Keywords: Generic phenological modelling, Lobesia botrana, voltinism, process-based model, temperature, photoperiod

The physiological development of insect pests is driven by temperature and photoperiod. Geographic variations in the speed of growth reflect current patterns in thermal conditions as a function of latitude and altitude. Global warming will likely lead to shifts in pests' phenology. Insects are expected to overwinter earlier and develop more generations, with implications for the risks of damage to agricultural crops. Understanding and monitoring of the voltinism of insect pests will be increasingly important to anticipate critical phases of pest development and devise options for adapting pest control measures. In this study, we describe a new generic phenological model that allows to reproduce the voltinism of Lobesia botrana, a major insect pest that affect grapevine production (Vitis vinifera L.) worldwide.

Inspired by existing models, the Lobesia Generic Model (LGM) combines two submodels representing the overwintering period and the dates of flight of subsequent generations of male insects. This model uses a unique Beta function for representing the temperature responses of both the overwintering generation as well as the adult generations. The results indicate that LGM is able to simulate L. botrana voltinism under climatic conditions ranging from those observed in Southern Spain to those recorded in the Alsace region (France). The LGM only requires a single set of parameters valid for all the generations with a precision of around 7 days (RMSE), allowing a simple use with parameters representative of natural behaviour and found in the existing literature.

Introduction

Modern agriculture relies on the massive use of pesticides to increase productivity [START_REF] Tilman | Agricultural sustainability and intensive production practices[END_REF]. This has caused considerable stress on biodiversity and made insect pests more resistant to pesticides [START_REF] Hatt | Spatial diversification of agroecosystems to enhance biological control and other regulating services: An agroecological perspective[END_REF]. Furthermore, extensive commercial trade as well as increasing temperatures have enhanced the spread of insect pests. As a result, invasive species have started to damage crops in remote areas [START_REF] Bale | Herbivory in global climate change research: direct effects of rising temperature on insect herbivores[END_REF][START_REF] Lin | Resilience in Agriculture through Crop Diversification: Adaptive Management for Environmental Change[END_REF][START_REF] Lamichhane | Robust cropping systems to tackle pests under climate change. A review[END_REF]. Understanding and predicting insect pest dynamics is necessary in order to ensure productivity while reducing the use of chemicals [START_REF] Bregaglio | Fungal infections of rice, wheat, and grape in Europe in 2030-2050[END_REF]). In the context of global warming, there is also a need to understand how pest species dynamics will evolve in the future. In this context, phenological models are interesting tools to monitor populations dynamics and to predict their evolution, e.g., under changing environmental and climatic conditions [START_REF] Steinbauer | Modelling a forest lepidopteran: phenological plasticity determines voltinism which influences population dynamics[END_REF][START_REF] Nietschke | A developmental database to support insect phenology models[END_REF][START_REF] Stoeckli | Impact of Climate Change on Voltinism and Prospective Diapause Induction of a Global Pest Insect -Cydia pomonella (L.)[END_REF]. Such models are capable of anticipating insects' voltinism and allows improving treatment periods (Moravie et al. 2006).

Process-based models aim to represent biological processes through equations that describe developmental, survival, fecundity or mortality rates for different life-stages of insects (from prediapause to overwintering). Among the different processes simulated, phenology (development) is probably one of the most important, because it defines the biological cycle [START_REF] Chuine | Plant Development Models_2013[END_REF].

Insects are ectotherms and consequently their physiological development is mainly driven by temperature [START_REF] Zhou | Effects of temperature on aphid phenology[END_REF][START_REF] Bale | Herbivory in global climate change research: direct effects of rising temperature on insect herbivores[END_REF][START_REF] Tobin | Historical and projected interactions between climate change and insect voltinism in a multivoltine species[END_REF]. They exhibit a response to thermal variation [START_REF] Singer | Phenological asynchrony between herbivorous insects and their hosts: signal of climate change or pre-existing adaptive strategy?[END_REF][START_REF] Bale | Insect overwintering in a changing climate[END_REF][START_REF] Brodeur | Impact des changements climatiques sur le synchronisme entre les ravageurs et leurs ennemis naturels: conséquences sur la lutte biologique en milieu agricole au Québec[END_REF][START_REF] Moiroux | Impact différentiel du réchanffement climatique sur les insectes ravageurs des cultures et leur ennemis naturels: implications en agriculture Moravie M-A[END_REF]) by adjusting life history traits like the date of overwintering and population growth [START_REF] Hance | Impact of Extreme Temperatures on Parasitoids in a Climate Change Perspective[END_REF][START_REF] Moreau | How Host Plant and Fluctuating Environments Affect Insect Reproductive Strategies?[END_REF]. Diapause and overwintering are further determined by photoperiod [START_REF] Pavan | Influence of the grape-growing area on the phenology of Lobesia botrana second generation[END_REF][START_REF] Svobodová | Determination of areas with the most significant shift in persistence of pests in Europe under climate change[END_REF]. Both temperature and photoperiod thus explain how insects' life cycle respond to local climatic conditions, latitude and altitude (Honêk 1996;[START_REF] Ioriatti | Chemical Ecology and Management of Lobesia botrana (Lepidoptera: Tortricidae)[END_REF].

Changes in the growing rate and geographical distribution of pests have already been observed in the last decades [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]) as a consequence of recent changes in climate.

Among the numerous species that affect agriculture, Lobesia botrana (Den. & Schiff) commonly named the European grapevine moth, is a good candidate for assessing effects of climate change on the development of insect pests. It is a major grapevine insect pest that is present worldwide, including Europe. As a multivoltine species, this pest is able to complete from two (in northern parts of Europe) to four (in southern parts of Europe) generations per year according to climate and latitude [START_REF] Martín-Vertedor | Global warming affects phenology and voltinism of Lobesia botrana in Spain[END_REF]. Under warmer conditions it has the potential of generating more damage than currently, as its development will begin earlier in the season and last longer [START_REF] Castex | Pest management under climate change: The importance of understanding tritrophic relations.pdf[END_REF][START_REF] Marchesini | Nel Veneto quattro generazioni di tignoletta della vite[END_REF]. The life cycle of L. botrana is characterized by its capacity to enter into diapause at the pupal phase when day length is less than 14 hours (12 hours is the limit for pupal overwintering). The individuals will overwinter as pupa and start developing before becoming adults and mate to start their adult life and reproduction cycle [START_REF] Thiery | Les Tordeuses Nuisibles à La Vigne[END_REF].

