PhD Caroline Méjean
email: c.mejean@uren.smbh.univ-paris13.fr

PhD Valérie Deschamps

MSc Constance Bellin-Lestienne

MSc Amivi Oleko

PhD Nicole Darmon

PhD Serge Hercberg

PhD Katia Castetbon

Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (The ABENA study 2004-2005)

Keywords: food aid, food supply, dietary behaviour, socioeconomic discrepancies, deprived population

Background/Objectives: Few studies in Europe have examined the relationship of sociodemographic and economic factors with diet in deprived populations. We analysed the association between socioeconomic characteristics and consumption of different food groups in food aid users. Subjects/Methods: A cross-sectional study was conducted among food aid users in four urban French zones (n=1,664). Associations of sociodemographic and economic factors and food aid use with frequency of consumption of the main food groups were tested using multivariate logistic regression models accounting for sampling weights.

Results: Both migrant status and consumption of fewer than 3 daily meals were associated with risk of low frequency of starchy food consumption (<3 times per day). Migrant status was also associated with low frequency of consumption of fruits and vegetables (<3.5 times per day) and dairy products (<2 times per day). Subjects with severe food insufficiency were more likely to be low consumers of fruits and vegetables, meat, seafood and eggs (<1 time per day), and dairy products. A low monthly food budget, temporary housing in a shelter and no source of household income were all associated with risk of low frequency of seafood consumption (< 2 times per week). Finally, duration of food aid use, type of food aid distribution and perception of poor health status were associated with low consumption of meat, seafood and eggs.

Conclusion: Economic level and other social characteristics were associated with an unhealthy diet within this deprived French population.

INTRODUCTION

Diet is influenced by sociodemographic, economic and cultural factors. It is well documented that low socioeconomic status, a poor education level and unemployment are associated with an unhealthier diet than that found for populations with higher economic status [START_REF] Darmon | Does social class predict diet quality?[END_REF][START_REF] Irala-Estevez | A systematic review of socio-economic differences in food habits in Europe: consumption of fruit and vegetables[END_REF][START_REF] Lallukka | Multiple socio-economic circumstances and healthy food habits[END_REF]. In addition, dietary patterns vary according to demographic profiles, including gender, marital status and acculturation [START_REF] Neuhouser | Higher fat intake and lower fruit and vegetables intakes are associated with greater acculturation among Mexicans living in Washington State[END_REF][START_REF] Sanchez-Villegas | Gender, age, socio-demographic and lifestyle factors associated with major dietary patterns in the Spanish Project SUN (Seguimiento Universidad de Navarra)[END_REF].

Associations between diet and the above determinants have been studied mainly within general populations or in deprived populations. Most available studies in deprived populations were conducted among participants in food assistance programs in the USA and Canada [START_REF] Bhargava | Socio-economic and behavioural factors are predictors of food use in the National Food Stamp Program Survey[END_REF][START_REF] Rose | Economic determinants and dietary consequences of food insecurity in the United States[END_REF]. They showed a gradient of unhealthy dietary patterns in parallel with lower socioeconomic status and increasing food insufficiency. Food insufficiency, defined as "an inadequate amount of food intake due to lack of resources" [START_REF] Alaimo | Food insufficiency exists in the United States: results from the third National Health and Nutrition Examination Survey (NHANES III)[END_REF], forms a part of a causal chain that begins with economic considerations and ends with nutritional outcome. As a consequence, poor nutritional status, i.e. insufficient quality and frequency of food intake [START_REF] Dixon | Dietary intakes and serum nutrients differ between adults from food-insufficient and food-sufficient families: Third National Health and Nutrition Examination Survey, 1988-1994[END_REF][START_REF] Sharkey | Diet and health outcomes in vulnerable populations[END_REF], can lead to poor health status [START_REF] Siefert | Food insufficiency and physical and mental health in a longitudinal survey of welfare recipients[END_REF]Vozoris & Tarasuk, 2003).

Although food insufficiency has become a matter of increasing concern in Europe over the past few decades, very few studies on this continent have assessed dietary intake and its determinants in deprived populations. In France, the French Nutrition and Health Programme ("Programme National Nutrition Santé", PNNS implemented in 2001) has incorporated a national programme of diet and social integration that was begun in 2003. One of its priorities was to improve the nutritional status of disadvantaged populations [START_REF] Hercberg | The French National Nutrition and Health Program: 2001-2006-2010[END_REF]. In this framework, the "Diet and nutritional status of beneficiaries of food aid" study ("Alimentation et état nutritionnel des Bénéficiaires de l'Aide Alimentaire", ABENA), conducted in 2004-2005, provided evidence of unhealthy diet and poor health profiles and highlighted the diversity of precarious situations and sociodemographic heterogeneity among recipients of various types of food aid [START_REF] Bellin-Lestienne | Food consumption and position of food aid among participants of the ABENA study, 2004-2005[END_REF]. French food aid organisations are charities engaged in directly distributing food to deprived populations; they target potential beneficiaries according to restrictive economic criteria. The food aid structure includes centres which serve meals, others that distribute food parcels (food is prepared beforehand) and social grocery stores (offering some choice of low-cost foods). Sociodemographic and/or economic high-risk profiles resulting in unhealthy diet might be emerging within this deprived European population. The aim of the present analysis was to elucidate, in food aid users participating in the ABENA study, possible associations of sociodemographic characteristics, economic factors and food insufficiency levels with inadequate dietary intake. Nutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Manuscrit sampling method was used to select individuals. For the first stage, 12 food aid centres in each zone were randomly selected among the one-hundred-forty centres which had been previously identified within the four urban areas (Darmon et al., 2008). Then, subjects aged ≥18 years were randomly selected at each selected food aid centre according to the usual manner of frequentation (with or without an appointment). Only one responder per household was enrolled. We selected subjects who spoke French unless an interpreter was available.

Indeed, given the diversity of countries of origin of migrants in France, specific translations for each language during the survey were not possible.

Interviewers questioned subjects on sociodemographic and economic status, diet, food supply and food aid use, and requested that they undergo clinical and biochemical examinations. We informed participants about voluntary participation, the confidentiality Since the first objective of the ABENA study was to assess the nutritional status of food aid users in France, for sample size determination, we assumed that the estimated prevalence of obesity among food aid recipients was twice as high as that of the general population, i.e.

20% [START_REF] Charles | Monitoring the Obesity Epidemic in France: The Obepi Surveys 1997-2006[END_REF] with an alpha-type error of 0.05 and statistical power of 0.90. This gave a designated sample of 250 persons in each zone.

Data collection. Data were collected by dieticians trained and standardised in the use of computer-assisted personal interviews, including quality checks (Ethnos©CAPI, Soft Concept, Lyon, France). [START_REF] Hercberg | The French National Nutrition and Health Program: 2001-2006-2010[END_REF] were specified at the time of the interview. Initially based on 8 questions, we finally described five food groups for which food specifications were as follows: The 'starchy foods' group included potatoes, pasta/semolina, rice, legumes, bread, and breakfast cereals. The fruits and vegetables group was composed of all fruits and vegetables and 100% juices. Milk, yoghurt, cheese and fresh cheese, but not sugared creamy desserts, were included in the 'dairy products' group. Finally, the meat, seafood and eggs category included red meat, white meat, offal, fish, crustaceans-molluscs and eggs. Since a specific recommendation had been elaborated for seafood in French dietary guidelines [START_REF] Hercberg | The French National Nutrition and Health Program: 2001-2006-2010[END_REF], this food group was separately analysed.

Sociodemographic and economic factors studied included gender, age, place of birth, marital status, having at least one child, housing, education level, current job status and primary source of household income. Food insufficiency was also measured using the USDA Food Sufficiency Indicator [START_REF] Radimer | Measurement of household food security in the USA and other industrialised countries[END_REF] and was classified into three categories:

'food-sufficiency', 'mild food insufficiency' and 'severe food insufficiency ' (Townsend et al., 2001). Food budget (per month and per person), maximum number of meals per day and duration of food aid use were also evaluated. Finally, general self-perceived health status was assessed.

Statistical analysis. To take into account the complex survey design, a survey weight equal to the inverse of the probability of selection was assigned to each sampled centre and each sampled subject, stratified by zone and type of organisation.

Low frequency of consumption was defined for each food group as follows: <3 times per day for starchy foods; <3.5 times per day for fruit and vegetables; <1 time per day for meat, seafood and eggs; <2 times per week for seafood; and <2 times per day for dairy products. fruits and vegetables, we used the public health objective which advises "reducing the prevalence of low consumers", defined as those eating fewer than 3.5 fruits and vegetables per day [START_REF] Hercberg | The French National Nutrition and Health Program: 2001-2006-2010[END_REF]. For dairy products, we used a lower threshold than the recommendation ("3 times per day") because too few subjects were above the recommended value.

Univariate logistic regressions were performed by calculating odds ratios (OR) and 95% CI to determine the strength of the association between 'low' frequency of food group consumption and each explanatory variable. Only explanatory variables associated with frequency of food group consumption at the 0.2 significance level, were retained for inclusion in the initial multivariate model. Subsequently, using stepwise backward elimination, multivariate logistic regression models were constructed. Gender was retained as a potential confounder in all models. Variables were removed from the model one by one using P>0.10 for exclusion.

Variables whose exclusion from the model caused large fluctuations in OR (>10%), as well as variables whose exclusion gave rise to significant likelihood ratio tests (P <0.05), were reentered into the model. Significance tests were 2-sided, with a P value set at <0.05.

Interaction effects between gender and other explanatory variables were also examined.

All analyses took sampling weights into account. Statistical analyses were conducted using the SAS procedures ' surveyfreq', and 'surveylogistic' (version 9.1; SAS Institute, Cary, USA).

The Taylor Series expansion method was used to adjust SE and CI for complex survey design.

RESULTS

Seventy-seven percent of eligible subjects (1,164/1,506) agreed to participate in the study.

General characteristics of the sample are presented in Table 1. For analyses of associated factors with frequencies of low consumption, none of the interaction terms between gender and the other main effect variables proved to be statistically significant in final models. For each food group, variables retained from univariate analyses for introduction into multivariate models are presented in Table 2.

Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon Subjects who frequented centres which served meals were more likely to be low consumers of seafood than those who frequented social grocery stores (Table 3). Food aid users who lived in a shelter were less likely to be low consumers of this food group than those who had their own housing. In addition, food budget and duration of food aid use were inversely associated with low consumption of seafood (Table 3). Individuals who ate at most 3 meals a day and who declared having medium or low health status perception were more likely to be Dairy products. Only 9.2% of participants met the recommendations of the PNNS for 3 dairy products per day, whereas 61.0% were low consumers (< 2 per day). Compared with localborn French, sub-Saharan migrants were more likely to be low consumers of dairy products, whereas Eastern European migrants were less likely to be low consumers (Table 4).

Individuals who did not work and those who did not have administrative approval for working were more likely to be low consumers of dairy products. In addition, food insufficiency was positively associated with low consumption of this food group (Table 4). Finally, subjects who ate at most 3 meals a day were more likely to be low consumers of dairy products.

DISCUSSION

Our study highlights the fact that economic factors and food insufficiency are strongly related to low consumption of certain food groups, even in food aid users in France. Although subjects all belonged to very low-income populations, such disparities were determinants of unhealthy diet. Moreover, our results showed no influence of the usual sociodemographic factors in this deprived population, i.e. age, marital status or educational level. Finally, frequency of consumption was influenced by behaviour relating to food aid, such as duration of food aid use.

Regarding dietary intake of food aid users, we found low levels of fruit and vegetable consumption in line with a recent national study among low-income households in the UK (Low Income Diet and Nutrition Survey) [START_REF] Nelson | Low income diet and nutrition survey. Summary of key findings[END_REF]. However, the dietary assessment methods and recruitment methods were very different (four 24-h recalls in the UK compared to an 8-question-food frequency questionnaire in our study).

In terms of socioeconomic factors, food aid users who lived in a shelter and those without any source of household income were less likely to be low consumers of seafood. Detailed analysis showed that more deprived individuals (in terms of housing and income) strongly depended on food aid for their seafood supply (data not shown). Indeed, because of distribution of canned seafood, access to seafood was better at food aid centres than at other seafood sources. Moreover, seafood was the sole food group for which consumption was strongly associated with food budget. Food aid users may have restricted their choices through less consumption of more expensive food products [START_REF] Maillot | Nutrient-dense food groups have high energy costs: an econometric approach to nutrient profiling[END_REF]. Our questionnaire was unable to differentiate fresh from canned seafood, but we hypothesize that this association mainly referred to canned seafood. Indeed, fresh seafood was less frequently distributed at food aid centres than were the other food groups and than canned seafood, which is heavily distributed at social grocery stores and centres distributing food parcels (Darmon et al., 2008). Moreover, subjects who had benefited from food aid for less than three years were lower consumers of seafood than long-term users. Long-term food aid users may have a better knowledge of the food aid system and consequently know how and where to obtain seafood so as to maintain their consumption.

Consistent with other studies on both general and low-income populations [START_REF] Cristofar | Dietary intakes and selected characteristics of women ages 19-50 years and their children ages 1-5 years by reported perception of food sufficiency[END_REF][START_REF] Dixon | Dietary intakes and serum nutrients differ between adults from food-insufficient and food-sufficient families: Third National Health and Nutrition Examination Survey, 1988-1994[END_REF][START_REF] Tarasuk | Household food insecurity with hunger is associated with women's food intakes, health and household circumstances[END_REF], our findings also highlighted the fact that, the more severe the food insufficiency, the lower the consumption of meat, seafood and eggs, dairy products and, fruits and vegetables. Although food aid users generally had much lower consumption of these foods than the general French population [START_REF] Castetbon | Dietary intake, physical activity and nutritional status in adults: the French nutrition and health survey (ENNS, 2006-2007)[END_REF], this observation underlines the fact that, irrespective of their common highly precarious situation, some food aid users considered themselves to be food-sufficient.

Various strategies may be employed by individuals when confronted with the problem of food insufficiency, including dietary changes, food-seeking strategies and rationing strategies, such as skipping meals and skipping eating for entire days [START_REF] Oldewage-Theron | Poverty, household food insecurity and nutrition: coping strategies in an informal settlement in the Vaal Triangle, South Africa[END_REF].

Food aid would appear to be insufficient for overcoming food insufficiency, as almost half of food aid users skipped one of the three daily meals [START_REF] Bellin-Lestienne | Food consumption and position of food aid among participants of the ABENA study, 2004-2005[END_REF].

Consequently, our results also showed that reduced meal frequency was strongly associated with low consumption of starchy foods, meat, seafood and eggs, and dairy products. (Darmon & Khlat, 2001). In contrast, unlike our findings for fruits and vegetables, other studies indicated that North African migrants conserved a traditionally high consumption of this food group (Darmon & Khlat, 2001;[START_REF] Mejean | Diet quality of North African migrants in France partly explains their lower prevalence of diet-related chronic conditions relative to their native French peers[END_REF]. Contrary to studies in the general population, country of birth in this deprived population probably reflected economic barriers to food access rather than sociocultural characteristics, which help to maintain traditional healthy dietary patterns [START_REF] Mejean | Influence of acculturation among Tunisian migrants in France and their past/present exposure to the home country on diet and physical activity[END_REF]. Our results also showed the substantial influence of country of birth in other migrant groups. To our knowledge, up to now, no study has specifically assessed the dietary patterns of these migrant groups in France. Furthermore, in contrast with studies on the French general population [START_REF] Kesse-Guyot | Dietary patterns and their sociodemographic and behavioural correlates in French middleaged adults from the SU.VI.MAX cohort[END_REF][START_REF] Perrin | Ten-year trends of dietary intake in a middle-aged French population: relationship with educational level[END_REF], an unhealthy dietary pattern among food aid users was not associated with age, marital status or education level. The influence of common sociodemographic factors seems to be lessened by differences in economic profiles and food insufficiency levels within this deprived population.

Characteristics of the study must be taken into account for interpreting results. Since the study was limited to four French areas, it did not intend to represent food aid centres at a national level. However, because of the random nature of the sample, our study was representative of food aid users in these four urban zones. Concerning selection bias, elimination of persons not meeting the French language requirement and who were not accompanied by a French speaker may have led to underestimating the dietary quality of food aid users. In contrast, since participants were interviewed at food aid centres, they were awaiting food assistance during the survey; consequently, they may have underreported their food consumption. Moreover, data collected using a very short food frequency questionnaire, without recording portion sizes, are not as accurate as data gathered using classical validated food frequency questionnaires. Moreover, food frequency methods are less precise than recall and food record methods (Willett, 1998). However, we did not aim to Nutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009 insufficiency because of a perceived reluctance to report problems with food. However, the literature recommends using direct rather than indirect indicators, since the latter, such as poverty or low income, would incorrectly identify a large percentage of households as being affected by food insufficiency [START_REF] Rose | Economic determinants and dietary consequences of food insecurity in the United States[END_REF].

Finally, various social and economic factors as well as food insufficiency levels were strong determinants of dietary inadequacy. Thus, our study would appear to confirm those carried out on general populations showing that access to healthy diet depends on the poverty gradient, even within this deprived population. Moreover, despite heterogeneity among food aid users, no specific sociodemographic high-risk profile for low consumption of food groups was observed, indicating only a weak influence of sociodemographic characteristics upon dietary patterns, as opposed to economic factors. Based on our results, specific strategies could be set up within food aid organisations to take into account economic disparities among food aid users. It is particularly important to improve food availability and diversity at food aid centres in order to improve the diet of food aid users.

Thus, our study provides useful observations on characteristics of food aid use and its association with diet, with the goal of assisting health policy decisions and those of food aid associations. In the context of a reform of the European "Most Deprived" food aid scheme, our results should help to more clearly identify the needs of food aid users, and consequently, to better define food aid distribution.

Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon Nutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009 1-Adjusted odds ratios 2-Persons who did not have administrative approval for working but who had access to food aid

  . The ABENA study was a cross-sectional study conducted from November 2004 to May 2005 among individuals frequenting food aid organisations in four urban French zones (Paris, Seine-St-Denis, Dijon and Marseille). A two-stage cluster

  agreement and their right to refuse to participate. The protocol was approved by the French data protection authorities (CNIL n°04.312) and by the Ethical Committee (Comité Consultatif pour la Protection des Personnes se prêtant aux Recherches Biomédicales, Hôpital Paris Cochin n°2178).

  These frequency cut-offs were based on French dietary guidelines with two exceptions. For Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153

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	Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C.
	(2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in
	France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4),
	374-382. DOI : 10.1038/ejcn.2009.153

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Starchy foods. Almost half of the subjects (48.7%) consumed at least 3 times per day. In the final model (results not shown), North African migrants were less likely to be low consumers

	Manuscrit d'auteur / Author manuscript	of starchy foods than local-born French (OR=0.60 [0.39-0.94]; P=0.03). Moreover, individuals who ate at most 3 meals a day were low consumers of starchy foods (OR=2.85 [1.86-4.37]; P<0.0001). Fruit and vegetables. Only 1.2 % of participants ate at least 5 fruits and vegetables daily and 94.5% ate less than 3.5 per day. North African migrants and 'other migrants' were significantly more likely to be low consumers of fruit and vegetables than local-born French (respectively OR=2.93 [1.01-8.54]; P=0.04 and OR=7.38 [2.36-23.10]; P=0.0006) (results not
	Manuscrit d'auteur / Author manuscript
		OR=3.30
	Manuscrit d'auteur / Author manuscript	[2.15-5.04]; P<0.0001 and OR=1.75 [1.14-2.67]; P=0.01). Concerning seafood, only 27.3% of participants ate seafood at least 2 times a week.
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, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

shown). Subjects experiencing severe food insufficiency were more likely to be low consumers than those who were food-sufficient (OR=5.

77 [1.49-22.33

]; P=0.01).

