James Raymer

Putting the Pieces of the Puzzle Together: Age and sex-specific estimates of migration between EU / EFTA countries, 2002-2007

Keywords: international migration, Europe, log-linear models, combining data migration internationale, Europe, modèles log-linéaire, données combinées

Because of inconsistencies in reported flows and large amounts of missing data, our knowledge of international migration patterns in Europe is limited. Methods for overcoming data obstacles and harmonising international migration data, however, are improving. In this paper, we provide a methodology for integrating various pieces of incomplete information together, including a partial set of harmonised migration flows, to estimate a complete set of migration flows by origin, destination, age and sex for the 31 countries in the European Union and European Free Trade Association from 2002 to 2007. The results represent a synthetic data base that can be used to inform population projections, policy decisions and migration theory.

Introduction

The development of European Community policies and legislation on migration and asylum has highlighted the need for comprehensive and comparable European statistics on a range of migration-related issues. The Thessaloniki European Council of 20 June 2003 concluded that more effective mechanisms are needed for the collection and analysis of information on migration and asylum in the European Union (EU). In 2007, the European Parliament passed a regulation to govern the supply of national statistics to the EU. Countries are now required to provide harmonised migration flow statistics to Eurostat in accordance to Regulation 862/2007 1 . The regulation obliges Member States to make the best use of available data and to produce statistics that are comparable across Europe, requiring a harmonised definition of migration and migrants. However, Member States are not required to introduce completely new data sources or to change existing administrative systems for immigration and asylum. In accordance with the principle of proportionality, the regulation confines itself to the minimum required to achieve the objective of harmonised Community statistics on migration and asylum. To help overcome obstacles regarding migration data, Article 9 of the Regulation states that 'As part of the statistics process, scientifically based and well documented statistical estimation methods may be used. ' (p. 7).

In this paper, we present a methodology to combine various pieces of information on migration to produce a consistent and complete set of age-and sex-specific migration flow estimates between the 31 countries in the EU2 and European Free Trade Association (EFTA) 3 from [START_REF] Thierry | Towards a harmonization of European statistics on international migration[END_REF][START_REF] Abel | Estimation of international migration flow tables in Europe[END_REF]. In this section, we summarise the main issues concerning the reported flows in Europe.

The availability of statistics on international migration flows is conditioned by the existence of a data collection system that has the potential of yielding meaningful statistical information on changes in place of usual residence. The major types of data sources used to produce statistics on international migration flows can be summarized as follows:

1) population registration systems, including centralised population registers and local population registers);

2) other administrative registers related to foreigners, alien's registers, residence permit databases or asylum seekers databases;

3) statistical forms filled in for all changes of residence; and 4) border crossing data collection and others sample surveys. Some information on international migration flows can also be derived from population censuses, but this source has a number of well-known limitations. The main ones are that they are (i) carried out at longer intervals, e.g., every five to ten years, (ii) not able to capture all of the migration events that occur between enumerations, and (iii) capable of only identifying immigrants, as emigrants are no longer present to be counted. Because of these reasons, migration flow data obtained from censuses are usually not considered for the reporting of international migration flows. The availability of statistics is not an end in itself. Even if data are available, their poor quality may render them useless. There are two main factors that make international migration statistics unreliable. The first is the under-registration of migrations, which applies in particular to countries where data-collection systems rely on self-declarations of international movements. The second relates to data coverage: the data collection system used in a country may not cover the whole target population and so some subsets are excluded from the statistics (e.g., asylum seekers or students). In addition to the above two factors, data might be unreliable if a lot of errors arise during data processing.

As a vast majority of international migration statistics in the EU / EFTA countries are derived from population registers,4 deficiencies in registration have the greatest influence on data reliability.

The willingness to report changes in place of residence vary from one country to another, but everywhere, people take into account the advantages and disadvantages resulting from being registered or not. In general, they have more interest in reporting their arrival than their departure.

Therefore, within a given country, immigration statistics are usually considered more reliable than emigration statistics. Origin-destination-specific migration data based on sample surveys are not considered reliable (except for very large flows) due to estimation errors and generally high volatility over time.

Regarding coverage, flows of undocumented migrants are generally not included (for obvious reasons). Furthermore, asylum seekers are often only included when they have been granted a refugee status and received a temporary or permanent residence permits. Students are another group of people who are in a grey area of the registration of international migrations. Not all EU students are included in the population registers of the receiving country or deregistered after they have left. For students originating from outside the EU / EFTA, the situation is considered more reliable, as all of them are required to obtain a specific residence permit.

Despite existing recommendations from the United Nations and the EU, the definitions of international migrants vary significantly between countries, within countries over time, and between different sources of statistical information. Moreover, the definitions of immigration and emigration that are applied in a particular country do not necessarily match in terms of the time criterion. Most countries base their definitions of international migration on a change of country of residence. A variety of possible interpretations of this term results in a lack of clarity in the statistics. It can be interpreted from a legal (de jure) or an actual (de facto) point of view. In the former, the laws and legislations binding in a country in question specify requirements that have to be fulfilled in order to become a resident. The conditions differ between nationals and non-nationals, and between nonnationals there are two distinct groups, namely foreigners with the right to free movement and others. In fact, nationals have an unconditional right of residence in their country of citizenship, whereas the rights of foreigners are hedged in with conditions. Nationals may still be counted as part of the population of their country of citizenship even after they have been living abroad for a number of years. Thus, having a place of residence in a country does not necessarily mean a physical presence on its territory. From the de facto perspective, residence is directly connected with presence in the country in question. Usually, presence must be for a specified minimum period of time.

Therefore, time should be considered as a supplementary concept to that of residence. However, the level of concreteness differs across countries. On the one hand, the definitions currently in use often specify that international migration takes place when there is a change in the country of residence for a minimum period of time. Such a period is precisely defined. On the other hand, some countries take only "permanent" changes of residence into account without specifying a precise duration.

When a precise period is used, another problem arises related to the distinction between intended and actual duration. The use of the actual duration concept means that the production of the statistics would be systematically delayed by the period used as the time criterion in the definition of migration. Currently, all countries which specify a precise period use the intended duration. As a consequence, the assumption is made that the intended duration will become the actual one. In reality, the two measures may differ considerably, depending on the country and situation.

As well as discrepancies in the definitions of crucial concepts described above, there are a number of other problems that considerably hinder the international comparability of flow data.

First, migration events are counted at various dates. For immigration this might be the date of issuing a permit, the date of arrival or the date of reporting for registration. For emigration, the date of expiry of a permit, the date of reporting the departure or the date of departure are variously used. Secondly, in some cases a reference period other than a calendar year might be applied (e.g., April to April in Ireland). In addition, when a very short (or no) duration of stay criterion is employed, an individual may migrate several times during the reference period. All of these events are counted separately in the international migration statistics. When the one year time limit is strictly applied and the data are collected on a yearly base, only one migration (immigration or emigration) can be counted for a given migrant and, accordingly, there should be no difference between the number of migrants and the number of migrations. This brief review leads to the general conclusion that currently available data on international migration flows are still far from being internationally comparable. This is evident when comparing data on flows between pairs of countries that are reported by countries of origin and countries of destination, using a so-called double-entry matrix. In an ideal world the emigration figures produced by sending countries and the immigration figures collected by receiving countries would be similar if the two data-collection systems use identical definitions and the data are reliable and complete. However, the real world demonstrates the weak comparability of the available data.

To provide an illustration of what the reported data actually look like, consider the subset of migration flows between ten countries in the EU for 2003 presented in Table 1. For each migration flow, there are two possible values: one reported by the receiving country (R) and one reported by the sending country (S). However, for the 2003 data, there are four data situations present: flows reported by both the receiving and sending country (e.g., Czech Republic to Germany or Spain to Italy), flows only reported by the receiving country (e.g., from France to Germany), flows only reported by the sending country (e.g., from Germany to Greece) or no flows reported (e.g., Belgium to France or France to Belgium). Furthermore, where flows are available from both the sending and receiving countries, the numbers rarely match. For example, one might take the average of the two reported flows from Germany to Spain (i.e.,13,746 and 16,236) as a reasonable estimate, as the numbers are relatively close to each other. However to take the average of the two reported flows from Spain to Germany (i.e., 14,647 and 2,109) would most likely result in a very poor estimate. In this situation, one might consider one flow to be more accurate than the other. Deciding which flow is more accurate than the other has consequences for the other situations where only one reported flow is available, e.g., from Spain to Belgium or from France to Spain.

--------Table 1 about here --------For the estimation of migration patterns in this paper, we take advantage of the recent work by [START_REF] De Beer | Overcoming the problems of inconsistent international migration data: A new method applied to flows in Europe[END_REF], who developed a methodology to harmonise migration flows benchmarked to the United Nations definition of duration for movements between 19 EU / EFTA countries from 2002 to 2007 (i.e., all the countries providing both countryspecific immigration and emigration flows). The methodology accounted for differences in definitions and the effects of measurement error due to, for example, under reporting and sampling fluctuations. The differences between the two sets of reported data were overcome by estimating a set of adjustment factors for each country's immigration and emigration data, taking into account any special cases where the origin-destination patterns did not match the overall patterns. More specifically, optimisation was used to minimise the differences between the two sets of reported data pooled over time. The estimated adjustment factors were then used to obtain harmonised estimates of migration flows for 19 countries providing both immigration and emigration flows by country of previous residence and next residence, respectively.

Methodology

Background

A migration flow table can be considered a two-way (origin by destination) contingency table, where the cells represent counts of migrants (or persons making moves). In the early 1980s, [START_REF] Willekens | Multidimensional population analysis with incomplete data[END_REF][START_REF] Willekens | Log-linear modelling of spatial interaction[END_REF] proposed a log-linear approach to model the main effect and interaction structures contained in migration flow tables. In this approach, auxiliary information may be included via offsets, including structural zeros to remove cells representing non-migrants or intra-national migrants from the estimation process. For example, a log-linear-with-offset model is specified as

) ln( ) ln( * ij D j O i ij n n , (1)
where * ij n represents the offset or auxiliary information, is the overall effect, O i is the origin main effect and D j is the destination main effect. This model provides estimates of migration that are consistent with the observed (or estimated) margins of the migration flow table (i.e., i n and j n ) but borrow the associations between origins and destinations from the offset, * ij n [START_REF] Rogers | Imposing age and spatial structures on inadequate migration-flow datasets[END_REF].

