Leaf Water Potential and Control of Water Loss in Droughted Sitka Spruce Seedlings

Sitka spruce seedlings were subjected to drought in experimentsin a growthroom, a greenhouse, and out of doors. The plantswere grown in a double chamber with the bulk of the roots inthe upper part where they dried out the soil when water waswithheld. A few new roots penetrated into the lower part inwhich the soil remained moist. The double chamber system enabledthe plant to attain a high water psotential by night and theshoot was only periodically under mild water stress. Measurementswere made on soil water potential (_solt), leaf water potential(₁), transpiration (E), and stomatal conductance (k_s). As soildecreased over a period of 4.5 d, E and k_s decreased progressively.The decline in E and k_s which indicated stomatal closure, occurredat a higher ₁ than has been reported for Sitka spruce. The behaviourof the stomata appeared to be modified by conditions at theroot, and it is proposed that differences in the response to₁,depend on Whether the latter is reduced by resistances in thexylem between root and leaf, as is known to occur in large treesin moist soil, or by stresses at the root itself.     

Critical Water Potential for Stomatal Closure in Sitka Spruce

Steady state rates of net photosynthesis and stomatal conductance at high water potentials were measured under controlled conditions in a leaf chamber on Sitka spruce [Picea sitchensis (Bong.) Carr.] shoots detached from the forest canopy or on seedlings. The water supply to the seedlings was terminated by excision and the shoot water potential (or critical water potential) and osmotic potential at the onset of stomatal closure measured. The turgor potential was calculated. The initial osmotic potential before insertion of the shoot into the chamber was also measured. Shoot water potential and osmotic potential at stomatal closure, and initial osmotic potential were significantly higher (less negative) in foliage from the lowest level in the canopy compared with foliage in the upper canopy, and higher in shoots of seedlings transferred to low light than in those at high light. Critical water potential also varied with season, being higher in July than in October and November. In all except one instance, turgor potential at the onset of stomatal closure was negative, possibly because of dilution of the cell sap by the extracellular water during the estimate of osmotic potential. Over all the experiments variation in critical water potential was correlated with variation in critical osmotic potential and, to a lesser extent, the initial osmotic potential. However, turgor potential at the critical potential varied from +0.6 to -4.6 bar. This suggests that difference in turgor between the guard cells and subsidiary cells, which controls stomatal aperture, is only loosely coupled with the bulk leaf turgor and hence that bulk leaf turgor is not a good index of the turbor relations of the guard cells.     

Genotypic Variation in Leaf Water Potential, Stomatal Conductance and Abscisic Acid Concentration in Spring Wheat Subjected to Artificial Drought Stress

A technique for studying variation in the accumulation of abscisicacid (ABA) in response to drought stress is described. Two experiments,each testing 26 spring wheat genotypes, were carried out usingpot grown plants in controlled environment cabinets with nutrientsolution culture, though the results of only one experimentare described in detail. Plants were subjected to water stressby withholding water as the fifth or sixth leaf on the mainstem was emerging. Two stressed plants of each genotype wereharvested 5 and 7 days after the treatment commenced and measurementsof leaf water potential, stomatal conductance and ABA concentrationwere taken. There was considerable genotypic variation in the rate at whichwater potential decreased, partly explained by variation inplant size. Inia 66 (a genotype common to both experiments)had consistently much lower water potentials than the othergenotypes. Stomatal conductances of all genotypes decreasedrapidly and after 5 and 7 days they were negatively correlatedwith the changes in water potential. ABA concentrations varied considerably between genotypes afterboth 5 and 7 days without water, the variation being associatedwith genotypic differences in water potential on these occasions.The overall relationship between ABA concentration and waterpotential was highly significant. Significant differences betweenthe slopes of the regressions for individual genotypes werefound. The cultivar Sirius accumulated the most ABA at any waterpotential and Pelissier, Wascana and Hybrid 46 accumulated theleast. The significance for drought resistance of variation in ABAaccumulation is discussed. Triticum aestivum L. ABA, wheat, absasic acid, leaf water potential, stomatal conductance     

Responses of Soybean Leaf Angle, Photosynthesis and Stomatal Conductance to Leaf and Soil Water Potential

