Changes in vascular and transpiration flows affect the seasonal and daily growth of kiwifruit (Actinidia deliciosa) berry

Background and Aims

The kiwifruit berry is characterized by an early stage of rapid growth, followed by a relatively long stage of slow increase in size. Vascular and transpiration flows are the main processes through which water and carbon enter/exit the fruit, determining the daily and seasonal changes in fruit size. This work investigates the biophysical mechanisms underpinning the change in fruit growth rate during the season.

Methods

The daily patterns of phloem, xylem and transpiration in/outflows have been determined at several stages of kiwifruit development, during two seasons. The different flows were quantified by comparing the diurnal patterns of diameter change of fruit, which were then girdled and subsequently detached while measurements continued. The diurnal courses of leaf and stem water potential and of fruit pressure potential were also monitored at different times during the season.

Key Results

Xylem and transpiration flows were high during the first period of rapid volume growth and sharply decreased with fruit development. Specific phloem import was lower and gradually decreased during the season, whereas it remained constant at whole-fruit level, in accordance with fruit dry matter gain. On a daily basis, transpiration always responded to vapour pressure deficit and contributed to the daily reduction of fruit hydrostatic pressure. Xylem flow was positively related to stem-to-fruit pressure potential gradient during the first but not the last part of the season, when xylem conductivity appeared to be reduced.

Conclusions

The fruit growth model adopted by this species changes during the season due to anatomical modifications in the fruit features.     

Fitting mixture models to birth weight data: a case study.

Birth weights by gestational age are compared in two birth cohorts from Northern Finland, the first from 1966 and the second from 1985-1986. A curious fact in the data is that mean birth weight before the 39th week was lower in the latter series although the mean birth weight for the total series was higher. Similar findings have been reported in other series. A mixture model with the nonparametric regression function is proposed for studying the hypothesis that the difference was caused by more frequent gross errors in gestational assessment in the earlier cohort. The probability of an error in gestational assessment then greatly depends on the observed gestational age, which makes the mixture model nonstandard. Maximum likelihood solutions to the parameters in the proposed model were computed employing the general expectation-maximization (EM) algorithm. A technique for studying the effect of errors on the intrauterine weight gain curve is proposed and applied to our two birth cohorts. The risk of underestimation of gestational age seems to be larger in the previous series and the differences between the growth curves almost totally vanish when "corrected" by means of the mixture model.     

Causes and effects of changes in xylem functionality in apple fruit

BACKGROUND AND AIMS: The xylem in fruit of a number of species becomes dysfunctional as the fruit develops, resulting in a reduction of xylem inflow to the fruit. Such a reduction may have consequential effects on the mineral balance of the fruit. The aim of this study was to elucidate the dynamics and nature of xylem failure in developing apples (Malus domestica) showing differing susceptibilities to bitter pit, a calcium-related disorder. METHODS: Developmental changes in xylem functionality of the fruit were investigated in "Braeburn" and "Granny Smith" apples by using a dye infusion technique, to stain the vasculature along the path of dye movement. The vascular bundles were clearly visible in transverse section when fruit were sectioned equatorially. The intensity of staining of the vascular bundles in the fruit was recorded at regular intervals throughout the season. Tissue containing dysfunctional bundles was fixed and embedded in wax for subsequent sectioning and examination. KEY RESULTS: As the season progressed, an increasing proportion of vascular bundles failed to show any staining, with the most marked change occurring in the primary bundles, and in nearly all bundles with increasing distance from the stalk end of the fruit. Decreased conductance in the primary bundles of "Braeburn" occurred earlier than in "Granny Smith". Microscopy revealed that the xylem in vascular bundles of the fruit suffered substantial damage, indicating that the mode of dysfunction was via the physical disruption of the xylem caused by expansion of the flesh. CONCLUSIONS: Results support the view that the relative calcium deficiency of apple fruit is due to a progressive breakdown of xylem conductance caused by growth-induced damage to the xylem strand in the bundle. The earlier onset of xylem dysfunction in the cultivar more susceptible to bitter pit suggests that the relative growth dynamics of the fruit may control the occurrence of calcium-related disorders.     

