Bayes Estimator of Survival Probability from Randomly Censored Observations with Weibull Distribution of Time to Death

This paper deals with Bayes estimation of survival probability when the data are randomly censored. Such a situation arises in case of a clinical trial which extends for a limited period T. A fixed number of patients (n) are observed whose times to death have identical Weibull distribution with parameters β and θ. The maximum times of observation for different patients are also independent uniform variables as the patients arrive randomly throughout the trial. For the joint prior distribution of (β, θ) as suggested by Sinha and Kale (1980, page 137) Bayes estimator of survival probability at time t (0<t<T) has been obtained. Considering squared error loss function it is the mean of the survival probability with respect to the posterior distribution of (β, θ). This estimator is then compared with the maximum likelihood estimator, by simulation, for various values of β, θ and censoring percentage. The proposed estimator is found to be better under certain conditions.     

A quantitative analysis of excluded-site effects for highly cooperative binding systems

Binding isotherms can provide quantitive information regarding the stability of a molecular complex. Theorectical studies in recent years have been directed to systems in which a single ligand can exclude more than one polymer site (excluded-site effect). This system has minium of thre parameters to describe the binding data: the intrinsic binding constant, B; the remote-neighbor cooperative paramaters, σ_q and the number of excluded sites, q. It is suggested in the present communication that precise values for these three parameters can be obtained by utilizing the characteristics of two forms of data representation: θ vs ln m and θ/m vs θ, where θ is the degree of saturation (0?θ?1) and m is the molality of free ligand. The matrix generation method is used to obtain empirical equations relating the midpoint location and slope at the midpoint of the θ vs ln m plot to the three molecular parameters. A modified Scatchard theory is also presented for highly cooperative systems, which results in an expression relaing the maximum in the θ/m vs θ plot to the molecular parameters σ_q and q, thus providing the third equation for the three unknown parameters. The novel method f analysis is illustrated with the AMP-poly(L -arginine) and oligocytidylate–T7 DNA sstems.     

Unconditional Non-Asymptotic One-Sided Tests for Independent Binomial Proportions When the Interest Lies in Showing Non-Inferiority and/or Superiority

For two independent binomial proportions Barnard (1947) has introduced a method to construct a non-asymptotic unconditional test by maximisation of the probabilities over the ‘classical’ null hypothesis H₀= {(θ₁, θ₂) ∈ [0, 1]²: θ₁ = θ₂}. It is shown that this method is also useful when studying test problems for different null hypotheses such as, for example, shifted null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ θ₁ ± Δ } for non-inferiority and 1-sided superiority problems (including the classical null hypothesis with a 1-sided alternative hypothesis). We will derive some results for the more general ‘shifted’ null hypotheses of the form H₀ = {(θ₁, θ₂) ∈ [0, 1]²: θ₂ ≤ g(θ₁ )} where g is a non decreasing curvilinear function of θ₁. Two examples for such null hypotheses in the regulatory setting are given. It is shown that the usual asymptotic approximations by the normal distribution may be quite unreliable. Non-asymptotic unconditional tests (and the corresponding p-values) may, therefore, be an alternative, particularly because the effort to compute non-asymptotic unconditional p-values for such more complex situations does not increase as compared to the classical situation. For ‘classical’ null hypotheses it is known that the number of possible p-values derived by the unconditional method is very large, albeit finite, and the same is true for the null hypotheses studied in this paper. In most of the situations investigated it becomes obvious that Barnard's CSM test (1947) when adapted to the respective null space is again a very powerful test. A theorem is provided which in addition to allowing fast algorithms to compute unconditional non-asymptotical p-values fills a methodological gap in the calculation of exact unconditional p-values as it is implemented, for example, in Stat Xact 3 for Windows (1995).     

