Comparison of modelling approaches to simulate the phenology of the European corn borer under future climate scenarios

Ecological Modelling 245 (2012) 65–74

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Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel

Comparison of modelling approaches to simulate the phenology of the European corn borer under future climate scenarios Andrea Maiorano a,∗ , Simone Bregaglio b , Marcello Donatelli a,c , Davide Fumagalli a , Antonio Zucchini a a b c

European Commission DG Joint Research Centre, Institute for Environment and Sustainability, MARS - AGRI4CAST, via Fermi, Ispra, VA, Italy University of Milan, Department of Plant Production, via Celoria 2, 20133 Milan, Italy Agricultural Research Council, CIN, Bologna, Italy

a r t i c l e

i n f o

Article history: Available online 28 April 2012 Keywords: Climate change European corn borer Phenological development Modelling approaches Linear vs nonlinear models

a b s t r a c t The phenological development of insects is simulated predominantly via models based on the response of the organisms to air temperature. Despite of a large body of literature supporting the evidence that the organism physiological response to temperature is nonlinear, including a declining phase, most of these models calculate the rate of development using a linear approach, implying that air temperatures mostly does not fall outside of the linear region of response to temperature of the organism. Another simplification is represented by the calculation of the rate of development using daily mean air temperature, which has already been demonstrated being a reliable method only in limited conditions. It can be hypothesized that the use of developmental models based on linear developmental rates, which can be successfully applied under climate conditions to which organisms are well adapted, could be inadequate under either future climatic scenarios or when extreme events occur (e.g., heat waves). In such contexts, linear responses might lead to interpretations of climate effects not consistent with the real organism physiological response to temperature. In this work the case of Ostrinia nubilalis Hübner (European corn borer, ECB) development was taken as an example to compare (i) a nonlinear approach with hourly air temperature as input (HNL approach), (ii) a linear based approach with hourly air temperature as input (HL approach), (iii) a linear based approach with daily air temperature as input (averaging method, DL approach), and (iv) a linear based approach using a cutoff temperature with daily air temperature as input (DLcutoff approach). The comparison was performed under the IPCC (Intergovernmental Panel for Climate Change) emission scenario A1B, and three time frames in Europe: 1995–2004 (baseline–2000s), 2015–2024 (2020s), and 2045–2054 (2050s). The SRES A1B was selected as one of those for which the projected raise of temperature is estimated to be one of the highest, although the projected difference comparing to the other SRES is estimated as evident in the 2050s time frame, among the ones considered. Using degree-days as a proxy for the rate of development, results showed that the DL approach predicts more than the HNL in all the time frames in almost all Europe with the exception of Southern Italy and the Mediterranean coasts of France and Spain where the differences were negligible. These effects were due (i) to the linear relationship used by the DL approach, and partially (ii) to the averaging operation that decrease the effects of high temperatures in regions with high (but not extreme) warm temperatures. The HNL and HL approach predicted the same pattern of degree-days accumulation in all Europe with the exception of the regions of Southern Iberian peninsula (across all the timeframes), Balkans, and Turkey (under the 2050 scenario). This effect was due to the different HNL and HL accumulation of degree-days at temperatures higher than the ECB optimum temperature. The comparison between the DLcutoff and the HNL approaches showed similar results to the DL vs HNL approach in central and Northern Europe, while in Southern Europe a negative difference (more DD accumulated for the HNL approach) were observed: in regions characterized by high temperatures, the cutoff temperature, setting a limit to the maximum temperatures diminished the calculated average temperature and as a consequence the calculated degree-days. The results of this work showed that according to the method chosen for simulations, different results can be obtained, hence leading to different conclusions about the effect of a warming climate on pest development. These results stress the need of reconsidering the appropriateness of models to be used, which cannot be assumed as correct on the basis of their effectiveness under current conditions. © 2012 Elsevier B.V. All rights reserved.