The hypothesis that soil water potential (_s) is better correlatedto heliotropic leaf orientation, photosaturated photosyntheticCO₂ assimilation and stomatal conductance during periods oflimited water availability than is bulk leaf water potential(₁) was examined in greenhouse-grown soybean (Glycine max) plants,submitted to a progressive drought. Paired plants were exposedto either 1000 or 100 µmol m^–2 s^–1 photonflux densities (PFD) for 45–60 mins. The higher irradianceinduced short-term decreases in ₁, due to increased transpiration,while _l in the plant exposed to low PFD did not decrease. Thesechanges in ₁ occurred independently of changes in soil waterstatus. Concurrent to the light treatments, a single attachedleaf from each of the two plants was isolated from the restof the plant by shading, and the pulvinus of its terminal leafletwas exposed to a perpendicular PFD of 500 µmol m–²S^–1. Leaf movement of this leaflet was recorded in responseto this light, until a stable leaflet angle was achieved. Valuesof _s and _l (before and after light treatment), and photosaturatedrates of photosynthesis and stomatal conductance, were thenmeasured on these leaves. Leaflet angle and gas exchange werebetter correlated with _s (r² = 0.50, 0.50 and 0.57 for angle,photosynthesis and conductance, respectively) than with _l especiallywhen _l was the result of short-term, high-light induced changesin leaf water status (r² = 0.36, 0.32 and 0.49, for the sameparameters). Leaflet angle was also correlated with stomatalconductance (r² = 0.61) and photosynthetic rate (r² = 0.60),suggesting a close association between leaf orientation, leafmetabolism and soil water availability. Glycine max (L.) Merr. cv. Essex, soybean, heliotropism, water potential, photosynthesis, stomatal conductance, solar tracking     

Correlations between Carbon Isotope Discrimination and Leaf Conductance to Water Vapor in Common Beans

Carbon isotope discrimination (Δ) was measured in the field on 10 cultivars of common bean (Phaseolus vulgaris L.). There was substantial variation (more than 2‰) in leaf Δ values and these differences were maintained between vegetative and reproductive developmental stages. These bean lines also exhibited substantial differences in leaf conductance to water vapor, and again these differences were maintained across developmental stages. The differences in leaf conductance were positively correlated with Δ values, whether conductance was measured as total leaf conductance or as the individual conductances of either upper or lower leaf surfaces. The observed differences in leaf conductance were not associated with differences in stomatal density. There were small differences among bean lines in their leaf Kjeldahl nitrogen contents, which is interpreted as indicating that photosynthetic capacity among bean lines was similar. Thus, because Δ values and leaf conductance were positively correlated, these data suggested that there may have been differences among bean lines in the extent to which stomata limited photosynthetic gas exchange rates.     

The Effect of Scion Water Potential on Graft Success in Sitka Spruce (Picea sitchensis)

The effect of scion storage on graft success in Sitka sprucehas been examined. Scions kept in cold store for up to 7 d werefound to graft successfully to active rootstocks in about 95%of cases. From 7 d, however, there was a marked decline in successuntil, after 14 d of storage prior to grafting less than 40%of grafts survived. Scion leaf-water potential decreased continuouslyduring storage and fell dramatically during the first 3 d aftergrafting. In successful grafts, scion water potential then recovered,reaching a stable level after 3 weeks. No recovery occurredin grafts, which eventually failed. The relationship betweenscion leaf water potential and graft success rate is discussedwith reference to the role of callus development in graft formation. Picea sitchensis, water potential, graft success     

Abscisic Acid Induces Rapid Reductions in Mesophyll Conductance to Carbon Dioxide

The rate of photosynthesis (A) of plants exposed to water deficit is a function of stomatal (g_s) and mesophyll (g_m) conductance determining the availability of CO₂ at the site of carboxylation within the chloroplast. Mesophyll conductance often represents the greatest impediment to photosynthetic uptake of CO₂, and a crucial determinant of the photosynthetic effects of drought. Abscisic acid (ABA) plays a fundamental role in signalling and co-ordination of plant responses to drought; however, the effect of ABA on g_m is not well-defined. Rose, cherry, olive and poplar were exposed to exogenous ABA and their leaf gas exchange parameters recorded over a four hour period. Application with ABA induced reductions in values of A, g_s and g_m in all four species. Reduced g_m occurred within one hour of ABA treatment in three of the four analysed species; indicating that the effect of ABA on g_m occurs on a shorter timescale than previously considered. These declines in g_m values associated with ABA were not the result of physical changes in leaf properties due to altered turgor affecting movement of CO₂, or caused by a reduction in the sub-stomatal concentration of CO₂ (C_i). Increased [ABA] likely induces biochemical changes in the properties of the interface between the sub-stomatal air-space and mesophyll layer through the actions of cooporins to regulate the transport of CO₂. The results of this study provide further evidence that g_m is highly responsive to fluctuations in the external environment, and stress signals such as ABA induce co-ordinated modifications of both g_s and g_m in the regulation of photosynthesis.     

