Simulation of carbon allocation and organ growth variability in apple tree by connecting architectural and source-sink models

The curvilinear responses of biomass accumulation and root morphology to a soil salt-nitrogen environment reflect the phytodesalination capability of the euhalophyte Suaeda salsa L

Under the sufficient nitrogen supply, it is of great significance to investigate the law of biomass allocation, root morphological traits, and the salt absorption capacity of euhalophytes to evaluate their biological desalination in saline soil. Although the curvilinear responses of biomass accumulation and root morphology in response to soil salinity have been recognized, these perceptions are still confined to the descriptions of inter-treatment population changes and lack details on biomass allocation in organs at an individual level. In this study, Suaeda salsa was grown in root boxes across a range of soil salt levels. The study showed that their growth and development were significantly affected by soil soluble salts. The law of biomass allocation was described as follows: increased soil soluble salts significantly increased the leaf mass ratio and decreased the stem mass ratio, and slightly increased the root mass ratio among treatments. For individuals at each treatment, leaf mass ratio > stem mass ratio > root mass ratio, except in the control treatment at the flower bud and fruit stages. Biomass responses of the control treatment indicated that salt was not rigorously required for Suaeda salsa in the presence of an adequate nitrogen supply, as verified by the correlation between biomass, nitrogen, and soil soluble salt. Salt could significantly inhibit the growth of Suaeda salsa (P<0.01), whereas nitrogen could significantly promote its growth (P<0.01). Root morphology in response to soil soluble salts showed that salt acquisition by the root was highest at a salt level of 0.70%, which corresponds to light saline soil. Consequently, we conclude that phytodesalination by Suaeda salsa was optimal in the light saline soil, followed by moderate saline soil.

Phenotypic Plasticity Strategy of Aeluropus lagopoides Grass in Response to Heterogenous Saline Habitats

Understanding the response variation of morphological parameters and biomass allocation of plants in heterogeneous saline environments is helpful in evaluating the internal correlation between plant phenotypic plasticity mechanism and biomass allocation. The plasticity of plants alters the interaction among individuals and their environment and consequently affects the population dynamics and aspects of community and ecosystem functioning. The current study aimed to assess the plasticity of Aeluropus lagopoides traits with variation in saline habitats. Understanding the habitat stress tolerance strategy of A. lagopoides is of great significance since it is one of the highly palatable forage grass in the summer period. Five different saline flat regions (coastal and inland) within Saudi Arabia were targeted, and the soil, as well as the morphological and physiological traits of A. lagopoides, were assessed. Comprehensive correlation analyses were performed to correlate the traits with soil, region, or among each other. The soil analysis revealed significant variation among the five studied regions for all measured parameters, as well as among the soil layers showing the highest values in the upper layer and decreased with the depth. Significant differences were determined for all tested parameters of the morphological and reproductive traits as well as for the biomass allocation of A. lagopoides, except for the leaf thickness. In the highly saline region, Qaseem, A. lagopoides showed stunted aerial growth, high root/shoot ratio, improved root development, and high biomass allocation. In contrast, the populations growing in the low saline region (Jizan) showed the opposite trend. Under the more stressful condition, like in Qaseem and Salwa, A. lagopoides produce low spikes in biomass and seeds per plant, compared to the lowest saline habitats, such as Jouf. There was no significant difference in physiological parameters except stomatal conductance (g_s), which is highest in the Jizan region. In conclusion, the population of A. lagopoides is tolerant of harsh environments through phenotypic plasticity. This could be a candidate species to rehabilitate the saline habitats, considering saline agriculture and saline soil remediation.