A hydrologic assessment of the Everglades Nutrient Removal Project, a subtropical constructed wetland in South Florida (USA)

The Everglades Nutrient Removal Project (ENRP), a 1544-ha constructed wetland in south Florida, was intensively monitored throughout its five-year operational history. Water budgets for the ENRP and each of its interior treatment cells were dominated by surface flows (≥85% of inflows; ≥68% of outflows) with smaller contributions from precipitation, evapotranspiration, groundwater flux, and change in storage. The mean water depth, hydraulic loading rate for surface water, and nominal hydraulic retention time for the entire wetland were 0.6 m, 3.1 cm d⁻¹ and 17.7 d, respectively, and were comparable to values anticipated in design. The east flow-way was slightly shallower (0.2 m) and received proportionately more flow (61%) than the west flow-way. The hydrology of other treatment wetlands is often driven by surface flows. All treatment cells in the ENRP were to some extent hydraulically short-circuited. There was net groundwater inflow to the ENRP from Water Conservation Area 1 (WCA-1) resulting from significant head differences between these wetlands. Groundwater outflow to the adjacent farmlands was greatest in Cell 2 and substantially exceeded groundwater inflow. All hydrologic parameters exhibited seasonality to some extent; fluctuation in water depth and groundwater inflows corresponded with the seasonal change in stage in WCA-1. Errors in the ENRP and individual cell water budgets were generally less than 10% and within the range of errors for water budgets from other wetlands.     

Vascular flows and transpiration affect peach (Prunus persica Batsch.) fruit daily growth

The relative contributions of xylem, phloem, and transpiration to fruit growth and the daily patterns of their flows have been determined in peach, during the two stages of rapid diameter increase, by precise and continuous monitoring of fruit diameter variations. Xylem, phloem, and transpiration contributions to growth were quantified by comparing the diurnal patterns of diameter change of fruits, which were then girdled and subsequently detached. Xylem supports peach growth by 70%, and phloem 30%, while transpiration accounts for approximately 60% of daily total inflows. These figures and their diurnal patterns were comparable among years, stages, and cultivars. Xylem was functional at both stage I and III, while fruit transpiration was high and strictly dependent on environmental conditions, causing periods of fruit shrinkage. Phloem imports were correlated to fruit shrinkage and appear to facilitate subsequent fruit enlargement. Peach displays a growth mechanism which can be explained on the basis of passive unloading of photoassimilates from the phloem. A pivotal role is played by the large amount of water flowing from the tree to the fruit and from the fruit to the atmosphere.     

Computational fluid dynamics simulations on a Devonian spiriferid Paraspirifer bownockeri (Brachiopoda): Generating mechanism of passive feeding flows

A mechanism of generating passive feeding flow for the Devonian spiriferide brachiopod Paraspirifer bownockeri was theoretically elucidated through fluid dynamics simulations for flow around rigid shells. The RANS equations were used as a turbulence model, and the unsteady incompressible flow was solved using the finite volume method. Two directions of ventral and dorsal flows were investigated as typical cases where little exchange flow occurs inside the shells. The digital model of the shell was constructed using image processing of X-ray CT images of a shell replica made by molding a polycarbonate plate to a well-preserved fossil specimen of Paraspirifer. To examine the effect of flow velocity, three conditions of ambient flow velocity were adopted for both the ventral and dorsal flows. The pressure distribution along the gape showed that a relatively high pressure occurred around the sulcus in all simulated cases. This high pressure generated inflow from the sulcus and subsequent spiral internal flow, especially in fast ambient flows. This means that the sulcus generated the considerable pressure gradient around the gape passively and generated the stable intake of seawater and a spiral flow of water inside the shell for feeding. We conclude that the shell form of certain spiriferides could generate spiral flows so as to promote passive feeding, and the sulcus is interpreted as an important form for the passive intake of water.     

Investigation of the Effect of Data Error in the Analysis of Biological Tracer Data

Data obtained from tracer studies often consist of serial measurements after administration of radioisotope. Very little work has been published on how the error in the data affects the mathematical analysis. Computer simulation was here employed to produce data with error of different magnitude and form for each of several values of rate constant and amplitude. The data were terminated when the value of the last point was 5% of the value of the first point, and also in other ways arranged to simulate experimental situations. The sets of simulated data for a two compartment system were analyzed by the gaussian iterative technique. With a rate constant ratio of at least four the technique converged for data errors of 5% or less. The calculated error in the rate constants ranged from 2 to 85%, and in the amplitudes from 1 to 50%, for data error of 0.5 to 10%. The lesser rate constant and amplitude had the greater errors. If a wrong assumption was made in the analysis about the variation of data error over the time interval of measurement, then the calculated values of parameter standard deviations were greatly in error. The results can be used to decide what experimental accuracy is needed for a given accuracy of model parameters for a variety of biological problems.     