Influence of Xylem Water Potential on Leaf Elongation and Osmotic Adjustment of Wheat and Lupin

The leaf elongation rate and osmotic pressure at full turgorof wheat (Triticum aestivum L.) and lupin (Lupinus cosentiniiGuss.) were measured in well watered plants, in plants thatwere allowed to dry the soil slowly over 7 d, and in plantsin which the water potential of the leaf xylem was maintainedhigh by applying pressure to the roots during the drying cycle.Maintenance of high xylem water potentials failed to preventa reduction in the rate of leaf elongation as the soil dried,while the osmotic pressure at full turgor and the degree ofosmotic adjustment increased as the soil water content decreased.The rate of leaf elongation was reduced more and the degreeof osmotic adjustment was higher in leaves with high xylem waterpotentials than in those in which leaf xylem potentials wereallowed to decrease as soil water content decreased. Osmoticadjustment was linearly correlated with the reduction in leafelongation rate in both wheat and lupin. Key words: Osmotic adjustment, leaf elongation, turgor regulation     

Effects of Periodical Soil Drying and Leaf Water Potential on the Sensitivity of Stomatal Response to Xylem ABA

The study on the changes of stomatal sensitivity in relation to xylem ABA during periodical soil drying and the effect of leaf water status on the stomatal sensitivity has confirmed that xylem ABA concentration is a good indicator of soil water status around roots and the relation between xylem ABA concentration and predawn leaf water potential remained constant during the three consecutive soil drying cycles based on the slopes of the fitted lines. The sensitivity of stomata to xylem ABA increased substantially as the soil drying cycles progressed, and the xylem ABA concentration needed to cause a 50% decrease of stomatal conductance was as low as 550 mnoL/L in the next two soil drying cycle, as compared with the 750 nmol/L ABA in the first cycle of soil drying. The results using the split-root system showed that leaf water deficit significantly enhanced the stomatal response to xylem ABA and the xylem ABA concentration needed to cause a 50% decrease in stomatal conductance was 2 to 4 times smaller in the whole-root-drying treatment than those in the semi-root- drying treatment. These results suggested that the sensitivity of stomata to xylem ABA concentration is not a fixed characteristic.     

周期性土壤干旱和叶片水势对气孔响应木质部ABA灵敏度的影响

研究了周期性土壤干旱期间气孔对木质部ＡＢＡ响应的灵敏度的变化以及叶片水势对灵敏度的影响。实验结果证明了木质部ＡＢＡ浓度是反映根系周围土壤水分状况的一个指标的结论。土壤周期性干旱不影响木质部ＡＢＡ浓度对土壤水分状况的依赖关系,但显著地提高了气孔对木质部ＡＢＡ 响应的灵敏度。根据对实测数据的数学模拟结果显示,引起气孔导度下降５０％ 所需的木质部ＡＢＡ浓度从第一轮土壤干旱的７５０ ｎｍｏｌ／Ｌ降至第二轮土壤干旱的５５０ ｎｍｏｌ／Ｌ。分根实验的结果表明,叶片水分亏缺显著提高了气孔对木质部ＡＢＡ 的响应的灵敏程度,全根干旱中引起气孔导度下降５０ ％ 所需的木质部ＡＢＡ 浓度比半根干旱的小２ ～４ 倍。这表明,气孔对木质部ＡＢＡ响应的灵敏度不是一个固定的特性,可随植物生长环境及许多其他因素的变化而表现出很大的差异     

Effects of Waterlogging on Water Relations of Actively-growing and Dormant Sitka Spruce Seedlings

