Partitioning Coefficients in Plant Models with Turn-over

Reynolds and Thornley have presented a model for the partitioningof newly synthesized dry matter between shoots and roots invegetative plants, which combines a whole-plant functional balancewith an adaptive partitioning pattern. It turns out, however,that the derived partitioning coefficients are only applicableto models with equal turn-over rates for shoot and roots. Itis shown in this paper that the method used for the derivationof these coefficients does not always provide a partitioningpattern that is well-behaved, and a more general derivationis presented which includes the Reynolds and Thornley modelas a special case. Partitioning, growth, models, functional balance, turn-over rates     

A Review of Evidence on the Control of Shoot: Root Ratio, in Relation to Models

Four basic models exist for the control of shoot: root ratio(S: R): (a) allometric models, proposing a fixed ratio of shootgrowth rate to root growth rate; (b) functional equilibriummodels, based on the ratio of shoot activity to root activity;(c) the Thornley model, based on carbon and nitrogen uptakeand transport, (d) hormone models, generally suggesting theroot produces a hormone that controls the shoot and vice versa.Models (a) and (b) are empirical, and therefore provide no testof the processes operating. Ontogenetic changes in S: R for fibrous-rooted herbs could befitted by a modified Thornley model. Ontogenetic effects mustbe excluded in judging other effects. Responses of S: R to deficits of water, major inorganic nutrients,light and carbon dioxide, and to defoliation and root pruning,usually conform to Thornley's model. With current knowledgeThornley's model cannot usefully be applied to minor nutrients,nutrient toxicity or temperature differences. S: R changes atreproduction usually conform to Thornley's model if it is assumedthat young reproductive structures are a strong sink, but thisbegs the question of what determines sink strength. There areapparent exceptions to most of these responses, which shouldbe studied further. Phytohormones can influence S: R, but may not be the controloperating in the normal, intact plant. Most of the availableevidence is compatible with a source-sink model of Thornley'stype, and therefore does not demand a hormonal theory of S:R control. There is a need for more critical tests. Shoot: root ratio, strategy, partitioning, models     

Above- and Below-ground Growth of Forest Stands: a Carbon Budget Model

The utilization and allocation of carbon by a forest stand areexamined through a simple dynamic, mechanistic model which incorporatesradiation interception, photosynthesis, respiration, assimilatepartitioning, litterfall, root mortality and turnover. Qualitativemathematical analysis of the balance between carbon gains andlosses provides an intuitive insight into the determinants ofabove- and below-ground growth. The patterns of dry matter accumulationproduced by the model are compared with observed trends in standdevelopment. Reported differences between biomass distributionon sites of high and low productivity are reproduced by adjustingthe coefficients of assimilate partitioning. Forest stand growth, model forest growth, carbon budget, photosynthesis, assimilate partitioning     

Response of Dry Matter Partitioning, Growth, and Carbon and Nitrogen Levels in the Tomato Plant to Changes in Root Temperature: Experiment and Theory

Growth, dry matter partitioning, and the levels of various substancesin tomato plants grown in liquid nutrient culture at four roottemperatures (15, 20, 25, and 30°C) in controlled environmentcabinets were measured. In order to understand the role of roottemperature in growth and development, the partitioning modelof Thornley (1972) was used to try and describe the observedbehaviour. The steady-state behaviour could be simulated reasonablyby the model, although certain aspects of the time-course datapresent problems. It was observed that relative growth rateis proportional to the product of the carbon and nitrogen levels(one of the two principal assumptions of the model). The modelalso made realistic predictions about the influence of roottemperature on the fraction of the plant dry matter in the root,and on the carbon and nitrogen levels. The effect of root temperaturewas incorporated into the model by assuming that certain valuesof specific root activity correspond to the different temperatures.In addition the model predicted an experimentally reasonablerelation between net assimilation rate and relative growth rate.     

