M Emily

G Gernigon

S Mahé

J Bickert

B Prioux

A Noury-Desvaux

Le Faucheur
email: alexis.lefaucheur@ens-rennes.fr

P.-Y De Müllenheim

S Chaudru

M Gernigon

G Mahé

S Bickert

J Prioux

B Noury-Desvaux

A Le Faucheur

Using GPS, accelerometry and heart rate to predict outdoor graded walking energy expenditure

Keywords:

Using GPS, accelerometry and heart rate to predict

outdoor graded walking energy expenditure

Introduction

Walking, the most popular physical activity (PA), has a substantial impact on public health and is a leading therapeutic modality. [START_REF] Lee | The importance of walking to public health[END_REF] An accurate assessment of walking-related energy expenditure (EE) is crucial to determine its overall biological impact on the human body [START_REF] Thompson | Multidimensional physical activity: an opportunity, not a problem[END_REF] and appropriately study its effects on health. From this perspective, accurately estimating walking EE in outdoor settings is of primary interest. Indeed, it has been shown that (i) walkers prefer neighborhood streets and parks for walking 3 ; (ii) accumulating walking trips at a sufficient intensity (≥3 metabolic equivalents of task (METs)) and of sufficient duration (≥10 min) to meet PA recommendations [START_REF]ACSM's Guidelines for Exercise Testing and Prescription[END_REF] may be easier outdoors; and (iii) outdoor walking sessions are of interest in clinical populations for both walking capacity assessment and rehabilitation purposes. [START_REF] Gernigon | Global positioning system use in the community to evaluate improvements in walking after revascularization: a prospective multicenter study with 6-month follow-up in patients with peripheral arterial disease[END_REF] Because the direct measurement of EE in real-life settings is challenging, wearable devices have been validated and used for years in field-based research to track walking EE. [START_REF] Chen | Redefining the roles of sensors in objective physical activity monitoring[END_REF] Historically, wearable devices relied on a single objective method for estimating EE. Accelerometry or heart rate (HR) monitoring have been among the most frequently used objective methods. [START_REF] Chen | Redefining the roles of sensors in objective physical activity monitoring[END_REF] However, accelerometry has several well-known drawbacks, including the inability to accurately assess EE during graded walking. [START_REF] Terrier | Can accelerometry accurately predict the energy cost of uphill/downhill walking?[END_REF] HR monitoring is of particular interest when measuring walking EE because the method relies on the measurement of the physiological response of a given individual. [START_REF] Achten | Heart rate monitoring: applications and limitations[END_REF] Unfortunately, a number of factors are responsible for the biological variability of HR, which lowers the accuracy of this method when the intensity of PA (including walking) is low. [START_REF] Achten | Heart rate monitoring: applications and limitations[END_REF] Interestingly, we recently showed that the use of speed and grade data obtained using a low-cost global positioning system (GPS) receiver allowed highly accurate estimations of EE during level and uphill outdoor walking compared to the use of actual speed and grade. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] Although that study supported the feasibility of using GPS alone for estimating EE during level and graded outdoor walking, it is unknown how GPS compares with classical methods, such as accelerometry or HR monitoring, for this purpose.

ARTICLE IN PRESS

Beyond determining the best single method for estimating outdoor walking EE, it would be helpful to identify the best combination of methods for this purpose. Technological development has allowed the measurement of PA and EE by various sensors embedded into either several small devices (e.g., an accelerometer and an HR monitor [START_REF] Fudge | Estimation of oxygen uptake during fast running using accelerometry and heart rate[END_REF][START_REF] Luke | Simultaneous monitoring of heart rate and motion to assess energy expenditure[END_REF] ) or a single device, such as the SenseWear Mini Armand [START_REF] Vernillo | Validity of the SenseWear Armband to assess energy expenditure in graded walking[END_REF] or the Actiheart. [START_REF] Brage | Hierarchy of individual calibration levels for heart rate and accelerometry to measure physical activity[END_REF] Moreover, ubiquitous consumer technologies, such as smartphones and watches, are now likely to embed several sensors (including GPS chipsets, accelerometers, and HR sensors), which has opened new perspectives in the field of mobile health. [START_REF] Chow | mHealth in Cardiovascular Health Care[END_REF] Several studies have investigated whether combining accelerometry with other methods could close the gap classically observed between actual and estimated EE values during graded walking when using accelerometry alone. [START_REF] Vernillo | Validity of the SenseWear Armband to assess energy expenditure in graded walking[END_REF][START_REF] Duncan | Measuring slope to improve energy expenditure estimates during field-based activities[END_REF][START_REF] Yamazaki | A new device to estimate VO2 during incline walking by accelerometry and barometry[END_REF] Some of these studies have assessed the benefits of combining accelerometry and measurements of altitude change (using barometry [START_REF] Duncan | Measuring slope to improve energy expenditure estimates during field-based activities[END_REF][START_REF] Yamazaki | A new device to estimate VO2 during incline walking by accelerometry and barometry[END_REF] or GPS [START_REF] Duncan | Measuring slope to improve energy expenditure estimates during field-based activities[END_REF] ) to improve the accuracy of EE estimates during outdoor uphill and downhill walking. The value of combining accelerometry and HR monitoring for estimating walking EE has also been assessed, but only on motorized treadmills, and studies have produced conflicting results: some authors found no improvement in the accuracy of EE estimates, [START_REF] Luke | Simultaneous monitoring of heart rate and motion to assess energy expenditure[END_REF] while others reported an improvement. [START_REF] Fudge | Estimation of oxygen uptake during fast running using accelerometry and heart rate[END_REF][START_REF] Corder | Comparison of PAEE from combined and separate heart rate and movement models in children[END_REF] Of note, accurately estimating EE when subjects are walking uphill or downhill seems to remain a challenge when combining accelerometry and physiological parameters. [START_REF] Vernillo | Validity of the SenseWear Armband to assess energy expenditure in graded walking[END_REF][START_REF] Brage | Hierarchy of individual calibration levels for heart rate and accelerometry to measure physical activity[END_REF] To our knowledge, no study has compared the accuracy of using different combinations of parameters, including GPS speed and grade, accelerometer counts, and HR parameters, for estimating outdoor walking EE. Therefore, we still do not know the optimal combination to be implemented by researchers and users to study outdoor walking EE when several methods are simultaneously available. Furthermore, it seems relevant to assess whether using several combined methods for estimating EE is worthwhile because increasing the number of methods and wearable devices would probably increase the burden perceived by subjects, limiting acceptability and compliance.

Thus, the purposes of the present study were the following: (i) to determine which method among GPS, accelerometry, and HR monitoring is the most accurate for estimating EE during level, uphill and downhill outdoor walking; and (ii) to determine the extent to which a combination of these methods increases the accuracy of EE estimates.

Methods

This cross-sectional study was part of the "Acti-GPS" project (NCT01805219), which was approved by the local Institutional Ethics Committee (CPP OUEST II, Angers). A total of 30 healthy par-ticipants were recruited for the present study, as recommended for criterion-related validity studies. [START_REF] Mahar | Construct validity in physical activity research[END_REF] Most of participants (26/30) were recruited from the Department of Sports Sciences and Physical Education of the University of Angers and the University of Rennes. The participants were between 20 and 30 years of age, with equal numbers of men and women. Each participant signed an informed consent form and underwent an inclusion visit, a resting metabolic rate measurement, a peak oxygen uptake ( VO 2peak ) measurement during an incremental field-running test, and three outdoor walking sessions. The incremental running test and the outdoor walking sessions were separated by at least 24 h. In addition, the three outdoor walking sessions, which corresponded to three different levels of grade (0.0%, 3.4% and 10.4% mean grades), were performed on 2 or 3 different days, with at least one and a half hours between two sessions. The sequential order of the outdoor walking sessions for each participant was counterbalanced according to the number of grade conditions (n = 3). The methods of the Acti-GPS project have been extensively described elsewhere. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] During the inclusion visit, the participants provided their medical histories and underwent a physical examination. Weight, height, and body fat percentage using the skin fold method were measured, as previously reported. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] The resting metabolic rate was measured early in the morning (between 07:00 and 10:30) in the supine position and in a noise-free and thermoneutral (22 ± 1 • C) room. Participants were asked to fast for at least 12 h, to refrain from vigorous PA and alcohol for 24 h, and to sleep for 8 h or more prior to testing. After a 20-min adaptation period, gas exchange was recorded over a 30min period. Resting HR and gas exchange were measured with a portable metabolic system (K4b 2 , Cosmed ® , Rome, Italy). The VO 2peak value was determined using the K4b 2 during an outdoor maximal incremental field-running test performed on a 400-m athletic track. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] On 2 or 3 other and different days, each participant completed six-minute walking periods at speeds of 2.0, 3.5 and 5.0 km h -1 during each of the three outdoor walking sessions (0.0%, 3.4% and 10.4% mean grades for the three sessions, respectively). During the outdoor walking sessions on the 3.4% and 10.4% mean grades, each walking speed was tested uphill and downhill (Supplemental material (SM) #1). Thus, each participant completed 15 walking periods through the study: 3 on the level; 6 on the 3.4% mean grade (3 uphill and 3 downhill); and 6 on the 10.4% mean grade (3 uphill and 3 downhill). The sequence of walking speeds within each walking session was randomized for each participant. The actual walking speed was calculated for each walking period by dividing the total distance walked (measured with an odometer) by the time (measured with a chronometer). At each location, the actual grade of the walking courses was measured every 25 m along the courses by a certified surveyor using a Trimble S6 Total Station (Trimble, Sunnyvale, CA) and a Trimble R8 Global Navigation Satellite System. All the locations were free of motorized vehicles, buildings and dense vegetation. For only one of the two hiking trails, there were trees at one extremity of the pathway. The K4b 2 was calibrated according to the manufacturer's guidelines before each test, and reliability data have been previously published. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] During all walking sessions, participants were equipped with a low-cost DG100 GPS receiver (GlobalSat ® Inc., Taipei, Taiwan; ∼AUD80) that recorded at a 1-Hz sampling rate, as previously described. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] Participants also wore a wGT3X+ set at a 90-Hz sampling rate on the iliac crest of the hip (ActiGraph TM , LLC, Pensacola, FL; ∼AUD295; firmware 2.2.1). The HR was recorded using the K4b (www.timeanddate.com/worldclock). At the end of each walking session, data were downloaded from all devices to a personal computer using the manufacturers' software. For each walking period, the mean values of weather parameters (temperature ( • C), relative humidity (RH in %), wind speed (km h -1 ), and barometric pressure (hPa)) were also recorded using information provided by French weather stations.