∗ Corresponding author. Tel.: +39 0332 78 6070. E-mail address: [email protected] (A. Maiorano). 0304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ecolmodel.2012.03.034

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1. Introduction The poikilothermic characteristic (i.e., the variation of internal temperature as a consequence of variation in the ambient environmental temperature) of many insects has been used for developing operational temperature-driven models applied in the integrated management of many agricultural pests (Régnière and Logan, 2003). The thermal time approach (also known as degree-days) is one of the most widely used method to simulate phenological development of insects: it represents the accumulation of heat units above a minimum temperature threshold required for an organism to develop from one stage to another in its life cycle, usually calculated on a daily basis (Honek, 1996; Trudgill et al., 2005). Despite a large body of literature supporting the evidence that the response of biological organisms to temperature is nonlinear (e.g., Stinner et al., 1974; Curry et al., 1978; Briere et al., 1999; Allen and Jason, 2000), thermal time based models adopt a linear approach to model the relationship between degree-day and the whole range of air temperature. The assumption of linearity has been widely accepted assuming adaptation of the insects to local climatic conditions, and that their exposure to extreme temperatures is rare in the field (Campbell et al., 1974). This formalization suggests that these models work properly only when air temperature do not fall outside of the linear region of the organism thermal response (Régnière and Logan, 2003). Furthermore, the application of these methods requires that consideration must be given to the geographical location, climate conditions and biology of the specific organism under study (Roltsch et al., 1999). Another simplification used by some thermal time models is the adoption of the averaging method (i.e., rectangle method; Arnold, 1960) which calculates degree-days starting from the daily mean air temperature. Roltsch et al. (1999) and Maiorano (2011) demonstrated that this method is less accurate than other approaches which take into account daily temperature fluctuations. In addition, Worner (1992) suggested that using mean air temperature, without considering daily fluctuations, is inappropriate to simulate insect response to temperature because their developmental rates at constant or variable temperatures are deeply diverse. The limit in the application of such methods is marked when daily air temperature exceeds the lower and upper threshold temperatures. Given all these considerations, there is the risk that using models based on linear developmental rates, which can be successfully applied under ‘standard’ climate conditions, could be inadequate under future changed climatic conditions or when extreme events occur (e.g., heat waves), possibly leading to interpretations of climate effects not consistent with the real organism physiological response to temperature. This problem is expected to be even more pronounced when using mean temperatures (i.e., the averaging method). In the last decade some studies were performed using thermal time methods to simulate insect development under climate change scenarios (Porter, 1995; Bergant et al., 2005; Trnka et al., 2007; Diffenbaugh et al., 2008; Luedeling et al., 2011). In this study we have chosen to analyze the case of the European corn borer (Ostrinia nubilalis Hübner, ECB). The ECB is a species of great concern for all the maize growers of Europe and North America. This pest develops through four stages of development: egg, larva (five instars), pupa, and the adult stage. Each generation is completed after the accumulation of around 670 degree-days (calculated from the occurrence of 50% adult first flight to the 50% of second flight, estimated from Bessin, 2003). It diapauses as a last instar larva and both induction and termination of diapause are photoperiodically controlled (Beck, 1962; Skopik and Bowen, 1976). In Europe, the ECB has been reported from the south of Spain to Finland. In almost all Southern Europe, the Balkans, Greece and Turkey, ECB

Fig. 1. Differences between linear (black dotted line) and nonlinear (grey full line) approaches for representing the relationships between temperature and development. Four regions (R1–R4) are represented. The nonlinear approach is based on three cardinal temperature: Tmin , Topt and Tmax which are the minimum, the optimum and the maximum temperature of development, respectively. Tbase is the base temperature of the linear approach.

can develop from two to three generations. In Central and Northern Europe usually one generation is observed. The studies so far conducted (Porter et al., 1991; Porter, 1995; Trnka et al., 2007; Diffenbaugh et al., 2008) agree in predicting an increase in the number of generations in all the areas where the ECB is already endemic and a northward extension (both in Europe and USA) of the limits of ECB. These works have been conducted using a linear approach to simulate the response to temperature, assuming that a rise in temperature of any magnitude results in one-sided more favourable conditions for the ECB. The objectives of this work were: (i) to show that different approaches to simulate ECB phenological development under actual and future climate can lead to different results and consequently to different considerations about the effect of climate warming, and (ii) to underline the importance of choosing the most appropriate approach while assessing ECB response to climate scenarios diverse from the one in which the organism is well adapted. 2. Materials and methods The hourly nonlinear degree-day approach proposed by Maiorano (2011) was compared to the degree-day methods that have been used to model the ECB development: (i) averaging method (Porter et al., 1991; Porter, 1995); (ii) averaging method with cutoff temperature (Trnka et al., 2007), and the hourly linear approach (Got and Rodolphe, 1989; Diffenbaugh et al., 2008). 2.1. Linear vs nonlinear approaches Fig. 1 shows a graphical example of the linear (L, black dotted line) and the nonlinear (NL, dark grey solid line) approaches to reproduce the response to temperature of biological organisms. The nonlinear one is based on three parameters: the minimum (Tmin ), the optimum (Topt ), and the maximum (Tmax ) cardinal temperatures for development and it is described by an exponential phase at low temperatures, which increases up to Topt and then it is followed by a decline to Tmax . Four regions can be observed in Fig. 1 (indicated from R1 to R4). The first region (R1) is bounded by Tmin and the starting point of the almost linear development. In R1, the NL approach calculates a higher development rate than the L approach. Moreover, the L approach assumes that the organism development starts from Tbase , which is an extrapolation from the exponential phase of development.

