An Unbalanced Nested Model with Random Effects Having Unequal Variances

Consider the model Y_ijk=μ + a_i + b_ij + e_ijk (i=1, 2,…, t; j=1,2,…, B_i; k=1,2…,n_ij), where μ is a constant and a¹,b_ij and e_ijk are distributed independently and normally with zero means and variances σ²_ad_ij and σ², respectively, where it is assumed that the d_i's and d_ij's are known. In this paper procedures for estimating the variance components (σ², σ²_a and σ²_b) and for testing the hypothesis σ²_b = 0 and σ²_a = 0 are presented. In the last section the mixed model y_ijk, where x_ijkkm are known constants and β_m's are unknown fixed effects (m = 1, 2,…,p), is transformed to a fixed effect model with equal variances so that least squares theory can be used to draw inferences about the β_m's.     

Cube law, condition factor and weight–length relationships: history, meta-analysis and recommendations

This study presents a historical review, a meta‐analysis, and recommendations for users about weight–length relationships, condition factors and relative weight equations. The historical review traces the developments of the respective concepts. The meta‐analysis explores 3929 weight–length relationships of the type W = aL^b for 1773 species of fishes. It shows that 82% of the variance in a plot of log a over b can be explained by allometric versus isometric growth patterns and by different body shapes of the respective species. Across species median b = 3.03 is significantly larger than 3.0, thus indicating a tendency towards slightly positive‐allometric growth (increase in relative body thickness or plumpness) in most fishes. The expected range of 2.5 < b < 3.5 is confirmed. Mean estimates of b outside this range are often based on only one or two weight–length relationships per species. However, true cases of strong allometric growth do exist and three examples are given. Within species, a plot of log a vs b can be used to detect outliers in weight–length relationships. An equation to calculate mean condition factors from weight–length relationships is given as K_mean = 100aL^b?3. Relative weight W_rm = 100W/(a_mL^bm) can be used for comparing the condition of individuals across populations, where a_m is the geometric mean of a and b_m is the mean of b across all available weight–length relationships for a given species. Twelve recommendations for proper use and presentation of weight–length relationships, condition factors and relative weight are given.     

Different strategies of photoacclimation by two strains of Emiliania huxleyi (Haptophyta)1

Photoacclimation involves the modification of components of the light and dark reactions to optimize photosynthesis following changes in available light. All of the energy required for photosynthesis comes from linear electron transport through PSII and PSI and is dependent upon the amount of light harvested by PSII relative to PSI (a*_PSII and a*_PSI). The amount of light harvested is determined by the effective absorption cross‐sections (σ_PSII, σ_PSI) and cellular contents of the PSII and PSI reaction center complexes (RCII, RCI). Here, we examine the effective absorption cross‐sections and reaction center contents for calcifying (B11) and noncalcifying (B92) strains of the globally important coccolithophorid Emiliania huxleyi (Lohmann) W. H. Hay et H. Mohler when grown under various photon flux densities (PFDs). The two strains displayed different “strategies” of acclimation. As growth PFD increased, B11 preferentially changed σ and the cellular content of chl a per cell over PSU “size” (the total cellular chl a content associated with the reaction center complexes); strain B92 preferentially changed PSU size over the cellular content of reaction complexes. Neither strategy was specifically consistent with the majority of previous studies from other microalgal species. For both strains, cellular light absorption for PSII and PSI was maintained close to unity across the range of growth PFDs since changes of σ_PSII and σ_PSI were reciprocated by those of RCIIs and RCIs per cell. Our results demonstrate a significant adaptive flexibility of E. huxleyi to photoacclimate. Finally, we calculated the amount of chl a associated with either photosystem to consider our interpretations of photoacclimation based on conventional determinations of PSU size.     

