用非线性模型估测恒温和变温下棉铃虫蛹的发育率

为了深入分析和探讨昆虫发育与环境温度的关系, 在恒温（15~37℃）和交替变温（12/18~34/40℃）下测定了棉铃虫Helicoverpa armigera蛹的发育历期(d),分别用线性模型和非线性模型（Logan模型﹑Lactin模型和王氏模型）拟合其发育率(1/d)数据。结果表明,这3个非线性模型能更准确地描述发育率与温度之间的曲线关系,判定系数（R2）在0.9878～0.9991之间。对全部观测数据的进一步研究表明,只要有6个分布合适的观测数据,就可以用这些非线性模型获得相当满意的估测效果。如果缺乏高温下的测定数据,用非线性模型预测的昆虫发育率可能失真。分析了蛹在恒温和变温下发育率差异的可能原因,讨论了应用这3个非线性模型预测蛹期发育的优点和缺点,指出用非线性模型取代线性日·度模型进行害虫发生预测和益虫饲养管理的合理性和必要性。     

From a descriptive toward an explicative growth-based model on immature Oulema duftschmidi (Coleoptera: Chrysomelidae) development at different temperatures

The developmental rates of Oulema duftschmidi (Redtenbacher) eggs, larvae, and pupae were studied at different constant temperatures. A linear regression model was fitted to the data obtained in this and in a previous study within a temperature range where the rate proportionally increases with temperature. Ratios of SEs to the mean thermal constant and to the mean developmental threshold indicated that reliable estimates have been obtained for the three life stages. Within the framework provided by the metabolic theory of ecology, a growth-based model was evaluated to explain developmental rates in the entire temperature range permissive of development of the three life stages. The model is based on component functions describing growth patterns through time, temperature-dependent consumption rates of biomass, transformation of consumed food into body biomass change, and respiration rates with respect to temperature. Experimental data were used for the selection and validation of models and for the estimation of the parameters of different regression models. Limitations and opportunities for using the growth-based model to explain developmental rates are discussed. An empirical function was used to describe the variability of developmental rates.     

How to compare the lower developmental thresholds

According to the hypothesis of isomorphy rate, all the lower developmental thresholds of different developmental stages of an insect are equal. However, there is lack of a formal statistical method for testing whether there is a significant difference among the lower developmental thresholds on the basis of the traditional linear model describing developmental rate as a linear function of temperature. For comparing the lower developmental thresholds of different developmental stages, a new method based on the Chow test is proposed in the current study. Another feasible way based on the linear model proposed by Ikemoto and Takai is also proposed. The lower developmental thresholds can be compared by the analysis of covariance on this linear model. The current study can be used to test the hypothesis of isomorphy rate. When comparing the lower developmental thresholds of different geographical populations for one insect species, the two methods proposed here are also applicable.     

A comparison of different thermal performance functions describing temperature-dependent development rates

The impact of temperature on developmental duration of insects has been long kept a high profile in the studies of insect pests. The relationship between developmental rate, which is the reciprocal of developmental duration, is generally represented by a straight line over a range of moderate temperature; over two ranges of extreme temperature (i.e., low temperatures and high temperatures), the relationship cannot be accurately reflected by a straight line (Campbell et al., 1974). For describing the effect of constant temperature on developmental rate over the full range of temperature, some non-linear models were proposed. To analyze the effect of temperature on ectothermic performance, twelve non-linear functions, including Gaussian, Logan1, Logan2, Performance, Wang–Lan–Ding, Sharpe–Schoolfield, Ratkowsky, Brière1, Brière2, Weibull, modified Gaussian and exponentially modified Gaussian functions, are compared using the coefficient of determination, adjusted coefficient of determination, Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected Akaike information criterion (AICC) and a new method best on a weighted average of the five listed indicators. These models were compared using the development rate data of two species of insects at the egg stage. We found that the Performance, Brière1 and Brière2 functions are all very suitable for explaining temperature-dependent development rates. The three functions both belong to the asymmetrical skew thermal performance curves, and show better goodness-of-fit than the symmetrical Gaussian function. The Performance function might be the best function, because it can reflect the linearity between temperatures and developmental rates below the optimal developmental temperature.     

