Andrew E Clark
email: andrew.clark@ens.fr.

Akiko Kamesaka

Teruyuki Tamura
email: tetamura@gmail.com.

Shiho Kawano

Yukinobu Kitamura

Fumio Ohtake

WORKING PAPER N° 2015 -08 Rising Aspirations Dampen Satisfaction

Keywords: Education, Satisfaction, Aspirations, Income Education, Satisfaction, Aspirations, Income. JEL codes: I26, I31

It is commonly-believed that education is a good thing for individuals. Yet its correlation with subjective well-being is most often only weakly positive, or even negative, despite the many associated better individual-level outcomes We here square the circle using novel Japanese data on happiness aspirations. If reported happiness comes from a comparison of outcomes to aspirations, then any phenomenon raising both at the same time will have only a muted effect on reported well-being. We find that around half of the happiness effect of education is cancelled out by higher aspirations, and suggest a similar dampening effect for income.

Introduction

There has been a great deal of empirical work on the correlates of self-reported happiness or subjective well-being over the past two decades across the social sciences.

One potential mystery in this fast-growing literature is why the correlation between satisfaction and education is often found to be only weakly positive, or even negative.

A number of explanations have been proposed. One possibility is that of sorting, whereby 'naturally' unhappy people are more likely to choose to become educated. In principle, this hypothesis can be tested using panel data. 1 In practice, however, many of the adults who appear in large-scale panel data sets do not change their levels of education. To evaluate the well-being effect of education using panel data, we would then require data that provides information on children's initial levels of subjective well-being, and then follow the same individuals up to the time at which their education is completed. The British Household Panel Survey (BHPS), 2 for example, has from Wave 4 included information on children of household members aged 11 to 15 that would potentially allow such analysis. A more complete picture of childhood development can be obtained, for example, from ALSPAC (Avon Longitudinal Study of Parents and Children) data, 3 in which children in the Avon area who were born between April 1991 and December 1992 have been closely and frequently followed. This data includes a number of different measures of child emotional health at various ages. 1 An alternative, which provides a local estimate of the effect of education, is to appeal to the natural experiment of the raising of the compulsory minimum school leaving age. [START_REF] Oreopoulos | Priceless: the Nonpecuniary Benefits of Schooling[END_REF] conclude that this directly raised the average happiness of those affected by the change, mainly via the effect of education on income. It is worth noting that this local effect refers to only quite low levels of (compulsory) schooling, and does not inform us the effect of higher education levels on happiness.

2 See https://www.iser.essex.ac.uk/bhps/.

3 See http://www.bristol.ac.uk/alspac/.

A second commonly-proposed solution of the satisfaction-education relationship is that education does indeed provide better outcomes for individuals, but also raises their expectations. This is an attractive solution to the mystery. Unfortunately it is nigh-on impossible to test for it in the data sets upon which research in this field typically relies, as we do not believe that these include useful information on individuals' expectations or aspirations. In some broad sense, we would like to know not only how well people do in terms of outcomes, but also how well that they think that they should be doing. It is the gap between these two that will arguably determine the individual's subjective wellbeing outcomes.

We here make some progress regarding expectations using novel data from the Economic and Social Research Institute (ESRI), Cabinet Office of Japan. This data set includes many of the common socio-demographic variables that have been analysed in the literature, as well as self-reported happiness. In this sense, the data set is entirely standard. Where we believe it adds new information to the literature is that respondents are also asked about how happy they think that they should be. [START_REF] Stutzer | The role of income aspirations in individual happiness[END_REF] focused on the link between income aspirations and self-reported happiness, finding both that higher income aspirations reduce self-reported happiness, and that higher average income in the community is associated with higher aspired levels of income. We are here along the same lines, but instead of considering expectations with respect to income, house or job, we consider broader expectations over well-being itself. Our hypothesis is that the level of well-being that individuals report will depend on the comparison of the 'pure' level of happiness that the individual feels to her happiness aspirations. Individuals' ideal levels of happiness arguably reflect such aspirations.

That individual aspirations may play a central role in determining self-reported happiness is reasonably commonplace in the subjective well-being literature. Following [START_REF] Gilboa | A Cognitive Model of Individual Well-Being[END_REF], individual aspirations can usefully be though thought to be formed in two broad ways. The first is based on social-comparisons theory, whereby individuals often care not only about the absolute level of income (say) that they receive, but also how their income shapes up compared to some group of others. Interpersonal comparisons are argued to affect the individual's level of aspirations (as in Stutzer), as seeing that others earn more may lead the individual to aspire to a higher level of income. Equally, adaption (comparisons to oneself in the past) may play a role, in that individuals often seem to become used to any higher level of income. Here, aspirations may rise with the individual's own level of past income: rather than involving a comparison to others, here the individual compares to her own past experience.

Aspirations will then track the individual's own income (potentially with a lag).

The second channel proposed by [START_REF] Gilboa | A Cognitive Model of Individual Well-Being[END_REF] relies on reasoning, whereby direct information is used to provide a justification for what the individual could or should expect. We can imagine these aspirations referring to all kinds of different aspects of the individual's life: their income, their job, their house etc. One of the few contributions which has been able use direct information on expectations, here with respect to income, is [START_REF] Mcbride | Money, Happiness and Aspirations: An Experimental Study[END_REF]. McBride adopts an experimental approach in which the amount of money that the individual expects to win in a simple matchingpennies game is changed via manipulations (about which the subject is informed) of the playing behaviour of the individual's (computerised) partner. Conditional on both the amount the individual ends up winning, and the amount other players playing the same game win, McBride shows that higher expectations of winnings significantly reduce reported satisfaction. [START_REF] Long | Happily Ever After? A Study of Job Satisfaction in Australia[END_REF] provides a number of pieces of evidence that the job satisfaction reported by workers in the first wave of HILDA is influenced by expectations. In particular, she is able to proxy job expectations by whether the individual considers themselves fairly paid, and the importance of family, work and other aspects of life to the individual. Education is shown to be negatively correlated with job satisfaction for both men and women. However, the addition of the expectations variables reduces the size of the estimated coefficient on education. Equally, education is shown to be positively correlated with job satisfaction for those who feel that they can use their own skills in their job. The argument is then that education my lower job satisfaction because the educated are less likely to feel that they are able to use their skills.

Perhaps the two papers most closely related to ours (although neither considers the role played by education per se) are [START_REF] Schwandt | Unmet Aspirations as an Explanation for the Age U-shape in Wellbeing[END_REF] and [START_REF] Barazzetta | Expectations and subjective well-being. Evidence from the BHPS[END_REF]. In the former, direct information on well-being aspirations is obtained in German Socio-Economic Panel (SOEP) data by asking individuals how satisfied they think that they will be with their life in five years' time. The comparison of this prediction to the satisfaction that the individuals actually report in this panel data five years later reveals that individual predictions are systematically wrong. These predictions in particular move from an overprediction of satisfaction when young to an underprediction when older, with the author suggesting that the regret from unmet aspirations may lie behind the well-known U-shape between subjective well-being and age. [START_REF] Barazzetta | Expectations and subjective well-being. Evidence from the BHPS[END_REF] is somewhat along the same lines, but refers to income expectations and outcomes in BHPS data. Specifically, BHPS respondents are asked each year whether they think their financial situation will worsen, stay the same or deteriorate over the next year. Equally, they are also asked how their financial situation has changed over the past year. By comparing the expectations of financial situation for time t made at time t-1 to the reported change in financial situation between t-1 and t reported at time t, Barazzetta is able to calculate a 'deviation' variable showing how outcomes relate to the expectations made one year earlier. She shows that this deviation variable is significantly correlated in the expected direction with both life satisfaction and a measure of psychological health, the GHQ.

