Some notes on the distribution and certain modifications of Mahalanobis' generalized distance (D2)

Different modifications of Mahalanobis' generalized distance (D²) utilized in anthropological research are given, and it is shown that they all derive from the distribution of D² when the distances between the populations investigated are real. To investigate whether observed distances are real, testing of D² for significance is stressed. It is demonstrated that D² ought to be tested for significance according to its relation to the F-distribution, but that it may be related to the chi-squared distribution as an approximation when the numbers of individuals in the samples are very large. The great disadvantages of utilizing this approximation for smaller numbers of individuals in the samples are demonstrated, as well as the dependence of D² on sample size and the number of measurements used when testing for significance.     

Density,biomass, and guild structure of arboreal arthropods as related to their inhabited tree size in aCryptomeria japonica plantation

Arboreal arthropods in a 15-year-old plantation ofCryptomeria japonica were surveyed using the smoking method under open conditions and also in the enclosed condition in which the whole above-ground part of a tree was covered by a cloth bag. Per tree, the number of individuals collected was 8200–14000, with a biomass of 340–1700 mg d.wt. Collembola and Acarina were major components in number, while Diplopoda, Collembola, and Araneae occupied the larger part of the biomass. About 60–70% of total numbers of individuals dropped within two hours after the open fumigation. Clear power-form regressions between total numbers of individuals and biomasses of all animals and their host tree size (stem diameter at clear length,D _B ) showed they were approximately proportional toD _B ². The guilds of scavengers and tourists demonstrated the most significant correlations between their numbers and biomasses and the tree size. Numbers and biomasses of Collembola, Diptera, and Araneae revealed remarkable dependence on the tree size. From these regressions, numbers of individuals and biomasses per unit ground area were estimated for all arthropods to be 3755/m² and 165.87 mg d.wt./m², respectively. Power-form regressions were observed between numbers and biomasses of prey and predators. The number-and biomass ratios of all predators to all prey tended to decrease with increasing tree size. A similar trend was observed in the corresponding ratios of parasitic Hymenoptera to lepidopteran larvae, while those of Araneae to Collembola were almost constant, irrespective of tree size.     

An estimate of spin diffusion in a spin subset: Application to iterative distance calculation from 3D 15N NOESY-HMQC

Summary A method for quantification of distances between amide hydrogens using only the 3D NOESY-HMQC experiment recorded on a ¹⁵N-labelled protein is presented. This method is based on an approximate expression of the NOE intensities between amide hydrogens obtained from continuum modelling of the non-amide spins; this expression is used in a distance calculation algorithm. The algorithm has been named CROWD, standing for Continuum approximation of Relaxati On path Ways between Dilute spins. This approximation as well as the CROWD algorithm are tested on a simulated case; the CROWD algorithm is then applied to experimental data, measured on a fragment of bacteriorhodopsin.     

Sampled‐based estimation of diversity sensu stricto by transforming Hurlbert diversities into effective number of species

A theoretical framework based on Hill numbers has recently been advocated to measure and partition diversity sensu stricto. Hill numbers can be interpreted intuitively as effective number of species (ENS). They conform to the so‐called replication principle allowing a mathematically coherent multiplicative partitioning of diversity. They form a family of ENS defined by the parameter q which controls the weight attributed to rare species. Despite its advantages, this framework was developed without considering its robustness when treating community samples. In this study, we first show that Hurlbert diversity indices (expected number of species among k individuals) can be transformed into ENS that conform asymptotically to the replication principle while controlling the weight given to rare species through parameter k. We investigate the statistical properties of Hill and Hurlbert ENS using simulated communities with contrasted diversity. The properties of multiplicative beta diversity estimators based on ENS are also characterized by simulating communities with different levels of differentiation. We show that Hurlbert ENS provides a better statistical performance than Hill numbers when dealing with small sample sizes. By contrast, Hill numbers and their estimators suffer from substantial bias except when rare species have a low weight (q= 2). An estimator of ENS estimating both Hill numbers for q= 2 and Hurlbert ENS for k= 2 is shown to give the best performance and is recommended for processing real datasets when rare species receive low weight. In order to better take account of rare species, current estimators of Hill numbers are not recommended when sample size is too low while Hurlbert’s ENS performs reliably. In conclusion, while Hill numbers possess some interesting mathematical properties that are not shared by Hurlbert’s ENS, the latter outperforms Hill numbers in terms of statistical properties and is well suited to processing community samples, as illustrated on a real dataset.     