A calorimetric investigation of the heats of binding of Mg ++ to poly A, to poly U, and to their complexes

The heats of binding of Mg⁺⁺ ions to poly A, poly U, and to their complexes, in the presence of Na⁺ ions, have been measurd calorimetrically. In all cases the heat, ΔH(θ), exhibitis a distinct dependence on the extent of binding, θ, and in the cases of poly A and poly U also on the Na⁺ concentration. The values of ΔH(θ) range from +2 to +3 kcal/mole of Mg⁺⁺ bound at θ = 0 to 1.3 kcal/mole at θ = 0.5 except in poly A where at θ = 0 ΔH(θ) = ?2 to ?3 kcal/mole. This is interpreted as being due to a facilitation of base stacking by the binding of Mg⁺⁺. The extent of facilitation is consistent with current estimates of base stacking. A similar effect but of much smaller magnitude is believed to obtain in poly A poly U. An interpretation of the dependence of ΔH(θ) on θ in terms of simple electrostatic interactions, but neglecting solvent effects, was attempted and found to be inadequate.     

The interaction of carboxymethylamylose and diethylaminoethylamylose with iodine

Spectrophotometric titrations of slightly substituted carboxymethylamylose (CM-Amy) and diethylaminoethylamylose (DEAE-Amy) with iodine in the presence of iodide (I₂/I^?) were carried out as a function of iodide concentration, temperature, and polymeric charge. Binding isotherms for the polymer-I₂/I^? complex are reported in terms of an apparent binding constant (K_a) plotted versus degree of saturation of the complex (θ). The dependence of K_a upon polymeric charge is interpreted as evidence for the negatively charged character of the bound species. The cooperative nature of the binding process is evident in the positive slope of K_a vs (θ). Whereas the apparent binding constants and binding cooperativities for the derivatives are smaller than for the amylose-I₂/I^? complex, the binding enthalpies deduced from the temperature dependence of K_a at θ = 0.5 appear to be the same for amylose and CM-Amy. A viscometric titration of fully charged CM-Amy with I₂/I^?, conducted at dialysis equilibrium between the CM-Amy-I₂/I^? solution and the polymer-free solvent phase, disclosed a maximum in the plot of intrinsic viscosity ([η]) vs θ. The increase in [η] at small θ was interpreted as a reflection of polyelectrolyte expansion provoked by absorption of the negatively charged bound species; the subsequent decline in [η] is attributed to stabilization by I₂/I^? of compact helical sequences or to the formation at higher θ of intermolecular aggregates.     

Consistency of the Asymptotic Quasi-Likelihood Estimate on Linear Models

Consider a model y_t = f_t(θ) + M_t, 0 ⩽ t ⩽ T where θ∈ Θ in an unknown parameter, f_t(θ) is a linear predictable process, M_t is a martingale difference, and the nature of E(M²_t/ℱ_t—1) is unknown. This paper presents an estimating procedure for θ based on the asymptotic quasi-likelihood methodology. Conditions under which the asymptotic quasi-likelihood estimate converges to the true parameter θ₀ are discussed. This method is applied to several simulated examples, and estimates of the unknown parameter are obtained by means of a two-stage technique. Comparison is made between the estimates obtained via this method and those obtained via the ordinary least squares method. Discussion is provided on the application of the model.     

Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions

Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ _R θ(x ₁,x ₂,t) dx ₁ dx ₂ of a biological species with an area-density distribution function θ=θ(x ₁,x ₂,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇²θ +fθ −gθ ⁿ⁺¹ whereD (>0),n (>0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(_{x 1},x ₂, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn>1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ _R θ(x ₁,x ₂, 0)² dx ₁ dx ₂ sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.     

Root biomass changes after drainage and fertilization of a low-shrub pine bog

The stump and root systems of Scots pine (Pinus sylvestris) and field-layer vegetation were sampled before (1984) and three growing seasons after drainage and fertilization (1987) of a low-shrub pine bog. Average below-ground biomass of the field layer was 548 gDW m^–2 in 1984, with no significant treatment effects during experimentation. The stump-plus-root biomass of the pine stands was 1464 gDW m^–2 in the virgin state, and had increased to 1854 gDW m^–2 three years after the NPK-fertilizer treatment. The distribution over fractions also changed with this treatment. The fraction of fine roots ( < 1 mm) in stump-root biomass increased from 4% (56 gDW m^–2) to 11% (196 gDW m^–2), while the other compartments changed less. Total pine root length was 729 mm^–2 in 1984. Root length increased by 94% to 1380 mm^–2 on NPK-fertilized plots. Most of the fine pine roots were in the surface layer (0–10 cm), 79% in 1984 and 88% in 1987, and few pine roots were deeper than 20 cm. Maximum root length of fine pine roots ( < 1 mm) was estimated to be 2710 mm^–2 at about 800 gDW m^–2 (NPK treatment), and the corresponding maximum for small pine roots (=1–10 mm) was 227 mm^–2 at 809 gDW m^–2. Drainage stimulated net growth of fine roots, but this treatment also caused higher mortality rates of small roots. The fine roots responded to fertilization with higher net growth rate, and secondary growth of the large roots ( > 10 mm) was improved. The observed changes in root biomass and structure are explained as strategic adaptations to altered hydrological and nutritional circumstances in the root zone after drainage and fertilization.     

