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Irrigation and nitrogen (N) are two crucial factors affecting perennial grass seed production. To investigate the effects of irrigation and N rate on seed yield (SY), yield components, and water use efficiency (WUE) of Cleistogenes songorica (Roshevitz) Ohwi, an ecologically significant perennial grass, a four-year (2016–2019) field trial was conducted in an arid region of northwestern China. Two irrigation regimes (I1 treatment: irrigation at tillering stage; I2 treatment: irrigation at tillering, spikelet initiation, and early flowering stages) and four N rates (0, 60, 120, 180 kg ha−1) were arranged. Increasing amounts of both irrigation and N improved SY, evapotranspiration, WUE, and related yield components like fertile tillers m−2 (FTSM) and seeds spikelet−1. Meanwhile, no significant difference was observed between 120 and 180 kg N ha−1 treatments for most variables. The highest SY and WUE was obtained with treatment combination of I2 plus 120 kg N ha−1 with four-year average values of 507.3 kg ha−1 and 1.8 kg ha−1 mm−1, respectively. Path coefficient and contribution analysis indicated that FTSM was the most important yield component for SY, with direct path coefficient and contribution coefficient of 0.626 and 0.592. Overall, we recommend I2 treatment (three irrigations) together with 120 kg N ha−1 to both increase SY and WUE, especially in arid regions. Future agronomic managements and breeding programs for seed should mainly focus on FTSM. This study will enable grass seed producers, plant breeders, and government program directors to more effectively target higher SY of C. songorica.

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.