Integrated likelihood functions for non-Bayesian inference

Consider a model with parameter = (, ), where is the parameterof interest, and let L(, ) denote the likelihood function. Oneapproach to likelihood inference for is to use an integratedlikelihood function, in which is eliminated from L(, ) by integratingwith respect to a density function (|). The goal of this paperis to consider the problem of selecting (|) so that the resultingintegrated likelihood function is useful for non-Bayesian likelihoodinference. The desirable properties of an integrated likelihoodfunction are analyzed and these suggest that (|) should be chosenby finding a nuisance parameter that is unrelated to and thentaking the prior density for to be independent of . Such anunrelated parameter is constructed and the resulting integratedlikelihood is shown to be closely related to the modified profilelikelihood.     

'Nonparametric inference in multivariate mixtures' * Biometrika (2005), 92, pp. 667 678

The left-hand side of equation (2·8), on p. 671, shouldread {₁ (1 – ₁)}^–1/2 (2₁ – 1) rather than{(1 – ₁)/₁}^1/2 (2₁ – 1). Reflecting this change,the left-hand side of equation (3·1) on the same pageshould be altered to , and the formula at the foot of p. 677 should be modified to {₁ (1– ₁)}^–1/2 (2₁ – 1) + O_p(n^–1/2). No otherformula is affected, and the left-hand side of (2·8)is still increasing in ₁. The numerical results, discussed in4, are influenced in minor ways. In the simulation study, absolutebias is reduced, and variance is either slightly increased orslightly decreased. In the real-data example, using the nonparametricapproach to analysis, mean squared error is further reduced,from 0·0011 to 0·0004. We are grateful to HiroKasahara and Katsumi Shimotsu for pointing out the error.     

Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models

We develop a proposal or importance density for state spacemodels with a nonlinear non-Gaussian observation vector y p(y¦)and an unobserved linear Gaussian signal vector p(). The proposaldensity is obtained from the Laplace approximation of the smoothingdensity p(¦y). We present efficient algorithms to calculatethe mode of p(¦y) and to sample from the proposal density.The samples can be used for importance sampling and Markov chainMonte Carlo methods. The new results allow the application ofthese methods to state space models where the observation densityp(y¦) is not log-concave. Additional results are presentedthat lead to computationally efficient implementations. We illustratethe methods for the stochastic volatility model with leverage.     

Weighted finite population sampling to maximize entropy

Attention is drawn to a method of sampling a finite populationof N units with unequal probabilities and without replacement.The method was originally proposed by Stern & Cover (1989)as a model for lotteries. The method can be characterized asmaximizing entropy given coverage probabilities _i, or equivalentlyas having the probability of a selected sample proportionalto the product of a set of ‘weights’ w_i. We showthe essential uniqueness of the w_i given the _i. We present twomethods for stepwise selection of sampling units, and correspondingschemes for removal of units that can be used in connectionwith sample rotation. Inclusion probabilities of any order canbe written explicitly in closed form. Second-order inclusionprobabilities _ij satisfy the condition O < _ij < _ij, whichguarantees Yates & Grundy‘s variance estimator tobe unbiased, definable for all samples and always nonnegativefor any sample size.     

Alternative Methods of Analysing Water Potential Isotherms: Some Cautions and Clarifications: I. THE IMPACT OF NON-IDEALITY AND OF SOME EXPERIMENTAL ERRORS

In recent years alternative ways have been proposed to transformmeasurements of leaf water potential, , and relative water content,R^*, in order to derive values of osmotic pressure at full turgidityin leaves and shoots, ^o(when 0). Two types of transformationsare usually considered: 1/ versus R^* and versus 1/R^*, and linearregression is used to fit the data in the region where turgoris thought to be zero. It appears that when ^o is estimated bylinear extrapolation of 1/Psi; versus R^* then apoplastic watermight not influence the accuracy of ^o but when the versus \/R^*transformation is used apoplastic water causes an underestimateof ^o. We examine the accuracy of the estimate of ^o obtainedfrom the two transformations when there are random errors in, systematic errors in , and when the osmotic solutions arenon-ideal. The 1/ versus R^* transformation generally producesthe best estimate of ⁰ by linear extrapolation.     

