Abstract This study focuses on the winter wheat–summer maize double-cropping system and aims to develop an annual process model that can accurately simulate crop growth and development along with soil moisture dynamics. Based on the field split-plot experimental data that combined different varieties with sowing date treatments, a wheat-maize double-cropping production system model was built, incorporating modules for crop development stages, leaf area dynamics, biomass accumulation and partitioning, yield formation, and soil moisture balance. The model parameters were calibrated using 2008–2009 data, and validated with independent 2009–2010 data, and model performance in key physiological and ecological processes and in yield formation is systematically evaluated by using root mean square error (RMSE) and normalized root mean square error (NRMSE). Validation results show: 1) excellent simulation of crop phenology, with NRMSE for development stages at 1.87% for winter wheat and 5.36% for summer maize; 2) the model capture of leaf area index dynamics, with NRMSE of 27.52% for winter wheat and 11.96% for summer maize; 3) aboveground biomass accumulation was simulated with NRMSE of 16.02% for winter wheat and 15.50% for summer maize; 4) yield simulation achieved NRMSE of 5.78% for winter wheat and 17.80% for summer maize; 5) soil water storage in the 0–60 cm soil layer was simulated with good accuracy (NRMSE = 15.13%). Under the specific site conditions and the tested genotype-by-sowing-date combinations, the model demonstrated reasonable capability in simulating key processes of the winter wheat–summer maize production system.
Abstract Mechanistic models built for prediction are often treated as a parameter estimation problem. Using Bayesian inference on a well-studied shoot branching ODE model, we show that multiple incompatible parameter calibrations can fit the same experimental data yet can make contradictory predictions under unseen treatment conditions. Given this behaviour, we decided to explore how well the causal connections of a network topology alone can be used to express biological outcomes. We developed PSoup, an R package that converts knowledge graphs directly into qualitative models free of kinetic parameters. Users draw their network diagram using standard SBGN-AF notation in the Newt Editor, capturing interactions across genes, hormones, and environmental interventions. PSoup then uses this diagram to automatically build a model using algebraic update rules anchored to a biologically interpretable baseline, enabling predictions of relative change without kinetic information. We validated PSoup against the shoot branching network of Bertheloot et al. (2019), spanning 78 experimental conditions across two plant species, two laboratories, and diverse treatments including hormone application, sucrose, decapitation, and mutant genotypes. PSoup correctly predicted 89.5\% of unique, biologically consistent comparisons, without any parameter fitting. In addition, PSoup is also useful to evaluate alternative network topologies, identifying which structural features drive observed behaviour and which experiments would best discriminate between competing hypotheses. PSoup offers an intuitive, accessible, and mathematically transparent framework for exploring biological networks. Its capacity to integrate diverse knowledge and test alternative hypotheses positions it as a powerful tool for biological discovery and a valuable complement to existing modelling approaches.
Abstract Understanding and managing genotype × environment (G × E) interactions remain a major challenge in developing climate-resilient crops. Accurate characterization of the environments experienced by crops within the target population of environments (TPE) is essential to improve this task. This study applied advanced crop modelling and envirotyping approaches to simulate the growth and development of barley cultivars and to quantify seasonal patterns of water stress index, vapour pressure deficit (VPD), and maximum temperature (MaxT), analysed both individually (univariate) and in combination (multivariate). Long-term APSIM simulations were conducted for standard cultivar, Gairdner, using 60 years of historical weather data (1965–2024) across 60 representative sites covering the Australian barley-growing regions. Simulations incorporated regionally representative management practices, and two additional cultivars differing in maturity type, Keel (quick) and Franklin (slow), were used to assess the effect of maturity on stress frequencies. Both univariate and multivariate environment types (ETs) were identified across the TPE for water stress, VPD, and MaxT. The frequency of ETs varied greatly across locations and cultivars, with the slow-maturing cultivar consistently being exposed to greater stress. Comparison of simulations from recent (1995–2024) and older (1965–94) climates indicated a 4%–14% increase in the frequency of the most stressful ETs, reflecting the influence of realized climate change. These findings provide a framework to support climate-resilient breeding and agronomy in Australian barley production systems. Overall, this study enhances understanding of environmental diversity and stress dynamics, contributing to the long-term sustainability and yield stability of barley production under Australia’s evolving climate.
