Maternal and direct genetic parameters for tail length, tail lesions, and growth traits in pigs

Abstract

Tail length and tail lesions are the major triggers for tail biting in pigs. Against this background, 2 datasets were analyzed to estimate genetic parameters for tail characteristics and growth traits. Dataset 1 considered measurements for trait tail length (T-LEN) and for the growth traits birth weight (BW), weaning weight (WW), postweaning weight (PWW), and average daily gain (ADG) from 9,348 piglets. Piglets were born in the period from 2015 to 2018 and kept on the university Gießen research station. Dataset 2 included 4,943 binary observations from 1,648 pigs from the birth years 2016 to 2019 for tail lesions (T-LES) as indicators for nail necrosis, tail abnormalities, or tail biting. T-LES were recorded at 30 ± 7 d after entry for rearing (T-Les-1), at 50 ± 7 d after entry for rearing (end of the rearing period, T-LES-2), and 130 ± 20 d after entry for rearing (end of fattening period, T-LES-3). Genetic statistical model evaluation for dataset 1 based on Akaike’s information criterion and likelihood ration tests suggested multiple-trait animal models considering covariances between direct and maternal genetic effects. The direct heritability for T-LEN was 0.42 (±0.03), indicating the potential for genetic selection on short tails. The maternal genetic heritability for T-LEN was 0.05 (±0.04), indicating the influence of uterine characteristics on morphological traits. The negative correlation between direct and maternal effects for T-LEN of –0.35 (±0.13), as well as the antagonistic relationships (i.e., positive direct genetic correlations in the range from 0.03 to 0.40) between T-LEN with the growth traits BW, WW, PWW, and ADG, complicate selection strategies and breeding goal definitions. The correlations between direct effects for T-LEN and maternal effects for breeding goal traits, and vice versa, were positive but associated with a quite large SE. The heritability for T-LES when considering the 3 repeated measurements was 0.23 (±0.04) from the linear (repeatability of 0.30) and 0.21 (±0.06; repeatability of 0.29) from the threshold model. The breeding value correlations between T-LES-3 with breeding values from the repeatability models were quite large (0.74 to 0.90), suggesting trait lesion recording at the end of the rearing period. To understand all genetic mechanisms in detail, ongoing studies are focusing on association analyses between T-LEN and T-LES, and the identification of tail biting from an actor’s perspective.

Introduction

Tail biting is a serious multifactorial animal welfare issue, causing injuries, pathological problems, and economic losses (D’Eath et al., 2014). One key trigger for tail biting is the length of the tail (Thodberg et al., 2018). To minimize tail biting, tail docking is a common management practice for decades, but it is not in line with legal animal welfare guidelines as defined in the EU Directive 2008/120/EG (European Union, 2008).

The genetic architecture of tail length across species comprises mono- or oligogenic as well as polygenic components (Xu et al., 2016), reflecting a mixture of qualitative Mendelian and quantitative additive genetic effects. In some animal species (e.g., in Manx cats), deformities and impairments of the embryo due to mutations in the T-gene were associated with a drastic shortening of tails (Buckingham et al., 2013a). Studies on tail length in sheep showed a Gaussian distribution for tail length, and an infinitesimal model of inheritance (Scobie and O’Connell, 2002). Quantitative genetic studies in sheep breeds estimated heritabilities for tail length in the range from 0.39 to 0.77 (James et al., 1991). Apart from sheep, quantitative genetic parameter estimates for tail length are available in different nonlivestock species, for example in Toque Macaques (Cheverud and Dittus, 1992) and in mice (Kramer et al., 1998). Heritabilities were 0.67 and 0.46, respectively. Short tails also occur in pigs. However, to the best of our knowledge, there is a substantial lack of scientific studies addressing the genetic variation of tail length in pigs, considering the direct genetic as well as the maternal genetic perspective.

Tail abnormalities and the responsible genetic mechanisms may differ from the early birth stage of young piglets (tail abnormality = trait of the individual) compared with trait observations later in life (tail abnormalities or tail lesions (T-LES) due to tail biting of contemporaries), suggesting analyses of a longitudinal data structure for tail traits with piglet aging. A new syndrome as detected and described by Reiner et al. (2019) and Reiner and Lechner (2019) is defined as “swine inflammation and necrosis syndrome (SINS)”. SINS contributes to signs of clinical inflammation and dead tissue in the acral regions but is independent from tail biting. T-LES due to SINS can appear in suckling piglets within the first days of life. First SINS indicators are inflammatory changes, continuing with tail necrosis, especially at the base and tip of the tail. In a German research experiment, more than 50% of all litters showed signs of SINS (Reiner and Lechner, 2019).

