Reducing effort in the use of benthic bioindicators

Hard-bottom invertebrates were visually sampled in a man-modified bay during a harbour enlargement scheme. Several environmental variables were repeatedly measured. Faunal assemblages were analysed using classification and ordination (MDS) techniques at different levels of resolution (species, families and indicators). Indicator taxa were selected from the full species data set by performing preliminary correlations between faunal and environmental variables. Similar results were observed at the three levels investigated. This suggests the existence of redundant information in the species level data set when applied to this case study. The implications of our findings for environmental monitoring are discussed.     

A comparative evaluation of models of cinnabar moth dynamics

Summary 1. A complex model of cinnabar moth dynamics proposed by Dempster and Lakhani (1979) with 23 parameters is reduced to a single equation with five parameters, and the behaviour of the reduced model shown to explain most features of the full model. 2. The efficiency of the full model is compared with the reduced model and with two even simpler models (the two parameter discrete logistic and a four parameter model based on a step-function for mortality) in their abilities to describe time series data of cinnabar moth population densities from Weeting Heath. Models with more parameters were not significantly better than few-parameter models in describing population trajectories. 3. Models that included a driving variable (in this case observed rainfall data) were no better at describing the data than simpler models without driving variables. It appears, therefore, that the routine inclusion of driving variables may be counterproductive, unless there is compelling empirical or theoretical evidence of their importance and the mode of action of the driving variables can be modelled mechanistically. For example, the regression model used to describe the relationship between rainfall and plant biomass in Dempster and Lakhani (1979), breaks down if rainfall is assumed to be constant, because there is no explicit model for the regulation of plant biomass. 4. The parameter values of the cinnabar-ragwort interaction suggest that cinnabar moth dynamics may be chaotic. Whether or not field data exhibit chaos or environmental stochasticity (or a mixture of both) is impossible to determine from inspection of time series data on population density. There is an urgent need for experimental and theoretical protocols to disentangle these two sources of population fluctuation.     

Spatial determinants of hazardous chemicals in surface water of Qiantang River,China

Spatial regression, incorporating spatial error or lag dependency, was performed to interpret determinants of hazardous chemicals at full sub-basin scale and at 500 m riparian buffer scale in Qiantang River, eastern coastal China. Monitoring data from 41 monitoring stations were collected between 1996 and 2003 and pretreated for 7 variables—petroleum, hexavalent chromium, total cadmium, total lead, total mercury, total cyanide, and volatile phenol. Results showed that primary predictors and the predictive ability of spatial regression differed with variables and scales. Topology, distance to river source, land use/land cover (LULC), population density, and gross domestic product (GDP) can be primary predictors for the pattern of certain hazardous chemical variables in 1996 and 2003. LULC types were good predictors for changes of cyanide and heavy metals, while GDP and population density contributed to petroleum dynamics between 1996 and 2003. This study demonstrated that spatial regression is a promising tool for generating indicators to tackle with hazardous chemical pollution. We also advocate applying multi-scale approaches to uncover the dynamics of hazardous chemicals.     

Reduction of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature

Hodgkin-Huxley-type models mimick the electrical behavior of excitable membranes quite realistically. However, inclusion of many different ionic channels into such a model yields a highly complex set of differential equations. In this paper a reduction of a full Hodgkin-Huxley-type model based on voltage-clamp data from small rat neurons in the supraoptic nucleus area is introduced. It was found that two of the ionic channel gating variables of the full model preserved a rather close relationship during simulations. This allowed to express one of these gating variables in terms of the other one thus reducing the number of differential equations the model is based on. The behavior of the reduced model was very similar to that of the full model. In particular, important physiological features as spike shape and constant-input-to-interspike-interval relationship were (almost) identical in the full and the reduced model.     

Improved Horvitz–Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology

The case-cohort study involves two-phase samplings: simple random sampling from an infinite superpopulation at phase one and stratified random sampling from a finite cohort at phase two. Standard analyses of case-cohort data involve solution of inverse probability weighted (IPW) estimating equations, with weights determined by the known phase two sampling fractions. The variance of parameter estimates in (semi)parametric models, including the Cox model, is the sum of two terms: (i) the model-based variance of the usual estimates that would be calculated if full data were available for the entire cohort; and (ii) the design-based variance from IPW estimation of the unknown cohort total of the efficient influence function (IF) contributions. This second variance component may be reduced by adjusting the sampling weights, either by calibration to known cohort totals of auxiliary variables correlated with the IF contributions or by their estimation using these same auxiliary variables. Both adjustment methods are implemented in the R survey package. We derive the limit laws of coefficients estimated using adjusted weights. The asymptotic results suggest practical methods for construction of auxiliary variables that are evaluated by simulation of case-cohort samples from the National Wilms Tumor Study and by log-linear modeling of case-cohort data from the Atherosclerosis Risk in Communities Study. Although not semiparametric efficient, estimators based on adjusted weights may come close to achieving full efficiency within the class of augmented IPW estimators.     

