Considerations for the use of SADIE statistics to quangify spatial patterns

The SADIE methodology has recently been developed to quangify spatial patterns, particularly in determining the randomness of observed patterns, estimating patches and gaps, and quangifying correlation between species. We used argificially generated data sets to investigate the relationship of the SADIE pattern and association statistics with patch number and spatial positions of the patches. Results showed that SADIE statistics are critically dependent on the absolute positions of quadrat counts, and not just on their relative positions. In particular, degree of patchiness increased as the patch was displaced away from the centre. Therefore, the dependence of SADIE statistics on absolute sampling positions should be taken into consideration when using and interpreting SADIE-based results.     

Quartet mapping and the extent of lateral transfer in bacterial genomes

Several recent analyses have used quartet-based methods to assess the congruence among phylogenies derived for large sets of genes from prokaryotic genomes. The principal conclusion from these studies is that lateral gene transfer (LGT) has blurred prokaryotic phylogenies to such a degree that the darwinian scheme of treelike evolution might be abandoned in favor of a net or web. Here, we focus on one of these methods, quartet mapping, and show that its application can lead to overestimation of the extent of inferred LGT in prokaryotes, particularly when applied to distantly related taxa.     

The spatial distribution of soils across Europe: A fractal approach

In this work we investigate the applicability of fractal modeling to the soil surface system in Europe, as described by the European Soil Database (V2.0) and the soil classification of the World Reference Base [FAO, 1999. World Reference Base for Soil Resources. ISSS–ISRIC–FAO, Rome, World Soil Resources Report No. 84]. Firstly, we observe the power law patterns of the distribution of pedotaxa as well as their pedorichness–area relationships. After this, we consider the 45 most abundant soils that cover 92% of the surface of Europe and estimate the box-counting fractal dimension of the areas covered by each of the pedotaxa within three orders of magnitude. Our analysis shows a remarkable scaling behavior of soil distribution and strongly suggests the fractal nature of pedotaxa distribution across Europe. These findings lead us to propose that considering the pedotaxa fractal dimension could play an important role in the analysis of the complexity of European soil systems.     

The lateral extent of the subsidy from an upland stream to riparian lycosid spiders

Adult aquatic insects emerging from streams can subsidize riparian food webs, but little is known of the spatial extent of these subsidies. Stable isotope (¹⁵N) enrichment of aquatic insects, principally a species of stonefly (Plecoptera: Leuctridae), emerging from an upland stream was used to trace the subsidy from the stream ecosystem to riparian spiders (Lycosidae). The downstream profile of spider δ¹⁵N correlated closely with that of adult stoneflies, indicating that they were deriving nutrition from aquatic sources. The contribution of adult aquatic insects to spider diets was determined using a two-source mixing model. Adult aquatic insects made up over 40% of spider diets adjacent to the stream, but <1% at 20 m from the stream. Enrichment of riparian spiders declined exponentially with distance from the stream channel. Aquatic-terrestrial subsidies were spatially restricted, but locally important, to riparian lycosid spiders at the study site.     

Dimensional statistics for estimation of lung volumes

The theory of dimension has been widely used in physics to check the validity of formulae. This theory has not been used more frequently in statistics as compared to physics for development of various prediction formulae/equations in applied physiology. An attempt has, therefore, been made in the present investigation to evolve formulae for estimation of lung volumes from cubic function of height based on dimensional considerations in boys and girls 8-13 and 16-21 years of age.     

Characterizing fishing effort and spatial extent of coastal fisheries

Biodiverse coastal zones are often areas of intense fishing pressure due to the high relative density of fishing capacity in these nearshore regions. Although overcapacity is one of the central challenges to fisheries sustainability in coastal zones, accurate estimates of fishing pressure in coastal zones are limited, hampering the assessment of the direct and collateral impacts (e.g., habitat degradation, bycatch) of fishing. We compiled a comprehensive database of fishing effort metrics and the corresponding spatial limits of fisheries and used a spatial analysis program (FEET) to map fishing effort density (measured as boat-meters per km2) in the coastal zones of six ocean regions. We also considered the utility of a number of socioeconomic variables as indicators of fishing pressure at the national level; fishing density increased as a function of population size and decreased as a function of coastline length. Our mapping exercise points to intra and interregional 'hotspots' of coastal fishing pressure. The significant and intuitive relationships we found between fishing density and population size and coastline length may help with coarse regional characterizations of fishing pressure. However, spatially-delimited fishing effort data are needed to accurately map fishing hotspots, i.e., areas of intense fishing activity. We suggest that estimates of fishing effort, not just target catch or yield, serve as a necessary measure of fishing activity, which is a key link to evaluating sustainability and environmental impacts of coastal fisheries.     

