# Quantifying germination cardinal temperatures of ten forage legumes using non-linear regression models

## TL;DR

This study determines the optimal temperature ranges for germinating ten forage legumes, revealing species-specific thermal preferences and aiding in better sowing practices.

## Contribution

The study introduces a novel application of non-linear regression models to quantify germination cardinal temperatures across ten forage legume species.

## Key findings

- Alfalfa, yellow medick, and erect milkvetch showed high thermal plasticity with wide germination temperature ranges.
- Sweet clover preferred cooler temperatures, while niuzhizi and white clover required higher temperatures for optimal germination.
- The intersected-lines model outperformed the quadratic polynomial model in predicting cardinal temperatures.

## Abstract

Forage legumes play a pivotal role in livestock production, environmental protection, sustainable cropping systems, and various industrial applications. Understanding the germination thermal requirements of forage legumes is necessary for optimizing their sowing and production. The response of germination rate to temperature can be described using non-linear regression models.

In this study, ten constant temperatures (from 0 to 45°C with 5°C interval) were evaluated, and two non-linear regression models (intersected-lines and quadratic polynomial) were applied to quantify cardinal temperatures and thermal ranges for ten important forage legumes.

Both germination percentage and germination speed were low in hot and cold temperatures outside the range of 15-25°C for these species. Notably, significant inter-species variation in thermal requirements was identified. Alfalfa (Medicago sativa), yellow medick (Medicago falcata), and erect milkvetch (Astragalus adsurgens) demonstrated high thermal plasticity, characterized by low minimum (base) temperature (Tb), high maximum temperature (Tm), and wide thermal ranges. Conversely, sweet clover (Melilotus officinalis) exhibited a preference for cooler thermal regimes, with the lowest optimum temperature (To) and Tm thresholds. Niuzhizi (Lespedeza potaninii) and white clover (Trifolium repens) were identified as thermophilic species, requiring higher temperatures for optimal germination, as evidenced by their higher To and Tm thresholds, whereas species of the genus Vicia and red clover (Trifolium pratense) were best adapted to moderate thermal environments. Furthermore, germination speed-related parameters were more sensitive to temperature fluctuations than germination percentage. Among the tested models, the intersected-lines model showed superior performance for predicting the cardinal temperatures of the ten forage legumes, as indicated by a lower root mean square of error (RMSE) and a higher coefficient of determination (R²). No statistically significant relationships between cardinal temperatures and germination parameters were observed. These findings provide a scientific basis for improving sowing practices and regional species selection, which is vital for forage legume cultivation and production. The identification of cardinal temperatures is also crucial for the development of plant growth and biomass prediction models that simulate growth and estimate yield under current and future climate scenarios.