Our paper is in the spirit of a number of the above contributions. We here demonstrate that certain variables are correlated in the same direction with both selfreported current subjective well-being and well-being aspirations. We concentrate in particular on the role of education in this respect. Higher education is shown to increase both outcomes and expectations, so that its final effect on subjective well-being is muted.

The remainder of this paper is organised as follows. Section 2 briefly reviews the literature related to the relationship between education and subjective well-being.

Section 3 then describes the characteristics of our data set and presents the estimation model. Section 4 discusses the empirical results and, last, Section 5 concludes.

Aspirations, Education and Happiness

We concentrate in this paper on the empirical relationship between education, on the one hand, and reported and aspired happiness on the other. Previous work has underlined the existence of both direct and indirect effects of education on happiness (see, for example, [START_REF] Castriota | Education and happiness: A further explanation to the Easterlin Paradox[END_REF][START_REF] Cunado | Does Education Affect Happiness? Evidence for Spain[END_REF][START_REF] Del | How Do Educational Attainment and Occupational and Wage-Earner Statuses Affect Life Satisfaction? A Gender Perspective Study[END_REF]. The direct effect is that the higher-educated have more selfconfidence, self-esteem and so on than do the lower-educated; there may well also be a direct effect of the acquisition of knowledge itself on subjective well-being. There are three main types of indirect effects. First, better education brings higher incomes and better opportunities on the labour market in general. Second, education is a signal of quality, and the higher-educated obtain indirect well-being from prestige. Third, the more educated on average have better habits and health behaviours.

With regard to existing empirical work, a number of authors find a positive correlation between education and subjective well-being [START_REF] Di Tella | Preferences over inflation and unemployment: Evidence from surveys of happiness[END_REF], Easterlin, 2005[START_REF] Layard | Happiness: Lessons From a New Science[END_REF][START_REF] Albert | Education, wages and job satisfaction[END_REF][START_REF] Becchetti | Climate, happiness and the Kyoto protocol[END_REF][START_REF] Castriota | Education and happiness: A further explanation to the Easterlin Paradox[END_REF][START_REF] Oreopoulos | Do dropouts drop out too soon? Wealth, health and happiness from compulsory schooling[END_REF][START_REF] Florida | The happiness of cities[END_REF]. However, other work has concluded that this relationship is actually ambiguous [START_REF] Veenhoven | Developments in satisfaction research[END_REF][START_REF] Inglehart | Genes, culture, democracy and happiness[END_REF][START_REF] Hickson | Is ignorance bliss: Exploring the links between education, expectations and happiness[END_REF]. [START_REF] Layard | The causes of happiness and misery[END_REF] find a positive correlation between education and subjective well-being in SOEP and World Values Survey data, but not in the BHPS or the Gallup World Poll.

Early results in [START_REF] Klein | Education Level and Satisfaction with Pay[END_REF] and [START_REF] Warr | Age and Occupational Well-Being[END_REF] reveal a negative relationship between education and satisfaction. Equally, in both Clark and Oswald (1996) and [START_REF] Clark | Are wages habit-forming? Evidence from micro data[END_REF], the analysis of BHPS data reveals that the higher-educated report lower levels of job satisfaction, ceteris paribus, than do the less-educated. In [START_REF] Blanchflower | What Makes an Entrepreneur?[END_REF] The proposed explanation for the a priori counter-intuitive result of a zero or negative correlation between subjective well-being and education is that the highereducated likely have higher expectations. We assume here that individual utility depends on the gap between outcomes and aspirations. Education will on the one hand increase aspirations or expectations regarding wages and job quality in general. Of course, it is on average indeed also associated with better labour-market outcomes. The sign of the unconditional correlation between education and happiness will then depend on whether it is aspirations or outcomes which rise the fastest. If aspirations outstrip outcomes, then education will be negatively correlated with happiness; if both rise at the same rate then the unconditional correlation will be zero. It is worth noting that much of the empirical analysis of the relation between subjective well-being and education actually controls for some of the outcome variables that are arguably caused by education (notably income): these are the indirect effects of education on well-being. This will yield a conditional correlation coefficient which is lower than the unconditional coefficient.

We here test the hypothesis that education affects aspirations directly. In particular, we ask whether education is correlated in the same way with self-reported happiness and individual aspirations. This will help us to better understand the relationship between education and happiness.

Data and Model

Our empirical analysis is based on Japanese cross-section data from the Economic and Social Research Institute (ESRI), Cabinet Office. The sample covers 6,236 (47% male and 53% female) Japanese respondents in early 2013. In the questionnaire, individuals are asked about both their current level of happiness and about how happy they wish to be. The wording of these happiness questions is as follows: "Currently, how happy do you feel? Score the degree of your happiness between 10 (very happy) and 0 (very unhappy)"; and "What is your desired condition, where 10 is very happy and 0 is very unhappy". The mean of these two happiness variables for men are 6.6 and 8.2 respectively, and for women 6.8 and 8.4. Around thirty per cent of individuals are as happy as they wish to be (in the sense that their two happiness scores coincide), and 65 per cent of individuals are less happy than they wish to be. This leaves just 6 per cent who are 'too happy' in this sense. When differences exist between actual and ideal happiness, they are most often of one or two points on the zero to ten scale. The full distribution of ideal minus actual happiness is illustrated in Figure 1.

[Figure 1 about here] With respect to education, respondents' highest educational attainment is captured by a number of dummy variables: junior high school (junior high school graduates or high-school dropouts); high school (high-school graduates, 2-year college dropouts or 4-year college dropouts); 2-year college (vocational, junior or technical junior college graduates); university (4-year college graduates and graduate dropouts); and graduateschool graduates. Figures 2 and3 show the relationship between actual and ideal happiness, on the one hand, and education on the other. Both actual and ideal happiness rise with education for men; for women there is something of a downturn for those with postgraduate qualifications, although the cell size is small here, and this drop could simply represent sample variability.

[Figure 2 about here]

[Figure 3 about here]

The satisfaction scores differ significantly by sex, with women reporting higher scores for both satisfaction measures (see [START_REF] Nolen-Hoeksema | Gender differences in well-being[END_REF]. As intimated in Figures 2 and3, this difference is particularly sharp at the 2-year college and university education levels. Our regression analysis below will be split by sex.

The data also includes other personal characteristics such as age, marital status, income,4 labour-force status, number of children,5 and region of residence. These will be introduced as control variables when we carry out regression analysis of the two happiness measures. The definitions of these different variables appear in Table 1, with descriptive statistics in Table 2. The actual questionnaire items are listed in Appendix A.

[Table 1 about here]

[Table 2 about here] The two tables in Appendix B present the correlation matrices between all of our variables, separately for men and women. The correlation coefficient between actual happiness and ideal happiness turns out to be very similar for men (0.47) and women (0.48).

The main idea to which we appeal is that, in line with a great deal of work across the social sciences, individuals' reported happiness levels will reflect the gap between what they receive (their outcome) and their aspirations or expectations. For an individual i we denote reported happiness by H Ri , and the aspired level of happiness by H Ai . The 'pure' level of happiness (before individual i's comparison of outcomes to aspirations) can be denoted by H Pi . Both of H Pi and H Ai will likely depend on some explanatory variables, X i . We can then imagine a relationship of the form

H Ri = f(H Pi (X i ) -H Ai (X i ))
Many surveys contain what are now becoming standard subjective well-being questions: these can be thought of as providing some measure of H Ri . These variables are then used as dependent variables in regressions, relating them to some set of explanatory variables, X i . The above equation makes clear that an insignificant relationship between H R and some variable X 1 , say, can actually reflect two very different scenarios.

