C Maurel

T Cardinal

P Vinatier

L Petit

K Richardson

N Carlie

F Guillen

M Lahaye

M Couzi

F Adamietz

V Rodriguez

F Lagugné-Labarthet

V Nazabal

A Royon

L Canioni

PREPARATION AND CHARACTERIZATION OF GERMANIUM OXYSULFIDE GLASSY FILMS FOR OPTICS

Keywords: Glasses, Film, Photo-sensitivity, Oxysulfide, Raman spectroscopy

Homogeneous amorphous films in the GeS 2 -GeO 2 system have been deposited by a RF sputtering technique. Optical characterizations has shown that the cut-off wavelength and the linear indices increase with an increase in the S/O ratio. Raman spectroscopy indicates the presence of new modes that can be assigned to intermediate germanium oxysulfide structural units. Photo-sensitivity of the oxysulfide films has been demonstrated for irradiation near the band-gap. Diffraction gratings inscribed using 488 nm exposure displayed a limited diffraction efficiency (≤3%) that weakens with a corresponding decrease in the glass S/O ratio.

Introduction

The nonlinear optical properties of oxide and sulfide glasses have been widely studied for use in the near infrared (NIR) optical domain. Oxide glasses exhibit lower optical breakdown threshold as compared to sulfides when used in the near IR, but their nonlinear properties such as the Kerr effect, are one order of magnitude lower than that of sulfide glasses [1]. Over the last fifteen years, different results have been obtained which have examined the structuring of oxide and chalcogenide glasses materials. Sulfide glasses exhibit higher polarisability and hyperpolarisability resulting in large photosensitivity with exposure to irradiation in the visible or the NIR. Often a trade-off has to be achieved when considering the possible use of sulfides in optical devices between the photo-sensitivity, of interest for structuring based on of the linear index of the materials, and the low damage threshold at high optical power density. Oxysulfide materials which combine moderate photosensitivity and enhanced damage threshold exhibit promise in meeting such device requirements. Prior efforts in these glasses has been mainly focused on using lithium ions as dopants for conductive materials in order to improve the chemical stability of the materials without dramatically affecting the performance as electrolyte [2] [3]. So far, very little optical characterization have been performed in vitreous oxysulfides as compared to inorganic crystalline materials such as RE 2 O 2 S (RE : rare earth) for instance [4]. In glassy state, studies have been mainly conducted on Ga 2 S 3 -La 2 S 3 -La 2 O 3 system and glasses containing germanium sulfide [5]. In term of linear and nonlinear optical indices, a compromise between the pure oxide and sulfide compositions has been found [1] [6]. The increase of the emission cross section of rare earth ions has been also recently demonstrated in TeO 2 based oxysulfide [7].

Several studies were devoted to germanium based glasses for optical applications. Photoinduced effects have been observed in GeS 2 , leading, in presence of air or oxygen, to diffusion of oxygen within the glass associated with interaction with the sulfide glassy network and to strain formation [8] [9]. Recently, the fabrication of bulk oxysulfide germanium glasses has been reported [10]. In the present work we report the synthesis of germanium oxysulfide thin film compositions in the GeS 2 -GeO 2 glass system. The optical characteristics of the films for the different compositions are discussed together with their respective structural properties studied using Raman spectroscopy. Photo-induced phenomena, dependent on the sulfur to oxygen ratio, are also demonstrated for the first time.

Experimental

Targets of 5 cm diameter and of average 6 mm thickness were prepared using an appropriate mixing of GeS 2 and GeO 2 powder in order to obtain the desire S/O ratio. GeO 2 amorphous powder (Aldrich, 99.99%) with grain size centered around 10 μm were chosen for this purpose. GeS 2 was obtained by doing two thermal treatments of the same GeO 2 amorphous powder for 15 hours above the glass transition temperature at 550°C under flowing H 2 S (Air Liquide Alphagaz, 99.5%) and milling the sulfinated powder between each treatment. The results of the O for S substitution were checked by weight gain, X-ray microprobe as well as by X-ray diffraction as the resulting GeS 2 materials were partially crystallized. The powder was pressed in a pellet press at a load of 5 Ton at room temperature, then the mold was heated at 120 °C prior removal of the target.

Radio-frequency (RF) magnetron sputtering of thin films was carried out in a chamber under Argon atmosphere. Pressure was maintained constant at 10 -2 mbar throughout the whole deposition experiment. The substrate was located about 6 cm away from the target, and a 15 W plasma was created. This plasma was switched on 20 minutes prior to the deposition of the thin films to ensure removal of target surface inhomogeneity and to warrant equilibrium of the constitutive elements considering their specific pulverization rate. Under these conditions, the deposition rate was found to vary between 3.6 Å.s -1 for the pure germanium sulfide target to 0.8 Å.s -1 for the pure germanium oxide target. The films were deposited on 1 mm thick silica substrate (fused quartz, Thuet B, spectrosil) in order to perform transmission spectra. Prior to deposition, the substrates were cleaned using ultrasonic bath and pure ethanol. Measurements with a mechanical profilometer have been used to measure the film thickness after creation of a step by masking part of the substrate during the deposition.

Auger depth profiles were mesured with a VG Microlab 310 F system. A primary electron source of 10 kV, 5 nA current was used on a 5 μm square surface. Dynamic etching of the thin films was performed with a 4 kV Ar + ion beam onto a 1 mm square surface with a mesured 0.5 μA current absorbed by the sample. This allowed sample to be analyzed with an accuracy of 5 atomic % for each element's profile. The position of the analyzed peaks were as follow: Ge LM2 at 1144 eV, S LM1 at 152 eV, O KL1 at 506 eV and Al KL1 at 1393 eV.

Optical transmission spectra were collected using a Varian Cary 5E spectrophotometer. Spontaneous Raman scattering measurements were conducted using a Raman microscope (Labram, Jobin Yvon Horiba) set-up. The 514 nm lines of a mixed Krypton Argon gas laser were used as the excitation source. The incoming vertically polarized (V) laser light was focused at the front surface of the sample through a 100X microscope objective, and the polarized (V) Raman scattered light was collected using a backscattering geometry. The CCD used for collection was from ANDOR, model FI UV. The typical instrumental spectral resolution was about 6 cm -1 . The Rayleigh line was suppressed with a holographic notch filter. For Raman measurement, the laser irradiance was kept below 1 kW/cm 2 in order to avoid any photo-induced effects. For irradiance of 100 kW/cm 2 , it was determined that such photo-induced effect could be distinguished on sulfide and oxysulfide films after 15 and 30 seconds of exposure. These times were identified as the threshold for modification and were used in subsequent exposure experiment.

Thickness and linear refractive indices at 1064 nm and 532 nm were obtained using an extended Brewster angle reflection method over the ± [10°; 80°] wide θ range. Best fits to the experimental patterns were conducted using a unique optical layer model, for both reflected R pp signals collected at 1064 nm and 532 nm; these measurements include an original multireflection layers procedure developed previously by our group [11]. This original procedure allows one to minimize errors on thickness, indices and also includes determination of the optical dispersion. The accuracy of the obtained indices of refraction from this ellipsometry measurement was better than 0.01.

The 488 nm wavelength of an Argon Laser has been used for recording the volume gratings on the films. The p-polarized Argon beam was first split using a 50/50 cube beamsplitter and recombined at the sample in order to obtain interferences fringes (figure 1). The angle between the two beams was about 2θ=30° leading to a periodicity of about 1 μm step according to Bragg's law. The diffraction efficiency of the photo-induced volume gratings was precisely measured by recording the intensity of the first diffracted order from a HeNe Laser at 632.8 nm perpendicular to the surface of the film which was used as the probe beam.

The total irradiance of the actinic 488 nm light was set to about 300 mW.cm -2 . All sulfide and oxysulfide films were exposed during 30 minutes, at which point no clear variation in intensity of the first order of diffraction of the probe beam could be seen anymore.