Water-Relations Parameters of the Phloem. Determinations of Volumetric Elastic Modulus and Membrane Conductivity using an Applied Force Method and Shrinkage and Swelling of Tissues in Solutions at Differing Osmotic Pressure

Water-relations parameters were measured on sections of secondaryphloem from red oak (Quercus borealis michx. f.) and white ash(Fraxinus americana var. biltmoreana [Beadle] J. Wright) usinga linear displacement transducer. Changes in tissue thicknessin response to changes in the osmotic pressure of the bathingsolution were used to calculate the volumetric elastic modulusplus osmotic pressure (_v + ) of the tissue, and an applied forcemethod was used to estimate the time constant for water equilibration(T). The hydraulic conductivity of the cell membranes (L_p) wascalculated utilizing _v + and r values. The time-dependent behaviour of the tissue was much more complexthan originally expected. A correction for a time-dependentprocess that we call ‘drift’ was required to obtainnumbers for _v + . Furthermore, _v + was calculated on two assumptionsin order to relate changes in tissue dimensions to sieve elementparameters. In the first case, a lower limit for _v + of thesieve elements was determined by attributing all changes intissue dimensions to these cells. For red oak the average _v+ on this assumption is 72 bars. Assuming that all cell typeswere equally responsible for the changes in tissue dimensionsresulted in an _v + value of 192 bars for oak. If _v + and rare the same for all cells in the tissue, L_p for the sieve elementsof oak is 9.6 x 10^–8 cm s^–1 bar^–1. Exudationfrom the sieve elements of white ash during excision of thephloem led to artificially high values of _v + for that species. Quercus borealis michx. f., Fraxinus americana var, biltmoreana (Beadle) J. Wright, red oak, white ash, water relations, phloem, volumetric elastic modulus, membrane hydraulic conductivity     

An NTP-Binding Protein That Cross with a Ras-Specific Antibody in the Myceia of Neurospora crassa

A Ras-related NTP-binding protein was partially purified froma membrane fraction derived from the mycelia of Neurospora crassa.[-³²P]ATP and [-³²P]GTP were incubated with mem brane and solublefractions which were then irradiated with UV light to inducecrosslinking of tightly bound nucleotides. After SDS-polyacrylamidegel electrophoresis, blotting onto a nitrocellulose filter andautoradiography it was apparent that most of the proteins thatbound [-³²P]-GTP also bound [-³²P]ATP. Pretreatment of the membranefraction with Ras-specific antibody effectively blocked thebinding of [-³²P]ATP and [-³²P]GTP to several ATP-GTP-bindingproteins. The band of a protein with a molecular weight of 26kDa on the SDS-polyacrylamide gel cross-reacted strongly withthe Ras-specific antibody. The protein was extracted from thegel and further purified by repeated gel electrophoresis. Thepurified protein bound [-³²P]ATP, [-³²P]-GTP, [-³²P]CTP and[-³²P]UTP at 1.6x10^– M and was autophosphorylated in thepresence of [-³²P]ATP and [-³²P]GTP at 1.7x10 M. Pretreatmentof the protein with Ras-specific antibody partially blockedthe autophosphorylation in the presence of these nucleotides.The binding of [-³²P]ATP to the NTP-binding protein was blockedby addition of ATP at 10^–4–10^–3 M. ATP ata concentration of 10^–4 M prevented the binding of [-³²P]to a greater extent than did GTP at the same concentration.Binding of [-³²P]CTP and [-³²P]UTP to the protein was also observed. (Received October 7, 1991; Accepted July 14, 1992)     

Adaptation of the Euryhaline Charophyte Lamprothamnium papulosum to Brackish and Freshwater: Turgor Pressure and Vacuolar Solute Concentrations During Steady-State Culture and After Hypo-osmotic Treatment

The euryhaline charophyte Lamprothamnium papulosum (Wallr.)J. Gr. was adapted to media with decreasing salinities rangingfrom 550 to 0 mosmol kg^–1. Vegetative plants grown inmedia with osmotic pressures (⁰) in the range of 550 to 130mosmol kg^–1 maintained a constant turgor pressure () at309 + 7 mosmol kg^–1. The ions K+, Na+ and Cl–, werethe predominant solutes in the vacuole. Changes in their concentrationsaccount for the variation in internal osmotic pressure (¹) with,⁰. The divalent ions Mg²⁺, Ca²⁺ and were also present in significant amounts, but their concentrationsdid not alter with changes in, ⁰. In cells subjected to hypo-osmotic shock the regulation of was incomplete. The turgor pressure increased from 302 to 383mosmol kg^–1. The first rapid response to the sudden decreasein ⁰ was a loss of K⁺ and Cl^–. In contrast to the decreasein ionic concentrations an accumulation of sucrose occurredwhich could account for the increase of . The increase in sucroseconcentration started 24 to 48 h after the downshock and reachedits highest value after 3 to 4 weeks. The sucrose concentrationin the vacuole was up to 320 mol m^–3. During this timethe ionic content continued to decrease but did not counterbalancethe sucrose concentration sufficiently to regain the original. High sucrose levels accompanied by an enhanced were also observedduring the period of fructification (sexual reproduction: formationof antheridia and oogonia) in Lamprothamnium kept under conditionsof constant salinity. It is concluded that high sucrose content and elevated arecharacteristic of sexual reproduction in this charophyte. Lamprothamniumis able to tolerate different during various developmentalstages (e.g. vegetative and reproductive phases). Key words: Lamprothamnium papulosum, sucrose, turgor pressure     