Approximating the Non-Null Distribution of the Likelihood Ratio Test Statistic

This paper is concerned with investigation into the behavior of the likelihood ratio test statistic G² when the alternative hypothesis M (QQ) is the true model. Exact moments of G² are computed empirically and three approximations are considered for approximating the non-null distribution of G². Our results show that the two parameter gamma distribution provides a closer approximation to the exact powers of G². A randomized procedure was employed to obtain critical values based on 1000 simulated samples.     

Spatial pattern indices based on distances between individuals on a line-segment with finite length

Let us consider a strip-wise habitat of line-segment, like a corridor, to simplify the subject mathematically, and assume that the length of the habitat is γ and there are n individuals. Here, we assume that the spatial pattern of the individuals is random if the n distances from the left end of the habitat to each individual follow a uniform distribution on the strip. Under such an assumption, the variance of the distances between any two neighbors is represented by the formula nθ²(n+1)⁻²(n+2)⁻¹ and the variance between n+1 distances between n individuals from the left end to the right end to the strip, is represented by the formula nθ²(n+1)⁻²(n+2)⁻¹. These two kinds of variances can be used for determining (1) the spatial pattern of a population on the strip and (2) the spatial structure within the population, by comparison with the variances calculated from the data. Two examples cited from the literature, a cattle population on a pasture and an aphid population on a sycamore leaf, are presented.     

Studies of twoH-2D b mutants: B6.C-H-2 bm13 and B6.C-H-2 bm14

Two new C57BL/6H-2 mutants,B6.C-H- 2^bm13 and B6.C-H- 2^bm14 are described. They arose independently in C57BL/6 as spontaneous mutations of the gain and loss type. Complementation studies map the mutations in both bm13 and bm14 to theH-2D ^b gene. How ever, these two mutant strains are not identical, but occurred as independent mutations at the same locus, as shown by reciprocal graft rejection and by the inability of the (bm13 × bm114)F₁ hybrid to accept C57BL/6 grafts. Serological studies by direct testing (cytotoxicity and hemagglutination) and by quantitative absorption demonstrated a decrease in the H-2D^b private specificity H-2.2 in both bm13 and bm14 when compared to C57BL/6. This was confirmed by SDS-PAGE analysis using antisera detecting the H-2.2 specificity. Attempts to produce antibodies to either the gained or lost specificities of the two mutant strains failed.     

Comparisons of Some Chi-Squared Goodness-of-Fit Test Statistics in Sparse One-Way Multinomials

The behavior of Pearson's X² test, the likelihood ratio test Y² and the two of its derivatives, G² and G_k², the Freeman-Tukey test (FT) and the Cressie and Read test Statistic I(2/3) are examined in this study. Estimated attained α levels based on 1000 simulated samples when the approximating distribution is χ_k-1², are computed for these tests for the various values of k, n and seven null hypotheses. Results from estimated power computations indicate that none of the test statistics has a clear advantage over any others, and that the choice of which test to use must therefore rest mainly on the performances with regards to the attained α levels when the χ² approximation is invoked. In this respect, the log-normal approximation proposed by Lawal and Upton (1980) is strongly recommended. This is closely followed by the I(2/3).     

Evaluation and implications of Andean potato weevil infestation sources for its management in the Andean region

The Andean potato weevil Premnotrypes suturicallus Kuschel (Coleoptera: Curculionidae) is one of the most damaging potato (Solanum spp.) pests in the Andes. The objective of this study was to get a better understanding of weevil infestation sources and its distribution in potato fields as well as on the effect of potato cropping intensity and farmers’ harvest practices on weevil infestation to provide better clues for its management. For this purpose, a methodology was developed to assess weevil field densities in potato. A Taylor’s power law indicated that 177 and 69 samples are necessary to assess low (0.5 weevils/m²) and high (5 weevils/m²) weevil densities for a moderate reliability or precision level (D = 0.5). In potato fields, overwintering weevil densities were highest at field borders with 3.5 weevils/m² at a distance of <2.5 m compared to 0.7 weevils/m² at distances >10 m from the field border. No effects of time of harvest could be detected on soil overwintering weevil densities. The quantification of the larval density per potato plant after harvest showed that fields after 2‐year potato rotations had eight times more overwintering weevils compared to 1‐year rotations. Weevil infestation sources were mainly potato fields with the highest infestation (89%) followed by olluco (Ullucus tuberosus) and oat (Avena sativa) fields having volunteer potato plants (35%). The results confirm and support previous assumptions about the importance of the cropping systems for Andean potato weevil infestation and management. The confirmation that weevils do not occur or only in neglected numbers on fallow fields supports the use of plastic barriers to effectively exclude migrating flightless adult weevils to potato fields cultivated after fallow. The distribution of overwintering weevils indicates that farmers could concentrate efforts to control adult weevils mainly to the first meters of potato fields.     