Many models have been developed to monitor the adult flights of L. botrana (Tab.1). They all can be considered as process-based models, despite using different temperature response functions [START_REF] Caffarra | Modelling the impact of climate change on the interaction between grapevine and its pests and pathogens: European grapevine moth and powdery mildew[END_REF][START_REF] Caffarelli | Heat accumulation for timing grapevine moth control measures[END_REF]Gabel and Mocko 1984;[START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF][START_REF] Logan | An analytic model for description of temperature dependent rate phenomena in arthropods[END_REF][START_REF] Milonas | Day-degree models for predicting the generation time and flight activity of local populations of Lobesia botrana (Den. & Schiff.) (Lep., Tortricidae) in Greece[END_REF][START_REF] Touzeau | Modélisation de l'évolution de l'Eudemis de la vigne pour la region Midi-Pyrénées[END_REF]. Other models adopt a statistical approach to represent biological responses to temperature (Moravie et al. 2006).

Existing models for L. botrana target different purposes. Some of them describe the growing length at different developmental phases [START_REF] Touzeau | Modélisation de l'évolution de l'Eudemis de la vigne pour la region Midi-Pyrénées[END_REF]Gabel and Mocko 1984;[START_REF] Caffarelli | Heat accumulation for timing grapevine moth control measures[END_REF]Briere and[START_REF] Briere | Comparison of temperature dependant growth models with the development of Lobesia botrana (Lepidoptera:Tortricidae)[END_REF]1999;[START_REF] Severini | Fenologia della vite, e della Lobesia botrana (Lep. Tortricidae) nella zona dei Castelli Romani[END_REF]. Others focus on the timing of maximum moth flight (Moravie et al. 2006;[START_REF] Amo-Salas | A new model for predicting the flight activity of Lobesia botrana (Lepidoptera: Tortricidae)[END_REF][START_REF] Ortega-López | Male flight phenology of the European grapevine moth Lobesia botrana (Lepidoptera: Tortricidae) in different wine-growing regions in Spain[END_REF], forecast the emergence timing [START_REF] Arca | Individuazione dei gradi giorno relativi allo sviluppo della Lobesia botrana(Den. et Schiff.) in Sardegna[END_REF][START_REF] Milonas | Day-degree models for predicting the generation time and flight activity of local populations of Lobesia botrana (Den. & Schiff.) (Lep., Tortricidae) in Greece[END_REF]) and population size [START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF]), the number of generations occurring before diapause [START_REF] Caffarra | Modelling the impact of climate change on the interaction between grapevine and its pests and pathogens: European grapevine moth and powdery mildew[END_REF] or model the overwintering process [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]. Finally, very complex models such as that of [START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF] try to simulate various processes simultaneously (grapevine phenology, adult development, survival and fecundity rates).

Tab.1 : Comparison between local models and the generic model described in this work. The following exhaustive literature review list the existing phenological models for L. botrana: (1) Gabel and Mocko 1984; (2) [START_REF] Caffarelli | Heat accumulation for timing grapevine moth control measures[END_REF] (3) [START_REF] Arca | Individuazione dei gradi giorno relativi allo sviluppo della Lobesia botrana(Den. et Schiff.) in Sardegna[END_REF](4) [START_REF] Briere | A novel rate model of temperature-dependent development for arthropods[END_REF](5) [START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF](6) Milonas et al. 2001, (7) [START_REF] Severini | Fenologia della vite, e della Lobesia botrana (Lep. Tortricidae) nella zona dei Castelli Romani[END_REF](8) Moravie et al. 2006;(9) [START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF](10) Amo-Salas et al. 2011, (11) [START_REF] Caffarra | Modelling the impact of climate change on the interaction between grapevine and its pests and pathogens: European grapevine moth and powdery mildew[END_REF](12) [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF](13) [START_REF] Ortega-López | Male flight phenology of the European grapevine moth Lobesia botrana (Lepidoptera: Tortricidae) in different wine-growing regions in Spain[END_REF](14) Alps, in Caffarra and Eccel 2011), and (b) to account for possible differences in thermal requirements between different generations, meaning that parameters are usually specified for each generation separately [START_REF] Touzeau | Modélisation de l'évolution de l'Eudemis de la vigne pour la region Midi-Pyrénées[END_REF]Gabel and Mocko 1984;[START_REF] Caffarelli | Heat accumulation for timing grapevine moth control measures[END_REF][START_REF] Milonas | Day-degree models for predicting the generation time and flight activity of local populations of Lobesia botrana (Den. & Schiff.) (Lep., Tortricidae) in Greece[END_REF][START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF][START_REF] Caffarra | Modelling the impact of climate change on the interaction between grapevine and its pests and pathogens: European grapevine moth and powdery mildew[END_REF]. For this reason, some authors have already highlighted the difficulty of using and comparing these models within a larger range of climatic conditions than initially targeted [START_REF] Flores | Modelos lineales para pronosticar la actividad de vuelo de Lobesia botrana (Denis & Schiffermüller) (Lepidoptera: Tortricidae) en la localidad de Russel, Mendoza, Argentina Gabel B, Mocko V (1984) Forecasting the cyclical timing of the grape vine moth, Lobesia botrana (Lepidoptera, Tortricidae)[END_REF][START_REF] Allen | A modified sine wave method for calculating degree days[END_REF][START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF][START_REF] Amo-Salas | A new model for predicting the flight activity of Lobesia botrana (Lepidoptera: Tortricidae)[END_REF]. In fact, a major downside with local models is that they need local adjustments when applied outside the geographic area targeted in first place. To the best of our knowledge, only a few models, such as the one developed by [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] or [START_REF] Ortega-López | Male flight phenology of the European grapevine moth Lobesia botrana (Lepidoptera: Tortricidae) in different wine-growing regions in Spain[END_REF] have been applied to large geographical scales.

The overall purpose of this work is to present a generic model for L. botrana (hereafter called Lobesia Generic Model or LGM) that considers a large scale of application and a single response to temperature or thermal time requirements for all generations (Tab.1). The model is built by assembling existing model components and calibrated in such a way as to obtain a generic set of parameters. Model development and calibration were carried out using PMP, a user-friendly software providing an interface for designing, setting up, testing and running phenological models [START_REF] Chuine | Plant Development Models_2013[END_REF].

The specific aims of this study are 1) to analyze existing models of L. botrana voltinism in order to propose a generic approach for simulating representative phase of development (10% and 50% of the male flights) of an adult population from diapause to last flight; and 2) to propose a validated standard set of parameters for applications at the large scale. We use for this purpose a large database of flight observations compiled in a wide latitudinal transect running from southern Spain to northern France (Fig. 1) and representing Mediterranean and Continental climate types [START_REF] Jongman | Objectives and Applications of a Statistical Environmental Stratification of Europe[END_REF][START_REF] Beck | Present and future Köppen-Geiger climate classification maps at 1-km resolution[END_REF].