Temperature thresholds and thermal requirements for development of Nasonovia ribisnigri (Hemiptera: Aphididae)

Early detection of Nasonovia ribisnigri (Mosley) (Hemiptera: Aphididae) on lettuce is of primary importance for its effective control. Temperature thresholds for development of this pest were estimated using developmental rates [r(T)] at different constant temperatures (8, 12, 16, 20, 24, 26, and 28 degrees C). Observed developmental rates data and temperature were fitted to two linear (Campbell and Mu?iz and Gil) and a nonlinear (Lactin) models. Lower temperature threshold estimated by the Campbell model was 3.6 degrees C for apterous, 4.1 degrees C for alates, and 3.1 degrees C for both aphid adult morphs together. Similar values of the lower temperature threshold were obtained with the Mu?iz and Gil model, for apterous (4.0 degrees C), alates (4.2 degrees C), and both adult morphs together (3.7 degrees C) of N. ribisnigri. Thermal requirements of N. ribisnigri to complete development were estimated by Campbell and Mu?iz and Gil models for apterous in 125 and 129 DD and for both adult morphs together in 143 and 139 DD, respectively. For complete development from birth to adulthood, the alate morph needed 15-18 DD more than the apterous morph. The lower temperature threshold determined by the Lactin model was 5.3 degrees C for alates, 2.3 degrees C for apterous, and 1.9 degrees C for both adult morphs together. The optimal and upper temperature thresholds were 25.2 and 33.6 degrees C, respectively, for the alate morph, 27 and 35.9 degrees C, respectively, for the apterous morph, and 26.1 and 35.3 degrees C, respectively, for the two adult morphs together. The Campbell model provided the best fit to the observed developmental rates data of N. ribisnigri. This information could be incorporated in forecasting models of this pest.     

Temperature related effects on embryonic development of the Mediterranean locust, Dociostaurus maroccanus

Laboratory studies were conducted to assess the effect of temperature on the development of the eggs of Dociostaurus maroccanus (Thunberg) (Orthoptera, Acrididae) during anatrepsis (stages I–XIV) and during catatrepsis (stages XV–XX). The developmental rates of anatrepsis were studied at five constant temperatures ranging from 10 to 30°C. Egg development occurred over the entire range but at 10°C the embryos were unable to complete anatrepsis. The relationship between temperature and developmental times for completing anatrepsis was analysed by the non‐linear Logan type III model. The optimal temperature estimated for the development of eggs during anatrepsis was 24.7°C; the lower and upper thermal thresholds were 9°C and 31°C, respectively. Once the embryos completed anatrepsis, only those incubated at 15°C continued morphogenesis beyond stage XIV (diapause stage) without a low‐temperature exposure period. The developmental rate of catatrepsis was studied at four constant temperatures ranging from 15°C to 30°C after exposure to low‐temperature, 10°C, for 30, 60 or 90 days. For catatrepsis, temperature and developmental time were linearly and inversely related. Linear regression was used to estimate the lower developmental threshold and the degree days requirements for catatrepsis. Both decreased with longer exposure to the low temperature; the former from 13.8°C to 10.5°C and the latter from 212.8 to 171.5 degree days, following 30 and 90 days at 10°C, respectively. Our results improve the ability of decision support systems for Mediterranean locust pest management by providing better forecasts to land managers and pest advisors.     

Reproductive and developmental biology of Gonatocerus ashmeadi (Hymenoptera: Mymaridae), an egg parasitoid of Homalodisca coagulata (Hemiptera: Cicadellidae)

The reproductive and developmental biology of Gonatocerus ashmeadi Girault, a parasitoid of the glassy-winged sharpshooter Homalodisca coagulata (Say), was determined at five constant temperatures in the laboratory: 15; 20; 25; 30; 33 °C. At 30 °C, G. ashmeadi maintained the highest successful parasitism rates with 46.1% of parasitoid larvae surviving to adulthood. Lifetime fecundity was greatest at 25 °C and fell sharply as temperature either increased or decreased around 25 °C. Temperature had no effect on sex ratio of parasitoid offspring. Mean adult longevity was inversely related to temperature with a maximum of 20 days at 15 °C to a minimum of eight days at 33 °C. Developmental rates increased nonlinearly with increasing temperatures. Developmental rate data were fitted with the modified Logan model for oviposition to adult development times across each of the five experimental temperatures to determine optimal and upper lethal temperature thresholds. The lower developmental threshold estimated by the Logan model and linear regression were 1.10 and 7.16 °C, respectively. Linear regression of developmental rate for temperatures 15–30 °C indicated that 222 degree-days were required above a minimum threshold of 7.16 °C to complete development. A temperature of 37.6 °C was determined to be the upper development threshold with optimal development occurring at 30.5 °C. Demographic parameters were calculated and pseudo-replicates for intrinsic rate of increase (r_m), net reproductive rates (R_o), generation time (T_c), population doubling time (T_d), and finite rate of increase (λ) were generated using the bootstrap method. Mean bootstrap estimates of demographic parameters were compared across temperatures using ANOVA and nonlinear regression.     