1) The variable X 1 has no effect on either pure and aspired well-being: dH P /dX 1 = 0 and dH A /dX 1 = 0.

2) The variable X 1 does affect pure well-being, but its effect is cancelled out by changing aspirations: dH P /dX 1 = dH A /dX 1 , so that dH R /dX 1 = 0 This second scenario is often mentioned in order to understand the relationship between education and subjective well-being. 6 Education raises income, and is associated with many other positive outcomes, as noted above. However, it may well also raise expectations or aspirations about what the individual should receive. This explains why, when we control for income, the estimated coefficient on education in a well-being regression is sometimes negative.

We consider the relationship between our two happiness measures and the explanatory variables using both OLS and ordered probit estimation. In the latter case, let the outcome i Y be the happiness measures, i.e.

  10 , , 1 , 0   Y . Assume that i Y is generated by the unobserved latent variable, *
Y , is a set of parameters to be estimated, and is a random error with mean zero and variance :

(1)

The first and third columns in both of these tables show what is by now a fairly standard set of results relating actual happiness to a set of socio-demographic variables.

Many of the results in Tables 3 and4 are well-known for both males and females.

Happiness is U-shaped in age, with a minimum in the early 50s (Clark et al., 1996).

Education in Japan is strongly positively correlated with happiness, even controlling for the level of income.8 Existing work on Western countries often finds insignificant or even negative correlations (see [START_REF] Layard | The causes of happiness and misery[END_REF], although recent work on income satisfaction in Japan also uncovered positive education coefficients [START_REF] Clark | The Joneses in Japan: Income Comparisons and Financial Satisfaction[END_REF].

This strong correlation of education with subjective well-being, even when controlling for income, may therefore be something of a Japanese specificity as compared to other OECD countries, and doubtless merits further investigation.

In the other results referring to actual happiness in Tables 3 and4, marriage attracts a positive estimated coefficient in this cross-section data, as does the log of income.

Last, the estimated coefficients on labour-force status reveal that those in education (the omitted category) report the highest levels of actual happiness. The estimated coefficients on employment are only slightly more positive than those on being out of work. This is consistent with the results in [START_REF] Sano | Rôdô to Kôfukudo (Employment and Happiness)[END_REF], who use Japanese panel data. It is worth mentioning that we are holding income constant in this regression, so that the coefficient on employment might be thought to just trace out the marginal value of leisure. The estimated coefficient on housework is especially large and negative for men; retirement equally is associated with sharply lower levels of subjective well-being for men, but much less so for women.

the estimated coefficients from the estimation of subjective well-being in BHPS data by ordered probit and OLS were correlated at over 0.98. This held for all four measures considered (Caseness GHQ-12, life satisfaction, vitality and resilience). We here find the same kind of results. If we compare the estimated coefficients in a given column of Table 3 to their equivalents in Table 4, we obtain correlation coefficients of over 0.99 for all four columns. This suggests that the function we are estimating is pretty much linear. As pointed out by [START_REF] Mavromaras | The role of education pathways in the relationship between job mismatch, wages and job satisfaction: a panel estimation approach[END_REF], it is more difficult to eliminate hidden common factor interpretations in cross-section than in panel data. This drawback applies to our work here, although in terms of our research question we would require any such factor to be systematically correlated with not only education and reported happiness, but also with ideal happiness as well.

[Table 3 about here]

[Table 4 about here]

Our main interest in this analysis is not the estimated coefficients in columns ( 1) and

(3) on 'Actual happiness' as such, but rather the relationship of these to their counterparts in columns ( 2) and ( 4), where we consider an analogous regression for 'Ideal happiness'. The coefficients in this second regression show which variables are correlated with how happy the individual would ideally like to be. We argue that this is analogous to a regression of H A in our model above. The results show that the patterns in desired happiness broadly reflect those in reported happiness. The comparison of the two estimated coefficients then allows us to calculate what the pure 'non-dampened' relationship between the explanatory variables and subjective well-being would be were there to be no change in aspirations.

Comparing the determinants of actual and ideal happiness, the coefficients on age are negative and statistically significant in both sets of estimation results. Equally, the estimated coefficients on single and divorced are negative and significant for both outcome measures, being associated with both actual and ideal happiness. Both actual and ideal happiness increase with education (although, again, not significantly so for 'graduate' for women). It is in particular notable that the level of ideal happiness is higher amongst the highly-educated relative to the relatively less-educated. This finding could be considered as providing support for the argument developed in [START_REF] Clark | Are wages habit-forming? Evidence from micro data[END_REF], that the lower-educated report higher levels of job satisfaction than do the highereducated in part due to their lower expectations. In our regression results, education does lead to higher reported happiness, but with an effect that would have been twice as large or more had aspirations not risen at the same time.

We can see the same broad type of result for the income variable: this is associated with both higher actual and desired happiness. Evidence from the Minimum Income Qustion [START_REF] Stutzer | The role of income aspirations in individual happiness[END_REF]) and more generally from the Leyden Welfare Function of Income has suggested that income and education may well act to raise aspirations (see [START_REF] Van Praag | The Welfare Function of Income in Belgium: An Empirical Investigation[END_REF][START_REF] Van Praag | The Welfare Function of Income in Belgium: An Empirical Investigation[END_REF][START_REF] Van Praag | Further Evidence on the Individual Welfare Function of Income: An Empirical Investigation in the Netherlands[END_REF]. 9 The argument is analogous to that proposed for education. Income is associated with greater reported well-being in the cross-section, but the correlation would have been even higher had aspirations not risen at the same time.

With regard to labour-force status, the estimated coefficients in the actual and ideal happiness always agree with each other. According to our interpretation, the correlation between labour-force status and pure happiness (H P ) is then larger than that revealed in the actual happiness regressions. In the OLS regressions in Table 4, we can calculate the pure effect as the sum of the estimated coefficients in the actual and ideal happiness regressions. This calculation reveals that the worst labour-force status (holding income constant) is housework, followed by unemployment for men. For women, it is rather unemployment, with housework being ranked as somewhat better than working.

Last, we include region dummies in our estimations. The control group here is the 'Kanto' region, which includes the Tokyo metropolis and ten prefectures. The 'Tohoku' region attracts the lowest estimated coefficient for actual happiness for men, and for both actual and ideal happiness for women.

Overall, the effect of education and employment is similar in sign, size and significance across the two happiness measures. As such, our reading is that the correlation between 'pure' subjective well-being and these two variables is twice as large as that which is revealed the reported level of subjective well-being; the other half is attenuated by changes in aspirations. 10 With respect to marital status and income, the coefficient in the ideal happiness equation is smaller than that in the reported happiness 9 In Income Evaluation Questions, individuals provide income levels corresponding to different verbal labels. In one of the Swiss datasets in [START_REF] Stutzer | The role of income aspirations in individual happiness[END_REF] "What household income per month would you consider an absolute minimum in order to make ends meet and without running into debt even if you reduce your needs to a minimum?" 10 We have experimented with a number of different specifications here. In one, we included the log of household income, as well as individual income. In another, we estimated actual and ideal happiness jointly in a SUR estimation, dropping the region dummies in the ideal happiness regression. The results (available upon request) were very similar in both of these new specifications.

equation. There is therefore still some attenuation, but it is much smaller in size than that with respect to education.

We can also split the sample according to the comparison of actual and ideal happiness. The left hand panel of Table 5 models the probability of being less happy than you would like to be (i.e. H R < H A ) while the right-hand panel models the probability of being 'too happy'. The effect of age is consistent, being hump-shaped for being less happy than you wish to be, and U-shaped for too happy. Marital status only matters for being less happy than you wish to be, and income only plays a significant role for women.