Estimating the product‐moment correlation in samples with censoring on both variables

Bivariate samples may be subject to censoring of both random variables. For example, for two toxins measured in batches of wheat grain, there may be specific detection limits. Alternatively, censoring may be incomplete over a certain domain, with the probability of detection depending on the toxin level. In either case, data are not missing at random, and the missing data pattern bears some information on the parameters of the underlying model (informative missingness), which can be exploited for a fully efficient analysis. Estimation (after suitable data transformation) of the correlation in such samples is the subject of the present paper. We consider several estimators. The first is based on the tetrachoric correlation. It is simple to compute, but does not exploit the full information. The other two estimators exploit all information and use full maximum likelihood, but involve heavier computations. The one assumes fixed detection limits, while the other involves a logistic model for the probability of detection. For a real data set, a logistic model for the probability of detection fitted markedly better than a model with fixed detection limits, suggesting that censoring is not complete.     

Spatial autocorrelation and red herrings in geographical ecology

Aim Spatial autocorrelation in ecological data can inflate Type I errors in statistical analyses. There has also been a recent claim that spatial autocorrelation generates ‘red herrings’, such that virtually all past analyses are flawed. We consider the origins of this phenomenon, the implications of spatial autocorrelation for macro‐scale patterns of species diversity and set out a clarification of the statistical problems generated by its presence. Location To illustrate the issues involved, we analyse the species richness of the birds of western/central Europe, north Africa and the Middle East. Methods Spatial correlograms for richness and five environmental variables were generated using Moran's I coefficients. Multiple regression, using both ordinary least‐squares (OLS) and generalized least squares (GLS) assuming a spatial structure in the residuals, were used to identify the strongest predictors of richness. Autocorrelation analyses of the residuals obtained after stepwise OLS regression were undertaken, and the ranks of variables in the full OLS and GLS models were compared. Results Bird richness is characterized by a quadratic north–south gradient. Spatial correlograms usually had positive autocorrelation up to c. 1600 km. Including the environmental variables successively in the OLS model reduced spatial autocorrelation in the residuals to non‐detectable levels, indicating that the variables explained all spatial structure in the data. In principle, if residuals are not autocorrelated then OLS is a special case of GLS. However, our comparison between OLS and GLS models including all environmental variables revealed that GLS de‐emphasized predictors with strong autocorrelation and long‐distance clinal structures, giving more importance to variables acting at smaller geographical scales. Conclusion Although spatial autocorrelation should always be investigated, it does not necessarily generate bias. Rather, it can be a useful tool to investigate mechanisms operating on richness at different spatial scales. Claims that analyses that do not take into account spatial autocorrelation are flawed are without foundation.     

Distinctive amino acid residue periodicities in terminal sequences of type III and type I secreted proteins from proteobacteria

The Fourier transform (FT) method was applied to specify the distribution of 14 predefined groups of amino acids (64 residues) at both termini of annotated type III and type I secreted proteins from proteobacteria. Type I proteins displayed a higher occurrence of significant periodicities at both C-and N-termini, indicating potent features to discriminate between secretion types, particularly by the use of variables selected from the full periodicity profiles at 19 orders of FT. The Fishers linear discriminant analysis, together with the stepwise selection of variables throughout equal pairs of combinations for all predefined groups of residues, revealed the C-terminal harmonics of aromatic (HFWY) and aliphatic (VLIA) residues as a set of strong predictor variables to classify both types of secreted proteins with an accuracy of 100% for original grouped cases and 96.4% for cross-validated grouped cases. The prediction accuracy of proposed discriminant function was estimated by repeated k-fold cross-validation procedures where the original data set was randomly divided into k subsets, with one of the k-subsets serving as the test set and the remaining data forming the training set. The average error rate computed across all k-trials and repeats did not exceed that of leave-one-out procedure. The proposed set of predictor variables could be used to assess the compatibility between secretion pathways and secretion substrates of proteobacteria by means of discriminant analysis.     

Visualizing rank deficient models: a row equation geometry of rank deficient matrices and constrained-regression

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency.     