Divergent responses of plant functional traits and biomass allocation to slope aspects in four perennial herbs of the alpine meadow ecosystem

Slope aspect can cause environmental heterogeneity over relatively short distances, which in turn affects plant distribution, community structure, and ecosystem function. However, the response and adaptation strategies of plants to slope aspects via regulating their physiological and morphological properties still remain poorly understood, especially in alpine ecosystems. Here, we selected four common species, including Bistorta macrophylla, Bistorta vivipara, Cremanthodium discoideum, and Deschampsia littoralis, to test how biomass allocation and functional traits of height, individual leaf area, individual leaf mass, and specific leaf area (SLA) respond to variation in slope aspect in the Minshan Mountain, eastern Tibetan Plateau. We found that the slope aspect affected SLA and stem, flower mass fraction with higher values at southwest slope aspect, which is potentially related to light environment. The low-temperature environment caused by the slope aspect facilitates the accumulation of root biomass especially at the northeast slope aspect. Cremanthodium discoideum and D. littoralis invested more in belowground biomass in southeast and southwest slope aspects, although a large number of significant isometric allocations were found in B. macrophylla and B. vivipara. Finally, we found that both biotic and abiotic factors are responsible for the variation in total biomass with contrasting effects across different species. These results suggest that slope aspect, as an important topographic variable, strongly influences plant survival, growth, and propagation. Therefore, habitat heterogeneity stemming from topographic factors (slope aspect) can prevent biotic homogenization and thus contribute to the improvement of diverse ecosystem functioning.

Investigation of the impact of supplemental reflective films to improve micro-light climate within tomato plant canopy in solar greenhouses

The non-uniform growth and development of crops within Chinese Solar Greenhouses (CSG) is directly related to the micro-light climate within canopy. In practice, reflective films are used to improve micro-light climate within plant canopy by homogenizing light distribution and so increasing total plant light interception. However, as to our knowledge, the contributions to light distribution within canopy have not been investigated for passive reflector like reflective films. Field experiments dealing with light conditions and growth behavior over time, are complicated to carry out, time-consuming and hard to control, while however, accurate measurements of how reflective films influence the micro-light climate of canopy are an essential step to improve the growth conditions for any crop. Here, we propose a supplementary light strategy using reflective films to improve light distribution within plant canopy. Based on the example of CSG, a 3D greenhouse model including a detailed 3D tomato canopy structure was constructed to simulate the influence of supplementary reflective films to improve micro-light climate. Comparison of measured solar radiation intensity with predicted model data demonstrated that the model could precisely predict light radiation intensity over time with different time points and positions in the greenhouse. A series of reflective film configurations were investigated based on features analysis of light distribution in the tomato canopy on sunny days using the proposed model. The reflective film configuration scheme with the highest impact significantly improved the evenness of horizontal and vertical light distribution in tomato canopy. The strategy provided here can be used to configure reflective films that will enhance light conditions in CSG, which can be applied and extended in different scenarios.

Environment-Driven Changes in the Functional Traits of Milk Thistle [Silybum marianum (L). Gaertn.] Along an Altitudinal Gradient in the Semi-Arid Environment: Perspective on Future Plant Invasion

The elevation is an important gradient across which the environmental variables and plant traits vary and is considered as a barrier to the recent global problem of plant invasion. However, certain invasive plants show plasticity traits to adapt and cope with the changes across the elevation. Silybum marianum (S. marianum) is one such invasive species widely spread in Khyber Pakhtunkhwa, Pakistan. Therefore, this study investigates the traits plasticity and invasive behaviors of this plant species across the elevation gradient. Plant functional traits (PFTs) and environmental variables were recorded in forty different low, middle, and high elevation sites. The plant shows a decrease in plant functional traits, i.e., above-ground plant height/plant, leaf length/leaf, leaf width/leaf, leaf dry weight/plant, vegetative dry weight/plant, and number of capitula/plant having the significance of p < 0.05. In contrast, the dry reproductive weight does not change significantly with elevation, while the root length increases across the elevation. The soil and environmental variables such as organic matter, lime percentage, and latitude significantly affected the PFTs. The importance value index of the species was also related to elevation and diversity indices, i.e., species richness, Shannon-Wiener diversity index, and evenness index, indicating that the invasion has strong effects on diversity. This study concludes that S. marianum has traits plasticity across the elevation and affects community diversity. Further investigation is required to understand the invasion and diversity parameters in a better way.

