Modelling time‐varying low‐temperature‐induced mortality rates for pupae of Tuta absoluta (Gelechiidae,Lepidoptera)

In a series of laboratory experiments, acclimated pupae of Tuta absoluta were exposed to various constant low temperatures in order to estimate their maximum survival times (Kaplan–Meier, Lt_99.99). A Weibull function was fitted to the data points, describing maximum survival time as a function of temperature. In another experiment at ?6°C, the progress of mortality increasing with exposure time was identified. These values were fitted by a sigmoidal function converging asymptotically to 100% mortality for very long exposure times. Analysing mortality data from the maximum survival experiment by a generalized linear model showed a significant common slope parameter (p < .001) that reveals parallelism of the survival curves at each temperature if a log time axis is used. These curves appear stretched (time scaled) if plotted with a nonlogarithmic time axis. By combining these mathematical relations, it was possible to calculate a species‐specific ‘mortality surface’ which exhibits mortalities, depending on temperature and duration of exposure. In order to accumulate hourly mortalities for courses of varying temperatures, an algorithm was developed which yields mortality values from that surface taking into account the attained mortality level. In validation experiments, recorded mortalities were compared against modelled mortalities. Prediction of mortality was partially supported by the model, but pupae experiencing intensely fluctuating temperatures showed decreased mortality, probably caused by rapid cold hardening during exposure. Despite this observation, mortality data converged to distinct levels very close to 100% depending on the intensity of temperature fluctuations that were characteristic for different types of experiments. The highest mortality limit occurred at intensely fluctuating temperatures in laboratory experiments. This constituted a benchmark that was not reached under various field conditions. Thus, it was possible to identify temperature limits for the extinction of field populations of Tuta absoluta pupae.