We are thrilled to share our latest Communications Earth & Environment publication, led by LEMONTREE’s Cai Wenjia (Imperial College London):
“A Unifying Principle for Global Greenness Patterns and Trends.”
This study introduces a minimalist framework for modelling Leaf Area Index (LAI), revealing new insights into the mechanisms driving vegetation greenness and its response to environmental changes. By combining theoretical ecohydrological principles with global datasets, our model delivers predictive accuracy that rivals or surpasses the most sophisticated Dynamic Global Vegetation Models (DGVMs) while maintaining simplicity and robustness.
This research underscores the power of Eco-Evolutionary Optimality (EEO) theory and simplicity in scientific modelling, demonstrating that even with minimal assumptions, we can understand the fundamental drivers of vegetation patterns and trends. Here, we provide an overview of the model’s foundations, key findings, and implications for the future of ecosystem science.
“Plants are smart enough to adjust the amount of leaves they have, so that they could maximize their carbon uptake through photosynthesis, while minimizing water lost through transpiration!”
Dr Cai Wenjia, ICL
Vegetation plays a pivotal role in regulating the exchange of carbon, water, and energy between terrestrial ecosystems and the atmosphere, often quantified by the leaf area index (LAI). This vegetation characteristic determines how plants absorb photosynthetically active radiation (PAR) and governs processes like transpiration, a major contributor to global evaporation. Additionally, LAI influences energy partitioning between latent and sensible heat fluxes, impacting local and regional climates. Current models for understanding vegetation and productivity, including light-use efficiency (LUE) models and dynamic global vegetation models (DGVMs), either simplify the canopy’s radiation use (such as in the Big-leaf model) or attempt to simulate LAI and gross primary production (GPP) through biomass partitioning. However, these approaches involve limitations, including poorly tested formulations and parameter uncertainties.
This study introduces an alternative approach based on eco-evolutionary optimality (EEO) principles, using an equation with only two globally fitted parameters to predict annual maximum fractional absorbed PAR (fAPARmax). The framework hypothesises that fAPARmax is constrained by water-limited and energy-limited conditions
Water Limited: The fraction of precipitation accessible to plants. This reflects the plant’s ability to capture water for growth, with higher values indicating greater water use efficiency.
fAPARmax = f0 P ca (1 – χ) / (1.6 D A0)
Energy- Limited: The cost of maintaining and replenishing the plant canopy, measured in terms of carbon allocation. This parameter reflects the balance plants must strike between above-ground (canopy) and below-ground (root) investments.
fAPARmax = 1 – z / (k A0)
Building on the universal P model—a first-principles LUE model tested across biomes—this framework predicts fAPARmax independently of plant functional types, reducing uncertainty and improving generality. By leveraging remotely-sensed fAPAR rather than LAI, the model avoids issues of reflectance saturation. When tested globally, the framework effectively reproduces vegetation greenness patterns and temporal trends seen in remote-sensing data, attributing observed greening to CO₂-driven efficiencies and environmental changes, while browning is linked to drying.
This approach demonstrates how minimalist modelling can capture key ecological processes with precision, advancing the understanding of vegetation responses to environmental changes and informing next-generation ecosystem models.
Key Findings
Global Comparisons to Observations
This LAI framework effectively captures global patterns of vegetation greenness, as shown by comparisons to both ground-based measurements and remote-sensing data. When compared to MODIS remote-sensing data, the predicted geographic distribution of annual maximum fAPAR closely matched observed patterns, with differences typically within ±0.1 and large discrepancies confined to regions like the Sahel, northeastern Brazil, and the Tibetan Plateau.
Figure 1. Temporal trends in observed and modelled fAPARmax during 2000-2017
In performance comparisons with 15 dynamic global vegetation models (DGVMs) from the TRENDY project, the LAI framework matched or outperformed the best models.
Figure 2. Comparison of our model with that of 15 DGVMs participating in the TRENDY project24 version 9
One of the main achievements of this study is the model’s ability to capture global patterns with remarkable precision. When compared to ground-based measurements and satellite observations, the predictions align closely with observed data. Differences between modelled and observed were within ±0.1 in over 53% of cases, and within ±0.15 in 72% of cases. These results demonstrate that even with simplified assumptions, it is possible to achieve robust predictive performance.
Greening trends dominate
The framework successfully replicated broad greening and browning trends in fAPARmax from 2000–2017. Widespread greening, driven largely by rising atmospheric CO₂ and, in some regions, increased precipitation, was evident in both observed and modelled data. Conversely, browning trends were observed and simulated in regions such as semi-arid Central Asia, southwestern Africa, northeastern Brazil, and California, where drying played a dominant role. The model underpredicted greening in regions like India and China, likely due to human influences such as agricultural intensification and reforestation.
Statistical analyses revealed predominantly linear trends in global fAPARmax with only minor regions showing non-linear patterns. The framework’s ability to simulate temporal trends was comparable to the best TRENDY models, achieving an R2 of 0.37 and a regression slope closest to 1 among the models.
Figure 3. Drivers of greening
Ecohydrological Insights
Our findings resonate with established ecohydrological theories, such as the Budyko framework, which relates water balance to aridity. For example, the relationship between f0 and the aridity index aligns with existing studies, where f0 peaks at intermediate aridity levels. The model also supports the concept of optimal canopy extinction coefficients (k) — values that govern light penetration in vegetation canopies. While k is influenced by leaf structure and density, our analysis shows that its specification is not critical to accurately predicting patterns and trends.
This minimalist approach compares favourably with complex DGVMs, matching or exceeding their performance while offering a clearer theoretical basis. The focus on principles rather than legacy-based complexity provides a pathway toward more robust ecosystem models.
Future Directions
Ecohydrological optimality concepts have a long but chequered history, but we have demonstrated that by keeping the formulations as simple as possible, we are still able to accurately predict parameters and vegetation greenness. The results highlight the model’s potential for broader application in ecosystem studies. By predicting fAPAR and linking it to below-ground carbon allocation, it could inform a general model of ecosystem function that integrates carbon allocation strategies, competition, and evolutionary dynamics. Such advancements are crucial for developing land models based on secure theoretical foundations, addressing legacy issues in carbon allocation modelling, and enhancing predictions of ecosystem responses to environmental change.
This research underscores the balance between simplicity and functionality in global vegetation modelling, demonstrating that ecohydrological principles can effectively predict spatial and temporal patterns in vegetation greenness while providing a theoretical basis for future improvements.
You can read the full paper here:
Cai, W., Zhu, Z., Harrison, S.P., Ryu, Y., Wang, H., Zhou, B. & Prentice, I.C. 2025. A unifying principle for global greenness patterns and trends. Communications Earth and Environment, https://doi.org/10.1038/s43247-025-01992-0