Fruit tree crop models: an update

Functional structural plant models of tree crops are useful tools that were introduced more than two decades ago. They can represent the growth and development of a plant through the in silico simulation of the 3D architecture in connection with physiological processes. In tree crops, physiological processes such as photosynthesis, carbon allocation and growth are usually integrated into these models, although other functions such as water and nutrient uptake are often disregarded. The implementation of the 3D architecture involves different techniques such as L-system frameworks, pipe model concepts and Markovian models to simulate branching processes, bud fates and elongation of stems based on the production of metamers. The simulation of root architecture is still a challenge for researchers due to a limited amount of information and experimental issues in dealing with roots, because root development is not based on the production of metamers. This review aims to focus on functional-structural models of fruit tree crops, highlighting their physiological components. The potential and limits of these tools are reviewed to point out the topics that still need more attention.

In situ experimental exposure of fruit-bearing shoots of apple trees to 13CO2 and construction of a dynamic transfer model of carbon

Evaluating the transfer and metabolism of carbon (C) in apple fruit is key to estimating the potential accumulation of atmospheric ¹⁴C in fruit near and around nuclear facilities. We developed a dynamic compartment model for apple fruit-bearing shoots, assuming that the shoots are a simple unit of source and sink for photoassimilates. Fruit-bearing shoots of Malus domestica "Fuji" at different fruit growth stages were exposed to ¹³CO₂in situ, followed by sampling at 72 h after exposure or at harvest. The ¹³C/(¹³C+¹²C) mole ratio in fruits, leaves, and current branch were measured to construct a five-compartment model of ¹³C (fruit, each fast and slow component of leaves, and current branch). The C inventories in the compartments were presented in accordance with the measured growth curves of C in the organs. The model simulated the ¹³C dynamics in plant tissues well. Simulation results of photoassimilate distribution using the model indicated that the retention of photoassimilated C at the harvest depended on the growth rate of C in the organs at the exposure.

Investigating tree and fruit growth through functional-structural modelling: implications of carbon autonomy at different scales

BACKGROUND AND AIMS

Many experimental studies assume that some topological units are autonomous with regard to carbon because it is convenient. Some plant models simulate carbon allocation, employing complex approaches that require calibration and fitted parameters. For whole-tree canopy simulations, simpler carbon allocation models can provide useful insights.

METHODS

We propose a new method for simulating carbon allocation in the whole tree canopy considering various scales of carbon autonomy, i.e. branchlets, branches, limbs, and no autonomy. This method was implemented in a functional-structural plant model of growth of individual organs for studying macadamia tree growth during one growing season.

KEY RESULTS

This model allows the simulation of various scales of carbon autonomy in a simple tree canopy, showing organ within-tree variability according to the scale of autonomy. Using a real tree canopy, we observed differences in growth variability within the tree and in tree growth, with several scales of carbon autonomy. The simulations that assumed autonomy at branch scale, i.e. 2-year-old wood, showed the most realistic results.

CONCLUSIONS

Simulations using this model were employed to investigate and explain aspects of differences in carbon autonomy between trees, organ growth variability, competition between shoot and fruit growth, and time of autonomy.

MuSCA: a multi-scale source-sink carbon allocation model to explore carbon allocation in plants. An application to static apple tree structures

BACKGROUND AND AIMS

Carbon allocation in plants is usually represented at a topological scale, specific to each model. This makes the results obtained with different models, and the impact of their scales of representation, difficult to compare. In this study, we developed a multi-scale carbon allocation model (MuSCA) that allows the use of different, user-defined, topological scales of a plant, and assessment of the impact of each spatial scale on simulated results and computation time.

METHODS

Model multi-scale consistency and behaviour were tested on three realistic apple tree structures. Carbon allocation was computed at five scales, spanning from the metamer (the finest scale, used as a reference) up to first-order branches, and for different values of a sap friction coefficient. Fruit dry mass increments were compared across spatial scales and with field data.

KEY RESULTS

The model was able to represent effects of competition for carbon assimilates on fruit growth. Intermediate friction parameter values provided results that best fitted field data. Fruit growth simulated at the metamer scale differed of ~1 % in respect to results obtained at growth unit scale and up to 60 % in respect to first order branch and fruiting unit scales. Generally, the coarser the spatial scale the more predicted fruit growth diverged from the reference. Coherence in fruit growth across scales was also differentially impacted, depending on the tree structure considered. Decreasing the topological resolution reduced computation time by up to four orders of magnitude.