Acclimation of photosynthetic capacity to irradiance in tree canopies in relation to leaf nitrogen concentration and leaf mass per unit area

The observation of acclimation in leaf photosynthetic capacity to differences in growth irradiance has been widely used as support for a hypothesis that enables a simplification of some soil‐vegetation‐atmosphere transfer (SVAT) photosynthesis models. The acclimation hypothesis requires that relative leaf nitrogen concentration declines with relative irradiance from the top of a canopy to the bottom, in 1 : 1 proportion. In combination with a light transmission model it enables a simple estimate of the vertical profile in leaf nitrogen concentration (which is assumed to determine maximum carboxylation capacity), and in combination with estimates of the fraction of absorbed radiation it also leads to simple ‘big‐leaf’ analytical solutions for canopy photosynthesis. We tested how forests deviate from this condition in five tree canopies, including four broadleaf stands, and one needle‐leaf stand: a mixed‐species tropical rain forest, oak (Quercus petraea (Matt.) Liebl), birch (Betula pendula Roth), beech (Fagus sylvatica L.) and Sitka spruce (Picea sitchensis (Bong.) Carr). Each canopy was studied when fully developed (mid‐to‐late summer for temperate stands). Irradiance (Q, µmol m^?2 s^?1) was measured for 20 d using quantum sensors placed throughout the vertical canopy profile. Measurements were made to obtain parameters from leaves adjacent to the radiation sensors: maximum carboxylation and electron transfer capacity (V_a, J_a, µmol m^?2 s^?1), day respiration (R_da, µmol m^?2 s^?1), leaf nitrogen concentration (N_m, mg g^?1) and leaf mass per unit area (L_a, g m^?2). Relative to upper‐canopy values, V_a declined linearly in 1 : 1 proportion with N_a. Relative V_a also declined linearly with relative Q, but with a significant intercept at zero irradiance (P < 0·01). This intercept was strongly related to L_a of the lowest leaves in each canopy (P < 0·01, r² = 0·98, n= 5). For each canopy, daily lnQ was also linearly related with lnV_a(P < 0·05), and the intercept was correlated with the value for photosynthetic capacity per unit nitrogen (PUN: V_a/N_a, µmol g^?1 s^?1) of the lowest leaves in each canopy (P < 0·05). V_a was linearly related with L_a and N_a(P < 0·01), but the slope of the V_a : N_a relationship varied widely among sites. Hence, whilst there was a unique V_a : N_a ratio in each stand, acclimation in V_a to Q varied predictably with L_a of the lowest leaves in each canopy. The specific leaf area, L_m(cm² g^?1), of the canopy‐bottom foliage was also found to predict carboxylation capacity (expressed on a mass basis; V_m, µmol g^?1 s^?1) at all sites (P < 0·01). These results invalidate the hypothesis of full acclimation to irradiance, but suggest that L_a and L_m of the most light‐limited leaves in a canopy are widely applicable indicators of the distribution of photosynthetic capacity with height in forests.     

Acute Changes In Knee‐Extensors Torque,Fiber Pennation,and Tendon Characteristics