Synthesis and binding assays of novel 3,3-dimethylpiperidine derivatives with various lipophilicities as σ1 receptor ligands

Starting from two carbocyclic analogs, a series of 3,3-dimethylpiperidine derivatives was prepared and tested in radioligand binding assays at σ₁ and σ₂ receptors, and at Δ₈–Δ₇ sterol isomerase (SI) site. The novel compounds mostly bear heterocyclic rings or bicyclic nucleus of differing lipophilicities. Compounds 18a and 19a,b demonstrated the highest σ₁ affinity (K_i = 0.14–0.38 nM) with a good selectivity versus σ₂ binding. Among them, 18a had the lowest C log D value (3.01) and only 19b was selective versus SI too. Generally, it was observed that more planar and hydrophilic heteronuclei conferred a decrease in affinity for both σ receptor subtypes.     

Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

PHOTOPHYSIOLOGICAL EVIDENCE OF NUTRIENT LIMITATION OF PLATELET ICE ALGAE IN MCMURDO SOUND, ANTARCTICA

Seasonally changing photophysiological and biochemical characteristics of sea ice microalgae are interpreted with respect to light availability and measurements of nutrient concentration made at high vertical resolution (12.5 cm) during a dense bloom in the platelet ice layer of McMurdo Sound during a 6-week study in austral spring of 1989. Platelet ice algae remained highly shade adapted throughout the spring as shown by their low photoadaptive index (E_k, 3.7–8.4 μmol photons·m⁻²·s⁻¹), low mean specific absorption coefficient (<0.009 m² mg⁻¹ Chl a), high optical cross-sectional area of photosystem II (σ_PSII, 3.0–8.2), and high molar ratio of fucoxanthin:chlorophyll a (mean = 1.62 ± 0.15 SD). Between 24 October and 8 November, the algae exhibited a photoacclimative response that was marked by a 30% decrease in photosynthetic efficiency (α^B), a 75% decrease in maximum photosynthetic rate (P^B/_m), and a 60% increase in σ_PSII. The photochemical conversion efficiency at photosystem II (F_v/F_m= ca. 0.5) and the quantum yield of photosynthesis (Ø_C= 0.062– 0.078 mol C mol⁻¹ photons) were ca. 80% of their maximal values. After 8 November, changes in algal photophysiology and biochemistry, which were inconsistent with a photoacclimation response, suggest that the platelet ice algae near the platelet/congelation ice interface became increasingly nutrient limited. The number of pennate diatoms increased threefold to 150 × 10⁹ cells m⁻³ between 8 and 14 November, then remained unchanged throughout the remainder of the field season. Following the increase in cell number, F_v/F_m, Ø_C, and C:Chla decreased by >40%, σ_PSII increased by 70%; and the biochemical ratios C:N and C:Si increased 25%–30%. Nutrient depletion was apparent from the high-resolution vertical profiles, but nutrient concentrations limiting algal growth were not observed. However, nutrient concentrations at the likely site of nutrient limitation near the platelet/congelation ice interface were not measured, indicating that higher resolution sampling is necessary to fully characterize this highly variable habitat.     

Alternate promoters direct stress-induced transcription of the Bacillus subtilis clpC operon

clpC ofBacillus subtilis is part of an operon containing six genes. Northern blot analysis suggested that all genes are co-transcribed and encode stress-inducible proteins. Two promoters (P_A and P_B) were mapped upstream of the first gene. P_A resembles promoters recognized by the vegetative RNA polymerase Eσ^A. The other promoter (P_B) was shown to be dependent on σ^B, the general stress σ factor in B. subtilis, suggesting that clpC, a potential chaperone, is expressed in a σ^B-dependent manner. This is the first evidence that σ^B in B, subtilis is involved in controlling the expression of a gene whose counterpart, clpB, is subject to regulation by σ³² in Escherichia coli, indicating a new function of σ^B-dependent general stress proteins. P_B deviated from the consensus sequence of σ^B promoters and was only slightly induced by starvation conditions. Nevertheless, strong induction by heat, ethanol, and salt stress occurred at the σ^B-dependent promoter, whereas the vegetative promoter was only weakly induced under these conditions. However, in a sigB mutant, the σ^A-like promoter became inducible by heat and ethanol stress, completely compensating for sigB deficiency. Only the downstream σ^A-like promoter was induced by certain stress conditions such as hydrogen peroxide or puromycin. These results suggest that novel stress-induction mechanisms are acting at a vegetative promoter. Involvement of additional elements in this mode of induction are discussed.     