For data analysis, all data were exported to Excel ® (Microsoft, Redmond, WA, version 2010) spreadsheets. The absolute resting VO 2 was recorded as the mean VO 2 value over the 30-min measurement period. The relative resting VO 2 was obtained by dividing the absolute resting VO 2 by the participant's body mass. The VO 2peak was the highest 30-s average VO 2 value measured during the maximal incremental field-running test. Participants were required to have a peak respiratory exchange ratio ≥1.10 and a peak HR ≥95% of the age-predicted maximum HR [START_REF] Tanaka | Age-predicted maximal heart rate revisited[END_REF] to ensure that the test value was maximal and to validate the obtained VO 2peak value.

The absolute gross VO 2 values obtained from the different walking sessions were averaged over the last three minutes of each walking period to reflect steady-state exercise. Values were adjusted using terrain coefficients for energy cost prediction, 20 as previously described. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] EE was calculated as kcal min -1 = [15.913 × VO 2 (L min -1 ) + 5.207 × VCO 2 (L min -1 )]/4.186. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] For each walking period, the GPS speed data were averaged over the last three minutes to match the average EE data. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] The corresponding mean uncorrected and corrected GPS grades were obtained using raw and corrected altitude data, respectively, according to our previously published procedure. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] The raw data recorded by the wGT3X+ accelerometer were accumulated into 1-s epoch data (i.e., into counts s -1 ) using the normal filter to compute the counts per second on the vertical axis (VA) and the vector magnitude (VM). Counts per second for both VA and VM were averaged over the last three minutes of each walking period. The average over the last three minutes of each walking period was calculated for the following HR-related parameters: (i) the raw HR recorded during the walking periods (HR (raw) , in beats per minute (bpm)); (ii) the HR above the resting HR value (HR (aR) , in bpm = HR (raw) -the average HR recorded during the resting metabolic rate measurement (HR (rest) ); and (iii) the HR reserve (HR (res) , in %). These HR parameters have previously been used alone (SM #2) or in combination with other parameters (e.g., accelerometer counts [START_REF] Fudge | Estimation of oxygen uptake during fast running using accelerometry and heart rate[END_REF][START_REF] Corder | Comparison of PAEE from combined and separate heart rate and movement models in children[END_REF] ) to estimate EE; however, to our knowledge, they have never been tested and compared for the study of outdoor walking.

The first step of our statistical analysis was to test linear mixed models (LMMs). [START_REF] Welk | Principles of design and analyses for the calibration of accelerometrybased activity monitors[END_REF] In that way, we developed equations to predict EE that used GPS speed and grade (uncorrected or corrected), accelerometer counts (VA or VM), HR-related parameters (HR (raw) , HR (aR) , or HR (res) ), or a combination of two (e.g., VA counts and HR (raw) ) or three (e.g., GPS speed and corrected grade, VA counts, and HR (raw) ) of these parameters. Separate equations were developed using (i) the level walking periods, (ii) both the level and uphill walking periods, or (iii) both the level and downhill walking periods. We developed separate equations because the relationship between the energy cost of walking and the gradient differs according to the gradient condition (uphill vs. downhill). [START_REF] Minetti | Energy cost of walking and running at extreme uphill and downhill slopes[END_REF] The use of both the level and graded walking periods to develop a single equation is in accordance with previous works and the components of commonly used equations. [START_REF]ACSM's Guidelines for Exercise Testing and Prescription[END_REF][START_REF] Pandolf | Predicting energy expenditure with loads while standing or walking very slowly[END_REF] Of note, the models that used GPS speed and grade were also compared to the models that used the actual speed and grade. The addition of the following covariates into the models was also tested: mass, gender, body fat percentage, and discomfort index (forward stepwise selection procedure). The discomfort index (thermohygrometric index [START_REF] Unger | Comparisons of urban and rural bioclimatological conditions in the case of a central-European city[END_REF] ) was calculated as follows: t -(0.55 -0.0055•RH) × (t -14.5), with air temperature (t) measured in • C and RH in %. The coefficient of determination (R 2 ), standard error of the estimate (SEE) and Akaike information criterion (AIC) were reported for each model. The higher the R 2 and the lower the SEE, the better the predictive model. The lower the AIC value, the better the quality of the model. The AIC value reflects both the goodness of fit and the "efficiency" (parsimony) of a model for a given number of predictor variables included in the model. An efficient or parsimonious model accomplishes a desired level of prediction with as few predictor variables as possible. The accuracy of the LMMs was tested using the leave-one-out (LOO) procedure [START_REF] Staudenmayer | Statistical considerations in the analysis of accelerometry-based activity monitor data[END_REF] and was reported as the average root-mean-square error (RMSE): the lower the RMSE, the higher the accuracy. Statistical modeling was performed using R software (R Foundation for Statistical Computing, Vienna, Austria, version 3.2.4). The second step of our statistical analysis was to crossvalidate available published equations for EE (kcal min -1 ) and MET on our own EE (kcal min -1 ) and MET data, respectively. These commonly used speed/grade-based, accelerometry-based, and HR-based equations are shown in SM #2. The cross-validation procedure was performed to quantify any potential "equation effect", that is, a change in the accuracy of the EE estimate according to the prediction equation used. MET values were computed by dividing the absolute gross VO 2 by the body mass plus equipment mass and then by 3.5. The cross-validation procedure was performed separately for the level, uphill, and downhill outdoor walking periods, when appropriate. RMSE, bias (95% confidence interval), limits of agreement and standard deviation of the differences (SD diff ) were computed. The prediction equations were ranked according to the RMSE.

Results

The participant characteristics are shown in Table 1. The medians [interquartile ranges (IQRs) = 25th-75th percentiles] of the weather parameters during outdoor walking periods were 17. All GPS data were correctly recorded, except for the data collected for one participant during the graded outdoor walking session on a 3.4% mean grade (due to loss of the GPS satellite signal). Regarding the HR data, 10% (9/90), 7% (13/180), and 13% (24/180) of the values were lost during the level, uphill, and downhill walking periods, respectively, due to a malfunction of the HR sensor. Therefore, 8% (22/270) and 12% (33/270) of the HR values were missing from tests of the level/uphill models and the level/downhill models that used HR data, respectively. All wGT3X+ data were correctly recorded.

The medians [IQR] for the EE, accelerometer counts, and HRrelated parameters measured during the last three minutes of the walking periods are shown in SM #3. Throughout the range of tested grades, the EE and HR parameters increased exponentially, whereas the accelerometer counts followed a U-shape curve. Notes: The models shown were the most accurate models (i.e., with the lowest RMSE) obtained in their respective categories, which were defined by both the number of parameters combined and the type of parameters used (GPS, ACC, or HR). Covariates appear in italics. The models were ranked according to the RMSE value. Actual (speed & grade) , model using the actual speed and grade; ACC (VA) , model using accelerometry and the vertical axis; ACC (VM) , model using accelerometry and the vector magnitude; AIC, Akaike information criterion; DI, discomfort index; Gen, gender; GPS (corrected) , model using both the GPS speed and corrected grade, with the grade calculated using GPS altitude data and corrected with map projection software; GPS (uncorrected) , model using both the GPS speed and uncorrected grade; HR (aR) , heart rate above the resting heart rate; HR (res) , heart rate reserve; Ht, height; M, body mass plus equipment mass; R 2 , R-squared for linear mixed model; RMSE, average root-mean-square error obtained with the leave-one-out methodology; SEE, standard error of estimate. All equations are available in SM #4.