Nitrogen partitioning in the photosynthetic apparatus of Plantago asiatica leaves grown under different temperature and light conditions: similarities and differences between temperature and light acclimation

Effects of growth temperature and irradiance on nitrogen partitioning among photosynthetic components were studied. Plantago asiatica was grown under different temperature and light conditions. Growth conditions were regulated such that the Chl a/b ratio in leaves grown at a low temperature with a low irradiance was similar to that in leaves grown at a high temperature with a high irradiance, suggesting that the balance between acquisition and utilization of light energy in the photosynthetic apparatus was similar between the two growth conditions. When plotted against the leaf nitrogen content, the RuBP (ribulose-1,5-bisphosphate) carboxylase content did not significantly differ depending on growth conditions. Both high irradiance and low temperature decreased nitrogen partitioning to Chl-protein complexes. Low temperature increased nitrogen allocation to stroma FBPase (fructose-1,6-phosphatase) irrespective of growth irradiance. Gas exchange measurement indicated that the ratio of the electron transport (J(max)) to the maximum carboxylation rate (V(cmax)) was not affected by growth irradiance but by growth temperature. It is concluded that nitrogen partitioning between acquisition and utilization of light energy responds to both growth temperature and irradiance, while nitrogen partitioning between carboxylation and regeneration of RuBP responds only to growth temperature.     

Carbon Balance of Tall Fescue (Festuca arundinacea Schreb.): Effects of Nitrogen Fertilization and the Growing Season

The C balance of a tall fescue sward grown under different ratesof N fertilization in summer, autumn, and spring was calculatedusing models derived from measurements of shoot growth, canopygross photosynthesis, shoot respiration and of C partitioningto the roots. Under the diverse growing conditions associatedwith the seasons and the N fertilization, C utilization forabove- and below-ground biomass accumulation never exceeded39 and 14% of the canopy gross photosynthesis, respectively.Carbon losses attributed to root respiration and exudation,which were estimated by difference between canopy net photosynthesisand total growth, ranged between 3 and 30% of canopy gross photosynthesis.Seasonal differences in shoot growth could be attributed tothe amount of intercepted radiation, the radiation-use efficiencyand the C partitioning to the roots. The effect of N deficiencyon shoot growth can be attributed to its effects on canopy photosynthesis(principally resulting from changes in intercepted photosyntheticallyactive radiation) and C partitioning. In comparison with theeffect on shoot growth, the effect of the N deficiency on thecanopy gross photosynthesis per unit of light intercepted overthe regrowth cycle was limited. It is concluded that most ofthe effect of N fertilization on shoot growth is due to changesin C partitioning which result in faster leaf area developmentand greater light interception.Copyright 1994, 1999 AcademicPress Tall rescue, Festuca arundinacea Schreb., carbon balance, nitrogen, grass, fertilization     

Time course of photosynthetic response to changes in incident light energy

The response of whole leaf photosynthetic rate in Fragaria virginiana to sudden changes in photosynthetically active radiation (PAR) is described. Two components of the response, consisting of a time lag and time constant, are estimated under varying PAR changes for plants grown under two different light regimes. Both the time lag and time constant are found to vary with PAR but not with growth light regime. A model of Thornley for leaf photosynthetic response is refuted and an alternative form is discussed.     

Integrated Analysis of Resource Capture and Utilization

A set of mathematical identities is derived which relates drymatter production to the availability of above- and below-groundresources, to the efficiency of resource capture, to the efficiencyof resource utilization, to the activity of above- and below-groundorgans and to the partitioning of dry matter in the plant. Thisintegrated analysis can be adapted in various ways accordingto the needs and objectives of the study in hand: it ultimatelyrests upon relatively simple primary data and gives clearlyrelevant derived quantities. Growth analysis, crop growth rate, relative growth rate, equations of growth, resource capture, resource utilization, photosynthetically active radiation, mineral nutrient uptake, water uptake, partitioning, root-shoot functional equilibria     

Simulating Growth and Root-shoot Partitioning in Prairie Grasses Under Elevated Atmospheric CO2and Water Stress

We constructed a model simulating growth, shoot-root partitioning,plant nitrogen (N) concentration and total non-structural carbohydratesin perennial grasses. Carbon (C) allocation was based on theconcept of a functional balance between root and shoot growth,which responded to variable plant C and N supplies. Interactionsbetween the plant and environment were made explicit by wayof variables for soil water and soil inorganic N. The modelwas fitted to data on the growth of two species of perennialgrass subjected to elevated atmospheric CO₂and water stresstreatments. The model exhibited complex feedbacks between plantand environment, and the indirect effects of CO₂and water treatmentson soil water and soil inorganic N supplies were important ininterpreting observed plant responses. Growth was surprisinglyinsensitive to shoot-root partitioning in the model, apparentlybecause of the limited soil N supply, which weakened the expectedpositive relationship between root growth and total N uptake.Alternative models for the regulation of allocation betweenshoots and roots were objectively compared by using optimizationto find the least squares fit of each model to the data. Regulationby various combinations of C and N uptake rates, C and N substrateconcentrations, and shoot and root biomass gave nearly equivalentfits to the data, apparently because these variables were correlatedwith each other. A partitioning function that maximized growthpredicted too high a root to shoot ratio, suggesting that partitioningdid not serve to maximize growth under the conditions of theexperiment.Copyright 1998 Annals of Botany Company plant growth model, optimization, nitrogen, non-structural carbohydrates, carbon partitioning, elevated CO₂, water stress,Pascopyrum smithii,Bouteloua gracilis, photosynthetic pathway, maximal growth     