Xylem and cell turgor pressure probe measurements in intact roots of glycophytes: transpiration induces a change in the radial and cellular reflection coefficients

Xylem probe measurements in the roots of intact plants of wheat and barley revealed that the xylem pressure decreased rapidly when the roots were subjected to osmotic stress (NaCl or sucrose). The magnitude of the xylem pressure response and, in turn, that of the radial reflection coefficients (σ_r) depended on the transpiration rate. Under very low transpiration conditions (darkness and high relative humidity), σ_r assumed values of the order of about 0·2–0·4. The σ_r values of excised roots were also found to be rather low, in agreement with data obtained using the root pressure probe of Steudle. For transpiring plants (light intensities at least 10 μmol m^?2 s^?1; relative humidity 20–40%) the response was nearly 1:1, corresponding to radial reflection coefficients of σ_r= 1. Further increase of the light intensity to about 400 μmol m^?2 s^?1 resulted in a slight but significant decrease of the σ_r values to about 0·8. Similar measurements on maize roots confirmed our previous results (Zhu et al. 1995, Plant, Cell and Environment 18, 906–912) that, in intact transpiring plants at low light intensities of about 10 μmol m^?2 s^?1 and at relative humidities of 20–40% as well as in excised roots, the xylem pressure response was much less than expected from the external osmotic pressure (σ_r values 0·3–0·5). In contrast to wheat and barley, very high light intensities (about 700 μmol m^?2 s^?1) were needed to shift the radial reflection coefficients of maize roots to values of about 0·9. Osmotically induced xylem pressure changes were apparently linked to changes in turgor pressure in the root cortical parenchyma cells, as shown by simultaneous measurements of xylem and cell turgor pressure. In analogy to the σ_r values of the respective glycophytes, the σ_c values of the root cortical cells of wheat and barley were close to unity, whereas σ_c for maize was significantly smaller (about 0·7) under laboratory conditions. When the light intensity was increased up to about 700 μmol m^?2 s^?1 the cellular reflection coefficient of maize roots increased to about 0·95. In contrast to the σ_r values, the σ_c values of the three species investigated remained almost unchanged when the leaves were exposed to darkness and humidified air or when the roots were cut. The transpiration-dependent (species-specific) pattern of the cellular and radial reflection coefficients of the root compartment of the three glycophytes apparently resulted from (flow-dependent) concentration-polarization and sweep-away effects in the roots of intact plants. The data could be explained straightforwardly terms of theoretical considerations outlined previously by Dainty (1985, Acta Horticulturae 171, 21–31). The far-reaching consequences of this finding for root pressure probe measurements on excised roots, for the occurrence of pressure gradients under transpiring conditions, and for the non-linear flow-force relationships in roots found by other investigators are discussed.     

Differential Modulation by Cations of Sigma and Phencyclidine Binding Sites in Rat Brain