All the tested models and their related equations and statistical outcomes are shown in SM #4. Summaries of the results obtained for the LMMs using the level walking periods, both the level and uphill walking periods, or both the level and downhill walking periods are shown in SM #5, Tables 2 and3, respectively. Except for the models using GPS data only (for which both of the models based on uncorrected and corrected grades are shown), these tables show only the models that reached the lowest RMSE in their respective categories, as defined by both the number of methods combined (1, 2, or 3) and the type of parameters used (GPS-, accelerometry-, and HR-related parameters).

For level walking, when each of the methods was used alone without covariates, higher R 2 values were obtained from the GPS models (SM #5, R 2 = 0.75-0.76), although the error in EE estimation was quite similar when using either GPS speed and grade (RMSE = 0.90-0.91 kcal min -1 ) or accelerometer VA counts (RMSE = 0.89 kcal min -1 ). When covariates were added to the single method-based models, the RMSE for accelerometry was slightly lower than for GPS, but the RMSE values for both of these models remained in a narrow range (0.63-0.71 kcal min -1 ). When HR monitoring was used, the RMSE was clearly increased compared to that with GPS or accelerometry, regardless of which HR-related parameter was used (RMSE ≥1.20 kcal min -1 without covariates and ≥0.99 kcal min -1 with covariates). Compared with GPS and accelerometry alone, no combination of methods produced a lower RMSE.

Table 2 shows the results for the LMMs tested using both the level and uphill outdoor walking periods. First, when the single method-based models ("No combination") were tested without covariates, the lowest RMSE was achieved using the actual speed and grade. The RMSE for the GPS-based models was lower than for the accelerometry-based models (by at least 0.40 kcal min -1 using corrected GPS grade) and HR-based models (by at least 0.55 kcal min -1 using corrected GPS grade). The RMSE for the GPSbased models was close to that obtained using the actual speed and grade. A slightly lower RMSE was achieved when using the corrected GPS grade than when using the uncorrected GPS grade (decrease of 0.19 kcal min -1 without covariates). Second, although combining GPS and HR, or combining the three tested methods, produced slightly higher R 2 coefficients and lower AIC than GPS alone, no combination of methods reduced the RMSE achieved by the most accurate single GPS-based model. Combining accelerometry and HR produced a lower RMSE than accelerometry or HR alone (RMSE decreased by 0.10 and 0.25 kcal min -1 for accelerometry and HR, respectively, without covariates).

Table 3 shows the results obtained for the LMMs tested using both the level and downhill outdoor walking periods. Overall, the ranking of the models was similar to that using both the level and uphill outdoor walking periods. Of note, both the RMSE values and the variance explained were reduced (e.g., all R 2 < 0.75) when models were tested using the downhill (Table 3) compared to the uphill walking periods (Table 2).

Mass was a significant covariate for most models. Height, gender and the discomfort index were also significant covariates in several models. As shown in SM #5, Tables 2 and3, the addition of significant covariates improved nearly all the models (increased R 2 and decreased AIC and RMSE), regardless of (i) the walking periods used (level, level/uphill, or level/downhill), (ii) the type of parameters used (GPS, accelerometry, or HR), and (iii) the number of methods combined (1, 2, or 3). However, the addition of a covariate did not markedly change the ranking of the models presented above.

The results obtained from the cross-validation of other EE and MET prediction equations for level walking are presented in SM #6. Regarding the EE predictions, the unique GPS-based equation tested (Pandolf et al. [START_REF] Pandolf | Predicting energy expenditure with loads while standing or walking very slowly[END_REF] ; SM #2) was less accurate than the best accelerometry-based equation (Brooks et al. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] ; SM #2), The models shown were the most accurate models (i.e., with the lowest RMSE) obtained in their respective categories, which were defined by both the number of parameters combined and the type of parameters used (GPS, ACC, or HR). Covariates appear in italics. The models were ranked according to the RMSE value. Actual (speed & grade) , model using the actual speed and grade; ACC (VA) , model using accelerometry and the vertical axis; ACC (VM) , model using accelerometry and the vector magnitude; AIC, Akaike information criterion; DI, discomfort index; GPS (corrected) , model using both the GPS speed and corrected grade, with the grade calculated using GPS altitude data and corrected with map projection software; GPS (uncorrected) , model using both the GPS speed and uncorrected grade; Ht, height; HR (raw) , raw heart rate; HR (aR) , heart rate above the resting heart rate; M, body mass plus equipment mass; R 2 , R-squared for linear mixed model; RMSE, average root-mean-square error obtained with the leave-one-out methodology; SEE, standard error of estimate. All equations are available in SM #4.

ARTICLE IN PRESS

with an RMSE of 1.23 kcal min -1 using uncorrected GPS grade (vs. RMSE = 1.00 kcal min -1 for the Brooks et al. equation, SM #2). Regarding MET predictions, the best GPS-based equation and the best accelerometry-based equation produced similar RMSE values (0.50 and 0.52 MET, respectively). The equation by Rue and Kramer (for the reference, see SM #2) led to the highest error in the estimation of MET (RMSE = 1.95 MET using corrected GPS grade) among the available GPS-based equations. Previously published HR-based equations were associated with higher RMSEs both for EE (RMSE ≥1.80 kcal min -1 ) and METs (RMSE ≥1.39 METs) than for most of the GPS-based or accelerometry-based equations.

Regarding uphill outdoor walking (SM #7), the GPS-based equations clearly allowed more accurate estimations of EE (RMSE range = 1.60-2.04 kcal min -1 ) and MET (RMSE range = 1.18-2.78 METs) than the accelerometry-(RMSE range = 2.34-3.74 kcal min -1 for EE and 2.12-3.05 for METs) or HR-based equations (RMSE range = 1.62-2.88 kcal min -1 for EE and 1.38-2.53 for METs). Compared to the best accelerometry-based equations, the estimation of EE and METs was more accurate with some of the available HR-based equations (SM #7). The trend obtained for downhill outdoor walking (SM #8) was quite different: the highest accuracy for estimating EE (RMSE = 1.31 kcal min -1 ) or METs (RMSE = 1.22 METs) was achieved using the accelerometry-based equations by Brooks et al. (SM #2), whereas the unique tested GPS-based equation by Rue and Kramer (SM #2) led to lower accuracy (RMSE = 1.74 kcal min -1 and 1.57 METS, using corrected GPS grade) than the best HR-based equations (RMSE = 1.63 kcal min -1 for EE and 1.23 for METs).

Discussion

The present study aimed to determine the best method and the most valuable combination of methods among GPS, accelerometry, and HR monitoring for estimating EE during outdoor walking. Our analyses led to different conclusions for studies of outdoor walking involving (i) level walking only or (ii) both level walking and walking under various grade conditions.

The LMMs and cross-validation results showed that GPS is as valuable as accelerometry and more valuable than HR monitoring for estimating EE during level outdoor walking. Interestingly, as shown by the LMMs, no combination of methods increased the accuracy of the EE estimates obtained for GPS or accelerometry alone.

Our finding of equivalence between GPS and accelerometry for estimating level walking EE challenges the use of accelerometry as the preferred method for measuring PA and EE. It has been claimed that from a theoretical point of view, acceleration is more directly reflective of the energy cost than speed. [START_REF] Chen | The technology of accelerometry-based activity monitors: current and future[END_REF] However, this point of view is not supported by the literature on walking. Indeed, several studies have shown that speed is an important predictor of EE during walking, [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] and only the study by Brooks et al. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] compared the use of speed and acceleration for estimating walking EE in the same sample of subjects. Of note, the authors [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] reported that walking speed was a better predictor of EE (prediction equations with higher R 2 coefficients) than accelerometer counts (VA) during level outdoor walking.

The differences between the conclusions drawn by Brooks et al. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] (superiority of speed on acceleration) and our findings (equivalence between GPS and accelerometry) are likely to be due to the statistical procedures implemented. Brooks et al. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] used the R 2 coefficient and did not cross-validate their equations using the LOO procedure, as we did in the present study. As shown in SM #5, although higher R 2 coefficient could be obtained for the GPSbased models vs. the accelerometry-based models, the same errors (RMSE) in EE estimation were finally obtained for both models following the LOO cross-validation. The error found for HR monitoring seems consistent with reports that showed that HR fails to have a linear relationship with EE at low intensities. [START_REF] Achten | Heart rate monitoring: applications and limitations[END_REF] Because of methodological considerations, the walking speeds tested in the present study were in the lower range of human level walking speeds (2-5 km h -1 ). Since cardiorespiratory fitness influences the relationship between HR and EE, [START_REF] Strath | Evaluation of heart rate as a method for assessing moderate intensity physical activity[END_REF] the HR-EE relationship obtained across the range of walking speeds and grades tested in the present study may have been even more flattened for the fittest subjects. As there were different levels of VO 2 peak among the study's participants, it could be assumed that adding VO 2 peak as covariate in the HR-based models would have increased their accuracy for predicting walking EE. It was indeed the case, but the accuracy remained inferior to that obtained with the parameters related to the other methods (data not shown). Importantly, HR is also influenced by factors other than PA intensity. [START_REF] Achten | Heart rate monitoring: applications and limitations[END_REF] In this way, the significant effect of the discomfort index on EE observed in the present study underlines a possible detrimental influence of environmental conditions on the prediction of EE when using HR. Of note, contrary to the results of most of laboratory studies, [START_REF] Fudge | Estimation of oxygen uptake during fast running using accelerometry and heart rate[END_REF][START_REF] Corder | Comparison of PAEE from combined and separate heart rate and movement models in children[END_REF] the accuracy of EE estimates during level outdoor walking was not increased by combining HR and accelerometry compared to using accelerometry alone.

