Nidhal Balti
email: nidhal.balti@irisa.fr

Baptiste Vrigneau
email: baptiste.vrigneau@irisa.fr

Pascal Scalart
email: pascal.scalart@irisa.fr

Sensor-aided NILM with Gaussian Mixture Models

Keywords: Energy disaggregation, NILM, GMM, Window-GRU, wireless sensor platform SmartSense

Energy disaggregation, also known as non-intrusive load monitoring (NILM), is the process of analyzing energy consumption in a building and identifying individual appliancelevel energy usage. This approach can provide valuable insights into energy consumption patterns and help reduce overall energy usage, costs, and carbon emissions. This paper proposes a new method for tackling the disaggregation problem by using data from low-cost wireless sensor networks. The proposed approach estimates appliance states using a GMM model and uses these states as features to improve energy disaggregation. The performance of the proposed method was evaluated on a real-world dataset called SmartSense deployed in our lab, and the results showed that it significantly improved the accuracy of conventional NILM disaggregation performance.

I. INTRODUCTION

The development of smart power consumption tactics is an urgent requirement for the future smart grid to adapt to the changing demands of production and lifestyle in the new era. It is also crucial for ensuring effective communication between supply and demand. An intelligent power consumption strategy significantly contributes to enhancing energy efficiency for consumers and reducing energy consumption [START_REF] Zhang | Multi-time scale home energy management strategy based on electricity demand response[END_REF], [START_REF] Li | Short-term load forecasting of smart grid based on long-short-term memory recurrent neural networks in condition of real-time electricity price[END_REF]. The foundation of creating an effective intelligent power consumption strategy lies in comprehending the energy consumption patterns and usage behavior of electrical devices. Energy disaggregation breaks down the total electricity usage recorded by the user's meter into individual appliance usage, serving as a technical foundation for the creation of smart grid power consumption tactics [START_REF] Liu | Conceptual cloud solution architecture and application scenarios of power consumption data based on load disaggregation[END_REF].

Visual representation of household appliance energy consumption can assist users in effectively considering energy conservation. By providing insights into appliance usage, time of use, and energy consumption, these visualizations encourage consumers to be more mindful of their energy consumption habits, leading to the adoption of more energyefficient practices. Previous research has shown that these visualizations can result in a reduction of energy consumption by as much as 15% [START_REF] Darby | The effectiveness of feedback on energy consumption[END_REF]. Additionally, connecting households to a smart grid makes efficient use of household energy demand

The authors thanks Lannion Trégor Communauté and Brittany region for their Phd founding. This work is supported by the EEWOK platform.

information [START_REF] Farhangi | The path of the smart grid[END_REF], [START_REF] Gungor | Smart grid technologies: Communication technologies and standards[END_REF]. A smart grid is a modern grid system that collects data on power generation and consumption through a two-way communication network in connected households. This enables the exchange of power-related information and simplifies demand-side energy management.

The paper is organized as follows. In Section II, we remind the state of the art and the work environment. Section III introduces our workflow process associating wireless sensors with NILM and our new platform SmartSense. Finally, we describe and analyze preliminary results.

II. RELATED WORKS

A. Non-Intrusive Load Monitoring concept

The concept of Non-Intrusive Load Monitoring (NILM), where energy meter data from the entry point could be used to disaggregate loads, was first introduced by Hart in the 1980s [START_REF] Hart | Nonintrusive appliance load monitoring[END_REF]. With the rise of smart meters, there has been a surge in publications on the subject of NILM [START_REF] Berges | Enhancing electricity audits in residential buildings with nonintrusive load monitoring[END_REF], [START_REF] Liang | Load signature study-part i: Basic concept, structure, and methodology[END_REF]. The ultimate aim is to analyze each appliance's state and power consumption using only a single reading of the total power usage. This is why a solved NILM problem is frequently referred to as "disaggregated" [START_REF] Zoha | Non-intrusive load monitoring approaches for disaggregated energy sensing: A survey[END_REF]. Figure 1 explains the basic NILM concept. For instance, from t = 12 to t = 28 minutes, an oven element is turned on. At t = 17, a stove burner is turned on. The first issue is identifying the precise moment when these appliances are turned on and off using their electrical signature, which can take the form of activation height, length, or shapes that are depicted with arrows. Estimating their power loads based on this trace is a second issue. This approach employs two techniques, namely pattern recognition and event-based methods, as well as combinatorial optimization. The algorithm learns the consumption pattern of appliances and compares it to the household meter reading in the former, whereas the latter involves learning the total consumption of appliances and comparing it to the household meter reading. These techniques have undergone extensive research and are now part of the Non-Intrusive Load Monitoring Tool-Kit (NILMTK), which is a disaggregation algorithm developed by an open-source community.

B. Non-Intrusive Load Monitoring Toolkit

Non-Intrusive Load Monitoring Toolkit or NILMTK [START_REF] Batra | Nilmtk: An open source toolkit for non-intrusive load monitoring[END_REF] is a tool used in analysing load usage in a building. It is an open source toolkit written in Python available on Github with a big community.

Prior NILMTK published, it was almost impossible to find a way to compare literature findings and experiments in NILM. No previous standard existed in terms of experiment setup, data acquiring, data format, etc. Therefore, NILMTK was introduced to tackle these issue. It is designed to be a standard tool for NILM tasks, and to be used among researchers. With NILMTK, researchers can have some guidelines on how obtained data and predicted data to be collected, stored, compared, evaluated and even represented in the similar manner or format. Thus, the results from disaggregation can be compared and discussed on the performance of an algorithm used. NILMTK includes several features such as dataset conversion tools (to import dataset into NILMTK environment), several disaggregation algorithms and evaluation tools. The most popular metrics used in NILM field are the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE):

RM SE = 1 T T t=1 | ŷt -yt| 2 and M AE = 1 T T t=1 | ŷt -yt| (1)
where ŷi represents the prediction of an appliance's energy usage at time t and y i represents the corresponding ground truth.

In fact, many public datasets are available for researchers to work on. Datasets in NILM contain both main power meter reading and an appliance power reading. The sampling rates of the dataset are typically in the range of 1 second to several seconds, but some datasets may also provide a higher sampling rate like 16kHz [START_REF] Kelly | The uk-dale dataset, domestic appliancelevel electricity demand and whole-house demand from five uk homes[END_REF]. Popular NILM datasets such as REDD [START_REF] Kolter | Redd: A public data set for energy disaggregation research[END_REF], BLUED [START_REF] Filip | Blued: A fully labeled public dataset for event-based nonintrusive load monitoring research[END_REF] and UKDALE [START_REF] Kelly | The uk-dale dataset, domestic appliancelevel electricity demand and whole-house demand from five uk homes[END_REF] are the most used by researchers to evaluate their algorithms since they are integrated in NILMTK. Moreover, NILMTK provides several deep learning models for energy disaggregation such as WindowGRU which will be used in our experiments.