Abstract

The present investigation attempted to differentiate haloperidol-sensitive sigma sites (σ_H) from phencyclidine (PCP) binding sites in rat brain membranes. We studied the effects of several cations at physiologically relevant concentrations on the binding of radioligands selective for σ_H sites ([³H]haloperidol, [³H](+)3-PPP**), and [³H](+)SKF10,047), or for PCP sites ([³H]PCP and [³H]TCP). The PCP sites displayed a markedly greater sensitivity to cations than σ_H sites. This property was reflected by a greater extent of inhibition of the binding of PCP-selective relative to σ_H-selective ligands at a given cation concentration, as well as by lower IC₅₀'s and by steeper slopes of the cation dose-response curves. Divalent cations were approximately 100 times more potent than monovalent cations. All cations were inhibitory, except Sr²⁺ and Ba²⁺ which, at micromolar concentrations, enhanced PCP binding but not σs_H binding. Thus, PCP-selective sites appeared to be distinct from σ_H sites with regards to several aspects of cation modulation. This is consistent with the view that PCP and σ_H sites are distinct molecular entities. Further, the marked cation sensitivity of the PCP site is consistent with the current hypothesis according to which the PCP site is linked to the N-methyl-D-aspartate (NMDA) receptor-cation channel complex.     

An Unbalanced Mixed Model with Random Effects Having Unequal Variances

Consider the mixed model where x_ijk's are known constants, β_k are unknown parameters and a_i, e_ij are random variables independently and normally distributed with zero means and variances σd_i and σ² respectively, where it is assumed that the d_i's are known (d_i >0). This paper presents procedures for estimating the variance components σ, σ², for testing the hypothesis σ = 0, and for making transformations to random variables with uncorrelated errors and constant variances in order to estimate as well as to test hypothesis concerning the β_k's in the model.     

Effect of torpor on the water economy of an arid-zone marsupial,the stripe-faced dunnart (<Emphasis Type="Italic">Sminthopsis macroura</Emphasis>)

Metabolic rate and evaporative water loss (EWL) were measured for a small, arid-zone marsupial, the stripe-faced dunnart (Sminthopsis macroura), when normothermic and torpid. Metabolic rate increased linearly with decreasing ambient temperature (T_a) for normothermic dunnarts, and calculated metabolic water production (MWP) ranged from 0.85±0.05 (T_a=30°C) to 3.13±0.22 mg H₂O g^–1 h^–1 (T_a=11°C). Torpor at T_a=11 and 16°C reduced MWP to 24–36% of normothermic values. EWL increased with decreasing T_a, and ranged from 1.81±0.37 (T_a=30°C) to 5.26±0.86 mg H₂O g^–1 h^–1 (T_a=11°C). Torpor significantly reduced absolute EWL to 23.5–42.3% of normothermic values, resulting in absolute water savings of 50–55 mg H₂O h^–1. The relative water economy (EWL/MWP) of the dunnarts was unfavourable, remaining >1 at all T_a investigated, and did not improve with torpor. Thus torpor in stripe-faced dunnarts results in absolute, but not relative, water savings.     

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.     

A cohesion/tension model for the gating of aquaporins allows estimation of water channel pore volumes in Chara