Estimating temperature‐dependent developmental rates of potato tuberworm,Phthorimaea operculella (Lepidoptera: Gelechiidae)

Abstract The potato tuberworm, Phthorimaea operculella (Zeller) (Lepidoptera: Gelechiidae), is the most destructive pest of potato, Solanum tuberosum L. (Solanaceae), in tropical and subtropical regions in both field and storeroom situations. The modeling of temperature‐dependent development can be useful in forecasting occurrence and population dynamics of the pests. Published developmental parameters for this pest vary greatly for many reasons. We determined temperature‐dependent development of P. operculella at seven constant temperatures (16, 20, 24, 28, 32, 34 and 36 °C). Developmental period of whole immature stage (egg to the end of the pupal stage) varied from 75.5 days at 16 °C to 17 days at 32 °C. The population failed to survive at 36 °C. The observed data was modeled to determine mathematical functions for simulating P. operculella development in each stage of development and overall. Two linear models, ordinary linear regression and the Ikemoto linear model were used to describe the relationship between temperature and development rate of the different stages of P. operculella and estimating the thermal constant and lower temperature threshold. The lower temperature threshold (t) and thermal constant (k) of whole immature stage were estimated to be 11.6 °C and 338.5 DD by Ikemoto linear model, and the estimated parameters were not substantially different with those estimated by ordinary linear models. Different models provided a better fit to the various developmental stages. Of the eleven nonlinear models fitted, the Beriere‐1, Logan‐6 and Lactin‐1 model was found to be the best for modeling development rate of egg, larva and pupa of P. operculella, respectively. Phenological models based on these findings can be part of a decision‐support tool to improve the efficiency of pest management programs.     

Common-intersection hypothesis of development rate lines of ectotherms within a taxon revisited

The relationship between development rate of an ectotherm and temperature in experiments where insects or mites are reared under several constant temperatures, while non-linear over the entire range, can be approximately described by a line in the mid-temperature range. It was hypothesized that the development rate lines of ectotherms within a taxon such as a family would have a common intersection. Thus for a given temperature, the development time should be the same for all the species within any specified taxon. In the current study, the data on temperature-dependent development rates of species of the Aphididae and Tetranychidae families were used to test the validity of the common-intersection hypothesis. The hypothesis was supported with either dataset used. In addition, the current study tested the common-intersection hypothesis through mathematical analysis on the basis of two linear relationships (i.e., the linear relationship between temperature and development rate and that between the lower developmental threshold and the sum of effective temperatures). An attempt was made to combine the rate isomorphy hypothesis that all the lower developmental thresholds of different stages were assumed to be equal for a single species with the common-intersection hypothesis for related species within a taxon and hypothesize that if these two hypotheses hold, then for any developmental stages a common temperature of all stages should exist.     

Estimation of developmental parameters for adult emergence of Gonatocerus morgani,a novel egg parasitoid of the glassy-winged sharpshooter,and development of a degree-day model

The effects of temperature on the development (egg–adult emergence) of Gonatocerus morgani Triapitsyn, a newly-described parasitoid of Homalodisca vitripennis (Germar), were determined at 14.8, 18.7, 23.5, 26.9, 28.7, 30.4, 32.8, and 33.8 °C in the laboratory. Survival rate (percent adult emergence from parasitized host eggs) varied significantly among the experimental temperatures, with the highest (59%) and lowest (0%) occurring at 30.4 and 33.8 °C, respectively. The survival rates (%) were fitted with a polynomial model to describe a temperature-dependent pattern. Developmental rates (1/d) across seven temperatures were fitted with the nonlinear Briere model, which estimated the lower threshold to be 8.06 °C, the optimal temperature to be 29.22 °C, and the upper threshold to be 33.49 °C. A linear model fitted to developmental rates at 14.8–28.7 °C indicated that 189.75 degree-days above the lower threshold of 9.71 °C were required to complete development. A simulation model of G. morgani adult emergence was constructed to predict daily counts over the entire range of constant temperatures by incorporating the survival rate model, the Briere model, and the Weibull model. In outdoor validation, a degree-day model for predicting adult emergence showed ?2 d differences between prediction and observation. Based on the observed temperature requirement, the insect could complete thirteen to sixteen generations per year in southern California, depending on weather and location.     

