Important information regarding the breeding programme was collected from the breeding organisation on demand. The breeding programme was analysed by identifying breeding goals and conventional traits with their relative weights and analysing their influence on total merit index (TMI). The breeding goal for GWM is defined as a robust, muscled, and well-growing mutton, which is well-adapted to grazing in damp and maritime climates and various ground conditions. The conventional TMI included the three traits of average daily gain under intensive circumstances (ADG_I), muscularity (MUSC), and wool (WOL) with consistent relative weights of 0.33 for each trait.

^aADG_E = average daily gain under extensive circumstances; UMFR = ultrasonic muscle-fat ratio.

The breed and its breeding history were analysed to identify special and valuable traits. A comprehensive literature review was carried out and, in addition, face to face interviews with farmers and staff of the breeding organisation were conducted to emphasise breed-specific traits. The main purpose of the GWM breed is landscape conservation on the dykes of the northern coasts of Germany. Thereby, their job with their browsing is it to make the dyke slip-proof, densify the ground, and to ensure against flooding. In general, the animals were kept outside on the dykes with their progeny the whole year and only received extensive feed without supplemented concentrates. However, when young rams became licensed for breeding purposes, farmers began to fatten their rams additionally with supplements to increase weights in order to obtain a higher breeder valuation later. Thus, valuation results for GWM rams were erroneously assumed to be correct for the trait of conventional ADG related to the constant feed environment. The trait of conventional ADG for GWM rams is biased, which has a major impact on the carcass value of the lambs. Currently, the main source of income from the GWM breed besides landscape conservation is to submit the lambs for slaughter. For the local sheep breed, a special feature of ADG based on extensive feed intake (ADG_E) was assumed due to the breeding history, demographic circumstances of husbandry, and economic value of this trait. In addition, it was assumed that the fattening period under extensive circumstances had an impact on the muscle and fat depth ratio (UMFR), which is an important meat-quality indicator.

To compute novel EBVs, linear mixed models (LMM) were applied using the R-package “asreml” from Butler et al. [18] . The LMM can be written as

y = X b + Z A a + ∑ k Z k u k + e (1)

where y denotes the n-vector of phenotypic values, b is the vector of fixed effects, a is the vector of random additive genetic effects of the animal distributed as a ~ N ( 0 , σ a 2 A ) , where σ a 2 is the additive genetic variance and A is the additive relationship matrix. Vector u k of independent random effects has distribution u k ~ N ( 0 , σ u k 2 I ) and e is the n-vector of independent residual errors with e ~ N ( 0 , σ e 2 I ) . Matrices X, Z_A, and Z are design matrices associating observations with the appropriate combination of effects. Fixed and random effects of sire, dam, sex, date of birth, and breeder were tested for significance using the R-package “asremlPlus” from Brien [19] . The statistical analyses were performed simultaneously in a bivariate analysis for each trait in order to estimate the repeatability (t) and the heritability (h²) for these traits. The repeatability following Lessells and Boag [20] was computed as

t = σ a 2 + ∑ k σ u k 2 σ a 2 + ∑ k σ u k 2 + σ e 2 (2)

and the heritability following Falconer and Mackay [21] was calculated as

h 2 = σ a 2 σ a 2 + ∑ k   σ u k 2 + σ e 2 (3)

The estimation of genetic ( r ^ G ) and phenotypic ( r ^ P ) correlations following Falconer and Mackay [21] between the traits were also conducted within the pairwise bivariate analysis by usage of the LMM. The genetic correlation was calculated as

r ^ G ( X , Y ) = cov ( σ a ( X ) 2 σ a ( Y ) 2 ) σ a ( X ) 2 σ a ( Y ) 2 (4)

and the phenotypic correlation was computed as

r ^ P ( X , Y ) = cov ( σ a ( X ) 2 σ a ( Y ) 2 ) + cov ( ∑ k ( σ u k 2 ) ( X ) ∑ k ( σ u k 2 ) ( Y ) ) σ a ( X ) 2 σ a ( Y ) 2 + ∑ k ( σ u k 2 ) ( X ) ∑ k ( σ u k 2 ) ( Y ) (5)

where X and Y denote distinct traits.

