Gregoire P Millet

Jean-François Toussaint
email: jean-francois.toussaint@aphp.fr

Quentin De Larochelambert

Andy Marc

Juliana Antero

Eric Le Bourg

Covid-19 Mortality: A Matter of Vulnerability Among Nations Facing Limited Margins of Adaptation

Keywords: COVID-19, demography, environment, public health, lockdown, niche adaptation De Larochelambert et al

Context: The human development territories have been severely constrained under the Covid-19 pandemic. A common dynamics has been observed, but its propagation has not been homogeneous over each continent. We aimed at characterizing the non-viral parameters that were most associated with death rate. Methods: We tested major indices from five domains (demography, public health, economy, politics, environment) and their potential associations with Covid-19 mortality during the first 8 months of 2020, through a Principal Component Analysis and a correlation matrix with a Pearson correlation test. Data of all countries, or states in federal countries, showing at least 10 fatality cases, were retrieved from official public sites. For countries that have not yet finished the first epidemic phase, a prospective model has been computed to provide options of death rates evolution.

Results: Higher Covid death rates are observed in the [25/65 • ] latitude and in the [-35/-125 • ] longitude ranges. The national criteria most associated with death rate are life expectancy and its slowdown, public health context (metabolic and non-communicable diseases (NCD) burden vs. infectious diseases prevalence), economy (growth national product, financial support), and environment (temperature, ultra-violet index). Stringency of the measures settled to fight pandemia, including lockdown, did not appear to be linked with death rate.

Conclusion:

Countries that already experienced a stagnation or regression of life expectancy, with high income and NCD rates, had the highest price to pay. This burden was not alleviated by more stringent public decisions. Inherent factors have predetermined the Covid-19 mortality: understanding them may improve prevention strategies by increasing population resilience through better physical fitness and immunity.

INTRODUCTION

Out of the many environmental options, human populations have concentrated in the most favorable development niche, characterized by a local mean annual temperature around 11-15 • C (1), corresponding to a narrow latitude strip. In the plains of that strip, the highest life expectancies have been experienced by the populations and most of the human longevity maxima have been recorded [START_REF] Olshansky | The future of human longevity[END_REF], showing that the niche coincides with and allows for the highest capacities of the human physiological development [START_REF] Xu | Future of the human climate niche[END_REF] and wealth creation, associated with elevated gross domestic product (GDP) [START_REF] Preston | The Changing relation between mortality and level of economic development[END_REF][START_REF]Global Burden of Disease Health Financing Collaborator Network. Trends in future health financing and coverage: future health spending and universal health coverage in 188 countries, 2016-40[END_REF].

Experiencing a recent phase of stagnation, nations encounter intrinsic and extrinsic limits: plateauing has been demonstrated in the progression of life expectancy [START_REF] Olshansky | Inconvenient truths about human longevity[END_REF][START_REF] Dong | Evidence for a limit to human lifespan[END_REF][START_REF] Antero-Jacquemin | Learning from leaders: life-span trends in olympians and supercentenarians[END_REF], adult height [START_REF]NCD Risk Factor Collaboration (NCD-RisC). A century of trends in adult human height[END_REF], or physiological maxima [START_REF] Berthelot | Has athletic performance reached its peak?[END_REF][START_REF] Marck | Are we reaching the limits of Homo sapiens?[END_REF]. As a consequence, societies seem to face reduced margins of adaptability (2, 10, and become more susceptible to new constraints. In fact, individuals have a limited organism shaped by physical [START_REF] West | The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization[END_REF] and evolutionary constraints [START_REF] Dhar | Laws of biology: why so few?[END_REF], and modulated by their interactions with the environment, resulting in an age-related decline in performances [START_REF] Marck | Are we reaching the limits of Homo sapiens?[END_REF] with a potential maximal longevity [START_REF] Antero-Jacquemin | Learning from leaders: life-span trends in olympians and supercentenarians[END_REF]. Hence, global threats may put the human development niche at higher risks. Demographical, social, economic, and health parameters may underline population vulnerabilities following the recent development phase.

Countries with the highest life expectancy have demographically transitioned to greater proportions of older and frailer populations, susceptible to increased mortality rates when facing physical or biological aggressors, such as temperature elevations [START_REF] Valleron | Epidemiology and heat waves: analysis of the 2003 episode in France[END_REF] or infections [START_REF] Evans | Place and cause of death in centenarians: a population-based observational study in England, 2001 to 2010[END_REF]. Concomitantly, the causes of death in these nations have transitioned from infectious to chronic diseases: mainly cardio-vascular diseases (CVD), metabolic (diabetes, high blood pressure), and neurodegenerative diseases or cancers. In addition, metabolic and CVD risk factors associated with high death rates, such as sedentary lifestyle, poor nutrition quality, or obesity, have a large prevalence in high income countries [START_REF] Olshansky | A potential decline in life expectancy in the United States in the 21st century[END_REF][START_REF] Daar | Grand challenges in chronic non-communicable diseases[END_REF] and rise in developing ones [START_REF] Abegunde | The burden and costs of chronic diseases in low-income and middle-income countries[END_REF][START_REF] Beaglehole | Improving the prevention and management of chronic disease in low-income and middle-income countries: a priority for primary health care[END_REF][START_REF] Oni | Chronic diseases and multi-morbidity -a conceptual modification to the WHO ICCC model for countries in health transition[END_REF]. Such comorbidities were early associated with a higher risk of death from Covid-19 [START_REF] Wang | Clinical characteristics of 138 hospitalized patients with 2019 novel coronavirus-infected pneumonia in Wuhan, China[END_REF].

The balance between the prior demographic, environmental, economic, health, or social factors in each nation may partially determine Covid-19 mortality rates, as well as the efforts made by governments to contain the pandemic. We hypothesized that nations characterized by limited progression of life expectancies, with high chronic disease rates, metabolic comorbidities, and high GDP produced higher vulnerabilities to Covid-19 and were associated with higher mortality rates during the first 8 months phase of the pandemic.

Hence, this study aimed to investigate the power of associations between Covid-19 death rates and demographic (e.g., life expectancy and its progression), health (e.g., major risk factors and lifestyles), environmental (temperature, humidity), and economic parameters (e.g., GDP and development index) as well as indices characterizing the governments' responses (e.g., stringency and containment measures) in every country affected by the pandemic.

METHODS

Studied Countries

From the 188 countries that have declared at least one case, only those counting a minimum of 10 deaths due to Covid-19 up to the study end point (31th August 2020) were included. China and US were also analyzed by states or regions, when each of them reached the 10 deaths threshold.

Variables of Interest

The studied outcome was the death rate due to Covid-19. Its association was tested with environmental [temperature, humidity, ultra-violet (UV) index]; demographic [life expectancy (LE), progression of LE]; health (CVD death rate, cancer death rate, infectious diseases death rate, obesity rate, sedentary, or inactive lifestyle); GDP and with each government response (containment and health index, stringency index, and economic support index).

The mortality rate due to Covid-19 was calculated as the ratio between the total number of deaths and the population size of each country, state, or region. It can be displayed as the number of deaths per 100,000 inhabitants and/or transformed into its decimal logarithm.

To test the optimal development niche effect, the Covid-19 mortality rates were analyzed according to the latitude and longitude of each country. Both were characterized by the barycenter of the country (GPS coordinates). Likewise, each state in the USA and each region in China was analyzed with its own latitude and longitude [as reported on the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University (JHU)] for the environmental analysis.

