Model selection criteria for overdispersed data and their application to the characterization of a host-parasite relationship

In the statistical modeling of a biological or ecological phenomenon, selecting an optimal model among a collection of candidates is a critical issue. To identify an optimal candidate model, a number of model selection criteria have been developed and investigated based on estimating Kullback’s (Information theory and statistics. Dover, Mineola, 1968) directed or symmetric divergence. Criteria that target the directed divergence include the Akaike (2nd international symposium on information theory. Akadémia Kiadó, Budapest, Hungary, pp 267–281, 1973, IEEE Trans Autom Control AC 19:716–723, 1974) information criterion, AIC, and the “corrected” Akaike information criterion (Hurvich and Tsai in Biometrika 76:297–307, 1989), AICc; criteria that target the symmetric divergence include the Kullback information criterion, KIC, and the “corrected” Kullback information criterion, KICc (Cavanaugh in Stat Probab Lett 42:333–343, 1999; Aust N Z J Stat 46:257–274, 2004). For overdispersed count data, simple modifications of AIC and AICc have been increasingly utilized: specifically, the quasi Akaike information criterion, QAIC, and its corrected version, QAICc (Lebreton et al. in Ecol Monogr 62(1):67–118 1992). In this paper, we propose analogues of QAIC and QAICc based on estimating the symmetric as opposed to the directed divergence: QKIC and QKICc. We evaluate the selection performance of AIC, AICc, QAIC, QAICc, KIC, KICc, QKIC, and QKICc in a simulation study, and illustrate their practical utility in an ecological application. In our application, we use the criteria to formulate statistical models of the tick (Dermacentor variabilis) load on a white-footed mouse (Peromyscus leucopus) in northern Missouri.     

A note on a non-stationary point source spatial model

A point source, non-stationary covariance structure model is proposed, having only one additional parameter over a standard, stationary covariance structure, spatial model. Additionally, the proposed model is demonstrated to fit better than the three extra parameter, point source, non-stationary spatial model proposed by Ecker and De Oliveira (Commun Stat Theory Methods 37:2066–2078, 2008). The proposed model is fit from a Bayesian perspective and illustrated using a house sales dataset from Cedar Falls, Iowa.     

Hydrolithon spp. (Rhodophyta, Corallinales) overgrow live corals (Cnidaria, Scleractinia) in Yemen

In Yemen, off the northwestern coast in the Gulf of Aden, the coralline algae Hydrolithon rupestre (Foslie) Penrose 1996 and H. murakoshii Iryu and Matsuda 1996 have been observed to overgrow and kill living Porites lutea Milne-Edwards and Haime, 1860. Similarly, Hydrolithon onkodes (Heydrich) Penrose and Woelkerling 1992 and H. rupestre were observed overgrowing Stylophora pistillata (Esper, 1797). Competitive interactions between P. lutea and H. murakoshii were monitored from 2006 to 2009 at two sites and showed an average linear growth of 8.3 (±1.9 SD) mm?year^?1 over the coral. The small polyps of S. pistillata and P. lutea combined with putative chemical compounds produced by Hydrolithon spp. are likely to allow the coralline overgrowth. Although corallines can locally kill coral tissues, the CCA/coral interactions do not seem to affect the overall live coral cover at the study sites.     

Bootstrap confidence intervals for adaptive cluster sampling design based on Horvitz–Thompson type estimators

Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) introduced several bootstrap methods under adaptive cluster sampling using a Horvitz–Thompson type estimator. Using a simulation study, they showed that their proposed methods provide confidence intervals with highly understated coverage rates. In this article, we first show that their bootstrap methods provide biased bootstrap estimates. We then define two bootstrap methods, based on the method of Gross (Proceeding of the survey research methods section. American Statistical Association, Alexandria, VA, pp 181–184, 1980) and Bootstrap With Replacement, that provide unbiased bootstrap estimates of the population mean with bootstrap variances matching the corresponding unbiased variance estimator. Using a simulation study, we show that the bootstrap confidence intervals based on our proposed methods have better performance than those based on available bootstrap methods, in the sense of having coverage proportion closer to the nominal coverage level. We also compare the proposed intervals to empirical likelihood based intervals in small samples.     