Shoot-Root-Nodule Partitioning in a Vegetative Legume--A Model

A dry-matter partitioning model of a vegetative legume whichis both utilizing nitrate nitrogen and carrying out N₂ fixationis described. It is an extension of a previously described root-shootmodel, and is based on assumed transport pathways for carbonand nitrogen substrates, and utilization of those substratesfor structural growth. The model is used to examine the consequencesof varying the photosynthetic activity, the nitrate uptake activity,and the N₂ fixation activity on the patterns of dry-matter partitioningand substrate fluxes within the plant. The predictions of themodel agree with physiological expectation, and the model cantherefore be used to provide an interpretation of experimentalobservations of such plant and crop responses. Model, partitioning, legume, nitrogen fixation     

The impact of consumer-resource cycles on the coexistence of competing consumers

This article seeks to determine the extent to which endogenous consumer-resource cycles can contribute to the coexistence of competing consumer species. It begins with a numerical analysis of a simple model proposed by Armstrong and McGehee. This model has a single resource and two consumers, one with a linear functional response and one with a saturating response. Coexistence of the two consumer species can occur when the species with a saturating response generates population cycles of the resource, and also has a lower resource requirement for zero population growth. Coexistence can be achieved over a wide range of relative efficiencies of the two consumers provided that the functional response of the saturating consumer reaches its half-saturation value when the resource population is a small fraction of its carrying capacity. In this case, the range of efficiencies allowing coexistence is comparable to that when two competitors have stable dynamics and a high degree of resource partitioning. A variety of modifications of this basic model are analyzed to investigate the consequences for coexistence of different resource growth equations, different functional and numerical response shapes, and other factors. Large differences in functional response shape appear to be the most important factor in producing robust coexistence via resource cycles. If the unstable species has a concave numerical response, this greatly expands the conditions allowing coexistence. If the stable consumer species has a convex (accelerating) functional and/or numerical response, the range of conditions allowing coexistence is also expanded. We argue that large between-species differences in functional response form can often be produced by between-consumer differences in the adaptive adjustments of foraging effort to food density. Consumer-resource cycles can also expand the conditions allowing coexistence when there is resource partitioning, but do so primarily when resource partitioning is relatively slight; this makes the ease of coexistence relatively independent of consumer similarity.     

Evaluating the carbon balance estimate from an automated ground‐level flux chamber system in artificial grass mesocosms

Measuring and modeling carbon (C) stock changes in terrestrial ecosystems are pivotal in addressing global C‐cycling model uncertainties. Difficulties in detecting small short‐term changes in relatively large C stocks require the development of robust sensitive flux measurement techniques. Net ecosystem exchange (NEE) ground‐level chambers are increasingly used to assess C dynamics in low vegetation ecosystems but, to date, have lacked formal rigorous field validation against measured C stock changes. We developed and deployed an automated and multiplexed C‐flux chamber system in grassland mesocosms in order rigorously to compare ecosystem total C budget obtained using hourly C‐flux measurements versus destructive net C balance. The system combines transparent NEE and opaque respiration chambers enabling partitioning of photosynthetic and respiratory fluxes. The C‐balance comparison showed good agreement between the two methods, but only after NEE fluxes were corrected for light reductions due to chamber presence. The dark chamber fluxes allowed assessing temperature sensitivity of ecosystem respiration (R_eco) components (i.e., heterotrophic vs. autotrophic) at different growth stages. We propose that such automated flux chamber systems can provide an accurate C balance, also enabling pivotal partitioning of the different C‐flux components (e.g., photosynthesis and respiration) suitable for model evaluation and developments.     