Developmental Models for Estimating Ecological Responses to Environmental Variability: Structural,Parametric, and Experimental Issues

Developmental models that account for the metabolic effect of temperature variability on poikilotherms, such as degree-day models, have been widely used to study organism emergence, range and development, particularly in agricultural and vector-borne disease contexts. Though simple and easy to use, structural and parametric issues can influence the outputs of such models, often substantially. Because the underlying assumptions and limitations of these models have rarely been considered, this paper reviews the structural, parametric, and experimental issues that arise when using degree-day models, including the implications of particular structural or parametric choices, as well as assumptions that underlie commonly used models. Linear and non-linear developmental functions are compared, as are common methods used to incorporate temperature thresholds and calculate daily degree-days. Substantial differences in predicted emergence time arose when using linear versus non-linear developmental functions to model the emergence time in a model organism. The optimal method for calculating degree-days depends upon where key temperature threshold parameters fall relative to the daily minimum and maximum temperatures, as well as the shape of the daily temperature curve. No method is shown to be universally superior, though one commonly used method, the daily average method, consistently provides accurate results. The sensitivity of model projections to these methodological issues highlights the need to make structural and parametric selections based on a careful consideration of the specific biological response of the organism under study, and the specific temperature conditions of the geographic regions of interest. When degree-day model limitations are considered and model assumptions met, the models can be a powerful tool for studying temperature-dependent development.     

Seed reserve-dependent growth responses to temperature and water potential in carrot (Daucus carota L.)

Both temperature and soil moisture vary greatly in the surface layers of the soil through which seedlings grow following germination. The work presented studied the impact of these environmental variables on post-germination carrot growth to nominal seedling emergence. The rapid pre-crook downward growth of both the hypocotyl and root was consistent with their requirement for establishment in soil drying from the surface. At all temperatures, both hypocotyl and root growth rates decreased as water stress increased and there was a very distinct temperature optimum that tended to occur at lower temperatures as water stress increased. A model based on the thermodynamics of reversible protein denaturation was adapted to include the effects of water potential in order to describe these growth rate responses. In general, the percentage of seedlings that reached the crook stage (start of upward hypocotyl growth) decreased at the extremes of the temperature range used and was progressively reduced by increasing water stress. A model was developed to describe this response based on the idea that each seedling within a population has lower and upper temperature thresholds and a water potential threshold which define the conditions within which it is able to grow. This threshold modelling approach which applies growth rates within a distribution of temperature and water potential thresholds could be used to simulate seedling growth by dividing time into suitable units.     

Effects of temperature on the immature development of the stone leek leafminer Liriomyza chinensis (Diptera: Agromyzidae)

The effect of nine constant temperatures (15, 17.5, 20, 22.5, 25, 27.5 30, 32.5, and 35 degrees C) on the development of the stone leek leafminer, Liriomyza chinensis (Kato), on Japanese bunching onion, Allium fistulosum L., was studied in the laboratory. Developmental times for immature stages were inversely proportional to temperature between 15 and 30 degrees C but increased at 32.5 degrees C. Total developmental times from egg to adult emergence decreased from 69.6 to 17.1 d for temperatures from 15 to 30 degrees C, with pupae requiring more time for development than the combined egg and larva stages. Both linear and nonlinear (Logan equation VI) models provided a reliable fit of development rates versus temperature for all immature stages. The lower developmental thresholds that were estimated from linear regression equations for the egg, first, second, and third instars, total larva, egg-larval, pupa, and total combined immature stages were 12.1, 10.6, 13.6, 8, 9.6, 11.3, 11.2, and 11.4 degrees C, respectively. The degree-day accumulation was calculated as 312.5 DD for development from egg to adult emergence. By fitting the nonlinear models to the data, the upper and optimal temperatures for egg, larva, pupa, and total immature stages were calculated as 37.8 and 31.7, 34.9 and 30.1, 35.8 and 30.6, and 35.0 and 30.9 degrees C, respectively. These data are useful for predicting population dynamics of L. chinensis under field conditions and determining the maximum proportion of susceptible individuals for facilitating improved timing of application of control measures.     