C. WindowGRU

The Windowed Gated Recurrent Unit (WindowGRU) is a novel Recurrent Neural Network (RNN) architecture that is designed to capture long-term dependencies in sequence data. The algorithm introduces a window-based processing technique that selectively focuses on relevant past information while suppressing irrelevant information. The WindowGRU algorithm showed its effectiveness on various sequence modeling tasks, and show that it outperforms traditional GRU models and other state-of-the-art approaches. Added to that, the WindowGRU algorithm has the potential to improve the performance of RNNs in various sequence modeling tasks that involve long-term dependencies.

The architecture in detail is the following: 1) Input is windowed with length optimised to the appliance 2) 1D Convolution with 16 filters, 4 kernels and linear activation 3) Bidirectional GRU with 64 units, tanh activation and 0.5 dropout rate 4) Bidirectional GRU with 128 units, tanh activation and 0.5 dropout rate 5) Fully connected with size of 128, tanh activation and 0.5 dropout rate 6) Fully connected with size of 128, tanh activation and 0.5 dropout rate

III. SEMI-INTRUSIVE LOAD MONITORING

A. SmartSense dataset

Using environmental sensing and diverse information can help overcome challenges faced by current NILM techniques [START_REF] Zoha | Load Disaggregation and Monitoring in a Smart Office Space[END_REF]. However, this can increase complexity. Hence, a more efficient approach could be to merge supplementary data with the overall power consumption of the building for load monitoring. Furthermore, the increasing number of intelligent sensors integrated into buildings for different purposes has made it more feasible to acquire this information without additional setup, which may explain the recent emphasis on this method.

The dataset used in this study is called SmartSense, which serves as a research platform that employs a sensor network designed for multiple data acquisition purposes. More than 120 nodes are deployed inside our lab and each node within the network comprises fifteen sensors that collect a diverse range of information (see Figure 2), including:

• Video sensors (Video-Graphic-Array (VGA), Infra-Red (IR) cameras) and audio sensors (4 microphones in tetrahedron authorizing localization); • Radio sensors (2.4 GHz, Sub-GHz, and Ultra-Wide-Band) to sense the radio-frequency band occupancy and to estimate positions; • Air quality sensors (temperature, humidity, carbon dioxide concentration, air pressure, etc.); • Light sensors (Ultraviolet and Red-Green-Blue-White);

• Distance sensor (Laser telemeter).

Additionally, SmartSense platform contains a record of power consumption in each floor in our lab as a classical NILM (figure 3):

• global power consumption recorded by an EcoCompteur with a frequency of 7Hz; • individual power consumption of various electrical appliances recorded by a ZigBee meter with a frequency of 100mHz. A summary of SmartSense features is shown in Table I. In fact, the SILM architecture is composed mainly of 2 parts:

• The first part called the features extraction phase intends to extract a useful information from sensors data and then feed them to the input of the next step; • The second part called the disaggregation phase in which the standard NILM workflow is kept. It entails three main phases, including data preprocessing, disaggregation, and performance evaluation. The aim of our work is to find a good way in exploiting sensors data and extracting a useful information that will help in improving NILM performance. The first naive idea we started with is to add raw sensors data to the aggregated power data as input and let the disaggregator algorithm deal with it. The results show that disaggregation performance compared with the typical NILM improved slightly for the kettle while they stayed almost the same for the coffee maker.

We recognize that raw sensors data could have noise that could limit the disaggreator algorithm's effectiveness. Consequently, it is essential to extract features, such as appliance states, from this data. The disaggregation process involves identifying when an appliance is being used and determining its state. We believe that by focusing on classifying appliances as either ON or OFF, we can further use this information to enhance the accuracy of the disaggregation process.

B. Proof of Concept

We thought that adding an a-priori information of appliances states could improve the disaggregation performance and gives a more accurate estimation of appliances individual power consumption. That is why before starting the implementation of our architecture, we made a Proof of Concept (POC). Indeed, the individual power consumption used as reference during the training phase of the disaggregation was transformed to 0 or 1 representing the states OFF and ON of an appliance, or No Activity and Activity. Then, these states information was added with the aggregated power data as an additional input of the standard NILM workflow. Finally, with this augmented input a typical disaggregation with NILMTK was performed. The duration of both the training and test dataset is 15 days. The results of disaggregation are depicted in Table II and Table III. The unmarked values indicate the outcomes obtained solely from the total power data, while the values marked with underlines show the results obtained from the suggested input, which includes both the total power data and the true states of a given appliance. The results show that adding an a-priori information can improve significantly the disaggregation of a given appliance. The results was validated for the coffee maker and the kettle. The challenge now is to implement the POC by finding a good estimator of the states of appliances from sensors data.

C. Gaussian Mixture Models as an estimator

Gaussian mixture models (GMM) are a probabilistic machine learning technique that can provide better approximation when the clusters are overlapping, as compared to k-means clustering [START_REF] Bora | A comparative study between fuzzy clustering algorithm and hard clustering algorithm[END_REF]. Thus, the GMM model will be used in our case as the estimator/classifier of appliances states as shown in Figure 4b. In Gaussian mixture models, each cluster is modeled as a multivariate Gaussian distribution with the probability density function defined as:

f (x) = 1 (2π) n |Σ| exp - 1 2 (x -µ) ⊤ Σ -1 (x -µ)
where x ∈ R n is the random vector, µ ∈ R n is the mean vector, Σ is the n × n positive-definite covariance matrix, and |Σ| is the determinant of Σ.

If a given appliance can be described by K different states, then for a mixture of Gaussians we have K Gaussian distributions.

p(X) = K k=1 π k N (X|µ k , Σ k )
where N (X|µ k , Σ k ) represents the multivariate Gaussian distribution with mean vector µ k and covariance matrix Σ k , K represents the number of Gaussian mixtures, and π k is the mixing proportion for the kth component, and

K k=1 π k = 1.
Since there is a mixture of Gaussians, the parameters µ k , Σ j , and π k have to be determined. These parameters are estimated by using the Expectation-Maximization (EM) method [START_REF] Dempster | Maximum likelihood from incomplete data via the em algorithm[END_REF]. EM consists of two steps (cf Algo 1). In the expectation step (E-Step), the initial estimates of the parameters are assigned using k-mean clustering and the probability of each latent variable is calculated. In the maximization step (M-Step), the parameters are modified to maximize the likelihood of the data with the initial assignments. These steps are repeated until a local optimum is achieved [START_REF] Pedregosa | Scikit-learn: Machine learning in python[END_REF].

