Plant Growth Model Research Articles

Multi-scale hybrid modeling of plant growth in response to environmental conditions and soil nutrients availability

Crop modeling plays a crucial role in agriculture, aiding our understanding and prediction of crop growth and yield in diverse environmental conditions. This study aims to develop a comprehensive mathematical model describing plant growth in response to environmental conditions and soil nutrient availability. To achieve this, we relied on a field experiment with lettuce plants under varying environmental conditions. Employing growth models such as logistic, Gompertz, Aikman & Scaife, and Scaife, Cox & Morris, we assessed the influence of time, day-degrees, and effective-day-degrees across different plant densities and during distinct periods throughout the year. In general, describing plant growth in terms of day-degrees or effective-day-degrees yielded an improved model fit and more precise estimations of growth parameters. As a result, we described the growth of plant length in terms of effective-day-degrees instead of time in the equations of the Bessonov-Volpert system. Additionally, we modified the equation describing plant length growth using previously fitted functions. By incorporating these adjustments, we characterized the one-dimensional growth of plant weight under varying environmental conditions without branching, using the Bessonov-Volpert model. This study contributes valuable insights into crop modeling techniques, refining our understanding of optimizing plant growth under different environmental conditions.

Pineapple growth and development modeling based on nitrogen rate and planting density

Plant growth models, derived from reliable databases, enable development of software for recommending cultural practices, harvest predictions, and enhancing productivity. This study aimed to create, refine, and simulate reference models for pineapple growth and development, adapting them based on nitrogen supply per plant and plant density per hectare. We utilized a field test database with periodic assessments of root, stem, leaf, fruit, and stem diameter fresh and dry weight, along with climate data from meteorological stations in or near the experimental areas. These growth models were developed, considering significant correlations and high correlation coefficients, using both simple non-destructive (stem diameter) and destructive (fresh or dry weight of D leaf) plant evaluations, either separately or in combination. The resulting models can provide estimated predictions for pineapple growth, adaptable to varying plant populations and nitrogen fertilization rates (measured in grams of N per plant)

Manipulation of photosensory and circadian signaling restricts phenotypic plasticity in response to changing environmental conditions in Arabidopsis

Plants exploit phenotypic plasticity to adapt their growth and development to prevailing environmental conditions. Interpretation of light and temperature signals is aided by the circadian system, which provides a temporal context. Phenotypic plasticity provides a selective and competitive advantage in nature but is obstructive during large-scale, intensive agricultural practices since economically important traits (including vegetative growth and flowering time) can vary widely depending on local environmental conditions. This prevents accurate prediction of harvesting times and produces a variable crop. In this study, we sought to restrict phenotypic plasticity and circadian regulation by manipulating signaling systems that govern plants’ responses to environmental signals. Mathematical modeling of plant growth and development predicted reduced plant responses to changing environments when circadian and light signaling pathways were manipulated. We tested this prediction by utilizing a constitutively active allele of the plant photoreceptor phytochrome B, along with disruption of the circadian system via mutation of EARLY FLOWERING3. We found that these manipulations produced plants that are less responsive to light and temperature cues and thus fail to anticipate dawn. These engineered plants have uniform vegetative growth and flowering time, demonstrating how phenotypic plasticity can be limited while maintaining plant productivity. This has significant implications for future agriculture in both open fields and controlled environments.

Data-driven definition and modelling of plant growth

Many horticultural tasks require a definition of and means to measure ‘plant state’, a quantity that is used to represent and compare plants. The plant state's evolution through time (plant growth) can then be tracked. This is often performed informally by humans based on heuristic features for particular plant types. It can be used for example to recommend interventions to catch up on expected growth, or to measure the effects of experimental interventions on growth. This work provides a purely data-driven definition, that is easy to train, easy to non-destructively acquire training data, does not require expert annotations, and is easy to compute for any new plant type and growing conditions. The presented method is applied to a dataset of lettuce plants where it exceeds the performance of a hard baseline. This work also demonstrates that the presented method retains the intuitive properties expected for a plant growth model. Open source code implementation and data is provided.