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.     

Sine-skewed axial distributions with an application for fallen tree data

An axis is an undirected line where there is no reason to distinguish one end of the line from the other. Phenomena in nature that can be described as axial data are numerous. In this paper a method of trigonometric moments for the axial normal or axial von Mises distribution as an alternative to the method by Arnold and SenGupta (Environ Ecol Stat 13:271–285, 2006) is discussed. Sine-skewed axial Jones–Pewsey, von Mises and wrapped Cauchy distributions are introduced as special cases of a more general construction of skew axial distributions. As an example the methods are applied to a data set which consists of the orientations of logs on the floor of a primeval spruce forest.     

The wave-induced solute flux from submerged sediment

The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water.     

Der Einsatz von Pflanzentests bei der Sedimentbewertung

Background and aim Aquatic organisms of the three trophic levels (producers, consumers, reducers) have been used for a long time for ecotoxicological assessments of water quality (HABAB 2000; HABAK 1999). In biotest systems that have become established standards, algae, daphnia, and luminescent bacteria as test organisms are often used so far. However, comparative studies have shown that algae are not sufficiently sensitive to all phytotoxic agents and thus cannot be the exclusive indicator organism of any toxic effects on autotrophic life. Moreover, the EU Water Framework Directive (EU-WFD 2000) sets macrobenthos, fish, phytoplankton, and macrophytes equally side by side as indicators of the status of waters. Nevertheless, biotest systems relying on higher plants have been rarely used in assessments of aquatic sediments so far. Against this background, the aquatic duckweed test (DIN EN ISO 20079) was developed and standardized, and a sediment contact test was developed with Myriophyllum aquaticum (Feiler et al. 2004). The latter was subject of a joint research project of the German Federal Ministry of Education and Research (BMBF-Verbundprojekt “SeKT”) that examined and compared several sediment contact tests (Feiler et al. 2005). Compared to tests with algae, a biotest using macrophytes has the advantage to be more representative of higher plants, since target organism and test organism are closer related in terms of evolutionary history. The present study demonstrates that the application of biotests with higher plants in analyses of contaminated sediments yields valuable results that may contribute to a concept for the integrative assessment of water quality.     

Using surface drifter observations to measure tidal vortices and relative diffusion at Aransas Pass,Texas

Tidal vortices play an important role in the flushing of coastal regions. At the mouth of a tidal inlet, the input of circulation by the ebb tide may force the formation of a starting-jet dipole vortex. The continuous ebb jet current also creates a periodic sequence of secondary vortices shed from the inlet mouth. In each case, these tidal vortices have a shallow aspect ratio, with a lateral extent much greater than the water depth. These shallow vortices affect the transport of passive tracers, such as nutrients and sediment from the estuary to the ocean and vice versa. Field observation of tidal vortices primarily relies on ensemble averaging over several vortex events that are repeatable in space and can be sampled by a fixed Eulerian measurement grid. This paper presents an adaptive approach for locating and measuring within tidal vortices that propagate offshore near inlets and advect along variable trajectories set by the wind-driven currents. A field experiment was conducted at Aransas Pass, Texas to measure these large-scale vortices. Locations of the vortices produced during ebb tide were determined using near real-time updates from surface drifters deployed near or within the inlet during ebb tide, and the paths of towed acoustic Doppler current profiler (ADCP) transects were selected by analysis of the drifter observations. This method allowed ADCP transects to be collected within ebb generated tidal vortices, and the paths of the drifters indicated the presence of both the starting-jet dipole and the secondary vortices of the unstable ebb tidal jet. Drifter trajectories were also used to estimate the size of each observed vortex as well as the statistics of relative diffusion offshore of Aransas Pass. The field data confirmed the starting-jet spin-up time (time until the vortex dipole begins to propagate offshore) measured in the laboratory by Bryant et al. [6] and that the Strouhal condition of \(St=0.2\) predicts the shedding of secondary vortices from the inlet mouth. The size of the rotational core of the vortex is also shown to be approximated physically by the inlet width or by \(0.02UT\) , where U is the maximum velocity through the inlet channel and T is the tidal period, and confirms results found in laboratory experiments by Nicolau del Roure et al. [23]. Additionally, the scale of diffusion was approximately 1–15 km and the apparent diffusivity was between 2–130  \(m^2/s\) following Richardsons law.     