Meat, seafood and eggs. Half of the participants consumed meat, seafood and eggs one to two times a day, in line with the PNNS, whereas 42.6% were low consumers of this food group. Food aid users who frequented centres which distributed food parcels were less likely to be low consumers of meat, seafood and eggs than those who frequented social grocery stores (OR=0.48 [0.31-0.74]; P=0.01) (result not shown). Individuals experiencing severe food insufficiency were more likely to be low consumers of this category than those with mild food insufficiency

(OR= 2.06 [1.33; 3.18]

; P=0.001). In addition, food aid users who ate at most than 3 meals a day, and those who declared having medium or low health status perception were more likely to be low consumers of this food group (respectively,

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153

		low consumers of this food group. Furthermore, subjects who had no source of household
		income had less probability of being low consumers of seafood than those who received
	Manuscrit d'auteur / Author manuscript	social assistance benefits (OR=0.31 [0.12; 0.77]; P=0.01) and those with other sources of income (OR=0.31 [0.12; 0.76]; P=0.01).
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Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153

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Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

  Version définitive du manuscrit dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153

		addition, low consumption of food groups was associated with country of birth. In
		accordance with our results, previous studies showed higher consumption of starchy foods
	Manuscrit d'auteur / Author manuscript	among North African migrants in France compared with local-born French
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Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

  Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of Clinical

Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

  .153 dietary intake. Rather, we were primarily interested in obtaining a high participation rate, in light of the difficulties in carrying out a survey at food aid centres. And finally, since the USDA indicator is a subjective appreciation of the food insufficiency level, this direct measurement might underestimate the prevalence of food

	comprehensively assess detailed
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Table 2 .

 2 Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Townsend MS, Peerson J, Love B, Achterberg C, Murphy SP (2001): Food insecurity is positively related to overweight in women. J.Nutr. 131, 1738-1745. Vozoris NT, Tarasuk VS (2003): Household food insufficiency is associated with poorer health. J Nutr. 133, 120-126. Willett, WC., Nutritional Epidemiology. 2nd ed. New York, NY: Oxford University Press: 1998.Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Univariate analysis of the association between explanatory variables and low consumption of food groups Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C.Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of ClinicalNutrition, 2010, vol.64, no.4, 374-382, DOI: 10.1038/ejcn.2009.153 Persons who did not have administrative approval for working but who had access to food aid Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153 Version définitive du manuscrit publié dans / Final version of the manuscript published in : European Journal of Clinical

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, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153 Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 374-382. DOI : 10.1038/ejcn.2009.153 (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153 Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon, N., Serge, H., Katia, C. (2010). Associations of socioeconomic factors with inadequate dietary intake in food aid users in France (the ABENA study 2004-2005). European Journal of Clinical Nutrition, 64 (4), 374-382. DOI : 10.1038/ejcn.2009.153

Table 3 .

 3 .153 Multivariate logistic analysis of the association between social and economic characteristics and low consumption of seafood

	Manuscrit d'auteur / Author manuscript	OR 1 Served meals 3.42 Food parcels 1.38 Social grocery 1.00 Male 1.68 Female 1.00 Homeless 0.68 Shelters 0.46 House/flat, housed by family 1.00 No current authorization for working Type of centre Gender Type of dwelling Current job status 2 1.47	Multivariate model CI 1.61-7.29 0.79-2.39 0.82-3.43 0.26-1.81 0.25-0.83 0.35-6.22	P-value 0.01 0.25 0.15 0.44 0.01 0.59
		Not working 2.90	0.95-8.89	0.06
		Working 1.00
		Primary source of household income
	Manuscrit d'auteur / Author manuscript	Other 1.23 None 0.38 Social assistance benefits 1.21 Employment, senior's pension or unemployment insurance 1.00 Food budget (per month/ per person) < 60 euros 3.37 60-120 euros 4.37 > 120 euros 1.00 Duration of food aid use < 1 year 3.59 1-3 years 3.96 ≥ 3 years 1.00 Maximum number of meals per day < 3 meals 2.47 ≥ 3 meals 1.00 Health status perception	0.41-3.69 0.12-1.13 0.59-2.51 1.64-6.79 2.06-9.29 1.92-6.72 1.93-8.13 1.40-4.36	0.72 0.08 0.60 0.0009 0.0001 <0.0001 0.0002 0.002
		Medium/low 2.01	1.20-3.36	0.008
		High 1.00
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ACKNOWLEDGEMENTS

The authors thank French associations involved in food aid for their kind cooperation. We are grateful to the Social Security Health Examination Centres and their laboratories in Bobigny, Paris, Dijon and Marseille, the "Département de Biologie intégrée" at Grenoble University

Diet in food aid users

This study was supported by the Institut de Veille Sanitaire (InVS), France

Comment citer ce document : Méjean, C., Deschamps, V., Bellin-Lestienne, C., Oleko, A., Darmon 1-Adjusted odds ratios 2-Persons who did not have administrative approval for working but who had access to food aid.


Professor Pierre Casal

Henri Gouin

Invariance Properties of Inviscid Fluids of Grade n

Keywords: Inviscid fluids, invariance properties of flows, classification of flows, complex fluids PACS: 47.10.-g, 47.10.ab, 47.15.ki 1991 MSC: 76A02, 76M60

. First integrals and theorems of circulation are deduced. A general classification of flows is proposed.

Introduction

In continuum mechanics, media of first gradient order cannot represent fluids with strong density variations. Material surfaces need their own characteristic behaviour and energy properties [START_REF] Barrere | Equations fondamentales de l'aérothermochimie[END_REF]. Fluids of grade n (n is any integer greater than 1 ) are continuous media with an internal energy per unit mass ε which is a function of the entropy s, the density ρ and spatial gradients up to the n -1 order: ε = ε s, grad s, ..., (grad) (n-1) s, ρ, grad ρ, ..., (grad) (n-1) ρ Email address: (Corresponding author) henri.gouin@univ-cezanne.fr (Henri Gouin).

Preprint submitted to Lecture Notes in Physics, vol. 344, p. 85-98, Springer, Berlin (1989) D.J. Korteweg pointed out the advantage of fluids of grade n with respect to the density and removed the discontinuity surfaces representing the capillary layers in liquid-vapour interfaces [START_REF] Korteweg | [END_REF]. We improve the model accuracy by taking into account the successive gradients of density. Recently, this approach was used in the case of dynamic changes of phase [START_REF] Serrin | New Perspectives in Thermodynamics[END_REF]. Till now, the thermodynamic part of the fluid has been neglected. Due to the fact it is not possible to consider a virtual displacement of temperature, it is necessary to use the entropy by the way of the internal energy. The equation of motion with both strong gradients of density and entropy is obtained. One can accord importance to the fact that the thermodynamic form of the equation of motion is independent of the order n. Flows with strong variations of temperature such as those associated with combustion phenomena or non-isothermal interfaces may be considered.

The conservative flows of classical perfect fluids are only a mathematical model. It is also the case for fluids of grade n. The study of their structure is necessary. The conclusions for fluids of grade n are of the same kind as for compressible fluid [START_REF] Serrin | Encyclopedia of Physics VIII/1[END_REF]: it is possible to obtain a Clebsh transformation of the motion equations (potential equations) and many invariance properties and first integrals. The potential equations may be used to classify motions in the same manner as in the case of perfect fluids [START_REF][END_REF]7]. The simplest case is for fluids of grad 2 (or thermocapillary fluids): the internal energy is a function only of the density, the entropy and their first spatial derivatives ε = ε(s, grad s, ρ, grad ρ) and n > 2 adds little except for complications in the momentum balance equation. If we consider flows through liquid-vapour interfaces and use convenient physical units, the equations of thermocapillary fluids are able to study non-isothermal motions and yield a possible interpretation of film boiling phenomena [START_REF] Casal | Sur les interfaces liquide-vapeur non-isothermes[END_REF][START_REF] Casal | A representation of liquid-vapour interfaces by using fluids of second grade[END_REF].

Thermodynamic form of the equation of motion for inviscid fluids of grade n

The principle of virtual works allows to obtain the equation of motion. In the case of a perfect fluid motion, it is written by means of the Hamilton principle [START_REF] Serrin | Encyclopedia of Physics VIII/1[END_REF][START_REF][END_REF]10]. The variations of particle motions are deduced from families of virtual motions of the fluid in the form [5]

X = Ψ(x, t, α)
where α is a parameter defined in a neighbourhood of zero. The real motion corresponds to α = 0. A particle is represented in Lagrange coordinates by X (X 1 , X 2 , X 3 ) as a position in a reference space D o . At time t its position is given in D t by the Eulerian representation x (x 1 , x 2 , x 3 ) (see Appendix). The virtual displacements associated with a variation of the real motion can be written

δX = ∂Ψ ∂α (x, t, α) α=0
The variation is dual with Serrin's [START_REF] Serrin | Encyclopedia of Physics VIII/1[END_REF]: the two variations are mathematically equivalent [11]. The Lagrangian of a fluid of grad n is defined as

L = ρ 1 2 V * V -ε -Ω ,
where V denotes the velocity, Ω denotes the extraneous force potential defined in D t and * is the transposition in D t such that V * V is the scalar product of V by V. Between times t 1 and time t 2 , the Hamiltonian action is

a = t 2 t 1 Dt

L dvdt

The density verifies the balance equation

ρ det F = ρ o (X),
where ρ o is defined in D o and F is the deformation gradient. We deduce

dρ dt + ρ div V = 0 (1)
The entropy variation is the sum of a variation associated with the virtual motion and another one, δ 1 s, related to the particle [START_REF] Casal | A representation of liquid-vapour interfaces by using fluids of second grade[END_REF] δs = ∂s ∂X δX + δ 1 s, where δ 1 s and δX are independent.To obtain the equation of motion, we consider the conservative case corresponding to δ 1 s = 0. Classical methods of variational calculus provide the Hamiltonian action variation δa = 0 A calculus as in [1] yields

δa = t 2 t 1 Dt ρ o d dt (V * F ) -θ grad * o s -grad * o m δX dv o dt,
where

                               m = 1 2 V * V -h -Ω h = ε + p ρ p = ρ 2 ε ′ ρ + ρ n-1 k=1 (-1) k div (k)   ρ ∂ε ∂ grad (k) ρ   θ = ε ′ s + 1 ρ n-1 k=1 (-1) k div (k)   ρ ∂ε ∂ grad (k) s   (2)
We have taken into account the relation δρ

= ρ div o (δX) + 1 det F ∂ρ o ∂X δX and δV = -F d(δX) dt
; div (k) and grad (k) are the divergence and the gradient operators in D t reiterated k-times; div o and grad o are the divergence and the gradient operators in D o . Obviously, p, θ and h have respectively the dimension of a pressure, a temperature and a specific enthalpy. We call these quantities the pressure, temperature and enthalpy of the fluid of grade n .

The Hamilton principle yields:

For any displacement δX null on the edge of D o , δa = 0 .