The aim of the current study was to examine the relationships between quadriceps torque, vastus lateralis pennation angle (θ), and patella tendon stiffness (K) at 07:45 and 17:45 h. Using short‐duration static contractions, simultaneous recordings were made of vastus lateralis (VL) electromyograph (EMG), θ and patella tendon K. Peak isometric extension torque (Peak torque Ext_corr) increased by 29.4±6.5% at a knee angle of 70° (p=0.03) in the evening compared to the morning. In the contracted muscle, a 35.0±11.0% (p=0.02) time‐of‐day (TOD)‐related change in θ (to a greater evening compared to morning θ) was observed. Morning and evening measures of θ were also made, both at rest and at a standardized force level (250 N), to separate architecture change effects from increased torque capacity effects. Significant increments in θ in both the resting muscle (13.0±5.1%, p=0.046) and during the standardized exertions (8.0±3.1%, p=0.04) were observed in the evening versus the morning. Increases in θ with TOD were significantly correlated with the 40% (p=0.018) decrease in K both during the standardized contractions (r=0.788, p<0.001) and at rest (r=0.77, p=0.026). These data show that TOD affects K and θ and that these two important factors involved in in‐vivo muscle torque generation capacity are associated. The data also show that despite the potentially deleterious effects of the direction of the changes in both K and θ with TOD, peak torque Ext_corr still shows a significant upward shift in the evening relative to the morning.     

Cell volume distribution dynamics of <Emphasis Type="Italic">Chlorella</Emphasis><Emphasis Type="Italic">vulgaris</Emphasis> Beij. in batch cultures under continuous light

Cell volume distribution in Chlorella vulgaris cultures coming out of senescence was measured by flow cytometry every 6 h for 114 h in a full-factorial experiment with initial nitrate (420–4200 g NO₃-N l^–1), phosphate (9–186 g PO₄-P l^–1), and continuous light (50–330 E m^–2 s^–1) as treatments. The maxima in median and median absolute deviation (MAD) of cell volume were achieved within 6 h of each other and their timing was not affected by any treatment. Population specific growth rate during the first 66 h calculated from volume distribution changes was significantly affected by light treatment only (p=0.002).Revisions requested 4 November 2004; Revisions received 17 January 2005     

Convergence to Normality of the Asymptotic Quasi‐Score Function on a Linear Model

The asymptotic quasi‐likelihood method is considered for the model y_t = f_t(θ) + M_t, t = 0,1, …,T where f_tθ) is a linear predictable process of the parameter of interest θ, M_t is a martingale difference, and the nature of E(M_t² | ℱ_t–1) is unknown. This paper is concerned with the limiting distribution of the asymptotic quasi‐score function of such a model. Confidence intervals and hypothesis testing of θ is derived from the limiting distribution. Comparison is made between the estimates obtained through this method and those obtained through the least squares method.     

Competitive exclusion as a mode of action of a novel Bacillus cereus aquaculture biological agent

Aims: To determine the contribution of potential modes of action of a Bacillus cereus aquaculture biological control agent in inhibition of the fish pathogen, Aeromonas hydrophila. Methods and Results: When B. cereus was tested in plate well inhibition studies, no production of antimicrobial compounds was detected. Bacillus cereus had a high growth rate (0·96 h^?1), whereas Aer. hydrophila concentration decreased by c. 70% in co‐culture experiments. In nutrient limitation studies, B. cereus had a significantly higher growth rate when cultured under glucose (P < 0·05) and iron (P < 0·01) limitation in comparison with Aer. hydrophila. Bacillus cereus glucose (0·30 g l^?1 h^?1) and iron (0·60 mg l^?1 h^?1) uptake rates were also significantly higher (P < 0·01) than the Aer. hydrophila glucose (0·14 g l^?1 h^?1) and iron (0·43 mg l^?1 h^?1) uptake rates. Iron uptake was facilitated by siderophore production shown in time profile studies where relative siderophore production was c. 60% through the late exponential and sporulation phases. Conclusions: Competitive exclusion by higher growth rate, competition for organic carbon and iron, facilitated by siderophore production, could be identified as mechanisms of pathogen growth inhibition by B. cereus. Significance and Impact of the Study: This study is the first elucidation of the mechanism of action of our novel B. cereus biological agent in growth attenuation of pathogenic Aer. hydrophila. This study enhances the application knowledge and attractiveness for adoption of B. cereus NRRL 100132 for exploitation in aquaculture.     