Hypothalamic AgRP-neurons control peripheral substrate utilization and nutrient partitioning

Obesity-related diseases such as diabetes and dyslipidemia result from metabolic alterations including the defective conversion, storage and utilization of nutrients, but the central mechanisms that regulate this process of nutrient partitioning remain elusive. As positive regulators of feeding behaviour, agouti-related protein (AgRP) producing neurons are indispensible for the hypothalamic integration of energy balance. Here, we demonstrate a role for AgRP-neurons in the control of nutrient partitioning. We report that ablation of AgRP-neurons leads to a change in autonomic output onto liver, muscle and pancreas affecting the relative balance between lipids and carbohydrates metabolism. As a consequence, mice lacking AgRP-neurons become obese and hyperinsulinemic on regular chow but display reduced body weight gain and paradoxical improvement in glucose tolerance on high-fat diet. These results provide a direct demonstration of a role for AgRP-neurons in the coordination of efferent organ activity and nutrient partitioning, providing a mechanistic link between obesity and obesity-related disorders.     

A Model of Shoot: Root Partitioning with Optimal Growth

A shoot: root partitioning model is presented, which is a developmentof previous approaches in the area. The model incorporates asa physiologically reasonable apparent ‘goal’ forthe plant, the assumption that the partitioning of growth betweenthe shoot and root maximizes the plant specific growth ratein balanced exponential growth. The analysis is concerned principallywith plant growth being a function of carbon and nitrogen only,although it is indicated how other nutrients, or growth factors,may be incorporated. Plant growth is driven by the environmentalconditions, and partitioning is defined entirely in terms ofthe shoot: root ratio and carbon and nitrogen status of theplant. In its basic form the model requires the definition ofa single plant growth parameter, along with the shoot and rootspecific activities and structural composition. Shoot: root partitioning, specific growth rate, vegetative phase     

Assessment of the efficiency of nitrogen utilization in the infant cebus monkey (Cebus albifrons) by nitrogen balance

Nitrogen (N) balance and growth were utilized to assess the efficiency of N utilization in the infant cebus monkey (Cebus albifrons). The efficiency of N utilization as calculated from N balance data was 35%. The efficiency of N utilization for growth was 37% as determined by weight change over a 28-day trial and by body composition data from the literature. These results indicate, therefore, that growth and N balance are comparable indicators of N utilization in these primates.     

A Model of the Partitioning of Growth between the Shoots and Roots of Vegetative Plants

A model of the partitioning of new growth between the shootsand roots of vegetative plants is presented. There are two partitioningfunctions, involving one partitioning parameter, which describethe priorities for new growth in both the shoots and roots.The dynamic responses, to changes in the environment and toshoot defoliation, of shoot and root specific growth rates,shoot: root ratio, and carbon and nitrogen substrate levels,are examined; realistic behaviour is observed. Balanced exponentialgrowth solutions are also examined and it is concluded thatrelationships between some derived plant growth quantities maybe non-unique, thus emphasizing the need for a critical understandingof the underlying physiological processes involved in plantgrowth. Mathematical model, partitioning of assimilates, shoot: root ratio, specific growth rate, carbon and nitrogen substrate levels     

A Model to Describe the Partitioning of Photosynthate during Vegetative Plant Growth

An approach is described to the problem of modelling quantitativelythe partitioning of photosynthate during vegetative plant growth.Two plant processes are important in the scheme: the first ofthese is the utilization of substrate for growth and how thisutilization depends upon substrate concentration, the secondconcerns the transport of substrate between different plantparts and how this depends upon the substrate concentrationsin the plant parts. In both cases simple phenomenological relationshave been assumed which seem to be in reasonable accord withexperimental data and with more basic theoretical considerations.The model is able to describe some of the features of steady-statevegetative plant growth in a natural manner. The limitationsof the present formulation are considered, and the implicationsof this type of approach for whole-plant models are discussed.     

Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110.

Flux balance models of metabolism use stoichiometry of metabolic pathways, metabolic demands of growth, and optimality principles to predict metabolic flux distribution and cellular growth under specified environmental conditions. These models have provided a mechanistic interpretation of systemic metabolic physiology, and they are also useful as a quantitative tool for metabolic pathway design. Quantitative predictions of cell growth and metabolic by-product secretion that are experimentally testable can be obtained from these models. In the present report, we used independent measurements to determine the model parameters for the wild-type Escherichia coli strain W3110. We experimentally determined the maximum oxygen utilization rate (15 mmol of O2 per g [dry weight] per h), the maximum aerobic glucose utilization rate (10.5 mmol of Glc per g [dry weight] per h), the maximum anaerobic glucose utilization rate (18.5 mmol of Glc per g [dry weight] per h), the non-growth-associated maintenance requirements (7.6 mmol of ATP per g [dry weight] per h), and the growth-associated maintenance requirements (13 mmol of ATP per g of biomass). The flux balance model specified by these parameters was found to quantitatively predict glucose and oxygen uptake rates as well as acetate secretion rates observed in chemostat experiments. We have formulated a predictive algorithm in order to apply the flux balance model to describe unsteady-state growth and by-product secretion in aerobic batch, fed-batch, and anaerobic batch cultures. In aerobic experiments we observed acetate secretion, accumulation in the culture medium, and reutilization from the culture medium. In fed-batch cultures acetate is cometabolized with glucose during the later part of the culture period.(ABSTRACT TRUNCATED AT 250 WORDS)     