Data Collection

Daily data on the number of cases and deaths due to Covid-19 were collected up to the study end point via the Johns Hopkins University data source (https://github. com/CSSEGISandData/COVID-19). The latest population sizes available, used to calculate the mortality rate were extracted from the UNdata website (http://data.un.org/Data.aspx?d=POP&f= tableCode%3A22). The same data source was used to obtain the GDP for each country, the last year with available data being used.

Daily environmental data (temperature, humidity, and UV index) were collected via the Darsky website (https://darksky. net/). They were recorded from the beginning of the pandemic (defined as the day when the country reached a total of 10 deaths due to Covid-19) until the peak of the pandemic. To calculate the pandemic peak (PP), the number of cumulative deaths was theorized with a non-symmetrical logistic regression:

Y (t) = c + d -c 1 + exp b( log (t) -log (e)) f
where Y: logarithm of the number of deaths per 100,000 population The maximum of the derivative of this function was used to determine PP in each country. We calculated the mean of each of the three variables (temperature, humidity, and UV) in each country for a period starting at the beginning of the epidemic and ending the day of the PP.

Several countries (e.g., India, Argentina, etc.) have not yet reached the peak of the epidemic first wave. In order to take this parameter into account, the analyzes were also done with a death number that was estimated at the 99% time point (i.e., when the epidemic reaches 99% of the total death toll from the first epidemic wave) according to the logistic regression above. The estimated number of deaths for each country as well as all analyzes with such simulated data are presented in the Supplementary Material (Supplementary Table 1, Supplementary Figures 123), where the actual number of deaths for each country at the last known date is compared to the theoretical number according to the model.

The geographical coordinates corresponding to the barycenter of each country were retrieved thanks to the package rgeos in the R software. Latitude is expressed negatively in the southern hemisphere, positively in the northern one. Relative to the Greenwich meridian, longitude is expressed negatively for the western countries, positively for the eastern ones.

The obesity rate was calculated as the percent of the country total population considered to be obese, according to the last year this prevalence data was publicly available. Adult obesity is defined through a Body Mass Index (BMI) greater to or equal to 30 kg/m 2 . Data were collected from The World Factbook from the US intelligence agency (https://www.cia.gov/library/publications /the-world-factbook/fields/367.html).

The inactive lifestyle was characterized by the prevalence (percentage of the population) of adults performing <150 min of moderate-intensity physical activity per week, or <75 min of vigorous-intensity physical activity per week, or equivalent. Data were retrieved from the website of the World Health Organization (https://apps.who.int/gho/data/node.main. A893?lang=en). This prevalence is based on self-reported physical activity captured using the GPAQ (Global Physical Activity Questionnaire), the IPAQ (International Physical Activity Questionnaire), or a similar questionnaire covering activity at work/in the household, for transport, and during leisure time.

The current life expectancies were collected from the World Bank, based on the last year these data were available (https:// data.worldbank.org/indicator/SP.DYN.LE00.IN). To calculate the progression of LE, we used data from 2010 up to now. The α coefficient of the linear regression between current LE and the 2010 one was determined to estimate the progression trend. The greater the index, the greater the life expectancy gains in the last decade.

The burden resulting from major chronic diseases (CVD, metabolic diseases, cancer) and from infectious diseases in the previous population death rates was estimated by the proportion of the mortality rates associated with these major causes compared to the all-cause mortality rates. Both sexes and all age classes were taken into account. Data were retrieved from the IHME "GDP results tools" (http://ghdx.healthdata.org/gbdresults-tool) up to the last year the mortality rate was available. They appear as "Neoplasms death rate, " "CV and MD death rate, " and "Infectious diseases death rate."

We used the Oxford university data source to characterize the state responses, regarding the containment and health index, the stringency index, and the economic support index (https://www .bsg.ox.ac.uk/research/research-projects/coronavirus-governme nt-response-tracker) including public health measures taken by each country at short term. The Oxford COVID-19 Government Response Tracker (OxCGRT) systematically collects information on several different common policy responses that governments have taken to respond to the pandemic on 17 indicators. The data from the 17 indicators were aggregated into a set of three common indices, reporting a number between 1 and 100 to reflect the level of government's action on each topic: (1) the containment and health index combines lockdown restrictions and closures with measures such as testing policies and contact tracing, short term investment in healthcare, as well as investments in vaccines; (2) the economic support index records measures such as income support and debt relief; (3) the original stringency index records the strictness of lockdown and policies that primarily aimed at restricting population mobility.

Statistical Analysis

To study the relationship between environmental variables and the Covid-19 mortality rate, we carried out a linear (y = α.x + β) and a two-degree polynomial (y = α 1 . x + α 2 .x 2 + β) analysis, taking into account the notion of physiological optima [START_REF] El Helou | Impact of environmental parameters on marathon running performance[END_REF] through an optimized link between thermodynamics and physiology/pathology (parameters of air-borne diseases such as influenza also show a maximal transmission rate for a specific range of ambient temperatures-20). For each of the three environmental variables, we kept the best of the two models based on the adjusted coefficient of determination, taking into account the complexity of the model.

To test potential associations between the studied parameters, a Principal Component Analysis (PCA) was computed. Pearson correlation coefficients and tests for association were computed to measure the correlation between each pair of parameters. The results are presented in a correlation matrix. For these analyzes, we used the absolute value of latitude, representing the deviation from latitude 0. Finally, when a polynomial regression was determined for environmental variables, the deviation from the maximal value was used to test the association with Covid mortality.

Results are considered significant at p < 0.05. All statistical analyses were performed with R (version 3.6.1; The R Foundation for Statistical Computing, Vienna, Austria).

RESULTS

One hundred and sixty countries were included in the study (Supplementary Table 1), accounting for a total of 846,395 deaths due to Covid-19 up to the study end point (31th August 2020).

Covid-19 Mortality and the Global Niche

The geographical relation between Covid-19 mortality rate and latitude shows that higher mortality rates were observed in the 25/65 • northern parallels (Figure 1, Supplementary Figure 4). The [25-65 • ] latitude intervals (North and South) delimited an area where 78% of all Covid-19 deaths were recorded (in the European continent, this area includes Spain and Italy up to the southern part of Sweden; in the Americas, it covers the state of Texas up to the Hudson Bay; the southern part of Brazil and the states under it; in the African continent: the Maghreb states and South Africa). This area includes the states with the highest recorded death rates (New-Jersey in the Americas, Belgium in Europe).

Negative longitudes (American Countries) were also associated with higher death rates (Figure 2). The [-35/-125 • ] longitude interval (West) delimited an area where 57% of all Covid-19 deaths were recorded.

Covid-19 Mortality and the Environment

Polynomial regression was used for the relationship between the number of deaths per 100,000 inhabitants according to temperature (R² = 0.21) and humidity (R² = 0.05) (Figure 3). A linear relationship was preferred for the UV index (R² = 0.11). Maximal death rates are obtained for a temperature T max of 10.1 • C, a humidity H max of 55%, and a zero UV index. Deviations from T max and H max were used for the multifactorial analysis of death rates with temperature and humidity.

Principal Component Analysis

Combining the studied parameters, the first and second factorial planes of the PCA represent 60.27% of the information (Figure 2). The first axis concentrates 37.55% of total inertia and axis 2 represents 13.56% of it. The third factorial axis represents FIGURE 2 | PCA first factorial plane: axis 1 is horizontal; axis 2 is vertical. The more distant a variable is from the center, the more it is correlated with the first or the second factorial axis. The studied parameters regrouped the countries associated with Covid-19 highest death rates on the right of the horizontal axis. These are the high income countries with a high LE but a low progression of it, high sedentarity, obesity, high deviation from latitude 0 and low longitude (Asian countries have a high longitude, while it is negative in the Americas). Countries associated with low Covid-19 death rates have a low GDP, a low LE but a great margin of progression for it, a high prevalence of infectious diseases, a greater deviation from optimum temperature and UV index; they occupy the left part of the axis. Lockdown stringency, containment index and ambiant humidity are not correlated with Covid-19 mortality, as they are linked to the second axis. The cloud of individuals on the first factorial plane is presented in the Supplementary Figure 5.