Prediction of peak occurrence of Dendrolimus punctatus larvae based on Bayes discriminant method

To improve the accuracy of forecasting the peak occurrence of Dendrolimus punctatus Walker, we here used the Bayes discriminant analysis to predict this peak occurrence for the first and second generation of Dendrolimus punctatus larvae based on these data from 1983 to 2016 in Qianshan County, Anhui Province. Our present results showed that this discriminant equation for the first generation was as follows: f⁽¹⁾ = ?3.2588‐6.2700x₁ + 1.2870x₂ + 0.7920x₃ + 0.4152x₄; f⁽²⁾ = ?14.5215‐8.5710x₁ + 2.9790x₂ + 2.0280x₃ + 0.5031x₄; f⁽³⁾ = ?3.5264; f⁽⁴⁾ = ?66.8312‐12.5216x₁ + 5.1740x₂ + 4.7162x₃ + 0.6033x₄. And that the prediction accuracy for the first generation was 97.22%. Whilst this discriminant equation for the second generation was as follows: f⁽¹⁾ = ?3.536‐1.192x₅ + 1.338x₆ + 0.638x_7?0.025x₈; f⁽²⁾ = ?7.317‐1.337x₅ + 4.240x₆ + 1.010x_7?0.295x₈; f⁽³⁾ = ?16.488‐3.192x₅ + 4.955x₆ + 1.900x₇–0.411x₈; f⁽⁴⁾ = ?34.502‐4.184x₅ + 7.484x₆ + 2.583x₇–0.443x₈. The prediction accuracy for the second generation was 85.71%. Overall, our findings revealed that the Bayes discriminant analysis could screen out key factors to significantly improve the prediction accuracy of peak occurrence of Dendrolimus punctatus larvae.     

THE WAVELENGTH DEPENDENCE OF MASSIVE CAROTENE SYNTHESIS IN DUNALIELLA BARDAWIL (CHLOROPHYCEAE)1

Dunaliella bardawil Ben-Amotz & Avron accumulates high concentrations of β-carotene when grown under high light intensity. The β-carotene is composed mainly of 9-cis and all-trans β-carotene. Accumulation of β-carotene and an increase in the ratio of the 9-cis to the all-trans isomer are strongly dependent on the light intensity under which the algae are cultivated but are independent of light quality within the photosynthetically active radiation range. Cells grown under continuous red (>645 nm) or white light of 500 W·m^?2 reach a value of about 32 pg β-carotene·cell^?1 and a ratio of 9-cis to all-trans β-carotene of around 2, whereas cells grown under low red or white light intensity of 25 W·m^?2 contain about 3 pg·cell^?1 and a ratio of isomers of around 0.3.     

Distribution of small phytoflagellates along an Arctic fjord transect

Phytoflagellates < 10 μm substantially contribute to the abundance, biomass and primary production in polar waters, but information on the distribution of specific groups is scarce. We applied catalysed reporter deposition‐fluorescence in situ hybridization to investigate the distribution of total phytoflagellates and of eight specific groups along a 100 km transect west off Kongsfjorden (Spitsbergen) from 29 to 31 July 2010. Phytoflagellates contributed to > 75% of the depth‐integrated abundance and biomass of total eukaryotes < 10 μm at all stations. Their depth‐integrated abundance and biomass decreased along the transect from 1.5 × 10¹² cells m^?2 (6.6 × 10¹² pgC m^?2) at the outermost station to 1.7 × 10¹⁰ cells m^?2 (4.7 × 10¹⁰ pgC m^?2) at the innermost station. Chlorophytes contributed to the total abundance of phytoflagellates with a range from 13% to 87% (0.7–30.5 × 10³ cells ml^?1), and predominated in open waters. The contribution of haptophytes was < 1–38% (10–4500 cells ml^?1). The other groups represented < 10%. The temperature and salinity positively correlated with the total abundance of phytoflagellates, chlorophytes, haptophytes, bolidophytes and pelagophytes. Cryptophytes, pedinellids and pavlovophytes were negatively associated with the nutrient concentrations. The community composition of phytoflagellates changed along the transect, which could have implications on food web dynamics and biogeochemical cycles between the open ocean environment and Kongsfjorden investigated here.     