The water permeability (hydraulic conductivity; Lp) of turgid, intact internodes of Chara corallina decreased exponentially as the concentration of osmolytes applied in the medium increased. Membranes were permeable to osmolytes and therefore they could be applied on both sides of the plasma membrane at concentrations of up to 2.0 m (5.0 MPa of osmotic pressure). Organic solutes of different molecular size (molecular weight, MW) and reflection coefficients (σ_s) were used [heavy water HDO, MW: 19, σ_s: 0.004; acetone, MW: 58, σ_s: 0.15; dimethyl formamide (DMF), MW: 73, σ_s: 0.76; ethylene glycol monomethyl ether (EGMME), MW: 76, σ_s: 0.59; diethylene glycol monomethyl ether (DEGMME), MW: 120, σ_s: 0.78 and triethylene glycol monoethyl ether (TEGMEE), MW: 178, σ_s: 0.80]. The larger the molecular size of the osmolyte, the more efficient it was in reducing cell Lp at a given concentration. The residual cell Lp decreased with increasing size of osmolytes. The findings are in agreement with a cohesion/tension model of the osmotic dehydration of water channels (aquaporins; AQPs), which predicts both reversible exponential dehydration curves and the dependence on the size of osmolytes which are more or less excluded from AQPs (Ye, Wiera & Steudle, Journal of Experimental Botany 55, 449–461, 2004). In the presence of big osmolytes, dehydration curves were best described by the sum of two exponentials (as predicted from the theory in the presence of two different types of AQPs with differing pore diameters and volumes). AQPs with big diameters could not be closed in the presence of osmolytes of small molecular size, even at very high concentrations. The cohesion/tension theory allowed pore volumes of AQPs to be evaluated, which was 2.3 ± 0.2 nm³ for the narrow pore and between 5.5 ± 0.8 and 6.1 ± 0.8 nm³ for the wider pores. The existence of different types of pores was also evident from differences in the residual Lp. Alternatively, pore volumes were estimated from ratios between osmotic (P_f) and diffusional (P_d) water flow, yielding the number of water molecules (N) in the pores. N-values ranged between 35 and 60, which referred to volumes of 0.51 and 0.88 nm³/pore. Values of pore volumes obtained by either method were bigger than those reported in the literature for other AQPs. Absolute values of pore volumes and differences obtained by the two methods are discussed in terms of an inclusion of mouth parts of AQPs during osmotic dehydration. It is concluded that the mouth part contributed to the absolute values of pore volumes depending on the size of osmolytes. However, this can not explain the finding of the existence of two different types or groups of AQPs in the plasma membrane of Chara.     

Optical characteristics of the harmful dinoflagellate Alexandrium tamarense in response to different nitrogen sources

The chlorophyll a specific absorption coefficient a_ph^* and absorption ratio (a_ph ratio) of Alexandrium tamarense at five concentrations of nitrate, ammonium and urea over a range from 6 to 100 μM were examined. The experimental results were compared to two coastal diatom species and a prymnesiophyte to identify differences in absorption ratios. Cells exposed to increasing nitrate concentrations were characterized by an increase in a_ph^* at 443, 490, 510, 555 and 675 nm. However, ammonium and urea induced low a_ph^* values at their lowest and highest concentrations. The a_ph relative to 510 or 555 nm was constant regardless of the concentration of the N source, but dependent on the N source. Oxidized N induced a lower a_ph ratio than the reduced form. Comparisons of the a_ph ratio among taxonomic groups revealed significant differences. The a_ph ratio of A. tamarense was 20–30 and >50% lower than those of two diatoms and a prymnesiophyte, respectively. The a_ph ratio of the present study could assist in increasing the capability for detecting harmful species such as A. tamarense.     

Estimation of a Conditional Mean in a Linear Regression Model

Consider the two linear regression models of Y_ij on X_ij, namely Y_ij = β_io + β_il X_ij + ε_ij,j = 1,2,…,n_i, i = 1,2, where ε_ij are assumed to be normally distributed with zero mean and common unknown variance σ². The estimated value of a mean of Y₁ for a given value of X₁ is made to depend on a preliminary test of significance of the hypothesis β₁₁ = β₂₁. The bias and the mean square error of the estimator for the conditional mean of Y₁ are given. The relative efficiency of the estimator to the usual estimator is computed and is used to determine a proper choice of the significance level of the preliminary test.     

Estimation of Finite Population Variance Using Ratio and Product Methods of Estimation

For estimating finite population variance σ_y² of a character y under our study, estimators using auxiliary information on a character x in the form of ratio, product, ratio-type or product-type estimators have been suggested, and their comparative study with the conventional unbiased estimator s_y² of σ_y² has been made in simple random sampling with replacement. A generalized estimator representing a class of estimators for the finite populations variance, has also been studied.     

A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments

A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk, v=p²k, …, treatments, for k≥p, in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k+1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p_s being the smallest prime factor of n, p_s + 1 for v = n², p_s²+ p_s + 1 for v = n³, …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero-one concurrence design. Procedures are described for obtaining additional zero-one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra-block and inter-block analyses are described.