9.16% of the information. The cloud of individuals on the first factorial plane is presented in Supplementary Figure 5.

The first axis of PCA opposes two groups of countries (Figures 2,4,5). High income northern countries are positively correlated to this axis: they provide high economic support, have higher LE but lower progression of LE, more frequent sedentary lifestyle, larger obesity rates, and higher mortality from CVD and cancer. Occupying the left part of the axis are countries with a low GDP, lower life expectancy but greater progression of LE, higher death rate from infectious diseases, greater deviation from optimum temperature, and UV index. Covid-19 death rate is higher in countries strongly and positively correlated with the first factorial axis on the right.

The government's responses (i.e., the severity index and the containment and health index) are strongly correlated with the second factorial axis (Figures 2,4). The death rate from Covid-19 is not correlated with this axis. Therefore, the death rate appears not to be linked with the responses of governments.

The third axis shows a relationship between Covid-19 mortality and longitude as well as obesity and sedentarity (Figures 4,5). American countries have a higher obesity rate and a higher Covid-19 mortality rate; Asian countries have lower obesity rates and lower Covid-19 mortality rates.

The correlation matrix (Figure 6) shows that the Covid-19 mortality rate is positively correlated to a group of variables composed of the inactive lifestyle (r = 0.46, p < 10 -6 ), obesity rate (r = 0.55, p < 10 -11 ), GDP (r = 0.40, p < 10 -7 ), economic support index (r = 0.31, p < 10 -3 ), life expectancy (r = 0.50, p < 10 -11 ), burden of mortality due to CVD (r = 0.33, p < 10 -3 ), cancer (r = 0.47, p < 10 -9 ), and deviation from latitude 0 (r = 0.41, p < 10 -3 ). The mortality rate due to Covid-19 is negatively correlated to another group of variables composed of the mortality rate from infectious diseases (r = -0.50, p < 10 -9 ), the progression of life expectancy (r = -0.37, p < 10 -4 ), longitude (r = -0.36, p < 10 -3 ), the deviation from optimum temperature (r = -0.39, p < 10 -5 ), UV index (r = -0.37, p < 10 -43 ). There is no significant correlation with the deviation from optimum humidity (r = 0.03, p = 0.52), the containment and health index (r = 0.07, p = 0.51), the original stringency index (r = 0.07, p = 0.36), and population size (r = -0.05, p = 0.35). A negative correlation also relates obesity and longitude (r = -0.33, p < 10 -4 ).

The principal component analysis as well as the correlation matrix with the estimated data are presented in Supplementary Figures 123. The analyzes with the estimated death number at the end of the first epidemic wave do not change the conclusions of the analyzes on the real data. The direction of the correlations as well as their significance in the correlation matrix are unchanged as well.

DISCUSSION

Main Findings

This analysis shows that higher Covid-19 mortality rates are mostly found in countries experiencing higher life expectancies and showing a recent slowdown of this progression. Most of these developed and aging societies are latitudinally located over the 25 • parallel. They also have higher GDP and chronic diseases levels (e.g., CVD and cancer) associated with major metabolic risk factors (e.g., inactive lifestyle, sedentarity, and obesity). High temperature and UV levels are associated with low death rates such that northern and western countries pay the most severe toll to Covid-19.

In the PCA, the first axis shows a strong correlation between Covid-19 death rates and countries inside the [25/65 • ] latitudinal strip, while the third axis reveals two correlations with Covid-19 death rates: one with longitude, a second one with obesity. This suggests that states in the Americas plagued with frequent inactive lifestyle and higher obesity rates than Asian countries experienced a higher death toll. This is consistent with the hypothesis of an optimal human development niche, that has aggregated favorable health, demographic, environment, and economic parameters (1). However, though previously positive, they now expose populations to higher vulnerabilities to both infectious (Covid- [START_REF] Oni | Chronic diseases and multi-morbidity -a conceptual modification to the WHO ICCC model for countries in health transition[END_REF] or physical constraints (heat waves). Regarding government's actions (i.e., containment and stringency index), no association was found with the outcome, suggesting that the other studied factors were more important in the Covid-19 mortality than political measures implemented to fight the virus, except for the economic support index. It may however be important to decipher this positive relation in a plausible chronological order: it does not seem that a higher economic support would induce a higher Covid-19 mortality, but rather that a higher death toll rate provoked a larger societal reaction, including a higher amount of economic measures, when available.

The design of this study aimed to draw a global description of the Covid-19 mortality and its associations with several major parameters. It is out of scope to speculate on any causeeffect relation. Nevertheless, some explanatory hypothesis may be proposed: countries displaying greater susceptibility (determined by a more fragile balance between health, demographic, environment, and economic parameters) seem to have narrower margins of adaptation and be therefore more vulnerable to main aggressors.

The crucial link between a hazard-or external threat-and a disaster is illustrated by the notion of vulnerable populations [START_REF] Schröder-Butterfill | A framework for understanding oldage vulnerabilities[END_REF]. Vulnerability is the result of complex interactions of distinct risks, exposure to the threat, and the lack of defenses or resources to deal with it. During a pandemic situation, the foremost indicator of countries health fragility may be seen in the proportion of older people (who were the SARS-CoV-2 major target), given the ineluctable diminished performances and resilience with age [START_REF] Berthelot | An integrative modeling approach to the age-performance relationship in mammals at the cellular scale[END_REF]. Resulting from both biological and social processes, the decline in health and physical strength and the increasing disabilities particularly affect old people, bringing them closer to vulnerability thresholds. The highest proportions of elderly people are observed in countries with higher life expectancy [START_REF] Waite | The demographic faces of the elderly[END_REF][START_REF] Bourg | Is life expectancy of french women going to plateau and oscillate?[END_REF]. Such nations may suffer from higher mortality levels when new aggressors appear.

Previous studies have illustrated the relation between frailty and mortality [START_REF] Buchman | Change in frailty and risk of death in older persons[END_REF]. For instance, the 2003 heatwave killed 30,000 to 50,000 people in Europe and 15,000 in France [START_REF] Valleron | Epidemiology and heat waves: analysis of the 2003 episode in France[END_REF][START_REF] Trigo | How exceptional was the early August 2003 heatwave in France?[END_REF], 80% of them being elderly people. Among centenarians, who are more likely to decline suddenly, mortality due to infections increases (e.g., pneumonia) [START_REF] Evans | Place and cause of death in centenarians: a population-based observational study in England, 2001 to 2010[END_REF]. Accordingly, the Covid-19 mortality was the highest among the elderly worldwide [START_REF] Baqui | Ethnic and regional variations in hospital mortality from COVID-19 in Brazil: a crosssectional observational study[END_REF]. Moving toward higher life expectancy will therefore expose greater proportions of people to high mortality rates, especially when facing mass threats or when environment conditions largely evolves.