Flow similarity model predicts allometric size dependence, curvature, and covariation of 285 North American tree species

AbstractScaling patterns in plants have long interested biologists, particularly whether different species share similar patterns of growth, and whether differences in growth trajectories depend on plant size. Using 8,794,737 measurements for 285 species from the U.S. Forest Inventory and Analysis database, we test several predictions emerging from a recently published “flow similarity” model for plant growth and allometry. We show that the model's predicted curvature for intraspecific relationships between height, dbh, and biomass is found in 88.1% of examined cases, and empirical slopes fall as predicted between the elastic similarity and flow similarity predictions in 71.1% of cases. We also find a strong size dependence in observed intraspecific allometric exponents, with large species, particularly gymnosperms, converging near the expectation for elastic similarity and the central tendency among small species approaching the expectations for flow similarity in most cases. Our results support the idea that differences in growth patterns across plant species depend on plant size and their attendant hydraulic and/or biomechanical demands and helps to delineate the bounds of the theoretical morphospace in which they occur.

Development of yield prediction model for wheat by using AquaCrop model with different nitrogen dose applications in Central Anatolia Region (semi arid) conditions

In this study, yield prediction was made for Tosunbey and Bayraktar bread wheat varieties under rainfall conditions and 4 different fertilizer ratios with AquaCrop model, one of the plant growth models. In this experiment conducted at Haymana Ikizce Research Farm, actual field observations and model predicted grain yield, biomass, and green area coverage ratio were evaluated. Mean deviation (α), standard error (RMSE), and model efficiency coefficient (E) tests were used to determine the performance of the model. The AquaCrop model was calibrated in the first year and validated based on observational data collected in the first and second years of the experiment, respectively. Based on the results obtained, it was observed that the AquaCrop model simulated grain yield at different levels of nitrogen fertilizer applications with higher precision for Bayraktar variety. For Bayraktar variety, grain yield E = 0.93 in the first year and 0.99 in the second year for grain yield, and E = 0.83 in the first year and 0.98 in the second year for biomass, indicating excellent agreement between model and observation was found. In Tosunbey variety, first-year grain yield E=0.66 and 2nd year grain yield 0.76 were found. The 2nd year RMSE value for grain yield of Bayraktar variety was 0.266, and the 2nd year RMSE value for the grain yield of Tosunbey variety was 0.664 and found to be statistically compatible. Grain yield, biomass, and percent cover (CC) values obtained from the model were found to be highly consistent with field observations.

Reaction norm for genomic prediction of plant growth: modeling drought stress response in soybean

Key messageWe proposed models to predict the effects of genomic and environmental factors on daily soybean growth and applied them to soybean growth data obtained with unmanned aerial vehicles.Advances in high-throughput phenotyping technology have made it possible to obtain time-series plant growth data in field trials, enabling genotype-by-environment interaction (G × E) modeling of plant growth. Although the reaction norm is an effective method for quantitatively evaluating G × E and has been implemented in genomic prediction models, no reaction norm models have been applied to plant growth data. Here, we propose a novel reaction norm model for plant growth using spline and random forest models, in which daily growth is explained by environmental factors one day prior. The proposed model was applied to soybean canopy area and height to evaluate the influence of drought stress levels. Changes in the canopy area and height of 198 cultivars were measured by remote sensing using unmanned aerial vehicles. Multiple drought stress levels were set as treatments, and their time-series soil moisture was measured. The models were evaluated using three cross-validation schemes. Although accuracy of the proposed models did not surpass that of single-trait genomic prediction, the results suggest that our model can capture G × E, especially the latter growth period for the random forest model. Also, significant variations in the G × E of the canopy height during the early growth period were visualized using the spline model. This result indicates the effectiveness of the proposed models on plant growth data and the possibility of revealing G × E in various growth stages in plant breeding by applying statistical or machine learning models to time-series phenotype data.

Plant science in the age of simulation intelligence.

Historically, plant and crop sciences have been quantitative fields that intensively use measurements and modeling. Traditionally, researchers choose between two dominant modeling approaches: mechanistic plant growth models or data-driven, statistical methodologies. At the intersection of both paradigms, a novel approach referred to as "simulation intelligence", has emerged as a powerful tool for comprehending and controlling complex systems, including plants and crops. This work explores the transformative potential for the plant science community of the nine simulation intelligence motifs, from understanding molecular plant processes to optimizing greenhouse control. Many of these concepts, such as surrogate models and agent-based modeling, have gained prominence in plant and crop sciences. In contrast, some motifs, such as open-ended optimization or program synthesis, still need to be explored further. The motifs of simulation intelligence can potentially revolutionize breeding and precision farming towards more sustainable food production.