Materials and Methods

Data used in the study

Phenological data of L. botrana

The observed data of L. botrana correspond to the number of individuals captured per week, by pheromone (sexual confusion) delta traps placed at the beginning of March. Traps are changed and counted weekly to represent the distribution of population from the first flight of the first generation (who overwintered) to the last adult flight of the last generation. Traps are considered one of the best way to capture and represent male flight activity [START_REF] Milonas | Day-degree models for predicting the generation time and flight activity of local populations of Lobesia botrana (Den. & Schiff.) (Lep., Tortricidae) in Greece[END_REF][START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF][START_REF] Ortega-López | Male flight phenology of the European grapevine moth Lobesia botrana (Lepidoptera: Tortricidae) in different wine-growing regions in Spain[END_REF]. Data were provided by private sector enterprises, inter professional councils in the agronomical and viticulture sectors and academic institutions (Tab.2). As illustrated in the map (Fig. 1), 12 sites were used to cover latitudes between Lat.36.710°N and Lat.48.213°N and an altitude range from 0 m a.s.l. (Saint Gilles, France) and 692 m a.s.l. (Requena, Spain). We have assumed that it was possible to combine all the data from different sites to calibrate and evaluate the model, even if there is no standardized protocol for the observation of adult flights in trap catches. Of the initially 90 records, 51 records of (non consecutive) observations of L. botrana adult flight (entire cycle of generations) on an annual basis (Tab.2) were retained after quality control. From those annual male flights, we identified two main phenological observations: the 10% and 50% of the total adult flights per generation as done in [START_REF] Gallardo | Forecasting the flight activity of Lobesia botrana (Denis and; Schiffermüller) (Lepidoptera, Tortricidae) in Southwestern Spain[END_REF]. To do so, we identified and separated the generations of adults as explained in ESM1 (Electronic Supplementary Material). Then, we calculated the cumulated sum of the number of individuals caught in the traps, for each generation (G1; G2; G3; G4). From this sum, we took the 10% and 50% of the cumulated sum per generation (G1-10%, G1-50%; G2-10%, G2-50%; etc.). This data was then related to its corresponding Day Of Year (DOY) of observation. The observed data are not continuous in time (from 1997 to 2016), because observations are not made systematically. Also, we only used the observed data when we could clearly identify the beginning, the peak and the end of the generations that represent around 70% of all the data we collected.

Meteorological data

Meteorological data were obtained from different meteorological services at each site (Tab.2). Daily minimum, maximum and mean temperatures were collected from meteorological stations in an array with a maximum distance of 10-15 km from the collection sites of L. botrana flights, and almost at the same altitude as the vineyards, which we considered reasonable for the representation of local meteorological conditions.

A generic phenological model for L. botrana 2.2.1 General description of the model

The LGM is a combination of two submodels allowing the simulation of at least five phases of development representing two development stages (Fig. 2): 1) The overwintering submodel: It considers three phases, prediapause, diapause and post diapause from the year n-1 to n; 2) The male adult flights submodel: reproduce the 10% and 50% of the total of the population of each generation for the year n. At least two generations can be reproduced, with an option for additional generations depending on local climatic conditions and latitude.

Phase is a specific part in a physiological development process (e.g., in the overwintering stage, we identify the prediapause phase). The adults flights consider two or more adults generations and depend on temperature and local climatic conditions. We propose to simulate the 10% and 50% of the total of the population of each generation. The calculation considers the adults that enter into diapause in the previous year (n-1).

We apply the following equation to describe the temperature effect (eq. 1):

𝑭 𝒔 (𝒕 𝒅 ) = ∑ 𝒇(𝒕 𝒅 ) 𝒅𝒔 𝒅 𝟎 𝑒𝑞. 1
where td is the daily temperature, f() is the function describing the temperature response (described later), d0 is the first date of the developmental phase, ds the day of the end of the developmental phase and Fs(td) represents the cumulated temperatures (forcing units).

According to [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF], d0 (first date of the developmental phase) depends on the latitude and the photoperiod. The analysis of the equations and the parameters proposed by where td, f(), d0, ds and Fs(td) represent the same variables and parameters as in (eq. 1), and g() is the function describing the photoperiod response and Pd is the daily photoperiod. The photoperiod function is varying between a low and a high threshold (Plow and Phigh respectively). We explored two possibilities of combination of the temperature and photoperiod effect: the multiplicative (usually used in other models as [START_REF] Wang | Simulation of phenological development of wheat crops[END_REF]) or the additive (as proposed by [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF])

Temperature response functions

We tested three different functions to describe the response of L. botrana development to temperature (Fig. 3):

1) The Richardson model (R) [START_REF] Richardson | A model for estimating the completion of Rest for "Redhaven" and "Elberta" Peach trees[END_REF]) is a step function that assumes a linear response of development to daily temperatures for temperatures in the range Tlow to Thigh:

𝑓(𝒕 𝒅 ) = { 𝟎, 𝒕 𝒅 -𝑻𝒍𝒐𝒘, 𝑻𝒉𝒊𝒈𝒉 -𝑻𝒍𝒐𝒘, 𝒕 𝒅 ≤ 𝑻𝒍𝒐𝒘 𝑻𝒍𝒐𝒘 < 𝒕 𝒅 < 𝑇ℎ𝑖𝑔ℎ 𝒕 𝒅 ≥ 𝑻𝒉𝒊𝒈𝒉 eq. 4
Such approaches have been used by [START_REF] Arca | Individuazione dei gradi giorno relativi allo sviluppo della Lobesia botrana(Den. et Schiff.) in Sardegna[END_REF] to calculate the emergence of adults and larvae of L. botrana.