System Relaxation and Thermodynamic Integration

Abstract

The thermodynamic integration (TI) method for calculating free energy differences has three inherent problems: statistics, numerical integration, and relaxation. In this paper the latter is analyzed for the nonequilibrium TI method introduced by Postma which combines molecular dynamics simulation and TI in a very effective way. A nontrivial extrapolation technique is presented to remove the relaxation error and to calculate the underlying relaxation time. It is shown that the optimal choice of grid points, derived in a previous paper, for minimizing statistical errors not only removes integration errors, but also minimizes relaxation errors. The methods are applied in a calculation of the free energy of cavity formation in water.     

Productivity of Peach Trees : Tree Growth and Water Stress in Relation to Fruit Growth and Assimilate Demand

The growth of the limbs of peach trees measured by dendrometerswas inhibited during periods when the rate of d. wt accumulationby the fruit was increasing. The diurnal shrinkage of theselimbs measured by the same dendrometers was greatest duringperiods when limb growth was inhibited. The increase in diurnalshrinkage of the limbs coinciding with inhibited limb growth,and increased assimilate demand, was greater than that causedby environmental factors at maximum soil water-potential andgreater than that caused by five days soil drying after irrigation.Leaf water potential and diurnal limb shrinkage were measuredcontinuously during two periods of maximum soil water-potentialand leaf area when the rate of d. wt increase of the fruit wasdecreasing (DW II) and then later when the rate of d. wt increaseof the fruit was increasing (DW III). The leaf water potentialwas lower and limb shrinkage greater during DW 111 than DW II.The hydraulic gradient also increased from 1 bar m^–1 inDW II to 2 bar m^–1 in DW III Environmental conditions during both periods were very similarand the data suggest total water use by the tree increased substantiallyduring periods of high assimilate demand by the fruit.     

Likelihood-based genetic mark-recapture estimates when genotype samples are incomplete and contain typing errors

Genotypes produced from samples collected non-invasively in harsh field conditions often lack the full complement of data from the selected microsatellite loci. The application to genetic mark-recapture methodology in wildlife species can therefore be prone to misidentifications leading to both ‘true non-recaptures’ being falsely accepted as recaptures (Type I errors) and ‘true recaptures’ being undetected (Type II errors). Here we present a new likelihood method that allows every pairwise genotype comparison to be evaluated independently. We apply this method to determine the total number of recaptures by estimating and optimising the balance between Type I errors and Type II errors. We show through simulation that the standard error of recapture estimates can be minimised through our algorithms. Interestingly, the precision of our recapture estimates actually improved when we included individuals with missing genotypes, as this increased the number of pairwise comparisons potentially uncovering more recaptures. Simulations suggest that the method is tolerant to per locus error rates of up to 5% per locus and can theoretically work in datasets with as little as 60% of loci genotyped. Our methods can be implemented in datasets where standard mismatch analyses fail to distinguish recaptures. Finally, we show that by assigning a low Type I error rate to our matching algorithms we can generate a dataset of individuals of known capture histories that is suitable for the downstream analysis with traditional mark-recapture methods.     

Modelling the effect of fruit growth on surface conductance to water vapour diffusion

