs with low replication. For any given design, relative performance at least doubles with each doubling of effective sample size. We show that relative performance is robustly approximated by the ratio of reference to alternative $\alpha $ quantiles of the $F$ distribution, multiplied by the ratio of alternative to reference effective sample sizes. The proxy is easy to calculate, and consistent with exact measures. Approximate or exact measurement of relative performance serves a useful purpose in enumerating trade-offs between error variance and error degrees of freedom when considering whether to block random variation or to sample from a more or less restricted domain.     

A role forAmanita muscaria L. in the circulation of cadmium and vanadium in a non-polluted woodland

The sporophore of the fungusAmanita muscaria L. contains greatiy elevated levels of cadmium (29.9 g g^–1 dwt) and vanadium (344.9 g g^–1 dwt) in comparison with the soil in a birch woodland (total (HNO₃-extractabie Cd 0.4 g g^–1 dwt, V 11.7 g g^–1 dwt). The significance of this remarkable concentration of normally rare and dispersed elements in terms of their circulation in the woodland has been investigated. Both elements are released from sporophore tissue in a form which can be taken up by a test plant (lettuce), cultivated in the woodland soil amended with different quantities of sporophore tissue, Cadmium levels in all plant tissues were elevated in comparison to the non-amended controls; only root vanadium levels responded to the amendment of the soil. The results are discussed in terms of their significance for the natural cycling of both elements. It is calculated that an abundant population of sporophores could circulate 1.4% of the total cadmium and 0.65% of the total vanadium pool found in the litter layer and 0–5 cm soil horizon in the sampled woodland over a period of 14 days (mean life span of a sporophore).     

DNA fingerprints of orange roughy,Hoplostethus atlanticus: a population comparison

Genetic variability among Hoplostethus atlanticus collected from two spawning grounds east and west of New Zealand was examined using DNA fingerprints as revealed by hybridization with three clonal probes: 33.15, M13 and 3HVR. The 33.15 and 3HVR fingerprints revealed a complex pattern of restriction fragments, apparently refecting a multi-locus system of highly variable minisatellite alleles similar to the pattern of alleles reported in other vertebrates. The M13 fingerprints revealed a distinct pattern of restriction fragments of high molecular weight, reflecting a single-locus system that overlapped with the family of minisatellite alleles observed in 33.15 fingerprints. In a sample of 12 orange roughy collected on a single regional spawning site, the average percent similarity of 33.15 fingerprints was 21.15% (SD=17.75), the average percent similarity of 3HVR fingerprints was 14.32% (SD=14.45) and the inferred average allelic frequency of the M13 single-locus system was 0.071. A comparison of 33.15 and M13 fingerprints from two distant spawning sites ground New Zealand revealed no obvious regional differences. The variability of orange roughy fingerprints was so great, however, that regional comparisons could not be considered conclusive indicators of genetic identity. Our results provide a preliminary assessment of the power and pitfalls of using DNA-level markers for the population analysis of marine fish.     

Statistical properties of concentration fluctuations in two merging plumes

The statistics of the fluctuating concentration field within a plume is important in the analysis of atmospheric dispersion of toxic, inflammable and odorous gases. Previous work has tended to focus on concentration fluctuations in single plumes released in the surface layer or at ground level and there is a general lack of information about the mixing of two adjacent plumes and how the statistical properties of the concentration fluctuations are modified in these circumstances. In this work, data from wind tunnel experiments are used to analyse the variance, skewness, kurtosis, intermittency, probability density function and power spectrum of the concentration field during the mixing of two identical plumes and results are compared with those obtained for an equivalent single plume. The normalised variance, skewness and kurtosis on the centre-lines of the combined plume increase with distance downwind of the stack and, in the two-source configuration, takes lower values than those found in the single plumes. The results reflect the merging process at short range, which is least protracted for cases in which the sources are in-line or up to 30 \(^{\circ }\) off-line. At angles of 45 \(^{\circ }\) and more, the plumes are effectively side-by-side during the merging process and the interaction between the vortex pairs in each plume is strong. Vertical asymmetry is observed between the upper and the lower parts of the plumes, with the upper part having greater intermittency (i.e. the probability that no plume material is present) and a more pronounced tail to the concentration probability distribution. This asymmetry tends to diminish at greater distances from the source but occurs in both buoyant and neutral plumes and is believed to be associated with the ‘bending-over’ of the emission in the cross-flow and the vortex pair that this generates. The results allowed us to identify three phases in plume development. The first, very near the stack, is dominated by turbulence generated within the plume and characterised by concentration spectra with distinct peaks corresponding to scales comparable with those of the counter-rotating vortex pair. A second phase follows at somewhat greater distances downwind, in which there are significant contributions to the concentration fluctuations from both the turbulence internal to the plume and the external turbulence. The third phase is one in which the concentration fluctuations appear to be controlled by the external turbulence present in the ambient flow.     

Active mate choice at cock-of-the-rock leks: tactics of sampling and comparison

Summary The importance of active mate choice as a component of sexual selection remains controversial, despite recent studies identifying traits that correlate with male mating success. We analyzed the sampling sequences of individual female Guianan cock-of-the-rock, providing quantitative documentation of active female choice in this lekbreeding species. We compared observed sampling patterns with null models of random female movement and of movement weighted by the observed distribution of male success. The courts actually visited by individual females were significantly more clumped and centrally located than predicted by computer simulations of either random or weighted movement. Contrary to simplified hypotheses of female choice, hen cock-of-the-rock were not limited either to sequential comparisons or to threshold decision rules when selecting mates. Instead, they repeatedly sampled a subset of potential mates, using the pool-comparison tactic. Within this pool, females preferentially mated with the males ranked highest in terms of total courtship visits received, and rejected low-ranking males. Our results suggest complex interactions between patterns of female sampling and male dispersion in lek mating systems, and also provide insights into the constraints on female sampling in lek species.