Results

Auger spectroscopy was used to study the chemical composition of the films as a function of film depth. These measurements were performed on films nominally 1 μm thick which had been deposited on aluminum foil substrates. This spectroscopy, coupled with ion etching, has allowed us to evaluate the film composition throughout its thickness to examine evidence of compositional variation during film deposition. For oxysulfide thin films, it was determined that the S/O ratio was found to be constant through the thickness of the sample. The result presented on figure 2 for GeOS thin film clearly indicates a homogeneous composition of the film throughout its depth. The etching rate of the film samples were found to vary slightly depending of the film's Oxygen / Sulfur ratio. Etch rates ranged from 1.5 Å.s -1 for pure GeO 2 film to 2.0 Å.s -1 for pure GeS 2 . The compositions were in agreement with the compositions of the targets. These composition measurements were cross-checked and reconfirmed by X-Ray microprobe.

Transmission spectra were collected from 1000 nm to 200 nm. The oscillations observed (not shown here) in the range between 1000 nm and the strong absorption in the visible UV frontier corresponds to the interference due to the index contrast between the film and the silica substrate. Absorption spectra were extracted in the UV range assuming that for high absorption coefficient of the film deposited interferences vanish due to disappearance of contrast. The absorption spectra of the films have been corrected or Fresnel reflections. They are reported in figure 3, plotted in logarithm scale of the absorption coefficient versus wavelength. In the UV region a progressive decrease of the wavelength position of the band edge as the oxygen content increase can be seen from about 430 nm for GeS 2 to about 270 nm for GeO 2 .

Ellipsometry measurements have been conducted on GeS 2 , GeOS and GeO 2 thin films deposited on silica substrates. Figure 4 exhibits the results of the GeOS and GeS 2 films. The ellipsometric treatments have shown that all films can be described as two-layers systems, including a thick bottom bulk layer corresponding to the expected composition and a second thin layer at the top of the film, but with lower index of refraction. For the germanium sulfide sample, the top layer has been evaluated as nominally 20 nm thick. For germanium oxysulfide and germanium oxide samples, thicker top layers of ~100 nm have been estimated. The obtained optical parameters, i.e. linear index values n 0 and thicknesses d, are gathered in table 1. The full thicknesses including both layers of the film are in agreement with the measurements done by the mechanical profilometer. For GeS 2 and GeO 2 films, the linear index values of bottom layers (the thickest one) are in full agreement with those expected for the corresponding bulk materials [12] [13]. In addition, both linear index of the thin top and bottom layers decrease with the oxygen concentration rise until they reach some minima for GeO 2 film. The value of the linear susceptibility χ (1) (n 0 2 = 1 + χ (1) ) of the oxysulfide composition corresponds to the average of the sulfide and oxide pure composition values taking into account the accuracy of the measurement (±0.01).

For comparison purpose, all Raman spectra of the five studied composition (GeO 2 , GeO 1 . 4 S 0.6 , GeOS, GeO 0.6 S 1.4 , GeS 2 ) were normalized to the most intense band because of the different Raman scattering cross-sections between sulfide and oxide samples. Therefore, sulfur-rich glasses exhibited a Raman signal at least one order of magnitude larger than oxygen-rich compositions due to the difference of polarisability between oxide and sulfide compounds. They are presented in Figure 5. In the spectrum range between 200 cm -1 and 325 cm -1 , for compositions from GeS 2 to GeOS, two bands located at 235 cm -1 and at 255 cm -1 can be distinguished. The later band increases in relative intensity with the progressive increase of the oxygen concentration. Similar bands at 250-260 cm -1 have been reported by several authors as the ethane-like S 3 Ge-GeS 3 units in which Ge atoms occupy corner site in GeS 4 tetrahedra in rich germanium samples [14] [15]. Recently, it had also been proposed that such vibration could appear also for three-fold coordinated sulfur atoms [16]. For larger oxygen concentration than that of the GeOS composition, no clear vibrational mode can be distinguished, but only a broad signal that could correspond to vibrational contributions involving sulfur and oxygen atoms. For the GeO 2 film composition, a band is observed at 345 cm -1 .

In the spectral range between 315 cm -1 and 650 cm -1 , the maximum of the broad Raman signal is progressively shifted from 342 cm -1 to 423 cm -1 as the oxygen concentration increases. These Raman spectra were simulated using Gaussian function and so, the spectrum for GeS 2 could be simulated using 5 main vibrations located at 345 cm -1 , 375 cm -1 , 410 cm -1 , 430 cm -1 and 480 cm -1 (figure 6a). The main band around 342 cm -1 has been associated to A 1 symmetric stretching vibrations of S atoms in GeS 4 units, and the vibration around 375 cm -1 , usually called the companion A 1 C band, is attributed to edge sharing tetrahedral sites [17]. For the weakest band at 410 cm -1 , the situation is not clear. According to Jackson et al., a band located around 400 cm -1 could come from edge sharing GeS 4 units. The bands around 430 cm - 1 and 475 cm -1 have been attributed respectively to short S-S chains between GeS 4 units and S-S bond stretching vibrations in S 8 like rings [14][15][18] [19].

The fitted Raman spectrum of GeO 2 film is reported in figure 6b. Five Gaussian bands at 340 cm -1 , 425 cm -1 , 480 cm -1 , 550 cm -1 and 590 cm -1 are necessary to fit this spectrum. In the literature a band at 347 cm -1 has been assigned to germanium motions in deformation modes of the glass network. The main band around 420 cm -1 has been attributed to symmetric stretching mode of Ge-O-Ge bridging oxygen atoms between GeO 4 tetrahedral sites. The vibration at 520 cm -1 has been assigned to the breathing motion of oxygen atoms in 3membered GeO 4 rings. Vibrations between 500 cm -1 to 620 cm -1 were associated to bending modes of Ge-O-Ge bridges. [20].

In a first approach, summations of the bands obtained from the simulation of pure GeO 2 and GeS 2 were used for to fit the spectral profiles of oxysulfide glasses. For the three compositions studied, the addition of a new band between 360 cm -1 and 400 cm -1 is necessary to correctly simulate these spectra. This band becomes the prominent one for the composition GeO 1.4 S 0.6 .

Photo-induced modifications of the films were obtained for sulfide and oxysulfide compositions. Figure 7 illustrates the Raman spectra of GeOS composition after 15 and 30 seconds of exposure with about 100 kW/cm 2 irradiance. After irradiation, between 360 cm -1 and 420 cm -1 a very similar shoulder to those already observed can be distinguished in the same spectral range with all sulfide and oxysulfide compositions. Exposure with a larger laser power density leads to an increase of the intensity of this band but also to damage of the surface of the glass, visible with an optical microscope.

Interference patterns have been written using Argon laser emitting at 488 nm with a low irradiance (300 mW/cm 2 ). The first order of diffraction intensity at 632.8 nm was measured following 30 minutes of exposure for sulfide and oxysulfide films (table 2). The diffraction intensities increase when the sulfur to oxygen ratio increases. First order diffraction efficiencies decrease from 3% for GeS 2 to ≤0.3% for GeO 1.4 S 0.6. It has been checked that the gratings remain unchanged after one week.

Discussion

Homogeneous oxysulfide thin films were obtained, with adjustable compositions correlated to the composition of the target used for RF sputtering. The absorption band edge of the films prepared in the system Ge-O-S are directly dependent on their sulfur content and systematically red shift with an increase in the S/O ratio (figure 3). As the sulfur concentration increases, the wavelength position of the band edge increases as suggested by ellipsometry measurements which exhibit a concurrent increase of the linear index with an increase in sulfur content. This effect is directly related to the larger polarisability of the sulfur ions as compared to the oxygen ions, which is followed by a lower band gap of the material. The GeOS composition exhibits a linear susceptibility which is the average between GeO 2 and GeS 2 film values suggesting that the evolution seems to be linearly dependant on the S/O ratio. This feature indicates that in terms of the refractive index evolution, sulfur replaces for the oxygen in the glass network without significant modification of the glass structure. The near-surface layers of the oxysulfide and oxide films exhibit a lower index of refraction. According to Auger spectroscopy, surface oxidation does not appear to be primarily responsible as the individual glass constituent distribution within the composition was found to be homogeneous in the depth of the sample. Nevertheless, we can not exclude a surface contamination by oxygen of about 10-20 nm which is below the detection limit in the Auger profile. A proposed hypothesis for this observation may involve some form of surface hydrolysis in the film that leads to a decrease of the density of the film without a strong diffusion of oxygen. Further investigations examining post deposition annealing may provide further insight into these observations, as no annealing was performed on the fresh films examinated in this study.