The nonlinear mechanics of highly extensible plant epidermal cell walls.

Plant epidermal cell walls maintain the mechanical integrity of plants and restrict organ growth. Mechanical analyses can give insights into wall structure and are inputs for mechanobiology models of plant growth. To better understand the intrinsic mechanics of epidermal cell walls and how they may accommodate large deformations during growth, we analyzed a geometrically simple material, onion epidermal strips consisting of only the outer (periclinal) cell wall, ~7 μm thick. With uniaxial stretching by >40%, the wall showed complex three-phase stress-strain responses while cyclic stretching revealed reversible and irreversible deformations and elastic hysteresis. Stretching at varying strain rates and temperatures indicated the wall behaved more like a network of flexible cellulose fibers capable of sliding than a viscoelastic composite with pectin viscosity. We developed an analytic framework to quantify nonlinear wall mechanics in terms of stiffness, deformation, and energy dissipation, finding that the wall stretches by combined elastic and plastic deformation without compromising its stiffness. We also analyzed mechanical changes in slightly dehydrated walls. Their extension became stiffer and more irreversible, highlighting the influence of water on cellulose stiffness and sliding. This study offers insights into the structure and deformation modes of primary cell walls and presents a framework that is also applicable to tissues and whole organs.

Lettuce Fresh Weight Prediction in a Plant Factory Using Plant Growth Models

Lettuce Fresh Weight Prediction in a Plant Factory Using Plant Growth Models

Practical Identifiability of Plant Growth Models: A Unifying Framework and Its Specification for Three Local Indices.

Amid the rise of machine learning models, a substantial portion of plant growth models remains mechanistic, seeking to capture an in-depth understanding of the underlying phenomena governing the system's dynamics. The development of these models typically involves parameter estimation from experimental data. Ensuring that the estimated parameters align closely with their respective "true" values is crucial since they hold biological interpretation, leading to the challenge of uniqueness in the solutions. Structural identifiability analysis addresses this issue under the assumption of perfect observations of system dynamics, whereas practical identifiability considers limited measurements and the accompanying noise. In the literature, definitions for structural identifiability vary only slightly among authors, whereas the concept and quantification of practical identifiability lack consensus, with several indices coexisting. In this work, we provide a unified framework for studying identifiability, accommodating different definitions that need to be instantiated depending on each application case. In a more applicative second step, we focus on three widely used methods for quantifying practical identifiability: collinearity indices, profile likelihood, and average relative error. We show the limitations of their local versions, and we propose a new risk index built on the profile likelihood-based confidence intervals. We illustrate the usefulness of these concepts for plant growth modeling using a discrete-time individual plant growth model, LNAS, and a continuous-time plant population epidemics model. Through this work, we aim to underline the significance of identifiability analysis as a complement to any parameter estimation study and offer guidance to the modeler.

Expected yield and economic improvements of a yam seed system in West Africa using agro‐physiological modelling

Societal Impact StatementYam is a major tropical root crop and a staple food for millions of people in West Africa. The model used in this study shows that promoting the use of improved seed tubers would help increase yields and profitability for farmers. This could lead to improved food security, increased income and higher standards of living. Additionally, the model serves as a useful decision‐support tool for farmers and technicians to choose, depending on the species, the optimum seed‐tuber weight and planting date. This study provides agronomic arguments to justify investments in the improvement of yam planting materials in West Africa.Summary Yam (Dioscorea spp.) is a major tropical root crop, grown mainly in West Africa using traditional extensive techniques. Farmers typically reuse seed tubers by setting aside up to 30% of their production for the next season, leading to high planting material variability that affects yields. Several initiatives aim to promote the use of improved seed tubers. However, to help their adoption, it is necessary to quantify the agronomic and economic advantages. To address this, a model for individual plant growth and development was developed based on six experiments in Benin from 2007 to 2009. This model simulates the combined effect of emergence (through photoperiod and temperature) and seed‐tuber weight on yam plant growth and development. Its predictions were highly correlated with observed plant tuber yield (R2 > 0.83). Results highlight the crucial role of key processes such as seed‐tuber physiological age and photoperiod sensitivity. The study shows that for the traditional planting dates, the use of improved planting material could lead to a yield increase of 22%–27% and a gain in profitability of 30% and 40% for Dioscorea alata and Dioscorea rotundata, respectively. The model proved to be a useful decision‐support tool for choosing an optimum seed‐tuber weight, depending on the species and the planting date. This study validates investments in yam seed systems in West Africa. However, beyond seed size and health, other factors such as dormancy, storage time and their management need to be considered to address emergence heterogeneity and its impact on yield.