The cross-validation results regarding the estimation of outdoor level walking EE/METs (SM #6) underline the major impact of the equations used. Future studies should, however, cross-validate our LMM-derived equations in other samples and compare them to these available published equations.

The LMMs clearly show that GPS offers more accurate estimates of EE for both level and graded (uphill and downhill) outdoor walking than accelerometry or HR monitoring. Further, it appears that no combination of methods provides a better estimation of EE than GPS alone. To the best of our knowledge, this finding is unique and confirms the value of very popular equations [START_REF]ACSM's Guidelines for Exercise Testing and Prescription[END_REF][START_REF] Pandolf | Predicting energy expenditure with loads while standing or walking very slowly[END_REF] developed in studies demonstrating the importance of speed and grade as two powerful predictors of walking EE (see SM #2 and de Müllenheim et al. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] ). The previously mentioned drawbacks of accelerometry during graded walking explain the lower accuracy obtained in the prediction of EE. [START_REF] Terrier | Can accelerometry accurately predict the energy cost of uphill/downhill walking?[END_REF] However, as suggested by our LMMs, if the GPS method is not available, combining HR and accelerometer counts could be better than using either method alone (except for both level and downhill walking). This last conclusion is in accordance with previous laboratory studies that combined HR and accelerometry during treadmill walking. [START_REF] Brage | Hierarchy of individual calibration levels for heart rate and accelerometry to measure physical activity[END_REF] When testing models using GPS data, the use of corrected grades from map projection software was particularly valuable for increasing the accuracy of the prediction of walking EE, particularly for both the level and uphill conditions (Table 2), which is consistent with a previous study. [START_REF] De Mullenheim | Predicting metabolic rate during level and uphill outdoor walking using a low-cost GPS receiver[END_REF] Although the prediction of walking EE using GPS for both level and downhill conditions was not affected by the use of uncorrected grades (Table 3), based on previous data, [START_REF] De Müllenheim | Accuracy of a low-cost global positioning system receiver for estimating grade during outdoor walking[END_REF] the use of corrected grades, if possible, is preferable.

Again, the cross-validation results (SM #7, SM #8) highlight the major impact of the equation used for the prediction of EE and METs during graded outdoor walking. For instance, when using the GPS method to estimate METs during outdoor uphill walking, the ACSM equation [START_REF]ACSM's Guidelines for Exercise Testing and Prescription[END_REF] seems to be the most suitable (lowest prediction error). In contrast, the equation provided by Rue and Kramer (SM #2) was highly inaccurate. The use of this last equation could explain why the GPS method did not provide a better EE prediction than accelerometry when considering the downhill walking periods for the cross-validation.

The finding that mass (mostly) and gender were significant covariates for several models is in accordance with previous studies. [START_REF] Brooks | Predicting walking METs and energy expenditure from speed or accelerometry[END_REF] However, to our knowledge, the present study is the first to show that the discomfort index could be a significant covariate in several models when estimating outdoor walking EE. This finding is of importance because outdoor walking can occur under very different atmospheric conditions on a day-to-day basis. However, the discomfort index does not take into account wind speed, and the possibility that high wind speed values might impact walking EE cannot be excluded. [START_REF] Pugh | The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces[END_REF] In the present study, adding wind speed as a covariate to the models had no effect on the prediction of walking EE (data not shown).

The R 2 coefficients obtained for the models tested using the downhill walking periods were lower than those obtained for the models tested using the uphill walking periods. This result may be partly explained by (i) the loss of linearity between the EE of walking and the grade when the grade is below 0.0% 23 and (ii) the lower range of measured (actual) EE values during downhill walking than during uphill walking (SM #3).

Although the RMSE values were decreased when testing the "level/downhill" models (Table 3) compared to those when testing the "level/uphill" models (Table 2), the median value of the actual EE data used for testing the "level/downhill" models was also decreased. Thus, when the RMSE values were normalized to the median of our EE data, the RMSE values for both conditions were within the same range (data not shown).

Our results regarding the GPS method might not extend to environments that have higher levels of obstruction than those encountered in the present study. However, finding the same experimental conditions as the present study in locations with high levels of obstruction would be almost impossible. Environmental obstruction should have only a moderate impact on the final estimation of EE during outdoor walking if the GPS altitude is corrected via map projection software, as proposed here. This issue, however, deserves additional research, particularly in view of free-living and prolonged measurements of walking EE.

The accelerometry-based equations that were cross-validated in the present study were originally validated using count data obtained from an older ActiGraph TM accelerometer (SM #2), which may have influenced the EE estimation. Furthermore, equations developed using accelerometer counts remain dependent on the monitor used because activity counts cannot be directly compared across monitors.

Finally, additional studies should be conducted to develop population-specific equations, which was not the aim of the present study. Furthermore, our equations developed herein should be cross-validated in other samples, particularly for level/downhill outdoor walking conditions since prediction equations for EE are lacking.

Conclusions

This study is the first to determine the best method among GPS, accelerometry and HR for estimating walking EE during level and graded (uphill and downhill) outdoor walking. This work involved testing LMMs using data obtained from participants who walked on both positive and negative grades at different walking speeds. Moreover, for the first time, both speed/grade (GPS)-, accelerometry-, and HR-based published equations were crossvalidated under these conditions.

Practical implications

• When the estimation of outdoor level walking EE is planned during a session, (i) either GPS or accelerometry can be used with similar accuracy; (ii) using HR monitoring alone is not recommended; and (iii) combining two or three methods adds no value. • When the estimation of outdoor walking EE is planned during a session of both level walking and various grades, (i) GPS should be preferred; (ii) the corrected GPS grade obtained from map soft-

JSAMS- 1723 ;

 1723 No. of Pages 7 2 P.-Y. de Müllenheim et al. / Journal of Science and Medicine in Sport xxx (2017) xxx-xxx

  5 • C [9.1-20.0], 54.0% [34.0-65.4], 11 km h -1 [2.0-16.0], and 1019.3 hPa [999.3-1023.9] for temperature, RH, wind speed, and barometric pressure, respectively.

  P.-Y. de Müllenheim et al. / Journal of Science and Medicine in Sport xxx (2017) xxx-xxx

Table 1

 1 Participants' characteristics.

	Variable	Women (n = 15)	Men (n = 15)	All (n = 30)
	Age, yr Height, cm Body mass, kg BMI, kg m -2 Body fat, % RMR, ml min -1 kg -1 VO 2peak , ml min -1 kg -1	22.2 ± 1.3 169 ± 5 62.2 ± 8.0 21.9 ± 2.2 17.8 ± 3.0 4.1 ± 0.5 48.1 ± 5.0	21.9 ± 1.6 176 ± 5 71.9 ± 8.1 23.2 ± 2.6 10.1 ± 4.5 3.8 ± 0.9 56.4 ± 7.7	22.0 ± 1.4 172 ± 6 67.1 ± 9.3 22.5 ± 2.4 14.0 ± 5.4 3.9 ± 0.7 52.1 ± 7.6
	Note: Values are the means ± standard deviation. All participants were Caucasian. BMI, body mass index; n, number of participants; RMR, resting metabolic rate;
	VO 2peak , peak oxygen uptake.

Table 2

 2 P.-Y. de Müllenheim et al. / Journal of Science and Medicine in Sport xxx (2017) xxx-xxx Best models for predicting energy expenditure (kcal min -1 ) during both level and uphill outdoor walking.

	Model	R 2	AIC	SEE	RMSE
	Without covariates
	No combination
	Actual (speed & grade)	0.91	586.74	1.22	1.25
	GPS (corrected)	0.87	735.96	1.31	1.34
	GPS (uncorrected)	0.73	867.18	1.49	1.53
	ACC (VM)	0.58	989.67	1.71	1.74
	HR (aR)	0.59	855.62	1.84	1.89
	Combination of 2 methods
	GPS (corrected) + ACC (VM)	0.87	740.14	1.30	1.34
	GPS (corrected) + HR (aR)	0.90	637.67	1.35	1.40
	ACC (VM) + HR (aR)	0.65	814.38	1.58	1.64
	Combination of 3 methods
	GPS (corrected) + ACC (VM) + HR (aR)	0.90	644.49	1.34	1.40
	With covariates
	No combination
	Actual (speed & grade) + DI + M	0.93	560.11	0.98	1.02
	GPS (corrected) + M	0.87	723.13	1.04	1.08
	GPS (uncorrected) + M	0.80	848.00	1.24	1.27
	ACC (VM) + M	0.67	974.69	1.50	1.53
	HR (res) + Gen	0.67	840.28	1.52	1.58
	Combination of 2 methods
	GPS (corrected) + ACC (VM) + M	0.87	727.87	1.04	1.07
	GPS (corrected) + HR (aR) + DI + Ht	0.90	630.44	1.20	1.27
	ACC (VM) + HR (res) + Gen + M	0.76	795.08	1.25	1.32
	Combination of 3 methods
	GPS (corrected) + ACC (VA) + HR (aR) + DI + Ht	0.89	637.15	1.18	1.26

Table 3

 3 P.-Y. de Müllenheim et al. / Journal of Science and Medicine in Sport xxx (2017) xxx-xxx 5 Best models for predicting energy expenditure (kcal min -1 ) during both level and downhill outdoor walking.