n-Octyl esters of long-chain fatty acids are not anthropogenic pollution markers

n-Octyl esters of higher fatty acids have been reported as markers of urban wastewater in sediments, polychaeta, fish, crabs and oysters (Chaler et al. in J Chromatogr A 1046:203–210, 2004)). However, up to date, there were no subsequent studies to confirm this claim. Likewise, Chaler and co-workers did not consider that the mentioned compounds might occur naturally in the environment. Here we found seven n-octyl straight-chain alkanoates, from C-20 to C-26, in the wild-growing plant Heracleum sphondylium L., Apiaceae, from 14 locations. Those plant metabolites were unambiguously identified by gas chromatographic co-injection of the synthesized esters with the inflorescence washings. All identified octyl esters represent new natural compounds, except for octyl docosanoate. Since we have demonstrated that n-octyl esters occur naturally, and in abundance, they cannot be recognized any longer as wastewater markers. Additionally, here we provide evidences that the compounds identified by Chaler et al. (2004) are in fact 2-ethylhexyl esters, mistakenly identified as n-octyl esters.     

Data depth for the uniform distribution

Given a set $X$ of $k$ points and a point $z$ in the $n$ -dimensional euclidean space, the Tukey depth of $z$ with respect to $X$ , is defined as $m/k$ , where $m$ is the minimum integer such that $z$ is not in the convex hull of some set of $k-m$ points of $X$ . If $z$ belongs to the closed region $B$ delimited by an ellipsoid, define the continuous depth of $z$ with respect to $B$ as the quotient $V(z)/\text{ Vol }(B)$ , where $V(z)$ is the minimum volume of the intersection of $B$ with the halfspaces defined by any hyperplane passing through $z$ , and $\text{ Vol }(B)$ is the volume of $B$ . We consider $z$ a random variable and prove that, if $z$ is uniformly distributed in $B$ , the continuous depth of $z$ with respect to $B$ has expected value $1/2^{n+1}$ . This result implies that if $z$ and $X$ are uniformly distributed in $B$ , the expected value of Tukey depth of $z$ with respect to $X$ converges to $1/2^{n+1}$ as the number of points $k$ goes to infinity. These findings have applications in ecology, namely within the niche theory, where it is useful to explore and characterize the distribution of points inside species niche.     

Comment on “Use of local tidal records to identify relative sea level change: accuracy and error for decision makers” by Powell VA, McGlashan DJ, Duck RW (2012) J Coast Conserv

In this Comment we refer to our strong reservations concerning the paper by Powell et al. J Coast Conserv, (2012) recently published on the Online First web site of the Journal of Coastal Conservation. The paper makes a number of comments on data obtained from the Permanent Service for Mean Sea Level (PSMSL) and British Oceanographic Data Centre (BODC) which are incorrect or misleading. In addition, some of their comments on sea-level science in general need to be challenged and corrected.     

A robust weighted EM algorithm for use-availability data

Wildlife sampling for habitat selection often combines a random background sample with a random sample of used sites, because the background sample could contain too few used sites to be informative for rare species. This approach is referred to as use-availability sampling. Two variants are considered where there is: (1) a random background sample including used and unused sites augmented with a sample of used sites, and (2) a sample of used sites augmented with a contaminated background sample, i.e. use is not recorded. A weighted estimator first proposed by Manski and Lerman (Econometrica 45(8):1977?C1988, 1977) forms the basis for our suggested approach. The weighted estimator has been shown to perform better than the usual unweighted approach with uncontaminated data and mis-specified logit models (Xie and Manski in Sociol Methods Res 17(3):283?C302, 1989). A weighted EM algorithm is developed for use with contaminated background data. We show that the weighted estimator continues to perform well with contaminated data and maintains its robustness to model mis-specification. The weighted estimator has not been previously used for use-availability sampling due to reliance on the assumption that only the intercept is biased, which is valid for a correct logit model. We show that adjusting the intercept may not eliminate the bias with an incorrect logit model. In this case, the weighted estimator is a relatively simple and effective alternative.     