We get the equation of motion

d(V * F ) dt -θ grad * o s -grad * o m = 0 Let us note that (Γ * + V * ∂V ∂x )F = d(V * F ) dt , we obtain Γ = θ grad s -grad(h + Ω) (3)
In case of inviscid thermocapillary fluids the dissipative function is null and the equations of motion and energy imply [12]:

ρ θ ds dt + div q -r = 0 ( 4
)
where q is the heat flux vector and r the heat supply. This result is extended to the fluids of grade n [START_REF] Cubisol | Contribution à une étude thermomécanique des milieux continus[END_REF].

A constitutive equation must be added to these equations, which yields the behaviour of the heat flux vector q. For example, the Fourier law is

q = -k grad θ and k ≥ 0 (5)
The heat supply is assumed to be given in similar way than the extraneous force potential. From the heat conduction inequality, we obtain the Clausius-Duhem inequality and the fluids of grade n are compatible with the second law of thermodynamics [START_REF] Truesdell | The Classical Field Theories[END_REF][START_REF] Truesdell | Encyclopedia of Physics III/3[END_REF]

ρ ds dt + div q θ - r θ ≥ 0
Consequently, the equations of motions of inviscid fluids of grade n verify

                     Γ = θ grad s -grad(h + Ω) dρ dt + ρ divV = 0 ρ θ ds dt + div q -r = 0 q = -k grad θ and k ≥ 0 (6)
The thermodynamic form of the motion equation of inviscid fluids is equivalent to the classic balance equation. The thermodynamic form is the same for all fluids (independently of the order n). Nevertheless, the complexity of balance equations increases with n. In fact, only the expressions for the temperature and the enthalpy become more complex and we have to modify the definitions of these quantities 1 .

Thermodynamic hypothesis on the motion

If we study the invariance properties of the motions, we must assume that the heat supply allows a behaviour expressing that a thermodynamic quantity T has a zero material derivative or -with a stronger assumption -is constant everywhere in the flow. Consequently equations ( 4) and ( 5) are replaced by one of the two conditions

dT dt = 0 or T = C ste (7)
For example, we will consider the case of an isentropic motion (T = s). Then,

ds dt = 0
For the case of an isothermal motion (T = θ). Then,

θ = C ste 1
The definitions are given by system (2).

They are two limit cases: one is associated with fast motions, the other with slow motions2 . Then, the fluid motions satisfy the system consisting of equations (1), ( 3) and (7).

We consider the more general case when T is a differentiable function of θ and s such that ∂T ∂θ = 0. Consequently, we denote by H(T, s) a differentiable function of the variables T and s such that ∂H ∂s = θ(T, s). The function H is defined, to an unknown function of T , by the differential form

dH = θ ds -u dT
The two variables u and T can be used instead of θ and s to study the general case by transforming Eq. ( 3) following the method of Lemma 1. Let us denote g = h -H, Eq. ( 3) can be written:

Γ = u grad T -grad (g + Ω) (8)
Let us note that if T = θ, g is the free enthalpy (g = hθs) and u = -s, and the motions satisfy System (( 1),( 7),( 8)).

First integrals are obtained by the research of invariant scalars as the state variables of the fluid (the density, the entropy, the velocity, with a zero material derivative) and expression [START_REF] Casal | Sur les interfaces liquide-vapeur non-isothermes[END_REF] allows us to make a single classification for the fluids.

The momentum equation expresses the balance of forces (inertial forces, body forces and stresses).

Let us note that System ((1),( 7),( 8)) is not in balance form, but expresses the fluid evolution: the relation dT dt = 0 implies T is constant along trajectory and the equation of continuity dρ dt = -ρ divV yields the density variation. It will be shown that equations (3) or ( 8) describe the evolution of the velocity field.

Material and convective derivatives

The material derivative of any tensorial quantity expressed in the physical space is the derivative with respect to time when one follows the particle along the motion.

The tensorial quantity has an image in the reference space. The image in the physical space of the derivative with respect to time of the tensorial quantity in the reference space is the value of the convective derivative. The convective derivative is denoted by d c (see Appendix).

The material and the convective derivatives of a scalar are equal. A tensor is convected by the flow when its convective derivative is null.

If we transpose Eq. ( 8), we get the convective derivative of the velocity covector V * in the form

d c V * = grad * 1 2 V 2 -g -Ω + u grad * T. (9)
Eq. ( 9) is equivalent to Eq. ( 8) and yields the Helmholtz-Kelvin theorem in its most general form: Let us consider an arbitrary fluid curve C such that I(t) = C V * dx is the circulation of the velocity field. The circulation of the convective derivative of the velocity field is

dI dt = C d c V * dx = C d 1 2 V 2 -g -Ω + C u dT If C is a closed curve, the integral C d 1 2 V 2 -g -Ω is null. Moreover, if
C is located on a T -surface (surfaces T = C ste are fluid surfaces and this assumption is compatible with the fact that C is a fluid curve), the second integral is null and I is constant along the motion.

When the entropy is constant all over the fluid (T = s = C ste ), the so-called Kelvin theorem corresponds to the special case of homentropic motions: the circulation of the velocity field on any closed curve is constant.

Due to Noether's theorem, it is known that any conservation law can be represented by a group of invariance. It has been shown the conservation law expressed by Helmholtz-Kelvin theorems associated with isentropic fluid curves corresponds to the group of the permutations of the particles of equal entropy [START_REF] Gouin | [END_REF][START_REF] Moreau | Sur les intégrales premières de la dynamique d'un fluide parfait barotrope et le théorème de Helmholtz-Kelvin[END_REF]. This group keeps the equations of motion invariant for both a classical perfect fluid and a perfect fluid of grade n. We propose to define a general perfect fluid as a fluid invariant by this group or as a continuous medium whose motions are submitted to Helmholtz-Kelvin theorems.

Potential equations

Let ϕ and ψ be two scalar fields such that the material derivatives verify

dϕ dt = 1 2 V 2 -g -Ω and dψ dt = u.
Equation ( 9) is equivalent to

d c V * = d c (grad * ϕ + ψ grad * T).
The covector V * and the covector W * = grad * ϕ + ψ grad * T have the same convective derivative. The difference (V -W) * is a covector convected by the flow, which leads to the system

             V = grad ϕ + ψ grad T + C, dT dt = 0, dϕ dt = 1 2 V 2 -g -Ω, dψ dt = u, d c C * = 0. (10)
System (( 1),( 7),( 8)) is equivalent to system ((1),( 10)).

In this case, the generalized Helmholtz-Kelvin theorem is reduced to the circulation of C along any fluid curve is constant.

Due to the Stokes formulae, the vector U = 1 ρ rot C is convected by the flow

(d c U = 0) i.e. : dU dt - ∂V ∂x U = 0 (11)
Due to the fact that C = γ grad ν, where γ and ν are two scalars convected by the flow and grad ϕ, grad ψ, grad ν are three independent vectors (see Lemma 2 and Theorem 3), the system (10) leads to the system of potential equations

             V = grad ϕ + ψ grad T + γ grad ν, dT dt = 0, dϕ dt = 1 2 V 2 -g -Ω, dψ dt = u, dγ dt = 0, dν dt = 0. ( 12
)
In the general case, the velocity field is associated with five potentials; T is one of them3 .

Classification of motions

As for T , the potentials γ and ν have a zero material derivative. They are first integrals of the motion [START_REF] Cartan | Leçons sur les invariants intégraux[END_REF]. These potentials have constant values on each trajectory; when they are constant in a fluid domain, the values remain constant in time-space.

In the domain convected by the flow, the fluid velocity is expressed by fewer potentials characterizing the kinematic properties of the motion. In an adjoining fluid domain, the motion may be different. Then, the flow is separated into different domains that move, remain adjacent and keep their own characteristics.

Due to the absence of viscosity, in hydrodynamics of incompressible perfect fluids the flow is divided into vortical and irrotational domains that do not mix. The following study shows that, for all inviscid fluids of any grade (compressible or not), the vortical domain may be divided into several parts of different kinds 4First integrals are tensorial quantities of different nature. For a non-scalar tensor, the first integral is a tensor convected by the flow (or with a zero convective derivative) i.e. has a constant tensorial image in a reference space.

Oligotropic motions

When the covector C * is zero (i.e. γ = 0 or ν = C ste . ), the velocity field has a particular kinematic type. We have the following properties:

(a) The velocity field can be expressed by the use of three potentials and the equations of motion are

             V = grad ϕ + ψ grad T, dT dt = 0, dϕ dt = 1 2 V 2 -g -Ω, dψ dt = u. (13)
(b) From System (13) we get rot V = grad ψ ∧ grad T,

then grad * T rot V = 0 (14)
Consequently, the vortex lines are located on the surfaces T = C ste .

Property ( 14) is equivalent to System [START_REF] Cubisol | Contribution à une étude thermomécanique des milieux continus[END_REF]. The motions, we call oligotropic motions, are intermediate between irrotational and general motions. In System [START_REF] Cubisol | Contribution à une étude thermomécanique des milieux continus[END_REF], the expression of the velocity is independent of time and the motion remains oligotropic at any moment.

Homentropic motions

The thermodynamic condition is T = C ste (which is stronger than dT dt = 0) and the velocity field is of another particular kind. When T = s , the motion is not only isentropic but also homentropic. We have the following properties:

(a) The velocity field can be expressed with the use of three potentials and the equations of motion are

             V = grad ϕ + ψ grad ν, dT dt = 0, dϕ dt = 1 2 V 2 -g -Ω, dγ dt = 0, dν dt = 0.
In fact the Clebsch representation [START_REF] Lamb | Hydrodynamics[END_REF] is practically worthless because the curves γ = C ste and ν = C ste are the vortical lines whose complexity is well known [START_REF] Villat | Leçons sur la théorie des tourbillons[END_REF]. It is easier to write the motion equations in an equivalent form:

             V = grad ϕ + C, dT dt = 0, dϕ dt = 1 2 V 2 -g -Ω, d c C * = 0. (b) Vector 1 ρ rot V is a convected vector d c 1 ρ rot V = 0 (15)
When a thermodynamic potential T is constant in the flow, the Cauchy theorem for homentropic motions is generalized and Eq. ( 15) is characteristic of these motions. Convected by the flow, the domains become deformed but do not mix.

Irrotational motion

If an oligotropic motion is a motion where T is constant, the velocity field derives from only one potential

             V = grad ϕ, dϕ dt = 1 2 V 2 -g -Ω
At every time, rot V = 05 . This is the case of irrotational motions: the velocity whose the evolution corresponds to the equation of Bernoulli is the gradient of a single potential.