Mono- and oligogenetic impact on tail length was associated with pleiotropic effects on tail conformation traits including lethal factors. The T-gene was identified as a major gene influencing tail length but causing serious pleiotropic effects (Herrmann et al., 1990). Thus, the reported mutations in the T- gene induced early embryonic death in mice, altered spine structures in cats and cattle (Buckingham et al., 2013b; Kromik et al., 2015) and increased embryonic mortality in dogs and sheep (DeForest and Basrur, 1979; Hytönen et al., 2009). To our knowledge, quantitative genetic analyses focusing on genetic relationships between tail lengths with growth traits (e.g., estimates of genetic correlations), are not available.

Consequently, the aim of the present study was to infer genetic (co)variance components for the traits tail length, tail abnormalities including T-LES and growth traits via quantitative-genetic modeling approaches with and without consideration of maternal genetic effects.

Material and Methods

Animal care and proceedings used in this study were in accordance with guidelines and principles of the statutes of the Justus Liebig University, Giessen, for safeguarding good scientific practice. Data included only traits from the conventional performance tests (existing database) and visual observations for T-LES. Therefore, no additional statement of institutional animal care and use committee is required.

Animals and traits

Two datasets were available for the present study. Dataset 1 was used to infer genetic (co)variance components between tail length (T-LEN) and growth traits. Dataset 1 only included pigs from the University Gießen research station “Oberer Hardthof”. Tails of these piglets were docked after measuring T-LEN. Dataset 2 included longitudinal measurements for T-LES from pigs kept on the performance test station of the respective breeding organization from the federal state of Hesse, Germany. Dataset 2 was used to estimate genetic parameters and to calculate breeding value correlations for T-LES from different ages. For such a research objective, the whole piglet raising and pig fattening period considered animals with their naturally long tails (no application of routinely tail docking). Apart from the German Landrace pigs with an average genetic relationship of 0.01, there was no genetic connectedness between animals from dataset 1 and dataset 2, suggesting separate dataset analyses.

Dataset 1. Dataset 1 considered the traits for T-LEN and growth traits from the breeds Pietrain, German Landrace, Duroc, German Edelschwein, and rotational crosses kept on the University Gießen research station “Oberer Hardthof. After editing, the data consisted of 9,348 records for T-LEN at birth, 12,112 records for birth weight (BW), 10,319 records for weaning weight (WW), 1,483 records for post-weaning weight (PWW), and 10,312 records for average daily gain (ADG) from piglets born in the period from 2015 to 2018. The piglets were offspring from 337 dams (on average 32.13 offspring per dam) and 206 sires (on average 58.80 offspring per sire) with complete pedigree information for four generations. Pedigree completeness and genetic structures were analyzed using the CFC software package (Sargolzaei et al., 2006).

On the “Oberer Hardhof” research stations, pigs are housed in modern and intensive management systems, with slatted floor pens and air-conditioning. Within the first 24 hr after birth, piglets were tattooed (ear numbers) for easy identification, and they received iron injections. In the context of this first management action, individual BW of piglets was recorded, and their tails were measured. Tail length comprised the distance (in cm) from the tail root to the tip of the tail. Afterward, as routinely done in conventional pig production systems, tails were docked. WW was recorded at the average age of 24 d (SD: 4 d), and PWW at the average age of 63 d (SD: 6 d). ADG was calculated considering BW and WW with the respective ages. Descriptive statistics for the pig traits from dataset 1 are given in Table 1.

Table 1.

Descriptive statistics for T-LEN, birth weight (BW), WW, PWW, and ADG

Trait	Mean age, d	No. of observations	Mean	SD	Min	Max	CV, in %
T-LEN, cm	0	9,348	8.87	1.21	01	16.80	13.61
BW, kg	0	12,112	1.45	0.40	0.26	2.95	27.59
WW, kg	24	10,329	7.16	1.61	1.32	13.60	22.49
PWW, kg	63	1,483	24.66	7.76	4.7	49.00	31.47
ADG, kg	24	10,285	0.23	0.06	0.01	0.50	26.09

¹Piglets with complete tail losses at birth.

Dataset 2. Dataset 2 included 4,943 observations from 1,648 pigs for T-LES as indicators for tail necrosis, tail abnormalities, or tail biting. Scoring for T-LES considered 3 categories: 1 = completely healthy tail without any abnormalities, 2 = partly tail losses with mild lesions, 3 = complete tail losses with severe lesions. In the next step of data preparation, T-LES observations were transformed into a binary T-LES data structure, with a score = 0 for the completely healthy tails without any abnormalities and a score = 1 for the remaining cases (i.e., combining the animals from categories 2 and 3). The scores 2 and 3 were merged into 1 category due to the small fraction of pigs showing complete tail losses with severe lesions. Tail scoring was performed at the following 3 different time points: T-LES-1: 30 ± 7 d after entry for rearing; T-LES-2: 50 ± 7 d after entry for rearing (end of rearing period); T-LES-3: 130 ± 20 d after entry for rearing (end of fattening period). Trait recoding on the performance test station was always done by the same trained person. The 1,648 recorded pigs were offspring from matings of German Landrace sows with Pietrain boars (1,441 pigs) and with German Landrace boars (207 pigs). The pigs were offspring from 39 sires (on average 42.25 offspring per sire) and from 54 dams (on average 30.52 offspring per dam). Recorded pigs were from the birth years 2016 to 2019. Pigs with trait records could be traced back to at least four generations. The pedigree dataset comprised 5,462 pigs with genetic relationships to the animals with records. The data distribution for the originally T-LES scores as well as for binary T-LES at the different recording dates is given in Table 2.