Innovative approach to prognostic plant growth modeling in SWAT+ for forest and perennial vegetation in tropical and Sub-Tropical climates

The growth of vegetation in ecosystems is influenced by hydro-climatic factors and biogeochemical cycles. Accurately modeling annual vegetation growth dynamics is essential for eco-hydrological modeling to estimate watershed hydrologic balance and nutrient cycling under changing environmental conditions. The Soil and Water Assessment Tool (SWAT) and its upgraded version SWAT+ are process-oriented river basin models widely used. However, the temperature-based approach to plant growth simulation in tropical regions has limitations due to the importance of soil moisture availability as a key driver of plant growth. This study proposes an innovative approach that incorporates a proxy soil moisture availability index based on monthly rainfall and potential evapotranspiration ratio. This approach identifies the start of the growing season within prescribed transition months and controls leaf drop rate throughout the year, a crucial process during leaf senescence. We evaluated the reliability of this approach by comparing SWAT+ simulated Leaf Area Index (LAI), evapotranspiration (ET), and net primary productivity (NPP) with benchmark remote sensing-based datasets for three landcover classes in the Mara River Basin (Kenya/Tanzania). Our results demonstrate that the improved plant growth module in SWAT+ developed in this study can simulate temporal vegetation growth dynamics of evergreen forest, savanna grassland, and shrubland land cover types consistently with good correlations (r > 0.5) and low average bias (<10%). Thus, the SWAT+ model with the enhanced plant growth module can be a robust tool for investigating the coupled carbon, nutrient, and water cycling in tropical and sub-tropical climates.

Changes in How Climate Forces the Vegetation of Southern Africa

Global climatic changes are altering ecosystem structure and functioning, yet detecting and forecasting such change is difficult. In this study, we use the concept of a phytoclime—a region where climate favours the growth of similar combinations of plant types—to examine how changes in climate forcing may impact on regional vegetation. We use species distribution data to estimate the parameters of a physiological plant growth model for 5006 vascular plant species common to southern Africa. Plant type suitability surfaces are calculated as the average climatic suitability of locations for all species belonging to a plant type. We calculated plant type suitability surfaces for ten different plant types. The resulting surfaces were used to produce a spatial classification of phytoclimes, which we interpret as regions that can climatically support particular plant type combinations. We use the phytoclime definitions and climatologies from five global circulation models (GCMs) simulating three shared economic pathways (SSPs) to forecast how the climatic forcing underlying the phytoclimes will change. Our analyses forecast that change in phytoclime state will be widespread throughout the region. There were, however, substantial differences in the timing of when changes would occur. The central interior of the region was forecast to change earlier than the arid west and southern coast. These differences in timing were driven by differences in the responses of trees, succulents, C3 and C4 grasses to the GCMs forecast aridification of the region’s central interior. Phytoclime modelling provides an indication of the potential of a region’s climate to support different plant types; it thereby provides forecasts of the potential impacts of climate change on regional vegetation structure and functioning.

Using Remote and Proximal Sensing in Organic Agriculture to Assess Yield and Environmental Performance