CO2 enrichment and carbon partitioning to phenolics: do plant responses accord better with the protein competition or the growth differentiation balance models?

Rising levels of atmospheric CO₂ can alter plant growth and partitioning to secondary metabolites. The protein competition model (PCM) and the extended growth/differentiation balance model (GDB_e) are similar but alternative models that address ontogenetic and environmental effects on whole‐plant carbon partitioning to the phenylpropanoid biosynthetic pathway, making many divergent predictions. To test the validity of the models, we compare plant responses to one key prediction: if CO₂ enrichment simultaneously stimulates both photosynthesis and growth, then PCM predicts that partitioning to phenolic compounds will decline, whereas GDB_e generally predicts the opposite. Elevated CO₂ (at 548 ppm) increased the biomass growth (ca 23%) as well as the net photosynthesis (ca 13%) of 1‐year‐old potted paper birch, Betula papyrifera Marsh., in a free air carbon dioxide enrichment study (FACE) in northern Wisconsin. Concomitantly, elevated CO₂ increased carbon partitioning to all measured classes of phenolics (Folin‐Denis phenolics, HPLC low molecular weight phenolics (i.e. cinnamic acid derivatives, flavonol glycosides, and flavon‐3‐ols), condensed tannins, and acid‐detergent lignin) in leaves. In stem tissues, tannins and lignin increased, but F‐D phenolics did not. In root tissues, F‐D phenolics, and tannins increased, but lignin did not. The data suggest that CO₂ enrichment stimulated pathway‐wide increase in carbon partitioning to phenylpropanoids. High CO₂ plants had 11.8% more F‐D phenolics, 19.3% more tannin, and 10% more lignin than ambient plants after adjusting for plant mass via analysis of covariance. In general, the results unequivocally support the predictions of the GDB_e model. By way of contrast, results from many parallel studies on FACE trembling aspen, Populus tremuloides Michx., suggest that although CO₂ enrichment has consistently stimulated both photosynthesis and growth, it apparently did not generally stimulate pathway‐wide increases, or decreases, in carbon partitioning to phenylpropanoids in leaves and wood, but rather has specifically, though not consistently, increased partitioning to foliar phenolic glycosides. Likewise, in this case, GDB_e's predictions better accord with the FACE aspen data than PCM's. If further tests of the two models also support GDB rather than PCM, then PCM's main assumption (whole‐plant N rather than C is limiting partitioning to phenolic synthesis) may be incorrect.     

Interactions among resource partitioning, sampling effect, and facilitation on the biodiversity effect: a modeling approach

Resource partitioning, facilitation, and sampling effect are the three mechanisms behind the biodiversity effect, which is depicted usually as the effect of plant-species richness on aboveground net primary production. These mechanisms operate simultaneously but their relative importance and interactions are difficult to unravel experimentally. Thus, niche differentiation and facilitation have been lumped together and separated from the sampling effect. Here, we propose three hypotheses about interactions among the three mechanisms and test them using a simulation model. The model simulated water movement through soil and vegetation, and net primary production mimicking the Patagonian steppe. Using the model, we created grass and shrub monocultures and mixtures, controlled root overlap and grass water-use efficiency (WUE) to simulate gradients of biodiversity, resource partitioning and facilitation. The presence of shrubs facilitated grass growth by increasing its WUE and in turn increased the sampling effect, whereas root overlap (resource partitioning) had, on average, no effect on sampling effect. Interestingly, resource partitioning and facilitation interacted so the effect of facilitation on sampling effect decreased as resource partitioning increased. Sampling effect was enhanced by the difference between the two functional groups in their efficiency in using resources. Morphological and physiological differences make one group outperform the other; once these differences were established further differences did not enhance the sampling effect. In addition, grass WUE and root overlap positively influence the biodiversity effect but showed no interactions.