In this code, K is the number of Gaussian components in the GMM, N is the number of data points, π j is the mixing coefficient for the j-th Gaussian component, µ j and Σ j are the mean and covariance of the j-th Gaussian component, γ ij is the responsibility assigned to the j-th Gaussian component for the i-th data point, N (x i | µ j , Σ j ) is the Gaussian density function evaluated at x i with mean µ j and covariance Σ j . The EM algorithm iterates between the E-step (Expectation step), Algorithm 1 Expectation-Maximization Algorithm for Gaussian Mixture Model Require: Data points x 1 , x 2 , . . . , x N ; number of mixture components K 1: Initialize parameters: π j , µ j , Σ j for j = 1, 2, . . . , K 2: while not converged do for j = 1 to K do 6:

γ ij ← πj N (xi|µj ,Σj ) K k=1 π k N (xi|µ k ,Σ k ) 7:
end for

π j ← N i=1 γij N 12: µ j ← N i=1 γij xi N i=1 γij 13: Σ j ← N i=1 γij (xi-µj )(xi-µj ) T N i=1 γij 14:
end for 15: end while where responsibilities are updated, and the M-step (Maximization step), where parameters of the Gaussian components are updated until convergence (classical threshold).

D. Results

a) Dataset: The dataset used for the simulations below was exported from SmartSense platform. In this paper we are interested in disaggregating the appliances of the lab's kitchen (Coffee maker, kettle, microwaves, oven and lights). The duration of the training and test dataset is 15 days. b) States estimation phase: During this stage, a GMM model was used through the Python library Scikit-Learn. For each appliance the training data was used to fit two models for each class, ON and OFF. The log-likelihoods of each class were then determined, and the test data samples were assigned to the class with the highest likelihood. For conciseness, the solution is first applied in 1 dimension with CO2 sensor but can be extended to higher dimensions. The duration of training data and test data is 15 days. They contains data from 25 different sensors such as CO2, humidity, temperature, etc. The initial findings focused on determining the states of the coffee maker and kettle and they are presented in Table IV and Table V. c) Disaggregation phase: During this stage, the previously estimated states were incorporated into the overall power consumption, and the standard NILM pipeline was executed According to the table above, our approach the conventional NILM disaggregation with only CO2 sensor and demonstrated that incorporating sensors data about the environment can enhance NILM disaggregation.

IV. CONCLUSION

Our study aimed to evaluate the effectiveness of a new NILM approach for disaggregating energy consumption data from smart meters and wireless sensors into individual appliance-level data. This new approach is based on integrating additionnal features to the input that were obtained from specific sensors data that provide additional information from each appliance environment. Our results show that the approach achieved high accuracy in identifying individual appliances compared to the conventional NILM approach.

However, our study also had some limitations that should be considered when interpreting the results. First, the algorithm was trained and tested on a relatively small dataset (15 days), which may limit its generalizability to other settings. Second, the accuracy of the algorithm varied not only across different appliance categories but also the sensors data (in this work we used only CO2 data). The difficulty here is to find the optimal combination off various sensors data that enhance the disaggregation performance for a given appliance but our solution is able to increase the GMM dimension.

Future research could explore ways to further improve the accuracy and robustness of NILM algorithms, particularly for challenging appliance categories such as printer and laptop whose consumption may depend on their activity.

Fig. 1 :

 1 Fig. 1: Concept of typical NILM as presented in [7].

Fig. 2 :

 2 Fig. 2: Different sensors in one node.

Fig. 3 :

 3 Fig. 3: Hardware devices used to collect power consumption data for SmartSense data

Fig. 4 :

 4 Fig. 4: Semi-Intrusive Load Monitoring synoptic

  for j = 1 to K do 11:

TABLE I :

 I SmartSense dataset features

	Measurement	Data type	Frequency	Appliances
	device
	EcoCompteur	global power	7.5 Hz	coffee maker,
		consumption		kettle, fridge, oven,
	ZigBee meter	individual	100 mHz	microwave, laptop,
		power		printer, light
		consumption
	Sensors node	sensors data	1 Hz

TABLE II :

 II Evaluation of disaggregation performance of NILM and the SILM POC (underlined values)

	Appliances	RMSE	MAE
	Kettle	69.82 15.37	6.69 1.28
	Coffee maker	26.27 7.21	2.65 1.04

TABLE III :

 III Confusion Matrix of coffee disaggregation performance using the power data and the ON/OFF states as input

		Predicted Class
	True Class	Negative	Positive	Support
	Negative	132077 132190	116 3	132193
	Positive	126 0	1241 1367	1367
		Precision	Recall	F1 Score
	Negative	1.00 1.00	1.00 1.00	1.00 1.00
	Positive	0.91 1.00	0.91 1.00	0.91 1.00

TABLE IV :

 IV Confusion Matrix of coffee maker states estimation from sensors data with K = 9 and CO2 sensor

		Predicted Class
	True Class	Negative	Positive	Support
	Negative	99726	32464	132190
	Positive	141	1229	1370
		Precision	Recall	F1 Score
	Negative	1.00	0.75	0.86
	Positive	0.04	0.90	0.07

TABLE V :

 V Confusion Matrix of kettle states estimation from sensors data with K = 7 and CO2 sensor Table VI presents the outcomes for the coffee maker and kettle and compares it with the disaggregation performance using only the power consumption as input. The unmarked values indicate the outcomes obtained solely from the total power data, while the values marked with underlines show the results obtained from the suggested input, which includes both the total power data and states information.

		Predicted Class
	True Class	Negative	Positive	Support
	Negative	91189	41380	132569
	Positive	315	676	991
		Precision	Recall	F1 Score
	Negative	1.00	0.69	0.81
	Positive	0.02	0.68	0.03
	using NILMTK.