Of most interest here are the estimated education coefficients. We can see that it is university education that is the culprit here, being significantly positively (negatively) correlated with the probability of being less happy than you would like to be (too happy). The estimated coefficients on post-graduate degrees are of the same shape, but are not significant (probably due to smaller cell sizes).

[Table 5 about here]

We may finally wonder whether the results are different for those who currently 'use' their education (and so drop those currently in education, in housework or retired).

The regression results for these male 'education users' are very similar to those in the whole sample (perhaps unsurprisingly), with the estimated education coefficients in both happiness regressions changing in size by less than 10% For women, the coefficients do move around more, in some cases by up to 50%. However, the ratio of the education coefficient in the actual happiness to that in the ideal happiness regression (which tells us about the deflation effect of changing aspirations) is remarkably robust for both men and women, moving by less than 15% in all cases.

Conclusion

This paper has used novel Japanese cross-section data including information on both actual happiness and the individual's ideal level of happiness. The main idea put forward here is that the individual's reported level of happiness will reflect the gap between what they actually receive and what they expected to receive. We estimate both reported happiness and happiness-aspirations equations, and the OLS and Ordered Probits yield very similar results. We find in particular that education leads to both higher reported happiness and desired happiness. This suggests that a significant part of the happiness effect of education is cancelled out by higher aspirations: education then does raise actual happiness but also raises expectations or aspirations about what the individual should receive. The same pattern of results is found for income, although the happiness attenuation effect here is smaller. We believe that these regression results underline the importance of changing aspiration levels in determining individual subjective well-being.

Our results do come from one country at one point in time. Japan is in a sense not a typical country in terms of subjective well-being, with low job satisfaction scores [START_REF] Sousa-Poza | Well-being at work: a cross-national analysis of the levels and determinants of job satisfaction[END_REF] and life satisfaction scores that are notably below those that its objective characteristics would predict [START_REF] Abdallah | Estimating worldwide life satisfaction[END_REF]. In addition, Japan in 2013 was in a recessionary period, which could have had a particular effect on either actual or aspired happiness. In particular, the relative lack of jobs for life, or at least satisfying jobs for life during recessions, might be reflected in a greater mismatch with education. The specific analysis of this point would require either cross-country data or time-series data within Japan, neither of are currently available as far as we know.

Japan is also dissimilar to some other countries in a number of other ways, including in terms of education and employment. In particular, Japan has very strong employment protection making it quite difficult to dismiss regular employees [START_REF] Kambayashi | Kaiko Kisei no Ho to Keizai[END_REF], Ohtake et al., 2004[START_REF] Okudaira | Employment protection and productivity: evidence from firm-level panel data in Japan[END_REF]. Once Japanese workers find a satisfactory position, they can usually remain in that position until retirement (although this may be somewhat less the case during the recessions of recent years). Those with higher education are more likely to find such satisfying and secure positions. In our terminology, it is then unsurprising that education and pure happiness, H P , be positively correlated. This positive correlation could be larger in Japan (and other similar Asian countries) than in countries where good jobs are allocated less with respect to education and ability, and more with respect to some other criteria (such as social class).

At the same time, education likely affects the aspired level of happiness (H A ) as well. We argued above that it was the comparison of H P to H A that determined reported happiness The fact that education is positively correlated with reported happiness suggests that H P rises more with education in Japan than does H A (and of course does not necessarily mean that there is no effect of education on aspired happiness in Japan). In other countries, where the aspiration effect is larger, or the outcome effect is smaller, these two terms may cancel each other out, so that there is no net effect of education on reported happiness. The worst possible world would be one where education raises hopes for the future (aspired happiness) but does not deliver on these promises. 11 Here we will see education and happiness being negatively correlated.

We think that this scenario is unlikely in Asia, but may well hold in other countries. Note: Both ideal and actual happiness are measured on zero to ten scales, with higher numbers indicating greater happiness. In the graph, those with a positive value of ideal happiness minus actual happiness are less happy than they would ideally like to be; the far fewer individuals with negative values in the graph are 'too happy'.

  , the respondents in the National Child Development Study with college degrees are the least satisfied with their work. An intriguing recent take on this finding appears two recent pieces of work, by Binder and Coad (2011) on BHPS data, and del Mar Salinas-Jiménez et al. (2014) using two waves of European Social Survey data. In both contributions education and life satisfaction are positively correlated at the lower end of the well-being distribution, with this correlation turning negative towards the top end of the well-being distribution.

Figure 1 .

 1 Figure 1. Ideal Happiness minus Actual Happiness.

Figure 3 .

 3 Figure 2. Education and Happiness: Men

  , income aspirations are measured by the answer to the question "What income would you indicate as good or bad in your circumstances? Please try to state what income per month (before taxes) for your entire household you consider to be [• • • ] sufficient". The Minimum Income Question, which appears in both of Stutzer's Swiss datasets, is of the same nature:

Table 2 . Descriptive Statistics

 2

	Variable	Male			Female
		Mean Std. Dev.	Mean Std. Dev.
	Actual happiness	6.62	2.08	6.83	2.02
	Ideal happiness	8.22	1.74	8.36	1.62
	Age	47.79	17.82	46.89	17.30
	Age-squared/1000	2.60	1.72	2.50	1.67
	Married	0.70	0.46	0.67	0.47
	Single	0.26	0.44	0.24	0.43
	Divorced	0.02	0.15	0.04	0.19
	Widowed	0.01	0.11	0.05	0.22
	lnIncome	5.28	1.74	3.89	2.06
	Edu: Junior high school	0.15	0.36	0.13	0.33
	Edu: High school	0.42	0.49	0.44	0.50
	Edu: 2-year college	0.12	0.32	0.30	0.46
	Edu: University	0.29	0.45	0.12	0.33
	Edu: Graduate	0.02	0.15	0.01	0.09
	Permanent employment	0.54	0.50	0.44	0.50
	Temporary employment	0.08	0.27	0.16	0.36
	Board member	0.06	0.23	0.02	0.14
	Self-employment	0.10	0.30	0.02	0.15
	Out of work	0.06	0.24	0.06	0.24
	Retired	0.11	0.31	0.07	0.26
	Housework	0.00	0.07	0.18	0.39
	In education	0.05	0.22	0.04	0.21
	No child	0.32	0.47	0.29	0.46
	Hokkaido	0.04	0.20	0.04	0.20
	Tohoku	0.09	0.29	0.09	0.29
	Kanto	0.31	0.46	0.30	0.46
	Hokuriku-Tohsan	0.10	0.30	0.09	0.29
	Tokai	0.13	0.33	0.12	0.33
	Kinki	0.14	0.35	0.15	0.35
	Chugoku-Shikoku	0.09	0.29	0.09	0.28
	Kyushu-Okinawa	0.10	0.30	0.11	0.32
	Note : Male (N=2951), Female (N=3285).

