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An Environment-Driven Dynamic Growth Model for Pleurotus citrinopileatus: Advancing Precision Control and Automation in Container Cultivation

This study develops an Environment-Driven Dynamic Growth Model (ED-DGM) based on the Richards function and key environmental factors to significantly improve the prediction accuracy of *Pleurotus citrinopileatus* growth in containerized cultivation, thereby enabling precision control and automation in intelligent mushroom production systems.

Original authors: Qingfeng WEI, Changshou LUO, Jun Yu, Chenzhong Cao, Yaming ZHEN, Yang LU, Rupeng LUAN

Published 2026-06-29

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CC BY 4.0

Original authors: Qingfeng WEI, Changshou LUO, Jun Yu, Chenzhong Cao, Yaming ZHEN, Yang LU, Rupeng LUAN

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to bake the perfect loaf of bread. If you just set the oven to a fixed temperature and hope for the best, you might get a decent loaf, but you won't get the perfect one every time. You need to watch the dough, smell the air, and adjust the heat as the baking happens.

This paper is about doing exactly that, but for Golden Oyster Mushrooms (Pleurotus citrinopileatus) growing inside high-tech, shipping-container-sized "fungal factories."

Here is the story of how the researchers built a "smart recipe" to predict how these mushrooms grow.

1. The Problem: The "Static" Recipe vs. The Real World

Traditionally, farmers and scientists used "static" growth models to predict mushroom growth. Think of these like a fixed GPS route. The map says, "In 8 days, the mushroom will be this big."

But the real world is messy. The temperature in the container might spike for an hour, or the humidity might drop. A static map doesn't know about these detours. It keeps predicting the mushroom will be big, even if the environment slowed it down. This leads to bad predictions and wasted time.

2. The Experiment: Watching Mushrooms Grow

The researchers set up a smart container (a retrofitted shipping container) with sensors that checked the temperature, humidity, light, and air quality every 10 seconds. They grew 72 bags of mushrooms and measured them every day for 8 days.

They found that the mushrooms grew in a specific "S-shape" pattern:

Days 1–3: Slow start (the mushroom is waking up).
Days 4–7: Explosive growth (the mushroom is eating and growing fast).
Day 8: Slowing down as it gets ready to be harvested.

3. The Detective Work: What Actually Drives Growth?

The team asked: What makes the mushroom grow faster or slower? They tested several suspects:

The "Heat Battery" (Accumulated Effective Temperature): Mushrooms need a certain amount of heat energy over time to grow. It's not just the temperature right now, but the total heat they've "banked" since they started growing.
The "Water Battery" (Accumulated Relative Humidity): Mushrooms are mostly water. They need a steady, high humidity over time to stay plump and expand.
The "Air Poison" (CO2): While mushrooms need some CO2, too much of it acts like a brake pedal, stopping the mushroom cap from opening properly and making the stem grow too long and thin.

They found that Heat and Humidity were the gas pedals, and CO2 was the brake.

4. The Solution: The "Smart Engine" (ED-DGM)

Instead of using a fixed map, the researchers built a dynamic engine called the Environment-Driven Dynamic Growth Model (ED-DGM).

Here is the analogy:

The Old Way (Static Model): A train running on a fixed track. It goes the same speed regardless of the weather outside.
The New Way (ED-DGM): A self-driving car. It has sensors that constantly check the road (the environment). If it sees rain (high humidity), it knows the car can go faster. If it sees a hill (low heat), it knows to slow down. If it sees a traffic jam (high CO2), it knows to brake.

The researchers took the best mathematical formula for mushroom growth (called the Richards model) and hooked it up to these sensors. Now, the model doesn't just guess based on "Day 5"; it calculates, "On Day 5, because we had 500 units of heat and 800 units of humidity, the mushroom should be this specific size."

5. The Results: A Sharper Crystal Ball

When they tested their new "Smart Engine" against the old "Fixed Map":

The new model was significantly more accurate.
It predicted the mushroom's length, width, height, and total volume much better.
Specifically, it improved the prediction for the mushroom's volume (how much "meat" it has) by 10.6%.

This might sound small, but in farming, knowing exactly when a mushroom is ready to harvest is huge. It means farmers don't have to guess or check every single mushroom by hand. The computer can tell them, "Harvest time is now," saving labor and ensuring the mushrooms are picked at the perfect moment.

Summary

The paper doesn't claim to cure diseases or change the world overnight. It simply says: We built a smarter calculator for growing mushrooms in containers.

By feeding real-time data about heat, water, and air into a mathematical formula, we can predict exactly how big a mushroom will get. This turns mushroom farming from a game of "guess and check" into a precise, automated science.