TABLE VI :

 VI Evaluation of disaggregation performance

	Appliances	RMSE	MAE
	Kettle	69.82 48.66	6.69 3.11
	Coffee maker	26.27 21.95	2.65 1.64


Thierry Hoch
email: thierry.hoch@inrae.fr

Aurélien Madouasse

Maude Jacquot

Phrutsamon Wongnak

Fréderic Beugnet

Laure Bournez

Jean-François Cosson

Frédéric Huard

Sara Moutailler

Olivier Plantard

Valérie Poux

Magalie René-Martellet

Muriel Vayssier-Taussat

Hélène Verheyden

Gwenaël Vourc'h

Karine Chalvet-Monfray

Albert Agoulon

Seasonality of host-seeking Ixodes ricinus nymph abundance in relation to climate

There is growing concern about climate change and its impact on human health. Specifically, global warming could increase the probability of emerging infectious diseases, notably because of changes in the geographical and seasonal distributions of disease vectors such as mosquitoes and ticks. For example, the range of Ixodes ricinus, the most common and widespread tick species in Europe, is currently expanding northward and at higher altitudes. However, little is known about the seasonal variation in tick abundance in different climates. Seasonality of I. ricinus is often based on expert opinions while field surveys are usually limited in time. Our objective was to describe seasonal variations in I. ricinus abundance under different climates. To this end, a seven-year longitudinal study, with monthly collections of I. ricinus host-seeking nymphs, was carried out in France, in six locations corresponding to different climates. Tick data were log-transformed and grouped between years so as to obtain seasonal variations for a typical year. Daily average temperature was measured during the study period. Seasonal patterns of nymph abundance were established for the six different locations using linear harmonic regression. Model parameters were estimated separately for each location. Seasonal patterns appeared different depending on the climate considered. Western temperate sites showed an early spring peak, a summer minimum and a moderate autumn and winter abundance. More continental sites showed a later peak in spring, and a minimum in winter. The peak occurred in summer for the mountainous site, with an absence of ticks in winter. In all cases except the mountainous site, the timing of the spring peak could be related to the sum of degree days since the beginning of the year. Winter abundance was positively correlated to the corresponding temperature. Our results highlight clear patterns in the different sites corresponding to different climates, which allow further forecast of tick seasonality under changing climate conditions.

Introduction

The effect of human activity on climate change is now recognised (IPCC, 2021), even though the extent of its impact remains open to debate. In particular, the influence of anthropogenic climate change on infectious disease incidence has to be assessed. Among infectious diseases, vector-borne diseases appear to be especially sensitive to climate change [START_REF] Semenza | Vector-borne diseases and climate change: a European perspective[END_REF] because changes in temperature and rainfall regime inevitably affect vector spatial distribution and phenology. However, climate change does not represent the unique disruptor of vector borne diseases (Rocklöv & Dubrow, 2020), which can also be impacted by biodiversity loss and land use change [START_REF] Rizzoli | Parasites and wildlife in a changing world: The vector-host-pathogen interaction as a learning case[END_REF].

Climate change may greatly affect the distribution of ticks, which are the main vectors of zoonotic pathogens in Europe [START_REF] Gray | Effects of Climate Change on Ticks and Tick-Borne Diseases in Europe[END_REF][START_REF] Ogden | Effects of Climate and Climate Change on Vectors and Vector-Borne Diseases: Ticks Are Different[END_REF]. Temperature influences tick physiology through the process of development, which is known to be accelerated with higher temperatures [START_REF] Randolph | An empirical quantitative framework for the seasonal population dynamics of the tick Ixodes ricinus[END_REF]. Tick host-seeking activity (referred to as "questing" for most tick species) also increases with temperature and relative humidity [START_REF] Vail | Air temperature and relative humidity effects on behavioral activity of blacklegged tick (Acari: Ixodidae) nymphs in New Jersey[END_REF][START_REF] Perret | Darkness induces mobility, and saturation deficit limits questing duration, in the tick Ixodes ricinus[END_REF]. Depending on the tick species, tick survival could, on the contrary, be reduced by higher temperatures and especially lower hygrometry [START_REF] Daniel | Influence of microclimate on the life cycle of the common tick Ixodes ricinus (L.) in thermophilic oak forest[END_REF]. The impact of climate change on the distribution of Ixodes ricinus particularly has already been observed and reported with a trend towards a northward expansion in Europe [START_REF] Lindgren | Impact of climatic change on the northern latitude limit and population density of the disease-transmitting European tick Ixodes ricinus[END_REF][START_REF] Hvidsten | The distribution limit of the common tick, Ixodes ricinus, and some associated pathogens in north-western Europe[END_REF] or its occurrence at higher altitude, in the Alps [START_REF] Garcia-Vozmediano | Ticks climb the mountains: Ixodid tick infestation and infection by tick-borne pathogens in the Western Alps[END_REF] or in mountain slopes in Norway [START_REF] De Pelsmaeker | High-elevational occurrence of two tick species, Ixodes ricinus and I. trianguliceps, at their northern distribution range[END_REF].

Data on tick occurrence and climate variables have been confronted to define climate suitability for ticks such as I. ricinus [START_REF] Estrada-Peña | Changes in Habitat Suitability for the Tick Ixodes ricinus (Acari: Ixodidae) in Europe (1900-1999)[END_REF]. Extrapolation to future climate projections were then derived from these suitability maps [START_REF] Estrada-Peña | Impact of climate trends on tick-borne pathogen transmission[END_REF]Poretta et al., 2013). Besides these statistical models, mechanistic models incorporating knowledge on biological processes were also developed, for instance for Hyalomma marginatum [START_REF] Estrada-Peña | A Population Model to Describe the Distribution and Seasonal Dynamics of the Tick Hyalomma marginatum in the Mediterranean Basin[END_REF] or I. ricinus [START_REF] Hoch | Influence of host migration between woodland and pasture on the population dynamics of the tick Ixodes ricinus: A modelling approach[END_REF]. These process-based models could allow the simulation of the impact of climate change through the effect of meteorological variables on the involved processes. They represent relevant tools to predict the evolution of the transmission of tick-borne pathogens such as Crimean Congo Haemorrhagic Fever Virus (CCHFV) [START_REF] Estrada-Peña | Factors driving the circulation and possible expansion of Crimean-Congo haemorrhagic fever virus in the western Palearctic[END_REF][START_REF] Hoch | Dynamic Modeling of Crimean Congo Hemorrhagic Fever Virus (CCHFV) Spread to Test Control Strategies[END_REF] or Lyme borreliosis agents, for which the northward expansion has been simulated in North America [START_REF] Ogden | Projected effects of climate change on tick phenology and fitness of pathogens transmitted by the North American tick Ixodes scapularis[END_REF]. More recently, [START_REF] Li | Modelling the seasonality of Lyme disease risk and the potential impacts of a warming climate within the heterogeneous landscapes of Scotland[END_REF] developed a mechanistic agent-based model to simulate the seasonality of Lyme borreliosis risk, estimated through the number of infected nymphs in Scotland. Their model predicts an increase in disease risk at higher latitude and altitude, but also in the duration of I. ricinus host-seeking season, with warmer conditions. Such a longer duration of the host-seeking season has also been predicted by the model developed by [START_REF] Hancock | Modelling the effect of temperature variation on the seasonal dynamics of Ixodes ricinus tick populations[END_REF], which focused on the evolution of the timing of I. ricinus peak of abundance in response to increasing temperature. Processes affecting the phenology of Ixodes scapularis were identified by a study linking simulation and data collection in different sites of the United States [START_REF] Ogden | Evidence for Geographic Variation in Life-Cycle Processes Affecting Phenology of the Lyme Disease Vector Ixodes scapularis (Acari: Ixodidae) in the United States[END_REF]. These authors identified different observed patterns of tick abundance depending on the site. They carried out several simulations considering different scenarios regarding temperature-independent diapause and development. The comparison of simulation outputs with observations suggested that diapause may be a major factor to explain geographical differences in tick phenology.