Table 3 . Ordered Probit Regressions: Actual and Ideal Happiness

 3

				Male	Female
			Actual	Ideal	Actual	Ideal
	Age		-0.074 ***	-0.022 **	-0.044 ***	-0.016 *
	Age-squared/1000		0.627 ***	0.053	0.359 ***	0.004
	Single		-0.929 ***	-0.422 ***	-0.456 ***	-0.311 ***
	Divorced		-0.775 ***	-0.534 ***	-0.447 ***	-0.191 *
	Widowed		-0.536 ***	-0.148	-0.229 **	-0.075
	lnIncome		0.087 ***	0.050 **	0.048 ***	0.027 **
	Edu: High school		0.230 ***	0.280 ***	0.226 ***	0.253 ***
	Edu: 2-year college		0.249 ***	0.317 ***	0.344 ***	0.380 ***
	Edu: University		0.305 ***	0.467 ***	0.505 ***	0.485 ***
	Edu: Graduate		0.446 ***	0.603 ***	0.156	0.298
	Permanent employment	-0.598 ***	-0.486 ***	-0.434 ***	-0.307 **
	Temporary employment	-0.681 ***	-0.426 ***	-0.380 ***	-0.312 **
	Board member		-0.391 **	-0.384 **	-0.145	-0.277
	Self-employment		-0.538 ***	-0.419 ***	-0.333 *	-0.156
	Out of work		-0.643 ***	-0.453 ***	-0.491 ***	-0.396 ***
	Retired		-0.598 ***	-0.315 **	-0.245 *	-0.087
	Housework		-0.748 **	-0.698 **	-0.182	-0.205
	No child		0.050	0.009	-0.098	-0.116
	Hokkaido		-0.031	-0.085	0.017	0.101
	Tohoku		-0.146 **	-0.100	-0.257 ***	-0.154 **
	Hokuriku-Tohsan		0.087	-0.009	0.049	0.039
	Tokai		-0.011	-0.078	0.066	-0.045
	Kinki		0.022	0.023	-0.011	0.049
	Chugoku-Shikoku		-0.045	-0.020	-0.011	-0.051
	Kyushu-Okinawa		0.070	0.004	0.038	0.035
	Log pseudo-likelihood	-5859.7	-4947.4	-6533.3	-5370.7
	Sample size		2951	2951	3285	3285
	Note : Significance levels:	*** p<0.01,	** p<0.05,	* p<0.1.

Table 4 . OLS Regressions: Actual and Ideal Happiness

 4 Note : Significance levels: *** p<0.01, ** p<0.05, * p<0.1.

	`

Table 5 . Probit Regressions on Actual minus Ideal Happiness

 5

				Actual < Ideal	Actual > Ideal
				Male		Female	Male	Femal
	Age			0.074 ***	0.030 ***	-0.039 **	-0.025 *
	Age-squared/1000		-0.759 ***	-0.330 ***	0.386 ***	0.251 *
	Single			0.493 ***	0.107	-0.193	-0.165
	Divorced			0.182		-0.013	-0.368	0.050
	Widowed			0.669 ***	0.063	0.064	-0.212
	lnIncome		-0.042		-0.033 **	0.041	0.065 *
	Edu: High school		-0.006		0.031	-0.202 *	-0.061
	Edu: 2-year college		-0.050		0.022	-0.136	-0.090
	Edu: University			0.188 **		0.013	-0.271 **	-0.296 *
	Edu: Graduate			0.181		0.235	-0.347	-0.253
	Permanent employment	-0.062		0.218	0.015	-0.303
	Temporary employment		0.178		0.089	0.011	-0.056
	Board member		-0.258		-0.230	-0.229	-0.115
	Self-employment		-0.068		0.217	0.048	-0.524
	Out of work		-0.125		0.071	0.264	0.057
	Retired			0.178		0.091	0.014	-0.086
	Housework		-0.437		-0.047	-0.014	-0.003
	No child		-0.028		0.078	0.017	0.130
	Hokkaido		-0.107		-0.110	-0.140	-0.408 *
	Tohoku		-0.040		0.109	-0.145	-0.088
	Hokuriku-Tohsan		-0.139		0.043	0.067	-0.031
	Tokai		-0.206 **		-0.076	-0.018	0.171
	Kinki		-0.113		0.003	-0.024	-0.146
	Chugoku-Shikoku		-0.031		0.032	-0.060	-0.177
	Kyushu-Okinawa		-0.122		-0.068	0.106	-0.050
	Constant		-1.032 ***	-0.228	-0.683 *	-1.014 *
	Log pseudo-likelihood	-1855.4		-2078.1	-675.1	-709.7
	Sample size			2951		3285	2951	3285
	Note : Significance levels:	*** p<0.01,	** p<0.05,	* p<0.1.

Gross annual income is measured on a twelve-point scale. We use the median value of each category in order to convert the answers into a continuous variable. We use a value of 20M Yen for the last openended 15M Yen or over category, as is common in Japan.

 5 We will introduce children as a simple binary variable for 'has any children'. Introducing more detailed categories including the number of children did not add any strong insights (there was something of a positive correlation with both happiness measures for women having three or more children).

See in particular[START_REF] Ferrante | Education, Aspirations and Life Satisfaction[END_REF], who produces some evidence consistent with this hypothesis for both education and perceived opportunities.

We can also estimate these happiness equations dropping variables that we think might be partially caused by education (income, labour-force status, marital status and number of children). This produces estimated coefficients on actual happiness that are some 20% higher for university education and above for men, but not much change in the other education coefficients.

See[START_REF] Duru-Bellat | L'inflation scolaire[END_REF] for the phenomenon of educational inflation in France.

thank Susumu Kuwahara for supporting this research project at the Economic and Social Research Institute (ESRI), Cabinet Office, Government of Japan. The second author's research is partly supported by Grants-in-Aid for Scientific Research (C) 24530358 from the Japan Society for the Promotion of Science.

With a continuous latent variable being the estimated threshold values, we have the following.

(2)

The probabilities of observing the outcomes are given by:

where is the univariate standard normal cumulative distribution function.

The following section describes the results of these various estimations.

Results

The results from the main part of our analysis appear in Tables 3 and4. We carry out both OLS and ordered probit estimation, although the choice of estimation method makes only little difference to the results (see [START_REF] Ferrer-I-Carbonell | How important is methodology for the estimates of the determinants of happiness?[END_REF][START_REF] Ferrer-I-Carbonell | How important is methodology for the estimates of the determinants of happiness?[END_REF][START_REF] Clark | Is Happiness the Best Measure of Well-Being?[END_REF]. 7 The advantage of the former is that the coefficients are the marginal effects, which makes comparisons across equations simpler.

7 Although it is worth pointing out that the equivalence in Ferrer-i-Carbonell and Frijters ( 2004) is established using panel data, and we are here working with a cross-section. In Section 5 of [START_REF] Clark | Is Happiness the Best Measure of Well-Being?[END_REF], Appendix A. Questionnaire

Actual and Ideal Happiness Questions:

1) Currently, how happy are you? Please score the degree of your happiness between 10 (very happy) and 0 (very unhappy).

2) What is your desired condition when 10 is "very happy", and 0 is "very unhappy.

Please score your desired condition.

Demographic Questions:

3) Please circle your sex.


Grégoire Leroy
email: gregoire.leroy@agroparistech.fr

Florence Phocas

Benoit Hedan

Etienne Verrier

Xavier Rognon

Inbreeding impact on litter size and survival in selected canine breeds

Keywords: Canine, Inbreeding depression, Survival, Longevity, Litter size

Data obtained from the French Kennel Club and the Fichier National Canin were used to estimate the effect of inbreeding on average litter size and survival in seven French breeds of dog. Depending on the breed, litter sizes were 3.5-6.3 puppies and longevities were 7.7-12.2 years. Estimated heritabilities were 6.0-10.9% for litter size and 6.1-10.1% for survival at 2 years of age. Regression coefficients indicated a negative effect of inbreeding on both individual survival and litter size. Although the impact of baseline inbreeding within breeds appears to be limited, the improper mating of close relatives will reduce biological fitness through significant reduction of litter size and longevity.

Highlights

• In dogs, litter size and 2 year survival are traits with relatively low heritability level.

• A large part of within-breed inbreeding is related to assortative mating practice.