A Transient Stimulation of Net Photosynthesis of Rye Leaves by {alpha}-Hydroxy-2-pyridinemethanesulphonic Acid ({alpha}-HPMS) due to Inhibition of Photorespiratory CO2 Release

The effects of -hydroxy-2-pyridinemethanesulphonic acid (-HPMS)upon net photosynthesis (P_n, the CO₂ compensation point (),post-lower illumination burst of CO₂ (PLIB) and post-lower temperatureburst of CO₂ (PLTB) in detached rye (Secale cereale L.) leaveswere investigated. At low concentrations ( 0.5 mol m^–3),-HPMS initially stimulated P_n and decreased the magnitude ofboth PLIB and PLTB. The decreased at all concentrations of-HPMS (0.05–5.0 mol m^–3. The effects of -HPMS onP_n and were time-dependent and, after a few minutes, the P_nwas inhibited while values increased considerably. At a higherconcentration (5.0 mol m ^–3), the transient effects of-HPMS were shorter () or not observed at all (P_n. Both PLIBand PLTB, when expressed in relation to P_n, increased at higherlevels of this compound. Similar data with respect to the effectsof -HPMS on PLIB and PLTB were found for leaves of dandelion(Taraxacum officinale L.). The results suggest that -HPMS may stimulate P_n by inhibitingphotorespiration, as originally suggested by Zelitch (1966),but only at low concentrations and over a short time span. Thedecrease of PLIB and PLTB values at low -HPMS levels is consistentwith these processes being a residual activity of the glycolatepathway. Key words: CO₂ compensation point, -hydroxy-2-pyridinemethanesulphonic acid, photorespiration, photosynthesis     

Isolation of Subunits of Coupling Factor 1 from Maize and Spinach Chloroplasts and Properties of Combinations of Subunits with ATPase Activity

Subunits (, ß, ) and mixtures of subunits ( ß, , ß , ß ) were isolated without denaturationfrom a chloroform extract of chloroplast coupling factor 1 (CF₁)from maize (Zea mays var. Ushiku 5-4) and from spinach by fastprotein liquid chromatography (FPLC), on an anion-exchange columnof Mono-Q in the presence of n-octylglucoside (OG) and on achromatofocusing column of Mono-P. The ß -subunitcomplex (CF¹ ß ) was the minimum unit required forATPase activity, as was confirmed by the reconstituted complexof ß and subunits. An subunit isolated from maizeinhibited the ATPase activity of CF₁ ß from bothmaize and spinach. CF₁ ß was found to contain anOG-dependent Mg²⁺-ATPase. The ATPase activity of CF₁ ß required divalent cations, such as Mg²⁺ or Mn²⁺, for its expressionin the presence of OG; its optimum pH was 8.0 and it was markedlyinhibited by NaN₃. The enzyme hydrolyzed ATP in prefernece toGTP but not CTP, UTP, ADP, AMP or pNPP. Lineweaver-Burk plotsof its activity were curvilinear in the range of 0.6–0.7mM ATP.Mg²⁺. ¹Present address: Department of Biology, School of Education,Waseda University, Shinjuku-ku, Tokyo, 160 Japan. (Received February 15, 1989; Accepted April 20, 1989)     

Characterization of Spring Wheat Genotypes Differing in Drought-Induced Abscisic Acid Accumulation: II. LEAF WATER RELATIONS