2) The Triangular model (T) [START_REF] Hänninen | Modelling bud dormancy release in trees from cool and temperate regions[END_REF]) assumes a linear, positive response to daily temperatures for t d in the range Tmin to Topt, and an linear but negative response for t d in the range Topt to Tmax [START_REF] Maiorano | Comparison of modelling approaches to simulate the phenology of the European corn borer under future climate scenarios[END_REF]:

𝒇(𝒕 𝒅 ) = { 𝟎, 𝒕 𝒅 -𝑻𝒎𝒊𝒏 𝑻𝒐𝒑𝒕-𝑻𝒎𝒊𝒏 , 𝒕 𝒅 -𝑻𝒎𝒂𝒙 𝑻𝒐𝒑𝒕-𝑻𝒎𝒂𝒙 , 𝟎, 𝒕 𝒅 ≤ 𝑻𝒎𝒊𝒏 𝑻𝒎𝒊𝒏 < 𝒕 𝒅 ≤ 𝑻𝒐𝒑𝒕 𝑻𝒐𝒑𝒕 < 𝒕 𝒅 < 𝑇𝑚𝑎𝑥 𝒕 𝒅 ≥ 𝑻𝒎𝒂𝒙 eq. 5
3) The Wang model (W) [START_REF] Wang | Simulation of phenological development of wheat crops[END_REF]

Modelling parameterization and evaluation framework

Overwintering submodel

We assume that the overwintering starts (dt0) when day length is more than 12 hours [START_REF] Roditakis | Effects of photoperiod and temperature on pupal diapause induction of grape berry moth Lobesia botrana[END_REF][START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]. Individuals that enter into prediapause in the year n (autumn) will overwinter (spring) in the following year. Diapause induction starts when the day length falls below <14 hours, with a critical threshold at <12hours (Fig. 2), According to this assumption and (eq.1, 2 and 3) of [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF], it is possible to define when the first cohort begins its diapause.

The diapause is a combination of temperature and photoperiod. The DOY of diapause induction was evaluated according to (eq.3) in [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] calculating the day-length as a function of the DOY and the latitude. In spite of the fact that (eq.3) predicts a critical day-length threshold increasing linearly with latitude, the DOY allowing diapause induction does not vary significantly with latitude, ranging from DOY 183 to DOY 193 across our sites. For this reason, we tested the sensibility of the model to different starting date (dt0), July 1 st for the southernest site and the July 15 th as an average date for all the sites.

The post-diapause depends on temperature to allow the emergence of the first generation of adults.

The cumulation of thermal accumulation from the prediapause to the post-diapause determines the first adult flights. This first sub model (overwintering) was necessary to determine the start of the calculation of the 10% of flight of the adults from the 1 st generation (G1-10%).

Submodel for the adults flights

In order to simulate the 10% and the 50% of each generation, we made the three following assumptions:

1. eggs laid by G1-10% (or G1-50%) adult will reach the adult stage at G2-10% (or G2-50%) and this hypothesis is valid for all the following generations (Gn-10% or Gn-50%);

2. the same functions and set of parameters can be used to simulate the thermal time accumulation between G1-10% and G2-10% (or G(n-1)-10% and Gn-10%), G(n-1)-50% and Gn-50%, as well as Gn-10% and Gn-50%;

3. the same set of parameters can be used for all sites (and generations) without significant repercussions on the quality of the simulations (if compared to results obtained with site specific parameters) [START_REF] Parker | General phenological model to characterise the timing of flowering and veraison of Vitis vinifera L.: Grapevine flowering and veraison model[END_REF].

We calibrated and tested the three models Richardson (R), Triangle (T) and Wang (W) for the 10%-10% and 50%-50% of adult flights between the generations and the 10%-50% of adult flights within the generation itself. Preliminary simulations were made with all parameters, called Allp, meaning that the model calculates alone without any restriction of parameters (ESM8).

At the same time we also tested different sets of parameters (Tmin=0°C, 5°C, 7°C; Tmax=28°C, 33°C) Gutierrez's ( 2012) parameters (Tmin=8.9°C, Topt=30.8°C and Tmax=33°C) and some [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] parameters (Tmin=4.5°C) (ESM6, 7 and 8).

Calibration of the model

For the purpose of calibration and testing, we split the original data into a calibration dataset (75% of the total sample selected randomly -CAL dataset) and a validation dataset (25% of the data -VAL dataset) [START_REF] Picard | Cross-Validation of Regression Models[END_REF]. The calibration of the parameters for the overwintering stage and the adult generations were made separately. Once the models and parameters were determined, we joined the two submodels to run the simulations with our calibration data set and validate it with the validation dataset. Finally in order to provide the best set of parameters, we recalibrated the entire model using all the database (ALL dataset) using a cross validation method [START_REF] Cleland | Shifting plant phenology in response to global change[END_REF]). The best parameters were selected according to the results of the statistical criteria described in Tab.3. The performance criteria were defined using the variance global of the observed data (STOT), the Sum of Squares Residuals (SRES), the Root Mean Square Error (RMSE), the efficiency of the model (EFF)

and the Akaike test (AIC). For more details on the description and the formulas, see the ESM3 and 8.

Software

To facilitate the development and the parameterization of this phenological model, the PMP software (Phenology Modelling Platform -PMP 5.5) has been used (downloaded from: http://www.cefe.cnrs.fr/en/logiciels/ressources-documentaires). PMP allows constructing, fitting and running simulations of a phenological model using meteorological data and phenological observations [START_REF] Chuine | Plant Development Models_2013[END_REF].

Results

In this section we describe the results obtained from the calibration and the validation of both submodels: 1) the first sub model describing the overwintering period; 2) the second sub-model which simulates the 10-10%, 50-50% and 10-50% of the different generations of adults.

Overwintering submodel

Model three phases testing R, T and W models with CAL, VAL and ALL data set

As described previously we tested different versions of the submodel for the three phases of overwintering (Fig. 2): 1) different functions for temperature responses (R,T,W); 2) different starting dates of prediapause (dt0) (July 1 st and July 15 th ), 3) different ways to combine temperature (T) and photoperiod (P) responses during the diapause period, using an additive (Sum) and multiplicative (Mult) factor. The best models obtained used the T and W functions, starting on 15 th July (d t0 ) and multiplying the temperature and photoperiod effects. Tab.3 describes only results obtained with CAL data set with a start date (dt0) on July 15 th and using a multiplicative (Mult) method for combining photoperiod and temperature (for further results concerning all dates and methods, see ESM4). The best results were obtained with the Triangle and Wang approaches showing EFF values of 0.77 and 0.74 respectively (Tab.3). The combination method of the functions had more impact on the results than the starting dates named (dt0). Moreover, the date of entry in prediapause was coherent with

Baumgärnter's values [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]. [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]Brière et al., 1999;[START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF]). The other one are free. The models 1 and 2 have free parameters. The models 3 and 4 have the parameters fixed from the models 1 and 2 and a fixed Tmin at 4.5°C as in [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] or BAUM. The models 5 and 6 consider Gutierrez's parameters (GUT) with free day length (DL). The models 7 and 8 have fixed parameters from GUT but the DL and Tmin for the 3rd phase of GUT are free. Gutierrez's or GUT parameters are Tmin=8.9°C, Topt=30.8°C and Tmax=33°C. To evaluate parameter sensitivity, we compare the two best models (models 1 and 2 in Tab.4), with various models using the same functions but fixing some of their parameters from the literature (Tab.4). Because Tmin and Topt values for the post-diapause phase were close to one another, we explored the impact of fixing Tmin value to 4.5°C according to [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] keeping all the other parameters from the best models. Results obtained for both models (models 3 and 4 in Tab.4) show that this parameter does not degrade the quality substantially (values of efficiency of 0.67 to 0.69).