CONCLUSIONS

MuSCA revealed that the topological scale has a major influence on the simulation of carbon allocation. This suggests that the scale should be a factor that is carefully evaluated when using a carbon allocation model, or when comparing results produced by different models. Finally, with MuSCA, trade-off between computation time and prediction accuracy can be evaluated by changing topological scales.

Parameter estimation for functional-structural plant models when data are scarce: using multiple patterns for rejecting unsuitable parameter sets

BACKGROUND AND AIMS

Functional-structural plant (FSP) models provide insights into the complex interactions between plant architecture and underlying developmental mechanisms. However, parameter estimation of FSP models remains challenging. We therefore used pattern-oriented modelling (POM) to test whether parameterization of FSP models can be made more efficient, systematic and powerful. With POM, a set of weak patterns is used to determine uncertain parameter values, instead of measuring them in experiments or observations, which often is infeasible.

METHODS

We used an existing FSP model of avocado (Persea americana 'Hass') and tested whether POM parameterization would converge to an existing manual parameterization. The model was run for 10 000 parameter sets and model outputs were compared with verification patterns. Each verification pattern served as a filter for rejecting unrealistic parameter sets. The model was then validated by running it with the surviving parameter sets that passed all filters and then comparing their pooled model outputs with additional validation patterns that were not used for parameterization.

KEY RESULTS

POM calibration led to 22 surviving parameter sets. Within these sets, most individual parameters varied over a large range. One of the resulting sets was similar to the manually parameterized set. Using the entire suite of surviving parameter sets, the model successfully predicted all validation patterns. However, two of the surviving parameter sets could not make the model predict all validation patterns.

CONCLUSIONS

Our findings suggest strong interactions among model parameters and their corresponding processes, respectively. Using all surviving parameter sets takes these interactions into account fully, thereby improving model performance regarding validation and model output uncertainty. We conclude that POM calibration allows FSP models to be developed in a timely manner without having to rely on field or laboratory experiments, or on cumbersome manual parameterization. POM also increases the predictive power of FSP models.

Modelling transport of inhibiting and activating signals and their combined effects on floral induction: application to apple tree

Floral induction (FI) in shoot apical meristems (SAM) is assumed to be triggered by antagonistic endogenous signals. In fruit trees, FI occurs in some SAM only and is determined by activating and inhibiting signals originating from leaves and fruit, respectively. We developed a model (SigFlow) to quantify on 3D structures the combined impact of such signals and distances at which they act on SAM. Signal transport was simulated considering a signal 'attenuation' parameter, whereas SAM fate was determined by probability functions depending on signal quantities. Model behaviour was assessed on simple structures before being calibrated and validated on a unique experimental dataset of 3D digitized apple trees with contrasted crop loads and subjected to leaf and fruit removal at different scales of tree organization. Model parameter estimations and comparisons of two signal combination functions led us to formulate new assumptions on the mechanisms involved: (i) the activating signal could be transported at shorter distances than the inhibiting one (roughly 50 cm vs 1 m) (ii) both signals jointly act to determine FI with SAM being more sensitive to inhibiting signal than activating one. Finally, the genericity of the model is promising to further understand the physiological and architectural determinisms of FI in plants.

Photosynthetical activity modelisation of olive trees growing under drought conditions

Predicting photosynthetic production in olive trees is a key feature in managing the effect of climate change on arid areas. Functional-structural plant modelling is a promising tool for achieving this goal. We used a photosynthetic sub-model that accounted for water and temperature stress and implemented it into LIGNUM model. We then conducted an experiment to validate the model at the leaf level using olive trees (Olea europaea) grown under various climatic condition. Then, we simulated photosynthetic production of three static olive tree models aged 1, 2, and 3 years. Results revealed a good fit between observed and predicted photosynthesis, with coefficient of determination (R²) values of 0.94 and 0.93 for Chemlali and Zarrazi cultivars, respectively. These results showed that the impact of water stress on photosynthetic production was marginal.