A. Maiorano et al. / Ecological Modelling 245 (2012) 65–74

The second region (R2) is the region of the organism’s linear response to temperature: in R2 the development rates computed according to the two approaches almost coincide. This is the region in which most of the values of air temperature registered in the current conditions fall. The third region (R3) is bounded by the end of R2 and by Topt of the NL approach. In R3, while development continues to linearly increase in the L approach, it slows down up to the Topt in the NL approach. In the last region (R4), developmental rate dramatically decreases according to the NL approach, while it continues to linearly increase in the case of the L approach. Other degree-day approaches include an upper temperature threshold coupled with a specific cut-off method (the manner in which the degree-day calculation area will be modified in relation to the upper threshold, University of California, http://www.ipm.ucdavis.edu/WEATHER/ddconcepts.html). When the two approaches are used at different time scales (e.g., hourly vs daily) a direct comparison is difficult because the daily approach is based on the calculation of the average temperature and differences depends on the pattern of hourly temperatures during the day. In general, in the daily linear approach, since the temperature is averaged it can be expected that (1) average temperatures difficultly reach levels around the optimum temperature of a species like the ECB (around 32 ◦ C), and (2) it misses completely the decline of response observed in R4. This is expected to be even more accentuated when a cutoff temperature is used. 2.2. Degree-day models Four different modelling solutions to calculate degree days were compared: (1) averaging method which is based on linear approach using daily mean temperatures as input (DL), (2) DL modelling solution using cut-off temperature (DLcutoff ), (3) linear approach using hourly air temperatures (HL), and (4) nonlinear approach using hourly air temperatures (HNL) (based on Maiorano, 2011). The comparison was conducted on the basis of simulations of ECB development under the A1B SRES climate scenario at three time frames in Europe (see Section 2.5). The DL modelling solution is based on the standard and widely used ‘averaging method’ (Arnold, 1960) with a lower temperature threshold (i.e., base temperature, ◦ C, T base ): ◦ D(d)

=

Tmax (d) + Tmin (d) − Tbase 2

where Tmin (d) = Tbase, if Tmin (d) < Tbase Tmax (d) = Tbase, if Tmax (d) < Tbase

(1)

where ◦ D(d) is the degree-day (DD) accumulated during day d, Tmin (d) is the daily minimum air temperature (◦ C) of day d, and Tmax (d) is the daily air maximum temperature (◦ C) of day d. When a cutoff temperature is used (Tcutoff − DLcutoff modelling solution) Eq. (1) is modified as follows: Tmax (d) = Tcutoff , Tmin (d) = Tcutoff ,

if Tmax (d) > Tcutoff if Tmin (d) > Tcutoff

=

base

h=1

where T (h) = Tbase , ◦ D(d)

if



◦

D(d) =

24 

◦

Dmax

T (h) − Tmin Topt − Tmin



Tmax − T (h) Tmax − Topt 24

(Tmax −Topt )/(Topt −Tmin ) c

(4)

h=1

where ◦ D(d) = 0 if

T (h) < Tmin or T (h) > Tmax

◦ D(d)