During the past ten years, there have been several papers focusing on describing and modelling the structures of internal migration found in tables cross-classified by origin, destination and age or some other categorical variable [START_REF] Rogers | Describing migration spatial structure[END_REF][START_REF] Rogers | Imposing age and spatial structures on inadequate migration-flow datasets[END_REF][START_REF] Sweeney | Population forecasting with nonstationary multiregional growth matrices[END_REF][START_REF] Raymer | Describing and projecting the age and spatial structures of interregional migration in Italy[END_REF][START_REF] Raymer | Using age and spatial flow structures in the indirect estimation of migration streams[END_REF][START_REF] Van Wissen | In search of a modelling strategy for projecting internal migration in European countries[END_REF]. The description and estimation centres on these structures rather than on the flows themselves. For instance, the multiplicative component model for describing the structures of an origin (O) by destination (D) table of migration flows is specified as

) )( )( )( ( ij j i ij OD D O T n , j i (2)
where ij n is a migration flow from origin i to destination j. There are four multiplicative components in total: an overall level, two main effects and one two-way interaction or association component. This decomposition, for example, can be used to assess whether an increase in a particular flow occurred because of an increase in overall attractiveness of the region (i.e., marginal effect), because of an increase in the connectedness between two places (i.e., interaction effect), or as a consequence of both.

The multiplicative components in Equation 2 are calculated with reference to the total level in the migration flow tables. The T component represents the total number of all migrants in the system. The main effect components, O i and D j , represent proportions of all migration from each origin and to each destination. The two-way interaction component represents the ratio of observed migration to expected migration (for the case of no interaction) and is calculated as

OD ij = n ij / [(T)(O i )(D j )].
The OD ij component captures the association or "connectivity" between origins and destinations.

The multiplicative component model is useful framework for estimating migration flows because it makes a distinction between an overall level, main effects, and interaction effects in contingency tables with parameters that can be used to guide the estimation process. This means that one can focus on modelling the underlying structures of migration flows via the multiplicative components. Also, the estimation process can be carried out in a systematic manner working from marginal effects to interaction effects. As described below, this model can also be extended to include other categorical variables, such as age groups and sex. In fact, this modelling framework has been used in a variety of settings, for example, to project future age-specific migration patterns in Italy [START_REF] Raymer | Describing and projecting the age and spatial structures of interregional migration in Italy[END_REF], to combine migration data from multiple sources to study economic activity flows in England [START_REF] Smith | Combining available migration data in England to study economic activity flows over time[END_REF] and to construct missing origin-destination associations for migration between countries in Europe [START_REF] Raymer | The estimation of international migration flows: A general technique focused on the origin-destination association structure[END_REF][START_REF] Raymer | Obtaining an overall picture of population movement in the European Union[END_REF].

Finally, the log-linear-with-offset model (Equation 1) produces the same estimates as those obtained from iterative proportional fitting [START_REF] Deming | On a least squares adjustment of a sampled frequency table when the expected marginal totals are known[END_REF][START_REF] Fienberg | An iterative procedure for estimation in contingency tables[END_REF][START_REF] Haining | A statistical approach to the problem of missing spatial data using a first-order Markov model[END_REF][START_REF] Wong | The reliability of using the iterative proportional fitting procedure[END_REF][START_REF] Johnston | Entropy-maximizing and the iterative proportional fitting procedure[END_REF], which is a relatively simple (mathematical) technique that has been used for "updating" incomplete migration flow tables [START_REF] Willekens | Multidimensional population analysis with incomplete data[END_REF][START_REF] Willekens | Log-linear modelling of spatial interaction[END_REF][START_REF] Nair | Estimation of period-specific gross migration flows from limited data: Biproportional adjustment approach[END_REF][START_REF] Rees | Methods for estimating missing data on migrants in the 1991 British census[END_REF]. As with the log-linear-with-offset model, this method may be used, for example, to revise a historical (or auxiliary) table of migration flows by forcing it to fit, biproportionally through iteration, a more recent set of marginal totals with missing cell counts, where the marginal totals may represent beginning and ending populations or total immigration and emigration by country.

Completing the Origin-Destination Matrix

Our starting point for estimating the complete and consistent set of migration flows between 31 EU / EFTA countries from 2002 to 2007 is a harmonised data set of migration flows between 19 EU / EFTA countries provided by [START_REF] De Beer | Overcoming the problems of inconsistent international migration data: A new method applied to flows in Europe[END_REF]. Our estimation procedure that we have developed is a hierarchical one based on the multiplicative component model (Equation 2). First, the 12 missing immigration and emigration totals5 of the complete migration flow table are estimated, followed by the corresponding origin-destination interaction terms (OD ij ). 6 In the next subsection, we describe how these flows can then be disaggregated by age and sex.7

For the migration totals, four similar ordinary least squares (OLS) regression models are used to estimate the natural logarithms of 1) immigration to the 31 EU / EFTA countries from the 31 EU / EFTA countries,

2) immigration to the 31 EU / EFTA countries from the rest of the world,

3) emigration from the 31 EU / EFTA countries to the 31 EU / EFTA countries, and 4) emigration from the 31 EU / EFTA countries to the rest of the world.

The main predictor variables are:

1) population size (in thousands, natural logarithm),

2) percentage of the population aged 65 and over,

3) life expectancy of females, 4) relative GDP, 5) percentage urban, and 6) indicator variables for the calendar years and Germany.

The selection of these variables, and the ones below for origin-destination associations, are based on migration theory, data availability and recent work by [START_REF] Jennissen | Macro-economic determinants of international migration in Europe[END_REF], [START_REF] Raymer | Obtaining an overall picture of population movement in the European Union[END_REF] andAbel (2010). In general, we expect large populations to both send and receive large numbers of migrants relative to countries with smaller populations; younger societies will send relatively more migrants than older societies; populations with higher levels of wellbeing (where life expectancy is a proxy) and GDP will attract relatively more migrants; and countries with higher proportions of urban populations to be more mobile than those with lower proportions. The indicator variable for Germany was used to control for its relatively large size, i.e., to prevent this country from dominating the patterns of smaller countries. With the exception of percentage urban, these variables were all available for the years 2002-2007. The regressions were carried out on the total harmonised migration flows estimated by [START_REF] De Beer | Overcoming the problems of inconsistent international migration data: A new method applied to flows in Europe[END_REF].

The estimated regression coefficients for the four models described above are set out in Table 2. The adjusted R 2 values were above 0.90 for all models except for the one predicting emigration to the rest of the world (R 2 = 0.75). The coefficients for population (positive) and percent 65 years and older (negative) were significant at the 0.05 level for all four models. The coefficients for female life expectancy (a proxy for wellbeing) were significant for three of the four models with the signs positive for immigration and negative for emigration to EU / EFTA countries. This means that countries with high life expectancies are relatively attractive to migrants from elsewhere and are also able to retain relatively more migrants as a result. The same story can be said, more or less, for GDP per capita (a proxy for earnings), also significant for three of the four models. Interestingly, the percent urban, the 2005-2007 indicator variables (increasing in a linear fashion) and the Germany indicator variables were significant only for the immigration and emigration models representing flows within the EU / EFTA. Here there is clear evidence that differences exist between migration within the EU / EFTA system and outside it. The above results are largely in agreement with macro-level migration theories. The only results that might appear strange are the negative coefficients for percent 65 years and older in the two immigration models. The idea that older societies attract fewer migrants makes sense if one remembers that life expectancy and GDP per capita are controlled for, and that these societies may be relatively less mobile overall due to their older populations.

The coefficients from the four regression models were used to obtain estimates of total immigration and emigration for the 12 countries with missing data. The EU / EFTA totals, however, had to be adjusted so that the sums of immigration and emigration matched. This was done by simply dividing the difference by two and proportionally subtracting that amount from the predicted immigration totals and proportionally adding it to the predicted emigration totals.

-----Table 2 about here -----

The next step in our model framework is to estimate the missing origin-destination associations (i.e., OD ij in Equation 2). Similar to the estimation of missing marginal totals, we used ordinary least squares regression, pooled over time, to estimate the natural logarithm of association terms for migration between the 12 missing EU / EFTA countries. The predictor variables are 1) contiguity (i.e., whether a country was a neighbour or not),

2) indicator variables for migration between the new accession countries and Ireland and the United Kingdom, 3) language family (i.e., 1 = same language family, 0 = different language family), 4) natural logarithm of gross national income in purchasing power parity (GNI PPP) per capita ratios, 8 5) natural logarithm of distance (between capital cities), 6) natural logarithm of foreign-born population stock associations between country i and j, 9 and 7) natural logarithm of trade flow associations between country i and j. 10

These variables capture the associations between regions by focusing on the social and physical 'distance' factors, as well as the economic factors representing relative wages and flows of trade.

The association terms for foreign-born population stocks and trade flows are calculated in the same way as the OD ij terms are in Equation ( 2). That is, the observed stocks or flows from i to j are divided by the overall level (n ++ ) multiplied by the proportion from origin i (n i+ / n ++ ) and the proportion to j (n +j / n ++ ), thus allowing us to control for the different "sending" and "receiving" levels in the foreignborn population stock and trade flow tables. These measures also correspond closely to what we are predicting, i.e., the association terms of migration from i to j. The regression resulted in an R 2 of 0.41 with all predictor variables being significant except language family and distance. The coefficients from this regression, set out in Table 3, were then used to estimate the origin-destination interactions between the 12 countries with missing data.

-----Table 3 about here -----

The predicted origin-destination association terms (i.e., OD ij ) are shown in the lower right hand corner of Table 4, along with the corresponding terms of the 2007 harmonised data. They range from 0.10 for the Romania to Liechtenstein flow to 5.85 for the Bulgaria to Romania flow. In other words, the migration flow from Romania to Liechtenstein is predicted to be much smaller than expected, whereas the flow from Bulgaria to Romania (i.e., two neighbouring countries) is predicted to be nearly six times larger than expected. Finally, multiplying the expected migration flows by these estimated interactions yielded the estimates of the flows between the 12 countries with missing data. The results are described below in Section 4. -----Table 4 about here -----

Disaggregating by Age and Sex

The complete set of origin-destination flows, estimated using the methodology described in the previous section, may be disaggregated by age and sex by using a multiplicative component model approach.

) ( ) )( )( )( ( ) )( )( )( )( )( ( ) )( )( )( )( ( ijxy jxy ijy ixy ijx xy jy jx iy ix ij y x j i ijxy ODAS DAS ODS OAS ODA AS DS DA OS OA OD S A D O T n (3)
where n ijxy is an observed flow of migration from origin i to destination j for age group x (i.e., 0-4, 5-9, ..., 85+ years) and sex y. There are sixteen multiplicative components in total: an overall level (T), four main effects, six two-way interaction components, four three-way interaction components and a single four-way interaction component. For this study, however, we do not have complete information. Instead we only have three separate tables: For the disaggregation by age and sex, one first needs to identify an overall model that can accurately predict the migration flows. We did this by comparing various unsaturated log-linear model fits of the two available three-way migration flow tables, i.e., OAS andDAS, for the 2002-2006 periods. Using the likelihood ratio statistic as a goodness-of-fit measure and visual comparisons of the predicted flows with the reported flows, we found that the two-way interaction models, OA, OS, AS and DA, DS, AS, did very well in predicting the OAS and DAS tables, respectively. For the OAS flows, the likelihood ratio statistic for the two-way interaction model was 38,927 with 357 residual degrees of freedom (rdf), which was considerably lower than any of the other unsaturated models.

