Triangle area model (TAM) for predicting germination: An approach to enhance hydrothermal time model applications

Abstract

A thorough examination of assumptions in hydrothermal time models revealed areas for enhancing model performance. We introduce the Triangle Area Model (TAM), which uses the area of right-angled triangles to calculate hydrothermal time for predicting population germination fractions (g). TAM is characterized by its depiction of triangles, considering insightful parameters such as the distance of germination temperature (T) to the base (T_b), optimal (T_o), and ceiling (T_c) temperatures, the range of T_c – T_o, T_o – T_b, and the germination water potential (Ψ), i.e. mean base water potential (Ψ_b(g)), along with potential g that may occur with T and Ψ combinations within T_c – T_b when Ψ > Ψ_b(g). Applied to germination data from Ambrosia psilostachya L., Cynanchum acutum L., and Bidens pilosa L., TAM achieves an RMSE of 0.03 for A. psilostachya and C. acutum, and 0.05 for B. pilosa. Moreover, TAM demonstrates an R² of 0.96, 0.97, and 0.98 for the respective species. TAM significantly outperforms earlier models through a comparison with varying T and Ψ. TAM determined T_b for A. psilostachya, C. acutum, and B. pilosa as 0.19, 14.57, and 5.76 °C; T_o as 25.1, 39.9, and 29.8 °C; and T_c as 46.7, 53, and 41°C, for the respective species. It also estimates Ψ_b(g) as -1.48 for A. psilostachya, -0.98 for C. acutum, and -0.97 for B. pilosa. The TAM approach deepens our understanding of temperature-moisture processes influencing plant survival, colonization, and habitat expansion for these three invasive alien species. Furthermore, it can be more widely applied for estimating TT and HTT across different growth stages, enhancing the prediction accuracy of plant phenological development.