	G Model
	JSAMS-1723; No. of Pages 7
	Model	R 2	AIC	SEE	RMSE
	Without covariates
	No combination
	Actual (speed & grade)	0.68	304.87	0.81	0.84
	GPS (uncorrected)	0.67	352.31	0.82	0.84
	GPS (corrected)	0.67	315.78	0.82	0.85
	ACC (VM)	0.16	686.09	1.00	1.02
	HR (aR)	0.29	577.83	1.07	1.09
	Combination of 2 methods
	GPS (corrected) + ACC (VM)	0.68	324.58	0.82	0.84
	GPS (corrected) + HR (raw)	0.71	292.16	0.83	0.86
	ACC (VM) + HR (aR)	0.29	573.93	1.01	1.04
	Combination of 3 methods
	GPS (corrected) + ACC (VM) + HR (raw)	0.71	300.40	0.82	0.85
	With covariates
	No combination
	GPS (uncorrected) + DI + M	0.71	325.55	0.66	0.68
	Actual (speed & grade) + DI + M	0.74	280.39	0.66	0.69
	GPS (corrected) + DI + M	0.72	281.66	0.68	0.71
	ACC (VM) + M	0.38	670.97	0.86	0.88
	HR (aR) + Ht + M	0.49	568.56	0.87	0.93
	Combination of 2 methods
	GPS (uncorrected) + ACC (VA) + DI + M	0.71	322.07	0.67	0.69
	GPS (uncorrected) + HR (raw) + DI + M	0.71	307.45	0.67	0.71
	ACC (VM) + HR (aR) + M + Ht	0.51	562.41	0.82	0.87
	Combination of 3 methods
	GPS (uncorrected) + ACC (VA) + HR (raw) + DI + M	0.71	306.16	0.68	0.72
	Note:

Acknowledgments

The authors are indebted to Nathan Caron for his help during the experiments. The authors thank Dr. Antoine Bruneau and Pr. Pierre Abraham for inclusion visits and their useful suggestions regarding the design of the Acti-GPS project. The authors also thank Antoine Gaudry from the Breizh Géo iMmo company for topographical measurements. Marie Gernigon is currently working at the CIAMS, univ. Paris-Saclay (Paris Sud), Orsay, France.

The Acti-GPS project was promoted by the University Hospital of Angers (NCT01805219) and was funded by the Genesia Foundation. Pierre-Yves de Müllenheim received a PhD scholarship from the "École normale supérieure de Cachan-Antenne de Bretagne" (CDSN). Ségolène Chaudru received a PhD scholarship from the Region of Brittany, France (ARED).

ARTICLE IN PRESS

ARTICLE IN PRESS


Guy Lemperiere

Keith R Day

Yves Petit-Berghem

Nicolas Robinet

Pérrine Portier

Simon R Leather

Damien Marage
email: marage.damien@gmail.com

Interannual population dynamics of the green spruce aphid Elatobium abietinum (Walker) in France

Keywords: Elatobium abietinum, Picea sitchensis, Population Dynamics, Forest Management, Biodiversity, Climate Elatobium abietinum, Picea sitchensis, Population time series, Climate, Forest management, Environment

 Context The hypothesis that similar processes govern interannual dynamics of green spruce aphid in the UK and France, is generally supported by the application of a general discrete model. A simple model based on relatively few parameters was able to closely characterise interannual population dynamics from completely independent aerial and arboreal samples of aphids. Long term field population estimates of the green spruce aphid Elatobium abietinum (Walker) in France have provided the

 Methods The model uses climate variables and aphid population data from regular samples in the two regions that were investigated. A general discrete model was used to predict aphid population densities.

 Results

The model performed well in tracking the interannual patterns of population but was less likely to predict absolute population density.

 Conclusion To improve predictions, further account would need to be taken of additional site-specific climate variables and the strength of overcompensating density dependence. Nevertheless it is clear that broadly similar processes are at work in the population dynamics of this insect across its biogeographical range.

| Introduction

The green spruce aphid Elatobium abietinum Walker 1949 (Homoptera: Aphididae) is one of the seven species of the genus Elatobium Mordvilko 1914 which belongs to the subfamily Aphidinae and tribe Macrosiphini [START_REF] Remaudière | Catalogue of the world's Aphididae (Homoptera Aphidoidea)[END_REF]. Three of those species are conifer feeders [START_REF] Blackman | Aphids on the world's trees[END_REF]. Of these, E. abietinum is the major pest of Sitka spruce Picea sitchensis (Bong.) Carr. throughout northern and western Europe where this tree species has been abundantly planted in reforestation areas since the early 1950s [START_REF] Hanson | The green spruce aphid, Neomyzaphis abietina Walker[END_REF][START_REF] Carter | Impact of Green Spruce Aphid on growth: can a tree forget its past?[END_REF][START_REF] Parry | A study of the relationship between defoliation of Sitka spruce and population levels of Elatobium abietinum (Walker)[END_REF][START_REF] Day | Systematic differences in the population density of green spruce Aphid, Elatobium abietinum in a provenance trial of Sitka spruce, Picea sitchensis[END_REF]Day & Crute, 1990) (Fig. 1). This sap-feeding insect was first described feeding on Norway spruce Picea abies (L.) Karst. which might be the original and normal host of E. abietinum. This host tree can tolerate heavy infestations without suffering severe defoliation and shows less reaction to its presence than does Sitka spruce [START_REF] Carter | The Green Spuce Aphid and Sitka Spruce Provenances in Britain[END_REF][START_REF] Day | Influence of the green spruce aphid on defoliation and radial stem growth of Sitka spruce[END_REF]. Norway spruce appears to have had time to evolve resistance mechanisms to the aphid forcing the insect to switch to a more susceptible host-plant.

The life cycle of the insect (Fig. 2) is dependent on the local climate and it is admitted that under maritime climates like in the UK but also in Normandy and Brittany, western France, anholocyclic populations are governed by low winter temperatures [START_REF] Powell | Effects of temperature on overwintering populations of the green spruce aphid Elatobium abietinum[END_REF] while in more continental regions like the Limousin (France) and the Massif Central (France) or in Denmark (Harding & Carter, 1997) holocyclic populations overwinter as dormant eggs. In Brittany and Normandy, the aphids overwinter as wingless viviparous females but severe frost in these regions will result in high aphid mortality.

Parthenogenetic reproduction can continue at low temperatures and aphids are present in large numbers at the end of winter when temperatures become more favourable for the insect [START_REF] Eds | Population responses of a conifer-dwelling aphid, to seasonal changes in its host[END_REF]). There is a period of maximum increase in the number of aphids during the spring damaging period when the needles contain a high concentration of aminoacids which is required by the insect [START_REF] Carter | The Green Spuce Aphid and Sitka Spruce Provenances in Britain[END_REF]. Peak density is reached in May. After bud flush, nutrients are moved to the newly formed needles which remain unattacked for up to 4 months after flushing. At the same time, in late spring, a winged viviparous female form (alatae) disperses and populations collapse until late summer, early autumn when the tree produces hard terminal buds and is in a dormant shoot growth condition. Simultaneously, the aphid starts increasing in numbers (Day op.cit.).

Elatobium abietinum only feeds on mature needles causing chlorotic bands while current-year needles deter aphid feeding (Carter & Nichols, op.cit.). These old needles rapidly become yellow and are prematurely abscissed. Trees that have suffered heavy damage have thin crowns and reduced annual rings. The aphid is especially damaging in winter on dormant trees. Substantial needle losses can cause a reduction in growth and hence timber yield which can be affected for two or three years after the attack [START_REF] Straw | Interactions between green spruce aphid (Elatobium Abietinum (Walker)) and Norway and Sitka spruce under high and low nutrient conditions[END_REF].

With the economic consequences of green spruce aphid population growth in mind, a numerical model of long-term trends in peak population has been developed using relatively few parameters and incorporating knowledge of endogenous and exogenous factors influencing population dynamics [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF]. This initiative was particularly promising because it robustly described field data derived not only from aphids feeding on trees in Northern Ireland but also from alate aphids in suction traps from Scotland. The potential for describing geographically independent data sets suggested that this model might perform equally well elsewhere in Europe.

In this investigation we examine a time series obtained over 12 years in two French forests. We hypothesise that the essential features of spruce aphid interannual population dynamics, endogenous density dependent feedback and exogenous weather factors, will play out in a similar way wherever anholocyclic populations of the aphids are found on Sitka

| Host-plant an aphid population data

A cartographic study of Sitka spruce plantations over the two regions has been carried using the IFN data set (Inventaire Forestier National, 1999) and regional vegetation maps (CORINE Land Cover France, 2009) and included an extensive field survey of Sitka spruce plantations.

The aphid populations were assessed using the protocol as described below.