The objective of our study was to assess the differences in seasonal patterns of I. ricinus nymph abundance associated with distinct climates observed in France. A seven-year longitudinal study, involving monthly I. ricinus collections, was carried out at six locations in France. The species I. ricinus was targeted because it is responsible for major human vector-borne diseases in Europe (Lyme borreliosis and Tick Borne Encephalitis). This dataset allowed the fitting of statistical models of nymph abundance with time. [START_REF] Wongnak | Meteorological and climatic variables predict the phenology of Ixodes ricinus nymph activity in France, accounting for habitat heterogeneity[END_REF] fitted a model on the same data set to explore the influence of meteorological variables on tick abundance for predictive purposes. Our modelling approach is complementary and aims to describe the seasonal patterns of I. ricinus by site and to relate them to climate features of the different geographical locations. Our objective was to assess these patterns for an average year, called typical year thereafter, by the use of the whole set of data for a given site, thus ignoring the between-year variations in the analyses. This approach can give insight into the evolution of tick phenology in relation to climate change.

Data and models

Tick Sampling

Tick collection was carried out between April 2014 and June 2021 at six locations across France (Figure 1) which will be thereafter called Carquefou, Etiolles, Gardouch, La Tour-de-Salvagny, Saint-Genès-Champanelle and Velaine-en-Haye. These locations were chosen in wooden habitats, selected for their high densities of host-seeking I. ricinus nymphs during spring, in different regions of France characterized by different climates (see Table S1, Supplementary Material, Hoch et al., 2023, for GPS coordinates of the locations, altitudes and corresponding climates). In Gardouch, two nearby sites were sampled over the entire period: "Gardouch in", an enclosed forest patch with a fenced controlled population of roe deer, and "Gardouch out", another part of the same forest, just outside the fence of "Gardouch-in" and with uncontrolled roe deer populations. In La Tour-de-Salvagny, a first site (called " La Tour-de-Salvagny a" thereafter) was sampled between April 2014 and September 2016, then became inaccessible and was replaced by a second site (called " La Tour-de-Salvagny b" thereafter, approximately 2 km apart), sampled between April 2017 and June 2021. There was therefore a total of eight sites at six locations.

Time-series of tick counts were obtained through 520 field campaigns carried out from April 2014 to June 2021, corresponding approximately to one collection session per month and per site (data were missing for 82 months due to several constraints: delay at the beginning, snow, Covid-19 lockdown...).

At each site, ten marked transects of 10 x 1 m long were chosen along trails covered by short grass or a leaf litter, with a minimum distance of 20 m between them. Each tick collection session corresponded to a single day, selected for the absence of rain or snow and the dryness of the grass and leaf litter cover. On that day, on each transect, a 1 m 2 white flannel was slowly dragged along the 10 m to collect host-seeking ticks [START_REF] Agoulon | A Vegetation Index qualifying pasture edges is related to Ixodes ricinus density and to Babesia divergens seroprevalence in dairy cattle herds[END_REF]: ticks were counted, removed from the cloth with tweezers and stored alive for further identification at stage and species level according to identification keys [START_REF] Pérez-Eid | Les tiques : identification, biologie, importance médicale et vétérinaire[END_REF]. Tick collection was repeated three times consecutively on the same marked transects in order to collect more individuals and to improve accuracy in the assessment of tick abundance [START_REF] Bord | Bayesian estimation of abundance based on removal sampling under weak assumption of closed population with catchability depending on environmental conditions. Application to tick abundance[END_REF]. This method simulates the natural detection and infestation of a host by host-seeking ticks. The number of collected ticks was therefore considered representative of the host-seeking tick abundance on the day of collection. Due to a low number of adult ticks collected and the known low involvement of larvae in disease transmission cycle, these development stages were not considered for further analyses: only I. ricinus nymphs were considered, reflecting the major risk of pathogen transmission to humans [START_REF] Kurtenbach | Fundamental processes in the evolutionary ecology of Lyme borreliosis[END_REF].

Local meteorological data

Weather stations were installed at the beginning of the period at each location to collect hourly air temperature and relative humidity records at a height of 1.5 meters. A single station was used for La Tourde-Salvagny a and b, and for Gardouch-in and Gardouch-out. Daily mean meteorological variables were obtained from those records. When data were missing, data from nearby MeteoFrance and INRAE automatic weather stations were collected to impute the missing values, with a random forest approach [START_REF] Wongnak | Meteorological and climatic variables predict the phenology of Ixodes ricinus nymph activity in France, accounting for habitat heterogeneity[END_REF].

Daily Vapor Pressure Deficit (VPD, in kPa) was computed by the following equation:

(1)

𝑉𝑃𝐷 !" = 𝑒 # -𝑒 $ = '0.6108𝑒 !".$"% &' $(".()% &' -. .1 - %& &'
'(( / where s and t indices represent the respective site and recording date, ea is the amount of moisture in the air, em the maximum water holding capacity, θ and RH the respective temperature and relative humidity of the day.

For each location, the daily mean temperatures and VPDs of an average year were obtained by averaging the corresponding daily mean meteorological data from 1 January to 31 December (see Figure S1 and S2, Supplementary Material, Hoch et al., 2023).

In order to assess the influence of temperature on the date of the estimated peak, a cumulative temperature (in degree-day) was computed for each location. It was calculated by summing the daily mean temperatures of an average year from the 1st January up to the estimated date of the peak.