Behavioural syndromes, syndrome deviation and the within- and between-individual components of phenotypic correlations: when reality does not meet statistics

Evolutionary mechanisms leading to correlations across different behaviours, called behavioural syndromes, are hard to study, mostly because behavioural syndromes are group/population level phenomena. Recently (Herczeg and Garamszegi Behav Ecol Sociobiol 66:161–169, 2012), we introduced the concept of syndrome deviation that allows the study of behavioural syndromes at the individual level by focusing on the individual deviation from the hypothetical perfect group-level behavioural correlation. Subsequently, Dingemanse et al. (Behav Ecol Sociobiol 66:1543–1548, 2012) emphasized that behavioural syndromes refer to the between-individual component of phenotypic correlations, and only this component is relevant for syndrome deviation. They also recommended mixed models to decompose the between- and within-individual correlations. We agree that separating these components is important, but the proposed approach is impractical to apply for functionally different behaviours because (1) the assumption of constant within-individual correlations is unjustified and (2) different behaviours cannot be measured at the same time. Further, our simulations based on mixed models show that the statistical differentiation between the within- and between-individual components is inefficient when using realistic sample sizes. Until the separation of between- and within-individual correlations is resolved, we recommend alternative approaches for empirical behavioural syndrome research that consider the repeatability of the behaviours and the optimal balance between within- and between-individual sample sizes. Syndrome deviation calculated from phenotypic correlations of traits that are proven to be individual specific, or from the between-individual correlations if possible, is a meaningful metric to describe behavioural consistency and to explain its evolutionary significance.     

Analysis of periodic patterns of daily precipitation through simultaneous modeling of its serially observed occurrence and amount

Precipitation is of great importance to agriculture, environment and ecosystem as a regular precipitation pattern is usually vital to healthy plants; excessive or insufficient rainfall can be harmful. Periodic patterns of precipitation can be studied based on regularly observed data over time. Since regularly observed precipitation data are generally skewed with many zeros, two common analysis approaches have been proposed recently. One approach investigates precipitation using a two-part model where the occurrence and positive amount of precipitation are analyzed separately (Piantadosi et al. in Environ Model Assess 14:431–438, 2009), whereas the other approach handles occurrence and amount simultaneously using a Tweedie’s compound Poisson model for independent observations (Hasan and Dunn in Int J Climatol 32:1006–1017, 2012). The former approach fails to maintain the regular temporal structure of serially observed precipitation, whereas the latter approach ignores serial dependence. As there is generally substantial serial correlation in the observed sequence of precipitation data over time, we introduce a compound Poisson state-space model with serially correlated random effects for daily precipitation data. This approach characterizes both occurrence and amount of precipitation simultaneously while accounting for the corresponding serial correlation. Our main results depend only on the first- and second-moment assumptions of unobserved random effects. We illustrate our method with the analysis of the daily precipitation data recorded at Mount Washington, NH, USA.     

Defining behavioural syndromes and the role of ‘syndrome deviation’ in understanding their evolution

This commentary highlights multivariate tools that have been used by evolutionary biologists in the study of syndromes and their evolution and discusses the insights that these methods provide into evolutionary processes relative to the metric ‘syndrome deviation’ that has recently been proposed by Herczeg and Garamszegi (Behav Ecol Sociobiol 66:161–169, 2012). We clarify that non-zero phenotypic correlations arise from the joint influences of within- and between-individual correlations, whereas only non-zero between-individual correlations represent behavioural syndromes, and discuss how acknowledgement of this subtle difference between phenotypic and between-individual correlations affects the applicability of syndrome deviation for the study of behavioural syndromes.     