Do-it-yourself statistics: A computer-assisted likelihood approach to analysis of data from genetic crosses

Graduate school programs in genetics have become so full that courses in statistics have often been eliminated. In addition, typical introductory statistics courses for the "statistics user" rather than the nascent statistician are laden with methods for analysis of measured variables while genetic data are most often discrete numbers. These courses are often seen by students and genetics professors alike as largely irrelevant cookbook courses. The powerful methods of likelihood analysis, although commonly employed in human genetics, are much less often used in other areas of genetics, even though current computational tools make this approach readily accessible. This article introduces the MLIKELY.PAS computer program and the logic of do-it-yourself maximum-likelihood statistics. The program itself, course materials, and expanded discussions of some examples that are only summarized here are available at http://www.unisi. it/ricerca/dip/bio_evol/sitomlikely/mlikely.h tml.     

Genetic algorithm optimization for pre-processing and variable selection of spectroscopic data

MOTIVATION: The major difficulties relating to mathematical modelling of spectroscopic data are inconsistencies in spectral reproducibility and the black box nature of the modelling techniques. For the analysis of biological samples the first problem is due to biological, experimental and machine variability which can lead to sample size differences and unavoidable baseline shifts. Consequently, there is often a requirement for mathematical correction(s) to be made to the raw data if the best possible model is to be formed. The second problem prevents interpretation of the results since the variables that most contribute to the analysis are not easily revealed; as a result, the opportunity to obtain new knowledge from such data is lost. METHODS: We used genetic algorithms (GAs) to select spectral pre-processing steps for Fourier transform infrared (FT-IR) spectroscopic data. We demonstrate a novel approach for the selection of important discriminatory variables by GA from FT-IR spectra for multi-class identification by discriminant function analysis (DFA). RESULTS: The GA selects sensible pre-processing steps from a total of approximately 10(10) possible mathematical transformations. Application of these algorithms results in a 16% reduction in the model error when compared against the raw data model. GA-DFA recovers six variables from the full set of 882 spectral variables against which a satisfactory DFA model can be formed; thus inferences can be made as to the biochemical differences that are reflected by these spectral bands.     

Presence‐only versus presence–absence data in species composition determinant analyses

Aim Studying relationships between species and their physical environment requires species distribution data, ideally based on presence–absence (P–A) data derived from surveys. Such data are limited in their spatial extent. Presence‐only (P‐O) data are considered inappropriate for such analyses. Our aim was to evaluate whether such data may be used when considering a multitude of species over a large spatial extent, in order to analyse the relationships between environmental factors and species composition. Location The study was conducted in virtual space. However, geographic origin of the data used is the contiguous USA. Methods We created distribution maps for 50 virtual species based on actual environmental conditions in the study. Sampling locations were based on true observations from the Global Biodiversity Information Facility. We produced P–A data by selecting ∼1000 random locations and recorded the presence/absence of all species. We produced two P‐O data sets. Full P‐O set was produced by sampling the species in locations of true occurrences of species. Partial P‐O was a subset of full P‐O data set matching the size of the P–A data set. For each data set, we recorded the environmental variables at the same locations. We used CCA to evaluate the amount of variance in species composition explained by each variable. We evaluated the bias in the data set by calculating the deviation of average values of the environmental variables in sampled locations compared to the entire area. Results P–A and P‐O data sets were similar in terms of the amount of variance explained by the different environmental variables. We found sizable environmental and spatial bias in the P‐O data set, compared to the entire study area. Main conclusions Our results suggest that although P‐O data from collections contain bias, the multitude of species, and thus the relatively large amount of information in the data, allow the use of P‐O data for analysing environmental determinants of species composition.     

Assessment of regional non-linear tissue deformation and air volume change of human lungs via image registration

We evaluate the non-linear characteristics of the human lung via image registration-derived local variables based on volumetric multi-detector-row computed tomographic (MDCT) lung image data of six normal human subjects acquired at three inflation levels: 20% of vital capacity (VC), 60% VC and 80% VC. Local variables include Jacobian (ratio of volume change) and maximum shear strain for assessment of lung deformation, and air volume change for assessment of air distribution. First, the variables linearly interpolated between 20% and 80% VC images to reflect deformation from 20% to 60% VC are compared with those of direct registration of 20% and 60% VC images. The result shows that the linearly-interpolated variables agree only qualitatively with those of registration (P<0.05). Then, a quadratic (or linear) interpolation is introduced to link local variables to global air volumes of three images (or 20% and 80% VC images). A sinusoidal breathing waveform is assumed for assessing the time rate of change of these variables. The results show significant differences between two-image and three-image results (P<0.05). The three-image results for the whole lung indicate that the peak of the maximum shear rate occurs at about 37% of the maximum volume difference between 20% and 80% VC, while the peaks for the Jacobian and flow rate occur at 50%. This is in agreement with accepted physiology whereby lung tissues deform more at lower lung volumes due to lower elasticity and greater compliance. Furthermore, the three-image results show that the upper and middle lobes, even in the recumbent, supine posture, reach full expansion earlier than the lower lobes.     