Satellite and sensor-based systems of site-specific fertilization have been developed almost exclusively in conventional farming. Agronomic and ecological advantages can also be expected from these digital methods in organic farming. However, it has not yet been investigated whether the algorithms and models are also applicable under organic farming conditions. In this study, the digital data and systems tested in the years 2021 and 2022 in southern Germany were (a) reflectance measurements with a tractor-mounted multispectral sensor, calculation of the vegetation index REIP, and application of algorithms; (b) satellite data in combination with the plant growth model PROMET; and (c) determination of the vegetation index NDVI based on satellite data. They were used to determine plant parameters (crop yield, biomass potential) and to calculate nitrogen balances at a high spatial resolution (10 × 10 m). The digital systems were tested at two sites with different organic farming systems (arable farming and dairy farming). Validation of the digital methods was carried out with ground-truth data from manual biomass sampling and combine harvester yield measurement. The nitrate leaching risk from the crop rotations of the farms was analyzed via site-specific N balancing using multi-year satellite data. The N balances were validated by measuring nitrate concentrations in leakage water. Additionally, soil properties, such as soil organic carbon (SOC) and total nitrogen (TN), were measured at the sub-field level. Using geostatistics, plant data, soil properties, and nitrate measurements were transferred into grids of the same resolution to enable correlation analyses. The correlations between yield determined with digital systems and the validation data were up to r = 0.77. Site-specific N balancing showed moderately positive correlations with nitrate concentrations in leakage water (r = 0.50–0.66). The strongly positive influence of the soil properties SOC and TN on crop yields underlines the importance of soil organic matter on soil fertility and site-specific yield potentials. The results show that digital methods allow the spatially high-resolution determination of yields and nitrogen balances in organic farming. This can be the basis for new management strategies in organic farming, e.g., the targeted use of limited nutrients to increase yields. Further validations under differentiated soil, climate, and management conditions are required to develop remote and proximal sensing applications in organic farming.

Life cycle assessment of microgreen production: effects of indoor vertical farm management on yield and environmental performance

The global production of plant-based foods is a significant contributor to greenhouse gas emissions. Indoor vertical farms (IVFs) have emerged as a promising approach to urban agriculture. However, their environmental performance is not well understood, particularly in relation to operational choices where global warming potentials (GWP) can vary between 0.01–54 kg CO2e/kg−1 of leafy greens produced. We conducted a life cycle assessment (LCA) of a building-integrated IVF for microgreen production to analyse a range of operational conditions for cultivation: air temperature, CO2 concentration, and photoperiod. We analyzed a dynamic LCA inventory that combined a process-based plant growth model and a mass balance model for air and heat exchange between the chamber and the outside. Results showed that the GWP of IVFs can vary greatly depending on the operation conditions set, ranging from 3.3 to 63.3 kg CO2e/kg−1. The optimal conditions for minimizing GWP were identified as 20 ℃, maximum CO2 concentration in the chamber, and maximum photoperiod, which led to a minimum GWP of 3.3 kg CO2e/kg−1 and maximum production of 290.5 kg fresh weight week-1. Intensification of production thus led to lower impacts because the marginal increase in yield due to increased resource use was larger than the marginal increase in impact. Therefore, adjusting growing conditions is essential for the sustainability of urban food production.

ОПРЕДЕЛЕНИЕ ТОЧЕК БИФУРКАЦИИ В ФУНКЦИОНИРОВАНИИ СИСТЕМЫ «ПОЧВА – РАСТЕНИЕ – ВОЗДУХ»

To date, a number of mathematical models of plant growth, developed by domestic and foreign scientists, are known. However, the issues of determining the bifurcation points that arise during the functioning of “soil-plant-air” system have not been sufficiently considered. In relation to the issues considered in the article, the bifurcation point is a critical state of the “plant” subsystem, at which it becomes unstable with respect to fluctuations in natural and climatic conditions (drought, frost, prolonged rains, etc.) and there is uncertainty in the development of plants (further growth or their death), as well as the intensive growth of plants as a result of the corresponding technological operations. For control and operational management of the formation of agricultural crops, it is desirable to know the bifurcation points determined by the biological time of plant growth and extreme weather situations. Therefore, the main goal of research is the analytical determination of bifurcation points observed during the vegetation of plants. The “plant” subsystem at the bifurcation point can be simultaneously in two or more states. As a result of the analysis of the obtained analytical dependences of various possible states of “soil-plant-air” system, it is proposed to subdivide bifurcations into negative and positive ones. A method has been obtained for determining bifurcation points during the functioning of “soil-plant-air” system. Under natural and climatic conditions, critical situations can arise with insufficient incoming substances to “soil-plant-air” system, such as light supply, moisture supply, heat supply, food supply and gas supply of plants. As a result of analytical studies, bifurcation points were determined in “soil-plant-air” system, depending on the radiation balance (R) formed on the underlying surface, slopes of different exposure and steepness, and coefficients characterizing light, moisture, heat, food and gas supply plants.