Model

In order to explore other values of parameters from the literature, we tested [START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF] parameters (GUT parameters are Tmin=8.9°C, Topt=30.8°C and Tmax=33°C) for all the temperature thresholds with free day length (DL) and limiting the post-diapause with BAUM Tmin=4.5°C (models 5 and 6 in Tab.4), and with the Tmin free for the post-diapause phase (models 7 and 8 in Tab.4).

Results obtained show that these parameters combination decrease significantly the quality of the model, having a higher effect when using the W function. In order to provide the best set of parameters we validated the defined best models (T and W) using the validation (VAL) data set (Tab.5). In contrast to CAL (39 data points), the validation data (VAL) include only 12, randomly chosen observations. For this reason, apart for a low value of EFF (0.1 and 0.08) the performance statistics for VAL are more than satisfactory, with RMSE=8.99 and AIC=52.7.

After a first screening the different model configurations, we calibrated T and W using all available data (dataset ALL). For both response functions EFF > 0.5 (0.59 for T, 0.70 for W, respectively).

Satisfactory were also the values of the RMSE (8.68 for T, and 7.47 for W, respectively) (Fig. 4). We also selected W to simulate the first flight in our model as it seems to be the more stable with all the simulations made, with fixed or free parameterization.

Submodel for the adults flights

We again tested different temperature response functions (R, W, T) to evaluate their performance to simulate adult flights between two consecutive generations (10-10%; 50-50%) and within a generation itself (10-50%). Following the same methodology as for the first flight, simulations were carried out by specifying all the parameters as free parameters (to be calibrated) or fixing some of them at values obtained from the literature. Summary statistics are presented in Tab.6.

Simulation the 10-10%-50-50% between the generations

According to the first assumption described in the modelling framework (see Material and Methods section), we explore the capacity of the model to represent with a single set of parameters all the 10%-10% and 50%-50% generations. The three models in Tab.6 had high values of EFF when all the parameters are fitted (around 0.95).

Values of the EFF decreased when some of the parameters were fixed (values varying between 0.25 to 0.95 depending on the model). We also validated the best model (Allp model) with the independent VAL dataset and we obtained good efficiency values for all the models (EFF = 0.84). As for the overwintering model, we propose to exclude R from our analysis because its structure to describe the development of L. botrana does not integrate maximum temperature (Tmax) even if the calibration did not show a significant effect of this threshold. Moreover, as in the overwintering model, the test using Gutierrez's parameters did not improve the simulation even if we obtained better results than with the overwintering models. Finally, the W function with Tmin=2.4°C, Topt=23.12°C and Tmax=32.13°C

was the best one with free parameters (see ESM7) and the closer to the known biological behaviour of L. botrana according to the literature.

Indeed, we also explored the sensitivity of each group (10-10% and 50-50%) separately and comparing the values of these parameters to the previously obtained. This analysis allowed evaluating their robustness to simulate each phase independently (Tab.7).

Tab.7. Crossed models separating the 10-10% and 50-50% between generations of L. botrana with CAL data set. Tests are made with free parameters and with the parameters of the best simulation from CAL Allp, testing the 10-10% /50-50% between generation. The statistical analysis use the RMSE and EFF. Gutierrez's or GUT parameters are Tmin=8.9°C, Topt=30.8°C and Tmax=33°C. Results obtained in Tab.7 show that the models simulate correctly the 10-10% and the 50-50% generations when we consider parameters from the first calibration (Tab.6) and with all parameters free but separating 10 -10% and 50 -50% in different datasets (for parameters values see in ESM3).

The EFF was around 0.92 and 0.94 and the RMSE between 7 and 8 days for the three functions (R, T and W). Indeed, when using Gutierrez's parameters, the R and T models showed good results (EFF=0.92), which was not the case for the W model that degraded (EFF=0.21 and 0.26). This analysis confirms the robustness of the model and its parameters, allowing to use a single function to simulate all the generations of one cycle for the 10 to 10% and 50 to 50% values for each generation.

Simulation 10%-50% of adults flights within a generation itself

As previously reported (Fig. 2) results presented in the following refer to simulations with no difference in parameter values between different generations. 2012) significantly degraded the results (EFF = -0.05). In line with the previous tests, the sensitivity of these models have been tested fixing some parameters (Tlow/Tmin and Tmax in ESM5 and 6). All the parameters found are close to the ones known in the literature so we kept them fixed (Tmin=8.9°C, Topt=30.8°C and Tmax=33°C in GUT or Tmin=4.5°C in [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]). In the first simulations with CAL data set and using free parameters (All parameters free), W seems to achieve better performances than T and R. Indeed, with fixed parameters the results did not improve with an RMSE around 5.5 days for the 3 functions and with parameters whose values are close to those found in the literature. We also validated the best model (All parameters free model) with the independent VAL dataset and we obtained good efficiency values for all the models (EFF=0.96) and an error of 9.84 days (RMSE). Fig. 5 illustrates the distribution of the simulated and observed data for the 10-50% of male flights within the same generation for the Wang model. The figure shows the good capacity of the model to simulate this phase. In general Fig. 6, the box size is proportional to the number of data and shows that the error for the simulation of all the generations for all the transect study have a small error (mean of +/-5 days) between simulated and observed data.

General discussion of the results

This study examined the possibility to assemble a simple, robust, generic, yet process-based model for simulating the voltinism of L. botrana. This model can be useful for large scale studies and impact studies targeting the behaviour of the insect pests under future climate change. The analysis of existing model indicated that two phases (overwintering and adults) are necessary to realistically represent the life cycle of L. botrana. The methodology to calculate the voltinism was based on the 10% and 50% of the total male flights per generation as significant reference to make simulations.

Data used for model development and testing were obtained from a wide latitudinal transect, allowing to test the possibility to apply the model at large scales.

The parameterization of the model was made by analysing different published models (Tab.1). Three types of temperature response functions were examined: Richardson, Triangle and Wang. The evaluation results showed that T and W are very close in their performance. The analysis provided good results with or without the use of certain specific parameter values found in the literature.

Moreover, the sensitivity of the models to different sets of parameters from the literature used by [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] and [START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF] did not improved the results of the parameterization tests with free parameters (Allp). On the contrary, the tests made with the Gutierrez's parameters degraded the results (Tab.8).