• Litter size is negatively affected by both litter and dam inbreeding.

• 2 year survival and longevity are negatively affected by inbreeding.

• Measures should therefore be taken by canine breed clubs to avoid mating of close relatives.

Introduction

Inbreeding is a phenomenon that is difficult to avoid in domestic species because breeds constitute selected populations with limited sizes [START_REF] Kristensen | Inbreeding -lessons from animal breeding, evolutionary biology and conservation genetics[END_REF]. In pet animals, mating between close relatives (e.g. between half-or full siblings) is still a common breeding practice [START_REF] Leroy | Mating practices and the dissemination of genetic disorders in domestic animals, based on the example of dog breeding[END_REF]. As an example, 24% of French dog breeders have declared having practised such matings [START_REF] Leroy | Breeding goals and breeding practices of French dog breeders: Results from a large survey[END_REF] with the main purpose being to 'fix the qualities of a given reproducer'. Given the deleterious consequences of inbreeding on health through inbreeding depression and diffusion of inherited diseases within the breed [START_REF] Bateson | Analysis of the canine genome and canine health: A commentary[END_REF], management of inbreeding should be a major concern for dog breeders.

Inbreeding depression is defined as the reduction of the mean phenotypic value shown by a given trait in relation to inbreeding (Falconer and Mackey, 1996). The phenomenon is well documented for several traits in livestock species [START_REF] Leroy | Inbreeding depression in livestock species: Review and meta-analysis[END_REF]. In dogs, consequences of inbreeding on traits related to reproduction or occurrence of some specific diseases have been reported previously (Ubbink et al., 1992;van der Beek et al., 1999;Maki et al., 2001;[START_REF] Ólafsdóttir | Correlated pedigree and molecular estimates of inbreeding and their ability to detect inbreeding depression in the Icelandic sheepdog, a recently bottlenecked population of domestic dogs[END_REF]Urfer, 2009).

Litter size and longevity constitute two interesting life history indicators because they are tightly linked to prenatal and postnatal survival. In dogs, there is strong variability of these two traits in relation to the large morphological differences existing amongst breeds. Longevity relating to body size or occurrence of various disorders has been studied in dogs [START_REF] Egenvall | Mortality in over 350,000 insured Swedish dogs from 1995-2000: II. Breed-specific age and survival patterns and relative risk for causes of death[END_REF][START_REF] Greer | Statistical analysis regarding the effects of height and weight on life span of the domestic dog[END_REF][START_REF] Kraus | The size-life span trade-off decomposed: Why large dogs die young[END_REF], but there is a lack of genetic characterisation of this trait. Similarly, litter size, which is genetically linked to female reproductive capacities and survival of the litter, also constitutes an interesting trait for the investigation of the impact of inbreeding depression.

Based on the hypothesis that individual inbreeding may have a significant impact on dog survival, the aim of this study was to provide a phenotypic and genetic characterisation of litter size and longevity in seven breeds of dogs in France. We investigated inheritance and the impact of inbreeding so as to provide practical recommendations for breeders.

Materials and methods

Source of population data

The French Kennel Club (Société Centrale Canine, SCC) has curated phenotypic and genealogical information on dogs in France since 1975, using a database comprising all purebred puppies registered at the age of 2 months. Dog owners are also supposed to indicate when their dog dies (without giving the cause of death) to a national identification file (Fichier National Canin, FNC). In practice, this information has been transmitted to and recorded in the FNC for only ~10% of dogs since 2005. To study litter size, we considered litters born from 1990 to 2012 with at least three equivalent generations of known ancestors [START_REF] Boichard | Value of using probabilities of gene origin to measure genetic variability in a population[END_REF]. To assess longevity, we considered individuals whose death had been registered in the years 2007 to 2012, with at least three equivalent generations of known ancestors.

We chose seven breeds to cover a large range of morphology, use and demography, namely the Bernese mountain dog (BMD), Basset hound (BSH), Cairn terrier (CAI), Epagneul Breton (EPB), German shepherd dog (GSD), Leonberger (LEO) and West Highland white terrier (WHW).

Statistical analysis

An equivalent number of known generations (EqG) and inbreeding coefficients (F) were computed with PEDIG software [START_REF] Boichard | PEDIG: A fortran package for pedigree analysis suited for large populations[END_REF], while estimates of variance components were obtained using ASREML software [START_REF] Gilmour | ASReml User Guide Release 3, VSN International[END_REF]. Analyses were independently performed for each breed.

Litter size was defined as the number of puppies alive at registration, i.e. at the age of 2 months. Data were based on records ranging from 3468 (BSH) to 39,080 (GSD) litters born from 1543 (BSH) to 15,869 (GSD) bitches (Table 1; see Appendix: Supplementary Table 1). The trait was analysed using a repeatability animal model and litter size as a trait of the dam (the 'animal' is therefore the dam of the litter):

Y irjmk = μ + P r + By j + b 1 F i +b 2 F ir + b 3 F m + Br k+ Pe i + A i + Ɛ irjlmk
where Y irjmk is the observed value of the rth litter bred by sire m and the dam i, raised by the breeder k, and μ is the overall mean. As environment factors, we included P r (the fixed effect of the litter rank r), By j (the fixed effect of birth year j of the litter), Pe i (the random permanent environmental effect of the dam i across all her litters) and Br k (the random effect of the breeder k of the litter). b 1 , b 2 , b 3 are the coefficients of regression of the phenotypic value (Y) on the coefficients of inbreeding of the dam (F i ), its rth litter (F ir ) and the sire of the r th litter (F m ), respectively. A i is the random genetic effect of dam i, and Ɛ irjmk the random residual.

Longevity analyses were based on 1113 (BSH) to 15,059 (GSD) dogs whose death was registered (Table 2). Models based on the trait itself did not lead to convergence during estimation (considering either linear mixed animal model or survival analysis). Given the bimodal distribution of longevity (Fig. 1), with a first mortality peak before 2 years in each breed, the trait was transformed into a binary variable describing juvenile survival; the value was equal to 0 if the longevity was < 2 years, and 1 otherwise. A linear model was written after a probit transformation of the observed survival trait. The underlying normal dependent variable Y ijkl was modelled as:

Y ijkl = μ + Sx j + Dy k + b i F i + BR l + A i + Ɛ ijkl
where μ is the mean, Sx j is the fixed effect of sex j of animal i, Dy k is the fixed effect of death year k, b i is the regression coefficient for inbreeding of the individual i, F i is the inbreeding coefficient of individual i, Br l is the random effect of breeder l, A i is the random genetic effect for animal i and Ɛ ijkl is the random residual.

Heritabilities (h²) and other variance ratios were computed by dividing genetic variance and variance components of all the other random effects by phenotypic variances for each statistical model. To assess juvenile survival, heritability on the observed scale (h² 01 ) was obtained by transforming heritability estimated on the underlying normal scale using the following equation [START_REF] Dempster | Heritability of threshold characters[END_REF]

:
where p is the proportion of the population showing the trait (survival at 2 years) and z is the ordinate on the standard normal density function corresponding to the threshold p.

Results

Demographic parameters

The coefficients of inbreeding were relatively low, ranging from 1.60 to 5.02%, with some contrasts across individuals; for example, the proportion of observations with inbreeding coefficient F ≥ 12.5% ranged from 2.4 (litter size for GSD) to 7.9% (litter size for CAI) (Tables 1 and2). The negative impact of inbreeding classes on litter size and longevity is illustrated in Fig. 2. In all breeds, litter size was significantly reduced (P < 0.05) for classes with more litter inbreeding. Litter size also decreased significantly (P < 0.05) for litters produced by dams of the BMD, CAI, GSD, LEO and WHW breeds with larger inbreeding coefficients. There were significant (P < 0.05) differences in longevity according to individual inbreeding levels for BMD, EPB, GSD, and LEO breeds (Fig. 2).