For instance, the likelihood ratio statistics for the simpler OA, AS and OA, OS models were 103,819 (rdf = 378) and 143,639 (rdf = 374), respectively. The same story was true for the DAS flows. Here, the likelihood ratio statistic for the two-way interaction model was 83,007 with rdf = 391, while the statistics for the competing DA, DS and DA, AS models were 171,780 (rdf = 408) and 147,288 (rdf = 414), respectively. Furthermore, an inspection of the age-specific patterns of the predicted flows based on the two-way interaction models (not shown for space reasons) showed that they were practically indistinguishable from the corresponding reported flows.

Because ODA tables are not available for migration between countries in the European Union, we were not able to test whether the three-way interaction between origin, destination and age was significant. However, based on recent analyses of age-specific internal migration, we can assume these terms, for the most part, would not contribute much to the estimation of the flows. [START_REF] Raymer | Using age and spatial flow structures in the indirect estimation of migration streams[END_REF] and [START_REF] Raymer | Describing and projecting the age and spatial structures of interregional migration in Italy[END_REF], for example, found that the models that included only the origin-age and destination-age interactions produced estimates that were nearly indistinguishable from the observed values in the complete ODA table. Interestingly, there tends to be very little difference between male and female migration patterns in analyses of internal migration, whereas for these international migration data, significant differences were found.

The above analyses provide us with some direction on how to proceed with the combining of migration flow data. First, we do not need to include the complete data to produce accurate results. In fact, based on our analyses of the available data and analyses of internal migration in other studies, we believe the following and relatively simple two-way interaction model should capture most of the international migration patterns between countries in the EU / EFTA:

) )( )( )( )( )( )( )( )( )( )( ( * xy jy jx iy ix ij y x j i ijxy AS DS DA OS OA OD S A D O T n , j i (4)
with * ijxy n denoting an initial estimated set of migration flows, not constrained to any set of margins.

The modelling strategy is therefore to calculate the multiplicative components in Equation 4for countries providing data, and to estimate the component values for countries not providing data.

Unfortunately, at the time of this writing, the 2007 age-and sex-specific data were not available.

However, as shown below, we believe this is not a major problem for the model expressed in Equation 4 as there are strong regularities exhibited in the age and sex patterns over time.

The following equations are used to estimate the initial (unconstrained) migration flows corresponding to the model in Equation 4. 11 The T component represents the total number of all migrants in the system, n n T ijxy ijxy .

(5)

The main effect components, O i , D j , A x , and S y , represent proportions of all migration from each origin, to each destination, in each age group and by sex, respectively, i.e.,

The T, O i and D j components were obtained directly from the estimated origin-destination migration flow tables (see Section 3.2). The A x components for the years 2002-2006 are presented in Figure 1.

Here, we find strong regularities in the patterns over time with a downward slope in the child years and a labour force peak in the young adult years, corresponding to the 'standard' schedule of agespecific migration (Rogers et al., 2010, p. 20). The S y components averaged 0.453 for females, with a minimum of 0.442 in 2003 and a maximum of 0.463 in 2005. Note, the A x and S y components represent the averages exhibited by the countries reporting data in the OAS and DAS tables provided by Eurostat.

-----Figure 1 about here -----

The two-way interaction components represent the ratios of observed migration to expected migration (for the case of no interaction) and are calculated as

) )( )( ( j i ij ij D O T n OD , ( 10
) ) )( )( ( x i x i ix A O T n OA , ( 11
) ) )( )( ( y i y i iy S O T n OS , ( 12)
) )( )( (

x j jx jx A D T n DA , ( 13
) ) )( )( ( y j y j jy S D T n DS , ( 14
)

) )( )( ( y x xy xy S A T n AS . ( 15
)
The OA ix , DA jx and AS xy components represent the deviations from the overall age profile of migration, A x . For estimation purposes, it is useful to know that they also represent ratios of the age compositions of emigration and immigration to the overall age composition of migration. Likewise, the OS iy and DS jy components represent the deviations from the overall proportions of migration in each sex group, S y . For estimation purposes, these also represent ratios of the sex-specific proportions of emigration and immigration from and to each country, respectively, to the corresponding overall proportions.

Because of the large number of cells resulting from the estimation process (i.e., 32 x 31 x 18

x 2 = 17,858 cells for each of the six years), we focus our illustration of multiplicative components on four flows:

1) Norway to Sweden (good data sources),

2) Germany to Spain (reasonable data sources),

3) Poland to United Kingdom (poor data sources), and 4) France to Belgium (missing data).

The origin-age components (i.e., OA ix ) for Norway, Germany and Poland and the destination-age components (i.e., DA jx ) for Sweden, Spain and the United Kingdom are presented in Figure 2. Note the ratios for France and Belgium were set to equal one, as data for these countries were not available. The same assumption was used for all countries not providing data with the result that the patterns for these countries came from the main effects of age and sex. The OS iy and DS jy components are presented in Table 5, and the AS xy components are presented in Figure 3. In all three cases, only the female patterns are presented, as the male patterns exhibited the reciprocal patterns. For example, in Figure 3, we find that relatively more women migrate at young and old ages, whereas men are overrepresented in the 30-54 ages.

-----Table 5 and Figures 2-3 about here -----

The estimation of migration flows based on the multiplicative components produces "initial"

estimates that need to be constrained to the estimated origin-destination migration flow totals.12 This is done by including the initial values as an offset in the following log-linear model:

* ln ln ijxy OD ij D j O i ijxy n n , ( 16
)
where * ijxy n denotes the offset of initial values, obtained by multiplying the multiplicative components together (i.e., Equation 4), and the lambda parameters represent the constraints in a log-linear model weighted to the origin-destination migration flow totals estimated previously (Section 3.2).

Results

In this section, we present some of our results from the models described in the previous section to estimate the missing marginal totals and origin-destination associations of the origin-destination matrices, and then the disaggregation of these tables by age and sex. The flows are estimated for the years 2002 to 2007. In our analysis, we first describe the changes over time in the aggregate flows and then show some of the estimated age and sex patterns.

Changes over time

The harmonised estimates of immigration, emigration and net migration, averaged from 2002-2007 and ordered by level of immigration, are presented in Figure 4. On average, Germany received the largest number of immigrants with nearly 600 thousand per year. The United Kingdom, Italy, Spain and France were the next largest receivers. Of these countries, four had shares of migration from the rest of the world that exceeded 60 percent. However, most countries in the EU / EFTA (i.e., 19 out of 31), including Germany, had shares from the rest of the world not exceeding 50 percent, illustrating the importance of the EU / EFTA migration system.

-----Figure 4 about here -----

The largest senders of migrants on average were, again, Germany (440 thousand), followed by Poland (307 thousand), United Kingdom (296 thousand), Romania (273 thousand) and Spain (231 thousand). Of the five largest senders of migrants, only the United Kingdom and Spain had shares to the rest of the world exceeding 50 percent. In fact, most countries (24 out of 31) had estimated shares below 50 percent. In terms of average net migration, the top receivers of migrants also had the largest net migration totals, with rest of the world migration being most important. However, amongst these countries, note that Italy received the largest net gain, while Germany only ranked fourth, below the United Kingdom and Spain. The two countries with the largest negative net migration were Poland and Romania, where the negative numbers were attributed mostly to migration between EU / EFTA countries.

According to our estimates, migration between countries in the EU / EFTA increased steadily from 1.3 million in 2002 to 2.0 million in 2007. This increase is not necessarily surprising as the EU added 10 countries to its membership in 2004 and another two in 2007, all of which had substantially lower GDP levels than in the existing EU / EFTA countries. Another factor contributing to this increase, as suggested in the results below, is corresponding increases in the migration levels during the six years between countries in the EU15 (i.e., the EU countries before accession in 2004) and EFTA.

The EU15 countries and the EFTA countries (i.e., Iceland, Liechtenstein, Norway and Switzerland) were consistent net receivers of migrants gaining between 246 thousand and 390 thousand per year. The sources of these migrants were the 2004 and 2007 EU accession countries (A2004 and A2007, respectively). The ratios of emigration to immigration were very high for these 12 countries. In 2002, the A2004 countries sent two migrants to the EU15 and EFTA countries for every one they received. However, despite considerable increases in the levels of emigration, this ratio decreased to 15 migrants sent for every 10 received in 2007. One possible explanation for this is that accession to the EU facilitated more return migration. The corresponding ratios for the A2007 countries (i.e., Romania and Bulgaria) were even greater, i.e., between 3.7 and 4.8 during the six year period.

----- -----Table 7 about here -----

Age and sex patterns

The average age patterns of migration are presented in Figure 1 (as main effects) for the years 2002-2006. In Figure 5, we present our estimates of age-specific net migration totals by sex for the EU15, EFTA, A2004 and A2007 countries. Interestingly, our estimates produce different patterns for each group. The estimates for the EU15 countries resulted in higher (positive) net migration totals of female migrants in the 20-24 and 25-29 age groups, whereas for the EFTA countries, there were considerably more males in the 25-59 ages. For the A2004 countries, the age-specific net migration patterns of females and males were nearly identical and mostly negative. The exceptions are the first age group and the 55-79 ages, which mostly likely reflects the age compositions of return migrants. Finally, for the A2007 countries, the estimated totals of net migration were much higher for females, at all ages, than for males.

-----Figure 5 about here -----To illustrate some of the detailed age-and sex-specific migration estimates, we have selected the same four flows as in Section 3.3 to present estimates between countries with good data (i.e., Norway to Sweden), reasonable data (i.e., Germany to Spain), poor data (i.e., Poland to the United Kingdom) and missing data (i.e., France to Belgium). In Figure 6 -----Figure 6 about here -----

Conclusion

In this paper, we have developed a methodology to estimate a complete set of migration flows by age and sex between all 31 countries in the EU / EFTA. To do this, we had to combine four pieces of information: a previously harmonised origin-destination migration flow A selection of our results has been presented to give an idea of the detail in our estimates. 13While these estimates are by no means perfect, we believe they provide a substantial and significant improvement over the patterns exhibited in the reported flows, which contain inconsistencies due to measurement, collection and availability. In general, the estimated patterns coincide with what we would expect based on migration theory. For instance, the largest estimated flows are between countries with the largest populations, more migration is observed between neighbouring countries than non-neighbouring countries, and net receivers of migrants are those with higher GDP levels.

Our estimates also reflect increases in the levels of migration associated with the expansion of countries in the EU.