Optimal Design of Plant Canopy Based on Light Interception: A Case Study With Loquat

Canopy architecture determines the light distribution and light interception in the canopy. Reasonable shaping and pruning can optimize tree structure; maximize the utilization of land, space and light energy; and lay the foundation for achieving early fruiting, high yield, health and longevity. Due to the complexity of loquat canopy architecture and the multi-year period of tree growth, the variables needed for experiments in canopy type training are hardly accessible through field measurements. In this paper, we concentrated on exploring the relationship between branching angle and light interception using a three-dimensional (3D) canopy model in loquat (Eriobotrya japonica Lindl). First, detailed 3D models of loquat trees were built by integrating branch and organ models. Second, the morphological models of different loquat trees were constructed by interactive editing. Third, the 3D individual-tree modeling software LSTree integrated with the OpenGL shadow technique, a radiosity model and a modified rectangular hyperbola model was used to calculate the silhouette to total area ratio, the distribution of photosynthetically active radiation within canopies and the net photosynthetic rate, respectively. Finally, the influence of loquat tree organ organization on the light interception of the trees was analyzed with different parameters. If the single branch angle between the level 2 scaffold branch and trunk is approximately 15° and the angles among the level 2 scaffold branches range from 60 to 90°, then a better light distribution can be obtained. The results showed that the branching angle has a significant impact on light interception, which is useful for grower manipulation of trees, e.g., shoot bending (scaffold branch angle). Based on this conclusion, a reasonable tree structure was selected for intercepting light. This quantitative simulation and analytical method provides a new digital and visual method that can aid in the design of tree architecture.

Growth and carbon balance are differently regulated by tree and shoot fruiting contexts: an integrative study on apple genotypes with contrasted bearing patterns

In plants, carbon source-sink relationships are assumed to affect their reproductive effort. In fruit trees, carbon source-sink relationships are likely to be involved in their fruiting behavior. In apple, a large variability in fruiting behaviors exists, from regular to biennial, which has been related to the within-tree synchronization vs desynchronization of floral induction in buds. In this study, we analyzed if carbon assimilation, availability and fluxes as well as shoot growth differ in apple genotypes with contrasted behaviors. Another aim was to determine the scale of plant organization at which growth and carbon balance are regulated. The study was carried out on 16 genotypes belonging to three classes: (i) biennial, (ii) regular with a high production of floral buds every year and (iii) regular, displaying desynchronized bud fates in each year. Three shoot categories, vegetative and reproductive shoots with or without fruits, were included. This study shows that shoot growth and carbon balance are differentially regulated by tree and shoot fruiting contexts. Shoot growth was determined by the shoot fruiting context, or by the type of shoot itself, since vegetative shoots were always longer than reproductive shoots whatever the tree crop load. Leaf photosynthesis depended on the tree crop load only, irrespective of the shoot category or the genotypic class. Starch content was also strongly affected by the tree crop load with some adjustments of the carbon balance among shoots since starch content was lower, at least at some dates, in shoots with fruits compared with the shoots without fruits within the same trees. Finally, the genotypic differences in terms of shoot carbon balance partly matched with genotypic bearing patterns. Nevertheless, carbon content in buds and the role of gibberellins produced by seeds as well as the distances at which they could affect floral induction should be further analyzed.

A new methodology based on sensitivity analysis to simplify the recalibration of functional-structural plant models in new conditions

Background and Aims

Functional-structural plant models (FSPMs) describe explicitly the interactions between plants and their environment at organ to plant scale. However, the high level of description of the structure or model mechanisms makes this type of model very complex and hard to calibrate. A two-step methodology to facilitate the calibration process is proposed here.

Methods

First, a global sensitivity analysis method was applied to the calibration loss function. It provided first-order and total-order sensitivity indexes that allow parameters to be ranked by importance in order to select the most influential ones. Second, the Akaike information criterion (AIC) was used to quantify the model's quality of fit after calibration with different combinations of selected parameters. The model with the lowest AIC gives the best combination of parameters to select. This methodology was validated by calibrating the model on an independent data set (same cultivar, another year) with the parameters selected in the second step. All the parameters were set to their nominal value; only the most influential ones were re-estimated.