Expression of deuterium-isotope-labelled protein in the yeast Pichia pastoris for NMR studies

Deuterium isotope labelling is important for NMR studies of large proteins and complexes. Many eukaryotic proteins are difficult to express in bacteria, but can be efficiently produced in the methylotrophic yeast Pichia pastoris. In order to facilitate NMR studies of the malaria parasite merozoite surface protein-1 (MSP1) complex and its interactions with antibodies, we have investigated production of the MSP1-19 protein in P. pastoris grown in deuterated media. The resulting deuteration patterns were analyzed by NMR and mass spectrometry. We have compared growth characteristics and levels of heterologous protein expression in cells adapted to growth in deuterated media (95% D₂O), compared with expression in non-adapted cells. We have also compared the relative deuteration levels and the distribution pattern of residual protiation in protein from cells grown either in 95% D₂O medium with protiated methanol as carbon source, or in 95% D₂O medium containing deuterated methanol. A high level of uniform C deuteration was demonstrated, and the consequent reduction of backbone amide signal linewidths in [¹H/¹⁵N]-correlation experiments was measured. Residual protiation at different positions in various amino acid residues, including the distribution of methyl isotopomers, was also investigated. The deuteration procedures examined here should facilitate economical expression of ²H/¹³C/¹⁵N-labelled protein samples for NMR studies of the structure and interactions of large proteins and protein complexes.     

Sample size in the monitoring of benthic macrofauna in the profundal of lakes: evaluation of the precision of estimates

We discuss here the influence of sample size (number of replicates) on the accuracy and precision of the results when sampling profundal benthos with an Ekman grab according to the Finnish standard, SFS 5076, which is equivalent to the Swedish and Norwegian standards. The aim was to find criteria for choosing a sample size which would avoid any powerful influence of chance on the results without entailing an unreasonable amount of work for monitoring purposes.Lake Haukivesi (area 620 km², total phosphorus 13 µg l^–1 and colour 35 Pt mg l^–1), Lake Paasivesi (116 km², 5 µg l^–1 and 35 Pt mg l^–1) and Lake Puruvesi (322 km², 4 µg l^–1 and 5 Pt mg l^–1) were sampled randomly in June and October 1991. 25 Replicate samples were taken on each occasion from the deep profundal area of each lake, defined here as 60-100% of the maximum depth. The sedimentation areas studied were fairly homogeneous, since the animal communities were not markedly affected by the variations in depth. Distribution estimates for the statistics studied, such as number of individuals, expected number of species, diversity and benthic quality indices, were calculated for a large set of random samples taken from the empirical data by computer (bootstrap sampling). The sample variance, s ², correlated with the mean animal density, m (ind. m^–2), according to the equation s ² = 31.77 m ^1.247. The sample size required to achieve the desired precision in mean animal density (D, expressed as the ratio standard error/mean) can thus be estimated as n = 31.77 m ^–0.753 D ^–2. The number of replicate samples needed to achieve a standard error of 20% of the mean density was 10 in Lake Haukivesi, seven in Lake Paasivesi and 11 in Lake Puruvesi. The accuracy and precision of the estimated number of species, Shannon's diversity and Benthic Quality Index improved markedly as the sample size was increased to 10 replicates. As a compromise between work load and statistical reliability, a figure of 10 replicate Ekman samples is proposed here for the monitoring of profundal benthos. The proposed sample size usually produces individual numbers which are high enough for practical purposes, probably at least 100 individuals, which is recommended as a minimum in the standard. The lower number of replicate samples recommended in recent Finnish handbook, 3–5, usually produces inadequate data, and this may detract from the comparability of the results and leave the changes in profundal communities undetected.     