BACKGROUND AND AIMS: A model of fruit surface conductance to water vapour diffusion driven by fruit growth is proposed. It computes the total fruit conductance by integrating each of its components: stomata, cuticle and cracks. METHODS: The stomatal conductance is computed from the stomatal density per fruit and the specific stomatal conductance. The cuticular component is equal to the proportion of cuticle per fruit multiplied by its specific conductance. Cracks are assumed to be generated when pulp expansion rate exceeds cuticle expansion rate. A constant percentage of cracks is assumed to heal each day. The proportion of cracks to total fruit surface area multiplied by the specific crack conductance accounts for the crack component. The model was applied to peach fruit (Prunus persica) and its parameters were estimated from field experiments with various crop load and irrigation regimes. KEY RESULTS: The predictions were in good agreement with the experimental measurements and for the different conditions (irrigation and crop load). Total fruit surface conductance decreased during early growth as stomatal density, and hence the contribution of the stomatal conductance, decreased from 80 to 20 % with fruit expansion. Cracks were generated for fruits exhibiting high growth rates during late growth and the crack component could account for up to 60 % of the total conductance during the rapid fruit growth. The cuticular contribution was slightly variable (around 20 %). Sensitivity analysis revealed that simulated conductance was highly affected by stomatal parameters during the early period of growth and by both crack and stomatal parameters during the late period. Large fruit growth rate leads to earlier and greater increase of conductance due to higher crack occurrence. Conversely, low fruit growth rate accounts for a delayed and lower increase of conductance. CONCLUSIONS: By predicting crack occurrence during fruit growth, this model could be helpful in managing cropping practices for integrated plant protection.     

Validation of the doubly labeled water method in growing precocial birds: the importance of assumptions concerning evaporative water loss

The doubly labeled water (DLW) method was validated against respiration gas analysis in growing precocial chicks of the black-tailed godwit (Limosa limosa) and the northern lapwing (Vanellus vanellus). To calculate the rate of CO2 production from DLW measurements, Lifson and McClintock's equations (6) and (35) were employed, as well as Speakman's equation (7.17) (all single-pool models). The average errors obtained with the first two equations (+7.2% and -11.6%, respectively) differed significantly from zero but not the error obtained with Speakman's equation (average: -2.9%). The latter error could be reduced by taking a fractional evaporative water loss of 0.13, instead of the value of 0. 25 recommended by Speakman. Application of different two-pool models resulted in relative errors of the DLW method of -15.9% or more. After employing the single-pool model with a fractional evaporative water loss value of 0.13, it was found that there was no relationship between the relative growth rate of the chick and the relative error of the DLW method. Recalculation of previously published results on Arctic tern (Sterna paradisaea) chicks revealed that the fit of the validation experiment could be considerably improved by employing a single-pool model and assuming a fractional evaporative water loss of 0.20 instead of the value of 0.50 taken originally. After employing the value of 0.20, it was found that there was no relationship between the relative growth rate of the chick and the relative error of the DLW method. This suggests that isotope incorporation into new body substances does not cause a detectable error. Thus, the DLW method seems to be applicable in young birds growing as fast as 20% d-1, after making adjustments for the fractional evaporative water loss. We recommend Speakman's equation (7.17) for general use in growing birds when evaporation is unknown.     

杂草果实的冰冻切片技术

介绍一种快速、简便的杂草果实解剖技术。以4种木质化程度高且能够漂浮的杂草果实为材料进行冰冻切片,经过材料固定、前处理、样品冷台固定、冷冻切片、展片、染色和观察并拍照等操作步骤,可以获得清晰的果实解剖照片,直观地揭示杂草果实适应漂浮的显微结构。杂草果实冰冻切片方法的优点是不需要对材料进行长时间的软化处理以及繁琐的脱水和包埋等过程。其关键环节是适宜的甘油浓度、冰冻温度和展片步骤。其中,15%的甘油浓度进行前处理最合适。     

Xylem, Phloem and Transpiration Flows in a Grape: Application of a Technique for Measuring the Volume of Attached Fruits to High Resolution Using Archimedes' Principle

The minute changes in volume of a grape berry which occur fromhour to hour were measured non-destructively in the field usingreadily available and cheap laboratory equipment and a modernelectronic balance. The method, applicable even to small (approximately10 g) fruits, is based on Archimedes' principle and gave a resolutionof about 1 part in 1 000 by measuring the buoyant upthrust experiencedby a berry when immersed in water. Volume data from control,pedicel-steamed, and detached berries were used to calculatethe magnitudes and directions of the fluid flows which tookplace through the stalk of the phloem and xylem streams andthrough the skin in the transpiration stream. In the latter stages of fruit development, after the onset ofripening, net volume growth more or less ceases in grapes althoughtheir rate of sugar import is at its strongest. Cessation ofvolume growth comes about because the strong inflow of sugarywater in the phloem is closely balanced in part by transpirationalwater loss through the skin and in part by the backflow of xylemwater to the parent vine. This xylem backflow appears to persistthroughout the diurnal cycle. The net backflow direction of the xylem stream, together withthe inability of the phloem stream to carry certain ions (notablycalcium), may explain how some mineral imbalance disorders arisein the later stages of fruit development. The intense manner in which fruiting sinks compete with vegetativesinks in Vitis finds its explanation in the breakdown of apoplast:symplast compartmentation in the berry which occurs around thetime of onset of ripening. The breakdown exposes the terminalsieve tubes of the berry to a highly negative water potentialenvironment, serving to increase both the speed and the concentrationof the translocation stream. Key words: Archimedes' principle, volume measurement, mineral nutrition, xylem, phloem, assimilate partitioning, fruit splitting     