The Raman spectroscopy indicates a progressive evolution of the glass structure from GeS 2 up to GeO 2 as the S/O ratio decreases. The vibrational features of GeO 2 and GeS 2 have been the subject of multiple articles [14][20]. The main bands located at 430 cm -1 and at 342 cm -1 correspond respectively to GeO 4 and GeS 4 vibrations. As the oxygen concentration increases, a shoulder can be distinguished at the high wavenumber side of the GeS 2 main vibration. For larger oxygen concentrations corresponding to the glass composition GeO 1.4 O 0.6 , this shoulder gives rise to a new band in between 360 cm -1 and 430 cm -1 , confirming the signature of new vibrational species different from GeO 4 or GeS 4 tetrahedral sites. Such a vibration could be related to the formation of entities such as GeO 3 S, GeO 2 S 2 or GeOS 3 tetrahedral units consistent with the suggestion of Kim et al's analysis of bulk oxysulfide glasses that germanium atoms are coordinated with both sulfur and oxygen [10]. Concerning the vibrations located at 235 cm -1 and at 255 cm -1 the interpretation is less clear. Such vibrations, usually assigned to the ethane-like S 3 Ge-GeS 3 entities, tend to appear for sulfur-deficient samples. In our case, we can not exclude the possibility that such phenomenon occur during film deposition. The chemical analysis using X Ray microprobe and Auger spectroscopy for sulfur and in particular for oxygen did not allow accuracy better than 5%. For the compositions with large oxygen concentration GeO 1.4 S 0.6 and GeO 2 , these bands cannot be observed, suggesting the disappearance of S 3 Ge-GeS 3 bridges. No additional band could be observed that could be related to the formation of similar homopolar bridges in oxysulfide environment.

Irradiation of the film at 514 nm induced, for large irradiance, structural changes on sulfurrich germanium oxysulfide and GeS 2 films (fig 7). The shoulder appearing in the Raman spectra between 360 cm -1 and 420 cm -1 has to be related to the new band observed for oxysulfide compositions. This band is attributed to the mixed sulfur and oxygen tetrahedral environment of the germanium ions. Such an effect could provide evidence of oxygen diffusion most probably from the top of the film or phase separation of the glass structure in the case of oxysulfide films. Considering the difference in the Raman cross-section of the sulfide and oxysulfide vibrations, these datas suggest significant species vibrating around 385 cm -1 have been formed upon illumination. Tanaka et al. suggested for GeS 2 that following light exposure in air Ge-Ge bridges break leading to formation of Ge-O-Ge bonds and photobleaching [21]. However in similar material, such as GeSe 2 , light illumination could be coupled, as Spence et al. mentioned [9], to strain appearance in the network leading to photodarkening. In the case of oxysulfide and sulfide films, the feature around 250 cm -1 in the Raman spectra could indicate that the Ge-Ge bridges are present for GeOS, GeO 0.4 S 1.6 and GeS 2 , however in this study no specific evolution could be observed (figure 5).

Interference patterns created upon exposure of the films at lower irradiance at 488 nm near the band gap has allowed recording Bragg gratings. The first order diffraction efficiency at 632.8 nm was found to increase with an increase in the sulfur to oxygen ratio, in agreement with a lower band gap for sulfur-rich film materials content which exhibit and an increase in absorption coefficient at 488 nm (figure 3). The diffraction efficiency measurement clearly demonstrates the presence of a volume grating. Spatially resolved Raman measurements using micro Raman apparatus could not clearly denote a modification in the Raman spectral features even though patterning can be seen using optical microscope and remains stable after several weeks. It is believed that grating inscription with shorter wavelengths and/or higher irradiances should be used to realize gratings with higher diffraction efficiencies.

Conclusion

Oxysulfide thin films have been obtained in the GeS 2 -GeO 2 glass system using magnetron RF ))

Wavelength (nm)

  sputtering of mixed oxide and sulfide targets. Optical and vibrational spectroscopic measurements indicate a progressive evolution of the properties from the oxide to the sulfide as the sulfur concentration increases. A new band located around 385 cm -1 attributed to a mixed anion (sulfur and oxygen) germanium tetrahedral sites has been observed by Raman spectroscopy. First photo-induced gratings have been observed in these new optical materials upon exposure with UV irradiation.

Figure captions Fig 1 3 Absorption spectra of oxysulfide thin films Fig 4 Fig 5 6 Fitting

 13456 Figure captions

Fig 7 Raman

 7 Fig 7

  Fig 1

Fig 3 :

 3 Fig 3 :

  Fig 4

Table Captions Table 1

 Captions1 Variation in refractive indices as a function of thin film compositions and thickness, for near and sub-surfaces regions of the glass films, obtained from ellipsometry measurements

		Sulfur percent			Thickness (d) /
	Composition
		(%)			Refractive index (n 0 )
				Film			Top layer
			d 1 (nm)	n 0	n 0	d 2 (nm)	n 0	n 0
	Table 2		± 5 %	± 0.01	± 0.01	± 5 %	± 0.01	± 0.01
	First order diffraction efficiency of sulfide and oxusulfide thin films compositions measured (532 nm) (1064 nm) (532 nm) (1064 nm)
	at 632.8 nm.
	GeO 2	0	1093	1.77	1.69	98	1.68	1.65
	GeOS	50	2670	1.89	1.85	119	1.75	1.71
	GeS 2	100	8330	2.11	2.06	19	1.80	1.75

Table 1

 1

Acknowledgments

This work was carried out with the support of a number of research, equipment, and educational French and US grants, including the Agence Nationale de la recherche ANR (grant ANR-05-BLAN-0212-01), the CNRS PICS grant 3179, a FACE grant from the French Embassy in the US, and funding from the National Science Foundation (international REU grant EEC-0244109) and DMR-031208.


Jörn Bennewitz
email: jbennewitz@tierzucht.uni-kiel.de

Norbert Reinsch

Cécile Grohs

Hubert H Levéziel

Alain Malafosse

J Thomsen

Ningying Xu

Christian Looft

C Kuhn

Gudrun A Brockmann

Hauke Thomsen

Christa Kühn

Manfred Schwerin

Christina Weimann

Stefan Hiendleder

Georg Erhardt

Ivica Medjugorac

Ingolf Russ

Martin Förster

Bertram Brenig

Fritz Reinhardt

Reinhard Reents H , Gottfried

Jürgen Blümel

Ernst Kalm

Combined analysis of data from two granddaughter designs: a

INTRODUCTION

With the aid of genetic markers, it was possible in several studies to detect quantitative trait loci (QTL) involved in the variation of traits of economic interest. In dairy cattle, most QTL experiments used a granddaughter design [START_REF] Churchill | Empirical threshold values for quantitative trait mapping[END_REF][START_REF] Georges | Mapping quantitative trait loci controlling milk production in dairy cattle by exploiting progeny testing[END_REF][START_REF] Spelman | Quantitative trait locus analysis for five milk production traits on chromosome six in the Dutch Holstein Friesian population[END_REF][START_REF] Thomsen | A male bovine linkage map for the ADR granddaughter design[END_REF][START_REF] Zhang | Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree[END_REF], where the number of sires genotyped in each family was typically below 150. The power to detect a QTL present in a granddaughter design is largely influenced by the number of families included in the experiment and by the size of the individual families [START_REF] Weller | Power of daughter and granddaughter designs for determining linkage between marker loci and quantitative trait loci in dairy cattle[END_REF]. Consequently, increasing family size in a granddaughter design is desirable but in many cases has its limitations in the availability of progeny tested sires and in the costs of determining genotypes.

Although the substitution effect estimates of the detected QTL tend to be overestimated [START_REF] Göring | Large upward bias in estimation of locus-specific effects from genomwide scans[END_REF], the most detected QTL are of sufficient magnitude to consider them in marker assisted selection (MAS), especially in preselection of young bulls entering progeny testing [START_REF] Kashi | Marker assisted selection of candidate bulls for progeny testing programmes[END_REF][START_REF] Mackinnon | Marker-assisted preselection of young dairy bulls prior to progeny testing[END_REF]. However, Lander and Kruglyak [START_REF] Lander | Genetic dissection of complex traits: guidelines for interpreting and reporting linkage results[END_REF] postulated that a detected marker-QTL linkage must be replicated to be credible. Similarly Spelman and Bovenhuis [START_REF] Spelman | Moving from QTL experimental results to the utilisation of QTL in breeding programmes[END_REF] suggested that a QTL confirmation study prior to starting MAS should be conducted in order to prevent a selection for a non-existing QTL.

