The generally accepted norm for controlled experiments with plants has traditionally been restricted to a simplified maintenance of a constant state of the surrounding medium. The ‘treatments’ and a ‘control’, as a reference for comparisons, have been applied without a clear specification of causality and function. However, for pure mathematical reasons, plants are in a constant physiological state (steady‐state) only when the internal concentrations of carbon and nutrients and the ratios between them remain constant. Consequently, experimental conditions are controlled in a meaningful sense only when carbon and nutrients are taken up with a constant relative uptake rate, Ru, that is equal to the relative growth rate, RG. The successful application of these fundamental rules to experimental procedures has been verified in numerous experiments. As for acclimatized plants in steady‐state, responses to limiting factors have been graded relative to maximum performance, which constitutes the ultimate reference value. Despite the comprehensive and straightforward material of evidence, the methodology is still a matter of argument.It is concluded that the driving variable commonly used for uptake, external concentration, should be abandoned since its form (lack of time dimension) makes it incompatible with the uptake rate. This calls for a shift of paradigm since the failure of recognition both of fundamental relationships and of experimental shortcomings has been harmful to the development of a sound scientific basis for specification of plant properties. Although fragmented knowledge of basic mechanisms may be good, understanding of causes and effects is poor in relationships between environmental, internal and inherited conditions on the one side, and plant performance on the other. A pseudo‐science has in an empirical ‘trial‐and‐error’ research been based upon statistical evaluation of data of low quality. This is a problem of major significance that needs open discussion and public attention.

Experimental methods to supply nutrients to culture solutions in order quantitatively to control plant nutrition are compared, In experiments with tomato and birch plants, for which the data are available in databases (Ingestad et al., 1994a, b), the nutrients were supplied at constant relative addition rates (R(A)) over sufficiently long periods of time to achieve acclimated plants and reliable measurements of plant responses. The plants were maintained under steady-state conditions, i.e. the internal nutrient concentrations (c(i)) remained constant, as a result of a numerical equality between the relative uptake rate (R(U)) and the relative growth rate (R(G)). These results are compared to experiments with pea plants (Macduff et al., 1993), In one series (a), R(A) was applied, but without strict control of internal steady-state, and in the other series (b), the external concentration (c(e)) was maintained constant, With limiting nitrogen, in both series, there was a substantial deviation from equality between R(U) and R(G). In (a), c(i) changed during the experimental period and the purpose of the R(A) approach was lost, In (b), a constant c(e) had little effect on nitrogen uptake and plant growth, At the three highest concentrations, steady-states were obtained at non-limiting uptake rates, At the lowest concentration, the uptake rate of nitrogen was about the same, but there was a decrease of R(G), which apparently was not caused by reduced uptake. Clear-cut relationships can not therefore be established between treatment variables and plant responses and the conclusions reached by Macduff et al. (1993) have little support in their experimental results, This indicates an urgent need to update both theories and experimental methods together: in particular, it is important to identify the system under investigation and to distinguish between control of the medium and control of the plant.