Aspects of the water relations of spring wheat (Triticum aestivumL.) are described for cultivars Highbury (low ABA) and TW269/9(high ABA), and low and high ABA accumulating F⁶selections derivedfrom a cross between them. In a pot experiment, pressure-volume (P-V) curves were constructedfor main stem leaf four (MSL4) of well-watered plants of Highburyand TW269/9. Estimates of solute potential (²) from these curveswere similar for the two cultivars, but varied with the timeof sampling and the time allowed for hydration in dim light. In a field experiment with four low and four high ABA F⁶lines,P-V curves for flag leaves from both droughted and irrigatedplants gave at both zero turgor (^p) and zero water potential(¹) which differed with degree of stress, sampling time andgenotype. ¹was strongly dependent on the initial_L of the leafand was reduced on average by c. 0.4 MPa per MPa decline ininitial L.5, was lower (more negative) by c. 0.1-MPa in theafternoon than in the morning. Overall, was also 0.1 MPa lowerin low ABA lines than in high ABA lines. In another field experiment, flag leaves of five low and fivehigh ABA F⁶lines were sampled over a 4 week period from droughtedplots and _L and 5, measured (the latter by osmometry with expressedsap). For these leaves 5, at zero p or zero _L was consistentlylower by 0.3–0.5 MPa than estimates of 5, from the P-Vcurves with flag leaves. However, data for the low ABA lineswere again lower (by c. 0.1 MPa) than those for high ABA lines. The consequences of these differences in 1 are discussed inrelation to the stimulation of ABA accumulation in low and highABA selections. Key words: Water potential, Solute potential, P-V curves, Wheat (Triticum aestivum), Drought stress     

Semiparametric model-based inference in the presence of missing responses

We consider a semiparametric model that parameterizes the conditionaldensity of the response, given covariates, but allows the marginaldistribution of the covariates to be completely arbitrary. Responsesmay be missing. A likelihood-based imputation estimator anda semi-empirical-likelihood-based estimator for the parametervector describing the conditional density are defined and provedto be asymptotically normal. Semi-empirical loglikelihood functionsfor the parameter vector and the response mean are derived.It is shown that the two semi-empirical loglikelihood functionsare distributed asymptotically as weighted ² and scaled ², respectively.     

The influence of temperature and light on the upper limit of Microcystis aeruginosa production in a hypertrophic reservoir

Primary production was measured for 7 years, using the in situ¹⁴C-method in hypertrophic Hartbeespoort Dam, South Africa,to examine the influence of light and water temperature on theupper limit of Microcystis aeruginosa production. Water temperaturesvaried from 11 to >25°C and chlorophyll concentrationsreached 6500 mg m^–3. The maximum volumetric rate of production(A_max) was 12->8800 mg C m^–3 h^–1 with areal productions(A) of 69->3300 mg C m^–2 h^–1 for euphotic zonedepths of <0.5–8.4 m. The intrinsic parameters of phytoplanktonproduction (, A_max/B, I_k) indicated that the phytoplankton populationwas adapted to high light levels. Both A_max/B and I_k were correlatedwith temperature. Under optimal conditions, , the theoreticalupper limit of A, was calculated to be 2.8 g Cm^–2 h^–1,while the measured rate was 2.5 g Cm^–2 h^–1. Measuredareal rates exceeding were overestimated due to methodologicalproblems when working with Microcystis scums. Light and watertemperature interacted to yield high production rates: watertemperature through its direct effect on photosynthetic ratesand indirectly in the formation of diurnal mixed layers; lightindirectly through water temperature and directly through itsattenuation and induction of light-adapted physiology in Microcystis.     

{delta}15N and {delta}13C Measurements of Antarctic Peninsula Fauna: Trophic Relationships and Assimilation of Benthic Seaweeds

Measurements of ¹³C, ¹⁵N, and C/N for a variety of Antarcticpeninsula fauna and flora were used to quantify the importanceof benthic brown algae to resident organisms and determine foodweb relationships among this diverse littoral fauna. ¹³C valuesranged from–16.8 for benthic algal herbivores (limpets)to –29.8 for the krill, Euphausia superba; the averagepooled value for brown macroalgae, including their attachedfilamentous diatoms, was–20.6. There was no correlationbetween biomass ¹³C or ¹⁵N with C/N content, and consequentlyboth ¹³C and ¹⁵N values were useful in evaluating trophic relationships.¹⁵N values of the fauna ranged from 3.1 to 12.5, with lowestvalues recorded in suspension feeders (e.g., bryozoans) andhighest values in Adelie penguins (12.5) collected in 1989.The comparatively lower ¹⁵N value for a Chinstrap penguin (6.9)collected in 1997 is attributed to the different dietary foodsources consumed by these species as reflected in their respective¹³C values. Significant amounts of benthic macroalgal carbonis incorporated into the tissues of invertebrates and fishesthat occupy up to four trophic levels. For many benthic andepibenthic species, including various crustaceans and molluscs,assimilation of benthic algal carbon through detrital pathwaysranges from 30 to 100%. Consequently, the trophic importanceof benthic brown algae may well extend to many pelagic organismsthat are key prey species for birds, fishes, and marine mammals.These data support the hypothesis that benthic seaweeeds, togetherwith their associated epiphytic diatoms, provide an importantcarbon source that is readily incorporated into Antarctic peninsulafood webs.     