Concomitantly to a high life expectancy, the development afforded by an elevated GDP usually favors inactive lifestyles, sedentary behaviors, and obesity [START_REF] Olshansky | A potential decline in life expectancy in the United States in the 21st century[END_REF][START_REF] Chaix | Tobacco and alcohol consumption, sedentary lifestyle and overweightness in france: a multilevel analysis of individual and area-level determinants[END_REF], increasing the risk for hypertension, diabetes, and CVD, the most frequent comorbidities associated with Covid-19 mortality [START_REF] Richardson | Presenting characteristics, comorbidities, and outcomes among 5700 patients hospitalized with COVID-19 in the New York City area[END_REF][START_REF] Yang | Prevalence of comorbidities and its effects in patients infected with SARS-CoV-2: a systematic review and meta-analysis[END_REF][START_REF] Abdelmassih | Obese communities among the best predictors of COVID-19-related deaths[END_REF]. With an epidemiological transition toward more prevalent chronic diseases, countries with high life expectancy have also increased concurrent risks, restraining their adaptability margins.

The associations found among two opposed groups of countries suggest important inherent factors, predetermining the consequences of global threats. Properly understanding the relations between those parameters may help to provide new prevention strategies. Covid-19 has prompted a wide range of responses from governments around the world, yet the contagion and mortality curves are very homologous among countries (33). This is reinforced by our findings regarding the lack of any association with the government's actions taken during the pandemic. In that sense, the determining demographic, health, development, and environment factors seem much more important to anticipate the lethal consequences of the Covid-19 than government's actions, especially when such actions are led by political goals more than by sanitary ones. This last result however cannot predict that other types of measure would not reduce the pandemia death load.

This study highlights the great difficulties of adaptation that most countries will face [START_REF] Toussaint | L'Homme Peut-il S'adapter à Lui-Même[END_REF][START_REF] Fauci | The perpetual challenge of infectious diseases[END_REF]. Climate change for instance will disturb the optimal niche by forcing the ideal development temperature toward north. Infection balance and human resilience supported by local species equilibrium may be impaired as a result. Understanding where the risks and weaknesses are in each country is an important starting point when preparing to face new threats. In the Covid-19 case, an advisable strategy may be to increase populations immunity and resilience [START_REF] Campbell | Debunking the myth of exercise-induced immune suppression: redefining the impact of exercise on immunological health across the lifespan[END_REF] and prevent sedentary behaviors through higher physical activity and better physical fitness. Hence, political strategies restricting physical activity (e.g., closing sport facilities) may refrain the enhancement of population immunity in response to present and future viral aggressors.

The first limitation of this study is the uncertainty and reliability of the recorded national data on Covid-19 deaths, given the diverse counting methods in the different countries. We also acknowledge the limit of the reliability of the input data, since it refers to worldwide data collections. However, these are the least uncertain and the most reliable sources. Furthermore, the large size of the datasets compensates for the internal variability.

Another limitation is that the pandemic is not over, with American countries displaying a kinetics partially diverging from the European ones. While a clear mortality peak was observed in Europe with a quick decrease after it, it is not the case in several American countries: Mexico, Peru, and Brazil show a lasting plateau for the time being and the USA experienced a spring peak in the eastern states and a summer peak in southern ones. If finally, Covid-linked mortality would be higher in countries of Latin America than in richer countries, it would be necessary to understand the peculiar features, absent of our analysis, explaining such a result. A large dependence to seasonal parameters may also modify some conclusions at the end of the pandemic (e.g., if mortality does not decrease for months in these countries). But it may not change the conclusions about the first phase we deal with in that study. Indeed, countries with the highest death toll could still be in the Americas as USA have already experienced a first regression of life expectancy, whereas Mexico also shows one of the highest obesity rates.

This study has focused on the explosive sub-exponential phase of Covid-19 epidemic in each country. However, a previous period of propagation has probably started in the summer or fall of 2019. It is difficult to account for it, but such a diffusion phase of SARS-CoV-2 may be investigated through both International Air Transport Association (IATA) databases and modeling of airplane transport [START_REF] Colizza | Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions[END_REF]. The situation in islands such as Taiwan, New Zealand, or Iceland, that quickly imposed restrictive measures on air transport, shows that the virus has not become endemic in these first 8 months. After a rapid propagation phase, only the re-importation of subjects contaminated outside the island provoked new local cases. Finally, we did not account for the various viral sub-types, that could modify the relations shown here, as they may theoretically have a different impact on death rate. The main recorded variants however did not appear to produce such a difference on mortality [START_REF] Grubaugh | Making sense of mutation: what D614G means for the COVID-19 pandemic remains unclear[END_REF].

DATA AVAILABILITY STATEMENT

The original contributions presented in the study are included in the article/Supplementary Materials, further inquiries can be directed to the corresponding author/s.

t

  : time in days b, c, d, e, f : model parameters The parameter d controls the height of the asymptote of the curve. The parameters b and f jointly control the magnitude, which represents the speed of transition between the two asymptotes. The parameter e controls the position of the slope and the parameter c the left asymptote of the curve.

FIGURE 1 |

 1 FIGURE 1 | Each point represents the Covid-19 mortality rate of a country or a state, according to its latitude. Greater mortality rates were mostly observed in the [25 /65] latitude interval.

FIGURE 3 |

 3 FIGURE 3 | Polynomial or linear regression between the logarithm of the mortality rates due to Covid-19 and the UV index, humidity, and average temperature from the local beginning of the pandemic up to the peak.

FIGURE 4 |

 4 FIGURE 4 | Coordinates of the variables on the first 3 factorial axes. The larger the circle, the more the variable is correlated with the axis. A blue circle indicates that the variable is negatively correlated, a red circle indicates that the variable is positively correlated. The scale shows the coordinates of the variables on the axis.

FIGURE 5 |

 5 FIGURE 5 | PCA third factorial plane: axis 1 is horizontal; axis 3 is vertical. The studied parameters regrouped the countries associated with Covid-19 highest death rates on the right of the horizontal axis. Longitude and obesity rates are related to the third axis.

FIGURE 6 |

 6 FIGURE 6 | Correlation matrix: a larger area in the circles indicates a stronger correlation between the row and the column variables. A blue circle indicates a positive correlation coefficient; a red circle indicates a negative one; a full circle corresponds to r = 1 or -1; an empty circle corresponds to r = 0. If the Pearson correlation test was not significant, a cross on the circle was added.

Frontiers in Public Health | www.frontiersin.org

November 2020 | Volume 8 | Article 604339

ACKNOWLEDGMENTS

We thank Bernard Swynghedauw and Gilles Boeuf for manuscript reading and fruitful discussion.

AUTHOR CONTRIBUTIONS

QD, AM, JA, ELB, and J-FT conceived, designed, performed, and analyzed the research. QD and AM conceived, designed, and collected data from website. QD, ELB, and J-FT carried out the statistical analyzes. QD, JA, ELB, and J-FT wrote the manuscript. All authors read, review and approved the final manuscript.

SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpubh. 2020.604339/full#supplementary-material Supplementary Table 1 | Number of deaths as of August 31th, 2020, number of theoretical deaths according to our model as of August 31th, 2020 and number of deaths estimated at the end of the first epidemic wave according to our model for each country included in the analysis. The estimated death number for each country was obtained from the logistic regression (see section Methods-Data collection) when the first epidemic wave was expected to reach 99% of the total death toll. The correlation matrix as well as the principal component analysis were performed with data to assess whether the results may change at the end of the first epidemic wave.

Supplementary Figure 1 | First factorial plan of the principal component analysis with the estimated data (see Section Methods-Data collection). Results are the same with estimated data and actual data.

Supplementary Figure 2 | Coordinates of the variables of the principal component analysis with the estimated data (see Section Methods-Data collection). Results are the same with estimated data and actual data.