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $(\overline{\hbox {Ri}_\mathrm{g} } >1)$ , but sometimes at smaller values $(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $\hbox {z/L}<1$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $\hbox {z/L}>1$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $\overline{\hbox {Ri}_\mathrm{g} }$ was identified. Eddy diffusivities of momentum $\hbox {K}_\mathrm{M}$ and heat $\hbox {K}_\mathrm{H}$ were dependent on wave activities, notably when $\overline{\hbox {Ri}_\mathrm{g} } > 1$ . The ratio $\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$ dropped well below unity at high $\overline{\hbox {Ri}_\mathrm{g} }$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.     

Estimating the spatial covariance structure using the geoadditive model

In geostatistics, both kriging and smoothing splines are commonly used to generate an interpolated map of a quantity of interest. The geoadditive model proposed by Kammann and Wand (J R Stat Soc: Ser C (Appl Stat) 52(1):1–18, 2003) represents a fusion of kriging and penalized spline additive models. Complex data issues, including non-linear covariate trends, multiple measurements at a location and clustered observations are easily handled using the geoadditive model. We propose a likelihood based estimation procedure that enables the estimation of the range (spatial decay) parameter associated with the penalized splines of the spatial component in the geoadditive model. We present how the spatial covariance structure (covariogram) can be derived from the geoadditive model. In a simulation study, we show that the underlying spatial process and prediction of the spatial map are estimated well using the proposed likelihood based estimation procedure. We present several applications of the proposed methods on real-life data examples.     

Component-specific toxic concerns of the inhalable fraction of urban road dust

Continuous global urbanisation causes an ever-growing ecological footprint of pollution. Road dust (RD), one of these pollutants, poses a health concern due to carcinogenic and toxic components potentially present in the micron-sized fractions. The literature reports on the concentrations of trace, toxic metals and metalloids present in RD (Hooker and Nathanail in Chem Geol 226:340–351, 2006), but the literature on its molecular composition is limited. Recent reports on the bioaccessibility of platinum group metals are also reported (Colombo et al. in Chem Geol 226:340–351, 2008). In vitro and animal toxicological studies confirmed that the chemical composition of inhaled particles plays a major role in its toxic, genotoxic and carcinogenic mechanisms, but the component-specific toxic effects are still not understood. Particle-bound airborne transition metals can also lead to the production of reactive oxygen species in lung tissue; a special concern amongst particularly susceptible cohorts (children and elderly). The characterisation of the molecular composition of the fine fraction is evidently of importance for public health. During a pilot study, partially characterised size-fractioned RD samples (Barrett et al. in Eviron Sci Technol 44:2940–2946, 2010) were analysed for their elemental concentration using X-ray fluorescence spectrometry and inductively coupled plasma mass spectrometry. In addition, separately dispersed particles (200 particles per size fraction) were analysed individually by means of computer-controlled electron probe X-ray micro-analysis (CC-EPXMA) and their molecular structure probed by studying elemental associations. These were correlated with micro-Raman spectroscopy (MRS) results. It was found that the fine fraction (<38?μm) had the highest Pb (238?ppm) and Cr (171?ppm) concentrations. The CC-EPXMA data showed >50?% association of Cr-rich particles with Pb, and the MRS data showed that the Cr was mostly present as lead chromate and therefore in the Cr(VI) oxidation state. Concentrations of both Pb and Cr decreased substantially (279 (<38?μm)–13?ppm (<1?mm); 171 (<38?μm)–91?ppm (<?1?mm), respectively) in the larger fractions. Apart from rather alarmingly high concentrations of oxidative stressors (Cu, Fe, Mn), the carcinogenic and toxic potential of the inhalable fraction is evident. Preliminary bioaccessibility data indicated that both Cr and Pb are readily mobilised in artificial lysosomal liquid and up to 19?% of Cr and 47?% of Pb were released.     

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.