Factors controlling primary production in a hypertrophic lake (Hartbeespoort Dam, South Africa)

The physical factors controlling algal primary production weredemonstrated from data collected for a hypertrophic lake. A_maxranged between 12.4 and 5916 mg C m^–3 h^–1. Arealrates (A) varied between 46.9 and 3381 mg C m^–2 h^–1.The factors permitting and controlling production were subjectivelyseparated into two categories. In category 1, nutrients (N +P), which were in overabundance, permitted large standing cropsof Microcystis aeruginosa to develop (>1000 µg chla 1^–1). Wind patterns determined the dramatic spatialand temporal changes in algal standing crop which could dropto 2.7 µg chl a 1^–1. In category 2 were the factorswhich affected the rate processes. The buoyancy mechanism ofMicrocystis usually kept the alga in the euphotic zone. A powerrelationship (r = 0.92, n = 54) between A and A_max/_min showedthat with increasing phytoplankton vertical stratification,A_max was increasingly important in the integral. The saturationparameter I_K and photosynthetic capacity were temperature dependent.Variations of A were significantly related to changes in watercolumn stability (g cm cm^–2) because both axes of thephotosynthesis depth-profile were affected by stability changes.     

Natural Abundance of {delta}15N Confirms Insectivorous Habit ofRoridula gorgonias, Despite it Having No Proteolytic Enzymes

Natural abundance values of plant ¹⁵N give an indication asto the source of nitrogen. In particular, carnivorous plantsare expected to be relatively enriched due to trophic enrichmentof their prey. Values of ¹⁵N for adultRoridula gorgonias(mean+3.02)are 4–9 greater than co-occurring non-carnivorous plantspecies and 5.24 greater than juvenileR. gorgoniasplants. Theyare also 3.5–4.26 greater than co-occurringDroseraspecieswhich, being sundews, are considered to be carnivorous. Thesehigh levels of ¹⁵N in adult plants are best explained as beingdue to access to trophically enriched N from insects. As isthe case for other carnivorous plants, leaves and stems ofR.gorgoniasare highly ultraviolet reflective and are thereforeprobably attractive to potential insect prey. This is furthersupport for this plant species being insectivorous.Copyright1998 Annals of Botany Company Nitrogen isotopes, carnivorous plants, insectivorous plant, ultraviolet,Roridula gorgoniasL.     

Mechanisms of Inhibition of Water Movement in Anaerobically Treated Roots of Zea mays L.

Changes in water flux (Jv) across detopped, 7-d-old, maize rootswere characterized during the initial 24 h of being made anoxicby exposure to an anaerobic nutrient solution. Suction (50 kPa)was applied to the xylem and samples of the xylem sap were collectedat intervals and the osmolality and ionic content were measured. Values of Jv through anoxic roots fell below those of aerobiccontrols 1 h after the equilibrium oxygen partial pressure inthe bathing medium dropped below 20 kPa (air = 20.6 kPa). Thereduction in Jv was due primarily to a nullification of thediurnal rhythm in hydraulic conductivity (Lp) that was measuredin aerobic roots. However, about one-quarter of the reductionin Jv could be accounted for by a smaller osmotic componentof the driving force () on water movement. The significance of changes in Jv in anoxic roots is discussedin terms of the reliability of estimates of Lp, the reflectioncoefficient () and . Key words: Anaerobiosis, hydraulic conductivity, osmotic potential, water     

Osmotic Properties of Drought Stressed Periwinkle (Catharanthus roseus) Genotypes