where is the degree-days (DD) accumulated during the day d, Tmin is the minimum temperature (◦ C) for insect development, Tmax is the maximum temperature (◦ C) for insect development, Topt is the optimum temperature (◦ C) for insect development, T(h) is the hourly air temperature (◦ C) at the hour h, ◦ Dmax is the maximum degree-days (DD) that can be accumulated at Topt , c (unitless) is a shape parameter, and 24 is used to convert the number to degree-days rather than degree-hours. In comparison to other betafunctions (e.g., Logan et al., 1976), this equation has the advantage that all parameters, with the only exception of c, have a clear biological meaning. 2.3. Parameters The HNL model was parameterized according to Maiorano (2011): Tmin = 8.20 ◦ C, Topt = 35.00 ◦ C, Tmax = 41.00 ◦ C, ◦ Dmax = 22.06 DD, and c = 1.47. According to Maiorano (2011) the initial date for accumulating degree-days (biofix) was fixed according to ECB diapause termination, which starts after 4 days with scotophase (the dark phase in a cycle of light and darkness) less than 10 h (Skopik and Bowen, 1976). Furthermore, if during the period up to the stage of the first flight initiation (flight of the overwintering generation), temperature drops below 0 ◦ C for three consecutive days, thermal time calculation is resumed from the beginning of the cycle (Maiorano, 2011). The day of year in which the degree-day accumulation was stopped was fixed according to the information found in literature about the induction to diapause of ECB. According to Beck (1962), and Skopik and Bowen (1976), the induction to diapause in ECB starts when scotophase is around 10 h and is maximum when scotophase is around 12 h. Thus, simulations were stopped, when 10 h scotophase were reached. 2.4. Sensitivity analysis assessment

24  T (h) − T

24

The DL and the HL methods share the feature to be linear assuming a linear relation between developmental rate and temperature (Wilson and Barnett, 1983). These three models, with Tbase set at 10 ◦ C, are the most commonly used for estimating ECB development times (Matteson and Decker, 1965; Got and Rodolphe, 1989; Mason et al., 1996). The DLcutoff method was used by Trnka et al. (2007) using a cutoff temperature of 32 ◦ C. According to Maiorano (2011), the HNL modelling solution is based on the beta-function developed by Yan and Hunt (1999), adapted to degree-day calculation:

(2)

The HL modelling solution is based on the hourly calculation of degree-days which is obtained by subtracting the Tbase from the hourly air temperature: ◦ D(d)

67

(3)

T (h) < Tbase

is the degree-day (DD) accumulated during the day where d, T(h) is the air temperature (◦ C) of the hour h, and 24 is used to convert the number to degree-days rather than degree-hours.

In order to understand the sensitivity of the HNL modelling solution to variations in its parameters (i.e., the optimum, minimum and maximum cardinal temperatures), a sensitivity analysis assessment was carried out using the variance-based global method of Sobol’ (1993), considered a reference in sensitivity analysis studies, even if the most demanding in terms of number of model runs. Sensitivity analysis (SA) experiments were performed on 5 years (2001–2005) on 16 grid cells, grouped by four and placed in Lower Saxony (Germany), in the Spanish region of Andalucia, and in the Veneto region in Northern Italy, in order to explore very heterogeneous climatic conditions. The adopted method is based on the partitioning of the total output variance into terms of increasing dimension, which are called partial variances and quantify the role