Another issue raised in our study was to integrate the photoperiod in a large latitudinal transect (from Lat.36.710°N to Lat.48.213°N) and understand its interaction with temperatures (as multiplicative or additive factor). The analysis of this interaction (Tab.3 and 4) showed that the multiplicative approach was better adapted to describe these interactions than the additive approach proposed by Baumgärtner et al. ( 2012) (ESM2). In any case, the multiplicative approach is the one commonly implemented in complex models and usually performs accurately [START_REF] Briere | Comparison of temperature dependant growth models with the development of Lobesia botrana (Lepidoptera:Tortricidae)[END_REF][START_REF] Wang | Simulation of phenological development of wheat crops[END_REF][START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF]. Finally, the analysis also indicated that assuming a common diapause starting date, (dt0) = July 15 th , for the entire transect was a reasonable choice.

We show that LGM is able to correctly represent the life cycle of L. botrana in various areas with the same set of parameters, with a model performance comparable to the one of local models [START_REF] Parker | General phenological model to characterise the timing of flowering and veraison of Vitis vinifera L.: Grapevine flowering and veraison model[END_REF]). This model is based on existing models but applied at other scale and consider less parameters that make its use easier. This approach is different to the previous one as it can be applied for large scale studies like climate change scenarios.

Proposal for a new model

The LGM uses a simplification of Baumgärtner's approach only to calculate the first cohort and not the entire population of L. botrana as in the original function. The overwintering submodel considers the general approach of the sum of temperatures (i.e. cumulation of temperatures as GDD or Growing Degree Days) and not the speed of growing as in Baumgärtner's original function. Then, the adults submodel uses the same parameters to cumulate heat between and within the generations. As we describe in the Fig. 7, the LGM model and Baumgärtner's model have the same range of errors to simulate the first cohort of a L. botrana population even with a simplification of the calculation methods. This comparison between both models provided a second partial validation of the LGM model, because it is not exhaustive as the years (observations) and sites (latitude) are different in both studies. Post-dia) and adult flights submodels. This is a classical approach using a first model with the calibration and validation data sets. A preliminary analysis revealed that the small divergence between the models allowed us to test another model with all the data sets. Tab.9 provides the statistical analysis with all the parameter values used for the calibration, validation and the entire data set. associated intermediate phases (i.e., end of prediapause and end of diapause). The calibration of this complex submodel was hence performed targeting the date of the 10% of the first generation at each site. The lack of intermediate information is a common problem faced in developing phenology models for plants [START_REF] Chuine | Can phenological models predict tree phenology accurately in the future? The unrevealed hurdle of endodormancy break[END_REF]). In our case, the data collection have been a long process and the quality selection of the male flights had to correspond to sites where we had meteorological data available close by (at least 15 years). Some authors like Amo-Salas et al. ( 2011) and [START_REF] Armendáriz | Cinco años de seguimiento de la polilla del racimo de la vid (Lobesia botrana) en la DO Arribes (Castilla y León, España)[END_REF] integrated relative humidity in their model, but they concluded that the value error with or without this parameter was not a significant influencing factor. Indeed, we did not consider relative humidity as in [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF], as we did not have such data available for all our sites.

Another limit of this study concerns the data that have been selected and converted to a comparable and standardized unit, but the observed data do not consider a protocol and the heterogeneity of the observed data can alter the quality of the calibration. Observation values obtained in the laboratory (in controlled conditions, at constant temperature), where rates of development are estimated approximately [START_REF] Briere | A novel rate model of temperature-dependent development for arthropods[END_REF][START_REF] Torres-Vila | Vine phenological stage during larval feeding affects male and female reproductive output of Lobesia botrana (Lepidoptera: Tortricidae)[END_REF][START_REF] Picart | Modélisation et estimation des paramètres liés au succès reproducteur d'un ravageur de la vigne (Lobesia botrana DEN. & SCHIFF[END_REF]) can differ considerably from those observed in the field and between the sites or by calibrating models using local conditions [START_REF] Arca | Individuazione dei gradi giorno relativi allo sviluppo della Lobesia botrana(Den. et Schiff.) in Sardegna[END_REF][START_REF] Torres-Vila | Vine phenological stage during larval feeding affects male and female reproductive output of Lobesia botrana (Lepidoptera: Tortricidae)[END_REF][START_REF] Severini | Fenologia della vite, e della Lobesia botrana (Lep. Tortricidae) nella zona dei Castelli Romani[END_REF]Moravie et al. 2006). The large latitudinal range of study is complex, as seen in Fig. 5, where some extreme values, representing the 4 th generations in south of Spain (not present at other sites), fall for the CAL dataset and not in the VAL dataset due to the randomization of the data selection and can alter the EFF of the tests. Nevertheless, the strength of this study has been to obtain a stable and robust model at a large spatial scale.

We believe that this work has contributed to raise new questions on scale applications for applied studies like climate change and on the methodologies used to simulate insect developmental processes.

The approach developed here, making use of a simple and unique set of parameters, representative of the biological response to temperatures, has shown very interesting and encouraging results.

Future model applications

We anticipate that LGM, as a model, is appropriate to conduct impact studies that integrate climate change scenarios in order to predict the future geographical distribution of ectothermic insects and the future extent of vulnerable areas. Multivoltine species are likely to develop more generations under warmer conditions [START_REF] Caffarra | Modelling the impact of climate change on the interaction between grapevine and its pests and pathogens: European grapevine moth and powdery mildew[END_REF]Reineke and Thiery 2016). Sensitivity analyses with LGM, combined with phenological models for plants, as grapevine for example, will allow to identify critical shifts in the synchrony or asynchrony of different trophic levels (host plants and insect pests) and the ensuing overlap periods [START_REF] Hoover | Tritrophic interactions in the context of climate change: a model of grasses, cereal Aphids and their parasitoids[END_REF][START_REF] Hirschi | Downscaling climate change scenarios for apple pest and disease modeling in Switzerland[END_REF][START_REF] Stoeckli | Impact of Climate Change on Voltinism and Prospective Diapause Induction of a Global Pest Insect -Cydia pomonella (L.)[END_REF][START_REF] Gilioli | A modelling framework for pest population dynamics and management: An application to the grape berry moth[END_REF]). Nevertheless, more data would have been useful to validate the choice of the best models.

This study could be improved by testing other regions of the world or by implementing the entire set

Fig. 1 .

 1 Fig.1. Map of the study sites in Europe (produced with MakeMap from an open source code). The numbers in the map represent the study sites introduced in Tab.2.