Two-year-old Sitka spruce [Picea sitchensis (Bong.) Carr.] seedlings,either actively growing or dormant, were waterlogged in a growthroom at 15 °C. Shoot and root growth, transpiration andleaf water potential were observed. In actively-growing plants shoot extension continued after waterlogging,though at a reduced rate, and shoots of dormant plants brokebud and extended during the waterlogging period. Root growthwas suppressed by waterlogging in both types of plant. The 22day waterlogging treatment eventually killed the actively-growingplants but plants which were dormant at the time of waterloggingwere more tolerant. Changes in plant water relations after waterloggingwere entirely different depending on the condition of the plantswhen the soil was flooded. Dormant plants showed a gradual reductionin transpiration and increased water stress over the waterloggingperiod; after the soil was drained leaf water potential increasedto equal the value of control plants which had been maintainedin a freely drained condition, but transpiration did not increaseuntil root growth began. Actively-growing plants exhibited amore complex behaviour, characterized by a very rapid reductionin transpiration after waterlogging, accompanied by a briefperiod of water stress, followed by a period of increasing transpirationrate in the absence of water stress. Finally a second reductionin transpiration occurred and water stress increased as theseedlings died. The importance of the stage of activity of theroot system to the response of plants to waterlogging is discussed. Picea sitchensis (Bong.) Carr., Sitka spruce, waterlogging, water relations, dormancy, transpiration, water potential     

Leaf Elongation in Relation to Leaf Water Potential in Soybean

Leaf water potential, turgor pressure, and leaf elongation ratewere measured in soybeans growing in controlled environmentchambers, greenhouses, and outdoors. Plants in chambers hadthe highest water potentials and turgor pressures, and plantsoutdoors the lowest. In all three environments there was a linearrelationship between elongation rate and turgor pressure. Leavesof plants in drier environments required less turgor for elongation,and showed a greater increase in elongation rate per unit increasein turgor. Elongation rates over a 72 h period were equal inthe three environments. Leaves reached the largest final sizein the greenhouse (intermediate in water potential). Epidermalcells were larger in chamber- and greenhouse-grown leaves thanin leaves of plants grown outdoors. The number of epidermalcells per leaf was greater in the greenhouse and outdoors thanin the chamber. Leaf elongation characteristics of greenhouseplants were duplicated by mildly stressing chamber plants, andleaf elongation characteristics of field plants were duplicatedby more severely stressing chamber plants. Leaves of mildlystressed chamber plants also reached a larger final size thanleaves of more severely stressed chamber plants, or leaves ofcontrol plants in the chamber. Water stress in the chamber increasedthe number of epidermal cells per leaf. More severe water stressin the chamber reduced epidermal cell size. Based on the waterstress experiments it is concluded that the differences in plantwater status in the chamber, greenhouse, and field caused differencesin elongation characteristics, and were responsible for thedifferences in leaf size.     

Changes in Transpiration, Net Carbon Dioxide Assimilation and Leaf Water Potential Resulting from Application of Hydrostatic Pressure to Roots of Intact Pepper Plants

Hydrostatic pressures varying from 0 to 6.0 bar were applied to roots of intact Capsicum annuum L. cv. California Wonder plants growing in nutrient solution and the rates of transpiration, and net CO₂ assimilation, apparent compensation point and leaf water potential measured. Increasing the pressure on the roots of plants with roots in solution with either -0.5 or -5.0 bar osmotic potential with 1 bar increments resulted in a decrease in transpiration. With the application of 1 or 2 bar pressure the rate of transpiration returned to near or above the original rate. An application of 3 or 4 bar pressure reduced the rate of transpiration of all plants. The transpiration of plants with roots in solution with -0.5 bar osmotic potential remained at the reduced rate for as long as these pressures were maintained. The transpiration of plants with roots in solution with -5.0 bar was only temporarily suppressed at these pressures. Changing the applied pressure from 3 or 4 bar to 0 resulted in a rapid increase in transpiration which lasted approximately 15 minutes. This was followed by a decrease in transpiration to a rate lower than before the pressure was applied. The pattern of response was similar for plants at low or high light intensity or at normal or low CO₂ concentrations. When leaf diffusive resistance was 6.0 s cm^?1 or greater, changes in net CO₂ assimilation were similar to those of transpiration. The apparent CO₂ compensation point increased as pressure was applied and decreased with a release in pressure. Leaf water potential increased with an increase in pressure and decreased with a decrease in pressure. The changes in leaf water potential were frequently but not always proportional to changes in pressure. It is postulated that the respouses noted were due to changes in resistance to flow of water from xylem terminals through the mesophyll cells and stomatal cavities to the atmosphere.     

