Fig. 5

Results of DLNMs and 4PL regression model fitted to the collected data. a Observed and predicted diapause incidence rates in the field in Guangzhou, China during 2016–2017. b Dose-response curve of (the differences in) diapause incidence and daylight duration in the laboratory and in the field. The blue points in a represent the observed diapause incidence; the red line represents the predicted diapause incidence based on a distributed lag non-linear model with a moving average of mean temperature over a lag of 0–2 weeks. The pink area indicates the corresponding 95% confidence interval (CI) of the predicted diapause incidence. The blue points in b represent the observed diapause incidence in the laboratory; the blue line is the fitted curve based on the 4-parameter logistic regression model: \( \widehat{y}=0.774+\frac{\left(92.113-0.774\right)}{1+{\left(\frac{Day\_ length}{12.312}\right)}^{44.073}} \) (\( \widehat{y} \) is the predicted diapause incidence in the laboratory). The red line in b represents the estimated difference in diapause incidence based on the model used in a, with reference at 13.450 h, and the pink area is the corresponding 95% CI of the estimated difference in diapause incidence