  [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] propose a complex model to simulate the overwintering stage and the adult development (at different phases) considering the speed of growth. In this study, we will only consider the first cohort (i.e., the emergence of the first individuals) of each generation (corresponding to our 10% of flight in Fig.2) considering the accumulation of thermal time.

Fig. 2 .

 2 Fig. 2. LGM conceptual modelling framework. This aims at reproducing the overwintering period and the adults flights :10%-10% and 50%-50% of flight between generations and the 10% and 50% within a generation itself (doted line). Also the variables used (T°=Temperature and P=Photoperiod) or the functions used in the model representing the temperature response: Richardson (R), Triangle (T) and Wang (W) are represented for each physiological developmental phase of L. botrana.

  [START_REF] Baumgärtner | A model for the overwintering process of European grapevine moth Lobesia botrana (Denis & Schiffermüller) (Lepidoptera, Tortricidae) populations[END_REF] to simulate the end of diapause, allowed us to propose a simplification of the original equations (described in ESM2) using daily values and considering a photoperiod threshold set at 12h to stop the development of the last generation. The final proposed equations can be described as following: 𝑭(𝒕 𝒅 ) = ∑(𝒇(𝒕 𝒅 ) 𝒅 𝒔 𝒅 𝟎 * 𝒈(𝑷 𝒅 ) ) 𝒐𝒓 𝑭(𝒕 𝒅 ) = ∑(𝒇(𝒕 𝒅 )

  is a Beta function that considers three cardinal temperatures Tmin, Tmax and Topt: 𝒇(𝒕 𝒅 ) = { 𝟎, 𝟐(𝒕 𝒅 -𝑻𝒎𝒊𝒏) ∝ (𝒕 𝒅 -𝑻𝒎𝒊𝒏) ∝ -(𝒕 𝒅 -𝑻𝒎𝒊𝒏) 𝟐∝ (This function is very similar to other functions described in the literature to simulate L. botrana response to the temperature (Wang and Engel 1998) and have been applied by Milonas et al. (2001), Briere and Pracros (1998), Logan et al. (1976) and Baumgärtner et al. (2012) for L. botrana.

Fig. 3 .

 3 Fig. 3. Comparison of three different approaches (Richardson, Triangle or Wang) of response to temperature with model parameters adapted to L. botrana. The three representations use the same parameters with Tmin=5°C, Topt=20°C and Tmax=30°C, except for Richardson that only uses Tlow=5°C and Thigh=20°C.

Fig. 4 :

 4 Fig.4: Representation of the day of the first flight of L. botrana male with a (dt0)=15 th of July and a multiplicative factor: a) Triangle model b) Wang model. Simulated and observed data in DOY (Julian days) show the quality of the simulation for each data set where CAL are in black circle and the results from the validation model VAL are in grey squares.

Fig. 5 .

 5 Fig. 5. Distribution of the simulated and observed data for the 10-50% of L. botrana male flights within the same generation with the Wang model. Simulated and observed data show here the correlation with both the results from the calibration model (CAL with crosses) and the results from the validation model (VAL with circles).

Fig. 6 .

 6 Fig. 6. Error between observation and simulations in number of days of the 10% and 50% of each generation of L. botrana flights, all site and years confounded. The errors fluctuate around 10 days before or after the observation data in the boxplots, with some extreme data, also present in the observed data. The last generations (G4.10 and G4.50) show a larger difference between observation and predictions, probably due to the sparsity of data that we disposed of, as only 2 sites had a 4 th generation. The size of the boxes is proportional to the number of data.

Fig. 7 :

 7 Fig.7: Comparison between LGM observed and simulated adults flights of L. botrana in DOY (Day of Year) andBaumgärtner's first and last cohort observations. From a geographical perspective, both models consider a wide range of sites and climates. The simulations of G1-10% and observations both fall within the spread of the first cohort appearing (in green) in Baugmärtner's model. The same observations can be made with the G1-50% that fall within the spread of the last cohort appearing (in red) in Baugmärtner's model.

165 166 Lobesia Botrana Meteorological station Site Number Site (data provider) Years obs Data provider Period Latitude (°N) Longitude (°E) Altitude

  Tab.2. L. botrana adult flights data and meteorological data acquisition per site in latitudinal order.

							(m a.s.l)
	Sanlucar (Junta de Andalucia) Trebujena (Junta de Andalucia)	2008, 2009, 2015 2013, 2014	Jerez de la frontera (Junta de Andalucia)	2007-2015	36.7	-6.1	56
	Yecla_C_abajo (O. comarcal Agraria de Alahama)	2010, 2011, 2012, 2014, 2015, 2016	Yecla-Pinillos (SIAM)	2007-2017	38.6	-1.1	602
	Fuente de la Higuera Alforins (Generalitat Valencia)	2012, 2013, 2014, 2015, 2016	Caudete (SIAR)	2010-2017	38.7	-1.0	625
	Requena Las Monjas (Generalitat Valencia)	2012, 2013, 2014, 2015, 2016	Requena Cerrito -Arcis (SIAR)	2010-2017	39.5	-1.11	692
	Villar del Arzobispo (Generalitat Valencia)	2012, 2013, 2014, 2015, 2016	Chullilla/ Villar (SIAR Riegos IVIA)	2010-2017	39.3	-0.8	380
	Cariñena (D.O.P-Vino las piedras)	2011, 2012, 2013, 2014	Calatayud (Sarga)	2004-2016	41.3	-1.6	591
	Avignon (Chambre Agri. Gard -France)	2005, 2009	Avignon (INRA Climatik)	2003-2016	43.9	4.8	24
	St Gilles (Chambre Agri. Gard -France)	2015, 2016	St-Gilles (INRA Climatik)	2010-2017	43.7	4.4	0
	Changins (Agroscope) Switzerland	1997, 1998, 1999, 2000, 2001, 2010	Changins (Meteosuisse IDAWEB)	1997-2017	46.4	6.2	455
	Eibindinger (Agroscope) Switzerland	2009, 2010, 2011, 2012, 2013, 2014	Staefa (agrometeo Meteosuisse)	2004-2017	47.2	8.7	408
	Scherwiller (Fredon Chambre Agri. Alsace -France)	2010, 2011, 2012, 2013, 2016	Bergheim (INRA-Climatik)	2009-2016	48.2	7.4	200

  Performance statistics with the CAL data set for three different choices of the temperature response function and the model version that combines temperature and photoperiod responses as multiplicative factors. Results presented here refer to simulation with parameter values taken form the literature. The statistical analysis use the RMSE (Root Mean Square Error) EFF (Efficiency of the model) and AIC (Akaike test).