Therefore it could be useful to combine data from different experiments that use the same experimental design and the same or closely related breeds. The potential benefits of the extraction of additional information could be substantial: a higher experimental power to detect QTL, especially if they have a small phenotypic effect, a confirmation of QTL previously detected in only one experiment, and more precise conclusions about the QTL position. Walling et al. [START_REF] Walling | Combined analyses of data from quantitative trait loci mapping studies: chromosome 4 effects on porcine growth and fatness[END_REF] mapped QTL in seven different F2 crosses with altogether almost 3000 pigs. The QTL analysis was conducted for three different traits on chromosome 4 either separately for each individual cross, or jointly for the combined data set. Their results emphazised the potential benefit of a joint analysis of data from independent mapping experiments although the families used were nested within the population. Compared to other species, dairy cattle are particularly suitable for a joint analysis of data from QTL experiments, since many Holstein sires, but also Simmental and Brown Swiss sires, are used across countries and therefore may be included in several different granddaughter designs. In a combined analysis, not only the total size of the granddaughter design is expanded, but also the individual family size may be increased, and, therefore, the experimental power is significantly higher [START_REF] Weller | Power of daughter and granddaughter designs for determining linkage between marker loci and quantitative trait loci in dairy cattle[END_REF]. Furthermore, QTL can be confirmed when specific families are included in different designs, because the probability that the same families show a type one error in several QTL experiments is low when the level of significance is sufficiently stringent. Prior to a joint analysis, however, several problems have to be solved: the phenotypes of individuals in the different designs might not be comparable due to the different environments of the individuals and/or different calculation of phenotypic parameters like estimated breeding values (e.g. different models based on data from different testing schemes). Different markers might have been genotyped in different designs and/or the marker genotypes could have been recorded by different techniques.

In this study we conducted a joint analysis of five Holstein families that are included in two different granddaughter designs described by Thomsen et al. [START_REF] Thomsen | A male bovine linkage map for the ADR granddaughter design[END_REF] and Boichard et al. [START_REF] Boichard | Detection of genes influencing economic traits in three French dairy cattle breeds[END_REF]. Nine chromosomes and six traits were investigated. The first aim of this study was QTL confirmation, where the data were analysed separately and a confirmed QTL should show a significant effect in both data sets. A second aim was a joint analysis of the two data sets in order to increase family size and, hence, statistical power to detect further QTL.

MATERIALS AND METHODS

Pedigree

Five paternal half-sib Holstein families were selected that are included in two different granddaughter designs. The first design was part of the common QTL mapping project of German AI and breeding organisations, several German animal breeding institutes and animal computing centres initiated by the German cattle breeders federation (ADR) [START_REF] Thomsen | A male bovine linkage map for the ADR granddaughter design[END_REF]. Final results of this project will be published elsewhere. The second design was part of the QTL mapping project of several French AI breeding organisations and Inra with results published by Boichard et al. [START_REF] Boichard | Detection of genes influencing economic traits in three French dairy cattle breeds[END_REF]. The sires were progeny-tested either in Germany (subsequently denoted as the ADR-design) or in France (referred ADR-design: sons that were progeny-tested in Germany; Inra-design: sons that were progeny-tested in France; JOINT-design: ADR-design and Inra-design merged.

to as the Inra-design) but no sire was progeny-tested in both countries. The combined data of both designs is denoted as the JOINT-design. For the family sizes see Table I.

Marker data

For the present study nine chromosomes were selected from the whole genome scan data sets. According to the literature reports and to our own experience, these chromosomes were of special interest to us. On these chromosomes, the individuals of the ADR-design were originally genotyped for 75 microsatellite markers, three single strand conformation polymorphisms (SSCP) and the EAC blood group system. The individuals of the Inra-design were genotyped for 53 microsatellites and the EAC blood group system on the same chromosomes. Microsatellite and SSCP genotypes were determined in both designs by automated fragment analysis (ALF, Amersham-Pharmacia or ABI377, Perkin-Elmer). The routine blood typing laboratories (two in Germany and one in France) determined the genotypes for the EAC system according to standard procedures. Only 21 markers including EAC were genotyped in both experiments making the derivation of haplotypes of the five grandsires for all markers difficult. Therefore, to generate a number of co-informative meioses between markers genotyped in the ADR-design and markers genotyped in the Inra-design, roughly 30 sires of each family of the ADR-design were additionally genotyped for markers that previously had been genotyped in the Inra-design only. These sires were genotyped for all markers included in the experiment. According to our practical experience this number is sufficient to derive the haplotypes of a sire in a half-sib design. All alleles from microsatellites were coded as follows: short paternal allele '1'; long paternal allele '2'; and all deviating maternal alleles '3'. A unified coding of the EAC blood group marker was done with haplotype analysis of the grandsires. Allele coding was performed to avoid a common standardisation of the genotypes and to ensure the anonymity of the individuals. All marker data were stored in the ADRDB database [START_REF] Reinsch | A multiple-species, multiple-project database for genotypes at codominant loci[END_REF] and were checked for their agreement with the Mendelian laws of inheritance. Multipoint marker maps were computed using CRIMAP [START_REF] Green | Documentation of CRI-MAP, Version 2.4[END_REF]. For chromosomes, markers, and the genetic maps see Table II. The marker order is in agreement with maps published previously [START_REF] Kappes | A second-generation linkage map of the bovine genome[END_REF].

Phenotypic data

Six traits were included: milk yield (MY), fat yield (FY), protein yield (PY), fat content (FC), protein content (PC), and somatic cell score (SCS). For the Inra-design, daughter yield deviations (DYD) were used for all six traits. DYD were by-products of the French genetic evaluation system based on a single trait repeatability animal model. For the ADR-design DYD were not available, therefore, estimated breeding values calculated with a BLUP animal model for all six traits were taken from the national sire evaluation and were de-regressed as described by Thomsen et al. [START_REF] Thomsen | Comparison of estimated breeding values, daughter yield deviations and deregressed proofs within a whole genome scan for QTL[END_REF]. To ensure the anonymity of the sires, the phenotypes were expressed in genetic standard deviation units as provided by each country and were slightly rounded (two decimal places). For further analysis the within family and design mean (ADR-design and Inradesign, respectively) was set to zero. It turned out that the phenotypes of the Inra-design were in general somewhat more variable than the phenotypes of the ADR-design (Tab. III).

Statistical analysis

The QTL analyses were performed for each trait separately across families with the programs BIGMAP and ADRQLT [START_REF] Reinsch | A multiple-species, multiple-project database for genotypes at codominant loci[END_REF] in Germany and Phenotypes are expressed in genetic standard deviation units. The mean was set to zero. ADR-design: sons that were progeny-tested in Germany; Inra-design: sons that were progeny-tested in France; JOINT-design: ADR-design and Inra-design merged.