Tick and meteorological data are available on line (Hoch et al., 2023)

Statistical analyses

The objective of the analyses was to describe the site-specific seasonal variations in the abundance of I. ricinus nymphs, hereafter referred to as tick abundance pattern. The distributions of the numbers of nymphs for each site were right skewed, typically with a mode below 10 nymphs collected per day and maximum values that could reach several hundred. Taking the natural logarithm of the number of nymphs allowed to make the distributions more symmetrical (see Figure S3, Supplementary Material, Hoch et al., 2023). The abundance patterns were modelled using harmonic regressions. Briefly, harmonic regression is a type of linear regression in which the days of the year are mapped onto a circle, and, functions of the sine and cosine of the corresponding angles are included as covariates in the regression.

The outcome of all models was the natural logarithm of the number of I. ricinus nymphs (+1 to avoid ln(0), which is not defined) collected at a given site on a given day. This outcome was modelled as a function of day of the year at the time of collection. The models' specifications were as follows:

(2)

𝑙𝑛(𝑦 !) + 1) = 𝜇 ! + ∑ .𝑎 !* cos .𝑘 +,) -./ / + 𝑏 !* sin .𝑘 +,) -./ // 0 *1' + 𝜀 !)
with:

(3)

𝜀 !) ~𝒩(0, 𝜎 ! + )
where 𝑦 !) was the number of nymphs collected at site s on day of year d (ranging from 1 to 365); 𝜇 ! was the model intercept for site s, k was the maximum number of periodic (also called Fourier) terms included; and 𝜀 !) was the residual error with mean 0 and variance σ 2 .

Increasing k makes it possible to model increasingly complex seasonal patterns. In order to mitigate the risk of overfitting with high values of k, models with k varying between 0 and 4 were compared based on the Akaike Information Criterion (AIC) value. For most locations, there was an important decrease in AIC between k = 0 and k = 2 (see Figure S4, Supplementary Material, Hoch et al., 2023) and we reach a plateau thereafter. Therefore, k = 2 was used in all models.

Using the fitted models, typical within-year evolutions of tick abundance were simulated. The characteristics of interest included the date of peak abundance, i.e. the date when the predicted number of I. ricinus was highest. The relation of the peak dates with cumulative mean temperatures was investigated.

Unlike peak tick abundance, which depends on many factors which have not been accounted for in the model (e.g. host abundance), we hypothesize that winter tick abundance relates to corresponding temperature, which has an influence on tick activity. To analyse these potential links, the average January daily mean temperature was related to the corresponding estimated mean tick abundance. To improve comparability among sites, average tick abundance in January was standardized by its maximum value in each site. Similarly, as VPD is recognized to lower tick activity [START_REF] Vail | Air temperature and relative humidity effects on behavioral activity of blacklegged tick (Acari: Ixodidae) nymphs in New Jersey[END_REF], we linked the average August VPD to the corresponding relative tick abundance.

Corresponding R script is available online (Hoch et al., 2023).

Results

Seasonal patterns of observed I. ricinus nymph abundance at the different sites

Figure 2 shows the natural logarithm of the number of I. ricinus nymphs (+1) collected as a function of the day of the year, for the eight sites and seven years of collection. At a given site, seasonal patterns were stable over years, whereas there were variations between sites exhibiting different patterns. Therefore, we fitted different models for the different locations, including data from all years for each site. When there were two sites for the same location (i.e. Gardouch in and out, La Tour-de-Salvagny a and b), the patterns looked similar. In those cases, we included site as a fixed effect in the harmonic regression (different mean for each site), but the same coefficients were used for the Fourier terms: this means that the fitted curves followed the same seasonal dynamics but were of different heights. The different models appear to correctly represent the observed dynamics (Figure 3) and particularly the spring peak. For Gardouch in and Gardouch out as well as for the two sites of La Tour-de-Salvagny, the choice of fitting the same model with a distinct intercept seems relevant. In particular, for the latter, the model succeeds in representing both the same dynamics and the difference in abundance between the two sites. When applied over the whole data set without accounting for the sampling year, such a modelling helps to identify the favourable and less favourable years for tick abundance, for which observed tick abundances are respectively above and below the fitted curve. Interestingly, favourable years seem to Thierry Hoch et al.

differ from one site to another, even on the same location (Gardouch in and out). For instance, the model revealed a favourable year in 2016 at Gardouch out (but not at Gardouch in), in 2017 at Carquefou, in 2018 at Velaine-en-Haye and in 2019 at La Tour-de-Salvagny b. To compare sites, we superimposed the predicted tick abundance for all sites over one year (Figure 4). The predicted patterns show a spring peak in all sites except Saint-Genès-Champanelle, where the maximal abundance is observed in summer. Some small differences in spring peak dates are predicted for the other sites. Tick peak occurs earlier for the western "oceanic" sites (Carquefou and Gardouch) and later for the eastern "continental" sites (Etiolles, La Tour-de-Salvagny and then Velaine-en-Haye). Winter abundance highlights another striking feature: in the western sites (Carquefou and Gardouch), predicted tick abundance is increasing from September to November to reach a plateau throughout the winter months, which is not observed elsewhere.

Links between predicted tick abundance and meteorological variables

The predicted spring peak date can be related to the cumulative sum of the mean daily temperatures from the beginning of the year, hence resulting in a degree-day effect (Figure 5). The order by which sites are ranked with respect to the cumulative temperature corresponds to the order of spring peak dates. The simulation exhibits an early peak in Gardouch and Carquefou, followed by Etiolles, La Tour-de-Salvagny, Velaine-en-Haye and Saint-Genès-Champanelle. For the four sites with the earliest spring peak, the peak occurs when temperature cumulative sum reaches c.a. 1000 °C.d (Table 1). At the more continental site of Velaine-en-Haye, the maximum is reached at a lower value for the cumulative temperature. The mountainous site, Saint-Genès-Champanelle, appears to have a different behaviour regarding temperature, with a cumulative temperature around 1600 °C.d at peak date. Table 1 shows the range of values of the mean daily temperature at the time of the peak between the different sites. The mountainous site of Saint-Genès-Champanelle shows again a clear different behaviour regarding temperature, with a peak of tick abundance corresponding to summer temperature (17.2°C). For the other sites, the peak of abundance is obtained in spring for intermediate temperature values, i.e. between 11.5°C (in Carquefou) and 14.1°C (in La Tour-de-Salvagny).

Moreover, average predicted tick abundance in January, standardized by the yearly maximum value at the corresponding site, can be directly related to the average temperature for the same period (Figure 6). This straightforward significant relationship shows that mild winter temperatures of Carquefou and Gardouch correspond to higher winter tick abundance than other sites. On the contrary, only a weak relationship was shown between average daily mean VPD and relative tick density (see Figure S5, Supplementary Material, Hoch et al., 2023), with an estimated Pearson coefficient of -0.24 (p=0.562).