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of single parameters (i.e., first order effect, without interactions among parameters), and of the combined effect of multiple parameters in explaining the model output variance. An evolution of the Sobol’ method was used in this study, the one proposed by Saltelli (2002), which quantify the overall effect of an input factor introducing the concept of total sensitivity index (St), thus reducing the computational cost of the method. Monte Carlo sampling techniques are used to explore the parameters’ hyperspace. The Sobol’ method was parameterized to get more than 1000 5-year executions for each parameter (Confalonieri et al., 2010), in turns leading to 4096 5-year executions for each SA, respectively, for a total of 327,680 model executions. For all SA experiments performed, the output considered was thermal time accumulated until the diapause induction. The generation of samples of possible combinations of crop parameters and for the computation of the sensitivity indices from simulation results was carried out using the SimLab dynamic link library (SimLab v.32.5, 2009). The parameters probability distributions needed by the Sobol’ method to compute the sensitivity measures were obtained by using as mean the value adopted for spatially distributed simulations (8.20 ◦ C for Tmin ; 35 ◦ C for Topt ; 42 ◦ C for Tmax ) and by setting the standard deviation to 5% of the mean value, as done in similar studies (e.g., Richter et al., 2010). 2.5. Climate projections and hourly temperature data Daily temperature time series were obtained from climate simulations derived from the regional climate model HIRHAM5 (Christensen et al., 2007) of the Danish Meteorological Institute, driven by the boundary conditions obtained from the GCM ECHAM5 (Roeckner et al., 2003) of the Max Planck Institute for Meteorology, downloaded from the FP6 European project ENSEMBLES (van der Linden and Mitchell, 2009) website. In the framework of ENSEMBLES, the HIRHAM5–ECHAM5 model was run for the period 1961–2100 with a horizontal resolution of 25 km and forced according to the SRES-A1B scenario of the Intergovernmental Panel on Climate Change (IPCC) (Nakicenovic and Swart, 2000). The temperature data used in this work were bias corrected by Dosio and Paruolo (2011). The choice of the GCM runs does not imply a specific endorsement of the GCM, instead, they are related to data availability in the lab, considered as adequate for the methodological aim of this paper. For this work data of three time frames were used: 1995–2004 (2000s–baseline), 2015–2024 (2020s), 2045–2054 (2050s). Hourly air temperatures data (used by HL and HNL modelling solutions) have been derived using the Campbell model (Campbell, 1985) included in the AirTemperature software component (Donatelli et al., 2010) (http://agsys.cra-cin.it/tools/ airtemperature/help/). 3. Results and discussion 3.1. Sensitivity analysis results The average St values obtained by the three parameters referring to European corn borer cardinal temperatures (Tmin , Topt and Tmax ) by using the HNL modelling solution are presented as box plots in Fig. 2. By considering all the grid cells in which SA was carried out, it emerges that this modelling solution is very sensitive to variations in the value of Topt , which explains more than 80% of the variance of the output (thermal time at diapause induction). The 2nd ranked parameter is Tmax , explaining around 20% of the total output variance, whereas Tmin results the less relevant one (responsible of less than 5% of the overall variance). These considerations clearly indicate (i) that the regions of the curve in which almost all

Fig. 2. Box-plots of average Sobol’ total order indices of the parameters minimum temperature (Tmin ), optimum temperature (Topt ) and maximum temperature (Tmax ) for insect development resulting from all the locations and years in which sensitivity analyses were carried out.

the response of European corn borer to hourly air temperature falls are R3 and R4 and (ii) that, in light of performing a calibration of the model against reference data, Topt results the parameter on which to concentrate the efforts. Table 1 shows the results of St divided per grid cell for each of the regions considered. It clearly emerges the presence of geographic patterns, despite of an overall homogeneity in the St values. In fact, the St values for Tmin in Germany are higher (mean value 0.0328) with respect to the ones obtained in the other regions. This suggests that in colder areas, the cardinal minimum temperature becomes more limiting for insect development; the opposite situation can be observed in Andalucia, where the highest St values for Tmax were obtained (mean value 0.321). These results demonstrate the ability of this modelling solution to modify its behaviour in response to changing climatic conditions, thus supporting its extensive use in climate change assessments. 3.2. Spatialized simulations results According to the projections of the HIRHAM5–ECHAM5 model (Ensemble project) maximum temperature is expected to increase progressively of more than 1.5 ◦ C from baseline (2000s) to 2050s in Europe (Fig. 3). The increase in maximum temperature is projected to be evident (higher than 0.5 ◦ C) only in Southern Spain, east of Italy and Eastern Europe under the 2020s scenario, while it embraces almost all Europe under the 2050 scenario, with the maximum differences expected in Spain, Greece, Macedonia, and Turkey. These synthetic data determined the accumulation of degree-days for the ECB (HNL modelling approach) showed in the same figure. Under the 2020 scenario degree-days are expected to increase up to 150–200 DD in Southern Europe and in the Balkans, while in Northern Europe the increase is more limited or even negative in Northern France and Germany, and in Great Britain and Ireland. On the contrary, under the 2050 scenario an increase in DD can be observed in all the European countries, with the highest increases (more than 300 DD, corresponding to almost the 50% DD require for an ECB generation) in Southern Europe, the Balkans and Turkey. Figs. 4–6 show the mapping of the differences in DD between the DL–HNL, HL–HNL, and the DLcutoff –HNL approaches. The discrepancy between the DL and HNL approaches (Fig. 4) is evident already in the Baseline time frame when the degree-days predicted by the DL approach are higher than the degree-days of the HNL approach in almost all Europe, with the exception of Southern Italy and the Mediterranean coasts of France and Spain where

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Table 1 Average Sobol’ total order indices obtained in the years from 2001 to 2005 in the grid cells tested, with latitude and longitude reported. Bold and italics indicate the highest and the lowest value for each parameter within the same geographic region, respectively. Grey areas indicate the overall highest and lowest values. Region