Permanent motions

For a permanent motion, Equation ( 8) may be written in a generalized Crocco-Vaszonyi form rotV

∧ V = u grad T -grad G (16)
where G = 1 2 V 2 + g + Ω. If T = s, g is the specific enthalpy and G the Lamb function [START_REF] Lamb | Hydrodynamics[END_REF] (surfaces where G = C ste are Lamb surfaces). Consequently,

dT dt = 0 ⇔ dG dt = 0
G is a scalar first integral of the motion and we use G for function ν. Potential equations for general permanent flows are

             V = grad ϕ 1 + ψ 1 grad T + γ 1 grad G, dϕ 1 dt = 1 2 V 2 -g -Ω, dψ dt = u, dT dt = 0, dγ 1 dt = 0, dG dt = 0.
Let us note:

dT dt = 0 and dG dt = 0 ⇒ ∂ϕ 1 ∂t = -G; if ϕ = ϕ 1 + tG, ϕ is independent of time.
Let us denote γ 1 = γ + t and ψ 1 = ψ, the equations of motion can be written with potentials independent of time

             V = grad ϕ + ψ grad T + γ grad G, dψ dt = u, dT dt = 0, dγ dt = -1, dG dt = 0. ( 17
Replacing ψ par ψ + γ G ′ T we get              V = grad ϕ + ψ grad T, dψ dt = u -G ′ (T ), dT dt = 0. ( 18
)
These equations characterize permanent oligotropic motions [START_REF][END_REF]. (c) G is constant and T is not constant. This is a particular case of (b): ( dψ dt = u).

(d) T is constant, G is not constant. The equations are

             V = grad ϕ + γ grad G, dγ dt = -1, dG dt = 0, T = T o . (19)
(e) T and G are constant.

We obtain the irrotational motions

V = grad ϕ, G = G o , T = T o
Let us note: All the irrotational motions are not represented by case (e) (such is the case of Hamel's motions [START_REF] Hamel | [END_REF]). In fact, relation [START_REF] Lamb | Hydrodynamics[END_REF] points out that if the motion is irrotational and if one of the mappings T or G is constant, the other mapping is also constant. If neither G nor T are constant, G must depend on T (case (b)): an irrotational motion is oligotropic.

Irrotational motions do not correspond to particular values of the first integrals (or values convected by the flow). In Fig. 2, we represent the flow of a fluid with different domains in D t . The domains are convected by the flow and do not overlap. If each domain has its own color, it keeps the color all along the motion.

Appendix

The motion of the medium consists of the t-dependent C 2 -diffeomorphism ϕ

t [5] X ∈ D o -→ x ∈ D t We deduce dF dt = ∂V ∂x F and dF -1 dt = -F -1 ∂V ∂x .
Let us write T * (D t ) for the cotangent fiber bundle of D t and T * x (D t ) for the cotangent linear space to D t at x; then,

x ∈ D t -→ L(x, t) ∈ T * x (D t )
L ∈ T * (D t ) ϕ -1 * t -→ LF ∈ T * (D o ) d c       d dt dL dt + L ∂V ∂x ϕ * t ←- dL dt F + L ∂V ∂x F ∈ T * (D o ) (20)
Let us note that dL dt + L ∂V ∂x is the Lie derivative of L with respect to the velocity field V6 . The velocity field V is the infinitesimal transformation of the one-parameter group of transformation ϕ t [START_REF] Germain | Cours de mécanique des milieux continus[END_REF]. Let us consider σ(t, x) = σ o [ϕ -1 t (X)], α(t, x) = α o [ϕ -1 t (X)] , β(t, x) = β o [ϕ -1 t (X)] and the field Ξ * of forms in D t corresponding to Ξ * o . Since σ, α, β, ω and δ have zero material derivatives, the previous forms and scalar functions have a zero convective derivatives.

Consequences:

From the representation of the form field C * and for δ = T , we can get two scalar fields ϕ and ψ in System (10); we obtain the potential representation (or Clebsch's representation) for the flows in System (12). We note that the choice of C * is arbitrary and ϕ and ψ are not unique.

Proof of system (18) : System (18) is directly obtained when G is independent of T . In the converse, only a modification is needed: for a given form field Ξ * o in D o , there exist -at least locally-two scalar fields α o and β o such that

Ξ * o = grad * o α o + β o grad * o T o
It is an analog representation as Clesch's [START_REF] Lamb | Hydrodynamics[END_REF]. In this case, we consider a transverse curve (Γ) of T -surfaces and a scalar field

Fig. 1 .

 1 Fig. 1. For perfect fluid motions, the fluid domains are distributed in four parts. Convected by the flow, the domains become deformed but do not mix.

)

  Let us note: C = (γ + t) grad G and d c C * = 0; the behaviour of ϕ ( dϕ dt = V 2 ) is a consequence of the previous equations. The two scalars T and G characterize the motion. The classification of motions is in accordance with the respective positions of the surfaces T = C ste and G = C ste (when T = s they are the isentropic and the Lamb surfaces). We have different cases (a) General case: T and G are independent (or grad T ∧ grad G = 0). The T -surfaces (isentropic surfaces) and the G-surfaces (Lamb surfaces) are different. (b) T is not constant and G = G(T ): the T -surfaces are G-surfaces.

Fig. 2 .

 2 Fig. 2. Classification of permanent motions: the different domains do not mix along the motion of the fluid.

  represents a field of differential forms on D t . Let us write T * (D o ) the cotangent fiber bundle of D o and T * X (D o ) the cotangent linear space to D o at X. The mapping ϕ * t is induced by ϕ t for the form fields. The convective derivation d c of a form field L is deduced from the diagram

Theorem 3

 3 Due to the fact that grad * o δ o and grad * o σ o are two independent forms of D o , the two surface-families δ o (X) = a 1 and σ o (X) = b 1 (where a 1 and b 1 are two arbitrary constants), generate a curve family denoted by (Γ) a 1 b 1 . Let (S) be any transverse surface of the curve family (Γ) a 1 b 1 , point M o denotes the current intersection between (Γ) a 1 b 1 and (S). We denote by M o M the arc of the curve (Γ) a 1 b 1 with origin at M o . We define a differential function as X ∈ D o -→ α o (X) = MoM Ξ * o dX such that dδ o = 0, dσ o = 0 and dα o = Ξ * o dX. Then, there exist -at least locally-two scalar field forms β o and ω o in D o such that Ξ * o dXdα o = β o dδ o + ω o dσ o . For any mapping σ of D t , independent of δ and verifying dσ dt = 0, for any form field Ξ * in D t with a zero convective derivation, there exist -at least locally-three mappings α, β and ω of D t , verifying dα dt = 0, dβ dt = 0 and dω dt = 0 such that Ξ * = grad * α + β grad * δ + ω grad * σ.

  on D o as the circulation of Ξ * o on an arbitrary curve on the T -surface connecting point X at point X o where the surface intersects (Γ). The circulation is independent of the curve connecting X o and X; when dT o = 0 then dα o = Ξ * o dX. Consequently there exists a Lagrangian multiplier β o (X) such that Ξ * o dX = dα o + β o dT o and the Clebsch form is obtained.

The Euler equation represents the equation of motion for classical inviscid fluids. Such motions can be obtained with non-negligible heat flux and heat supply. They correspond to physical situations. As a matter of fact, in the non-dimensional equation of motion for viscous fluids[START_REF] Lamb | Hydrodynamics[END_REF][START_REF] Landau | Fluid Mechanics[END_REF], it is often justified to neglect the viscous terms when, with respect to other physical quantities, the Reynolds number is large. Nevertheless, for large temperature gradients and with a Prandlt number of order one, it is not possible to remove the terms of thermal conductivity. Such a case arises when we study the "thermal" boundary layer[START_REF] Goldsworthy | [END_REF]19] and slow motions of natural convection in fluid with gravity and heat sources associated with large differences of temperature[START_REF] Mandel | Cours de mécanique des milieux continus[END_REF].

The velocity field depends also on the density which is not considered as a potential.

System (12) assumes the flow to be without discontinuity. A shock wave transforms the nature of flow[11,[START_REF] Gouin | Contribution à une étude géométrique et variationnelle des milieux continus[END_REF].

When at one moment rot V = 0, this property is not necessarily verified at every time as in hydrodynamics of compressible fluids.

Generally, for any tensor, the convective derivative is the Lie derivative with respect to the velocity field.

Consequences : D t is assumed to be an Euclidian space; let b be a scalar field on D t . We define two form-fields as V * and (grad b) * . From [START_REF] Mandel | Cours de mécanique des milieux continus[END_REF] we deduce

where Γ is the acceleration vector. Taking into account that

Eq. (3) yields

Lemma 1 Let θ and s be two differential scalars fields in D t .

There exist three scalar fields α, β, γ such that

is equivalent to: there exists a function ϕ such that

Proof :

-If grad θ ∧ grad s = 0 then θ = Φ ′ (s), θ grad s = grad Φ(s) and β = 0.

-If on an open set, grad θ ∧ grad s = 0 then (i) ⇒ grad θ ∧ grad s = grad α ∧ grad β. Consequently, grad θ, grad s, grad α and grad β are in the same plane and there exist ϕ, ψ, χ such that β = ϕ(θ, s), α = ψ(θ, s) and γ = χ(θ, s). So, (i) ⇒ (ii).

(ii) yields locally θ = h(β, s).

There exists γ = H(β, s) such that


domain: sdv info

text:
Chih-Feng Chen
email: cfchen@dragon.nchu.edu.tw

David Gourichon
email: david.gourichon@tours.inra.fr

Nein-Zu Huang

Yen-Pai Lee
email: yplee@dragon.nchu.edu.tw

André Bordas
email: andre.bordas@jouy.inra.fr

Michèle Tixier-Boichard
email: michele.boichard@jouy.inra.fr

Performance comparison of dwarf laying hens segregating for the naked neck gene in temperate and subtropical environments

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Performance comparison of dwarf laying hens segregating for the naked neck gene in temperate and subtropical environments

Chih-Feng Chen, David Gourichon, Nein-Zu Huang, Yen-Pai Lee, André A.