Biomedical Applications of Synthetic Melanotropins

Alpha-melanotropin (alpha-melanocyte stimulating hormone, alpha-MSH) is a hormone produced by the pituitary gland of most vertebrate animals. This melanotropic peptide, Ac-Ser-Tyr-Ser-Met-Glu-His-Phe-Arg-Trp-Gly-Lys-Pro-Val-NH2, regulates melanin pigmentation of the skin of some mammals. Although MSH may be absent from the human pituitary gland, this peptide can stimulate pigment formation in human skin. We have synthesized several analogues of alpha-MSH, which are superpotent, prolonged-acting, and resistant to inactivation by serum enzymes. One such analogue, [NLe⁴, D-Phe⁷]alpha-MSH, has proven particularly useful in a number of physiological studies. In addition, some [Nle⁴, D-Phe⁷]-substituted fragment analogues of MSH are even more active than the native hormone, alpha-MSH. For example, these analogues are 100–1,000 times more active than alpha-MSH in stimulating S-91 mouse melanoma tyrosinase activity in vitro. We have successfully labeled one such peptide to high specific activity; this melanotropin, [³H]-Ac-[Nle⁴, D-Phe⁷]alpha-MSH_4–11NH₂, has been shown by others to bind to B16 melanoma cells. We have also conjugated several ligands (fluorescein and biotin) to [Nle⁴, D-Phe⁷]alpha-MSH. These melanotropin conjugates might prove useful for melanotropin receptor studies and for the clinical localization of metastatic melanoma. We have demonstrated that [Nle⁴, D-Phe⁴]alpha-MSH can be topically applied and transdermally delivered across the skin of mice and humans in vitro, as determined by bioassay and RIA. Initial toxicologic studies indicate that the analogue is nontoxic to mice and is not mutagenic. Studies are underway to determine whether this analogue may prove useful as a “tanning hormone” for increasing the pigmentation of light-skinned individuals or possibly even for treating people with certain hypopigmentary disorders.     

Patterns of within and between-colony microsatellite variation in the endangered Vancouver Island marmot (Marmota vancouverensis): implications for conservation

Among the 14 extant species of the genus Marmota the Vancouver Island marmot (Marmota vancouverensis) is the most endangered. In 2007 as few as 85 individuals were left in the wild, with an additional 162 individuals maintained in captivity. To facilitate genetic monitoring of both wild and captive populations, polymorphic genetic markers were identified. Thirty-three different microsatellite loci were tested for amplification and variability in ≥30 wild-born individuals. Only 11 of these loci proved to be polymorphic and were subsequently analysed in 105 samples collected from wild Vancouver Island marmots. The average number of alleles (A) at those 11 loci was only 2.1, and the intraspecific variation (H _E between 8 and 23% within colonies) was low compared to other marmot species. Variation within the small and geographically isolated Mt. Washington colony was particularly low (A = 1.3, H _E = 0.08). Genetic distances between the Mt. Washington colony (11 individuals) and those of the Nanaimo Lakes region (94 individuals) on southern Vancouver Island were large (D values ranging from 0.42 to 0.50), while genetic distances among colonies within the latter area were much smaller (D values from 0.01 to 0.13). Given the low within-population genetic variation, and the resulting risk of inbreeding depression at Mt. Washington, we support the decision to maximize overall genetic variation of the species by crossbreeding marmots from the two different areas despite the possibility of local adaptation.     

Coccolithophores in the equatorial Atlantic Ocean: response to seasonal and Late Quaternary surface water variability

The present study was initiated to ascertain the significance of coccolithophores as a proxy for paleoceanographic and paleoproductivity studies in the equatorial Atlantic. Data from a range of different samples, from the plankton, surface sediments as well as sediment cores are shown and compared with each other.In general, the living coccolithophores in the surface and subsurface waters show considerable variation in cell numbers and distribution patterns. Cell densities reached a maximum of up to 300×10³ coccospheres/l in the upwelling area of the equatorial Atlantic. Here, Emiliania huxleyi is the dominant species with relatively high cell numbers, whereas Umbellosphaera irregularis and Umbellosphaera tenuis are characteristic for oligotrophic surface waters. Although they are observed in high relative abundances, these species only occur in low absolute numbers. The lower photic zone is dominated by high abundances and considerable cell numbers of Florisphaera profunda.The geographical distribution pattern of coccoliths in surface sediments reflects the conditions of the overlying surface water masses. However, abundances of the oligotrophic species Umbellosphaera irregularis and Umbellosphaera tenuis are strongly diminished, causing an increase in relative abundance of the lower photic zone taxa Florisphaera profunda and Gladiolithus flabellatus.During the past 140,000 years the surface water circulation of the equatorial Atlantic has changed drastically, as can be seen from changes in the coccolithophore species composition, absolute coccolith numbers, as well as coccolith accumulation rates. Significant increases in coccolith numbers and accumulation rates is observed in the southern equatorial Atlantic during the last glacial interval (oxygen isotope stages 2–4), which we attribute to enhanced upwelling intensities and advection of cool nutrient rich waters at this site. In the western equatorial Atlantic we observe an opposite trend with decreasing numbers of coccoliths during glacial periods, which probably is caused by a deepening of the thermocline.     