The pressure-volume technique was employed to compare waterrelations and moisture stress-induced osmotic adjustment ofPeriwinkle (Catharanthus roseus) cv. Pink (PC), Oscillatus (REC)and White (WC). Leaf water potential (_w), osmotic potential(_s), turgor potential (_p), bulk modulus of elasticity (), boundwater (RWC_w) and leaf hydration (H), were estimated by exposingthe plants to a drying cycle during which well watered plantswere dehydrated to zero turgor, and then irrigated. Osmoticadjustment (_w ¹⁰⁰) was calculated by comparing _a at full hydration(_a ¹⁰⁰) in stressed plants after recovery, with _a ¹⁰⁰ in controlplants. Values of ₂¹⁰⁰ were 0.76, 0.33 and 0.11 MPa in cv. PC,REC and WC, respectively. Maintenance of _p at lower ₃ and relativeleaf water content (RWC) in prestressed PC was attributableto a higher alkaloid content and greater leaf cell wall elasticity.RWCW was plotted against _p to determine its contribution tohydration maintenance at lower _p. Genotype PC showed greaterRWC_w at lower _p compared with REC and WC. The present studyhas demonstrated that there are cultivar differences in alkaloidaccumulation and water relations in acclimated plants and thatthe relative ranking for drought resistance within periwinkleappeared to correspond with the changes in osmotic properties. Medicinal plant, drought resistance, alkaloids, periwinkle [Catharanthus roseus (L.) G. Don]     

Contractile Proteins of a Benthic Fish.I. Effects of Temperature and Pressure on Myosin ATPase.

SYNOPSIS. Studies are described on the adenosine triphosphatase(ATPase) properties of myosin isolated from skeletal muscleof Coryphaenoides, a benthic fish captured at 2,200 meters depth.Ca²⁺-ATPase and EDTA-ATPase of Coryphaenoides myosin show thesame pH dependence as ATPase of mammalian myosin; however, ratesof ATP hydrolysis by Coryphaenoides myosin are only 5–10%of rates of ATP hydrolysis by rabbit skeletal myosin. Coryphaenoidesmyosin ATPase shows a decrease from Q₁₀ of 2.0 at 25°C toQ₁₀ of 1.4 a t 2°C, and undergoes irreversible denaturationat temperatures above 25°C. At pH 6.8 to pH 8.5, Coryphaenoidesmyosin ATPase undergoes activation by pressure at 25°C,but at 2°C shows negligible effect of pressure at valuesbelow 3,000 psi. The kinetic data on Ca²⁺-ATPase indicate valuesof 11 kcal/mole for H, –7.5 kcal/mole for TS, and –5.7cc/mole for V at 25°C, pH 7.6. Comparable data at 2°Cindicate values of 5 kcal/mole for H. –13 kcal/mole forTS, and negligible V. According to the results of 25°C,Ca²⁺-activatkm of myosin-ATP may involve disruption of fouror five hydrophobic or polar groups, presumably due to an "opening-up"of the myosin molecule at or near the site for ATP binding.It would also appear that Coryphaenoides myosin has undergonean adaptive change in the enzyme mechanism for ATPase such thatthe rate of ATP hydrolysis is relatively insensitive to pressureand temperature under conditions encountered by the living fish.     

Analysis of Pressure-Volume Curves of Leaves of Rosa hybrida cv. Sonia

By analysing the relationship between inverse water potential(^–1), and relative water content (RWC) measured on leavesof roses (Rosa hybrida cv. Sonia), grown soilless, it was foundthat a non-linear (NL) model was better suited than a linearmodel to reproduce values observed in the non-turgid region.To explain this apparent curvature, it is assumed that a reductionof the non-osmotic water fraction (A_p) takes place when decreases.Osmotic potentials () measured on fresh and frozen leaf discstend to support this hypothesis. A method for exploiting PVcurves, which takes into account the variation of A_p, is described.It delivers values for the turgor pressure (_p), the relativeosmotic water content, and the mean bulk volumetric elasticitycoefficient, lower than those given by the linear model. Onthe other hand, it gives higher estimates for A_p and for . Whenapplying the traditional model to obtain estimates for waterrelations characteristics of rose leaves, and comparing resultsfrom two distinct salinity treatments (electrical conductivitiesof 1·8 mS cm^–1 and 3·8 mS cm^–1, respectively),one deduces a significant reduction of at turgor-loss in thehigh salinity treatment. The NL method is, in addition, ablesimultaneously to reveal a reduction of and a significant increasein _p at RWC=100% this proves that soilless–grown roseplants are able to osmoregulate when subjected to a constantand relatively high degree of salinity. Key words: Apoplastic water, non-linear regression, pressure-volume curves, tissue-water relations