Key Results

Sensitivity analysis applied to the calibration loss function is a relevant method to underline the most significant parameters in the estimation process. For the studied winter oilseed rape model, 11 out of 26 estimated parameters were selected. Then, the model could be recalibrated for a different data set by re-estimating only three parameters selected with the model selection method.

Conclusions

Fitting only a small number of parameters dramatically increases the efficiency of recalibration, increases the robustness of the model and helps identify the principal sources of variation in varying environmental conditions. This innovative method still needs to be more widely validated but already gives interesting avenues to improve the calibration of FSPMs.

Quantifying within-plant spatial heterogeneity in carbohydrate availability in cotton using a local-pool model

Background and Aims

Within-plant spatial heterogeneity in the production of and demand for assimilates may have major implications for the formation of fruits. Spatial heterogeneity is related to organ age, but also to position on the plant. This study quantifies the variation in local carbohydrate availability for the phytomers in the same cohort using a cotton growth model that captures carbohydrate production in phytomers and carbohydrate movement between phytomers.

Methods

Based on field observations, we developed a functional-structural plant model of cotton that simulates production and storage of carbohydrates in individual phytomers and transport of surplus to other phytomers. Simulated total leaf area, total above-ground dry mass, dry mass distribution along the stem, and dry mass allocation fractions to each organ at the plant level were compared with field observations for plants grown at different densities. The distribution of local carbohydrate availability throughout the plant was characterized and a sensitivity analysis was conducted regarding the value of the carbohydrate transport coefficient.

Key Results

The model reproduced cotton leaf expansion and dry mass allocation across plant densities adequately. Individual leaf area was underestimated at very high plant densities. Best correspondence with measured plant traits was obtained for a value of the transport coefficient of 0.1 d-1. The simulated translocation of carbohydrates agreed well with results from C-labelling studies. Moreover, simulation results revealed the heterogeneous pattern of local carbohydrate availability over the plant as an emergent model property.

Conclusions

This modelling study shows how heterogeneity in local carbohydrate production within the plant structure in combination with limitations in transport result in heterogeneous satisfaction of demand over the plant. This model provides a tool to explore phenomena in cotton that are thought to be determined by local carbohydrate availability, such as branching pattern and fruit abortion in relation to climate and crop management.

Pattern-oriented modelling as a novel way to verify and validate functional-structural plant models: a demonstration with the annual growth module of avocado

Background and Aims

Functional-structural plant (FSP) models have been widely used to understand the complex interactions between plant architecture and underlying developmental mechanisms. However, to obtain evidence that a model captures these mechanisms correctly, a clear distinction must be made between model outputs used for calibration and thus verification, and outputs used for validation. In pattern-oriented modelling (POM), multiple verification patterns are used as filters for rejecting unrealistic model structures and parameter combinations, while a second, independent set of patterns is used for validation.

Methods

To test the potential of POM for FSP modelling, a model of avocado (Persea americana 'Hass') was developed. The model of shoot growth is based on a conceptual model, the annual growth module (AGM), and simulates photosynthesis and adaptive carbon allocation at the organ level. The model was first calibrated using a set of observed patterns from a published article. Then, for validation, model predictions were compared with a different set of empirical patterns from various field studies that were not used for calibration.

Key Results

After calibration, our model simultaneously reproduced multiple observed architectural patterns. The model then successfully predicted, without further calibration, the validation patterns. The model supports the hypothesis that carbon allocation can be modelled as being dependent on current organ biomass and sink strength of each organ type, and also predicted the observed developmental timing of the leaf sink-source transition stage.

Conclusions

These findings suggest that POM can help to improve the 'structural realism' of FSP models, i.e. the likelihood that a model reproduces observed patterns for the right reasons. Structural realism increases predictive power so that the response of an AGM to changing environmental conditions can be predicted. Accordingly, our FSP model provides a better but still parsimonious understanding of the mechanisms underlying known patterns of AGM growth.