A review of the status and decline in abundance of the Irish Hare (Lepus timidus hibernicus) in Northern Ireland

The Northern Ireland Hare Survey documented the distribution of the Irish Hare (Lepus timidus hibernicus). Historical game bag records and other, more contemporary, records of hare distribution were examined. These data indicate how numbers of L. t. hibernicus may have changed over the last 140 years. The results of the Northern Ireland Hare Survey suggested that L. t. hibernicus was widespread throughout Northern Ireland. Current average densities are no more than 0.65 hares/km². Game bag records indicate that hare densities may have been much higher in the past, with a maximum of 138 hares/km² recorded on Crom Estate, Co. Fermanagh, in 1864. Evidence from hare distribution recorded during the Northern Ireland Rabbit Survey indicates that hare numbers declined between 1984 and 1994. Evidence from all sources suggests that L. t. hibernicus has declined in abundance substantially, with present total population estimates for Northern Ireland ranging from 8250 to 21 000 individuals. Flushing data indicate that rushes and hedgerows are important diurnal resting areas for hares. While the principal reason for the decline in numbers of L. t. hibernicus in Northern Ireland is not clear, more species‐rich pasture and provision of areas of cover, such as rushes, may arrest further declines, or indeed promote numbers of hares, particularly in lowland areas.     

Stock structure of pallid sturgeon analyzed with microsatellite loci

Recovery efforts for the endangered pallid sturgeon (Scaphirhynchus albus) include supplementation of wild stocks with hatchery reared progeny. Identifying the extent of genetic stock structure, which has previously been detected in samples from the range extremes, will help to determine whether stock transfers might be harmful. DNA microsatellite genotypes were screened in pallid sturgeon from the upper Missouri River, lower Missouri River, middle Mississippi River and Atchafalaya River and analyzed using a combination of Bayesian model‐based and more traditional F‐statistic based methods to characterize genetic differentiation. Scaphirhynchus specimens were collected by researchers active in the recovery effort and genotypes were screened at 16 microsatellite loci. Because there is considerable genetic and morphological overlap between pallid sturgeon, shovelnose sturgeon, and their hybrids, a combination of morphological and genetic techniques were used to eliminate shovelnose and possible hybrids from the sample. Genetic differentiation was detected among samples (overall θ = 0.050, P = 0.001). Pairwise θ, genetic distances, and Bayesian assignment testing reveal that pallid sturgeon from the upper Missouri River are the most distinct group with pairwise comparisons of pallid sturgeon among all the remaining samples exhibiting lower θ values, higher genetic distances, and self assignment scores. Our results indicate that using local broodstock, when available, should be used for pallid sturgeon propagation. If local broodstock are not available, geographically proximate individuals would limit genetic differences between native and stocked individuals.     

Enhanced axon outgrowth and improved long‐distance axon regeneration in sprouty2 deficient mice