Methods to control carbon and nutrient uptake at different availability of carbon were tested on plants of birch (Betula pendula Roth.) and tomato (Lycopersicon esculentum Mill. cv. Solentos). The present paper accounts for the methods and the possibility to maintain steady‐state, i.e., a long‐term and stable physiological state of acclimated plants. Steady‐state comprises, by definition, equality between constant relative growth rates, and relative uptake rates of carbon and nutrients. Two methods were tested. The first, not previously applied, method (a), was based on a constant relative addition rate of carbon, RAC. In the second method (b), a constant concentration of CO2 in the air, ca, was used to attain non‐limiting conditions. The methods are analogous to those used by us to control plant nutrition, and the generality of fluxes to quantify supply as well as uptake and growth was verified. Thus, different RAC resulted in clear‐cut responses, from strong reduction to non‐limitation of uptake and growth, whereas different ca levels in the range 100 to 700 ppm had comparatively small effects, with an unclear causality. Non‐limiting conditions were achieved at ca≥ 200 ppm. Effects reported in the literature have been based upon the control of ca, similarly to method (b), whereas results comparable to those obtained with method (a) are lacking.Transpiration rate increased rapidly at ca < 200 ppm CO2, and at low RAC levels, ≤ 0.1 day−1, wilting tendencies were observed. Elevated ca, 500 or 700 ppm, did not increase the relative growth rate (RG) but reduced transpiration and increased both nitrogen productivity (growth rate per unit of nitrogen in the plant) and transpiration productivity (growth rate per unit of water transpired by the plant). Obviously, effects of ca may be due to changed transpiration rate rather than to changed quantitative availability of CO2.Relative uptake (RUC) and growth (RG) rates were closely equal to the RAC applied (RAC≅ RUC≅ RG); i.e., the purely mathematical conditions defining steady‐state were fulfilled. This unambiguous and straightforward test of reliability confirms that experimental artefacts did not produce uncontrolled or unintended effects, so that the new technique allows an accurate control of CO2 uptake and plant growth. The results add to previous databases and reference systems, where limiting conditions grade and classify plant performance as deviations from maximum growth. Evidently, methodology in experimentation and in evaluation of plant responses, can be based upon unifying concepts and general theories.

Strictly controlled experiments with plants, acclimatized under steady-state conditions and grown for a sufficiently long time period to get reliable and representative measurements, are necessary to obtain plant responses in precise terms (reference values). It is then possible to reproduce and compare experimental results with a high accuracy and to establish fundamental plant properties in an unambiguous and unifying terminology. Two kinds of growth determining factors can be distinguished:

A theory comprising two basic concepts relating nutrition and growth is presented. The first concept is a nutrient flux model and is based upon studies of plants at constant internal nutrient concentrations, where a formal mathematical derivation shows that the relative uptake rate (R U ) and the relative growth rate (R G ) are equal. Deviations from equality are results of experimental insufficiencies and errors. The second concept is based on the observation that R G is linearly related to the internal nutrient concentration. The slope represents nutrient productivity (P n ), an important parameter expressing growth rate per unit of nutrient. Light and the plant genome, for example, influence the value of the proportionality factor, P n , but not the formal relationship between the internal nutrient concentration and R G Not only the theory itself but many results and conclusions are very different from those obtained with traditional methods. In experiments where R U was controlled during the exponential period of growth, the relationships between treatment (the relative addition rate, R A ), nutrient uptake (R U ) and growth (R G ) were reproduced with extremely low variability. In agreement with theory, internal nutrient concentration and R G remained stable over time (steady‐state). An extension of the theory is based upon the empirical assumption that after exponential growth, self‐shading and ageing reduce P n in proportion to biomass. This assumption has been successfully applied in predicting growth of forest stands, but the nature of the growth reduction is little understood. The generalized model has few parameters and can easily be rewritten to suit different experimental aims, for example to establish reference values and to model changes in soil fertility. Further extension and understanding of the model and different interpretations of the parameters are discussed.

Small birch plants (Betula pendula Roth.) were grown in a climate chamber at different, exponentially increasing rates of nitrogen supply and at different photon flux densities. This resulted in treatments with relative growth rate equal to the relative rate of increase in nitrogen supply and with different equilibrium values of plant nitrogen concentration. Nitrogen productivity (rate of dry matter increase per plant nitrogen) was largely independent of nitrogen supply and was greater at higher photon flux density. Leaf weight ratio, average specific leaf area (and thus leaf area ratio) were all greater at better nitrogen supply and at lower values of photon flux density. The dependencies were such that the ratio of total projected leaf area to plant nitrogen at a given photon flux density was similar at all rates of nitrogen supply. The ratio was greater at lower values of photon flux density. At a given value of photon flux density, net assimilation rate and net photosynthetic rate per shoot area (measured at the growth climate) were only slightly greater at better rates of nitrogen supply. Values were greater at higher photon flux densities. Acclimation of the total leaf area to plant nitrogen ratio and of net assimilation rate was such that nitrogen productivity was largely saturated with respect to photon flux density at values greater than 230 μmol m-2 s-1. At higher photon flux densities, any potential gain in nitrogen productivity associated with higher net assimilation rates was apparently offset by lower ratios of total leaf area to plant nitrogen.