The Role of Recent Climate Change in Explaining the Statistical Yield Increase of Maize in Northern Bavaria—A Model Study

Maize yields in many regions of the world have increased significantly since the 1960s. The increase is mainly attributed to technological improvements and climate change. On a regional scale and in recent decades, climate change has altered growth conditions of maize and this, in turn, has influenced changes in yield. In order to analyze the contribution of different factors to yield changes, and to obtain a model setup that could be used for further analyses of yield development, this study systematically investigated the effects of recent climate change, irrigation, cultivar selection and nutrient availability on historical yields in Northern Bavaria. Four sets of simulations were conducted with the mechanistic plant growth model PROMET, during the time period between 1997 and 2020, and the resulting yields were compared to county statistics. In addition, three scenarios were simulated in order to determine yield increase potentials for the highly mechanized agricultural region of Northern Bavaria. The results showed a good agreement with the observed yields (R2 = 0.76), when considering altered nutrient availability, suggesting that an increase in nutrient uptake by plants plays a key role in reproducing yield statistics and has a main contribution to the observed increasing yield trends. Moreover, other factors considered individually, such as recent climate change, irrigation and cultivar selection, could not explain the yield levels and trends shown by the statistics. The scenario simulations demonstrated potential increases in yield due to irrigation and cultivar adaptation. The yield response to irrigation shows a trend, with recent climate change progressing, of 0–25% when irrigating currently grown cultivars and 10–50% when irrigating an adapted cultivar; rainfed cultivar adaptation consistently increased the level of yields by approximately 10%. This study highlights the importance of a dynamic consideration of growth conditions in the course of climate change, rather than static assumptions of model parameters, and emphasizes the importance of the second-order effects of climate change.

Determining cardinal temperatures for eight cover crop species

AbstractGrowing degree days (GDD) is a tool to predict plant growth and can be adapted for use in any plant species, including cover crops. A limitation of the GDD calculation is accurate temperature parameters used to predict plant development. For most cover crop species, the cardinal temperatures are not well defined in the literature, leading to a less accurate calculation of GDD. The objective of this study was to determine the cardinal temperatures of eight cover crop species, including Austrian winter pea (Pisum sativum), balansa clover (Trifolium michelianum), barley (Hordeum vulgare), black‐seeded oats (Avena sativa), common vetch (Vicia sativa), cereal rye (Secale cereale), crimson clover (Trifolium incarnatum), and hairy vetch (Vicia villosa), using a growth chamber experiment. Seven different temperature regimes from 4 to 34°C were implemented, and the number of leaves was counted from day 0 to 21. As a result, the data were regressed to estimate the cardinal temperatures for each species. The results of this research identified base (2), optimum (3), and maximum (8) temperatures for cover crops that were not previously reported. Five cardinal temperatures determined in this study were different from what was previously recorded; base and optimum temperatures were −4.5 and 24.8°C for cereal rye, 3.9 and 26.6°C for crimson clover, and the base temperature was 3.4°C for balansa clover. The successful identification of these cardinal temperatures for cover crops will allow the development of plant growth and biomass prediction models to aid in cover crop termination decision support tools.

Plant Growth Modeling and Response from Broadband Phosphor-Converted Lighting for Indoor Agriculture.

The rapid change in population, environment, and climate is accompanied by the food crisis. As a new type of farming, indoor agriculture opens the possibility of addressing this crisis in the future. In this study, a phosphor-converted light-emitting diode (pc-LED), as energy-saving lighting for indoor agriculture, was used to evaluate the response and effect on the growth of Lactuca sativa. Red phosphors, SrLiAl3N4:Eu2+ (SLA) and CaAlSiN3:Eu2+ (CASN), were characterized and analyzed with crystal structure, morphology, and optical properties. Eu2+-doped phosphors provided the red emission of around 650 nm which is highly matched with the absorption of chlorophyll. Under the same luminescence intensity, broader emission of CASN pc-LED demonstrated a 100% increase of photosynthetically active photon flux density and 130% promotion of plant weight than the SLA pc-LED, which reflected the positive result of the carbon fixation. The chlorophyll and nitrate responses have also revealed the effect of broader red light on indoor agriculture.