In this work, we investigate modeling plant traits over time using neural processes, a class of machine learning models that learn distributions over functions. Plant growth is an inherently stochastic process with complex dynamics measured mostly at irregular times throughout the growing seasons. While individual trait trajectories may be simple, their distributions are shaped by complex interactions between genotype, environment, and other factors. In particular, we focus on plant height in wheat, a deceptively simple-looking trait with complex dynamics. To model these trajectory distributions, we evaluate neural processes and in particular extensions using normalizing flows, with different combinations of genotype and environmental covariates. For controlled evaluations, we generate synthetic wheat height trajectories calibrated against Swiss weather station records and the Field Phenotyping Platform 1.0 ( FIP1 ) wheat dataset. To fully evaluate these trajectory distributions, we use signatures, vector representations of sequential data, together with the signature maximum mean discrepancy ( Sig-MMD ) and its recently introduced censored variant ( CSig-MMD ). Sig-MMD enables direct pathwise comparison of predicted and simulator trajectory distributions, while CSig-MMD focuses this comparison on the tail, including lodged trajectories. Together, these metrics allow us to assess whether the models capture the full distribution of growth trajectories, including rare outcomes. We compare the neural processes with a lodging-mixture spline baseline and apply them to the FIP1 data. ### Competing Interest Statement The authors have declared no competing interest. * ### List of Abbreviations ACNP : attentive conditional neural process ANP : attentive neural process ANP-NF-Prior : attentive neural process with normalizing flow prior AR(1) : first-order autoregressive ANP-NF-Prior-Posterior : attentive neural process with normalizing flow prior and posterior BLUE : best linear unbiased estimate CNP : conditional neural process CRPS : continuous ranked probability score CSig-MMD : censored signature maximum mean discrepancy ELBO : evidence lower bound FIP1 : Field Phenotyping Platform 1.0 KL : Kullback–Leibler divergence LNP : latent neural process LNP-NF-Prior : latent neural process with normalizing flow prior MLP : multi-layer perceptron LNP-NF-Prior-Posterior : latent neural process with normalizing flow prior and posterior MMD : maximum mean discrepancy MRCD : minimum regularized covariance determinant NF : normalizing flow NP : neural process NSF : neural spline flow PDE : partial differential equation RBF : radial basis function RMS : root mean square RMSE : root mean squared error RMSNorm : root mean square layer normalization SD : standard deviation Sig-MMD : signature maximum mean discrepancy SwiGLU : Swish-gated linear unit VAE : variational auto-encoder Swiss National Science Foundation, https://ror.org/00yjd3n13, PHENO-MINE C21--04, IZSEZ0 230796, PreDiMix 10002207
Abstract Crop models are essential for predicting climate change impacts on agriculture, yet their validation under multi-stress conditions remains limited. This study evaluated two widely used wheat models, APSIM and STICS, using data from three Free-Air CO2 Enrichment (FACE) experiments (USA, Germany, Australia) combining elevated CO2 (eCO2), water deficit, and warming. Environmental characterization using simulation-based stress indices revealed that intended ‘controls’ frequently experienced hidden heat and water stress, meaning models were calibrated on crops already undergoing physiological adjustments. Evaluation of simulated yield and components revealed a clear hierarchy in prediction errors (RRMSE): unlimited conditions (3%–9%) < single stress (4%–27%, with a need to improve response to heat stress) < combined stress (17%–123%). eCO2 generally increased prediction uncertainty for crops experiencing water stress. Our results suggest that current stress functions from the models fail to capture the synergistic coupling between drought and heat stress. This highlights the urgent need for more mechanistic modelling to improve the reliability of climate change impact assessments.