Discussion

The tick abundance patterns modeled in this work can be divided into three types: two types exhibiting a unimodal curve, with a peak either in spring (Etiolles, La Tour-de-Salvagny, Velaine-en-Haye) or in summer (mountainous site of Saint-Genès-Champanelle), and a third type exhibiting a bimodal pattern in Carquefou and Gardouch, with a peak in spring, a minimum in summer and an increase with a plateau in autumn and winter. When comparing sites that exhibit a spring peak, the predicted peak occurs later as the site is located further east. Collected tick abundance declines thereafter in summer in these sites, which might be due to a decrease in the host-seeking nymph population (due to the fixation of nymphs on hosts in the spring) or a decrease in the questing behaviour of the remaining nymphs due to a lower relative humidity in summer. These fitted tick abundance patterns are consistent with the literature. We used the same data set as [START_REF] Wongnak | Meteorological and climatic variables predict the phenology of Ixodes ricinus nymph activity in France, accounting for habitat heterogeneity[END_REF], who derived patterns applied to the different sites. However, their results relied on a descriptive analysis of the data, whereas our conclusions are based on a statistical model using harmonic regression relating tick abundance with time, thus dedicated to the assessment of tick phenology. Even though both analyses often converge, some differences may be highlighted, as for instance the absence of any autumn peak in eastern sites in our analysis. Several field studies highlight differences in tick phenology according to climate. Thanks to seven year monthly samplings, [START_REF] Alonso-Carné | Modelling the phenological relationships of questing immature Ixodes ricinus (Ixodidae) using temperature and NDVI data[END_REF] depicted a unimodal or a bimodal curve in two locations in Spain differing from their respective climatic characteristics (continental vs temperate). From Bregnard et al. (2021a) tick phenology is expected to be unimodal at northern latitudes and bimodal in areas with warmer and longer summers. They also reported 12 different studies on tick phenology across Europe where the authors identified a unimodal or a bimodal phenology, but observed phenology does not always follow these rules, possibly due to year-toyear variations. [START_REF] Babenko | On geographic variation in the seasonal dynamics of activity of Ixodes ricinus and I. persulcatus ticks and on factors responsible for long-term fluctuations of their abundance[END_REF] (in [START_REF] Korenberg | Seasonal population dynamics of Ixodes ticks and tick-borne encephalitis virus[END_REF] depicted four stylized types of seasonal changes in the abundance of I. ricinus adults. More specifically, he considered bimodal curves for temperate zones (i.e. Crimea) and unimodal ones with a peak in summer for continental areas of Russia. Even applied to adult ticks, these curves can be compared with our predictions for the nymph stage in Carquefou and Gardouch (oceanic and southwestern basin climate respectively), and in Saint-Genès-Champanelle (continental climate), respectively. Concerning the influence of altitude, differences in tick phenology were shown between transects situated respectively at 100 and 400 meter high in Norway [START_REF] Qviller | Temporal pattern of questing tick Ixodes ricinus density at differing elevations in the coastal region of western Norway[END_REF]. In Switzerland, Bregnard et al. (2021a) showed a cline ranging from bimodal to unimodal curves when reaching higher altitude (altitude ranging from 620 to 1073 m in their study). According to [START_REF] Gray | Diapause in ticks of the medically important Ixodes ricinus species complex[END_REF], I. ricinus abundance patterns for larvae, nymphs and adults follow a bimodal curve in Central and Western Europe, but these authors also point out that there are variations on this expert-based pattern. Our fitted model based on harmonic regression and using longitudinal data resulting from seven years of monthly surveys allows us to relate these seasonal variations to observations. It also suggests that these two types of patterns are both present in different locations of the French territory.

The abundance patterns can be directly related to what we know about the specific climate of the different sites. A gradient in spring peak date is exhibited from the western sites located in temperate areas to the more eastern ones, corresponding to a semi-continental climate (see the climate typology in France from [START_REF] Joly | Les types de climats en France, une construction spatiale[END_REF] on Figure 1). Mountainous areas can be assimilated to even more continental zones, with however a heat deficit during summer. An early spring peak corresponds to temperate sites where temperatures are warmer in winter and at the beginning of spring. [START_REF] Diuk-Wasser | Spatiotemporal patterns of host-seeking Ixodes scapularis nymphs (Acari: Ixodidae) in the United States[END_REF] also highlighted an earlier peak for I. scapularis nymphs in southern vs northern sites in USA. Temperature has long been identified as the major factor acting on tick development [START_REF] Randolph | Tick ecology: processes and patterns behind the epidemiological risk posed by ixodid ticks as vectors[END_REF], each stage necessitating a certain amount of degree-days to develop to the next stage [START_REF] Hoch | Influence of host migration between woodland and pasture on the population dynamics of the tick Ixodes ricinus: A modelling approach[END_REF]. The spring peaks in the different sites logically occur successively in accordance with the cumulative temperature curves (Figure 5). Four locations (Carquefou, Etiolles, Gardouch and La Tour-de-Salvagny) exhibit a spring peak for comparable degree-day values (around 1000 °C.d). This is not the case in Saint-Genès-Champanelle (around 1600 °C.d) and to a lesser extent in Velaine-en-Haye (around 800 °C.d). For the mountainous location, in Saint-Genès-Champanelle, a peak is hardly identified in summer and the tick density curve looks smoothed, which generates uncertainty in the estimation of the peak date: the amount of degree-days may be over-estimated. Temperature data measured at 1.5 meter from the ground may not represent the temperature experienced by the ticks at ground level. Furthermore, factors other than cumulative temperature may influence the date of the peak. The date of the peak may depend on the proportion of larvae which are developing into nymphs during the spring: if development from larvae to nymphs occurs before the spring, i.e. in the autumn of the previous year (as suggested by [START_REF] Randolph | An empirical quantitative framework for the seasonal population dynamics of the tick Ixodes ricinus[END_REF], resulting host-seeking nymphs may be active very early in the spring, at the onset of warming. It has also been shown that the host-seeking behaviour (questing) of different tick populations may respond differently to temperature, depending on the climate considered [START_REF] Tomkins | Towards an Evolutionary Understanding of Questing Behaviour in the Tick Ixodes ricinus[END_REF]. Ticks that have achieved their development start questing with a rate that depends on relative humidity and temperature. According to [START_REF] Beugnet | FleaTickRisk: a meteorological model developed to monitor and predict the activity and density of three tick species and the cat flea in Europe[END_REF], this proportion of questing ticks is maximal for intermediate temperatures, i.e. between 10 and 20°C. A field study also reported maximum values of collected ticks for intermediate temperatures in Germany [START_REF] Gethmann | Research paper on abiotic factors and their influence on Ixodes ricinus activity-observations over a two-year period at several tick collection sites in Germany[END_REF], i.e. 13-15°C of ground temperature, which is comparable to our mean daily air temperature at peak date (Table 1). Our values for temperature at the peak are consistent with these expert-and data-based questing rates. Finally, a clear relationship has been shown between winter (January) abundance in host-seeking nymphs and corresponding average temperature in the different sites. This is supported by findings of [START_REF] Furness | Ixodes ricinus parasitism of birds increases at higher winter temperatures[END_REF], who showed a winter increase in the infestation of birds by immature I. ricinus ticks with temperature. As stated by [START_REF] Gray | Effects of Climate Change on Ticks and Tick-Borne Diseases in Europe[END_REF], climate change is likely to increase the duration of the host-seeking period of ticks, thus highlighting the need of winter tick collections to monitor the risk of tick bite.