Sprouty (Spry) proteins are negative feedback inhibitors of receptor tyrosine kinase signaling. Downregulation of Spry2 has been demonstrated to promote elongative axon growth of cultured peripheral and central neurons. Here, we analyzed Spry2 global knockout mice with respect to axon outgrowth in vitro and peripheral axon regeneration in vivo. Neurons dissociated from adult Spry2 deficient sensory ganglia revealed stronger extracellular signal‐regulated kinase activation and enhanced axon outgrowth. Prominent axon elongation was observed in heterozygous Spry2^+/? neuron cultures, whereas homozygous Spry2^?/? neurons predominantly exhibited a branching phenotype. Following sciatic nerve crush, Spry2^+/? mice recovered faster in motor but not sensory testing paradigms (Spry2^?/? mice did not tolerate anesthesia required for nerve surgery). We attribute the improvement in the rotarod test to higher numbers of myelinated fibers in the regenerating sciatic nerve, higher densities of motor endplates in hind limb muscles and increased levels of GAP‐43 mRNA, a downstream target of extracellular regulated kinase signaling. Conversely, homozygous Spry2^?/? mice revealed enhanced mechanosensory function (von Frey's test) that was accompanied by an increased innervation of the epidermis, elevated numbers of nonmyelinated axons and more IB4‐positive neurons in dorsal root ganglia. The present results corroborate the functional significance of receptor tyrosine kinase signaling inhibitors for axon outgrowth during development and nerve regeneration and propose Spry2 as a novel potential target for pharmacological inhibition to accelerate long‐distance axon regeneration in injured peripheral nerves. © 2014 Wiley Periodicals, Inc. Develop Neurobiol 75: 217–231, 2015     

Cation binding to β-casein. a comparison of electrostatic models

The binding of cations of β-casein at pH 6.6 was considered previously. Available for three sodium concentiations, I = 0.04, 0.08, or 0.16 M are: [1] proton releases between I and [2] for each I, as calcium activity is increased, correlated sequences of monomer net charge, proton release, site bound calcium and protein Solvation- Models for ion binding are examined. Critical considerations are the intrinsic binding constants between hydrogen[H], calcium[Ca] and sodium[Na] ions and phosphate[P] and caiboxyIate[C] sites, and the effects of electrostatic interaction between sites as influenced by spatial fixed charge distribution, ionic strength and dielectric constant [D]. Anticipated intrinsic binding constants are k_H,P^o = 3 × 10⁶, k_Ca,P^o = 120, k_Na,P^o = 1, k_H,C^o = 7 × 10⁴ and k_Ca,C^o = 5.6Distributed charge models, either surface or volume, are inadequate since any reasonable monomer size yields fixed charge densities requiring k_H,P^o and k_Ca,C^o which are too low when the maximum in D is 75. Also, with increasing calcium binding, calculated proton release is only 0.4 to 0.5 of that observed.Discrete charge models accept anticipated k^o and yield calculated sequences of calcium binding and proton release which are in good agreement with those observed provided that: (1) using the known amino acid sequence of the phosphate-containing acidic peptide portion of the molecule, pep tide fixed charge is distributed at the lowest I so as to minimize electrostatic free energy; (2) in the region of fixed charge, D is approximately 5; (3) the distances between peptide fixed charges decrease with increasing ionic strength or calcium binding and (4) while protein is in solution, the acidic peptide and the remainder of the molecule are essentially electrostatically independent.     

Using the Mahalanobis distance statistic with unplanned presence-only survey data for biogeographical models of species distribution and abundance: a case study of badger setts

Aim Project‐specific data for biogeographical models are often logistically impractical to collect, forcing the use of existing data from a variety of sources. Use of these data is complicated when neither absence nor an estimate of the area sampled is available, as these are requirements of most analytical techniques. We demonstrate the Mahalanobis distance statistic (D²), which is a presence‐only modelling technique and does not require information on species absence or the sampled area. We use badger (Meles meles) setts as the basis for this investigation, as their landscape associations are well understood, and survey data exist against which to compare estimates of sett distribution and abundance. Location  England and Wales (151,403 km²). Methods We used stratified random samples of sett locations, and landscape variables that are known to be important for choice of badger sett location within a geographic information system at a cell resolution of 100 × 100 m. Landscape conditions at two scales were extracted, at and around sett locations, and the D² was used to classify all cells in England and Wales into a sett suitability model. Comparison of this sett suitability model with known main sett densities allowed estimates of main sett density to be made across England and Wales, with associated uncertainty. Results The sett suitability model was shown through iterative sampling and model evaluation using independent data to be stable and accurate. Main sett density estimates were biologically plausible in comparison with previous field‐derived estimates. We estimate 58,000 main setts within England and Wales, with 95% confidence intervals suggesting a value between 31,000 and 93,000. Main conclusions The D², which could be applied to other species and locations, proved useful in our context, where absence data were not available and the sampled area could not be reliably established. We were able to predict sett suitability across a large area and at a fine resolution, and to generate plausible estimates of main sett density. The final model provides valuable information on probable badger sett distribution and abundance, and may contribute to future research on the spatial ecology of badgers in England and Wales.