QTLMAP [START_REF] Elsen | Alternative models for QTL detection in livestock, I. General information[END_REF] in France. Both softwares are based on the multimarker regression approach [START_REF] Knott | Methods for multiple-marker mapping of quantitative trait loci in half-sib populations[END_REF]. For each cM on the chromosome, the phenotypes were regressed on the corresponding QTL transition probabilities and the position with the highest test statistic (F-ratio) was taken as the most likely position of the QTL on each chromosome. The following model was applied:

y ijk = gs i + b ik * tp ijk + e ijk
where y ijk is the trait value of the jth sire of the ith grandsire, gs i is the fixed effect of the ith grandsire, b ik is the regression coefficient for the ith grandsire at the kth chromosomal location, tp ijk is the probability of the jth sire receiving the chromosomal segment for gamete one (gamete numbers were randomly assigned) from the ith grandsire at the kth chromosomal position, and e ijk is the random residual. Test statistic critical values were calculated empirically for each trait separately using the permutation method [START_REF] Churchill | Empirical threshold values for quantitative trait mapping[END_REF]. Briefly, by shuffling the phenotypic data 10 000 times randomly while keeping the marker data constant the genotype-phenotype association was uncoupled and, hence, after applying the mapping procedure every QTL estimate indicated a type I error per definition. The chromosomewise critical values α = 1%, 5%, and 10% were calculated by taking the 99th, 95th, and 90th quantile from the corresponding distribution of the test statistic, respectively. Because only nine chromosomes were analysed, the genomewise significance levels were computed using the Bonferroni correction assuming 30 chromosomes: 30 where p g ( p c ) is the genomewise (chromosomewise) error probability. Additionally, the QTL position estimates from each evaluated permuted data set were recorded for permutation bootstrapping. The distribution of the QTL position estimates along each chromosome was termed the null distribution.

p g = 1 -(1 -p c )
A single family was assumed as heterozygous at a significant QTL when it showed a significant haplotype contrast (P ≤ 0.05, t-test) at the estimated position from the across family analysis.

For each QTL position that deemed to be significant ( p c ≤ 0.05) a noncentral confidence interval was computed with permutation bootstrapping [START_REF] Bennewitz | Improved confindence intervals in Quantitative Trait Loci mapping by permutation bootstrapping[END_REF]. First 250 bootstrap samples were generated and analysed [START_REF] Visscher | Confidence intervals in QTL mapping by bootstrapping[END_REF]. The distribution of the QTL position estimates along the chromosome was termed linkage distribution and was corrected for the marker impact in a second step. This was done by dividing the frequency of each chromosomal position of the linkage distribution by the corresponding frequency of the null distribution resulting in the marker corrected distribution. From this distribution, noncentral 95% confidence intervals were computed with an analogous highest posterior density method [START_REF] Bennewitz | Improved confindence intervals in Quantitative Trait Loci mapping by permutation bootstrapping[END_REF].

To account for the problem of multiple testing across traits, the expected false discovery rate (FDR), i.e. the expected proportion of a true null hypothesis within the class of rejected null hypotheses [START_REF] Weller | A new approach to the problem of multiple comparisons in the genetic dissection of complex traits[END_REF], was computed for all 54 hypotheses tested (m = 54, 6 traits × 9 chromosomes). The FDR was computed for the ordered set of chromosomewise error probabilities p c [START_REF] Ashwell | Detection of loci affecting milk production and health traits in an elite US Holstein population using microsatellite markers[END_REF]

≤ • • • p c (m)
for each chromosomewise error probability p c (i) (i = 1, . . . , m) as:

q(i) = mp c (i)/i.
The FDR can be controlled at some level q * by determining the largest rank i for which: q * < mp c (i)/i. The results of the calculated FDR can be used as a guide to present a ranking of significant chromosomes, which could be suggested for a further analysis, e.g. fine mapping.

All statistical analyses were done once with the ADR-design and once with the Inra-design to carry out a QTL confirmation study. Furthermore, the same statistics were applied to the JOINT-design to detect QTL that were not declared as significant in the other two. This could be done because the additional genotypings of the sons from the ADR-design with markers used only in the Inra-design so far ensured a high accuracy of the sires haplotype derivation.

RESULTS

General results

The results will be presented only for the analysis carried out in Germany with the BIGMAP and ADRQLT programmes, which were essentially equal to those obtained in France with the QTLMAP programme. A QTL was considered as chromosomewise (genomewise) significant when the error probability p c ( p g ) was ≤ 0.05. In Table IV all significant QTL together with the error probabilities p c and p g , the estimated location, the 95% confidence interval, and the number of heterozygous families are presented. Note that p g was only calculated when p c was below 0.03. Significant QTL were found for all traits and all three designs, but no QTL for any trait could be mapped on the chromosomes 6 and 20. The highest number of QTL (genomewise significance) was found in the JOINT-design, followed by the Inra-Design, and the fewest in the ADR-design. The number of significant heterozygous families was in general 2 or 3 out of 5. The sign of the QTL effect of significant families was in the same direction in all three designs. When comparing confidence intervals of different designs for the same significant trait × chromosome combination, suprisingly they were in general the largest for the JOINT-design. For a few QTL with an estimated position at the start or at the end of the chromosome, the confidence interval did not include the estimated position. For an example see the QTL for SCS on chromosome 18 in the ADR-design (Tab. IV). Confidence intervals computed with the classical bootstrap method [START_REF] Visscher | Confidence intervals in QTL mapping by bootstrapping[END_REF] were always larger (not shown).

QTL-results for milk production traits

Chromosomewise significant QTL were found on chromosome 5 for MY in all three designs, for FY in the ADR-design, for FC for the JOINT-design, and additionally, a genomewise significant QTL for PC was found in the JOINT-design. Chromosome 14 harboured highly significant QTL for all three designs. The estimated positions were always at the start of the chromosome at position 0 cM for the QTL detected in the ADR-design, whereas for the Inraand the JOINT-design it was in some cases a few cM closer to the middle part. However, the plot of the test statistic for all QTL detected on chromosome 14 and all designs were very similar, being on a high level in the first part and then dropping down rapidly between 30 and 50 cM (not shown). The sign of the QTL effects for the heterozygous families for PY and FY were in the opposite direction, i.e. the paternal haplotype that increased PY lowered FY. Genomewise significant QTL were found on chromosome 19 for FY in the Inra-and the JOINT-design at a very similar position. For FC, genomewise QTL were found on the same chromosome in the Inra-and the JOINT-design and a chromosomewise QTL in the ADR-design, with a similar shape of the test statistic (see Fig. 1). On chromosome 23 only chromosomewise significant QTL were found. The ADR-design showed an effect for MY and PY at similar positions (around 60 cM). Additionally the JOINT design showed an effect on this chromosome for PC with an estimated position at the start of the chromosome. In the Inra-and the JOINT-design, genomewise QTL were mapped on chromosome 26 for MY, FY, and PY, and the JOINT-design showed an additional chromosomewise significant effect for PC. The estimated QTL positions were 51 cM and around 23 cM for the Inra-design and the JOINTdesign respectively. The plots of the test statistics for MY and chromosome 26 are presented in Figure 1.

QTL-results for somatic cell score

Chromosome 2 harboured a chromosomewise significant QTL for SCS in the ADR-design and a genomewise significant QTL in the JOINT-design. Note that the Inra-design showed an effect with p c = 0.1 for SCS on the same chromosome. For the plots of the test statistics see Figure 1. The ADR-design showed a genomewise significant QTL for SCS on chromosome 18, but no effect could be observed in the Inra-and the JOINT-design on this chromosome. In contrast, the Inra-and the JOINT-design showed a genomewise significant effect for SCS on chromosome 19 whereas no significant effects could be observed for SCS in the ADR-design on this chromosome. The results are listed for QTL that show a chromosomewise error probability p c ≤ 0.05. Genomewise error probabilities p g were only computed when p c was below 0.03. a MY: milk yield; FY: fat yield; PY: protein yield; FC: fat content; PC: protein content; SCS: somatic cell score. b ADR-design: sons that were progenytested in Germany; Inra-design: sons that were progeny-tested in France; JOINTdesign: ADR-design and Inra-design merged. c Estimated QTL location (in cM map position).