Developmental temperature responses of Chrysoperla agilis (Neuroptera: Chrysopidae), a member of the European carnea cryptic species group

Chrysoperla agilis Henry et al. is one of the five cryptic species of the carnea group found in Europe. Identification of these species is mainly based on the distinct mating signals produced by both females and males prior to copulation, although there are also morphological traits that can be used to distinguish among different cryptic species. Ecological and physiological cryptic species-specific differences may affect their potential as important biological agents in certain agroecosystems. To understand the effects of temperature on the life-history traits of C. agilis preimaginal development, adult longevity and reproduction were studied at seven temperatures. Temperature affected the development, survival and reproduction of C. agilis. Developmental time ranged from approximately 62 days at 15 °C to 15 days at 30 °C. Survival percentages ranged from 42% at 15 °C to 76% at 27 °C. One linear and five nonlinear models (Briere I, II, Logan 6, Lactin and Taylor) used to model preimaginal development were tested to describe the relationship between temperature and developmental rate. Logan 6 model fitted the data of egg to adult development best according to the criteria adopted for the model evaluation. The predicted lower developmental threshold temperatures were 11.4 °C and 11.8 °C (linear model), whereas the predicted upper threshold temperatures (Logan 6 model) were 36.6 and 36.9 °C for females and males, respectively. Adult life span, preoviposition period and lifetime cumulative oviposition were significantly affected by temperature. The effect of rearing temperature on the demographic parameters is well summarized with the estimated values of the intrinsic rate of increase (r_m) which ranged from 0.0269 at 15 °C to 0.0890 at 32 °C and the highest value recorded at 27 °C (0.1530). These results could be useful in mass rearing C. agilis and predicting its population dynamics in the field.     

Modelling as a tool for analysing the temperature‐dependent future of the Colorado potato beetle in Europe

A warmer climate may increase the risk of attacks by insect pests on agricultural crops, and questions on how to adapt management practice have created a need for impact models. Phenological models driven by climate data can be used for assessing the potential distribution and voltinism of different insect species, but the quality of the simulations is influenced by a range of uncertainties. In this study, we model the temperature‐dependent activity and development of the Colorado potato beetle, and analyse the influence of uncertainty associated with parameterization of temperature and day length response. We found that the developmental threshold has a major impact on the simulated number of generations per year. Little is known about local adaptations and individual variations, but the use of an upper and a lower developmental threshold gave an indication on the potential variation. The day length conditions triggering diapause are known only for a few populations. We used gridded observed temperature data to estimate local adaptations, hypothesizing that cold autumns can leave a footprint in the population genetics by low survival of individuals not reaching the adult stage before winter. Our study indicated that the potential selection pressure caused by climate conditions varies between European regions. Provided that there is enough genetic variation, a local adaption at the northern distribution limit would reduce the number of unsuccessful initiations and thereby increase the potential for spreading to areas currently not infested. The simulations of the impact model were highly sensitive to biases in climate model data, i.e. systematic deviations in comparison with observed weather, highlightening the need of improved performance of regional climate models. Even a moderate temperature increase could change the voltinism of Leptinotarsa decemlineata in Europe, but knowledge on agricultural practice and strategies for countermeasures is needed to evaluate changes in risk of attacks.     

Developmental times and life table statistics of Aulacorthum solani (Hemiptera: Aphididae) at six constant temperatures, with recommendations on the application of temperature-dependent development models

Aulacorthum solani (Kaltenbach) (known as foxglove aphid or glasshouse potato aphid) is a pest of increasing economic importance in several agricultural crops worldwide, including greenhouse vegetables and ornamentals. Developmental rates and age-specific life tables for a North American population of A. solani on pansy (Viola × wittrockiana) (Gams.) were determined at six constant temperatures, and comparisons were made to previous studies of A. solani from differing geographic regions and host crops. On pansy, A. solani developed fastest at 25°C, passing through the four nymphal instars in an average of 6.9 d. The highest intrinsic rates of population increase (0.410 and 0.445) and shortest population doubling times (1.69 and 1.56 d) were recorded at 20 and 25°C, respectively. Average total fecundity remained high from 10 to 20°C (74-68 nymphs/adult); a significant decrease to 39 nymphs/adult occurred at 25°C. For calculating developmental thresholds, we present here a method of adjusting the lower developmental threshold (t(min)) using estimates from nonlinear models to provide an improved estimate of the thermal constant (K, in degree-days). We also call attention to the necessity of using a simulation method to estimate the true upper developmental threshold (t(max)) and optimum developmental temperature (t(opt)) from the Lactin-2 model of temperature-dependent development.