Auxin Transport as Related to Leaf Abscission during Water Stress in Cotton

Plant water deficits reduced the basipetal transport of auxin in cotyledonary petiole sections taken from cotton (Gossypium hirsutum L.) seedings. A pulse-labeling technique was employed to eliminate complications of uptake or exit of ¹⁴C-indoleacetic acid from the tissue. The transport capacity or the relative amount of radioactivity in a 30-minute pulse which was basipetally translocated was approximately 30% per hour in petioles excised from well watered seedlings (plant water potentials of approximately -4 to -8 bars). No cotyledonary leaf abscission took place in well watered seedlings. Plant water potentials from -8 to -12 bars reduced the transport capacity from 30 to 15% per hour, and although the leaves were wilted, cotyledonary abscission did not increase appreciably at these levels of stress. The threshold water potential sufficient to induce leaf abscission was approximately -13 bars and abscission increased with increasing stress while the auxin transport capacity of the petioles remained relatively constant (15% per hour). The basipetal transport capacity of well watered petioles tested under anaerobic conditions and acropetal transport tested under all conditions were typically less than basipetal transport under the most severe stress conditions. Cotyledonary abscission took place during and 24 hours after relief of stress with little or no abscission taking place 48 hours after relief of stress. Although the water potential returned to -4 bars within hours after rewatering the stressed plants, partial recovery of the basipetal transport capacity of the petioles was not apparent until 48 hours after rewatering, and at least 72 hours was required to return the transport capacity to near normal values. These data support the view that decreased levels of auxin reaching the abscission zone from the leaf blade influence the abscission process and further suggest that the length of time that the auxin supply is maximally reduced is more critical than the degree of reduction.     

Leaf Conductance in Relation to Assimilation in Eucalyptus pauciflora Sieb. ex Spreng: Influence of Irradiance and Partial Pressure of Carbon Dioxide

Rates of assimilation and transpiration in Eucalyptus pauciflora Sieb. ex Spreng were measured at various ambient partial pressures of CO₂ and various irradiances and were used to estimate leaf conductance and intercellular partial pressure of CO₂. The responses of leaf conductance and rate of assimilation to change in intercellular partial pressure of CO₂ were expressed in terms of feedback. They are small in the sense that their combined effect was to reduce disturbances in intercellular partial pressure of CO₂ by 30% only. The magnitude of the feedback had no influence on the system as affected by irradiance, because the direct responses of conductance and rate of assimilation to changes in irradiance in the range 0.25 to 2 millieinsteins per meter per second were such that intercellular partial pressure was maintained almost constant.     

Water Stress and Day-To-Day Variation in Apparent Photosynthetic Acclimation of Field-Grown Soybeans to Elevated Carbon Dioxide Concentration

Midday measurements of single leaf gas exchange rates of upper canopy leaves of soybeans grown in the field at 350 (AC) and 700 (EC) µmol(CO₂) mol^–1 in open topped chambers sometimes indicated up to 50 % higher net photosynthetic rates (P _N) measured at EC in plants grown at AC compared to EC. On other days mean P _N were nearly identical in the two growth [CO₂] treatments. There was no seasonal pattern to the variable photosynthetic responses of soybean to growth [CO₂]. Even on days with significantly lower P _N in the plants grown at EC, there was no reduction in ribulose-1,5-bisphosphate carboxylase/oxygenase, chlorophyll, or soluble protein contents per unit of leaf area. Over three years, gas exchange evidence of acclimation occurred on days when either soil was dry or the water vapor pressure deficit was high (n = 12 d) and did not occur on days after rain or on days with low water vapor pressure deficit (n = 9 d). On days when photosynthetic acclimation was evident, midday leaf water potentials were consistently 0.2 to 0.3 MPa lower for the plants grown at EC than at AC. This suggested that greater susceptibility to water stress in plants grown at EC cause the apparent photosynthetic acclimation. In other experiments, plants were grown in well-watered pots in field chambers and removed to the laboratory early in the morning for gas exchange measurements. In these experiments, the amount of photosynthetic acclimation evident in the gas exchange measurements increased with the maximum water vapor pressure deficit on the day prior to the measurements, indicating a lag in the recovery of photosynthesis from water stress. The apparent increase in susceptibility to water stress in soybean plants grown at EC is opposite to that observed in some other species, where photosynthetic acclimation was evident under wet but not dry conditions, and may be related to the observation that hydraulic conductance is reduced in soybeans when grown at EC. The day-to-day variation in photosynthetic acclimation observed here may account for some of the conflicting results in the literature concerning the existence of acclimation to EC in field-grown plants.     