Supplementary Figure 3 | Correlation matrix with the estimated death numbers obtained from the logistic equation (see Section Methods-Data collection). Results are the same with estimated data and actual data.

Supplementary Figure 4 | Covid-19 mortality is expressed in numbers in the top figures and in rates in the bottom figures. It is expressed in raw data on the left and in decimal logarithm on the right.

Supplementary Figure 5 | The position of the countries on the graph represents their correlation according to the variables of the first factorial plane. For example, countries positively correlated to axis 1 (right), will be positively correlated to variables to the right of axis 1.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2020 De Larochelambert, Marc, Antero, Le Bourg and Toussaint. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.


Ph.D Clara Bled
email: clara.bled@univ-tlse2.fr

L Bouvet

Validation of the French version of Object Spatial Imagery and Verbal Questionnaire

Keywords: cognitive style, object imagery, spatial imagery, psychometric proprieties, questionnaire, French validation

The Object Spatial Imagery and Verbal Questionnaire (OSIVQ) measures individual differences in Visual-Verbal cognitive style and distinguishes between spatial and object visual imagery. This article aims to validate the francophone version of the OSIVQ using sensitive measures of spatial imagery, object imagery and verbal abilities among a French sample (N = 752). Principal component analyses of the OSIVQ showed good internal construct although 11 items had to be removed. Individual differences were found with participants that tended to rate themselves higher on the object scale. Results also revealed a significant gender effect. Indeed, males had higher spatial scores while females had higher object scores. Confirmatory factorial analyses gave support to three-dimensional model of cognitive style. Furthermore, correlations were observed across the different dimensions of the questionnaire and specific paper-and-pencil tasks. In the end, this study highlights the good psychometric properties of the French version of the OSIVQ.

Cognitive styles refer to psychological dimensions representing consistencies in an individual's manner of cognitive functioning, particularly with respect to acquiring and processing information (Messik, 1976). Many forms of cognitive styles have been described but the most frequently used is the visual-verbal style [START_REF] Kozhevnikov | Cognitive styles in the context of modern psychology: Toward an integrated framework of cognitive style[END_REF]. The visual-verbal style is based on the dual-coding theory according to which information is processed and mentally represented in two ways: verbally and visually [START_REF] Paivio | Dual coding theory: Retrospect and current status[END_REF]. Visual-Verbal cognitive style therefore describes consistencies and preferences in processing visual versus verbal information. [START_REF] Mayer | Three Facets of Visual and Verbal Learners: Cognitive Ability, Cognitive Style, and Learning Preference[END_REF], further define the "visualizer-verbalizer cognitive style" as thinking in pictures or words. These preferences reflect "heuristics and individual uses to process information about his or her environment" [START_REF] Kozhevnikov | Cognitive styles in the context of modern psychology: Toward an integrated framework of cognitive style[END_REF].

Visual representation (or visual mental imagery) has long been considered to be of a unitary nature, but Koshevnikov and her team have provided evidence for two distinct types of visual mental imagery: object and spatial imagery [START_REF] Kozhevnikov | Revising the Visualizer-Verbalizer Dimension: Evidence for Two Types of Visualizers[END_REF][START_REF] Kozhevnikov | Spatial visualization in physics problem solving[END_REF]. Object imagery allows pictorial and analogous representations of objects and scenes, whereas spatial imagery is more a schematic representation of objects and patterns with their spatial relationships. This conception is supported by brain research showing the existence of two distinct neuronal pathways for the processing of different aspects of visual information [START_REF] Farah | Visual and spatial mental imagery: Dissociable systems of representation[END_REF][START_REF] Kosslyn | Mental images and the Brain[END_REF][START_REF] Kosslyn | The case for mental imagery[END_REF]. The ventral pathway is dedicated to processing the visual appearance of objects and scenes in terms of their shape, color and texture. The dorsal pathway processes object location, movement, spatial relationships and transformations [START_REF] Kosslyn | Neural foundations of imagery[END_REF][START_REF] Mazard | A PET meta-analysis of object and spatial mental imagery[END_REF]. Furthermore, visuo-spatial abilities are associated with a more efficient use of the dorsal pathway [START_REF] Mayer | Three Facets of Visual and Verbal Learners: Cognitive Ability, Cognitive Style, and Learning Preference[END_REF]Lamm, Bauer, Vitouch, & Gstattner, 1999) whereas visuo-object abilities are associated with a more efficient use of the ventral pathway [START_REF] Motes | Object-processing neural efficiency differentiates object from spatial visualizers[END_REF]. In this context, object versus spatial cognitive styles refer to an individual's preferences or habits of processing information in terms of object and spatial visual mental imagery.

Numerous self-reported questionnaires were created to assess cognitive style, the most famous one being the Verbalizer-Visualizer Questionnaire (VVQ; [START_REF] Richardson | Verbalizer-visualizer: A cognitive style dimension[END_REF]. However, the VVQ has been criticized for poor internal reliability [START_REF] Boswell | A study of the internal consistency and factor structure of the Verbalizer-Visualizer Questionnaire[END_REF]. Moreover, the visual subscale of this questionnaire did not correlate with visual-spatial aptitude measures, which suggests a lack of predictive validity of the VVQ [START_REF] Mayer | Three Facets of Visual and Verbal Learners: Cognitive Ability, Cognitive Style, and Learning Preference[END_REF]. This lack of predictive validity is also observed in other cognitive style questionnaires as noted in Kozhevnikov's review on cognitive style [START_REF] Kozhevnikov | Cognitive styles in the context of modern psychology: Toward an integrated framework of cognitive style[END_REF]. As pre-existing questionnaires presented certain flaws and none of them evaluated the two dimensions of visual mental imagery, Blajenkova and Kozhevnikov developed the Object Spatial Imagery and Verbal Questionnaire (OSIVQ; [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF]. The OSIVQ thus evaluates three dimensions of cognitive style: object imagery, spatial imagery and verbal.

Blajenkova and Kozhevnikov evaluated the psychometric properties of the OSIVQ on 625 students. They found that the OSIVQ showed good internal construct (with a three-factor solution of a principal component analysis), good internal consistency (for the verbal scale, Cronbach alpha reached .74; for the object scale, α = .83 and for the spatial scale, α = .79) [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF]. Furthermore, the OSIVQ demonstrated acceptable testretest reliability with significant correlations between testing sessions (r = .73 for the verbal scale, r = .75 for the object scale and r = .84 for the spatial scale).

Moreover, unlike many previous questionnaires, OSIVQ scores significantly correlated with performances on different tasks assuring convergent validity of the instrument. "Object visualizers" were found to have good performances in object imagery tasks that require vivid visualization of pictorial properties (e.g., recognizing degraded objects) whereas "spatial visualizers" had good performances during spatial imagery tasks that involve visualization of schematic representations and spatial transformations (e.g., mental rotation) [START_REF] Blajenkova | Object-spatial imagery: A new self-report imagery questionnaire[END_REF][START_REF] Kozhevnikov | Spatial versus object visualizers: A new characterization of visual cognitive style[END_REF]. Finally, OSIVQ scores predicted professional interests or courses choices. Visual artists were generally "object visualizers" and had high object imagery ability, while scientists and engineers were generally "spatial visualizers" and had high spatial imagery ability [START_REF] Blajenkova | Object-spatial imagery: A new self-report imagery questionnaire[END_REF][START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF]; Blazhenkova & Kozhevnikov, 2010;[START_REF] Kozhevnikov | Trade-off in object versus spatial visualization abilities: Restriction in the development of visual-processing resources[END_REF]. The OSIVQ is therefore an ecologically valid scale with good predictive validity and psychometric proprieties.