Correlations between novel and conventional EBVs were estimated with the “cor.test” function from the R-package “stats” [22] .

Selection on breed-specific traits was carried out for 10 years with genetic evaluation of all animals once a year. The genetic evaluation was based on the estimation of genetic response with the formula from Rendel and Robertson [23] , calculated as

Δ G = i ∗ r B V ∗ σ A L (6)

where i is the selection intensity, r B V is the correlation between true and estimated breeding value, σ A is the additive genetic standard deviation of the trait, and L is the generation interval of the species or breed. Four scenarios with different i were considered based on the selected proportions (p%) of the reference sires. To translate p% to the corresponding i, different tables were used from Falconer and Mackay [21] . First scenario had a p% of 50 and was translated to an i₁ of 0.798, which meant 7 out of 14 reference sires. Second, third, and fourth scenarios had different p% of 36, 21, and 14 and were compiled to corresponding i₂ of 1.039, i₃ of 1.372, and i₄ of 1.590, which implemented 5, 3, and 2 out of 14 reference sires. Correlation between true and estimated breeding value (accuracy of breeding value estimation) as well as the values for trait-specific σ A were calculated within the LMM. Average generation interval for ewes ( L e ) was defined as 3.5 years and the average generation interval for reference sires ( L s ) was considered as 2.7 years [17] . The true generation interval of L is the average

of both parameters and had a value of 3.1 computed as L = L e + L s 2 . Reference

sires were chosen based on their phenotypic measurements for the goal trait. Within a flock, 20 ewes were mated to one of the selected reference sires depending on different i-scenarios. For i₁ in total 7 flocks with each of them 20 ewes were mated with 7 different reference sires over 10 years. For i₂, i₃, and i₄ in total 5, 3, and 2 flocks with each of them 20 ewes were mated with 5, 3, and 2 different reference sires over 10 years. Average phenotypic measurements ( G i ) was obtained for selected reference sires in the ith year and the annual rate of response between years j and i was computed as

Δ G i − j = ( G j − G i ) / ( j − i )

where j > i [17] .

The effects of sex and date of birth were significant (p ≤ 0.001) for both traits, thus they were included as fixed effects in the models. However, the random effect of dam was included in the genetic analysis as a random effect in order to avoid an over-estimation of heritability, an under-estimation of maternal effects, and to increase the reliability. The repeatability for the trait ADG_E was 0.42 and 0.46 for the trait of UMFR. The corresponding heritability was 0.70 for ADG_E and 0.83 for UMFR (Table 2). Phenotypic and genetic correlations are positive between both traits with 0.62 and 0.61 (Table 3). The correlation between true and estimated breeding value ( r B V ) was fixed and had an accuracy of 0.725 for both traits. Investigated trait-specific parameters of σ A were 186.81 g for ADG_E and 0.49 for UMFR. Correlations between novel and conventional EBVs are shown in Table 4. ADG_I was moderately positive correlated with MUSC (0.60), whereas ADG_E was moderately negative correlated with MUSC (−0.68). The EBV of ADG_E was also moderately positive correlated with the EBV of UMFR (0.64). Other correlations between EBVs were not statistically significant.

^aADG_E = average daily gain under extensive circumstances; UMFR = ultrasonic muscle-fat ratio.

^aADG_E = average daily gain under extensive circumstances; UMFR = ultrasonic muscle-fat ratio.

^aEstimates were tested for statistical significance: p-value ≥ 0.05 (n.s.), <0.05 (*), <0.01 (**), <0.001 (***); ADG_I = average daily gain under intensive circumstances, MUSC = muscularity, WOL = wool, ADG_E = average daily gain under extensive circumstances, UMFR = ultrasonic muscle-fat ratio.