The aphid population time series was derived from estimates of aphid abundance on spruce needles at the forest of Monnaye (Normandy) (02°08 'W, 48°51'N, mean elevation 280 m) and forest of Malaunay (Brittany) (03°05 'W, 48°54' N, mean elevation 135m).

Both forests are privately owned and managed by private forest experts. The forest of Monnaye is located in the department of the Orne and covers 620.3 ha including 64 ha of Sitka spruce. The forest of Malaunay is located in the Côtes d'Armor on the north coast of Brittany and covers 672 ha including 296 ha of Sitka spruce.

Four forests compartments of different ages (forest plots planted in 1954 and 1967 in

Monnaye; forest planted in 1965 and 1990 in Malaunay) have been selected in the two forests and sampled at regular intervals every two weeks from 1997 up to 1999 and four times per year from 2000 until 2008 providing a representation of year-to-year fluctuations in abundance (Day & Crute, 1990). The abundance of aphid populations within and between trees was assessed using a transect method called Central Point Quarter Method (CPQM) [START_REF] Dahdouh-Guebas | Empirical estimate of the reliability of the use of the point-centred quarter method (pcqm): Solutions to ambiguous field situations and description of the pcqm+ protocol[END_REF] in the four forests plots that were visited. 80 trees per random transect were sampled using the modified plotless technique CPQM. This plot-less method involves measuring distances for a random sample of trees, typically along a transect, and recording the characteristics of interest for this sample. The advantage to using plot-less methods rather than standard plot-based techniques is that they tend to be more efficient. Plot- Many authors tested and stated that CPQM will highly recommended and used in forest inventory [START_REF] Eds | The use of distance measure in phytosociological sampling[END_REF][START_REF] Beasom | A comparison of four distance sampling techniques in south texas live oak mottes[END_REF]. For each tree, five branches were collected in a total of 400 samples per forest plot and date.

Population estimates were expressed as mean total aphids per 100 needles and sample shoot in order to standardize the results with existing protocols [START_REF] Day | Systematic differences in the population density of green spruce Aphid, Elatobium abietinum in a provenance trial of Sitka spruce, Picea sitchensis[END_REF][START_REF] Day | Population growth and spatial patterns of spruce aphids (Elatobium abietinum) on individual trees[END_REF].

In particular, the samples capture the point at which the aphid population reaches its annual maximum, and this has been used to represent annual populations in the analysis.

| Climate variables

The selection of climate variables and metrics was based on their known relationship to aphid population processes. The green spruce aphid passes the entire year anholocyclicly as nymph or adult and as such its rate of development, and that of its populations are at least partly temperature dependent. A decline in availability of plant sap nutrients following spruce budburst means that aphids can benefit most from higher temperature prior to this point.

Thermal time (phys) accumulated through the months prior to budburst reflected the ability of aphids to develop and reproduce, and hence was likely to be linked to population growth. On the other hand, spruce aphids are susceptible to subzero temperatures, despite their ability to supercool, and a metric reflecting this was incorporated in earlier versions of the population model. However, when tested with UK field data no signal of demographic effects from this metric was found in the model as winters in the areas from which UK data was derived were insufficiently severe. Another low temperature metric (coma) was derived to account for aphid mortality by starvation or chill coma experienced after prolonged periods when temperature is below the aphid developmental threshold. These two climate variables became the most successful metrics in generating a model applied to spatially heterogeneous independent data [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF].

| Model description and application

| General description and background

We employed a general discrete model of population dynamics [START_REF] Turchin | Complex dynamics in ecological time series[END_REF] where interannual per capita growth rate = R t =ln(N t / N t-1 ) where N t = N t-1 x e R (with N t = aphid abundance in late spring of year t). We also hypothesized that there would be negative feedback (density-dependence) on aphid abundance i.e., R t =f(N t ) + Ɛ t , with Ɛ representing sampling error in density estimates plus exogenous (density-independent) effects on aphid population dynamics. Thus we evaluated alternative models for climatic effects on aphid populations by examining relations between Ɛ and specific climate parameters.

Alternative models for climatic effects were compared with respect to three criteria:

(1) the pattern with respect to climate should be consistent with theoretical expectations (e.g., extreme winter cold is expected to yield lower per capita growth rates); (2) a model that includes one or more climatic drivers should be defensibly favoured over simpler alternative models based upon information theory; (3) and we favoured models in which the regression coefficients that were retained were statistically distinguishable from 0. Our rationale for the latter criterion was that most of the statistical null hypotheses were nontrivial (e.g. spring rain, a variable tested but discarded, might or might not matter to aphid populations). We began analyses with shoot-based aphid abundance data collected over a period of 10 years in Northern Ireland, identified the best models for this data set, tested those models against independent 37 year time series data on aerial abundance from Scotland and then settled on a single model, as follows, that could reasonably be applied to both situations. Population densities of aphids were predicted using this model for each year and forest area (Normandy and Brittany).

| Model parameters phys

Physiological time [START_REF] Campbell | Temperature requirements of some aphids and their parasites[END_REF]Day, 1984a;[START_REF] Fisher | Role of photoperiod in the timing of dispersal in the green spruce aphid Elatobium abietinum[END_REF]Crute & Day, 1990;Day & Crute, op.cit.;Day et al., 2004, op.cit.) is the thermal time accumulated from 1 January to the approximate date of budburst respectively 20 April for Brittany and 30 April for Normandy. It has been assumed that growth and reproduction are temperature dependent [START_REF] Eds | Population responses of a conifer-dwelling aphid, to seasonal changes in its host[END_REF]) and that 4°C is the threshold for aphid development. Phys expressed in degree days is then a function that accumulates degree days above 4°C over the period which is most favourable for aphid development. In the development of the model, values of physiological time were adjusted for each year relative to the site average to yield the metric phys. coma Prefreeze mortality is known to be potentially important for spruce aphids living in maritime climates [START_REF] Powell | Effects of temperature on overwintering populations of the green spruce aphid Elatobium abietinum[END_REF][START_REF] Bale | Low temperature mortality of the peachpotato aphid Myzus persicae[END_REF][START_REF] Dixon | Aphid ecology: an optimization approach[END_REF]. To account for this the number of chill days with a daily mean temperature ≤5 o C from 1 October to budburst was In Normandy, the forest of Monnaye belongs to the Seine biogeographical region. The average temperature of 10°C is lower and the moisture greater than in the neighbouring departments. The west winds are the most frequent and the rainfall, distributed over 160 up to 180 days annually, amounts to nearly 100 cm, or half as much again as the average for France. Consequently, aphids experience cold winters and low temperatures which affect the population dynamics by reducing the growth in winter [START_REF] Carter | Winter temperatures and survival of the green spruce aphid, Elatobium abietinum (Walker)[END_REF]Day et al., 2009, op.cit.).

Aphid physiological time (phys) was variable (between 290.5 and 606.6 day°C) as a result of cold or mild winter and spring weather. Warm weather with a large accumulation of physiological time as observed in 1998,1999,2002,2003 and 2007 allowed a rapid aphid recruitment and population growth. Periods showing a number of five consecutive chill days with a daily mean temperature ≤5°C from 1 October to budburst (coma) had a negative effect on population growth [START_REF] Powell | Effects of temperature on overwintering populations of the green spruce aphid Elatobium abietinum[END_REF]Day & Crute, 1990) as observed in 1997, 2005 and 2006. The two metrics phys and coma were negatively correlated (r= -0.65) for this site.

Aphid populations remained relatively low and below a threshold where visible damage to foliage would be widespread.

The forest of Malaunay, on the north coast of Brittany is influenced by the Gulf Stream and by constant west winds bringing wet air from the Atlantic Ocean. The resulting moderate oceanic climate is characterized by mild winters and lime summers. An average temperature of 12°C is observed on the coast and rarely come under zero while an average temperature of 10°C is recorded inland. Relative humidity remains high over the year. The west wind blowing practically constantly brings wet air from the Atlantic Ocean that it rains relatively often even if rain quantities are not particularly important. Aphid physiological time (phys) was variable (between 280 and 508.9 day°C) as a result of cold or mild winter and spring weather. Warm weather with a large accumulation of physiological time as observed in 1997, 1999, 2001, 2007 and 2008 allowed a rapid aphid recruitment and population growth (Fig. 3a andb). As seen at Monnaye, periods showing a number of five consecutive chill days with a daily mean temperature ≤5°C from 1 October to budburst (coma) had a negative effect on population growth [START_REF] Powell | Effects of temperature on overwintering populations of the green spruce aphid Elatobium abietinum[END_REF]Day & Crute, 1990) as observed in 1999, 2005[START_REF] Dahdouh-Guebas | Empirical estimate of the reliability of the use of the point-centred quarter method (pcqm): Solutions to ambiguous field situations and description of the pcqm+ protocol[END_REF]. The two metrics phys and coma were negatively correlated (r= -0.65) for this site.

Climate metrics that were used in the model consistently explained the variations in field data [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF].

The annual populations of aphids predicted by the model and informed by local meteorological data, were not close to observed values in absolute terms but the predicted patterns of change from year to year were very similar to those observed (Fig. 4).