	Tab.3. Simulations			Statistics
	Function	(d t0 )	Nb data	RMSE	EFF	AIC
	R	July 15th	39	9.47	0.58	98.71
	T	July 15th	39	7.02	0.77	118.28
	W	July 15th	39	7.49	0.74	123.22

Tab.4. Comparison of the best fitting of T (Triangle) and W (Wang) simulations to represent the overwintering with CAL data and using a multiplicative factor. Parameters in bold are fixed parameters. Parameters with an * are from the literature

  Simulation of the model hypothesis testing the 10-10%/50-50% between the L. botrana generations with the calibration (CAL) and validation (VAL) data set. The statistical analysis use the RMSE (Root Mean Square

	Tab.6. Error) and EFF (efficiency of the model). GUT parameters are Tmin=8.9°C, Topt=30.8°C and Tmax=33°C.
		10-10%-50-50% between generations		Statistics
		Simulation	Data set	Nb data	RMSE	EFF
	R Allp R ParGUT	10-10 / 50-50	CAL	140	6.97 8.35	0.95 0.93
	R ParAllp (VAL)		VAL	46	11.00	0.84
		Simulation	Data set	Nb data	RMSE	EFF
	T Allp T ParGUT	10-10 / 50-50	CAL	140	6.93 8.32	0.95 0.93
	T ParAllp (VAL)		VAL	46	11.08	0.84
		Simulation	Data set	Nb data	RMSE	EFF
	W Allp W ParGUT	10-10 / 50-50	CAL	140	6.93 27.96	0.95 0.25
	W ParAllp (VAL)		VAL	46	11.15	0.84

  Simulation of the 10-50% of L. botrana adults flights within a generation itself with CAL, VAL and ALL data set. The statistical analysis use the RMSE (Root Mean Square Error) and EFF (model efficiency).

	Tab.8: Gutierrez's or GUT parameters are Tmin=8.9°C, Topt=30.8°C and Tmax=33°C.
	10%-50% within a generation itself		Statistics
	Model R 10-50%	Nb data	Data set	RMSE	EFF
	R CAL Allp			5.59	0.99
	R CAL ParCAL_Allp10-10 R ParGUT	107	CAL	5.93 6.24	0.98 0.98
	R VAL Allp	37	VAL	10.93	0.95
	R ALL	144	ALL	8.56	0.97
	Model T 10-50%	Nb data	Data set	RMSE	EFF
	T CAL Allp			5.53	0.99
	T CAL ParCAL_Allp10-10 T ParGUT	107	CAL	5.91 6.24	0.98 0.98
	T VAL Allp	37	VAL	10.02	0.96
	T ALL	144	ALL	7.33	0.98
	Model W 10-50%	Nb data	Data set	RMSE	EFF
	W CAL Allp			5.55	0.99
	W CAL ParCAL_Allp10-10 W ParGUT	107	CAL	5.94 48.04	0.98 -0.05
	W VAL Allp	37	VAL	9.84	0.96
	W ALL	144	ALL	7.15	0.98
	Results described in Tab.8 show that very high values of EFF (from 0.98 to 0.99) were obtained
	irrespective of the model configuration. Fixing parameters for the W model to the values suggested by
	Gutierrez et al. (

(dt0) July 15th July 15th July 15th July 15th July 15th July 15th July 15th July

of data used.

In concert with phenological models for crops, LGM will help raise the awareness of producers on the emergence of new threats and adaptation of future treatment practices according to geographic areas.

Again, the advantages of LGM are its conceptual simplicity and generic parameterization, which allow the implementation of climate change studies at the large scale for both plants and insect pests. Acknowledgments A particular thanks to the Ernst and Lucie Schmidheiny Foundation for providing the funding that enabled the first author to conduct a short stay at the AgroClim Unit at INRA in Avignon (France) and Denis Thierry at INRA Bordeaux. This work would have not been possible without the help of data providers for meteorological data (MeteoSuisse, Agrometeo, IDAWEB, SIAR, SIAM, riegos.ivia, Phenoclim INRA) and for L. botrana male flight data, A. L. Espadas (Oficina Comarcal Agraria de Alhama), J. Serrano Palao (Servicio de Sanidad Vegetal de Jumilla), J. V. Badia Ballester (GVA-Generalitat Valencia) L. García de Arboleya Puerto (Junta de Andalucia), Oficina del regante de Zarragoza, J. Isiegas Mainar (D.O.P Cariñena), Mme Lauer (CA Alsace), Mr Genevet and Mr Cassarini (CA Gard), Mr Pasquier and Mr Goëlles (Agroscope) and especially Dr. Josep Armengol from the Universitat Politècnica de València for his collaboration.

It summarizes the proposed model, LGM model, showing the different parameter sets used to simulate the three phases of the overwintering period, but the single, common set of parameters used to simulate all the phases (10% and 50%) of the different generations of the adults flights.

Tab.9. Final submodels selected for their efficiency according to the calibration (CAL), validation (VAL) and the full data set (ALL) of samples and the stability of their biological response to temperature. Both set of parameters obtained using the 10% and 50% between the generations of the L. botrana adults flights and the 10-10%/50-50% within the generations are presented. The final results for the Wang model are close to biological thresholds reported in the literature, particularly those published by [START_REF] Gutierrez | Prospective analysis of the invasive potential of the European grapevine moth Lobesia botrana (Den. & Schiff.) in California[END_REF]. Concerning the adult development stage, the results confirm our hypothesis that a standard set of parameters is sufficient to accurately simulate the voltinism of L. botrana from diapause to last flight in terms of the 10% and 50% of the male flights. This finding is important because, as we described in the introduction, it is common practice to recalibrate phenological models for each generation [START_REF] Beddow | Potential global crop pest distributions using CLIMEX: HarvestChoice applications[END_REF]). Thus, in previous studies (Tab.1) authors proposed a different set of parameters or models for each generation considering that the biological response was different during the entire cycle. We are convinced that our approach introduces more robustness into the simulation of the life cycle of L. botrana. Indeed, it allows applications at large geographical scales without adapting the model to local parameters. Whether this can also be extended to other species remains to be investigated.

Models

Advantages and limits of the generic model

To define the LGM, we considered the models with the best statistical criteria and the most representative biological processes known from the literature (ESM7). One of the major difficulties we encountered was to model the overwintering phase, as we did not dispose of data to represent the

Author Contribution Statement

VC and IGCA conceived and designed the research and analyzed the data. PC and JM contributed new reagents and analytical tools. MB reviewed and corrected the manuscript. All authors read and approved the manuscript.

Compliance with Ethical Standards:

All authors declare that they have no conflict of interest. This article does not contain any studies with animals or human participants performed by any of the authors.