The contributions of this paper are many. First, we have expanded the estimates in de Beer et al. ( 2010) to include missing flows, and thus completing the matrix of flows between EU / EFTA countries. This involved developing models for the estimation of total immigration and emigration and for the estimation of the associations between origins and destinations. Second, we have developed a model and a set of assumptions for disaggregating these flows by age and sex based on incomplete information. Third, we have shown how our results can be used to better understand the migration patterns in the EU / EFTA. Fourth, we have compared our estimates against reported values and identified where important differences arise. In combination with the harmonisation methodology developed in de Beer et al. ( 2010), we believe our methodology and resulting estimates can be used to improve current population estimation methods. Finally, we have provided a base for countries to improve their statistics on migration as required in the 2007 Regulation on migration statistics passed by the European Parliament. Our methodology is based on the idea of combining data. Countries could benefit from this approach, at the very least, by comparing their reported figures of, say, immigration from Germany with Germany's emigration figures. However, this will only help, if the user knows that Germany applies a relatively loose definition of migration and therefore its figures are higher than those using, say, a six month or twelve month definition.

While we believe we have produced six years of reasonable estimates of migration flows, they are by no means without error. The estimates are based on a hierarchical methodology. First the available origin-destination-specific data are harmonised based on reports by sending and receiving countries, then the missing data are estimated by using covariates, and finally the flows are disaggregated into age and sex based on the patterns exhibited by countries providing data. Further improvements could be made to integrate the various steps. Also, there are no measures of uncertainty associated with our estimates. It would be useful to know which of our estimated flows are considered to be very reliable and which are akin to rough guesses. However, we believe we have made an important start towards the improvement of providing usable migration statistics to the community. In fact, work has already started on the next stage of modelling, namely the Integrated Modelling of European Migration (IMEM) project recently funded by New Opportunities for Research Funding Agency Co-operation in Europe (NORFACE). Over the next couple of years, this project aims to integrate the harmonisation and estimation of missing data into a single (Bayesian) model that also includes measures of uncertainty and expert judgements. 14 We hope this work provides an important foundation for work such as this and others aiming to improve our knowledge and understanding of the complexity in international migration.

In conclusion, the methodology we have presented in this paper for estimating international migration flows is the first of its kind. We have overcome major obstacles concerning inconsistencies in the reported data and completely missing data to produce what we believe are very reasonable estimates of detailed flows over time. In fact, we believe our estimates are much better than those currently reported in, say, the Eurostat database. These estimates provide a complete and more consistent picture of population movements occurring in Europe. The approach is based on a closed system of movements, that is, an emigrant from one place must be an immigrant to another. The methodology is flexible to account for various types of migration data, as well as other categorical information, such as flows by broad citizenship groups or education levels. The data can be used for many purposes, including to improve our understanding of recent patterns of migration, as inputs into population projections, to compare against reported figures and to test any estimation procedure countries may adopt for improving the reporting of their statistics. Most importantly, we have shown that it is not impossible to overcome the complex nature of international migration data to produce reasonable estimates of migration based on information from multiple sources.

  , we present the results for these flows by age and sex for 2002 and 2007. The main differences found in the Norway to Sweden flow are the lower levels of migration in the child to young adult age groups in 2007 in comparison to 2002. Between 2002 and 2007, large increases in the levels of 20-54 year old migration were estimated for both the Germany to Spain and France to Belgium flows. In both cases, females also exhibited much higher levels of migration than males. The estimated Poland to the United Kingdom flows exhibited similar levels by age for males and females. The increase in the levels was largely due to two age groups, 20-24 and 25-29 year olds.

  Notes: R = receiving country's reported flows; S = sending country's reported flow; ... = no reported data available; ; n.a. = not applicable; BE = Belgium, CZ = Czech Republic, DK = Denmark, DE = Germany, EE = Estonia, GR = Greece, ES = Spain, FR = France, IE = Ireland and IT = Italy.

Figure 5 .Figure 6 .

 56 Figure 5. Estimated net migration totals for EU15, EFTA, A2004 and A2007 countries by sex, 2007

  Because the tables now have four dimensions, we denote cross-classified tables by letters. For example, OD is a two-way (origin by destination) table of migration flows, OAS is a threeway (origin by age by sex) table of migration flows and ODAS is a four-way (origin by destination by

age by sex) table of migration flows. The (saturated) multiplicative component model for an ODAS table of migration flows is specified as

  1) a complete OD table (estimated) for the years 2002-2007, 2) an incomplete OAS table provided by Eurostat for the years 2002-2006, and 3) an incomplete DAS table provided by Eurostat for the years 2002-2006.

  about the same (with the exception of 2006). The A2007 countries exhibited a sharp increase in migration to EU / EFTA countries between 2002 and 2003 and then levelled off until another increase in 2007. The first increase in the patterns is surprising particularly since emigration to the rest of the world did not increase and emigration from the A2007 countries increased only slightly. The second increase, on the other hand, conforms to our expectations in relation to the Third, for some countries, we estimate considerably different net migration totals. These include the much lower estimates for Portugal, Spain and Slovenia and the much higher estimates for Latvia, Poland and Romania. Finally, we have produced estimates for countries who have not given migration data to Eurostat. These include figures for Belgium, Bulgaria, Estonia and Ireland.

	accession that occurred in 2007. Likewise, the results confirm our expectations regarding the A2004
	countries joining the EU in 2004, where emigration steadily increased in 2004 and thereafter. Note
	that there were corresponding increases in the immigration to A2004 and A2007 countries from EU /
	EFTA countries (i.e., return migration), albeit at lower levels.
	EFTA area. Here, the immigration and emigration levels increased by 56 percent, whereas migration
	from the rest of the world only increased by 28 percent. In terms of numbers, immigration from EU /
	EFTA countries increased by 719 thousand, whereas immigration from the rest of the world
	increased by 512 thousand. Thus, less than half of the increase in immigration between 2002 and
	2007 came from outside the EU / EFTA. The main drivers of this increase were most likely the EU

Table

6

about here -----Relative to migration from the rest of the world, EU15 countries received smaller shares of migrants from EU / EFTA countries, whereas EFTA, A2004 and A2007 countries received (slightly) larger shares (see Table

6

). In terms of emigration, all four groups of countries exhibited larger shares going to EU / EFTA countries relative to the rest of the world. Finally, in terms of overall changes in the levels over time, we found the largest increases to have occurred within the EU / accessions of ten countries in 2004 and two more in 2007. Migration from the A2004 countries to the EU / EFTA increased by 63 percent from 2002 to 2007, whereas the migration to the rest of the world remained

In comparison to the reported numbers provided by Eurostat, our results have several implications as shown by the net migration totals in Table

7

. First, our estimated net migration totals for the EU / EFTA countries are considerably lower than Eurostat's figures, even with missing data considered. For example, in 2007, we estimated the net migration for EU / EFTA countries to be 864 thousand. The corresponding figure from Eurostat is 2089 thousand. One likely explanation for this is that emigration statistics have much higher levels of underreporting relative to immigration statistics. Second, our estimates resulted in opposite net migration totals for several countries. Cyprus, Czech Republic, Hungary, Liechtenstein, Malta and Slovakia all reported positive net migration totals between 2002 and 2007, whereas in most of these cases, we estimate negative totals.

  table representing flows between 19 EU / EFTA countries (de Beer et al. 2010), an incomplete emigration by age by sex table, an incomplete immigration by age by sex table, and covariate information. The result is a synthetic data base that can be used for many purposes.

Table 1 .

 1 Reported flows of migration between selected countries in the EuropeanUnion, 2003

			To
	From		BE	CZ	DK	DE	EE	GR	ES	FR	IE	IT
	BE	R	n.a.	80	587	4,291	…	…	3,037	…	…	1,959
		S	n.a.	…	…	…	…	…	…	…	…	…
	CZ	R	…	n.a.	232	9,258	…	…	388	…	…	915
		S	78	n.a.	47	950	2	66	70	283	31	197
	DK	R	…	65	n.a.	2,693	…	…	764	…	…	281
		S	511	180	n.a.	2,540	133	229	1,720	1,333	264	782
	DE	R	… 1,228 3,221	n.a.	…	… 13,746	…	… 12,902
		S 4,623 8,909 2,712	n.a.	597 18,106 16,236 19,060 2,415 33,802
	EE	R	…	4	169	947	n.a.	…	60	…	…	103
		S	…	…	…	…	n.a.	…	…	…	…	…
	GR	R	…	57	278 12,959	…	n.a.	273	…	…	638
		S	…	…	…	…	…	n.a.	…	…	…	…
	ES	R	…	103 1,665 14,647	…	…	n.a.	…	…	2,051
		S	647	34	130	2,109	4	38	n.a.	2,474	487	801
	FR	R	…	462 1,488 18,133	…	…	8,847	n.a.	…	4,647
		S	…	…	…	…	…	…	…	n.a.	…	…
	IE	R	…	45	306	2,046	…	…	1,649	…	n.a.	292
		S	…	…	…	…	…	…	…	…	n.a.	…
	IT	R	…	274	895 23,702	…	…	5,796	…	…	n.a.
		S 1,414	20	155	9,778	1	211	895	2,933	130	n.a.

Table 2 .

 2 Regression coefficients for models predicting the natural logarithm of total harmonised immigration and emigration flows for 19 countries in the EU /EFTA, 2002EFTA, -2007

			Coefficients			Standard Error
		Immigration	Emigration	Immigration	Emigration
							Rest		Rest
		EU/	Rest of	EU/	Rest of	EU/	of	EU/	of
		EFTA	World	EFTA	World	EFTA World EFTA World
	Constant	-3.573 -13.005	10.365	6.223	2.164 2.629 1.739 3.964
	ln(population)	0.919	1.163	0.869	0.935	0.037 0.045 0.030 0.068
	Percent 65+	-0.188	-0.076	-0.236	-0.182	0.028 0.034 0.022 0.051
	Life expectancy (females)	0.081	0.168	-0.070	-0.031	0.029 0.035 0.023 0.053
	GDP per capita (EU27 =
	100)	0.008	-0.002	0.005	-0.006	0.001 0.002 0.001 0.002
	Percent urban	0.010	0.008	0.008	0.013	0.004 0.005 0.003 0.007
	2003 (indicator)	0.119	0.029	0.062	0.053	0.148 0.179 0.119 0.270
	2004 (indicator)	0.270	0.029	0.207	0.142	0.148 0.180 0.119 0.271
	2005 (indicator)	0.401	0.049	0.304	0.239	0.149 0.181 0.119 0.272
	2006 (indicator)	0.483	0.096	0.416	0.403	0.150 0.182 0.120 0.274
	2007 (indicator)	0.659	0.115	0.530	0.413	0.150 0.183 0.121 0.275
	Germany (indicator)	0.507	-0.383	0.802	0.499	0.216 0.262 0.173 0.395
	R 2	0.90	0.92	0.91	0.75
	Notes: Italics = not significant at 0.05 level; Number of observations = 114.

Table 3 .