Genetic response and corresponding ∆F were simulated for the implementation of the trait ADG_E regarding different i-scenarios over 10 years of selection (Figure 4). Genetic response of ADG_E increased with an increasing i. In total, genetic response enhanced from the average of 318.45 g/day to values of 481.09 g/day for i₁ and 639.97 g/day for i₂ after 10 years of selection. However, genetic response for i₃ and i₄ reached values > 700 g/day and >850 g/day after 7 years of selection (Figure 4(a)). Corresponding ∆F decreased from an average F of 2.22 at year 0 of selection to the first years of selection depending on different i, whereas ∆F started to increase rapidly with an increasing value of i after some years of selection. After 10 years of selection, ∆F had values of 1.4%, 2.7%, 5.1%, and 7.9% for i₁, i₂, i₃ and i₄ (Figure 4(b)). For UMFR the same simulations were performed and are shown in Figure 5. Genetic response increased from an average of 0.49

and reached values of 0.92, 1.34, 2.41, and >2.75 for i₁, i₂, i₃ and i₄ after 10 years of selection (Figure 5(a)). Remaining ∆F increased to values of 1.1%, 2.2%, 5.1%, and 7.9% for i₁, i₂, i₃ and i₄ after 10 years (Figure 5(b)).

The number of reference sires and their tested progeny in the experimental design was small due to the small number of living herd book rams of the GWM breed (Figure 1(a)). The field design depended mainly on the farmers’ motivation and conviction regarding this project. Consequently, just a few farmers consented to participate and provide their young rams for the trial. Nevertheless, the reference sire lines were mostly widely selected to achieve genetic variance within the traits but showed still inbreeding and relatedness with each other (Figure 2). The phenotypic information was collected separately for each trait by one person to avoid bias. For the calculation of UMFR, QUS measurements for the muscle and fat depth were measured under predetermined conditions to achieve consistency. In general, repeatability set the upper limit to heritability as a very useful interpretation since the heritability of traits cannot often be obtained and there is a risk of overestimation [24] . For ADG_E, the repeatability and heritability were 0.42 and 0.70 (Table 2). In the studies of María et al. [25] , Hassen et al. [26] , and Gowane et al. [27] , heritability estimated for conventional ADG was low until moderate and varied between 0.15 and 0.26. It can be assumed that conventional ADG and ADG_E are similar traits dependent on feeding as they show the same fixed and random effects. The repeatability and heritability estimated for UMFR were 0.46 and 0.83 (Table 2). Gilmour et al. [28] estimated a heritability for muscle depth and fat depth of between 0.05 and 0.29. The UMFR can be assumed as a meat-quality trait and these traits exhibits a heritability < 0.18 [29] . Safari et al. [30] provided a heritability for meat-quality traits between 0.05 and 0.18. Hence, the heritability of ADG_E and UMFR with 0.70 and 0.83 was obviously over-estimated in this model. The true values for the heritability of these traits are limited by the repeatability of 0.42 for ADG_E and 0.46 for UMFR. This moderate heritability for both traits was also strengthened by the literature. The genetic correlation between ADG_E and UMFR of 0.61 (Table 3) is probably over-estimated in comparison with the study by Safari et al. [30] , where the genetic correlations for live weight and muscle depth and live weight and fat depth were between 0.34 and 0.36. Strong overestimation of heritability and genetic correlation was due to the small number of animals used in the animal model. Probably, some fixed and random effects become significant with an increased number of animals and, hence, heritability may decrease and approximate reality. The high standard error was due to the small number of individuals and limited reference sire lines within the model. Unrelated males and generally animal sizes are often the limiting factors especially in context of local breeds’ small populations (Figure 1(a)). Thus, repeatability cannot be ignored in the interpretation of the heritability of these novel traits for the GWM breed. Investigated correlations in Table 4 show, that ADG_I was positively correlated with MUSC (0.60), whereas ADG_E was negatively correlated with MUSC (−0.68). This result strengthens the assumption of a biased trait observation regarding ADG_I and ADG_E, which were negatively (−0.11) but not statistically significant correlated (Table 4). Additionally, the unbiased trait of ADG_E was positively correlated with the meat-quality trait of UMFR (0.64), which is in accordance with the investigated positive regression and correlation of 0.62 between collected phenotypes for both traits (Figure 3). Hence, a positive impact on meat-quality aspects regarding utilisation of ADG_E can be assumed.