How much do we overestimate future local extinction rates when restricting the range of occurrence data in climate suitability models?

Climate suitability models are used to make projections of species’ potential future distribution under climate change. When studying the species richness with such modeling methods, the extent of the study range is of particular importance, especially when the full range of occurrence is not considered for some species, often because of geographical or political limits. Here we examine biases induced by the use of range‐restricted occurrence data on predicted changes in species richness and predicted extinction rates, at study area margins. We compared projections of future suitable climate space for 179 bird species breeding in Iberia and North Africa (27 of them breeding only in North Africa though potential colonizers in Europe), using occurrence data from the full Western Palaearctic (WP) species range and from the often‐considered European‐restricted range. Current and future suitable climatic spaces were modeled using an ensemble forecast technique applied to five general circulation models and three climate scenarios, with eight climatic variables and eight modeling techniques. The use of range‐restricted compared to the full WP occurrence data of a species led to an underestimate of its suitable climatic space. The projected changes in species richness across the focus area (Iberia) varied considerably according to the occurrence data we used, with higher local extinction rates with European‐restricted data (on average 38 vs 12% for WP data). Modeling results for species currently breeding only in North Africa revealed potential colonization of the Iberian Peninsula (from a climatic point of view), which highlights the necessity to consider species outside the focus area if interested in forecasted changes in species richness. Therefore, the modeling of current and future species richness can lead to misleading conclusions when data from a restricted range of occurrence is used. Consequently, climate suitability models should use occurrence data from the complete distribution range of species, or at least within biogeographical areas.     

Climatic influences on the mortality of sheep during long-distance sea transport

Research on the causes of sheep death in sea voyages from Australia to the Middle East is limited, in particular little is known about the influence of climatic factors. Mortality data from 417 shipments of sheep exported over an 11-year period (November 2004 to June 2015) were modelled retrospectively to determine associated climatic factors. The statistical analysis were performed for both the full data set with 417 voyages based on actual and estimated departure and arrival dates and a restricted data set with 71 voyages based on actual dates. The results of the full data set demonstrated a seasonal mortality pattern, with more deaths occurring on sea voyages leaving Australia in the southern hemisphere winter or spring than those departing in Australian summer or autumn. Heat stress and inadequate fat mobilisation for energy supply when sheep are inappetant on shipments may explain this seasonality. Based on these two models, the voyage and weather factors associated with sheep mortalities included departure year, autumn departure in the southern hemisphere, voyage duration, single or multiple loading port(s), weekly mean dry bulb temperature and wind speed at departure ports, and humidity at destination ports. Significant correlations were observed between weather variables at the departure ports in the Australian winter and a high sheep mortality rate during voyages. This, together with the anticipated increased heat stress risk as a result of climate change, suggests that there could be review of the trade from Australia in the southern hemisphere winter. The influence of weather at the departure ports should be considered in sheep mortality prediction models, especially Australia’s heat stress risk assessment model.     

Meteorological determinants of spider ballooning: the roles of thermals vs. the vertical windspeed gradient in becoming airborne

Summary Spiders disperse by ballooning, a form of aeronautic behavior which they initiate by launching themselves into thermals. An attempt was made to define meteorological variables related to production and maintenance of thermals and use them as predictors of the number of aeronauts. Ballooning spiders were collected throughout a full growing season at an agricultural site and a native tall grass prairie 25 km distant, and numbers of ballooners were regressed against variables derived from meteorological data taken at locations near each site. The variables were the proportions of cloud cover and of possible sunshine, differences between maximum and minimum daily temperature (DT), wind speed, and a modification of the aeronautic index of Vugts and van Wingerden (1976). Ballooner numbers and meteorological variables used in the regressions were all weekly means. Significant one-step models were derived for both sites, but the addition of a second variable did not significantly increase the proportion of variation explained in either model. The modified aeronautic index explained 23% of the variation in ballooner numbers at the prairie site, while the proportion of possible sunshine explained 82% of the variation at the agricultural site. However the signs of the partial regression coefficients were contrary to expected. This may be due to the masking of short term meteorological and behavioral events by the averaging of meteorological variables and aeronaut numbers over a week. Alternatively it may indicate that the source of updrafts used by aeronauts may not always be thermals, but may sometimes be the vertical gradient in windspeed, a model which is consistent with the contrary signs of the regression coefficients.