 3 Coefficients from regression to predict the natural logarithm of origin-destination association terms (OD ij ),2002-2007 average

	Variable	B	Std. Error	Sig.
	(Constant)	-0.4900	0.2416	0.0426
	Contiguity	0.5501	0.0684	0.0000
	Accession dummy	0.9980	0.1545	0.0000
	Language family	0.1002	0.0705	0.1549
	ln GNI PPP ratios	0.1300	0.0157	0.0000
	ln Distance	0.0405	0.0339	0.2316
	ln Foreign-born	0.2471	0.0123	0.0000
	association
	ln Trade association	0.3291	0.0201	0.0000

Table 4 .

 4 Estimated origin-destination association terms (OD ij ) for the flows between the 19 countries with data and the 12 countries with missing data, 2007

		Destination
	Origin AT	CY	CZ	DE	DK	ES	FI	IS	IT	LT	LU	LV	NL	NO	PL	SE	S
	AT		0.18 0.73 1.53 0.47 0.15 0.48 0.23 0.36 0.12 0.10 0.37 0.50 0.17 1.04 0.47 8
	CY	0.09		0.09 0.10 0.14 0.01 0.35 0.00 0.04 0.16 0.00 0.29 0.18 0.07 0.13 0.36 0
	CZ	1.35	0.63		0.87 0.51 0.19 0.32 0.50 0.38 0.28 0.12 1.24 0.58 0.28 0.31 0.39 0
	DE	1.81	0.16 0.34		0.79 0.32 0.39 0.18 0.63 0.63 0.80 0.46 0.89 0.54 3.06 0.64 2
	DK	0.29	0.22 0.22 0.52		0.37 2.70 18.80 0.25 2.05 0.23 2.45 0.84 7.36 0.39 17.33 0
	ES	0.20	0.05 0.04 0.40 0.67		0.73 0.11 0.25 1.11 0.10 0.24 0.79 0.27 0.18 0.52 0
	FI	0.86	0.36 0.33 0.81 2.22 0.60		0.98 0.41 0.64 0.25 2.34 1.24 3.63 0.13 13.97 0
	IS	0.26	0.00 0.11 0.22 28.34 0.30 2.23		0.19 2.41 0.20 2.63 0.92 4.94 0.78 7.05 0
	IT	0.81	0.11 0.30 1.01 0.76 0.90 0.56 0.30		0.47 0.53 0.59 0.84 0.19 0.90 0.53 2

Table 5 .

 5 Origin-sex (OS iy ) and destination-sex (DS jy ) components of femalemigration, 2002-2006

		Origin-Sex (OS iy )	Destination-Sex (DS jy )
	Country 2002 2003 2004 2005 2006	2002 2003 2004 2005 2006
	AT	0.914 0.914 0.914 0.876 0.889	1.026 1.026 1.026 1.021 1.021
	BE
	BG
	CH	1.063 1.082 1.051 1.024 1.037	1.095 1.093 1.101 1.084 1.071
	CY	1.153 1.447 1.508 1.430 1.503	1.201 1.048 1.188 1.288 1.435
	CZ	0.694 0.691 0.667 0.855 0.855	0.846 0.755 0.810 0.846 0.846
	DE	0.828 0.845 0.826 0.819 0.838	0.952 0.948 0.944 0.952 0.922
	DK	1.053 1.077 1.050 1.031 1.027	1.114 1.101 1.127 1.128 1.098
	EE
	ES	1.137 1.038 0.973 0.946 0.924	1.054 1.056 1.029 1.046 1.079
	FI	1.129 1.172 1.101 1.106 1.097	1.107 1.113 1.139 1.121 1.099
	FR
	GR
	HU	1.010 1.016 1.000 0.824 0.799	0.989 0.939 1.104 0.985 1.025
	IE
	IS	1.084 1

.084 1.084 1.084 1.084 1.144 1.144 1.144 1.144 1.144

	IT	0.971 0.996 0.996 0.996 0.996	1.127 1.128 1

.128 1.128 1.128

	PL	0.918 0.918 0.918 0.918 0.918	1.024 1.024 1.024 1.024 1.024
	PT		1.178 1.175 1.240 1.240 1.240
	RO	1.212 1.327 1.374 1.349 1.364	1.068 1.031 0.985 0.976 0.871
	SE	1.061 1.101 1.055 1.014 1.023	1.089 1.110 1.143 1.110 1.070
	SI	1.132 1.121 0.995 1.139 1.123	0.709 0.728 0.599 0.592 0.485
	SK	1.425 0.915 0.917 1.140 1.042	0.981 0.902 0.887 0.824 0.827
	UK	1.047 0.962 1.091 1.000 1.000	1.071 1.263 1.157 1.073 1.057
	REST
	Notes: (1) Boldface denotes estimated; (2) the corresponding male patterns are (basically) the reciprocals of
	these ratios.
	LI
	LT	1.072 1.202 1.167 1.112 1.123	0.997 1.000 1.057 0.997 0.991
	LU	0.995 1.080 0.958 0.898 0.943	1.018 1.035 1.014 1.036 1.036
	LV	1.020 1.137 1.114 1.203 1.158	0.951 0.747 0.915 0.990 1.032
	MT		0.947 0.947 0.947 0.947 0.947
	NL	1.037 1.067 1.045 1.027 1.046	1.083 1.103 1.154 1.139 1.112
	NO	1.073 1.068 1.070 1.056 1.056	1.149 1.133 1.160 1.134 1.134

Table 6 .

 6 Harmonised estimates of immigration and emigration (in thousands) for countries in the EU15,EFTA, A2004 and A2007: 2002EFTA, A2004 and A2007: -2007

			Immigration				Emigration
	Year EU15 EFTA A2004 A2007 Total	EU15 EFTA A2004 A2007 Total
		A. From EU / EFTA countries		B. To EU / EFTA countries
	2002 1,002	90	149	46 1,286	766	80	297	143 1,286
	2003 1,158	87	165	53 1,462	810	79	318	255 1,462
	2004 1,226	87	205	55 1,573	867	79	384	244 1,573
	2005 1,233	90	236	58 1,617	891	79	428	219 1,617
	2006 1,353	106	268	67 1,795	984	85	481	245 1,795
	2007 1,452	145	327	80 2,005	1,125	89	486	305 2,005
		C. From rest of world		D. To rest of world
	2002 1,560	72	141	44 1,817	656	25	317	96 1,093
	2003 1,837	65	164	46 2,112	716	24	304	95 1,139
	2004 1,865	67	176	48 2,155	721	27	312	97 1,157
	2005 1,705	66	198	50 2,017	758	28	287	102 1,176
	2006 1,841	64	226	53 2,183	921	30	406	114 1,471
	2007 1,909	77	287	55 2,329	1,014	28	312	111 1,465
		E. From all countries		F. To all countries
	2002 2,562	162	290	90 3,104	1,421	105	614	239 2,380
	2003 2,995	152	328	99 3,575	1,526	103	622	350 2,601
	2004 3,090	154	381	103 3,728	1,587	106	696	341 2,730
	2005 2,938	156	433	108 3,634	1,649	107	715	321 2,793
	2006 3,194	170	494	120 3,978	1,905	114	887	360 3,266
	2007 3,361	222	615	136 4,334	2,139	117	799	416 3,470

Table 7 .

 7 Comparison of net migration totals provided by Eurostat and our harmonised estimates: EU / EFTA countries 2004-2007

			Reported by Eurostat			Our Estimates
	Country	2004	2005	2006	2007	2004	2005	2006	2007
	AT	50.6	50.3	27.5	32.7	61.4	57.3	28.9	35.1
	BE	43.3	N/A	N/A	55.4	30.5	35.1	44.2	48.5
	BG	N/A	N/A	N/A	-1.4	-30.1	-29.6	-33.7	-53.5
	CH	40.5	33.9	39.4	75.5	40.5	36.2	39.4	75.5
	CY	15.7	14.4	8.7	7.6	-11.2	-24.4	-19.1	-34.9
	CZ	18.6	36.2	34.7	83.9	-100.9	-36.9	-74.2	68.3
	DE	82.5	95.0	22.8	43.9	145.1	128.7	78.6	48.4
	DK	4.8	6.6	10.0	23.1	5.0	6.0	7.3	14.5
	EE	N/A	N/A	N/A	N/A	-5.2	-5.8	-6.5	-7.0
	ES	629.5	651.3	698.5	731.2	276.9	274.2	205.2	110.4
	FI	6.7	9.0	10.3	13.6	8.9	11.4	12.5	16.3
	FR	109.0	97.5	93.6	71.0	99.1	107.2	139.7	155.0
	GR	41.4	40.0	40.0	41.0	25.0	26.3	28.5	28.5
	HU	18.2	17.3	17.9	19.9	-18.3	-22.7	-25.6	-28.6
	IE	N/A	N/A	64.4	46.2	15.1	19.6	32.3	24.6
	IS	0.5	3.9	5.3	3.1	0.1	0.8	1.3	1.5
	IT	379.7	260.6	222.4	491.5	496.9	329.5	389.1	381.6
	LI	0.1	0.1	0.1	0.1	-0.1	-0.1	0.1	0.2
	LT	-9.6	-8.8	-4.9	-5.2	-17.4	-15.5	-11.5	-11.2
	LU	4.4	6.1	5.4	6.0	6.5	6.5	4.9	4.7
	LV	-1.1	-0.6	-2.5	-0.6	-11.5	-9.4	-17.8	-10.9
	MT	1.0	0.1	-0.1	1.7	-1.6	-1.3	-1.8	-1.5
	NL	19.0	9.2	10.1	25.5	18.1	7.9	10.0	23.9
	NO	13.2	18.4	23.7	39.7	8.0	11.8	15.4	28.4

Note: Proportions based on available data. Figure 1. The age main effect component of (A x ) migration, 2002-2006

http://europa.eu/legislation_summaries/justice_freedom_security/free_movement_of_persons_asylum_immigra tion/l14508_en.htm

The 27 countries in the EU are Austria (AT), Belgium (BE), Bulgaria (BG), Cyprus (CY), Czech Republic (CZ), Denmark (DK), Estonia (EE), Finland (FI), France (FR), Germany (DE), Greece (GR), Hungary (HU),

The United Kingdom and Cyprus use a passenger survey to obtain information on migration flows. Ireland uses a Labour Force Survey.

The 12 countries with missing data are Belgium, Bulgaria, Estonia, France, Greece, Hungary, Ireland, Lichtenstein, Malta, Portugal, Romania and Switzerland.

In both cases, we used SPSS's linear regression procedure.

Here, we used SPSS's log-linear procedure.

Obtained from the Population Reference Bureau's World Population Data Sheets (http://www.prb.org/).

We used Excel for this.

We used SPSS's log-linear procedure for this.

The complete set of results is available at http://www-oud.nidi.knaw.nl/en/projects/230211/.

See http://www.norface.org/migration12.html.

Note: Missing data estimates are based on the harmonised data of 19 EU / EFTA countries pooled from 2002 to 2007.

