Thermal time models have been widely applied to predict temperature requirements for seed germination. Generally, a log-normal distribution for thermal time [θT(g)] is used in such models at suboptimal temperatures to examine the variation in time to germination arising from variation in θT(g) within a seed population. Recently, additional distribution functions have been used in thermal time models to predict seed germination dynamics. However, the most suitable kind of the distribution function to use in thermal time models, especially at suboptimal temperatures, has not been determined. Five distributions (log-normal, Gumbel, logistic, Weibull and log-logistic) were used in thermal time models over a range of temperatures to fit the germination data for 15 species. The results showed that a more flexible model with the log-logistic distribution, rather than the log-normal distribution, provided the best explanation of θT(g) variation in 13 species at suboptimal temperatures. Thus, at least at suboptimal temperatures, the log-logistic distribution is an appropriate candidate among the five distributions used in this study. Therefore, the distribution of parameters [θT(g)] should be considered when using thermal time models to prevent large deviations; furthermore, an appropriate equation should be selected before using such a model to make predictions.

中文翻译：

---

15种种子萌发热时间模型参数估计：分布函数的重要性

热时间模型已广泛应用于预测种子萌发的温度要求。通常，热时间的对数正态分布 [θ吨（克）] 在次优温度下用于此类模型，以检查由 θ 变化引起的发芽时间变化吨（克）种子种群内。最近，在热时间模型中使用了额外的分布函数来预测种子萌发动态。然而，尚未确定在热时间模型中使用的最合适的分布函数类型，尤其是在次优温度下。在一定温度范围内的热时间模型中使用了五种分布（对数正态、Gumbel、逻辑、威布尔和对数逻辑），以拟合 15 个物种的发芽数据。结果表明，具有对数逻辑分布而不是对数正态分布的更灵活模型提供了对 θ 的最佳解释吨（克）13 个物种在次优温度下的变异。因此，至少在次优温度下，对数逻辑分布是本研究中使用的五种分布中的合适候选者。因此，参数的分布 [θ吨（克）] 在使用热时间模型时应考虑，以防止出现较大偏差；此外，在使用这种模型进行预测之前，应选择适当的方程。