DISCUSSION

Number of QTL

A critical question in QTL mapping studies is how many of the statistical significant QTL represent real QTL rather than a type I error. Assuming six uncorrelated traits and a genomewise error probability p g of 0.05, the number of QTL that would be expected to be genomewise significant by chance under the null hypothesis (H 0 ) of no linked QTL is below 1 in each design. The number of expected QTL under H 0 would be even lower when taking the correlation of the traits into account [START_REF] Spelman | Quantitative trait locus analysis for five milk production traits on chromosome six in the Dutch Holstein Friesian population[END_REF][START_REF] Zhang | Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree[END_REF]. The number of actual QTL found on a genomewise significance level was above the expected number under H 0 in every design (Tab. IV). Controlling the FDR at a stringent level of 0.01, i.e. 1 out of 100 rejected null hypotheses are true, revealed 1 QTL of the ADR-design, 4 QTL of the Inra-design and 6 QTL of the JOINT-design (Tab. V). Note that with respect to Winter et al. [START_REF] Winter | Association of a lysine-232/alanine polymorphism in a bovine gene encoding acyl-CoA:diacylglycerol acyltransferase (DGAT1) with variation at a quantitative trait locus for milk fat content[END_REF] and Grisart et al. [START_REF] Grisart | Positional candidate cloning of a QTL in dairy cattle: identification of a missense mutation in the bovine DGAT1 gene with major effect on milk yield and composition[END_REF], it was assumed that the QTL of milk production traits on chromosome 14 was a single one. Additionally, because of the very similar shape of the test statistic for the QTL of the milk production traits on chromosome 26 (not shown) and the known genetic correlation of the five traits, these QTL were also considered as a single one. Three different QTL showed at least chromosomewise effects in all three designs (Tab. IV). Additionally, some families showed a significant effect in all three designs for QTL (P < 0.05) that were chromosomewise significant only in one or two designs in the initial analysis (not shown). As expected, the number of QTL that appeared to be genomewise significant increased with increasing size of the design. This was attributed to the increased experimental power of the Inra-design compared to the ADR-design, and of the JOINT-design compared with the two other designs. Additionally the more variable phenotypes of the Inra-design (Tab. II) resulted in a larger haplotype contrast compared to the ADR-design. The reasons for the higher variability could not be clarified completely. A possible explanation is the different unit of measurement in the two designs (DYD vs. de-regressed estimated breeding values). Because of the higher power of the Inra-design, it dominated the JOINT-design. As a consequence all 6 chromosomewise significant QTL of the Inra-design, but only 4 of the ADR-design, were also detected in the JOINTdesign. However, the number of detected QTL that were only chromosomewise significant was greater for the ADR-design than for the Inra-design. When the FDR was controlled at a statistically lower level, e.g. 0.2, it revealed 7 QTL for the ADR-design and only 4 QTL for the Inra-design (Tab. V). In our opinion, however, it seems to be appropriate for this point to put more emphasis on the stringent significance level of genomewise significance.

Comparison of QTL results across designs and with literature reports

For QTL confirmation, no fixed rules concerning the significance level have been established, mainly because the choice of an appropriate null hypothesis is unclear and the aim of the confirmation study can differ [START_REF] Spelman | Moving from QTL experimental results to the utilisation of QTL in breeding programmes[END_REF]. The aim of our confirmation study was to confirm that a significant QTL is a real effect. Therefore, we declared a QTL as confirmed within this study, if it showed a chromosomewise significant effect of p c ≤ 0.05 in both the ADR-and the Inra-design within similar chromosomal regions, although we are aware that this is a stringent criterion. Due to the applied stringent significance level for confirmation, the conclusion that a significant not confirmed QTL is a type I error should be treated with caution as long as single families show a significant effect in the same direction in both designs. The QTL results were also compared to some extent with literature reports, keeping in mind that an across study comparison of QTL results is difficult because different studies used different designs with different sets of markers and different levels of significance.

Chromosome 2: The chromosomewise significant QTL for SCS in the ADR-design was not confirmed by the Inra-design, this design showed only a p c of 0.1. The large F5 family, however, was identified as QTL heterozygous (P < 0.01) in both designs, and the plots of the test statistics (Fig. 1) looked very similar with the highest value at 100 cM for both designs. The JOINT-design showed an increased test statistic (Fig. 1), which resulted in a genomewise significance. As far as we know, this QTL has not been reported previously. One of the most important findings of this study was this QTL, because SCS is very attractive for MAS due to the high economic importance of the correlated trait, mastitis, and due to its low heritability.

Chromosome 5: The chromosomewise significant QTL for MY on chromosome 5 was found to be significant in all three designs with the F2 family identified as QTL heterozygous; consequently this QTL was confirmed within the present study. The QTL for PC found in the JOINT-design on this chromosome was not confirmed within the present study. The F4 family, however, showed a significant effect in all three designs (P < 0.01 in every design, calculated at the QTL position estimated in the JOINT-design).

In contrast to the estimated position for the MY QTL, the PC QTL was located closer to the start of the chromosome (marker interval BM103 CSSM34), indicating that different QTL are segregating for MY and PC on chromosome 5, which is also supported by visual comparison of the plots of the corresponding test statistics (not shown) and by the fact that different families showed an effect for these QTL.

The weak QTL for FC in the JOINT-design on this chromosome was previously reported near the same marker (BM315) [START_REF] Heyen | A genome scan for QTL influencing milk production and health traits in dairy cattle[END_REF].

Chromosome 14: Based on literature reports [START_REF] Heyen | A genome scan for QTL influencing milk production and health traits in dairy cattle[END_REF][START_REF] Zhang | Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree[END_REF], the QTL for milk production traits on chromosome 14 was expected. Looft et al. [START_REF] Looft | A mammary gland EST showing linkage disequilibrium to a milk production QTL on bovine chromosome 14[END_REF] mapped the expressed sequence tag KIEL_E8 to the proximal region of this chromosome and found a linkage disequilibrium to the milk production QTL. The estimated effects were in the opposite direction for fat yield and protein yield [START_REF] Looft | A mammary gland EST showing linkage disequilibrium to a milk production QTL on bovine chromosome 14[END_REF]. Identical results were obtained in the present study. KIEL_E8 and ILSTS039 was only genotyped in the ADR-design (Tab. II), probably generating small differences in the estimated positions of the QTL between the three designs. Recently Grisart et al. [START_REF] Grisart | Positional candidate cloning of a QTL in dairy cattle: identification of a missense mutation in the bovine DGAT1 gene with major effect on milk yield and composition[END_REF] and Winter et al. [START_REF] Winter | Association of a lysine-232/alanine polymorphism in a bovine gene encoding acyl-CoA:diacylglycerol acyltransferase (DGAT1) with variation at a quantitative trait locus for milk fat content[END_REF] reported the identification of a positional candidate gene (DGAT1) with a mutation most likely causing the chromosome 14 QTL effect.

Chromosome 18: The QTL on chromosome 18 for SCS found in the ADRdesign has been reported in the literature. Ashwell et al. [START_REF] Ashwell | Detection of loci affecting milk production and health traits in an elite US Holstein population using microsatellite markers[END_REF] found a significant effect on SCS in the neighbourhood of the BM2078 marker. In our study this marker was located near the estimated SCS QTL position at the end of the chromosome (Tab. II). Schrooten et al. [START_REF] Schrooten | Whole genome scan to detect quantitative trait loci for conformation and functional traits in dairy cattle[END_REF] mapped a QTL for SCS in the middle part of the chromosome (marker interval BM7109 ILSTS002).

Chromosome 19: The genomewise significant QTL for FC in the JOINTdesign was confirmed in the present study (chromosomewise significant in both the ADR-and Inra-Design). The plots of the test statistics (Fig. 1) show that the shapes for the ADR-and the Inra-design were very similar. As expected, the test statistic of the JOINT-design showed the highest value. To our knowledge no FC QTL on chromosome 19 has been reported by any QTL study. The genomewise significant QTL for FY found in the Inra-and JOINT-design, could not be confirmed in the study. Probably the identified QTL for FC and FY represents a single one, because the plots of the test statistics had a similar shape (not shown).

Additionally we found a QTL for SCS on this chromosome in the Inraand JOINT-design, which was not confirmed by the ADR-design. To our knowledge, this QTL has not been reported previously.

Chromosome 23:

The QTL for PC was only significant in the JOINTdesign, hence it was not confirmed within this study. Two families (F4 and F5), however, showed significant haplotype contrast in all three designs at the estimated QTL position in the JOINT-design. No families were heterozygous in the Inra-design for the QTL for MY and PY found in the ADR-design, hence it could not be confirmed in this study.

Chromosome 26: The results on this chromosome were very contradictory. While the QTL for MY, FY and PY was highly significant in the Inra-and in the JOINT-design, it was not found in the ADR-design, and hence, could not be confirmed within the study. The plots of the test statistics for MY (Fig. 1) show the substantial difference between the shapes of the Inra-and JOINT-design on the one hand and the ADR-design on the other hand. It was not possible to uncover the reason for these discrepancies from our data. The differences between the plots of the Inra-and the JOINT-design were attributed to the fact that the Inra-design was genotyped only for two markers in the distal chromosomal region (Inra081 and IDVGA59), but the ADR-design was genotyped for three additional markers located between the two markers (see Tab. II) with the consequence that the average information content of the JOINT-design in this marker bracket was increased.