Country

Grid cell

Parameter

Latitude ◦



Longitude 

◦

 

Tmin

Topt

Tmax

Andalucia

Spain

37 43 10 37◦ 45 46 37◦ 56 29 37◦ 59 6

−4 50 3 −4◦ 33 23 −4◦ 53 0 −4◦ 36 15

0.0186 0.0190 0.0179 0.0181

0.7729 0.7761 0.7674 0.7694

0.3189 0.3140 0.3269 0.3244

Veneto

Italy

45◦ 11 21 44◦ 57 50 44◦ 58 5 45◦ 11 36

11◦ 28 48 11◦ 28 26 11◦ 9 28 11◦ 9 45

0.0092 0.0087 0.0081 0.0082

0.8133 0.8146 0.8137 0.8127

0.2768 0.2812 0.2850 0.2851

Lower Saxony

Germany

53◦ 31 13 53◦ 31 13 53◦ 17 44 53◦ 17 44

10◦ 14 55 9◦ 52 18 10◦ 14 50 9◦ 52 21

0.0336 0.0340 0.0308 0.0326

0.8138 0.8132 0.8175 0.8149

0.2838 0.2828 0.2904 0.2858

the differences are negligible. The highest increases are observed in the Spanish regions of Andalucia and Extremadura, where the highest temperature in Europe are usually observed, and in the Scandinavian Peninsula. The differences observed between the DL and the HNL approach can be ascribed (i) to the linear relationship used by the DL approach, and partially (ii) to the use of mean daily

temperatures (DL approach) which do not take into account the daily temperature fluctuations, determining a faster accumulation of degree-days as already observed by Worner (1992), Roltsch et al. (1999), and Maiorano (2011). The results shown in Fig. 4 suggest that this last statement is only partially true, and this is due to the use of the average temperature: in fact, in regions

Fig. 3. Differences in summer average maximum air temperature (two maps above), and cumulated degree days of the hourly nonlinear approach (two maps below), between SRES-A1B scenario in time frames 2020 and 2050 vs baseline weather series (1995–2004) generated using HIRHAM5–ECHAM5 model (data coming from ENSEMBLE project).

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Fig. 4. Difference between cumulated degree-days calculated using daily linear (DL) vs hourly nonlinear (HNL) approaches in baseline weather series (1995–2004), and in time frames 2020 (2015–2024) and 2050 (2045–2054) generated using SRES-A1B scenario (HIRHAM5–ECHAM5, data from ENSEMBLE project).

like Southern Italy where in summer temperatures are high but not extreme like in Southern Spain (where in summer average temperature can rise up to 40 ◦ C due to both high minimum and maximum temperatures), the result of the averaging operation lead to a temperature that take place mostly in the region R2 or sometimes R3 of Fig. 1, leading to not substantial differences in the cumulated degree-days compared to the HNL approach. By analyzing the maps of the differences between the HL and the HNL approaches (Fig. 5) a diverse assessment emerged. No appreciable differences can be observed for any of the three time frames in almost all Europe, meaning that most of the temperatures under the condition tested lay mainly on the linear region of development (region R2, Fig. 1). Also in this case, a diverse behaviour can be observed in the area between Andalucia and Extremadura (Spain), and Alentejo (Portugal) approximately. In this area differences are observable from the Baseline time frame and increases markedly under the 2020 and the 2050 scenarios, where the differences rise up to 100–150 DD. Under the 2050 scenario positive differences appear also in the Balkans, Greece, and Turkey. The main reason of such pattern is the very high temperatures characterizing these areas that fall in R3 and R4 of Fig. 1. In these two temperature ranges,

the developmental rate computed according these two methods are dramatically different, i.e., in the nonlinear approach the development firstly slow down and then dramatically decreases, while in the linear one it continues increasing linearly. The results of the comparison between the DLcutoff and the HNL approaches are shown in Fig. 6. These results are similar to the ones observed for the comparison DL vs HNL with the exception of Southern Europe, where a negative difference (that is more DD accumulated for the HNL approach) can be observed. The areas with negative differences increase progressively from the Baseline to the 2050 scenario. The reason of the negative differences is to be ascribed to the use of a cutoff temperature (32 ◦ C in this case) in the averaging operation which extremes the behaviour already observed for the DL approach: in fact the cutoff temperature, setting a limit to the maximum temperatures diminishes the calculated average temperature and as a consequence the calculated degreedays. At least three similar studies about the effects of climate change on ECB development and spread have been conducted. Porter et al. (1991) published a work about the ECB distribution given a 1 ◦ C warming of European climate and under GISS 2XCO2 projected