Bordas, Michèle Tixier-Boichard

To cite this version:

Introduction

In poultry selection programmes, birds are generally raised in a uniform environment to record the selected traits and evaluate genetic values. Thus, most commercial populations are obtained from breeding farms with a controlled environment and are delivered to production farms with variable environments across the world. As a consequence, genotype × environment (GxE) interactions may occur. Under subtropical environments, growth rate as well as egg production are generally depressed by high ambient temperature [START_REF] Bordas | Effects of the naked-neck gene on traits associated with egg laying in dwarf stock at two temperatures[END_REF][START_REF] Deeb | Genotype-by-environment interaction with broiler genotypes differing in growth rate, 1. The effects of high ambient temperature and necked-neck genotype on lines differing in genetic background[END_REF]. Introduction of some major genes, such as the naked neck (NA) gene, in chicken lines can be used to alleviate heat stress, as discussed in several studies carried out at high ambient temperatures [START_REF] Bordas | Effects of the naked-neck gene on traits associated with egg laying in dwarf stock at two temperatures[END_REF][START_REF] Chen | Effect of high ambient temperature and naked neck genotype on performance of dwarf brown-egg layers selected for improved clutch length[END_REF][START_REF] Deeb | The effects of the naked neck genotypes, ambient temperature, and feeding status and their interactions on body temperature and performance of broilers[END_REF][START_REF] Horst | Significance of the naked neck gene (Na gene) in poultry breeding in the tropics[END_REF]. Heat tolerance of laying hens is an important issue for the impact of G × E on egg production because the productive period is long and the impact of heat stress increases with the hens' age [START_REF] Bordas | Egg production performances of hens of the NaNa (homozygous naked neck), Nana+ (heterozygous) and na+na+ (normal plumage) genotype from a brown-egg dwarf (dw) line submitted to high constant temperature or to high temperature with periodic fluctuations[END_REF].

At INRA, a selection experiment was undertaken to improve egg production of brown-egg layers by increasing clutch length, in the presence of two major genes known to improve heat tolerance, the naked neck gene [START_REF] Mérat | Potential usefulness of the Na (Naked Neck) gene in poultry production[END_REF] and the sex-linked dwarf gene [START_REF] Mérat | The sex-linked dwarf gene in the broiler chicken industry[END_REF]. After 16 generations, significant genetic progress on egg production was observed in two dwarf lines, one carrying the NA gene and one not carrying it [START_REF] Chen | Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not naked neck gene[END_REF][START_REF] Chen | Correlated response to long-term selection for clutch length in dwarf brown-egg layers carrying or not the naked neck gene[END_REF][START_REF] Tixier-Boichard | Genetic improvement of clutch length in dwarf brown-egg layers: additional selection response with the naked neck gene[END_REF]. The reduction of feather mass due to the NA gene is lower in heterozygous birds than in homozygous birds, i.e. 27% and 22% respectively for heterozygous females and males, and 41% and 33% respectively for homozygous females and males [START_REF] Bordas | Influence of the Na (naked neck) gene on growth, feed consumption and body composition of chicken according to environmental temperature[END_REF]. Heat tolerance is significantly improved by the presence of the NA gene and significant genotype by temperature interactions were observed for egg production, egg mass and feed intake under a 32°C constant temperature environment, which represents a severe temperature stress [START_REF] Chen | Effect of high ambient temperature and naked neck genotype on performance of dwarf brown-egg layers selected for improved clutch length[END_REF]. The purpose of this paper was to study the laying performance in real subtropical conditions of the genotypes obtained from the selection experiment on clutch length, in comparison to the performance in the selection environment.

In order to investigate adaptation of hens, genetic parameters for laying traits were estimated in each environment and the ranking of sire breeding values was compared between environments.

Methods

Genetic background

Two lines of dwarf brown-egg layers established from a common base population in 1985 have been selected on average clutch length for 16 generations. The selection procedure has been described by Chen and Tixier-Boichard [START_REF] Chen | Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not naked neck gene[END_REF]. One line (L1) was normally feathered and the other (L2) was homozygous for the NA*NA mutation; a control line segregating for the NA*NA mutation was also maintained. In order to satisfy the classical hypothesis for describing traits with polygenic inheritance via a linear model with normal error, Box-Cox power transformation was used to normalize trait distribution [START_REF] Besbes | Box-Cox transformation of egg-production traits of laying hens to improve genetic parameter estimation and breeding evaluation[END_REF][START_REF] Chen | Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not naked neck gene[END_REF]. The parameters (t) were found to be -0.214, and 1.40 for the transformed value of average clutch length (TCL) and for transformed value of total egg number (TEN), respectively.

Statistical analysis

The linear model used for the ANOVA of those traits was as follows:

Y ijkl = μ + E i + L j + G k + (E × L) ij + (ExG) ik + (L × G) jk + (E × L × G) ijk + e ijkl
where Y ijkl = individual observation, μ = overall mean, E i = fixed effect of environment, i = 1 to 2, L j = fixed effect of line, j = 1 to 2, G k = fixed effect of the naked neck genotype, k = 1 to 3, (E × L × G) ijk = fixed effect of the third order interaction between all fixed effects, (E × L) ij = fixed effect of environment-by-line interaction, (E × G) ik = fixed effect of genotype-by-environment interaction, (L × G) jk = fixed effect of line-by-genotype interaction, and e ijkl = random error. All analyses were carried with the GLM procedure of the SAS ® program library [14]. Means were considered significantly different at P < 0.05.

Genetic analysis

Variance and covariance components were estimated using the Restricted Maximum Likelihood (REML) procedure with the VCE package of Groeneveld [START_REF] Groeneveld | VCE4 User's Manual[END_REF]. The following animal model was applied to all traits on the whole data set:

Y ij = μ + G i + a j + e ij
where Y ij = individual observation for traits, μ = overall mean, G i = fixed effect of genotype at the NA locus, a j = random animal effect and e ij = random error. Expectation and variance of the vector of performance, y, were distributed as follows, in matrix notation:

where y = observed performance, a = individual additive genetic value, e = residual, β = vector of genotype fixed effect, X = incidence matrix of vector β, A = numerator relationship matrix; and G = variance-covariance matrix

E y a e X V a e A G R j k j ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ = ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = ⊗ ⊕ ⎡ ⎣ ⎢ ⎢ = β 0 0 0 0 1 and ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥
The average maximum and minimum ambient temperature by two weeks in Taiwan (TW) and during the laying period in France (FR) Figure 1 The average maximum and minimum ambient temperature by two weeks in Taiwan (TW) and during the laying period in France (FR). (average temperature, 22 ± 1°C, during the rearing period in France). for the additive genetic effect; k = the number of records, and Rj = residual variance-covariance matrix for animal j.

The direct product and direct sum of matrices are indicated by and ⊕, respectively.

In order to estimate the genetic correlation between performance measured in the two environments, traits measured in France (F) and Taiwan (T) were treated as distinct BW16 T and BW16 F , the subscript indicating the environment. Because a significant environment-by-line interaction was observed for most of the traits, multi-trait analyses were performed separately for each line. It was not possible to analyse all the traits together because of large computing requirements. Therefore eight analyses with four traits each were implemented in the present study. For instance, concerning body weight traits, one four-trait analysis (BW16 F , BW16 T , ABW F , ABW T ) was performed in each line.

Sire breeding values were evaluated in each environment for each trait by best linear unbiased prediction (BLUP) using a mixed linear model with the PEST package [START_REF] Groeneveld | PEST User's Manual Neustadt[END_REF], with the same model described above. A Spearman correlation analysis was used to compare the sire breeding values obtained either in France or in Taiwan.

Results

Total mortality in Taiwan was 22.8% and 23.6% for control and selected lines, respectively, whereas it was below 5% in France. There was no occurrence of epidemic infectious disease in either country. In Taiwan, a hot foehn wind caused a rise in temperature up to 40.3°C during 7 h on July 1 st . On that day, mortalities were 6.2%, 13.6% and 5.5% for NA*N/NA*N, NA*NA/NA*N and NA*NA/ NA*NA genotypes, respectively. During that week, cumulative mortalities were 7.8%, 14.6% and 9.4% for each of the three genotypes, respectively. Finally, the experiment included 297 hens in France and 216 hens in Taiwan. The proportion of hens carrying the homozygous NA*NA/ NA*NA genotype was slightly lower in Taiwan (20-22%) as compared to France (25%).

Effects of environment, line, genotype and interactions

The third order interaction between main effects was never significant, although it was at the limit of significance for egg weight (P < 0.10). There were no significant interactions between the naked neck genotype and either the line or the environment (Table 1).

The line by environment interaction was highly significant for BW16, clutch length and egg number, with or without Box-Cox transformation (Table 1). Body weight differed between lines in Taiwan to a larger extent than in France: the decrease in body weight observed in Taiwan as compared to France was stronger for the selected line. Clutch length and egg number were smaller in Taiwan and to a larger extent for the selected line i.e. the decrease in average clutch length, the selected trait, was 26.6% (3.19 vs. 2.34) and 59.4% (13.89 vs. 5.64) in the control and the selected lines, respectively. However, performance of the selected line still remained much higher than that of the control line in both environments.

The naked neck genotype had a significant effect on body weight at 16 weeks (BW16), age at first egg (AFE) and egg weight (EW) (Table 1). Homozygous naked neck hens had a lower BW16 and a higher AFE, except in the control line in France. They also exhibited a larger EW, but the difference was significant only for the control line in France, and for the selected line in Taiwan (Tables 2 and3). Thus, the NA gene limited the negative impact of the change in environment on egg weight in the selected line.

All traits were significantly influenced by environment and line. For all traits, the performance measured in France was better than the performance obtained in Taiwan. In France, the mean values for CL, EN and LR were respectively 3.19 (untransformed), 120 (untransformed), and 66.9 in the control line and 13.17 (untransformed), 163 (untransformed), and 89.4 in the selected line. In Taiwan, the average clutch length was 2.34 and 5.64 (untransformed values) for the control and selected lines, respectively. After normalization by Box-Cox transformation, the relative decrease of average clutch length in Taiwan was similar for both lines and close to -30% except for the normally feathered hens in the control line, but, in absolute values, the decrease was larger in the higher performing line After normalization, the total egg number in Taiwan as compared to France was even more reduced (by about 40%) as a result of the increase in age at first egg observed in Taiwan (by about 15%). Laying rate was reduced by 20% in Taiwan in both lines.

Comparison of the laying curves obtained in France and Taiwan (Figures 2 and3) showed differences due to a delayed onset of lay, a lower peak of egg production with a slightly better persistency of lay until the age of 44 weeks. There was a three-week delay of the onset of lay for both lines in Taiwan and, in the selected line, the homozygous NA*NA/NA*NA genotype reached the peak of egg production later, but this was not significant in the control line.