Our objective is to create a French version of the Object Spatial Imagery and Verbal Questionnaire (OSIVQ) and to explore its psychometric properties with a large sample of the population. The aim is to provide a robust tool to assess cognitive style in the French community while making the distinction between spatial and object imagery.

Material and method

Participants

For the exploratory study, 450 participants (121 males and 329 females; age range 18 to 50, Mean = 31.51, SD = 8.90) completed the questionnaire. According to the formula N = Z*10 (with N = number of subjects and Z = number of items) a minimum of 450 subjects is necessary for accurate validation of a questionnaire with 45 items [START_REF] Hair | Multivariate data analysis[END_REF].

For the confirmatory study, 302 new participants (63 males and 239 females; age range 18 to 50, Mean = 27.84, SD = 8.85) were recruited. 144 of them also took a paper-and-pencil assessment to evaluate spatial imagery, object imagery and verbal abilities in addition to the questionnaire. This number of participants is slightly below the number required according to the formula (N = 34*10 = 340).

Participants were recruited by posting an advertisement on social media.

General procedure

The original English version of the Object Spatial Imagery and Verbal Questionnaire (OSIVQ; [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF] was translated to French using a classical translation-back translation procedure: the original version of the questionnaire was first translated from English into French by a native English-speaking person who is fluent in French. This French version was then translated back into English by a native Frenchspeaking English teacher. The two English versions were then compared in order to validate the French translation. The translated version of the questionnaire is presented in supplementary data.

For the exploratory study, participants responded to our French version of the Object Spatial Imagery and Verbal Questionnaire (OSIVQ) online. The online questionnaire was created using LimeSurvey©, and securely hosted by the University of Toulouse.

For the confirmatory study, participants were administered the French version of the OSIVQ and the following paper-and-pencil assessments: one spatial imagery test (Mental Rotation Test;Vandenberg & Kuse, 1978), one object imagery assessment (Vividness of Visual Imagery Questionnaire; [START_REF] Marks | Visual imagery differences in the recall of pictures[END_REF] and one verbal test (Mill Hill vocabulary test; Raven, J., Raven, J.C., & Court, J.H., 2003) described below. The order of tests was randomized.

All participants read an information notice with explanations concerning the study and indicated their consent before beginning.

This study was approved by the Research Ethics Committee of Toulouse University and received authorization by the French National Commission for Informatics and Freedoms (CNIL) regarding the protection and anonymization of personal data.

Measures

Object Spatial Imagery and Verbal Questionnaire (OSIVQ; [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF] French translation: OSIVQ is a 45-item self-report questionnaire designed to assess separately an individual's propensities for three different cognitive style dimensions (object imagery, spatial processing and verbal processing). The following instructions were provided to the participants: "This is a questionnaire about the way you think. Please, read the following statements and rate each of them on a 5-point scale. Select 5 to indicate that you absolutely agree that the statement describes you, and select 1 to indicate that you totally disagree with the statement. Select 3 if you are not sure, but try to make a choice. It is very important that you answer all the items in the questionnaire". There was no time limit for the completion of the questionnaire and participants could go back to correct their answers if they wanted. they were asked to create (e.g. "The sun is rising above the horizon into a hazy sky and a strong wind blows on the trees and on the lake, causing waves"). Participants responded on a 5-point scale (from "no picture at all" to "a perfectly clear and vivid picture"). There are 16 items and each item is scored from 1 to 5 and the total score (sum of the scores of all items)

Mental Rotation

gives an indication of the importance of the vividness of mental images.

Mill Hill vocabulary test (Raven, J., Raven, J.C., & Court, J.H., 2003 French adaptation by J.J. [START_REF] Deltour | Echelle de vocabulaire de Mill Hill de JC Raven[END_REF]: This test assesses vocabulary knowledge and verbal skills. In this paper and pencil test, participants had to choose and circle the word that has either the same meaning or nearly the same meaning (synonym) as the target word, among six others in a printed list. There are 34 items.

Data analysis

One spatial and three verbal items were negatively formulated and therefore reversed for the analysis. Exploratory analyses were realized using principal component factor analysis with Varimax rotation using SPSS V23.0 (IBM Corp, 2015). The internal consistency was measured with Cronbach alphas for each subscale of the OSIVQ. [START_REF] Mckelvie | Guidelines for judging psychometric properties of imagery questionnaires as research instruments: A quantitative proposal[END_REF] recommended alpha coefficients of .85 in order to accept validity of scales and the minimum acceptable coefficient should not be less than .70 [START_REF] Nunnally | Psychometric theory. 2nd Edition[END_REF]. For descriptive statistics and in order to evaluate a possible gender effect, Student's t-test and repeated measures ANOVA were performed.

In order to assess the psychometric properties of the OSIVQ and its factorial validity, confirmatory factor analysis (CFA) and path analysis were used and computed using AMOS (IBM Corp, 2015). We compared the two models: a two-factor model, as in the traditional model, and a three-factor model, as in Blazhenkova & Kozhevnikov's model, with a second order CFA analysis. We compared the different models by using fit indices: chi-square test (χ²/df), root mean square error of approximation (RMSEA), Bentler's comparative fit index (CFI), goodness of fit index (GFI) and Akaike information criterion (AIC). It was assumed that the model can be considered satisfactory when the χ²/df is lower than 3, RMSEA and CFI lower than .08 and GFI higher than .90 (Tabachnick and Fidell, 2001). The AIC is a comparative measure of fit and so it is meaningful when two different models are estimated: the lower the value is, the better the fit [START_REF] Tabachnick | Using multivariate statistics[END_REF].

Convergent validity of the OSIVQ was measured with correlations between the OSIVQ subscales' scores and paper-and-pencil assessment's scores. A correlation with .30 < r < .50 is considered as low, moderate with .50 < r < .70 and strong with r > .70 (Tabachnick and Fidell, 2001).

Results

Exploratory study

Principal component analysis

The initial principal component analysis revealed 11 factors with eigenvalues above 1. Only three factors, however, had eigenvalues markedly higher (6.23, 5.73 and 3.29) than the others (ranging from 2.05 to 1.02), and these first three factors explained a total of 33.88% of the variance (13.84%, 12.73% and 7.31%). None of the other factors met the recommendations for component saturation [START_REF] Guadagnoli | Relation of sample size to the stability of component patterns[END_REF] and the analysis of the decreasing eigenvalue curve ("scree plot") also revealed a three-factor solution. Therefore, other solutions were not considered further.

Based on these results, a second principal component analysis with Varimax rotation was performed with 3 factors. First of all, the test's conditions of use were checked using the Bartlett test. The sphericity test was significant (χ²(990) = 7321.69, p < .001), and the Kaiser-Meyer-Olkin test (KMO) was greater than 0.80 (KMO = 0.839), indicating sufficient correlations for component analysis. Items that loaded significantly on multiple factors were removed from the analysis, as were items that did not load significantly (below the critical value of .35) and therefore did not correlate with any factor [START_REF] Hair | Multivariate data analysis[END_REF]. Thus, 11 items (3, 10, 15, 19, 21, 22, 24, 25, 28, 36 and 38) were removed from the original questionnaire in order to obtain a coherent structure. The 34 remaining items of the OSIVQ (14 items for the object scale, 11 items for the spatial scale and 9 items for the verbal scale) and their loadings on the 3 factors are presented in Table 1. 33 Sometimes my images are so vivid and persistent that it is difficult to ignore them .62

6 My images are very colorful and bright .62

13 I have a photographic memory .62

43 My visual images are in my head all the time. They are just right there .61

26 When I imagine the face of a friend, I have a perfectly clear and bright image .57

11 When reading fiction, I usually form a clear and detailed mental picture of a scene or room that has been described .53

45 When I hear a radio announcer or a DJ I've never actually seen

OSIVQ items

The first factor was identified as object imagery factor, since all of the items designed to assess object imagery experiences positively loading on this factor, whereas all of the items designed to assess spatial imagery or verbal preferences either did not load. The second factor was identified as spatial imagery factor, since all of the items designed to assess spatial imagery preferences loaded positively on the second factor, whereas all of other items did not load on this factor. Finally, the third factor was identified as verbal factor, since all of the items designed to assess verbal preferences loaded positively on the third factor and other items did not load on this factor.