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Fig. 5. Difference between cumulated degree-days calculated using hourly linear (HL) vs hourly nonlinear (HNL) approaches in baseline weather series (1995–2004), and in time frames 2020 (2015–2024) and 2050 (2045–2054) generated using SRES-A1B scenario (HIRHAM5–ECHAM5, data from ENSEMBLE project).

climate change (Hansen et al., 1983) using a degree-day model based on the averaging method. They found that (i) a warming of the climate in Europe would be expected to induce a northward extension in limits of the ECB, and (ii) an additional generation of ECB could be expected in nearly all areas where it is currently known to exist. Four years later (1995), Porter published a similar work about the effects of two GISS climate change scenarios (A and C, Hansen et al., 1988) for the 1990s, 2020s and 2050s. The same model of the previous work was used and the conclusions were similar. In 2007, Trnka et al. (2007) published a work about the effect of global warming in the potential distribution of the ECB in the Czech Republic, using the averaging method with cutoff temperature at 32 ◦ C. The results of their work lead to the conclusion that an increase in the number of generation might be expected for the 2025–2050 timeframe. In 2008, Diffenbaugh et al. (2008) published a work about the effect of global warming on the potential distribution of four maize pests in United States, including the ECB. Using the linear degree-day model with hourly time step resolution, they concluded that the future climate will probably lead to an enhanced degree-day accumulation with a consequent (i) ECB range expansion, (ii) an increase of the number of generations, (iii)

an increased opportunity for damage and (iv) a significant increase in the overwintering population. The reason of the success and the diffusion of the linear methods is not difficult to understand: they requires minimal data for formulation, they are very easy to calculate and apply, and usually yield approximately correct values with negligible differences in accuracy from more complex models (Kontodimas et al., 2004). Also, if models are applied on temperate climates, high temperatures may occur at most over 3 months over the year, hence possibly nonrepresenting a substantial percentage of data. Comparing a linear method to different nonlinear methods to estimate the development of Nephus includes and Nephus bisignatus, Kontodimas (2004): reported that the best models were the linear one and the Lactin et al. model (1995). Nevertheless, the same Kontodimas evidenced the limits of this approach: (1) the assumed relationship holds only for a medium range of temperatures (usually 15–30 ◦ C), and (2) the estimated threshold is an extrapolation into a region where the relationship is unlikely to be linear. Hence, the use of linear model appears not fully adequate for climate change studies including areas where air temperatures are estimated to grow beyond optimum temperature for growth.

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Fig. 6. Difference between cumulated degree-days using daily linear with cutoff temperature (DLcutoff) set at 32 ◦ C, vs hourly nonlinear (HNL) approaches in baseline weather series (1995–2004), and in time frames 2020 (2015–2024) and 2050 (2045–2054) generated using SRES-A1B scenario (HIRHAM5–ECHAM5, data from ENSEMBLE project).

In the light of the results of this work, it can be hypothesized some of the results obtained by the three authors cited above that predicted an increased number of generations for the ECB development under climate change scenarios might be overestimated due to the approaches they used. The magnitude of this overestimation should be further investigated as it might depend not only on the approach used but also on the projected climate data used for the simulations. In this work we used a set of data generated by a specific realization of the A1B emission scenario (HIRHAM5–ECHAM5) that can be described as ‘cold’ if compared to other realization of the same scenario used in the same project (ENSEMBLE), such the one based on the HadleyCM3 model. Finally, our work has been circumscribed to Europe (latitude range 35–70◦ ) and to the time horizon 2050s. It is expected that if the same analysis is made under lower latitude range and/or faraway in time horizon, as in similar works (e.g., 2100s, Diffenbaugh et al., 2008; Luedeling et al., 2011) the differences observed will be more pronounced. In fact, in case of a more extreme climate scenario (higher mean temperature and/or higher temperature fluctuations), according to the result of this work, comparing the three approaches to the HNL we would expect

that: (i) the DL approach increase its positive difference, leading to a further overestimate of the speed of development, (ii) the HL approach increase the positive difference in the Iberian Peninsula and extend this difference to other areas of Southern Europe, and (iii) the DLcutoff increase the area of negative difference towards central Europe, leading to a projected decreased speed of development. Beyond the numerical evidence of the comparison presented, the use of a nonlinear model better represents the real response of organisms to temperature, and its parameters have a clear biological meaning (the shape parameters can be eliminated with little loss of precision once a more articulated dataset of reference data becomes available). The increase of computing time and of complexity of the model is negligible.