The influence of nutrition on the allocation of dry matter is investigated using data from previously published experiments with the forest tree species (Betula pendular Roth., Picea babies (L.) Karst., Pinus contorta Doug., and Pinus Sibbaldia L.) where the nutrient status of the plants was maintained constant over a considerable period of time and biomass increase (steady-state nutrition and growth). We demonstrated that the allocation patterns of a plant species under limiting nutrient conditions and at optimum can be derived from parameters that have been used to characterize relationships between nutrient status, nutrient uptake, and growth of the species. The properties of the plant that control biomass allocation are discussed on the basis of these findings.

Application of large doses of fertilizer at widely spaced time intervals has become the accepted way of increasing crop production. That does not mean that it is the most effective way. The underlying relationships between nutrition and plant growth are poorly understood, the author points out, and the current practice arose from empirical observations based on pragmatic and short-term concerns. The availability of cheap fertilizers has led to careless and imprecise use of them, and environmental concerns are calling current practices into question.Ingestad introduces several time-dependent and theoretically related parameters for nutrient addition, nutrient uptake, and plant growth. Current fertilization practices are aimed at increasing nutrient concentrations in the soil, but they overlook the continuous weather-and season-dependent processes of soil fertility and nutrient uptake. Fertilizer should be entered into the system continuously to supplement the mineralization process, Ingestad argues.The proposed model is quite radical, but the experimental results show a high general validity, striking similarity between laboratory and field observations, and unexpectedly high growth and production responses to fertilization.

Ingestad, T. and Ågren, G. I. 1988. Nutrient uptake and allocation at steady‐state nutrition. ‐ Physiol. Plant. 72: 450–459. Net nutrient uptake and translocation rates are discussed for conditions of steady‐state nutrition and growth. Under these conditions, the relative uptake rate is equal to the relative growth rate, for whole plants as well as for plant parts, since the root/shoot ratio and internal concentrations remain stable. The nutrient productivity and the minimum internal concentration are parameters characteristic for the plant and the nutrient. A conceptual, mathematical model, based on these two fundamental parameters is used for calculation and prediction of the net nutrient uptake rate, which is required to maintain steady‐state nutrition at a specified internal nutrient concentration or relative growth rate. When uptake rate is expressed on the basis of the root growth rate, there is, up to optimum, a strong linear relationship between uptake rate and the internal concentration of the limiting nutrient. More complicated and less consistent relationships are obtained when uptake rate is related to root biomass. The limiting factor for suboptimum uptake is the amount of nutrients becoming available at the root surface. When replenishment is efficient, e.g. with vigorous stirring, the concentration requirement at the root surface appears to be extremely low, even at optimum. In the suboptimum range of nutrition, the effect of nutrient status on root growth rate is a critical factor with a strong feed‐back on nutrition, growth and allocation. At supraoptimum conditions, the uptake mechanism is interpreted as a protection against too high uptake rates and internal concentrations at high external concentration. In birch ( Betula pendula Roth.), the allocation of nitrogen to the shoots is high compared to that of potassium and also to that of phosphorus at low nitrogen or phosphorus status. With decreasing stress, phosphorus allocation becomes more and more similar to nitrogen allocation. The formulation of a mathematical model for calculation of allocation of biomass and nutrients requires more exact information on the quantitative dependence of the growth‐regulating processes on nutrition.

