Developmental rate models and biological parameters estimated from them, especially lower and upper temperature thresholds and optimal temperature, can help to forecast phenological events of codling moth, Cydia pomonella L. (Lepidoptera: Tortricidae), in apple orchards. We studied the developmental time of immature stages of codling moth at eight constant temperatures ranging from 10 to 35 degrees C and modeled their developmental rate as a function of temperature using 13 published nonlinear and 2 linear models. Data were fitted to developmental rate models and temperature thresholds and the optimal temperatures were estimated. The models were evaluated based on adjusted coefficient of determination (R(2)(adj)) and Akaike information criterion (AIC), in addition to coefficient of determination (R(2)) and residual sum of squares (RSS). The thermal constants were 79.80, 312.60, 232.03, and 615.32 DD for egg, larva, pupa, and overall immature stages of codling moth, respectively, using the Ikemoto and Takai linear model. The Ikemoto and Takai linear model estimated lower temperature thresholds as 9.97, 8.94, 10.04, and 9.63 degrees C for egg, larva, pupa, and overall immature stages, respectively. Among the nonlinear models, the third-order polynomial fit the data well. This model estimates optimal temperature accurately. Brière-1 and Brière-2 accurately estimated the lower and upper temperature thresholds considering model evaluation criteria and accuracy of estimations.

Age-specific life table parameters and survivorship, adult longevity, reproduction periods, fertility, and sex ratio of the codling moth were studied at eight constant temperatures (10, 14, 20, 25, 27, 30, 33, and 35 ±0.5°C). Among the examined temperatures, the highest values of net reproductive rate, intrinsic rate of increase, and finite rate of increase were 18.28 (females/female), 0.08 (females/female/d), and 1.08 at 27°C, respectively. Similarly, the highest value of sex ratio was 0.56 [females/ (females + males)] at 27°C. The highest mean generation time and doubling time were 72.26 and 23.09 d, respectively, at 20°C. To present a suitable model for intrinsic rate of increase at different temperatures, a nonlinear Lactin model was fitted to our observations. The longest preoviposition period was 2.77 and 2.55 d at 20 and 30°C, respectively. Also, the longest oviposition period was 8.46 d at 20°C. Postoviposition period was not statistically different at examined temperatures. The Weibull frequency distribution was used to describe the age-specific survival of the female adults. Based on the Weibull distribution parameters, the survival curves were type I at all examined temperatures, which indicates that mortality mostly occurred in old individuals. These findings confirmed that temperature is a critical environmental factor affecting codling moth population growth.

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Developmental rate of immature stages and age-specific fertility of females of codling moth at constant temperatures was modeled using non-linear models. The equations of Enkegaard, Analytis, and Bieri 1 and 2 were evaluated based on the value of adjusted R2 (R2adj) and Akaike information criterion (AIC) besides coefficient of determination (R2) and residual sum of squares (RSS). All models have goodness of fit to data especially for development [R2, R2adj, RSS and AIC ranged 0.9673-0.9917, 0.8601-0.9861, 0.08-6.7x10-4 and (-75.29) – (-46.26) respectively]. Optimum temperature (Topt) and upper threshold (Tmax) were calculated accurately (Topt and Tmax ranged 29.9-31.2oC and 35.9-36.7oC) by all models. Lower temperature threshold (Tmin) was calculated accurately by Bieri-1 model (9,9-10,8oC) whereas Analytis model (7,0-8,4oC) underestimated it. As far as fertility is concerned the respective values were better fitted near the optimum temperature (in 30oC) [R2 ,R2adj, RSS and AIC ranged 0,6966-0,7744, 0,5756-0,6455, 2,44-3,33 x10-4 and (-9,15)-7,15 respectively].

The development rate of the predatory ladybird, Stethorus gilvifrons (Mulsant), fed on Tetranychus urticae Koch, was determined at 15, 20, 25, 27, 30, 34, and 38 °C. The total development time from egg to adult emergence for females was estimated to be 61.4, 31.6, 14.4, 13.3, 12.5, and 11.7 days, respectively. The development time decreased with increasing temperature from 15 to 34 °C, but all eggs failed to hatch at 38 °C. The lower temperature threshold (T0) for the entire development period and the thermal constant (K) for female S. gilvifrons were estimated to be 11.64 °C and 194.50 degree-days (DD) using the common linear model, and 11.96 °C and 187.87 DD using the Ikemoto and Takai model, respectively. Data were fitted to 20 non-linear development rate models and the thermal thresholds (Tmin and Tmax) and optimal temperature (Topt) were estimated. Among non-linear models, the Briere-2 and Ikemoto and Takai linear model provided adequate descriptions of the temperature-dependent development of S. gilvifrons. The upper-temperature threshold was estimated to be about 44 °C using the Logan-10 non-linear model. The estimated thermal development characteristics can be used to predict the occurrence and the population dynamics, as well as to improve the mass rearing and release, of S. gilvifrons for the biological control of T. urticae.

Effect of temperature on development of pink stem borer, Sesamia cretica Lederer, was studied at eight constant temperatures (15, 18, 20.5, 24, 27, 30, 34, and 38°C), a photoperiod of 16:8 (L:D) h, and 50–60% rela\tive humidity. The larvae of pink stem borer were reared on cutting stems of maize. The results showed that temperature had statistically significant effect on developmental times of the all developmental stages. The most commonly used six nonlinear models applied for modeling developmental rate of immature stages as a function of temperature. Evaluation of the models fit to data took place based on the coefficient of determination, residual sum of squires, adjusted coefficient of determination, and Akaike information criterion. Besides statistical criteria, biological significance was used to determine the best model. All the examined models statistically fit the data well. In addition, Briere-2 was selected as the best model considering biological significance of the estimated values for the biologically interpretable parameters of models. Based on the results, the values of the lower temperature threshold were 10.82, 11.81, 9.35, and 10.67°C, the optimal temperature were 35.50, 31.80, 33.35, and 32.22°C, and the upper temperature threshold were 38.93, 39.19, 37.41, and 36.55°C, for incubation period, larva, pupa, and overall immature stages of pink stem borer, respectively.