Modeling pollination response to temperature and photoperiod in different quinoa cultivars

Background and objectives: Quinoa is a valuable food product that helps ensure food security worldwide. Accurate phenological predictions are essential for understanding a plant species' growth potential and performance. One of the most important studies required for this purpose is quantifying and estimating cardinal temperatures and day length parameters for the pollination stage, which is a crucial step in understanding the growth and performance of plants. Given that quantitative information on quinoa phenology is scarce, such data regarding pollination responses to temperature and day length can be useful in understanding the growth and performance of this plant. Therefore, the objectives of the present study are: (1) to develop a multiple model for predicting pollination in quinoa, and (2) to determine cardinal temperatures and day length parameters for pollination.



Materials and Methods: A field experiment was conducted with 12 planting dates from 2019 to 2021 on three quinoa varieties in Galugah city. In this study, 10 plants were randomly selected and marked in each subplot to record the pollination initiation time for each planting date. The time taken to reach the pollination initiation stage was also recorded, where at least 50% of the plants had at least one flower at any position on the plant. To quantify the pollination stage against temperature and day length, a multiple model using combined temperature and day length functions was used. The temperature function was represented as a piecewise function, and the day length function was represented exponentially. The model was executed using the Proc nlin procedure in SAS software. To evaluate the model's accuracy, criteria such as RMSD, R², comparison of 1:1 line coefficients with coefficients a and b from linear regression between predicted and observed values, and the correlation coefficient between them were used.

Results:The results showed that the RMSD values for different varieties ranged from 1.6 to 6.9 days, with lower values indicating higher model efficiency. The R² coefficient for describing the relationship between pollination rate and temperature and day length in the three quinoa varieties was estimated to be above 0.97. A high R² value indicates that the model is appropriate for describing the relationship between pollination rate, temperature, and day length. The base temperatures for the different varieties were estimated to be between 1.6 and 4.2 degrees Celsius, but no statistically significant differences were observed in the base temperatures of these three varieties. The optimal temperature estimated among the varieties ranged from 22.1 to 27.9 degrees Celsius. Further analysis using the error of estimating the optimal temperature revealed significant differences among the varieties regarding base temperature, with the Q12 variety having the highest optimal temperature value. The sensitivity coefficients to day length for varieties Q12, Titicaca, and Giz1 were estimated to be 0.025, 0.065, and 0.096 hours per day, respectively. Statistically significant differences were observed among the studied varieties with respect to sensitivity to day length. The biological day (the minimum number of days to pollination under optimal temperature and day length conditions) estimated through the model for the varieties Q12, Titicaca, and Giz1 were 31.7, 32.1, and 36.1 days, respectively.

Conclusion: The results showed that due to the low value of RMSD (less than 6.9 days) and high values of R2 (above 0.97) and r (above 0.95) in different cultivars, the bipartite-exponential model was able to describe the relationship between pollination well. Describe the temperature and length of the day. This model can be used to optimize management decisions, adjust phenological responses to diverse environmental conditions, and predict phenological responses to temperature and day length changes in the future.

Key Words: Temperature function, biological day, optimal temperature, phenology.