Acknowledgements

This work was supported by a European Commission / Eurostat tender n° 2006/S100 106607 (OJ 27/05/2006) for the supply of statistical services. The authors would like to thank the other team members of the MIMOSA (MIgration MOdelling for Statistical Analyses) project and two reviewers of European Journal of Population for their comments and suggestions on earlier efforts. The estimates described in this paper are freely available on the Netherlands Interdisciplinary Demographic Institute's website at http://www-oud.nidi.knaw.nl/en/projects/230211/.


Julia Vogt

Juergen Kohlhase

Silvia Kastler

Susanne Morlot

Lan Kluwe

Victor-Felix Mautner

David N Cooper

Hildegard Kehrer-Sawatzki
email: hildegard.kehrer-sawatzki@uni-ulm.de

Jürgen Kohlhase

Monozygotic twins discordant for neurofibromatosis type 1 due to a postzygotic NF1 gene mutation

Keywords: neurofibromatotis type 1, monozygotic twins, mosaicism, postzygotic mutation Neurofibromatosis type 1, monozygotic twins, phenotype discordance, mosaicism, postzygotic mutation

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INTRODUCTION

Neurofibromatosis type 1 (NF1; MIM#162200) is a hereditary cancer predisposition syndrome characterized predominantly by neurocutaneous pathology. The diagnostic hallmarks of the disease are dermal neurofibromas (benign nerve sheath tumours), pigmentation changes such as café-au-lait spots, axillary and inguinal freckling, and Lisch nodules of the iris. Other complications occurring at increased frequency in NF1 include optic gliomas, malignant peripheral nerve sheath tumours, skeletal anomalies and learning difficulties. NF1 is caused by mutations of the NF1 tumour suppressor gene located at 17q11.2. Although NF1 is inherited in simple autosomal dominant fashion with complete penetrance, highly variable clinical expressivity is frequently observed, manifesting as marked inter-and intra-familial variation in relation to the major clinical features of the disease and the co-occurrence of complications [START_REF] Riccardi | Neurofibromatosis: Phenotype, Natural History and Pathogenesis[END_REF][START_REF] Friedman | Neurofibromatosis: Phenotype, Natural History, and Pathogenesis[END_REF].

Monozygotic twins (MZ) with NF1 have been intensively studied as a means to investigate the genetic components of variable expressivity in NF1. A high degree of concordance with respect to clinical symptoms (e.g. café-au-lait spots and neurofibromas) has been observed in many MZ with NF1, suggesting that genetic factors exert a major influence on the inter-and intra-familial clinical variability evident in this disease [START_REF] Samuelsson | Neurofibromatosis in Gothenburg, Sweden. IV. Genetic analyses[END_REF][START_REF] Easton | An analysis of variation in expression of neurofibromatosis (NF) type 1 (NF1): evidence for modifying genes[END_REF][START_REF] Huson | The Neurofibromatoses. A Pathogenetic and Clinical Overview[END_REF][START_REF] Lubinsky | Non-random associations and vascular fields in neurofibromatosis 1: a pathogenetic hypothesis[END_REF][START_REF] Payne | Congenital glaucoma and neurofibromatosis in a monozygotic twin: case report and review of the literature[END_REF][START_REF] Sabbagh | Unravelling the genetic basis of variable clinical expression in neurofibromatosis 1[END_REF][START_REF] Melean | Monozygotic twins with neurofibromatosis type 1, concordant phenotype and synchronous development of MPNST and metastasis[END_REF]. In principle, this concordance is readily explicable, not simply in terms of the presence of identical mutations in the MZ, but also as a consequence of the virtual genetic identity of the MZ genome-wide, and their shared experience of very similar pre-and peri-natal environments. Cases of MZ with NF1 who differ quite markedly with respect to the clinical manifestations of the disease have however also been reported [START_REF] Akesson | Neurofibromatosis in monozygotic twins: a case report[END_REF][START_REF] Bauer | Variable expressivity of neurofibromatosis-1 in identical twins[END_REF][START_REF] Kelly | Discordant puberty in monozygotic twin sisters with neurofibromatosis type 1 (NF1)[END_REF][START_REF] Koul | Dandy-Walker syndrome in association with neurofibromatosis in monozygotic twins[END_REF][START_REF] Detjen | Analysis of mitochondrial DNA in discordant monozygotic twins with neurofibromatosis type 1[END_REF] testifying to the likely complexity of the underlying biology. However, the causative mutation has not been identified in such cases and the nature of the factors responsible for bringing about the discordance of clinical symptoms in these MZ twin pairs has remained enigmatic. In this study, we report on a unique pair of monozygotic twins discordant for NF1 in which mutational analysis allowed us to infer the occurrence of a postzygotic NF1 gene mutation exclusively in the affected twin leading to somatic mosaicism for the NF1 mutation.

SUBJECTS AND METHODS

Clinical evaluation

The monozygotic male twins were born in May 2007, after an uneventful pregnancy, by spontaneous vaginal delivery to a 28-year-old mother (gravida-1, para-0) and her nonconsanguineous 30-year-old partner. The attending gynaecologist reported that the monozygotic twins had a dichorionic placenta and were diamniotic. The postnatal course was uneventful. However, clinical investigation at the age of 11 months indicated 7 café-au-lait spots on the trunk of twin II/1 (4 of them being >5mm in diameter). His brother (II/2; Figure 1) did not possess any café-au-lait spots at this age. Inguinal or axillary freckling, Lisch nodules or neurofibromas were observed in neither twin at the age of 11 months. The brothers did not ). The presence of 7 café-au-lait spots suggested that twin II/1 might be affected by neurofibromatosis type-1 (NF1), and this was subsequently confirmed by sequence analysis of the NF1 gene when he was 18 months old.

At the age of three years, the twins were reinvestigated clinically. In addition to the caféau-lait spots, patient II/1 had by now also acquired inguinal and axillary freckling. Consequently, the minimum diagnostic criteria for NF1 were fulfilled (i.e. more than 6 café-auspots plus additional NF1-associated symptoms such as axillary and inguinal freckling [National Institutes of Health Consensus Development Conference, 1988]. His brother (II/2) manifested 2 café-au-lait spots at this age, but neither freckling nor other NF1-associated features were apparent. The presence of two café-au-lait spots has been noted in 4.1-6.9% of healthy white European children [START_REF] Whitehouse | Diagnostic value of the café-au-lait spot in children[END_REF][START_REF] Mclean | Sunburn" freckles, café-au-lait macules, and other pigmented lesions of schoolchildren: the Vancouver Mole Study[END_REF]reviewed by Shah, 2010] and hence cannot be held to be indicative of this individual's NF1 carrier status. Finally, a delay in speech and articulation development was noted in both twins by the investigating clinician (V.-F. M.) but this was not specifically tested.

No neurofibromas, café-au-lait spots, axillary or inguinal freckling, or Lisch nodules were evident in either parent. The patients' parents provided informed consent for the genetic analysis.

Figure 1

Molecular analysis

Blood samples and buccal swabs were taken from the twins at the age of 11 months and 3 years, respectively. Urine samples were collected from the twins at the age of 3 years. Blood and saliva samples were also obtained from the parents. DNA was isolated from blood and urine samples using the DNeasy Blood and Tissue Kit (Qiagen) and from buccal swabs by means of the NucleoSpin Tissue Kit (Machery-Nagel).

Mutation analysis of the NF1 gene

For mutation identification, the exons included in NF1 transcript variant 2 (GenBank accession no. NM_000267.2) were PCR amplified from blood-derived DNA of patient II/1. After clean-up with MultiScreen HTS PCR plates (Millipore), the PCR products were sequenced from both ends on an ABI 3100 DNA Analyzer (Applied Biosystems).

In order to search specifically for the presence of the identified NF1 mutation in the brother and the parents of patient II/1 as well as in samples of his DNA isolated from buccal swabs and urine, NF1 exon 23-2 was PCR amplified using primers Ex23-2for (5' TTTTGTAGGTTAGAACCATCAGAGAG 3' and Ex23-2rev (5' TCAATGTATTATTCATCCAAACTGA 3') and subsequently sequenced as described above.

SNP analysis

Genotyping of SNP rs7216033 (located 1493-bp centromeric to NF1 cDNA position c.4108C) and rs7220483 (located 1113-bp telomeric to cDNA position c.4108C) was performed by PCR and sequence analysis. Primers used for this analysis were: rs7216033-SNP_1for: 5' GGGAGGGGACATCTAGCAG 3' and SNP_1rev: 5'GGGGAGAGAGGGGACAGATA 3' and rs7220483 SNP_2for: 5' AAAGCTGTTTGAGGCTGCTC 3' and SNP_2rev: 5' CTAGGCCAACCAAGAAGCTG 3'.

SNaPshot analysis

To estimate the proportion of cells with the mutant NF1 allele in the peripheral blood of patient II/1, we performed SNaPshot™ (Applied Biosystems), a primer extension-based method which makes possible the quantification of differences in the peak heights between two alleles. First, PCRs were performed with the primer combination Ex23-2for/Ex23-2rev on genomic DNA derived from the blood of patient II/1. The resulting PCR products were purified with ExoI/FastAP (Fermentas) for 15 min at 37 °C and subsequently heat-inactivated. SNaPshot reactions were then performed with 2pmol primer 5' GTGTGTGCCACTGTTTATAC 3', 1.5 µl of the purified PCR products, and 2.5 µl SNaPshot master mix (Applied Biosystems). Reactions were carried out at 96°C for 10 s, 50°C for 5 s and 60°C for 30 s, and repeated for a total of 25 cycles. Following cycling, samples were incubated with calf intestinal phosphatase at 37°C for 45 min. Samples were then analysed on an ABI 3100 Genetic Analyzer using the GeneScan 6.0 software to determine the relative peak heights of mutant vs normal alleles. The relative proportions of the mutant NF1 allele were then determined by integration of the values into a standard curve.

Multi-allelic marker analysis

The twins' monozygosity was confirmed by genotyping 15 STR loci distributed across the genome using the AmpF/STR Identifier System (Applied Biosystems) as well as 15 microsatellite markers on chromosome 17 (listed in Supp. Fig. S1). PCR primers used to analyse the microsatellite markers are available from the authors upon request.

The parental origin of the chromosome 17 on which the NF1 gene mutation occurred in II/1 was determined by microsatellite marker analysis. Haplotypes were reconstructed by inference from the marker haplotype of a somatic hybrid cell line carrying only the normal chromosome of patient II/1. This somatic cell hybrid line was generated by the polyethylene glycol-mediated fusion of the thymidine kinase-deficient mouse cell line B82 with lymphoblastoid cells from the patient, with subsequent cultivation of hybrids in selection medium containing hypoxanthine, aminopterin and thymidine.

Cloning of PCR products

PCR products obtained with the primers Ex23-2for/Ex23-2rev on genomic DNA derived from blood, urine and buccal swabs of the twin brothers were cloned using the StrataClone PCR cloning kit (Agilent Technologies). To determine the proportion of fragments in each PCR reactions harbouring either the mutant or the wild-type allele at NF1 cDNA position c.4108, DNA was isolated from single plasmid clones and analysed by restriction enzyme digestion using BstNI (New England Biolabs) and sequence analysis on an ABI 3100 Genetic Analyzer.

