Understanding factors influencing the time of weed seedling establishment can contribute to developing predictive models for control measures at early growth stages. Non-linear regression models (Dent-like and Quadratic polynomial) and hydrothermal time models were considered for estimating cardinal temperature and predicting the emergence time of the Setaria species (S. viridis, S. verticillata, and S. glauca) at different constant temperatures and water potentials. Field experiments were also conducted, in which seeds of the species were sown and seedling emergence was recorded daily. The optimum temperature for germination was 27.7, 30.2, and 30.5 °C as estimated by a Dent-like model at 0 MPa water potential for S. glauca, S. viridis and S. verticillata, respectively. According to the hydrotime model, the minimum amount of base water potential (Ψb) was observed at the optimum temperatures, while it reached its highest value at temperatures exceeding the optimum. Overall, at sub-optimal temperatures, with the decrease in water potential, the thermal time (TT) constant increased linearly until − 0.6 MPa, but this trend was downward at supra-optimal temperatures. The hydrothermal time constant (θHT) was 213.5, 228.8, and 318.8 MPa °C h for S. viridis, S. verticillata, and S. glauca, respectively. Non-linear regression and hydrothermal models showed that S. glauca can emerge earlier than other species because of lower base temperature and a higher hydrothermal time constant. Setaria species did not show a significant difference in their tolerance to water stress by similar base water potential (Ψb(50) ~ − 0.5).

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