Birch (Betula pendula Roth.) was investigated under steady state nutrition and growth at different relative addition rates of phosphorus (Rp). Phosphorus deficiency symptoms appeared on the leaves when the internal phosphorus concentration decreased, but disappeared again under steady state nutrition, independent of the stress level. The increased root/shoot ratio and the exploratory type of root systems developed during the adjustment stage remained under steady state conditions. At nonoptimum and close to optimum relative addition rates, independent of the rate, the phosphorus concentration of the culture solution did not exceed 2 μmol dm−3 and was generally < 1 μmol dm−3 immediately after phosphorus additions. The phosphorus concentration just before additions was generally < 0.5 μmol dm−3. The nutrition/growth relationships were similar to those for nitrogen, with relative growth rate (Rg) closely related to the Rp applied and with a strong linear relationship between internal phosphorus concentration and Rg. Regression was much steeper than that for nitrogen. The slope of the optimum nutrition was attained at a lower phosphorus weight proportion to nitrogen (8–10 P: 100 N) than previously estimated (= 13 P: 100 N), but a higher relative phosphorus requirement was observed under stress conditions. Birch seedlings had a strong tendency to consume phosphorus in excess of immediate requirements with a small effect on growth above optimum. This resulted in rapidly decreasing phosphorus productivity (Pp, growth rate per unit of phosphorus) with increasing internal phosphorus concentrations above optimum.

Fertilization is modelled on the basis of two concepts, nutrient flux density in the soil (amount of nutrient available per unit of soil and unit of time) and nutrient productivity (growth rate per unit of nutrient in plant). The nutrient productivity is used to calculate the nutrient uptake rate which is required to maintain the internal nutrient status constant at optimum and which, therefore, is required to be matched by the nutrient flux density. By supplying fertilizer nutrients as an addition to the flux density, high utilization of the added nutrients may result. A simple application of the model is, therefore, to increase the current nutrient flux density to a specified rate by the fertilizer additions. Increased accuracy of fertilization is possible by adjustment of the dosage also to the potential uptake rate of the crop. The relationships in the model are discussed on the basis of nitrogen nutrition but the use of complete fertilizers is recommended. The parameters needed, including weather data, to calculate fertilizer dosages over the growing season are discussed. A computer-adapted technique is suggested, using an irrigation system to distribute a liquid fertilizer. In this way experiments can be done to increase knowledge about nutrient dynamics and crop properties and to improve the model so as to develop more efficient fertilization routines with minimal nutrient leaching and environmental hazards.

The response of forest tree seedlings to aluminum concentrations was investigated. A growth technique was used in which nutrients were present in low concentrations in a circulating solution. Plant nutrition and relative growth rate were maintained in steady-state by adding the nutrients in Optimum proportions at a constant relative addition rate. After a period of steady-state growth, aluminum was added to the nutrient solution in different concentrations.

The interrelationships and use of a series of general concepts in modelling plant nutrition and growth are exemplified with laboratory and field experiments with steady state nutrition and growth mainly of forest tree species. It follows from mathematical derivations that in order to maintain a constant nutrient concentration in the plant, the relative uptake rate, RU, and therefore the relative addition rate, RA, must equal the relative growth rate, RG. A concept corresponding to RA has been introduced to specify the rate of nutrient supply under field conditions, the nutrient flux density, Dn. The ability of the plant to take up the nutrients made available is expressed in the concept of utilization capacity, Un. The experimental results suggest that plant nutrient requirements can be defined by two variables: complete nutrient proportions in plant and fertilizer and rate of application of fertilizer to support current growth.