Endogenous, overcompensated regulation is strongly signaled by the "see-saw" fluctuation of observed populations, something that is captured well in the model. While populations in Normandy remained relatively low, and below a threshold where visible damage to foliage would be widespread, populations in Brittany tended to fluctuate around a higher equilibrium density and occasionally (4 out of 12 years) rose to a level at which needle loss would be expected.

| Discussion

Intra-annual population dynamics of green spruce aphid follow a familiar pattern in Western Europe and have been attributed to the combined influences of the thermal environment, host plant sap quality, aphid dispersal and predation [START_REF] Day | The growth and decline of a population of the spruce aphid Elatobium abietinum during a three year study, and the changing Pattern of fecundity, recruitment and alary polymorphism in a Northern Ireland Forest[END_REF][START_REF] Day | Population growth and spatial patterns of spruce aphids (Elatobium abietinum) on individual trees[END_REF][START_REF] Eds | Population responses of a conifer-dwelling aphid, to seasonal changes in its host[END_REF]Day at al., , 2006;;[START_REF] Straw | Variation in the abundance of invertebrate predators of the green spruce aphid Elatobium abietinum (Walker) (Homoptera: Aphididae) along an altitudinal transect[END_REF]. By contrast, the trajectory of populations across years was less studied until very long-term data became available through the Rothamsted Insect Survey (Harrington et al., 1992). Green spruce aphids suction-trapped during their early summer flight period across Great Britain became an accepted surrogate for aphid population density at a local level and with 40 years of data it was possible to assess the influence of the North Atlantic Oscillation (NAO), and latitudinal gradients in climate effects, on inter-annual changes [START_REF] Saldana | North Atlantic Oscillation effects on the temporal and spatial dynamics of spruce aphid populations in the UK[END_REF]Westgarth-Smith et al., 2007;[START_REF] Lima | Non-linear feedback processes and a latitudinal gradient in the climatic effects determine green spruce aphid outbreaks in the UK[END_REF]. [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF] demonstrated similarities between the data obtained from suction traps and more intensively sampled foliar habitats where the aphids spend most of their lives. A simple model based on relatively few parameters was able to closely characterize interannual population dynamics from completely independent aerial and arboreal samples of aphids. This was made possible by a unique 9-year time series of forest aphid data [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF].

The hypothesis that similar processes govern interannual dynamics of green spruce aphid in the UK and France, is generally supported by the application of a general discrete model developed for aphid data in the north of the UK, to aphid populations in northern France. The model had a tendency to overestimate population density in France because values of phys in France (12 year means, Normandy 332,5; Brittany 412) are understandably well above those experienced in Northern Ireland and Scotland (78 year mean East Craigs, 239). We deduce that aphid populations in the Phys period (January to April) did not increase at a rate anticipated by the model which was derived from lower UK Phys values. Despite The effects of winter temperature on aphids in France was probably similar to that in the northern UK. Aphids in Northern Ireland and Scotland showed no demographic effects from accumulated degree days below -7°C [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF] but were sensitive to sustained « chill periods ». The coma metric showed that the French forests were not colder in winter than those in Scotland included in the model (mean coma values, Normandy 3.7, Brittany 7.6 and East Craigs 11.2) (Fig. 5). The observed French populations demonstrate the"see-saw" fluctuations resulting from overcompensated density dependence. This type of behaviour is common in aphid populations associated with trees [START_REF] Sequeira | Population dynamics of tree-dwelling aphids: the importance of seasonality and time scale[END_REF] and arises from a number of processes such as discussed by [START_REF] Day | Interannual dynamics of aerial and arboreal green spruce aphid populations[END_REF].

Records in western France show that the aphid has existed on non-indigenous spruce forests like Sitka spruce plantations since the 1950s [START_REF] Joly | Les causes animales dans le jaunissement et la chute des aiguilles de l'épicéa de Sitka Picea sitchensis et d'autres épicéas[END_REF]. This pattern did not seem to affect the dispersal ability of aphid populations. It has been assumed that increases in mean temperatures at local and regional scales might increase the abundance of aphid populations over the next 50-100 years and that newly planted trees might experience more severe defoliations [START_REF] Straw | Climate change and the impact of green spruce aphid, Elatobium Abietinum (Walker), in the UK[END_REF]Straw et al.m 1998a,b).

Green spruce aphid outbreaks that have affected the health and growth of Sitka spruce through successive regular defoliations, as observed in the UK [START_REF] Carter | The Green Spuce Aphid and Sitka Spruce Provenances in Britain[END_REF][START_REF] Thomas | The interaction of green spruce aphid and Fertilizer applications on the growth of Sitka spruce[END_REF] have occurred in Normandy and Brittany every 10 years as confirmed by our study and by historical records in 1958 [START_REF] Joly | Les causes animales dans le jaunissement et la chute des aiguilles de l'épicéa de Sitka Picea sitchensis et d'autres épicéas[END_REF]), 1968[START_REF] Leroy | Premières constatations sur les attaques du Puceron vert vis-à-vis des plantations de Sitka installées en mauvais sol dans l'ouest de la France[END_REF]. Heavy defoliations were also observed in the Limousin in 1968 by [START_REF] Leroy | Premières constatations sur les attaques du Puceron vert vis-à-vis des plantations de Sitka installées en mauvais sol dans l'ouest de la France[END_REF] and in 1999 during our survey. Sitka spruce has been successfully introduced in the two regions by foresters since the middle of the 19 th century (Leroy & Malphettes, op.cit.) and more intensively planted following major projects of wetland afforestation and/or reforestation since the 50s covering a total surface of nearly 20 000 ha for the two regions. Changes in land use including forest and conservation issues have had a quick and deep impact on the plantations of Sitka spruce and consequently aphid populations in the two regions. A major change in the management of public forests has led to the restoration of wetlands while private forestry is still using Sitka spruce in reforestation areas (Lemperiere et al., in prep.). As a result, the patches that have been formed by the Sitka spruce plantations within large agricultural landscapes follow a pattern which is linked with the nature of the soil. Most of those patches are not connected and could then be considered as biogeographical islands (Woiwod & Hanski, 1992).

Metapopulations of the green spruce aphid that were mostly distributed throughout the Sitka spruce growing areas seem to follow this general patchiness which was observed in the two regions.

Another major impact on aphid distribution could be a shift from Sitka spruce to Norway spruce which is considered as its normal host in northern Europe (Austara et al., 1997;[START_REF] Halldorsson | Genetic diversity of the green spruce aphid Elatobium abietinum Walker in north-west Europe[END_REF] and causing more cryptic damages as observed in some parts of the Alps (Fig. 6). An interesting complementary study could be carried out to improve the model since the observed outbreaks that have occurred after the last field assessments in 2008 Westgarth-Smith, A.R., Leroy, S.A.G., Collins, P.E.F., & Harrington, R. (2007). Temporal variations in English populations of a forest insect pest, the green spruce aphid (Elatobium abietinum), associated with the North Atlantic Oscillation and global warming. Quaternary International, pp. 173-174;153-160. Woiwod, I.P., Hanski, I. (1992). Patterns of density dependence in moths and aphids. Journal of Animal Ecology, 61, 619-629.

Figure Legends

Fig. 1 Distribution of the green spruce aphid Elatobium abietinum (Walker) (in grey) and Norway spruce (hatched) in Europe. After Halldorsson et al.2004, redrawn from (Anon., 1966) and Sigurgeirsson & Szmidt, 1992. abietinum (1997-2008).

  and evaluate the generality of a model which was developed in the UK to explain the year-to-year variations in peak abundance of the aphid. Aims The objective was to observe the influence of the local climates and disturbing climate factors on the population densities of the insect in two regions of France.

  Europe. Populations in northern and western France are a good test of the generality of this hypothesis, and are a considerable geographical distance from the regions for which the model we employ was originally developed.

  faster, require less equipment, and are not dependent on the size of quadrats.

  74 (± 0.40) -1.28 (± 0.11) • ln(N) -0.047 (± 0.20) • coma + 0.0045 (± 0.0014) • phys,[Eq.1] This was the model used in the present study with mean daily temperature records obtained from the local Meteo France stations in Dinard and Côtes d'Armor for Brittany and Pré-en-ail, Orne for Normandy.

  metric coma used in the model was then represented by the number of chill periods, each a consecutive run of 5 days with daily mean temperature of ≤5 o C.

  in France, aphids were unable to take advantage by developing more quickly, probably because needle sap nutrients remained low for a greater proportion of the Phys period.

(

  local annual reports for Normandy and Brittany from the Département de Santé des Forêts surveys on forest pests) confirm that the general model performs well in tracking the interannual trajectories of the populations from 2008 up to 2018 with outbreaks in 2012 and 2015 in Brittany and 2014 and 2017 in Normandy.

F

Fig. 2

 2 Fig. 2 Life cycles of Elatobium abietinum after Carter & Halldorsson (1998).

Fig. 3

 3 Fig. 3 Population time series for Elatobium at Monnaye (Normandy) (a) and Malaunay (Brittany) (b), France. Mean aphid population density (n= 400 samples) at annual peak population (April/June) each year.