Technical Summary: An Environment-Driven Dynamic Growth Model for Pleurotus citrinopileatus

Problem Statement
The industrial cultivation of Pleurotus citrinopileatus (golden oyster mushroom) in intelligent containerized facilities faces a critical bottleneck: the lack of quantitative theoretical frameworks for environmental control. While Controlled Environment Agriculture (CEA) offers high controllability, current management relies heavily on empirical practices. Traditional growth models (e.g., Logistic, Richards) used in precision agriculture typically treat growth parameters as static constants, failing to account for dynamic environmental fluctuations inherent in automated systems. Furthermore, while machine learning approaches exist, they often lack biological interpretability ("black box" nature) and struggle with generalization under novel conditions. There is a specific need for a model that bridges biological interpretability with real-time responsiveness to environmental drivers to enable autonomous, precision cultivation.

Methodology
The study was conducted in a retrofitted 40-foot shipping container equipped with a precision environmental control system (temperature, humidity, light, CO₂).

Data Collection: Researchers monitored 72 substrate bags over an 8-day fruiting period, collecting 576 initial observations. After outlier removal, 459 valid datasets were analyzed. Morphological parameters (length, width, height) were measured daily, and volume was estimated using an ellipsoid-based formula calibrated with drainage methods.
Environmental Variables: Raw data (temperature, RH, light, CO₂) were processed into derived variables, including Accumulated Effective Temperature (AET), Accumulated Relative Humidity (ARH), and instantaneous mean values (MT, MRH, MCO₂, MLI).
Model Selection: Three non-linear models (Logistic, Weibull, Richards) were evaluated against the empirical growth data. The Richards model was selected as the baseline due to its superior fit to the asymmetric S-shaped growth curves observed in P. citrinopileatus.
Driver Identification: Pearson correlation analysis, significance testing, and Variance Inflation Factor (VIF) diagnostics were used to identify core environmental drivers. This process filtered out multicollinear variables (e.g., Mean Temperature) and identified AET, ARH, and Mean CO₂ (MCO₂) as the significant predictors.
Model Construction (ED-DGM): The core innovation involved transforming the static parameters of the Richards model—the asymptotic limit ( $A$ ) and the growth rate ( $K$ )—into dynamic linear functions of the identified environmental drivers (AET, ARH, MCO₂). This created the Environment-Driven Dynamic Growth Model (ED-DGM).
Evaluation: The model was validated using a 7:3 train-test split. Performance was assessed via $R^2$ , RMSE, MAPE, and residual analysis, comparing the ED-DGM against the traditional static Richards model.

Key Results

Growth Dynamics: P. citrinopileatus exhibited a distinct asymmetric S-shaped growth trajectory. Volume showed the most dramatic increase (219.9-fold over 8 days), characterized by a lag phase followed by explosive expansion.
Environmental Drivers:
- ARH (Accumulated Relative Humidity) was the strongest positive driver ( $r = 0.8447$ ), explaining 71.35% of volume variation.
- AET (Accumulated Effective Temperature) was the second strongest positive driver ( $r = 0.8093$ ).
- MCO₂ (Mean CO₂) showed a moderate negative correlation ( $r = -0.446$ ), consistent with the known inhibition of cap differentiation by high CO₂.
- Light intensity and instantaneous humidity showed negligible effects on volume growth.
Model Performance: The ED-DGM significantly outperformed the static Richards model across all morphological indicators:
- Length: $R^2$ improved by 9.1%.
- Width: $R^2$ improved by 9.3%.
- Height: $R^2$ improved by 6.7%.
- Volume: $R^2$ improved by 10.6%.
Residual Analysis: The ED-DGM eliminated the systematic negative bias (underestimation) observed in the static model, particularly for volume. Residuals were centered near zero with reduced standard deviation, indicating higher stability and unbiasedness.

Significance and Claims
The paper claims that the ED-DGM represents a paradigm shift from "experience-dependent" to "algorithm-driven" cultivation. By coupling classical growth curve biology with cumulative environmental drivers, the model overcomes the limitations of static parameterization.

Interpretability: Unlike "black box" machine learning models, the ED-DGM retains biological interpretability, allowing growers to understand how specific environmental fluctuations (e.g., heat accumulation or humidity deficits) directly impact growth rates and final yield.
Automation Readiness: The model is designed as a high-precision algorithmic engine suitable for integration into IoT-based environmental control platforms. It enables real-time growth forecasting and autonomous feedback regulation (e.g., adjusting HVAC or humidification based on predicted deviations from optimal trajectories).
Precision Control: The research provides a robust framework for optimizing harvest scheduling and reducing labor in containerized production systems, addressing the technical bottlenecks of high-density, season-independent mushroom farming.

Limitations Noted
The authors acknowledge that the current model focuses on the 8-day rapid fruiting phase and does not yet cover primordial initiation or multi-flush cycles. Additionally, the current linear coupling of environmental factors does not fully capture complex non-linear interactions or synergistic effects, suggesting a need for future non-linear coupling research. The model's generalizability to other fungal species remains to be verified.