Genetic parameters

Estimates of heritability and genetic correlations between traits measured in the two environments are shown in Table 4 for each line. Heritability values estimated for the 2 The values are mean ± standard error a, b Different superscripts indicate significant differences within lines at a given environment selected line were generally higher for traits measured in France and the difference was noticeable for body weight, egg number, laying rate and egg weight. Heritability values obtained in Taiwan for the selected line were very low for egg number and laying rate. Since in most cases, the estimated heritability values exhibited larger asymptotic errors for the control line than for the selected line (because of a limited number of animals), the differences in estimates between the two environments were not as remarkable. However, in some cases high values were obtained i.e. for normalized clutch length, which showed a higher estimated heritability in Taiwan (0.91) than in France (0.57).

Genetic correlations between traits measured in the two environments for the selected line were high and not different from 1 for body weight and egg weight (from 0.82 to 0.96); values were lower and much less accurate for egg laying traits, so that it may be suggested that most of these correlations were null; only age at first egg exhibited a reasonably low asymptotic error, supporting the hypothesis that the correlation did not differ from zero. A different picture was observed for the control line: the highest correlation was observed for clutch length in both environments and was very close to 1, whereas correlations obtained for egg number, laying rate and body weight ranged from 0.34 to 0.48. Actually, correlations for body weight, egg weight and age at first egg were rather lower than in the selected line and exhibited the largest standard errors of all estimates for the control line, suggesting that they may not differ from zero.

The Spearman rank correlations of sire breeding values estimated between the two environments are listed in Table 5 together with their probability values. Most of these correlations were not significant but some differences between lines may be pointed out. Correlations for egg production traits (clutch length, egg number) were moderate to high in the control line (0.72 to 0.88) and differed significantly from zero, whereas they did not differ from zero in the selected line. On the opposite, correlations for body weight and egg weight were higher in the selected line (0.48 to 0.70) than in the control line; the correlation was significant for egg weight in the selected line but not in the control line. The correlation for age at first egg was low and non significant in both lines.

Hen-day laying rate by two weeks for three genotypes of the control line in France and Taiwan

Effects of environment, line, genotype and interaction

The effect of environment was quite large. The performances of all traits were lower in Taiwan and mortality was very high for both lines. Since there was no outbreak of infectious disease, this high level of mortality is rather difficult to explain. It may be due to the cumulated effect of several environmental and husbandry factors differing between France and Taiwan, which affected lines to a similar extent. For instance, these lines are never debeaked in France. To our knowledge, it has never been reported that debeaking has an effect on feed intake and behaviour in dwarf brown-egg layers. Since hens were housed in indi-Hen-day laying rate by two weeks for three genotypes of selected lines in France and Taiwan A significant interaction between environments and lines was found for laying traits, which indicated that the selected line was more sensitive to environmental changes than the control line for production level. Thus, performance level influenced the adaptation of laying hens. However, it should be noted that, in Taiwan, the selected line maintained a higher performance for laying rate than the control line. Among the main differences between the two environments, ambient temperature, lighting regimen and diet composition are discussed in more detail below.

Concerning ambient temperature, a favourable effect on hens' adaptation was expected with the naked neck gene. Indeed, at a constant ambient temperature of 32°C, the NA gene has been shown to limit the negative effect of long-term heat stress on egg production and feed efficiency traits [START_REF] Chen | Effect of high ambient temperature and naked neck genotype on performance of dwarf brown-egg layers selected for improved clutch length[END_REF], because of its effect on sensible heat loss, which is increased due to lower feather cover [START_REF] Bordas | Influence of the Na (naked neck) gene on growth, feed consumption and body composition of chicken according to environmental temperature[END_REF][START_REF] Cahaner | Effect of the plumage-reducing naked-neck (Na) gene on the performance of fast-growing broilers at normal and high ambient temperatures[END_REF]. In the present study, the average daily minimum and maximum temperatures ranged between 24.1°C to 32.4°C during the laying period. However, there was no significant effect of the naked neck genotype on laying traits and no interaction between naked neck genotype and environment. This suggests that the naturally cycling temperature was not so stressful for laying hens. In broilers, chickens exposed to temperature cycling over a wide range of 24°C -35°C, exhibit a similar growth rate to that recorded in birds exposed to a constant temperature [START_REF] Deaton | Effect of differing temperature cycles on broiler performance[END_REF].

Furthermore, the NA gene was not expected to influence adaptation to other husbandry factors than temperature, such as lighting or feed composition. Indeed, since all these factors differed between France and Taiwan, the resulting effect of the NA gene could not be identical to the effect observed when only the temperature factor was changed. This study suggests that ambient temperature is not the main driving factor of adaptation of layers to subtropical environments in experimental conditions.

Concerning lighting regimen, it has been shown to play a very important role in the onset of sexual maturity. A constant or decreasing amount of daily light will delay sexual maturity in growing birds. Indeed, in the present study, the amount of daily light in Taiwan decreased during the rearing period, which probably explains the three-week delay for the onset of lay observed in both lines. The control line exhibited the highest values for onset of lay, as previously reported [START_REF] Chen | Correlated response to long-term selection for clutch length in dwarf brown-egg layers carrying or not the naked neck gene[END_REF]. The delay appeared to be longer for the naked neck hens in both lines, which may also be due to the lower body weight observed with this genotype in Taiwan and in France for the selected line only. Chen and Tixier-Boichard [START_REF] Chen | Correlated response to long-term selection for clutch length in dwarf brown-egg layers carrying or not the naked neck gene[END_REF] have already observed this effect of the naked neck gene on sexual maturity for the same dwarf lines.

Concerning feed composition, the higher protein percentage used in Taiwan is expected to have a positive effect on egg weight [START_REF] Keshavarz | The effect of dietary manipulations of energy, protein, and fat during the growing and laying periods on early egg weight and egg components[END_REF], but this is not what we observed. Since egg weight is generally strongly correlated to body weight, the negative effect of the subtropical environment on body weight is probably the main explanation for the lower egg weight observed in Taiwan.

Genetic parameters

Changes in environment affected genetic parameters to a larger extent in the selected line than in the control line. In the selected line, the estimated heritabilities exhibited higher values for performance recorded in France than in Taiwan, which could be explained by the large environmental variability in Taiwan. Coefficients of variation for clutch length, egg number and laying rate were much larger in Taiwan than in France for the selected line except for the homozygous naked neck hens; the same trend was observed, with a lower magnitude, in the control line (Table 6). Coefficients of variation were generally smaller and remained more stable between environments for body weight, egg weight and sexual maturity in both lines (Table 6). The heritability values for AFE (0.49), TEN (0.32) and LR (0.27) obtained for the selected line in France were close to estimates previously published for the same population [START_REF] Chen | Correlated response to long-term selection for clutch length in dwarf brown-egg layers carrying or not the naked neck gene[END_REF]. For the selected trait TCL and traits strongly correlated with it (egg number and laying rate), heritability values were higher in the control line, whatever the environment, which is consistent with the decrease in genetic variance due to past selection. This suggests that selection to improve laying performance in Taiwan may be difficult in the selected line.

Estimating genetic correlations between traits measured in two environments is one approach to reveal within-line genotype × environment (G × E) interactions [START_REF] Mathur | Methods for evaluating genotype × environment interactions illustrated with laying hens[END_REF]. Correlations significantly lower than 1 indicate the occurrence of GxE interactions. Our results indicate that G × E interactions are more important for laying traits than for body weight and egg weight in the selected line but absent for clutch length in the control line. This is consistent with Rank correlations between sire breeding values, calculated for 9 and 12 sires from control and selected lines respectively show no correlation for egg production traits in the selected line, and positive but moderate correlations for body weight and egg weight. The situation is almost opposite in the control line, with a significantly positive correlation for egg production traits and low to moderate correlations for body weight and egg weight. Similarly, rank correlation results confirm genetic correlations results. This emphasizes the high impact of GxE interaction on the within-line selection process that should not be ignored in a breeding program. Within the selected line, a few sires (sire 19 and 16) showed a good ranking in both environments for the selected trait, clutch length (Table 7) suggesting that it may be possible to identify some families with a better adaptation capacity to environmental changes.

Conclusion

Breeders regularly mention the importance of GxE interactions within commercial lines, but data obtained for similar families in contrasted environments, as shown here, are generally not published. Use of a control line, derived from the same base population as the selected line, clearly shows that the sensitivity to a new environment, particularly subtropical climate, is increased by past selection. This greater sensitivity is associated with a decrease in heritability of selected traits. Regular testing of a given line across various environments, and integrating such data in the evaluation programme could monitor this impact.

Considering the current predictions on future climate changes, this result shows that the components of adaptation to real subtropical conditions need to be better identified in order to anticipate the negative consequences on the climate change. Indeed, the heat tolerance described for naked neck layers in experimental conditions was not found to particularly improve adaptation to the naked neck layers in Taiwan. Identification of a few sire families capable of achieving a good performance in both environments, temperate and subtropical, suggests that selection for improved adaptation capacity may be feasible. However, a large genetic base will be necessary to identify a sufficiently large number of sires to start a selection programme. Other differences between selected lines, not included in the present study, may also have an influence and should be investigated in the future.

  Chih-Feng Chen, David Gourichon, Nein-Zu Huang, Yen-Pai Lee, André A. Bordas, et al.. Performance comparison of dwarf laying hens segregating for the naked neck gene in temperate and subtropical environments. Genetics Selection Evolution, 2009, 41 (january), Non paginé. 10.1186/1297-9686-41-13. hal-02662179

Feed consumption was measured

  between 31 and 34 weeks of age in Taiwan only. There were no significant differences between lines (2163 vs 2267 for control line vs selection line), or among genotypes (2171, 2281, 2219 for NA*N/NA*N, NA*NA/NA*N, NA*NA/NA*NA genotypes).