A weak relationship was put in evidence between August tick abundance and VPD. [START_REF] Perret | Influence of saturation deficit and temperature on Ixodes ricinus tick questing activity in a Lyme borreliosis-endemic area (Switzerland)[END_REF] found a higher negative relationship between the evolution of monthly nymph abundance between April and September and the corresponding variation in VPD. Although the relationship could be due to a negative effect of high VPD on tick activity, which has been experimentally demonstrated by [START_REF] Vail | Air temperature and relative humidity effects on behavioral activity of blacklegged tick (Acari: Ixodidae) nymphs in New Jersey[END_REF] with a weekly sampling, it also results from a natural decline of questing tick abundance after the spring peak. In our study, a between-site effect of VPD could possibly not be shown due to our monthly sampling since tick host-seeking activity in summer may be highly fluctuating due to very variable conditions of hygrometry, especially at ground level.

Concerning inter-annual variations in tick abundance, we note that years with relatively high observed abundance compared with simulated abundance are not the same for different sites. While these variations can be explained by inter-annual variations of local meteorological conditions, other factors may also be involved, including host densities. Nymph abundance is known to be related to the rodent abundance of the previous year, as shown by [START_REF] Perez | Effect of landscape features on the relationship between Ixodes ricinus ticks and their small mammal hosts[END_REF] for the effect of wood mice (Apodemus sylvaticus) abundance on I. ricinus densities. The indirect effect of beech fructification two years before on nymph density and acarological risk (density of infected nymphs) has also been demonstrated respectively by [START_REF] Brugger | Forecasting next season's Ixodes ricinus nymphal density: the example of southern Germany 2018[END_REF] and Bregnard et al. (2021b).

In this study, tick abundance at different sites in France showed repeatable within year patterns across a seven-year period. At a given site, inter-annual variation was usually low compared with seasonal variation. The identified associations between climate characteristics and seasonal patterns of tick abundance corroborate expert opinions. Peak abundance usually occurred for cumulative temperatures of around 1000°C, with extremes of 780°C and 1600°C. The different profiles identified at the scale of France are a first step towards the understanding of tick phenology and its variation according to climate, and give new insight into the influence of climate change on I. ricinus tick activity that has to be put in perspective with disease risks.

Figure 1 -

 1 Figure 1 -Map of France with the different climates encountered (from Joly et al., 2010). Tick sampling locations are indicated.

Figure 2 -

 2 Figure 2 -Natural logarithm of the observed number of Ixodes ricinus nymphs (+1) collected as a function of day of the year, at eight French sites over seven years.

Figure 3 -

 3 Figure 3 -Natural logarithm of the number of Ixodes ricinus nymphs (+1) predicted by the models (black curves) and number of nymphs effectively collected (red dots), at eight French sites over seven years.

Figure 4 -

 4 Figure 4 -Predicted annual log-transformed abundance patterns of host-seeking Ixodes ricinus nymphs for the different sampling sites. The dots represent the maximum of each curve, i.e. the peak of abundance.

Figure 5 -

 5 Figure 5 -Cumulative temperatures over time for the six locations, with dots corresponding on the X-axis to the predicted dates of I. ricinus host-seeking nymph peak abundance at each location.

Figure 6 -

 6 Figure 6 -Predicted mean nymph abundance in January, standardized by the yearly maximum value, as a function of corresponding mean temperature in January for the different sites. Equation of the regression line : 𝑦 = -0.206 + 0.124𝑥, p=0.001.

Table 1 -

 1 Peak date (predicted date of Ixodes ricinus host-seeking nymph peak abundance), cumulative temperature (°C.d) and mean daily temperature (°C) at peak date for the different locations.

		Carquefou	Gardouch	Velaine-en-	La Tour-de-	Etiolles	Saint-Genès-
				Haye	Salvagny		Champanelle
	Peak date (d)	May 2	May 3	May 23 (143) May 18 (138)	May 15	July 25 (206)
		(122)	(123)			(135)
	Cumulative temperature (°C.d)	1034.5	1112.8	781.5	1093.3	1092.1	1593.2
	at peak date
	Mean daily temperature (°C) at	11.5	12.6	12.7	14.1	12.5	17.2
	peak date
	Average January nymph	0.637	0.643 (in)	0.076	0.086 (a)	0.338	0.
	abundance		0.593 (out)		0.305 (b)
	Average January daily	6.55	6.04	1.65	4.06	5.03	1.37
	temperature (°C)

Peer Community Journal, Vol. 4 (2024), article e2 https://doi.org/10.24072/pcjournal.355

Acknowledgements

Preprint version 4 of this article has been peer-reviewed and recommended by Peer Community In Ecology (https://doi.org/10.24072/pci.ecology.100507, Yoccoz, 2023) Thierry Hoch et al. Peer Community Journal, Vol. 4 (2024), article e2 https://doi.org/10.24072/pcjournal.355

Funding

Tick observatories were supported by the CC-EID and Climatick projects: "Adaptation of Agriculture and Forests to Climate Change" metaprogramme of the French National Research Institute for Agriculture, Food and Environment (INRAE). We also would like to thank the TEMPO French Network (https://tempo.pheno.fr/) for providing resources to support this study.

Data, scripts, code, and supplementary information availability

Data, R scripts and supplementary information are available online: https://doi.org/10.5281/zenodo.10044216 (Hoch et al., 2023).

Conflict of interest disclosure

The authors declare that they comply with the PCI rule of having no financial conflicts of interest in relation to the content of the article. Thierry Hoch, Aurélien Madouasse and Sara Moutailler are recommenders of a PCI, respectively Ecology, Animal Science and Infections.