Internal consistency

The internal consistency was measured with Cronbach alphas. For the verbal scale, α .76; for the object scale, α = .84 and for the spatial scale, α = .85. Cronbach alphas showed a good internal consistency for the three sub-scales, with the selected items.

Descriptive statistics and gender differences

As the result of the selection of the 34 items, the number of items per subscale is not equivalent. Thus, for each participant, the scores for each subscale were transformed into percentages.

For the three subscales, Spatial score's mean is 60.65 (± 17.09); Object score's mean is 72.10 (± 14.39) and Verbal score's mean is 66.64 (± 15.48).

We then examined the effect of gender on object-spatial-verbal preferences for information processing, using repeated measures ANOVA, with gender as a between-subject variable, and three OSIVQ scales as within-subject variables. The repeated measures ANOVA demonstrated a significant difference between the three scales of the OSIVQ, F(2, 896) = 21.375, p < .001, η 2 = .046. Participants tended to rate themselves higher on Object imagery than on Spatial imagery (p < .001) or Verbal dimensions (p < .001) but there was no difference between Spatial imagery scores and Verbal scores (p = .092).

The repeated measures ANOVA also showed a trend effect of gender, F(1, 448) = 3.396, p = .066, η 2 = .008 and a significant Gender*OSIVQ interaction, F(2, 896) = 34.968, p < .001, η 2 = .072.

Confirmatory study

Confirmatory factor analysis

According to the traditional model of Visual-Verbal style, Verbal and Visual styles constitute two opposite dimensions whereas Blazhenkova and Kozhevnikov's theoretical approach distinguishes two types of imagery (object and spatial). Indeed, according to Blazhenkova and Kozhevnikov's revised model of cognitive style, there should be three separate dimensions (object, spatial and verbal). Figure 1 shows the results of the estimated threefactor model, and the values of fit for the different models are reported in Table 2. As seen in Figure 1, items from the verbal scale's scores loaded on a "verbal" factor, items from the spatial imagery scale's scores loaded on a "spatial" factor and items from the object imagery scale's scores loaded on an "object" factor. Interestingly, results of the confirmatory factor analysis indicated no significant correlation between our three factors (r = -.16 between spatial and verbal factors; r = .08 between spatial and object factors and r = .19 between object and verbal factors) (see Figure 1).

In order to confirm our item selection, we tested the fit of the three-factor model with all 45 originals items of our translation. According to the values, the fit of our 34 selected items scale is better than the one with the 45 original items (see Table 2).

Secondly, we compared the three-factor and the two-factor models using our 34 selected items. The two-factor model showed poor fit indices and the AIC score was lower than with the three-factor model. Overall, indices suggested that the three-factor model fits the data well which indicates that this model does explain the data. This is why the three-factor solution was retained.

Convergent validity

Correlations among the measures of verbal, spatial and object ability are presented in Table 3.

OSIVQ verbal scores were positively correlated with the verbal measure (Mill Hill scores) (p < .001). OSIVQ spatial scores were positively correlated with the measure of spatial imagery (MRT scores) (p < .001). Finally, OSIVQ object imagery scores were positively correlated with the measure of object imagery (VVIQ scores) (p < .001). Thus, all three scales of the OSIVQ Regarding the discriminant validity of the three scales, although none of the OSIVQ scales correlated positively with any task corresponding to the other scales, there is a significant but weak negative correlation between the OSIVQ verbal scores and MRT scores (r = -.29, p = .001).

Discussion

We developed a French version of the Object Spatial Imagery and Verbal Questionnaire (OSIVQ), a self-report instrument that allows the evaluation of the visual-verbal cognitive style in three dimensions with two imagery (object and spatial) scales and one verbal scale.

The first important outcome of the exploratory study is that our translated version of the OSIVQ (with the 34 selected items) demonstrated acceptable internal consistency for all three scales. Furthermore, our principal component analysis also revealed three distinct factors (object, spatial and verbal). These results are thus consistent with Blazhenkova & Kozhevnikov's model of cognitive style [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF].

Another important finding is that the distribution of object, spatial and verbal scores differs among the three subscales. Indeed, participants tend to rate themselves higher on the object imagery scale than on other scales. This trend is consistent with previous findings [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF][START_REF] Chabris | Spatial and Object Visualization Cognitive Styles: Validation Studies in 3800 Individuals[END_REF]. In addition, we also reported a significant gender effect with females tending to report themselves as object visualizers and males as spatial visualizers. This difference is not surprising as preceding studies reported a gender difference on spatial tasks with males performing better than females [START_REF] Linn | Emergence and characterization of sex differences in spatial ability: A meta-analysis[END_REF] and higher spatial imagery ratings for males while females tend to report higher object imagery and imagery vividness [START_REF] Blajenkova | Object-spatial imagery: A new self-report imagery questionnaire[END_REF]. According to Blajenkova et al., difference between spatial and object visualizers, however, cannot be reduced to gender differences [START_REF] Blajenkova | Object-spatial imagery: A new self-report imagery questionnaire[END_REF][START_REF] Kozhevnikov | Spatial versus object visualizers: A new characterization of visual cognitive style[END_REF]. Actually, 40.42% of our female participants reported above average spatial imagery preferences and 38.02% of male participants reported above average object imagery preferences. Furthermore, using partial correlations, Blajenkova and Kozhevnikov found that all the significant correlations between different object, spatial and verbal scales and corresponding objective measures remained significant even after the effect of gender was partialled out [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF].

Regarding the confirmatory study, it provides further validation of our French version of the OSIVQ. The traditional two-factor model that describes Visual-Verbal cognitive style as a bipolar dimension was compared to the three-factor model that comprises three independent dimensions (verbal, object and spatial). The results of our confirmatory factor analysis indicate that the overall fit of the three-factor model was indeed significantly greater than that of the two-factor model. It should be noted that our number of participants for the confirmatory study is a little below the recommended minimal number needed which might explain why the fit of our three-factor model is satisfactory but could be improved if a larger sample was tested. Overall, these findings provide again support for the Blazhenkova & Kozhevnikov's three-dimensional model of cognitive style.

At last, our translation demonstrated acceptable convergent validity. Indeed, participants' ratings on the object, spatial and verbal scales correlate positively with the corresponding task only. Although we did not find significant correlations between the verbal and spatial factors nor between OSIVQ verbal and spatial scores, we did find a weak but significant negative correlation between the OSIVQ verbal scores and MRT scores. This suggests that there might be some interference between spatial and verbal information processing. It is worth noting that a negative correlation between verbal and spatial factors was similarly found by [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF]. They also found negative correlations between OSIVQ object and spatial imagery measures which we did not find. Rather, our results indicate that object and spatial imagery are independent. The difference might be due to the number of items used in the two studies.