Figure 2

 2 Hen-day laying rate by two weeks for three genotypes of the control line in France and Taiwan.

Figure 3

 3 Hen-day laying rate by two weeks for three genotypes of selected lines in France and Taiwan.

Table 1 : Results of the analysis of variance for the performance of laying hens according to environment (France or Taiwan) to selection background (selected line or control line) and to the naked neck genotype (homozygous normal, heterozygous or homozygous for the naked neck mutation)

 1

	Traits	Environment (E)	Line (L)	Genotype (G)	E × L	G × E	G × L	G × E × L
	Body weight at 16 weeks	***	***	*	***
	Age at first egg	***	***	*
	Clutch length	***	***		***
	Clutch length (Trans.)	**	***		***
	Egg number at 44 weeks	***	***		*
	Egg number at 44 weeks (Trans.)	***	***		***
	Laying rate	***	***
	Adult body weight	***	***
	Egg weight	***	*	*				+

Significant at +, P < 0.1; *, P < 0.05; **, P < 0.01; *** P < 0.001

Table 2 : Performances of egg production in France Control line Selection line Traits NA*N/NA*N 1 NA*NA/NA*N NA*NA/NA*NA NA*N/NA*N NA*NA/NA*N NA*NA/NA*NA (Number of birds

 2 NA*N/NA*N: normally feathered; NA*NA/NA*N: heterozygous naked neck; NA*NA/NA*NA: homozygous naked neck 2 The values are mean ± standard error a, b Different superscripts indicate significant difference within line at a given environment

	)	(20)	(56)	(31)	(43)	(93)	(44)
	Body weight at 16 weeks, g	1420 ± 37 2	1435 ± 16	1443 ± 33	1457 ± 21 a	1441 ± 18 a	1371 ± 18 b
	Age at first egg, day	139.5 ± 4.0	135.5 ± 1.2	139.4 ± 1.7	130.1 ± 1.2	133.8 ± 2.1	132.8 ± 1.2
	Clutch length, egg	2.93 ± 0.24	3.32 ± 0.18	3.11 ± 0.20	13.35 ± 1.76	13.67 ± 0.86	11.93 ± 0.92
	Clutch length (Trans.)	6.69 ± 0.50	7.38 ± 0.29	7.04 ± 0.40	14.01 ± 0.32	13.96 ± 0.30	13.62 ± 0.36
	Egg number at 44 weeks	111.5 ± 8.1	123.0 ± 3.9	120.1 ± 5.0	167.4 ± 1.6	163.6 ± 2.8	157.8 ± 4.1
	Egg number at 44 weeks (Trans.)	81.4 ± 7.1	92.0 ± 3.6	88.9 ± 4.8	139.5 ± 1.9	136.2 ± 2.7	129.5 ± 4.1
	Laying rate, %	63.0 ± 4.4	68.9 ± 2.1	68.8 ± 2.7	91.0 ± 0.8	90.3 ± 1.2	87.0 ± 2.1
	Adult body weight, g	2156 ± 71	2141 ± 39	2181 ± 67	2071 ± 27 a	2004 ± 26 ab	1924 ± 36 b
	Egg weight, g	49.8 ± 1.1 b	51.8 ± 0.6 ab	52.4 ± 0.8 a	51.0 ± 0.6	51.2 ± 0.5	50.3 ± 0.5
	1

Table 3 : Performances of egg production in Taiwan Control line Selection line Traits

 3

	(Number of birds)	(25)	(36)	(16)	(49)	(59)	(31)
	Body weight at 16 weeks, g	1360 ± 38 2,a	1295 ± 32 ab	1261 ± 21 b	1213 ± 23 a	1213 ± 19 a	1143 ± 24 b
	Age at first egg, day	157.6 ± 2.6 a	160.7 ± 2.8 ab	167.4 ± 3.1 b	153.4 ± 2.0	152.2 ± 1.4	157.4 ± 2.6
	Clutch length, egg	2.60 ± 0.17	2.27 ± 0.11	2.09 ± 0.15	5.53 ± 0.40	6.50 ± 0.52	5.46 ± 0.62
	Clutch length (Trans.)	6.11 ± 0.35	5.30 ± 0.28	4.81 ± 0.44	9.85 ± 0.39	10.34 ± 0.42	9.68 ± 0.51
	Egg number at 44 weeks	80.8 ± 5.2	76.8 ± 4.1	76.7 ± 4.9	112.4 ± 3.7	110.9 ± 4.1	107.4 ± 3.5
	Egg number at 44 weeks (Trans.)	51.7 ± 4.3	48.2 ± 3.4	47.5 ± 4.1	81.1 ± 3.4	80.3 ± 3.7	75.5 ± 3.4
	Laying rate, %	53.7 ± 3.3	52.3 ± 2.6	54.4 ± 3.1	72.6 ± 2.1	71.0 ± 2.5	71.4 ± 2.2
	Adult body weight, g	1720 ± 42	1748 ± 41	1677 ± 36	1587 ± 28	1585 ± 25	1551 ± 37
	Egg weight, g	48.3 ± 0.5	49.5 ± 0.7	49.6 ± 0.9	46.6 ± 0.4 b	47.2 ± 0.5 b	49.3 ± 0.6 a

NA*N/NA*N 1 NA*NA/NA*N NA*NA/NA*NA NA*N/NA*N NA*NA/NA*N NA*NA/NA*NA 1 NA*N/NA*N: normally feathered; NA*NA/NA*N: heterozygous naked neck; NA*NA/NA*NA: homozygous naked neck

Table 4 : Estimated heritability for each trait measured in each environment and genetic correlations considering the records of a given performance in both environments (France-Taiwan) as different traits within each line Traits h 2 in France h 2 in Taiwan Genetic correlation between traits defined for each measurement in each environment Control line Selection line Control line Selection line Control line Selection line

 4

	Body weight at 16	0.51 ± 0.16 1	0.85 ± 0.15	0.64 ± 0.16	0.46 ± 0.12	0.44 ± 0.25	0.82 ± 0.13
	weeks
	Age at first egg	0.17 ± 0.11	0.49 ± 0.11	0.31 ± 0.14	0.42 ± 0.12	-0.45 ± 0.38	0.16 ± 0.16
	Clutch length (trans.)	0.57 ± 0.11	0.20 ± 0.08	0.91 ± 0.13	0.12 ± 0.07	0.98 ± 0.06	0.49 ± 0.45
	Egg number at 44	0.49 ± 0.17	0.32 ± 0.12	0.37 ± 0.18	0.01 ± 0.03	0.48 ± 0.09	-0.10 ± 1.48
	weeks (trans.)
	Laying rate	0.50 ± 0.18	0.27 ± 0.10	0.35 ± 0.16	0.07 ± 0.06	0.23 ± 0.09	0.14 ± 0.58
	Adult body weight	0.52 ± 0.14	0.69 ± 0.14	0.38 ± 0.17	0.34 ± 0.13	0.34 ± 0.25	0.96 ± 0.05
	Egg weight	0.39 ± 0.09	0.60 ± 0.10	0.18 ± 0.09	0.38 ± 0.10	0.42 ± 0.35	0.86 ± 0.13
	1 asymptotic standard error

Table 5 : Spearman correlation coefficients between sire breeding values estimated in both environments

 5

	Traits	Control line	Selected line
		(sire number = 9)	(sire number = 12)
	Body weight at 16 weeks	0.45, P = 0.224	0.50, P = 0.101
	Age at first egg	-0.20, P = 0.606	0.07, P = 0.829
	Clutch length (Trans.)	0.88, P = 0.002	0.23, P = 0.471
	Egg number at 44 weeks (Trans.)	0.72, P = 0.030	-0.21, P = 0.513
	Laying rate	0.57, P = 0.112	-0.01, P = 0.966
	Adult body weight	0.12, P = 0.765	0.48, P = 0.112
	Egg weight	0.47, P = 0.205	0.70, P = 0.011

Table 6 : Coefficients of variation for traits measured in France and Taiwan, for each line and each genotype at the naked neck locus

 6

	Control line	Selection line

Table 7 : Sire breeding values in the selected line, for traits measured in both environments, data are sorted according to the breeding value for clutch length (transformed for normalization) estimated from performance recorded in France

 7 the fact that the highest performing line was more susceptible to environmental change. Concerning age at first egg, very low correlations were observed in both lines, which were similarly affected by the difference in lighting regimen.

	Sire ID	Clutch length (Trans.)	Egg number at 44 weeks (Trans.)	Laying rate	Adult body weight	Egg weight
		France	Taiwan	France	Taiwan	France	Taiwan	France	Taiwan	France	Taiwan
	23	1.3375	-0.6509	9.774	-0.3085	4.26	-1.1137	91.14	-2.08	2.8653	0.2951
	19	1.1622	0.4122	5.462	0.4112	4.242	1.4648	-95.65	65.05	0.9138	-0.0335
	16	0.4291	0.6636	1.453	0.4402	2.64	2.681	-183.05	-86.1	-0.5016	0.2148
	21	0.4168	-0.6866	9.636	-0.4325	2.453	-2.4114	-28.82	-57.71	1.269	0.5487
	12	0.3184	0.6349	-17.522	0.258	-2.653	2.0701	244.85	72.69	5.6541	2.8713
	17	0.2211	0.1083	8.155	0.3474	2.263	0.2681	-69.44	-16.66	-5.4449	-2.4796
	18	-0.025	0.3935	7.5	0.2238	1.128	0.3332	9.24	38.79	0.0707	-0.7562
	15	-0.127	-0.3903	-4.79	-0.2068	-0.565	0.9742	-222.19	-9.06	-2.2545	1.3863
	22	-0.2054	0.121	5.669	-0.3079	1.886	-2.2254	2.83	-96.1	-2.3982	-3.7489
	13	-1.0237	0.4648	-0.058	0.2109	-1.338	1.1587	143.12	75.12	-2.6192	-0.8452
	14	-1.1715	0.0366	-22.879	0.2269	-13.281	0.1669	103.45	-21.82	3.8258	1.5172
	20	-1.3385	-1.1083	-2.386	-0.8631	-1.053	-3.3693	4.54	37.88	-1.3587	1.0144

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Acknowledgements

The current study is part of a scientific collaboration programme between INRA-NCHU and was supported by INRA and the Council of Agriculture (92AS-1.4.1-ID-I7, 93AS-1.4.1-ID-I7). Animal caretakers at the experimental unit of INRA, Nouzilly, and at the experimental farm of NCHU, Taichung, are gratefully acknowledged.

Authors' contributions

CFC designed the study, wrote the paper, imported animals, and performed the statistical analysis. DG and NZH supervised, organized and carried out the data collection. YPL and AB participated in the design of the experiment, commented on drafts of the paper. MTB participated in the coordination and design of the study, exported animals, discussed the interpretation of the results and commented on drafts of the paper.