RESULTS

The analysis of multi-allelic markers confirmed the monozygosity of the twins whilst microsatellite marker analysis of the family members indicated the correctness of assumed paternity (Supp. Fig. S1). Mutation analysis revealed a novel NF1 nonsense mutation in the blood cells of the clinically affected twin II/1 (Fig. 2A). The mutation at cDNA position c.4108C>T (p.Q1370X) is located within exon 23-2 of the NF1 gene according to the historical nomenclature (GenBank accession number: NM_000267.2) and within exon 30 according to NCBI nomenclature. SNaPshot analysis indicated that the mutation is present in 30-40% of cells in the venous blood of the affected twin II/1. Although the mutation was readily identified in blood cells from patient II/1, it was not detected in his buccal epithelial (Fig. 2B) and uroephithelial cells by Sanger sequencing of whole PCR reactions containing multiple PCR products. This notwithstanding, the cloning of single PCR fragments and their subsequent sequence analysis indicated that 4% of the PCR fragments from buccal swabs of twin II/1 carried the mutant T-allele (Table 1). Using this cloning assay, the mutation was not however detected in the uroepithelial cells of II/1. We concluded that the affected twin (II/1) must be somatically mosaic for the NF1 mutation. Importantly, the c.4108C>T mutation was not detected in either blood, buccal swabs (Fig. 2C,D) or urine from the unaffected twin (II/2), either by Sanger sequencing of whole PCR reactions or by cloning of single PCR products as summarized in Table 1. The mutation was also not detected in either parent. In seeking an explanation for the mosaicism of the NF1 gene mutation observed in only one of the monozygotic twins, two possible mechanisms were considered (schematically drawn in Figure 3). First, the c.4108C>T mutation could have occurred postzygotically, after the twinning event, and only in twin II/1, leading to somatic mosaicism for the mutation (Fig. 3A). In this scenario, since the twins were dichorionic, the twinning event must have taken place within 3 days of fertilisation, during the pre-morula stage [reviewed by [START_REF] Scott | The origin of monozygotic twinning[END_REF][START_REF] Nikkels | Pathology of twin placentas with special attention to monochorionic twin placentas[END_REF]]. An alternative scenario that could in principle also account for the observed mosaicism would be if the zygote had already harboured the mutation, and normal cells lacking the mutation would subsequently have arisen by either gene conversion or mitotic recombination (Fig. 3B). This reversion of the mutation to wild-type would have had to have preceded the twinning event. That mosaicism for the mutation was observed only in the affected twin (II/1) and not in his brother (II/2) would then be explicable in terms of the unequal allocation of mutation-harbouring cells into the two embryos during the process of splitting/twinning.

To distinguish between these two mechanisms, we analysed the phase of two intronic SNPs, rs7216033 and rs7220483. These SNPs are located 1493-bp proximal and 1113-bp distal to the site of mutation (at the genomic DNA level), respectively. These are the only polymorphic variants listed in HapMap (http://hapmap.ncbi.nlm.nih.gov/cgiperl/gbrowse/hapmap28_B36/; public data release #28) that occur in the vicinity of the mutation and which could be used to assess local heterozygosity. The phase of the SNP alleles with respect to the mutant c.4108 T-allele was determined by PCR (Supp. Fig. S2). Since heterozygosity for both SNPs was observed in the blood cells of both twins, a gene conversion event encompassing the region tagged by these SNP markers would appear to be highly unlikely. However, we cannot unequivocally exclude the occurrence of a mutation-reversing gene conversion event that encompassed a shorter region, spanning the site of mutation but neither of the flanking SNPs. Mitotic recombination, encompassing the NF1 gene and the extended regions located distal to it, could in principle also have caused a reversion of the mutation (as schematically indicated in Fig. 3B). However, microsatellite marker analysis revealed heterozygosity distal to the NF1 gene in the blood of both twins (Supp. Fig. S1). This observation, in addition to the observed heterozygosity for the flanking SNPs rs7216033 and rs7220483 renders mitotic recombination unlikely as a mechanism leading to reversion of the mutation, since mitotic recombination would be expected to have generated an extended region of homozygosity encompassing several Mb flanking the mutation. Taken together, our findings strongly suggest that the most likely explanation for the presence of the NF1 gene mutation in twin II/1 but not in his brother was that this lesion occurred during the postzygotic cell divisions after the twinning event, leading to somatic mosaicism for the mutation in II/1.

Microsatellite marker and SNP analysis of blood samples derived from patient II/1 and his relatives, as well as DNA isolated from somatic cell hybrids carrying only the normal

DISCUSSION

Monozygotic twins (MZ) are generally considered to represent the epitomy of interindividual identity. However, the unequal allocation of blastomeres to the MZ inner cell mass during the twinning event, lateral asymmetry, differences experienced in the pre-and peri-natal environments, and the consequences of intra-uterine twin-to-twin blood transfusion, all have the potential to give rise to phenotypic differences between MZ [reviewed by [START_REF] Machin | Non-identical monozygotic twins, intermediate twin types, zygosity testing, and the non-random nature of monozygotic twinning: a review[END_REF]. Further, it is increasingly recognized that molecular mechanisms such as skewed Xinactivation, newly acquired epigenetic differences, mosaicism for chromosomal aberrations and postzygotic gene mutations may also result in phenotypic discordance for monogenic disorders in MZ [reviewed by Machin et al., 2006[START_REF] Machin | Non-identical monozygotic twins, intermediate twin types, zygosity testing, and the non-random nature of monozygotic twinning: a review[END_REF][START_REF] Baranzini | Genome, epigenome and RNA sequences of monozygotic twins discordant for multiple sclerosis[END_REF][START_REF] Ollikainen | DNA methylation analysis of multiple tissues from newborn twins reveals both genetic and intrauterine components to variation in the human neonatal epigenome[END_REF][START_REF] Lopriore | Discordance for Schimmelpenning-Feuerstein-Mims syndrome in monochorionic twins supports the concept of a postzygotic mutation[END_REF].

It is clear that the timing of postzygotic gene mutation can have a very considerable impact on the discordance of clinical symptoms between MZ. Recently, an intriguing case of phenotypic discordance in MZ, resulting from a postzygotic gene mutation in the SCN1A gene [MIM#182389] causing Dravet's syndrome, was reported by [START_REF] Vadlamudi | Timing of de novo mutagenesis -a twin study of sodium-channel mutations[END_REF]. In this remarkable case, an unusually precise assessment of the timing of the postzygotic mutation proved possible. A truncating mutation c.664C→T in exon 5 within the SCN1A gene was identified in the clinically affected girl but not in her unaffected monozygotic twin sister. However, neither twin displayed any evidence for mosaicism with respect to cells either harbouring or lacking this mutation. Consequently, the respective mutation must have occurred in the pre-morula embryo stage, and most likely at the two-cell stage post-fertilization prior to the twinning event that gave rise to two distinct embryos differing genetically in terms of the presence or absence of the SCN1A mutation [START_REF] Vadlamudi | Timing of de novo mutagenesis -a twin study of sodium-channel mutations[END_REF]. Postzygotic gene mutations occurring during later stages of embryonic development can also cause phenotypic discordance for single gene disorders in MZ. In these cases, however, mosaicism with normal cells can play a key role as exemplified by the case of the MZ reported here. We identified mosaicism for the mutation c.4108C>T (p.Q1370X), located in exon 23-2 of the NF1 gene, in the affected twin II/1 but not in his unaffected twin brother (Fig. 1 and2). These twins were dichorionic and diamniotic. This type of pregnancy arises when the splitting event, which gives rise to the twin embryos, occurs early (within three days of fertilization) before the inner cell mass and the trophectoderm have formed [reviewed by [START_REF] Scott | The origin of monozygotic twinning[END_REF][START_REF] Nikkels | Pathology of twin placentas with special attention to monochorionic twin placentas[END_REF]. On the basis of SNP and microsatellite marker analyses, we were able to deduce that the mutation c.4108C>T is likely to have occurred after the twinning event (and hence after the third day of embryonic development), leading to mosaicism for the mutation in only one of the twins (Figure 4).

In contrast to the discordant MZ described here, a second example of MZ discordant for NF1 reported by [START_REF] Kaplan | Monozygotic twins discordant for neurofibromatosis 1[END_REF] were found to be monochorionic and diamniotic. A heterozygous truncating NF1 gene mutation [R1968X according to NF1 transcript variant 1 (NM_001042492.2) or R1947X according to NF1 transcript variant 2 (NM_000267)] was identified in all cells from the affected twin, whereas mosaicism involving normal cells and cells harbouring the mutation was detected in the unaffected twin. Owing to the monochorionic nature of these twins, the NF1 mutation is likely to have preceded the twinning event, which supposedly occurred between 4 and 8 days post-fertilization (Figure 4). MZ arise if the twinning event occurs after the formation of the two cell layers, the inner cell mass and the trophectoderm, at the early blastocyst stage of embryogenesis [reviewed by [START_REF] Scott | The origin of monozygotic twinning[END_REF][START_REF] Nikkels | Pathology of twin placentas with special attention to monochorionic twin placentas[END_REF]. When the molecular findings in the MZ reported by [START_REF] Kaplan | Monozygotic twins discordant for neurofibromatosis 1[END_REF] are taken together with those described here, it is clear that the relative timing of the postzygotic mutation and twinning events can exert a major influence on the extent of the subsequent phenotypic discordance in MZ (Figure 4).