A critical evaluation of models for complex molecular dynamics: application of NMR studies of double- and single-stranded DNA

The nature of internal and overall motions in native (double-stranded) and denatured (single-stranded) DNA fragments 120–160 base pairs (bp) long is examined by molecular-dynamics modeling using ¹³C-nmr spin-relaxation data obtained over the frequency range of 37–125 MHz. The broad range of ¹³C frequencies is required to differentiate among various models. Relatively narrow linewidths, large nuclear Overhauser enhancements (NOEs), and short T₁ values all vary significantly with frequency and indicate the presence of rapid, restricted internal motions on the nanosecond time scale. For double-stranded DNA monomer fragments (147 bp, 24 Å diam at 32°C), the overall motion is that of an axially symmetric cylinder (τ_x = ～10^?6 s;τ_Z = ～1.8 × 10^?8s), which is in good agreement with values calculated from hydrodynamic theory (τ_x = ～1.8 × 10^?6 s; τ_Z = ～2.7 × 10^?8 s). The DNA internal motion can be modeled as restricted amplitude internal diffusion of individual C? H vectors of deoxyribose methine carbons C1′, C3′, and C4′, either with conic boundary conditions (τ_w = ～4 × 10^?9 s, θ_cone = ～21°) or as a bistable jump (τ_A = τ_B = ～2 × 10^?9 s, θ = ～15°). We discuss the critical role in molecular-dynamics modeling played by the angle (β) that individual C? H vectors make with the long axis of the DNA helix. Heat denaturation brings about increases in both the rate and amplitude of the internal motion (described by the wobble model with τ_W = ～0.2 × 10^?9 s, θ_cone = ～50°), and overall motion is affected by becoming essentially isotropic (τ_x = τ_Z = ～5 × 10^?8 s) for the single-stranded molecules. Since ¹³C-nmr data obtained at various DNA concentrations for C2′ of the deoxyribose ring is not described well by the above models, a new model incorporating an additional internal motion is proposed to take into account the rapid, extensive, and weakly coupled motion of C2′.     

The Negative Binomial Distribution of Order k and Some of Its Properties

The negative binomial distribution of order k is introduced and briefly studied. First it is shown that it is a proper probability distribution. Then its probability generating function, mean and variance are derived. Finally it is shown that the number of trials until the rth kth consecutive success (r ≧ 1, k ≧ 1) in independent trials with constant success probability p (0 < p < 1) is distributed as negative binomial distribution of order k. The present paper generalizes results of SHANE (1973), PHILIPPOU and MUWAFI (1982), and PHILIPPOU, GEORGHIOU and PHILIPPOU (1982).     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

Distribution, standing stock, growth, mortality and production of Strongylocentrotus pallidus (Echinodermata: Echinoidea) in the northern Barents Sea

The regular sea urchin, Strongylocentrotus pallidus (G.O. Sars, 1871), is a widespread epibenthic species in high-Arctic waters. However, little is known about its distribution, standing stock, population dynamics and production. In the northern Barents Sea, S. pallidus was recorded on seabed still photographs at 10 out of 11 stations in water depths of 80–360?m. Mean abundances along photographic transects of 150–300 m length ranged between <0.1 and 14.7?ind. m^?2 yielding a grand average of 3.6?ind.?m^?2. The small-scale distribution along the transects was patchy, with densities varying from nil to an overall maximum of 25.5 ind. m^?2, and exhibited a significant relation to the number of stones present. Sea urchin test diameters, measured on scaled photographs, extended from 7 to 90?mm. Median values at single stations varied from 14 to 46?mm, showing a significant inverse relationship to water depth. Biomass, estimated by combining photographic abundances, size frequencies and a size-mass function established with trawled specimens, ranged between <0.1 and 3.0?g ash-free dry mass m^?2, averaging about 1.0?g ash free dry mass m^?2. An analysis of skeletal growth bands in genital plates was carried out with 143 trawled individuals ranging in test diameter (D) from 4 to 48?mm. Assuming these bands to represent annual growth marks, the ages of the specimens analysed ranged between 3 and 42 years. A von Bertalanffy function was fitted to size-at-age data to model individual growth pattern (D_∞?=?102.3?mm, k?=?0.011 year^?1, t₀?=?0.633?year). The annual mortality rate Z of the population in the northern Barents Sea was estimated from a size-converted catch curve to be 0.08 year^?1. Applying the weight-specific growth rate method, the average P/B ratio and the mean annual production of this population were estimated as 0.07 year^?1 and 0.076?g AFDM m^?2 year^?1, respectively. In conclusion, S. pallidus is characterized by slow growth, low mortality, high longevity and low productivity. Because of its relatively high biomass, it is considered to contribute significantly to total benthic standing stock and carbon flux in the study area.