The test statistics for FY, PY and FC followed the test statistics presented in Figure 1 for all three designs very well (not shown). Therefore, it may be assumed that at this position there could be a single pleiotropic QTL which affects several milk production traits rather than different closely linked QTL, although we do not have definitive proof for this.

Chromosomes 6 and 20: Many studies report QTL for various milk production traits on chromosome 20 [START_REF] Georges | Mapping quantitative trait loci controlling milk production in dairy cattle by exploiting progeny testing[END_REF][START_REF] Zhang | Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree[END_REF], and, so even more, on chromosome 6 [START_REF] Coppieters | The great-grand-daughter design: a simple strategy to increase the power of a grand-daughter design for QTL mapping[END_REF][START_REF] Kühn | Detection of QTL for milk production traits in cattle by application of a specifically developed marker map of BTA6[END_REF][START_REF] Spelman | Quantitative trait locus analysis for five milk production traits on chromosome six in the Dutch Holstein Friesian population[END_REF][START_REF] Zhang | Mapping quantitative trait loci for milk production and health of dairy cattle in a large outbred pedigree[END_REF]. Ron et al. [START_REF] Kliger | Multiple Quantitative Trait Locus analysis of bovine chromosome 6 in the Israeli Holstein population by a daughter design[END_REF] verified the hypothesis that two QTL are segregating on chromosome 6. With respect to these studies, it was surprising that no significant effect for any trait in any design could be detected on chromosomes 6 and 20, probably due to QTL homozygosity of the families included in the present study.

Discrepancies between the ADR-and Inra-design

The comparison of QTL results for the ADR-and Inra-design revealed three substantial discrepancies: For the SCS QTL on chromosomes 18 and 19 and for the milk production QTL on chromosome 26. Based on our data, the reasons for this lack of congruency could not be elucidated. An explanation might be that the QTL allele frequencies differ between the populations and the QTL shows a dominance effect. A further explanation might be that genotype by environment interaction plays an important role. This seems to be more likely for the SCS trait rather than for the milk production traits.

According to Interbull evaluations, the correlation between breeding values for this trait estimated in Germany and in France is above 0.9 [START_REF] Mark | Summary of Mace pilot-runs for somatic cell count and clinical mastitis[END_REF], which can be interpreted as an argument against a genotype by environment interaction on a whole genome level. Nevertheless, a genotype by environment interaction might exist for a single QTL, especially when the interaction causes an allele substitution effect to show a different size but equal sign of effect in two environments. Additionally, a QTL by polygenic genotype interaction might exist, indicating that there might be different background genes for the traits with the consequence that some QTL appear only as significant in one of the two designs. Note that these hypotheses are very speculative.

Experimental strategy

This study demonstrated the advantages of a joint analysis of families that are included in different granddaughter designs. Because of the optimal allocation of limited resources it was not possible to include all families of both initial granddaughter designs, therefore a subset of families was chosen that were included in both experiments. However, Walling et al. [START_REF] Walling | Combined analyses of data from quantitative trait loci mapping studies: chromosome 4 effects on porcine growth and fatness[END_REF] showed that there is even a benefit in a combined analysis of data from different designs when families are nested within experiments. Due to the coding of genotypes, phenotypes and animals, the information was only exchanged on a family level, and therefore, individual anonymity was ensured. The large family size of the JOINT-design resulted in a high experimental power. As a consequence, a number of QTL could be mapped, which met the stringent significance level of genomewise significance. Three QTL showed an at least chromosomewise significant effect in both the ADR-and in the Inra-design, and therefore, were confirmed in this study. However, it was not possible to draw more precise conclusions about the position of the QTL, because the confidence intervals were in general the largest for the JOINT-design. This was surprising, because it is known from simulation studies that bootstrap confidence intervals for the QTL positions become smaller with increasing population size [START_REF] Bennewitz | Improved confindence intervals in Quantitative Trait Loci mapping by permutation bootstrapping[END_REF][START_REF] Visscher | Confidence intervals in QTL mapping by bootstrapping[END_REF]]. An explanation is that the JOINT-design was genotyped heterogeneously, i.e. individuals from one family were genotyped for a different set of markers (see Tab. II). Following this, an increased number of markers genotyped in all individuals of the ADR-and the Inra-design would be necessary to reduce the interval width to a desired size of 10 to 20 cM. Hence, the low number of common markers is the weak point of this study, a higher number would have probably resulted in more precise estimates of the QTL position. However, for a derivation of haplotypes of the grandsires, the number of common markers was large enough due to the additional typings of sires from the ADR-design with markers that had been genotyped only for the sires of the Inra-design so far. The comparison of the haplotypes of the sires derived once from the Inradesign data and once from the ADR-design data did not reveal any conflicts.

The noninclusion of the estimated QTL position in the confidence intervals in some cases was attributed to the fact that these positions were also marker locations and, therefore, might be biased by the markers [START_REF] Walling | On the mapping of quantitative trait loci at marker and non-marker locations[END_REF]. Permutation bootstrap produces confidence intervals that are corrected for the marker impact [START_REF] Bennewitz | Improved confindence intervals in Quantitative Trait Loci mapping by permutation bootstrapping[END_REF].

CONCLUSION

The potential benefit of a combined analysis of data from different granddaughter designs for QTL analysis was demonstrated. It was possible to detect and confirm a number of QTL simultaneously. Important prerequisites for this type of study are comparable phenotypes across studies and a sufficient number of common markers genotyped in all members of a family. This number was limited in the present study with the consequence, that it was not possible to estimate QTL positions more precisely. Since many Holstein families are bred worldwide and most QTL experiments used a granddaughter design, similar studies for traits that are comparable across experiments should be performed.

Figure 1 .

 1 Figure 1. Test statistic profiles for all three designs (indicated by arrows) for fat content and chromosome 19 (top), milk yield and chromosome 26 (middle), and somatic cell score (SCS) and chromosome 2 (bottom).

Table I .

 I Size of the five Holstein paternal half-sib families included in the experiment.

	Family	ADR-design	Inra-design	JOINT-design
	F1	42	102	144
	F2	50	83	133
	F3	127	95	222
	F4	126	168	294
	F5	126	236	362
	Totals	471	684	1155

Table II .

 II Chromosomes (BTA) included in the experiment and genetic maps.

	BTA Marker, distance from the start of the chromosome in cM
	02	TGLA44 0.0, BM3627 5.0, TGLA431 13.9, CSFM50 23.7, TGLA377 36.8,
		CSSM42 44.9, BMS1300 59.3, ILSTS98 74.5, ILSTS82 78.6,
		BMS778 90.4, MM8 113.0, TGLA110 113.1, BMS1987 124.9,
		Inra135 127.3, BM2113 135.2, Inra231 136.7, IDVGA2 157.8
	05	BM6026 0.0, RM103 27.3, CSSM34 42.9, RM500 60.0, Lysmic 69.0,
		ETH10 76.3, CSSM022 84.6, RM29 98.3, BM1248 112.9, BM2830 133.8,
		BM315 149.4, ETH2 167.6, ETH152 177.9
	06	ILSTS93 0.0, ILSTS90 13.0, URB16 38.6, BM1329 41.1, DIK82 57.6,
		IL97 79.5, FBN14 86.5, InraK 92.0, CSN3 92.01, BP7 106.6,
		BMC4203 127.1, BM2320 135.2
	14	KIEL_E8 0.0, ILSTS039 1.3, CSSM66 9.0, RM180 42.8, BM4630 57.6,
		RM11 58.8, RM192 77.4, BMS1899 87.9, BM4513 118.1, BL1036 147.5,
		Inra092 148.7, Inra100 148.71
	18	IDVGA31 0.0, TGLA357 16.9, ABS13 23.8, HAUT14 55.1, BM7109 62.6,