The use of bootstrap resampling to assess the uncertainty of cooper statistics

The predictive abilities of two-group classification models (CMs) are often expressed in terms of their Cooper statistics. These statistics are often reported without any indication of their uncertainty, making it impossible to judge whether the predicted classifications are significantly better than the predictions made by a different CM, or whether the predictive performance of the CM exceeds predefined performance criteria in a statistically significant way. Bootstrap resampling routines are reported that provide a means of expressing the uncertainty associated with Cooper statistics. The usefulness of the bootstrapping routines is illustrated by constructing 95% confidence intervals for the Cooper statistics of four alternative skin-corrosivity tests (the rat skin transcutaneous electrical resistance assay, EPISKIN, Skin(2) and CORROSITEX), and four two-step sequences in which each in vitro test is used in combination with a physicochemical test for skin corrosion based on pH measurements.     

Model-supervised kernel smoothing for the estimation of spatial usage

The analysis of telemetry data obtained from tagged animals often requires that a smooth surface of spatial usage is fitted to the observations. Well‐established statistical techniques for doing this, such as kernel smoothing (KS), are based on asymptotic arguments that guarantee the convergence of their estimates to the truth with increasing sample size. Often, in addition to telemetry data, ecologists have access to a wealth of information relating to the animals’ distribution and movement. This additional information is potentially useful for the estimation of spatial usage but currently remains unused by existing methods. In this paper, I outline and begin the validation of model‐supervised kernel smoothing (MSKS), a modification of KS that uses such information to supervise surface‐fitting to telemetry data. MSKS initially requires an ad‐hoc synthesis of all the available information, excluding telemetry, into an auxiliary usage surface (the model). This is then combined with the kernel‐smoothed telemetry data into a hybrid surface that is the weighted average of the two. Automatic selection of the smoothing coefficient and the weight associated with the model is done by means of likelihood cross‐validation. I examine the performance of MSKS first, by extensive, numerical exploration on simulated data in one‐dimensional space and second, on two‐dimensional data obtained from an individual‐based simulation of a central‐place forager. The results for different models and sample sizes indicate that MSKS has three important properties. Firstly, it generally outperforms KS by an extent that depends on the quality of the auxiliary model. Secondly, when the auxiliary model is not informative, MSKS automatically reverts to a similar output as KS. Finally, in practical terms, MSKS is easy to implement and adds little to the computational requirements already made by KS methods. I illustrate the application of MSKS and further validate its performance on satellite telemetry data collected from a grey seal on the east coast of Scotland.     

Abundance estimation of rocky shore invertebrates at small spatial scale by high-resolution digital photography and digital image analysis

We have tested both the usefulness of high-resolution digital photography for data acquisition and digital image analysis, by non-supervised classification and high pass filter, for recognition and abundance estimation of benthic intertidal organisms. These digital tools were compared with visual scan and photo quadrat conventional methods. The comparison was done using 40 quadrats (10×5 cm) randomly selected along a 5-m transect on the rocky shore of the Pemaquid Point, Maine, USA. ANOVA for repeated measures was used to test differences among methods. Monte Carlo simulation analysis was used to explore differences among methods over a large set of data (n=100, 500, 1000 quadrats). Differences among methods were observed when 40 quadrats were used. Tukey multiple comparison test showed that abundance estimation from visual scan, photo quadrat and digital image analysis by high pass filter do not differ significantly among them but differ from non-supervised classification results. Due to its accurate estimation, high pass filter (Prewitt) method was chosen as the most reliable digital method to estimate species abundance. Monte Carlo simulation of visual scan, photo quadrat and high pass filter results showed significant differences when the number of quadrats was larger. These results showed that the combined use of digital photography and digital image analysis techniques for the acquisition and analysis of recorded data is a powerful method for the study of intertidal benthic organisms. Results produced using these techniques were similar than those produced by conventional methods but were obtained in a much-reduced time.     

Notes on the implementation of the mass - radius method of fractal dimension estimation

The graphical implementation in computers and image analysersof the mass – radius method of fractal dimension estimationhas two sources of error. The first is associated with underestitnationof area of the ‘circle scan’in a square matrix;the second arises from the overestimation of areas at smallradii. Methods of coping with these problems are described.     

Variance estimation for systematic designs in spatial surveys

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over‐reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip‐sampling, distance‐sampling, and quadrat‐sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.