It is well known that mosaicism due to postzygotic gene mutation can have a major impact on variable expressivity in many monogenic disorders including NF1 [reviewed by [START_REF] Youssoufian | Mechanisms and consequences of somatic mosaicism in humans[END_REF]Kehrer-Sawatzki and Cooper, 2008;[START_REF] Erickson | Somatic gene mutation and human disease other than cancer: An update[END_REF]. Mosaic NF1 microdeletions, which include the NF1 gene and its flanking regions, are frequently associated with a relatively mild disease phenotype [START_REF] Petek | Mitotic recombination mediated by the JJAZ1 (KIAA0160) gene causing somatic mosaicism and a new type of constitutional NF1 microdeletion in two children of a mosaic female with only few manifestations[END_REF][START_REF] Kehrer-Sawatzki | High frequency of mosaicism among patients with neurofibromatosis type 1 (NF1) with microdeletions caused by somatic recombination of the JJAZ1 gene[END_REF][START_REF] Maertens | Molecular dissection of isolated disease features in mosaic neurofibromatosis type 1[END_REF][START_REF] Steinmann | Type 2 NF1 deletions are highly unusual by virtue of the absence of nonallelic homologous recombination hotspots and an apparent preference for female mitotic recombination[END_REF][START_REF] Roehl | Intrachromosomal mitotic nonallelic homologous recombination is the major molecular mechanism underlying type-2 NF1 deletions[END_REF] whereas patients with germline NF1 microdeletions are often severely affected, with for example a high tumour burden [DeRaedt et al., 2003;Mensink et al., 2004;[START_REF] Venturin | Mental retardation and cardiovascular malformations in NF1 microdeleted patients point to candidate genes in 17q11.2[END_REF][START_REF] Pasmant | NF1 microdeletions in neurofibromatosis type 1: from genotype to phenotype[END_REF][START_REF] Mautner | Clinical characterisation of 29 neurofibromatosis type-1 patients with molecularly ascertained 1.4 Mb type-1 NF1 deletions[END_REF]. Although only a relatively small number of cases of mosaic intragenic NF1 mutations have so far been identified [START_REF] Consoli | Gonosomal mosaicism for a nonsense mutation (R1947X) in the NF1 gene in segmental neurofibromatosis type 1[END_REF][START_REF] Maertens | Molecular dissection of isolated disease features in mosaic neurofibromatosis type 1[END_REF][START_REF] Bottillo | Germline mosaicism in neurofibromatosis type 1 due to a paternally derived multi-exon deletion[END_REF][START_REF] Muram-Zborovski | NF1 exon 22 analysis of individuals with the clinical diagnosis of neurofibromatosis type 1[END_REF], we may nevertheless surmise that postzygotic NF1 mutations leading to mosaicism are associated with a wide spectrum of clinical phenotypes including a mild generalized form of NF1 (with NF1 symptoms that are not restricted to specific regions of the body) or segmental NF1, where disease symptoms such as neurofibromas and pigmentary changes are confined to a few body segments [reviewed by [START_REF] Ruggieri | The clinical and diagnostic implications of mosaicism in the neurofibromatoses[END_REF]Kehrer-Sawatzki and Cooper, 2008;[START_REF] Messiaen | Mosaic type-1 NF1 microdeletions as a cause of both generalized and segmental neurofibromatosis type-1 (NF1)[END_REF]. At the extreme end of the spectrum of phenotypic variability associated with mosaicism for an NF1 gene mutation is the complete absence of NF1-associated features as documented by the unaffected 57-year old twin sister of the phenotypically discordant MZ reported by [START_REF] Kaplan | Monozygotic twins discordant for neurofibromatosis 1[END_REF]. Remarkably, even at that age, the unaffected twin with mosaicism for the NF1 gene mutation did not display any disease features. We may surmise that, in those tissues of this unaffected twin that are normally affected by NF1 disease features, the proportion of cells harbouring the NF1 mutation is likely to be very low, presumably occurring in insufficient number to give rise to clinically overt NF1.

In contrast to the middle-aged MZ reported by [START_REF] Kaplan | Monozygotic twins discordant for neurofibromatosis 1[END_REF], the twins described here were only three years old. Although the c.4108C>T mutation was not identified in blood, buccal and bladder epithelial cells of the unaffected twin, we cannot unequivocally exclude the possibility that the mutation could be present in only a small subset of cells in his body and that he may also come to develop clinical symptoms of NF1 later in life. If this indeed turns out to be the case, and both MZ reported here are shown to exhibit mosaicism, then we would be able to infer that the NF1 mutation had occurred before the twinning event (within the first 3 days post-fertilization), at a stage when the embryo comprises only 2-16 cells. The marked difference in the number of cells harbouring the mutation between the MZ would then in principle be explicable in terms of the different allocation of normal vs. mutated cells to the two pre-morulae and/or subsequent unequal proliferation of normal vs. mutated cells. Since placental anastomoses that can give rise to twin-twin blood transfusion are extremely rare in dichorionic placentas [START_REF] Ramos-Arroyo | Twin study: relationship between birth weight, zygosity, placentation, and pathologic placental changes[END_REF][START_REF] French | Twins, placentas, and genetics: acardiac twinning in a dichorionic, diamniotic, monozygotic twin gestation[END_REF][START_REF] Foschini | Vascular anastomoses in dichorionic diamniotic-fused placentas. 1[END_REF], blood exchange between the twins is most unlikely to have influenced the proportions of normal vs. mutated cells in the twins described here. Although gene conversion and mitotic recombination have both been shown to be capable of causing mutation reversion [and hence somatic mosaicism in other monogenic disorders; [START_REF] Choate | Mitotic recombination in patients with ichthyosis causes reversion of dominant mutations in KRT10[END_REF], the heterozygosity observed for two SNPs flanking the c.4108C>T mutation identified in the affected twin (II/1) renders it unlikely that either gene conversion or mitotic recombination gave rise to the mosaicism via mutation reversion in this particular case (Fig. 3). Therefore, the most likely scenario is that the c.4108C>T mutation occurred during postzygotic cell divisions, leading to the presence of somatic mosaicism with normal cells lacking the mutation. Irrespective of whether or not twin II/2 harbours the c.4108C>T mutation in a small subset of his body cells, mosaicism for this postzygotic NF1 gene mutation appears to be responsible for the observed phenotypic discordance of NF1 clinical symptoms in the twins described here. Hence, our study serves to emphasize the point that genetic factors can exert a major influence on the clinical inter-and intra-familial variability evident in NF1. S1: Microsatellite marker and SNP analysis performed in order to investigate homozygosity vs. heterozygosity telomeric to the NF1 gene and to determine the parental origin of the chromosome on which the c.4108C>T mutation occurred in patient II/1. The hybrid cell line carrying the normal chromosome of patient II/1 was generated by fusion of the thymidine kinase-deficient mouse cell line B82 with lymphoblastoid cells taken from the patient. Markers highlighted in bold type are located within the NF1 gene. Haplotypes were reconstructed by inference from the phase of markers observed in the hybrid cell line derived from patient II/1 (employing the maximum parsimony principle). a: The genomic position indicates the position of the primers used to PCR amplify the respective microsatellite markers. In the case of the SNPs rs7216033 and rs7220483, the exact positions of the SNPs are indicated. Received <date>; accepted revised manuscript <date>.

FIGURE LEGENDS

Figure 1: Pedigree of the family investigated. NF1 was diagnosed in patient II/1 on the basis that he exhibited 7 café-au-lait spots as well as axillary and inguinal freckling. Although his monozygotic twin brother did not fulfil the diagnostic criteria for NF1, he nevertheless possessed 2 café-au-lait spots. The observed heterozygosity of SNPs rs7216033 and rs7220483 (that flank c.4108 in the centromeric and telomeric directions, respectively) is compatible with this explanation. (B) Alternatively, the NF1 gene mutation (c.4108C>T) may already have been present in the zygote prior to the twinning event. In principle, either gene conversion or mitotic recombination could then have been responsible for a reversion of the mutant allele (Tmut) to wild-type (Crev). To investigate whether a large gene conversion event could have been responsible for mutation reversion, SNPs rs7216033 and rs7220483 flanking the NF1 cDNA position c.4108 were analysed. However, heterozygosity for both SNPs was observed in both twins. If mitotic recombination were to have given rise to the mutation reversion, then homozygosity for SNP rs7220483 and for other microsatellite markers located distal to the NF1 gene mutation must be assumed, and this was not observed.

Figure 4: Inferred relative timing of the postzygotic NF1 gene mutations in relation to the monozygotic twinning event in the analysis reported here and that of [START_REF] Kaplan | Monozygotic twins discordant for neurofibromatosis 1[END_REF].

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Human Mutation

  terms of the following features: height (both 74 cm [P25]), weight (twin II/1: 9.3kg [P10]; twin II/2: 8.6kg [P10]) and head circumference (twin II/1: 46 cm [P25-50]; twin II/2: 46.7 cm [P50]

  II/1, indicated that the mutation must have occurred on the chromosome 17 inherited from the twin's mother, I/2 (Supp. Fig.S1).

Figure 2 II

 2 Figure 2

  Figure 4

  Relative locations of SNPs rs7216033 and rs7220483, respectively, 1493 bp centromeric and 1113 bp telomeric to position c.4108 within exon 23-2 of the NF1 gene. The phase of the SNP alleles (in relation to the mutant c.4108 T allele) was determined by PCR using blood-derived DNA from patient II/1 as a template followed by sequence analysis of the PCR products. The primers used to amplify PCR products 1 and 2 are indicated by black arrows.

Figure 2 :

 2 Figure2: DNA sequence traces of the NF1 gene mutation, c.4108C>T (p.Q1370X), in the blood of the affected twin II/1 (A). The mutation was not however detected in his buccal mucosa (B) as determined by Sanger sequencing of uncloned PCR products or in blood (C) or buccal swabs (D) from his unaffected twin brother.

Figure 3 :

 3 Figure3: Potential mechanisms that could have given rise to mosaicism for the NF1 gene mutation c.4108C>T in twin II/1. (A) The mutation c.4108C>T (Tmut) may have occurred postzygotically, subsequent to the twinning event, and exclusively in the affected twin (II/1). The observed heterozygosity of SNPs rs7216033 and rs7220483 (that flank c.4108 in the centromeric and telomeric directions, respectively) is compatible with this explanation. (B) Alternatively, the NF1 gene mutation (c.4108C>T) may already have been present in the zygote prior to the twinning event. In principle, either gene conversion or mitotic recombination could then have been responsible for a reversion of the mutant allele (Tmut) to wild-type (Crev). To investigate whether a large gene conversion event could have been responsible for mutation reversion, SNPs rs7216033 and rs7220483 flanking the NF1 cDNA position c.4108 were analysed. However, heterozygosity for both SNPs was observed in both twins. If mitotic recombination were to have given rise to the mutation reversion, then homozygosity for SNP rs7220483 and for other microsatellite markers located distal to the NF1 gene mutation must be assumed, and this was not observed.

Table 1 :

 1 Relative number of wild-type and mutant alleles carrying the NF1 mutation (c.4108C>T a ) as determined by cloning PCR products amplified from different tissues of the clinically affected twin II/1 and his unaffected twin brother II/2 Nucleotide numbering reflects cDNA numbering with +1 corresponding to the A of the ATG translational initiation codon in the reference sequence.

			II/1			II/2
		blood	buccal smear	urine	blood	buccal smear	urine
	Number of wild-type	32	48	47	50	50	49
	PCR products
	Number of PCR products	13	2	0	0	0	0
	with the mutation
	Proportion of PCR	29	4	0	0	0	0
	products with the

John Wiley & Sons, Inc.Human Mutation

<First Author et al.> Shah KN. 2010. The diagnostic and clinical significance of café-au-lait macules. Pediatr Clin North Am 57:1131-1153.

ACKNOWLEDGEMENTS

We are most grateful to Ludwine Messiaen for her insightful suggestions in relation to the manuscript, and to Helene Spöri and Sigrid Wieland-Lange for their technical support. This work was supported by the Deutsche Krebshilfe (grant #108793, H.K.-S.; V.-F.M.). J. V. holds a fellowship from the International Graduate School in Molecular Medicine, Ulm.

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