Influence of Rate of Development of Leaf Water Deficits upon Photosynthesis, Leaf Conductance, Water Use Efficiency, and Osmotic Potential in Sorghum

This study reports the effect of rate of development of leaf water deficits in soil-grown sorghum (Sorghum bicolor) on the relationship of net photosynthesis, leaf conductance, and water use efficiency to leaf water potential, and on the degree of solute accumulation (osmotic adjustment). Recovery of these processes on rewatering, and responses during a second stress cycle were also studied. The most rapid rate of stress (1.2 MPa day^?1) resulted in no solute accumulation and the lowest rate of net photosynthesis and leaf conductance for any given leaf water potential during stress. Stress at 0.7 and 0.15 MPa day^?1 led to equal solute accumulations of approximately 0.6 MPa, but net photosynthesis, leaf conductance, and water use efficiency at a given leaf water potential were lower with the faster rate of stress (0.7 MPa day^?1). Additionally, leaf conductance at a given leaf turgor potential was lowest at the 1.2 MPa day^?1 stress rate, slightly higher at the intermediate rate of stress, and clearly highest at the slowest rate of stress. Recovery of both net photosynthesis and leaf conductance upon rewatering was rapid, taking less than 3 days, but full recovery of osmotic potential took between 6 and 11 days. One slow stress cycle had no influence on relationships during a second cycle. The concept of a threshold leaf water potential for stomatal closure is discussed and the conclusion reached that stomatal closure occurs slowly over a wide range of leaf water potential (> 1.0 MPa), the range being greater for slower rates of stress.     

Drought-induced Closure of Phaseolus vulgaris L. Stomata Precedes Leaf Water Deficit and any Increase in Xylem ABA Concentration

Young seedlings of two cultivars of Phaseolus vulgaris L. (cv.Cacahuate-72 and Michoacan-12A3) were subjected to a soil dryingtreatment. Stomata started to close before any leaf water deficitcould be detected. Soil drying promoted a small degree of ABAaccumulation in roots, but, at the time stomatal closure wasinitiated, at least in one cultivar, xylem ABA and bulk leafABA concentration were not enhanced. The mechanism of the stomatalresponse is discussed in terms of an as-yet unidentified regulatorof stomatal behaviour, redistribution of existing ABA in plants,and a high sensitivity of stomata to small changes in ABA concentration.     

The Effects of Shoot Water Status on Some Photosynthetic Partial Processes in Sitka Spruce

Clonal cuttings of Picea sitchensis (Bong.) Carr. were grown in a controlled environment and, after completion of shoot extension and maturation, subjected to a drying cycle. Photosynthesis and stomatal conductance were measured in situ using ¹⁴CO₂ and a porometer, respectively. Shoot water potential was measured with the pressure chamber. Photosystem and carboxylase activities of chloroplast preparations were measured in vitro. A considerable fall in photosynthetic rate occurred at low water potential. This was associated with stomatal closure and a decrease in CO₂ transfer or fixation processes in the mesophyll. Little change in activity of photosystem I, photosystem II, and ribulose 1,5-diphosphate carboxylase was detected during the drying cycle. Any decline in activity of the photosynthetic partial processes in vivo under severe water stress (Ψ < – 30 bar) was probably masked in vitro as a result of rehydration prior to assay.     

The Simulation of Leaf Conductance Responses to Changes in Environmental Water Status

A simulation model of stomatal response to change of environmental water status was set up based on the works on the mechanism of stomatal movement. The variations of leaf conductance, water potential and turgot pressure in guard cells, subsidiary cells and the other cells or tissues in leaf with leaf-air vapour pressure difference and soil water potential have been calculated by our model. The calculated results fit very well with the data from experiments. The different patterns of leaf transpiration variation with the difference between leaf-air and vapour pressure can be explained quantitatively.