Ectomycorrhizal seedlings of Scots pine (Pinus sylvestris L. cv.), inoculated with the fungus Suillus bovinus (L. ex Fr.) O. Kuntze, and non‐mycorrhizal controls were grown in growth units with a circulating culture solution. Steady‐state nutrition and constant relative growth rates were achieved by means of varied relative nutrient addition rates and free access of nutrients. Typical mycorrhizas always formed within a short period of time after inoculation. The nutrition/growth relationships were in principle similar to previous studies under steady‐state conditions: there were close linear relationships between relative addition rate, relative growth rate and internal nitrogen concentration, i.e. an equilibrium established between nutrients added and taken up. This occurred when infected and uninfected seedlings were grown separately. When grown together in the same growth unit, there are indications that the fungus influenced the exudation pattern of the uninfected seedlings. More carbon was thus provided to the unspecified microflora in the cultivation system, and it was able to grow and withhold nitrogen from the seedlings. The mycorrhizal infection did not increase the specific uptake capacity of the roots, and the fungus constituted a sink for carbon. However, the nitrogen productivity (growth rate per unit of nitrogen per unit of time) was similar for mycorrhizal and non‐mycorrhizal seedlings, so that there might be mechanisms which compensate for the carbon cost.

The experimental use of the relative addition rate as the driving variable for plant nutrition and growth is reviewed with special attention to the theoretical background and the technical and methodological problems. In this technique the culture solution is not a “nutrient solution” in the classical sense, i.e. a solution with a specified initial concentration of nutrient salts. Instead the solution is a carrier of repeatedly added nutrients to the roots. The nutrients are added quantitatively for a specified growth rate and period of time, to permit a steady state relative uptake rate. High accuracy in the control of nutrition and growth has been obtained in solution culture experiments in which the relative addition rate was applied as the treatment variable, when all necessary nutrients were accounted for, when the additions were made very often, and when the culture solution was in darkness and in good physical contact with the roots.

The growth of two provenances of Pinus sylvestris L. were compared with two provenances of Picea abies (L.) Karst. and with Pinus contorta Dougl. when grown in solution cultures with low nutrient concentrations. Nitrogen was added at different exponentially increasing rates, and the other nutrients were added at a rate high enough to ensure free access of them to the seedlings.During an initial period of the culture (a lag phase), when the internal nutrient status was changing from optimum to the level of the treatment, deficiency symptoms appeared. The needles yellowed and the root/shoot ratio increased. The initial phase was followed by a period of exponential growth and steady‐state nutrition. The needles turned green again, and the root/shoot ratio stabilized at a level characteristic of the treatment. These patterns were the same as previously reported for other tree species.The relative growth rate during exponential growth was numerically closely equal to the relative nitrogen addition rate. The maximum relative growth rates were about 6 to 7.5% dry weight increase day‐1. This is a much lower maximum than for broad‐leaved species (about 20 to 30% day‐1) under similar growth conditions.The internal nitrogen concentrations of the seedlings and the relative growth rates were stable during the exponential period. Close linear relationships were found between these parameters and the relative addition rate up to maximum growth.During steady state the relative growth rates of the different plant parts were equal. However, there were large differences between genotypes in absolute root growth rate at the same seedling size because of differences in root/shoot ratio. Lodgepole pine had the highest root growth rate, whereas that of Norway spruce, especially the southern provenance, was remarkably low. Yet, Norway spruce had a high ability to utilize available nutrients. In treatments with free nutrient access, growth allocation to the shoot had a high priority in all genotypes, but there was still a marked tendency for luxury uptake of nutrients. Nitrogen productivity (growth rate per unit of nitrogen) was lower than in broadleaved species and highest in lodgepole pine. The relevance of the dynamic factors, i.e. maximum relative growth rate, nutrient uptake rate, nitrogen productivity, growth allocation and root growth rate, are discussed with regard to conifer characteristics and selection value.

Plant, Cell & EnvironmentVolume 7, Issue 5 p. 368-369 ENCYCLOPEDIA OF PLANT PHYSIOLOGY, VOLUME 12D, PHYSIOLOGICAL PLANT ECOLOGY IV (Book). Torsten Ingestad, Torsten IngestadSearch for more papers by this author Torsten Ingestad, Torsten IngestadSearch for more papers by this author First published: July 1984 https://doi.org/10.1111/1365-3040.ep11589828AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume7, Issue5July 1984Pages 368-369 RelatedInformation