The regression coefficients for inbreeding were negative in all breeds for both litter size (litter and dam inbreeding effect) and 2 year survival (individual inbreeding effect). On average over all breeds, litter sizes were reduced by 0.026 per % of litter inbreeding and by 0.02 per % of dam inbreeding. In other words, we would expect, for litters with an inbreeding coefficient of 25% (equivalent to a mating between full siblings), a reduction of 0.65 puppies per litter on average in comparison with non-inbred litters. Females with this inbreeding coefficient could be expected to produce 0.5 puppies fewer per litter in comparison with non-inbred females. The coefficient of inbreeding for the sire had a significant effect on litter size only for EPB (r = 0.73; P = 0.04) and WHW (r = 1.16; P = 0.007).

Variance components and quantitative genetic parameters

Estimated heritabilities for litter size were 6.0 (BSH) to 10.9% (BMD) (Table 3). Breeder and environment ratios (i.e. permanent environment variance divided by phenotypic variance) for litter size ranged from 2.4 (BSH) to 8.1% (EPB), and 0 (BSH) to 9.81% (BMD), respectively (see Appendix: Supplementary Table 2).

No convergence was obtained for the estimation of variance components for survival for LEO. Estimated values of heritability for survival for the different breeds (excluding LEO) were 22.4 (BSH) to 34.5% (GSD) on the underlying normal scale (see Appendix: Supplementary Table 3). Corresponding heritability values on the 0-1 bimodal scale were 5.9 (WHW) to 10.1% (GSD) (Table 3).

Discussion

The larger litter sizes and lower longevities for breeds of large size (BMD and LEO) were in agreement with the results of previous studies [START_REF] Borge | Litter size at birth in purebred dogs -A retrospective study of 224 breeds[END_REF][START_REF] Kraus | The size-life span trade-off decomposed: Why large dogs die young[END_REF].

Distribution of mortality was similar to those found by [START_REF] Egenvall | Mortality in over 350,000 insured Swedish dogs from 1995-2000: II. Breed-specific age and survival patterns and relative risk for causes of death[END_REF] and O'Neill et al.

(2013). The particularly low life expectancy of BMD (mean 7.7 years) may be a consequence of the high prevalence of histiocytic sarcoma within this breed [START_REF] Abadie | Epidemiology, pathology, and genetics of histiocytic sarcoma in the Bernese mountain dog breed[END_REF].

The significantly lower life expectancy for male BMD and GSD are consistent with previously published data [START_REF] Bonnett | Mortality in over 350,000 insured Swedish dogs from 1995-2000: I. Breed-, gender-, age-and cause-specific rates[END_REF][START_REF] O'neill | Longevity and mortality of owned dogs in England[END_REF]. The significantly higher male longevity in the two terrier breeds is unexpected. However, mortality risks related to sex differ when considering different disorders; for example, [START_REF] Bonnett | Mortality in over 350,000 insured Swedish dogs from 1995-2000: I. Breed-, gender-, age-and cause-specific rates[END_REF] showed that, in general, females had up to two times greater risk of dying from tumours than males. Dog breeds have large variations in disease prevalence and, therefore, variation between breeds in risk related to sex is to be expected. There were many (statistical) cells with few data because of low numbers of performances per reproducer or per breeder (see Appendix A: Supplementary Table 1), which led to difficulties in adjusting genetic models. It was possible to assess heritabilities for litter sizes with low to moderate heritabilities (6.0-10.9%), of the same order to those estimated in sheep, rabbits or pigs (Van Wyk et al., 2009;[START_REF] Nagy | The contribution of dominance and inbreeding depression in estimating variance components for litter size in Pannon white rabbits[END_REF]Rodriguez et al., 2013).

However, a study on German shepherd and Labrador retriever guide dogs revealed much larger heritabilities for litter size at 49 days (31 and 26%, respectively) [START_REF] Hare | Estimation of heritability of litter size in Labrador retrievers and German shepherd dogs[END_REF], which may result from better monitoring of those populations and a larger number of litters per reproducer.

The structure of the data set did not allow identification of censured data (animals still alive at the end of the study) and so it was not possible to perform direct survival analysis on longevity data. Heritabilities estimated for 2 year survival were found in the same range (5.9-10.1% according to breeds) as those reported for piglet and calf survival (4.2-19%) (Gerra et al., 2006;Rohe et al., 2009;[START_REF] Fuerst-Waltl | Genetic analysis of calf and heifer losses in Danish Holstein[END_REF].

Since litter size was measured at 2 months of age, i.e. after weaning, it was related to female prolificacy, and embryo and early puppy survival. Therefore, it was not surprising to find a negative impact of both litter and dam inbreeding on the trait. This result is in contrast with a study on the Irish Wolfhound (Urfer, 2009), which found a limited impact of dam inbreeding on litter size, although the data set was relatively small (822 litters). Inbreeding depression appeared to be larger for breeds of larger body size, which could be linked to the larger litter size estimated for those breeds. Supposing a similar impact of inbreeding on embryo and puppy survival, the consequence of inbreeding on litter size could be expected to be higher for more prolific breeds.

The scaled estimation of inbreeding depression (dividing the regression coefficient by the mean of the phenotypic trait computed for the breed) was -0.27 to -0.65 for litter inbreeding and -0.13 and -0.76 for dam inbreeding, with no notable difference according to breed size. This result was within the range of values estimated in livestock for the number of offspring weaned per litter, i.e. -0.69 (standard error 0.15) for litter inbreeding and -0.46 (standard error 0.17), for dam inbreeding [START_REF] Leroy | Inbreeding depression in livestock species: Review and meta-analysis[END_REF]. This result is illustrated by the reduction in BMD of 0.8 puppies between litters with inbreeding coefficients < 6.25%, and litters with inbreeding coefficients > 12.5% (Fig. 2). In EPB and GSD, there was a difference of longevity of > 1 year between dogs with inbreeding coefficients < 6.25% and those with inbreeding coefficients > 12.5%.

Although it was not possible to identify the causes of death, reduced longevity may be linked to increased early mortality, early onset of senescence or increased rate of aging [START_REF] Kraus | The size-life span trade-off decomposed: Why large dogs die young[END_REF]. However, given the importance of inherited disorders with a potential impact on dog survival within dog breeds [START_REF] Nicholas | Internet resources cataloguing inherited disorders in dogs[END_REF], it is probable that dogs with high inbreeding have higher incidences of those disorders, which may significantly reduce their lifespan. As emphasised by Leroy and Baumung (2010), high individual values of inbreeding coefficients (> 6.25%, 12.5 or even 25%) are most of the time caused by recent inbreeding, i.e. mating between close relatives (cousins, half or full siblings, parent-offspring matings).

We consider that a large part of within-breed inbreeding is related to this breeding practice. In 60 dog breeds studied, average coancestry at the breed scale was lower (2.1% on average) than inbreeding (3.5% on average) (Leroy et al., 2013). The coefficient of coancestry estimates the genetic similarity between two individuals and is equal to the coefficient of inbreeding of a potential offspring of these two individuals. At the population scale, average coancestry corresponds to baseline inbreeding, i.e. inbreeding because of the reduction of genetic variability at the population scale. Therefore, within a breed under random mating conditions, those two estimators should be similar, the difference here being explained by mating between close relatives. Given the low value of coancestry, this baseline inbreeding has a limited effect on longevity. In contrast, at the individual level, Fig. 2 illustrates the deleterious impact of mating between close-relatives on litter size and longevity. Therefore, measures should be taken by breed clubs to avoid mating of close relatives (at least between parents-offspring, and half and full siblings), for example, following the decision taken by the UK Kennel Club in 2009 1 .