The conventional breeding programme of GWM was geared towards ADG_I, MUSC, and WOL, although the measurement for the trait of ADG_I is biased and WOL has now become a subsidiary income in Germany. Additionally, the sole trait of MUSC cannot provide any information concerning meat-quality aspects. It is simply an aspect of appearance without any profitability for the breed and shows a strong dependency on ADG_I (Table 4). Furthermore, the conventional breeding programme focused on biased ADG_I and, hence, could have led to a reduction in the native genetic variance for the unbiased breed-specific ADG_E trait and the loss of this native genetic diversity. The latter can cause long-term degradation of the GWM breed and may discount profitability potentials and competitiveness for the future developments in breed-specific environments. Gandini and Oldenbroek [31] and Meuwissen [3] mentioned that the definition of relevant breeding goals, the improvement of breed genetics, and the enhancement of profitability are the best strategies to move from the conservation to utilisation of a local breed. Such improvements of genetic response were qualified depending on different i in Figure 4 and Figure 5 with special focus on ∆F. Especially in a small, local breed such trait implementations and genetic improvements within a breeding programme have consequences for ∆F depending on i. There exists a link between genetic response and inbreeding (Figure 4 and Figure 5). An increased rate of genetic gain also led to higher rates of inbreeding [32] [33] . In general, inbreeding results in biological risks of genetic variance reduction, inbreeding depression, and accumulation of deleterious alleles [34] . In order to achieve a small population of a local breed with their native genetic diversity and fitness the mating of close relatives and an increased inbreeding should be avoided or restricted. Therefore, a maximum for ∆F of 1% per generation was predefined from different authors [35] [36] , which means a maximum for ∆F of 0.3% per annum in case of sheep. For both traits the inbreeding level of the first scenario i₁ stayed under this threshold of 0.3% per annum, all other i-scenarios had a ∆F > 0.3% per annum (Figure 4(b) and Figure 5(b)). The differences of ∆F regarding i₁ and i₂ in Figure 4 and Figure 5 were due to different selected reference sires with distinct inbreeding coefficients between both traits. In addition, the whole population of GWM depicts a rapidly increased ∆F since 2007 (Figure 1(b)) and some selected reference sires exhibits inbreeding and relatedness among each other (Figure 2). Consequently, a p% of 50 and i₁ of 0.798 should be chosen for an optimal use of reference sires to achieve genetic response with simultaneously acceptable rates of inbreeding. Nevertheless, with scenario i₁ genetic response of 481.09 g/day for ADG_E and 0.92 for UMFR would be theoretically possible after 10 years of selection (Figure 4(a) and Figure 5(a)). This implies a trait improvement of 51% for ADG_E and 87% for UMFR. ADG_I could be replaced by ADG_E within the breeding programme in order to achieve the special yield characteristics of the GWM breed. In addition, profitability and competitiveness could be positively influenced compared to conventional sheep breeds in the same environment due to an increased average daily gain based on extensive feed at the dykes. On extensive grassy landscapes, the GWM breed may have higher weight gain by comparison with conventional, intensive mutton breeds (e.g. Texel and German Black-Headed Mutton).With an implemented trait for an unbiased average daily gain, the selection response for the true average daily gain (ADG_E) could be processed and improved by breeders and, thus, the competitiveness and genetic gain of this local breed could probably increase. Furthermore, an implementation of ADG_E would have an impact on meat-quality aspects due to positive correlations between ADG_E and UMFR (Table 4 and Figure 3). Consequently, a positive selection response can be expected for both traits at the same time while implementing one or the other trait (ADG_E or UMFR) within a breeding programme. This implementation of a meat-quality trait (UMFR) may lead to enhanced profitability and a unique selling position due to the selection response of increased meat quality. However, the implementation of ADG_E has a negative impact on the conventional trait of MUSC (Table 4). This conventional trait underlies high subjectivity during the live valuation of animals and has no objective data collection. Beyond, MUSC has a strong dependency on ADG_I, as already mentioned. The trait of WOL has no economic value for sheep breeders in Germany. Subsequently, negative consequences for WOL would not sustainably threaten the local GWM breed and might be not fatal for farmers. Additionally, the monetary value for wool from land sheep breeds is minor due to the rough wool fibre.