4. Conclusions Process based models represent valid instruments to get information about the impact of future climate scenarios on biological and agricultural systems. The reliability of the simulations is based

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on the adherence of the model formalization to the real processes and on the assumptions and limits at the basis of the models themselves (Grant and Swannack, 2008). One of the reasons of the success of the linear approach in thermal time based models is the temperature range of the climate considered and the adaptation of the organisms studied in such conditions. Rightly, the principle of parsimony in building models led to approaches easy to implement and adequate for such contexts (Smith and Smith, 2007). Also, the fact that most of the initial studies were run in temperate areas at medium latitudes, that is with a sizeable part of the year with raising temperatures, and consequently in the linear phase of organism response to temperature, made the choice of linear daily time step models appropriate. Nevertheless, given the improved computing capabilities, which make the increase of complexity of physiological models irrelevant from the point of view of their use, and the availability of nonlinear functions with parameters having biological meanings, there is no obstacle in using nonlinear approaches and hourly time steps/temperatures. Such models should be used whenever simulations must cover temperatures over the full range of physiological activity (Régnière and Logan, 2003). Using the degree-day proxy as notation for thermal-based development, we tested different approaches for degree-day accumulation, characterized by a diverse degree of coherence to the biological system analyzed. We highlighted that the choice of the model can lead to different results and consequently divergent assessments about the effect of the warming climate can be drawn above all in the warmest areas. In these conditions, the linear approaches evaluated in this study do not represent anymore an adequate simplification of the real system under study based on the knowledge available. Moreover, the SA experiments support the suitability of using a nonlinear function for modelling insect development response to air temperature, thanks to its capability to modify its behaviour according to the meteorological input data, thus indicating the appropriateness of such method to be adopted in climate change scenario assessments. Acknowledgments This research was supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Programme, and partially supported by the project AgroScenari of the Italian Ministry of Agricultural, Food and Forestry Policies. References Allen, J.C., Jason, H., 2000. Byrd Computer modeling of insect growth and its application to forensic entomology (Report No. 181992). National Institute of Justice, U.S. Department of Justice. Arnold, C.Y., 1960. Maximum–minimum temperatures as a basis for computing heat units. Proc. Am. Soc. Horticult. Sci. 76, 682–692. Beck, S.D., 1962. Photoperiodic induction of diapause in an insect. Biol. Bull. 122, 1–12. ˇ Bergant, K., Trdan, S., Zˇ nidarˇciˇc, D., Crepinˇ sek, Z., Kajfeˇz-Bogataj, L., 2005. Impact of climate change on developmental dynamics of Thrips tabaci (Thysanoptera: Thripidae): can it be quantified? Environ. Entomol. 34, 755–766. Bessin, R., 2003. Predicting European Corn Borer Development. University of Kentucky - College of Agriculture, Entomology web page: http://www.ca.uky.edu/ entomology/entfacts/ef106.asp (accessed 31.03.11). Briere, J.-F., Pracros, P., Le Roux, A.-Y., Pierre, J.-S., 1999. A novel rate model of temperature-dependent development for arthropods. Environ. Entomol. 28, 22–29. Campbell, A., Frazer, B.D., Gilbert, N., Gutierrez, A.P., Mackauer, M., 1974. Temperature requirements of some aphids and their parasites. J. Appl. Entomol. 11, 431–438. Campbell, G.S., 1985. Soil Physics with BASIC—Transport Models for Soil–Plant Systems, Development in Soil Science. Elsevier, Amsterdam. Christensen, O.B., Drews, M., Christensen, J.H., Dethloff, K., Ketelsen, K., Hebestadt, I., Rinke, A., Wegener, A., 2007. The HIRHAM Regional Climate Model, Version 5 (beta). Technical report 06-17. Danish Meteorological Institute, Copenaghen. Confalonieri, R., Bellocchi, G., Bregaglio, S., Donatelli, M., Acutis, M., 2010. Comparison of sensitivity analysis techniques: a case study with the rice model WARM. Ecol. Model. 221, 1897–1906.

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