Conclusions

The results presented in this study illustrate that inbreeding affects reproduction parameters and survival at different stages of life in dogs. Improvement of these traits is required, since the reduction of survival is generally related to health problems affecting animal welfare. From a genetic point of view, survival of dogs could be improved by restricting mating between close relatives, as well as through the implementation of efficient selection programmes against widely spread inherited disorders. A third approach could be to consider a direct selection on survival traits, given the heritabilities measured here. However there is a need to improve the recording of phenotypes, in number and quality, before such a selection approach could be implemented. Also, the development of molecular tools, allowing, among others, genome-wide estimates of inbreeding, should improve our capacity to better understand and manage inbreeding depression phenomenon.

Conflict of interest statement

None of the authors of this paper has a financial or personal relationship with other people or organisations that could inappropriately influence or bias the content of the paper.

Figure legends

Supplementary Table 2

Estimated variance ratios for models estimating litter size according to breeds.

Fig. 1 .

 1 Fig. 1. Distribution of mortality over years according to breed. BMD, Bernese mountain dog;

Fig. 2 .

 2 Fig. 2. Average litter size and longevities according to inbreeding classes, considering for litter size the coefficient of inbreeding of the litter (a) or its dam (b), and for longevity the coefficient of the individual considered (c). BMD, Bernese mountain dog; BSH, Basset hound; CAI, Cairn terrier; EPB, Epagneul Breton; GSD, German shepherd dog; LEO , Leonberger West; WHW, Highland white terrier. NS non-significant; * P < 0.05; ** P < 0.01; *** P < 0.001.

Table 1

 1 Main characteristics of litter size data according to breeds.

	Breed a	Number of litters	Litter size (mean ± standard deviation)	Litter rank (mean ± standard deviation)	Mean F b (%)	Litter inbreeding < 6.25 6.25-12.5 (%) (%)	≥ 12.5 (%)
	BMD	7566	5.51 ± 2.78	2.5 ± 1.72	2.08	88.8	7.1	4.1
	BSH	3468	5.14 ± 2.66	2.21 ± 1.42	3.92	76.6	16.8	6.5
	CAI	8846	3.89 ± 1.77	3.04 ± 2.04	3.25	82.6	9.5	7.9
	EPB	23,005	5.32 ± 2.25	2.53 ± 1.96	5.02	75.7	16.9	7.3
	GSD	39,080	5.1 ± 2.44	2.87 ± 1.98	2.42	88	8.3	3.6
	LEO	3246	6.33 ± 3.08	1.92 ± 1.17	3.21	85.9	10.5	3.7
	WHW	16,163	3.47 ± 1.69	2.87 ± 1.92	2.35	87.2	7.1	5.7

a BMD, Bernese mountain dog; BSH, Basset hound; CAI, Cairn terrier; EPB, Epagneul Breton; GSD, German shepherd dog; LEO , Leonberger West; WHW, Highland white terrier. b Inbreeding coefficient.

Table 2

 2 Main characteristics of longevity data according to breeds.

	Breed a	Number of litters	Longevity (mean ± standard deviation)	Longevity (median)	2 year survivability (%)	Mean F b (%)	Inbreeding < 6.25 6.25-12.5 (%) (%)	≥ 12.5 (%)
	BMD	2831	7.74 ± 3.03	8.15	93.7	1.59	91.7	5.1	3.2
	BSH	1113	9.33 ± 3.67	10.3	92	3.51	80.4	13.4	6.2
	CAI	2111	12.23 ± 4.18	13.42	95.4	3.2	82.3	10.2	7.4
	EPB	6286	11.34 ± 4.28	12.58	94.1	4.57	78.2	15.6	6.1
	GSD	15,056	9.16 ± 3.72	10.08	92.3	1.9	91	6.6	2.4
	LEO	1775	8.18 ± 3.1	8.75	94.5	3.26	84.6	11.5	3.9
	WHW	3559	11.89 ± 3.92	12.93	95.6	2.08	88.3	6.8	4.9

a BMD, Bernese mountain dog; BSH, Basset hound; CAI, Cairn terrier; EPB, Epagneul Breton; GSD, German shepherd dog; LEO , Leonberger West; WHW, Highland white terrier. b Inbreeding coefficient.

Table 3

 3 Heritabilities and estimates of inbreeding depression on litter size and 2 year survival. , heritability; h² 01 , heritability on the observed scale; NS non-significant; * P < 0.05; ** P < 0.01; *** P < 0.001.

				Litter size			2 year survival
	Breed a	h²	Inbreeding regression coefficient Litter Dam Sire	h² 01	Inbreeding regression coefficient
	BMD	0.109	-3.06 **	-4.18 **	-1.89 NS	0.061	-2.04 NS
	BSH	0.06	-1.36 NS	-0.67 NS	0.02 NS	0.067	-0.98 NS
	CAI	0.098	-2.20 ***	-1.18 *	0.14 NS	0.064	-1.57 NS
	EPB	0.1	-2.94 ***	-0.9 NS	0.73 *	0.063	-2.70 ***
	GSD	0.091	-3.30 ***	-2.19 ***	0.90 NS	0.101	-2.80 ***
	LEO	0.882	-3.80 *	-3.81 NS	1.50 NS	-	-
	WHW	0.105	-1.32 ***	-1.35 **	1.16 *	0.059	-1.1 NS

a BMD, Bernese mountain dog; BSH, Basset hound; CAI, Cairn terrier; EPB, Epagneul Breton; GSD, German shepherd dog; LEO , Leonberger West; WHW, Highland white terrier. h²

EqG, equivalent number of known generations.

Acknowledgements

1 See: http://www.thekennelclub.org.uk.

The authors would like to thank the Société Centrale Canine for the data provided and Wendy Brand-Williams for linguistic revision.

Individual breeds had different population sizes, with the number of observations ranging from 1775 (longevity for LEO breed) to 39080 (litter size for GSD breed) (Table 1). Among the breeds studied, BMD showed an increase in the number of litters produced over the 1990-2012 period (see Appendix: Supplementary Fig. 1). Since there are many hobby breeders, there was only a small number of observations per female, per male or per breeder (see Appendix: Supplementary Table 1); as an example, the average number of litters produced per male over the 1990-2012 period ranged from 3.8 (LEO) to 9.9 (WHW). In each data set, the pedigree knowledge was relatively good, with average EqG ranging from 5.02 (longevity for BMD and GSD) to 8.77 (litter size for EPB).

Characterisation of traits

The seven breeds showed large variations in the studied traits; average litter size ranged from 3.5 (WHW) to 6.3 (LEO) puppies, with variations between years (Table 1; see Appendix: Supplementary Fig. 1) and according to litter rank (Table 1; see Appendix: Supplementary Fig. 2). There was an increase in litter size until the second (BSH, EPB, GSD, LEO) or the third litter (BMD, CAI, WHW), and then a decrease in subsequent ranks.

Mean longevity ranged from 7.7 (BMD) to 12.2 (CAI) years (Table 2), with three breeds (CAI, EPB, WHW) showing a regular increase in longevity over the 6 year period of the study (see Appendix: Supplementary Fig. 3). Male longevity was significantly lower (P<0.001) than female longevity for BMD and GSD, but higher for CAI and WHW (see Appendix: Supplementary Fig. 4).

Inbreeding depression

Appendix

Supplementary Table 3

Estimated variance ratios for models estimating 2 year survival according to breeds.