Apoplastic water fraction and rehydration techniques introduce significant errors in measurements of relative water content and osmotic potential in plant leaves

Relative water content (RWC) and the osmotic potential (π) of plant leaves are important plant traits that can be used to assess drought tolerance or adaptation of plants. We estimated the magnitude of errors that are introduced by dilution of π from apoplastic water in osmometry methods and the errors that occur during rehydration of leaves for RWC and π in 14 different plant species from trees, grasses and herbs. Our data indicate that rehydration technique and length of rehydration can introduce significant errors in both RWC and π. Leaves from all species were fully turgid after 1–3 h of rehydration and increasing the rehydration time resulted in a significant underprediction of RWC. Standing rehydration via the petiole introduced the least errors while rehydration via floating disks and submerging leaves for rehydration led to a greater underprediction of RWC. The same effect was also observed for π. The π values following standing rehydration could be corrected by applying a dilution factor from apoplastic water dilution using an osmometric method but not by using apoplastic water fraction (AWF) from pressure volume (PV) curves. The apoplastic water dilution error was between 5 and 18%, while the two other rehydration methods introduced much greater errors. We recommend the use of the standing rehydration method because (1) the correct rehydration time can be evaluated by measuring water potential, (2) overhydration effects were smallest, and (3) π can be accurately corrected by using osmometric methods to estimate apoplastic water dilution.     

Sugar demand of ripening grape berries leads to recycling of surplus phloem water via the xylem

We tested the common assumption that fleshy fruits become dependent on phloem water supply because xylem inflow declines at the onset of ripening. Using two distinct grape genotypes exposed to drought stress, we found that a sink‐driven rise in phloem inflow at the beginning of ripening was sufficient to reverse drought‐induced berry shrinkage. Rewatering accelerated berry growth and sugar accumulation concurrently with leaf photosynthetic recovery. Interrupting phloem flow through the peduncle prevented the increase in berry growth after rewatering, but interrupting xylem flow did not. Nevertheless, xylem flow in ripening berries, but not berry size, remained responsive to root or shoot pressurization. A mass balance analysis on ripening berries sampled in the field suggested that phloem water inflow may exceed growth and transpiration water demands. Collecting apoplastic sap from ripening berries showed that osmotic pressure increased at distinct rates in berry vacuoles and apoplast. Our results indicate that the decrease in xylem inflow at the onset of ripening may be a consequence of the sink‐driven increase in phloem inflow. We propose a conceptual model in which surplus phloem water bypasses the fruit cells and partly evaporates from the berry surface and partly moves apoplastically to the xylem for outflow.     

Vascular functioning and the water balance of ripening kiwifruit (Actinidia chinensis) berries

Indirect evidence suggests that water supply to fleshy fruits during the final stages of development occurs through the phloem, with the xylem providing little water, or acting as a pathway for water loss back to the plant. This inference was tested by examining the water balance and vascular functioning of ripening kiwifruit berries (Actinidia chinensis var. chinensis 'Hort16A') exhibiting a pre-harvest 'shrivel' disorder in California, and normal development in New Zealand. Dye labelling and mass balance experiments indicated that the xylem and phloem were both functional and contributed approximately equally to the fruit water supply during this stage of development. The modelled fruit water balance was dominated by transpiration, with net water loss under high vapour pressure deficit (D(a)) conditions in California, but a net gain under cooler New Zealand conditions. Direct measurement of pedicel sap flow under controlled conditions confirmed inward flows in both the phloem and xylem under conditions of both low and high D(a). Phloem flows were required for growth, with gradual recovery after a step increase in D(a). Xylem flows alone were unable to support growth, but did supply transpiration and were responsive to D(a)-induced pressure fluctuations. The results suggest that the shrivel disorder was a consequence of a high fruit transpiration rate, and that the perception of complete loss or reversal of inward xylem flows in ripening fruits should be re-examined.     