One limit of our study is that we were not able to evaluate the test-retest reliability and the ecological validity of this translated questionnaire. It could be interesting in the future to reevaluate some of our participants. Similarly, we could assess cognitive style in different professional domains or university courses as did [START_REF] Blazhenkova | The new object-spatial-verbal cognitive style model: Theory and measurement[END_REF]. Our translated questionnaire still showed good psychometric properties. We believe that it was necessary to translate this questionnaire in order to provide a French tool that evaluates cognitive style while making the distinction between object and spatial imagery. Indeed, cognitive styles have important every-day life implications that need to be understood.

In fact, the original version of the OSIVQ has allowed many psychology and cognition researches that showed the importance of cognitive style. For instance, when learning with texts and pictures, learners' cognitive style might have a direct influence on learning behavior and preferences. Indeed, when learning with text-picture combinations, participants scoring high on the object scale and/or the spatial scale of the OSIVQ, relied more heavily on pictures than on texts while participants scoring high on the verbal scale tended to rely more on text [START_REF] Höffler | More Evidence for Three Types of Cognitive Style: Validating the Object-Spatial Imagery and Verbal Questionnaire Using Eye Tracking when Learning with Texts and Pictures: Evidence for three types of cognitive style[END_REF]. Moreover, cognitive style seems also be linked with mathematical performances. "Spatial visualizers" had significantly higher spatial ability and performed better in mathematical tests than "object visualizers" [START_REF] Haciomeroglu | Object-spatial Visualization and Verbal Cognitive Styles, and Their Relation to Cognitive Abilities and Mathematical Performance[END_REF]. Finally, cognitive style has been shown to influence spatial orientation. "Object visualizers" were better than "spatial visualizers" at recognizing visuals clues in an orientation task whereas "spatial visualizers" were better than "object visualizers" for judging relative positions between the visual clues [START_REF] Kraemer | Verbalizing, visualizing, and navigating: The effect of strategies on encoding a large-scale virtual environment[END_REF]. A link between cognitive style and creativity was also established. Object visualization seems to be linked to artistic creativity (physical creativity), spatial visualization is linked to scientific creativity (creativity in math and science), while both are distinct from verbal creativity (creativity in interpersonal relationships, communication, and writing) [START_REF] Kozhevnikov | Creativity, visualization abilities, and visual cognitive style[END_REF].

In conclusion, our French translation of the OSIVQ presents good psychometric properties and is in agreement with the latest theories on cognitive style. Furthermore, this French version of the OSIVQ can certainly be a valuable tool for future researches. Mes images mentales de différents objets ressemblent beaucoup, en termes de taille, de forme et de couleur, aux vrais objets que j'ai vus 1 -2 -3 -4 -5 24 Habituellement, je n'essaie pas de visualiser ou de dessiner des diagrammes lors de la lecture d'un manuel 1 -2 -3 -4 -5

  figures were rotated versions of the target figure, and the other two comparison figures were

Figure 1 .

 1 Figure 1. Estimated three-factor model. Numbers above the arrows indicate the standardized factor loadings.

9

  Il est difficile pour moi de rédiger des dissertations et je n'aime pas du tout faire de la fiction, je me forme habituellement une image mentale claire et détaillée d'une scène ou d'une pièce qui a été décrite 1 -2 -3 -4 -5 12 Si on me demandait de choisir entre un métier d'ingénieur et un métier dans les arts visuels, je choisirais les arts visuels 1 les images avec des couleurs vives et des formes inhabituelles comme celles en art moderne 1 à un concept abstrait (ou à une construction), j'imagine mentalement une construction abstraite schématique ou son plan plutôt quentre dans un magasin familier pour obtenir un article spécifique, je peux facilement visualiser la localisation exacte de cet article, l'étagère sur laquelle il se trouve, comment il est arrangé et les articles environnants 1 plus facile pour moi d'assembler des meubles (par exemple, un meuble de télévision ou une chaise) lorsque j'ai des instructions verbales détaillées que lorsque je n'ai qu'un schéma ou une image 1 explique quelque chose, je préfère donner des explications verbales plutôt que de faire des dessins ou des croquis 1 un devait me donner des nombres à deux chiffres à additionner (par exemple, 43 et 32), je ferais simplement l'addition sans visualiser

Table 1 . Principal component loadings, after Varimax rotation, for the translated OSIVQ items.

 1

, I usually find myself picturing what he or she might look like .47 23 My mental images of different objects very much resemble the size, shape and color of actual objects that I have seen .40 18 When entering a familiar store to get a specific item, I can easily picture the exact location of the target item, the shelf it stands on, how it is arranged and the surrounding articles .39 12 If I were asked to choose among engineering professions, or visual arts, I would choose visual arts .35 1 I was very good in 3D geometry as a student .79 14 I can easily imagine and mentally rotate three-dimensional geometric figures .76 31 In school, I had no problems with geometry .74 32 I am good in playing spatial games involving constructing from blocks and paper (e.g. Lego, Tetris, Origami) .71 44 My graphic abilities would make a career in architecture relatively easy for me .68 27 I have excellent abilities in technical graphics .68 42 I find it difficult to imagine how a three-dimensional geometric figure would exactly look like when rotated .66 30 I can easily sketch a blueprint for a building I am familiar with .65 7 I prefer schematic diagrams and sketches when reading a textbook instead of colorful and pictorial illustrations .45 17 When thinking about an abstract concept (or building), I imagine an abstract schematic building in my mind or its blueprint rather than a specific concrete building .40 5 Architecture interests me more than painting .36 16 My verbal skills are excellent .79 35 I have better than average fluency in using words .76 4 My verbal abilities would make a career in language arts relatively easy for me .64 39 I enjoy being able to rephrase my thoughts in many ways for variety's sake in both writing and speaking .62 37 I am always aware of sentence structure .58 9 Essay writing is difficult for me and I do not enjoy doing it at all .52 2 I have difficulty expressing myself in writing .52 41 I sometimes have a problem expressing exactly what I want to say .48 8 I tell jokes and stories better than most people .38

Table 2 .

 2 Values of fit for the different models

	Model	X²	df	p -value X ²/df	CFI	GFI	RMSEA	AIC
	Three-factor with 45 items 2459.8	942	.001	2.61	.62	.72	.07	2645.8
	Three-factor with 34 items 1156.1	524	.001	2.21	.79	.82	.06	1298.1
	Two-factor with 34 items	2087.3	526	.001	3.97	.48	.61	.09	2225.3

Table 3 .

 3 Matrix of correlations among the OSIVQ spatial, object and verbal scores and paperand-pencil measures demonstrated acceptable convergent validity.

	Measure	1	2	3	4	5	6
	1. Spatial score __	.04	-.17**	-.01	.54**	.04
	2. Object score		__	.15**	.50**	-.05	-.17*
	3. Verbal score			__	.02	-.29**	.32**
	4. VVIQ				__	-.05	-.05
	5. MRT					__	-.01
	6. Mill Hill						__
	** p < .01
	* p < .05

Acknowledgments

We thank Teresa Blicharska Strayer for her help in the translation of this questionnaire and Patrick Raynal for his insights on this article. We also thank undergraduate students for their assistance in data collection. We are grateful for participants' time and commitment.

Funding

This work was funded by the French National Research Agency (ANR-19-CE28-0012).

Tabachnick BG, Fidell LS. Principal components and factor analysis. Using multivariate statistics 2001;4:582-633. Vandenberg, S. G., & Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills,47(2), 599-604.

Supplementary data