ILSTS002 70.6, IDVGA55 94.7, EAC 109.7, BM2078 117.6, TGLA227 141.2

	19	BM9202 0.0, ILSTS73 2.0,

HEL10 17.9, URB44 43.6, UWCA40

	61.3,
	BMS2389 61.6, BM17132 67.1, URB32 72.4, DIK39 75.5, CSSM65 78.9,
	FBN501 82.0,

BMS1069 88.7, ETH3 92.0, RM388 102.5, BMC1013 110.7

	20	HEL12 0.0, BM3517 0.5, BM1225 5.9, TGLA126 24.7, BM713 30.1,
		ILSTS072 43.5, BM5004 66.9, UWCA26 79.0
	23	IOBT528 0.0, Inra132 10.3, Inra064 10.4, BM47 26.2, RM033 34.8,
		UWCA1 44.8, BM1258 49.2, DRB3 60.1, BOLADRBP 64.1, BTN 64.2,
		MB026 64.3, MB025 65.0, CYP21 65.7, BM7233 76.3, BM1818 78.4,
		BM1905 96.6
	26	ABS12 0.0, BMS651 5.0, BMS907 13.9, BM1314 24.6, Inra081 27.6,
		RM26 37.2, BM4505 41.1, BM6041 50.4, IDVGA59 51.9
	Markers genotyped in both the ADR-design and Inra-design are written bold-face
	and underlined, markers genotyped only in the ADR design are written regularly.
	Markers genotyped in the Inra-design and additionally for a number of sons from the
	ADR-design are written in italics. The numbers indicate the chromosomal position
	of the markers.

Table III .

 III Standard deviations, minimum and maximum of phenotypic parameters by design.

	Trait	Design	Standard dev.	Minimum	Maximum
	Milk yield	ADR	0.93	-2.58	3.00
		Inra	1.13	-3.97	3.93
	Fat yield	ADR	0.84	-2.46	2.65
		Inra	1.30	-5.56	3.74
	Protein yield	ADR	0.92	-2.83	2.82
		Inra	1.08	-3.88	3.36
	Fat content	ADR	0.93	-2.47	2.88
		Inra	1.09	-2.87	3.29
	Protein content	ADR	0.96	-2.71	3.00
		Inra	0.90	-3.08	2.73
	Somatic cell score	ADR	0.92	-2.77	2.56
		Inra	1.07	-3.26	2.94

Table IV .

 IV Results of QTL analyses with chromosomewise ( p c ) and genomewise ( p g ) error probabilities, estimated QTL location, 95% confidence interval (CI95) and the heterozygous families.

							(continued on the next page)
	BTA Trait a Design b	p c	p g Location c	CI95	Heterozygous
						(cM)	(cM)	Families
	02	SCS	ADR	0.01	0.32	100	0-128	F3, F5
		SCS	JOINT < 0.01	0.02	99	6-157	F3, F5
	05	MY	ADR	0.05		109	7-150	F2, F4
		MY	Inra	0.05		157	7-168	F1, F2
		MY	JOINT	0.01	0.26	158	1-168	F1, F2
		FY	ADR	0.02	0.45	151	2-167	F2, F5
		FC	JOINT	0.05		154	28-149 F1
		PC	JOINT < 0.01	0.03	42	13-149 F4
	14	MY	ADR	< 0.01 < 0.01	0	1-78	F3, F4
		MY	Inra	< 0.01 < 0.01	7	0-7	F2, F3, F4
		MY	JOINT < 0.01 < 0.01	0	1-119	F2, F3, F4
		FY	ADR	< 0.01 < 0.01	0	0-77	F3, F4
		FY	Inra	< 0.01 < 0.01	7	0-8	F3, F4
		FY	JOINT < 0.01 < 0.01	8	8-97	F3, F4
		PY	ADR	0.03		0	2-78	F4
		PY	JOINT < 0.01	0.14	0	0-87	F2, F4
		FC	ADR	< 0.01 < 0.01	0	0-2	F2, F3, F4, F5
		FC	Inra	< 0.01 < 0.01	0	0-7	F2, F3, F5
		FC	JOINT < 0.01 < 0.01	9	9-9	F2, F3, F5
		PC	ADR	< 0.01 < 0.01	0	0-86	F3, F4
		PC	Inra	< 0.01 < 0.01	29	0-113	F2, F3, F4
		PC	JOINT < 0.01 < 0.01	0	0-148	F2, F3, F4
	18	SCS	ADR	< 0.01	0.05	141	11-137 F2, F3, F4
	19	SCS	Inra	< 0.01	0.04	32	3-108	F3, F4
		SCS	JOINT < 0.01	0.05	50	1-105	F3, F4
		FY	Inra	< 0.01 < 0.01	59	57-109 F4
		FY	JOINT < 0.01 < 0.01	61	1-105	F2, F4
		FC	ADR	0.01	0.26	77	26-102 F2, F3
		FC	Inra	0.04		65	10-110 F2, F3
		FC	JOINT < 0.01 < 0.01	76	1-108	F2, F4
	23	MY	ADR	0.01	0.26	55	44-94	F4, F5
		PY	ADR	0.03		69	12-90	F4, F5
		PC	JOINT	0.01	0.26	4	1-95	F4, F5

Table IV .

 IV Continued.

	BTA Trait a Design b	p c	p g Location c	CI95	Heteroygous
						(cM)	(cM)	Families
	26	MY	Inra	< 0.01	0.06	51	6-51	F1, F5
		MY	JOINT < 0.01	0.02	25	4-50	F1, F5
		FY	Inra	< 0.01 < 0.01	51	13-51	F1, F2, F5
		FY	JOINT < 0.01 < 0.01	21	6-50	F1, F5
		PY	Inra	< 0.01 < 0.01	51	9-51	F1, F5
		PY	JOINT < 0.01	0.05	23	4-50	F1, F5
		PC	JOINT	0.03		25	4-50	F2, F4

Table V .

 V Computation of the false discovery rate (q) across traits within each design. ADR-design: sons that were progeny-tested in Germany; Inra-design: sons that were progeny-tested in France; JOINT-design: ADR-design and Inra-design merged. b Rank. c MY: milk yield; FY: fat yield; PY: protein yield; FC: fat content; PC: protein content; SCS: somatic cell score.

			ADR-design a		Inra-design a	JOINT-design a
	i b	BTA	Trait c	q	BTA	Trait	q	BTA	Trait	q
	1	14	MY	0.000	14	MY	0.000	14	MY	0.000
	2	14	FC	0.000	26	FY	0.000	14	FY	0.000
	3	14	PC	0.000	14	FC	0.000	19	FY	0.000
	4	18	SCS	0.031	14	PC	0.000	14	FC	0.000
	5	14	FY	0.031	14	FY	0.001	14	PC	0.000
	6	19	FC	0.110	19	FY	0.001	19	FC	0.001
	7	23	MY	0.131	26	PY	0.001	26	FY	0.002
	8	02	SCS	0.158	19	SCS	0.010	26	PY	0.003
	9	05	FY	0.148	26	MY	0.011	26	MY	0.003
	10	14	PY	0.141	19	FC	0.242	02	SCS	0.006
	11	23	PY	0.163	05	MY	0.241	19	SCS	0.006
	12	05	MY	0.221	26	FC	0.437	14	PY	0.006
	13	19	MY	0.335	05	FC	0.430	05	PC	0.039
	14	05	PY	0.362	05	PC	0.409	05	MY	0.055
	15	23	PC	0.364	23	PC	0.487	23	PC	0.057
	16	06	FY	0.345	26	PC	0.475	26	PC	0.073
	17	19	FY	0.372	14	PY	0.473	05	FC	0.129
	18	19	PC	0.356	02	SCS	0.480	19	PC	0.154
	19	02	PY	0.417	23	FY	0.513	23	MY	0.150
	20	19	PY	0.419	19	PY	0.520	19	PY	0.168
	21	06	PC	0.435	18	FY	0.509	23	FY	0.212
	22	23	FY	0.428	20	PC	0.490	06	SCS	0.212
	23	06	PY	0.498	06	SCS	0.584	18	PY	0.245

a

ACKNOWLEDGEMENTS

This research was supported by the German Cattle Breeders Federation (ADR) and the German Ministry of Education, Science, Research and Technology (BMBF). It has benefited from the helpful comments of two anonymous reviewers.