Changes in Photosynthesis and Fruit Characteristics in Olive in Response to Assimilate Availability

The source level in the olive cultivar Leccino was varied by girdling at different stages of fruit growth. Afterwards, the effects on gas exchange, fruit growth, and ripening and blooming were studied. Girdling during fruit growth did not significantly influence net photosynthetic rate (P _N) except in the last phase of fruit growth when the P _N was reduced. In the girdled branch, P _N began to decrease at the onset of starch accumulation because fruit growth ceased. In mid-November stomatal conductance (g _s) and transpiration rate (E) were also reduced by girdling, whereas sub-stomatal CO₂ concentration (C _i) increased in leaves from the girdled branches. The total chlorophyll content (Chl) tended to decrease in parallel with the reduced P _N. Girdling did not substantially influence the leaf and shoot water contents. The large availability of assimilates seems to cause an earlier fruit ripening. In general, girdling increased fruit dry mass. Healing before the time when the majority of pulp growth occurs reduced the effect of girdling. June girdling increased the pit dry mass. Girdling at the beginning of August and September, compared to the control, increased the pulp dry mass, but the pit dry mass did not differ with respect to the control. The percentage of oil in the fruit, on a dry mass basis, increased with August and September girdlings, but the percentage of oil in the pulp did not change. Girdling reduced shoot growth, but the internode length was unchanged. Girdling slightly stimulated differentiation of flower buds.     

The margin for error when releasing the asymmetric bars for dismounts

It has previously been shown that male gymnasts using the "scooped" giant circling technique were able to flatten the path followed by their mass center, resulting in a larger margin for error when releasing the high bar (Hiley and Yeadon, 2003a). The circling technique prior to performing double layout somersault dismounts from the asymmetric bars in women's artistic gymnastics appears to be similar to the "traditional" technique used by some male gymnasts on the high bar. It was speculated that as a result the female gymnasts would have margins for error similar to those of male gymnasts who use the traditional technique. However, it is unclear how the technique of the female gymnasts is affected by the need to avoid the lower bar. A 4-segment planar simulation model of the gymnast and upper bar was used to determine the margins for error when releasing the bar for 9 double layout somersault dismounts at the Sydney 2000 Olympics. The elastic properties of the gymnast and bar were modeled using damped linear springs. Model parameters, primarily the inertia and spring parameters, were optimized to obtain a close match between simulated and actual performances in terms of rotation angle (1.2 degrees), bar displacement (0.011 m), and release velocities (<1%). Each matching simulation was used to determine the time window around the actual point of release for which the model had appropriate release parameters to complete the dismount successfully. The margins for error of the 9 female gymnasts (release window 43-102 ms) were comparable to those of the 3 male gymnasts using the traditional technique (release window 79-84 ms).     

温室秸秆不同还田量条件下DSSAT-CROPGRO-Tomato模型的调参与验证

为了探讨番茄生长模拟模型DSSAT-CROPGRO-Tomato能否准确模拟秸秆还田条件下北方日光温室番茄的生长发育和产量形成过程,基于2016年和2018年温室番茄小区试验数据对模型进行验证。试验设置4个秸秆还田量处理,分别为0(S₀)、1.5×10⁴(S₁)、3×10⁴(S₂)和4.5×10⁴kg·hm^-2(S₃)。利用GLUE参数估计模块获得不同方案相应的作物遗传参数,通过分析和对比番茄物候期、鲜果产量、最大叶面积指数、土壤水分、土壤无机态氮和地上干物质量的实测值与模拟值,验证模型模拟精度并确定最优方案。结果表明,参数PODUR(最优条件下最终果实负载所需光热时长)和SLAVR(比叶面积)的变异系数较大,分别为28.53%和14.13%。模型在2016年所有处理为参数估计方案时模拟精度最高,其ARE和nRMSE分别为10.33%和7.12%。模型对温室土壤水分、番茄生长和产量的模拟精度较高。留一交叉验证法体现模型对温室番茄产量总体误差在18.68%~21.95%。说明CROPGRO-Tomato模型可以较准确模拟秸秆不同还田量条件下沈阳日光温室番茄生长和产量形成过程。