Fig. 4

 4 Fig. 4 Population time series for Elatobium at Monnaye (Normandy) (a) and Malaunay (Brittany) (b), France. Mean aphid population density (n= 400 samples) at annual peak population (April/June) each year.

Fig. 5

 5 Fig. 5 Historical patterns in two climatic metrics relevant to the population dynamics of Elatobium abietinum patterns near Monnaye (Normandy) and Malaunay (Brittany) and .East Craigs, Scotland (1951, Scotland ( -2007)).

Fig. 6

 6 Fig. 6 Distribution of Sitka spruce in France and location of study sites with presence and absence of Elatobium abietinum (1997-2008).

  Distribution of the green spruce aphid Elatobium abietinum (Walker) (in grey) and Norway spruce (hatched) in Europe. After[START_REF] Halldorsson | Genetic diversity of the green spruce aphid Elatobium abietinum Walker in north-west Europe[END_REF], redrawn from Anon.(1966) and[START_REF] Halldorsson | Genetic diversity of the green spruce aphid Elatobium abietinum Walker in north-west Europe[END_REF] Szmidt (1992).

  Life cycles of Elatobium abietinum afterCarter & Halldorsson (1998).

  Population time series for Elato bium at Monnaye (Normandy) (a) and Malaunay (Brittany) (b), France. Mean aphid population density (n= 400 samples) at annual peak population (April/June) each year. ) and predicted (open) annual maximum population densities of the green spruce aphid in two forests, a) Monnaye forest (Normandy) and b) Malaunay forest (Brittany). Population estimates were derived from spruce needle samples. The predictions were based on the preferred model (equation 1) in Day et al. (2009), developed for northerly UK aphid populations.

  Distribution of Sitka spruce in France and location of study sites with presence and absence of Elatobium

Acknowledgements


-Préciser les pièces reçues sur lesquelles vous vous appuierez, mettre une référence, une pagination -Risque d'oubli ?

Accomplir la mission

• Rechercher et extraire tous les éléments en lien avec l'affaire -Toutes les Information s relatives à une personne, à un pseudo -Toute information relative à la possession et à la diffusion de contenu

-Tous les contacts, toutes les discussions et interactions, en lien avec l'affaire

• Deux grands types d'information :

-Le texte -Les photos et vidéos Analyse de traces horodatées

• Une analyse est par essence multi-source :

-Logs, réseaux sociaux, mails, activité internet, les documents et fichiers multimédias

• Une analyse est souvent cross-device :

-Stockage externe ou plusieurs ordinateurs saisis -Usage simultané de plusieurs matériels : discussion sur téléphone et envoi d'un document par mail depuis l'ordinateur

• Facteur commun : Horodage des contenus = Timestamped content

• Reconstruire la chronologie des événements = timeline

• Problématique : Fiabilité de l'horodage -Quelle date ? date d'enregistrement sur le système de fichier, date de création du fichier (métadonnée), date du document (en entête)

-Modification volontaire, involontaire, pb horloge, de synchro, de fuseaux Le rapport d'expertise

• Objet : répondre à la mission

• La forme du rapport :

-Ecriture lisible pour un non expert -Met en avant les éléments les plus probants -Rester factuel, éviter la sur-interprétation, attention aux certitudes -les éventuelles incohérences détectés ou problèmes rencontrés

-

  Utilise une méthode forensique, des matériels forensiques, des logiciels forensiques -Rechercher toute trace d'activités numériques en lien avec une affaire -Pour confirmer ou infirmer des dires ou des hypothèses -Identifier et mettre en relation des traces pertinentes, vérifier la cohérence -Tirer des conclusions • Spécificité de certaines expertises -Le principe du contradictoire -Tout élément doit pouvoir être débattu L'expertise au tribunal de commerce et le principe du contradictoire • Prendre connaissance et comprendre la mission -Éventuellement appeler le magistrat -Tenter de saisir la pertinence, le bien-fondé avant d'accepter -Apprécier l'assistance d'un sapiteur / tenter d'apprécier les délais • Se préparer à la mission -Attendre la consignation = avance sur frais -Vérifier si la mission est toujours d'actualité -Demander au magistrat les éléments de la procédure • Prendre contact avec les parties et leur avocat -Fixer un premier rendez-vous -Demander les pièces jugées nécessaires à considérer et le délai pour les fournir -Les obtenir avant le premier rendez-vous -Négocier le lieu du rendez-vous • Respecter le contradictoire -Toutes les pièces reçues doivent être portées à la connaissance des autres parties • Informer par courrier recommandé avec AR la date et lieu du rendez-vous (GPS)

--

  Utilise une méthode et des outils forensiques : acceptabilité -Analyse qui garantit l'intégrité des données : conservation de la preuve -Analyse systématique et exhaustive -Analyse reproductible • Doit accomplir la mission -Rendre un rapport lisible dans un délai correct -Répondre aux questions posées Les types de mission • 3 grands types de mission (réquisition) -Au cours de l'enquête (matériel déjà saisi), à domicile -Pendant une perquisition, chez le suspect -En garde à vue • Type de mission détermine le scénario d'analyse -Contrainte de temps -Reproductible et intégrité -Priorisation différente -Traitements longs différés Accomplir la mission : • Prendre connaissance et comprendre la mission • Prendre en charge les scellés -Vérifier l'intégrité, briser les scellés • Identifier les matériels et les supports numériques -Marque, modèle, numéro de série, capacité -Recherche des supports de stockage internes • Rechercher et extraire toute trace en lien avec l'affaire -Ou susceptible d'éclairer l'affaire • Rédiger un rapport et des conclusions • Reconstituer les scellés • Rapporter les scellés Prise en charge et identification d'un scellé Identification des matériels et supports La boîte à outils de l'expert • Appareil photo, adaptateurs, câbles, pinces, tournevis, boitiers, disques, rallonges, ciseaux, cutter, scotch, trombones, aimant... Matériels d'acquisition • Bloqueurs, dupliqueurs, tour d'investigation Acquisition de données sécurisée • Importance de la méthode -Garantir l'intégrité des données : conservation de la preuve -S'assurer que l'expertise sera recevable (et reproductible) -Travailler dans un environnement protégé, sécurisé, en toute tranquilité : réduire les risques d'erreur de manipulation • Blocage logiciel des écritures -Désactiver l'automount et l'autorun -Montage en lecture seule : mount -ro • Blocage matériel des écritures -La sérénité : bloqueur & duplicateur Acquisition de données sécurisée • Préserver l'intégrité des données -Hash en début d'expertise = Hash en fin d'expertise • Réaliser une image disque à l'identique : clonage -Copie bit à bit avec calcul de hash à la volée : dcfldd, dc3dd -Soit avec un bloqueur -Soit avec un duplicateur de disque • Limites à l'utilisation intensive -Défaillance technique : Disk stress -Les contraintes de temps Les champs de l'investigation numérique • Disk forensics Documents accessibles depuis le système de fichiers : Text & Multimedia Forensics -Données accessibles mais à décoder et analyser : Metadonnées de fichiers, Log • Social Media Forensics : contacts, partages, discussions, interactions • Web Browser Forensics : sites visités, recherches effectuées, téléchargements • Ad-hoc app Forensics : Cache et bibliothèque d'applications • Forensics Data Carving : fichiers effacés, stockés en espace non alloué, fragments de fichier, fragments de données • Memory forensics Récupération de mots de passe ou de hash de mots de passe -Analyse de l'activité non sauvegardée : en cours de consultation, de création • Cloud forensics and Network forensics -Contraintes légales liées aux juridictions et au périmètre de l'expertise • Contenu chiffré : -Difficile à identifier, à différencier de l'aléatoire -Recherche d'applications installées, de containers suspects, de noms d'extension -Solution préconisée : demander les clés pour le déchiffrementS L'analyse et l'environnement logiciel • Les suites logicielles d'investigation numérique : -EnCase, FTK, Autopsy, X-Ways, Magnet IEF/Axiom -Aide à l'analyse des traces et la recherche de preuves -Aide à gérer le cas : ± gestion de projet et éviter les oublis -Agrégation de modules spécifiques à certaines traces/logiciels -Vers l'automatisation totale ? Risque d'oubli • Aller au-delà : les outils, protos, et développements spécifiques -Extraire des traces de logiciels ou de sites moins populaires -Recherche et Veille sur des sites/forums : Forensics Focus / Github • Payant, souvent non open-source, non evalué :

•

  Conclusion : Reprend les principaux résultats obtenus en lien avec la mission • Peut contenir des annexes numériques Reconstitution d'un scellé Digital Forensics Issues • Towards Forensics Labs ? -Coûts initiaux : Matériels (computers, storage devices, write blockers, disk imagers, connectors) et logiciels -Coûts récurrents : licence logicielle / frais de maintenance • Accroître la confiance dans les technologies -Need to handle new technologies, usages, software, services, versions -Besoin de plus d'évaluation indépendantes et d'outils open-source • Savoir-faire & Souveraineté -Comment adresse le chiffremant natif / Module de sécurité matériel -Multiplication des entreprises spécialisées • Recherche sur des technologies à base d'IA -Text : Aller plus loin qu'une recherche par mot-clé ou expression régulière -Image/Video : Recherche à partir du contenu & Détection de modification du contenu