Table 2.

Distribution of the original scorings for T-LES from different ages and incidences after transformation into a binary trait distribution

	Original scoring			Binary trait definition
Trait (date)1	1 = healthy	2 = mild lesions	3 = severe lesions	0 = healthy	1 = diseased	Incidence, in %	Total no. of obs.
T-LES-1	1,289	603	60	1,289	663	33.97	1,952
T-LES-2	1,001	640	19	1,001	659	39.69	1,660
T-LES-3	926	403	2	926	405	30.43	1,331
T-LES	3,216	1,646	81	3,216	1,727	34.94	4,943

¹T-LES-1, 30 ± 7 d after entry for rearing; T-LES-2, 50 ± 7 d after entry for rearing (end of rearing period); T-LES-3, 130 ± 20 d after entry for rearing (end of fattening period); T-LES, repeated measurements for T-LES as used for the repeatability model.

Statistical analysis

Dataset 1. First, to identify the most appropriate model, single-trait analyses were performed considering 5 different models. The evaluated models in matrix notation were defined as follows:

$$\text{Model 1}:y=Xb+Z_{a}a+e$$ (1)

$$\text{Model 2}:y=Xb+Z_{a}a+Z_{m}m+e\text{\hspace{0.17em}with\hspace{0.17em}Cov} \left(a,m\right)=0$$ (2)

$$\text{Model 3}:y=Xb+Z_{a}a+Z_{m}m+e\text{\hspace{0.17em}with\hspace{0.17em}Cov} \left(a,m\right)=A{\sigma }_{am}$$ (3)

$$\text{Model 4}:y=Xb+Z_{a}a+Z_{m}m+Z_{c}c+e\text{\hspace{0.17em}with\hspace{0.17em}Cov} \left(a,m\right)=0$$ (4)

$$\text{Model 5}:y=Xb+Z_{a}a+Z_{m}m+Z_{c}c+e\text{\hspace{0.17em}with\hspace{0.17em}Cov} \left(a,m\right)=A{\sigma }_{am}$$ (5)

where y is the observation vector for T-LEN, BW, WW, PWW, or ADG; b is a vector for fixed effects (sex, breed, year-month at recording, litter size, parity number of the sow, age of the sow at farrowing, and age of pig at trait recording); a is a vector for random direct additive genetic effects; m is a vector for random maternal genetic effects; c is a vector for random maternal permanent environmental effects; and e is a vector for random residual effects; X,  $Z_{\mathbf{a}}$, $Z_{\mathbf{m}}$_, and $Z_{\mathbf{c}}$ were incidence matrices relating the records to fixed, additive direct genetic, maternal genetic and maternal permanent environmental effects, respectively.

The (co)variance structure for random effects in model 5 was (and correspondingly reduced in the remaining models with a smaller number of random effects):

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{v}\mathrm{a}\mathrm{r}\left[\begin{array}{l}a\\ \begin{array}{l}m\\ c\\ e\end{array}\end{array}\right]=\left[\begin{array}{ll}\begin{array}{ll}\begin{array}{c}A{\mathrm{\sigma }}_a^2\\ \begin{array}{c}A{\mathrm{\sigma }}_{am}\\ 0\\ 0\end{array}\end{array}& {\displaystyle \begin{array}{c}A{\mathrm{\sigma }}_{am}\\ \begin{array}{c}A{\mathrm{\sigma }}_m^2\\ 0\\ 0\end{array}\end{array}}\end{array}& {\displaystyle \begin{array}{cc}\begin{array}{c}0\\ \begin{array}{c}0\\ I_c{\mathrm{\sigma }}_c^2\\ 0\end{array}\end{array}& {\displaystyle \begin{array}{c}0\\ \begin{array}{c}0\\ 0\\ I_n{\mathrm{\sigma }}_e^2\end{array}\end{array}}\end{array}}\end{array}\right]}\end{array}}$$

where A is the numerator relationship matrix between animals; σ _am is the covariance between direct and maternal genetic effects; I_c and I_n are identity matrices for permanent environmental effects considering c sows and residual effects considering n records, respectively. The direct heritability ($h_d^2$), maternal heritability ($h_m^2$), maternal permanent environmental variance as a proportion of the phenotypic variance $(c^2)$, and direct-maternal genetic correlation r_am are calculated as follows:

$${\displaystyle \begin{array}{l}{\displaystyle h_d^2=\frac{{\mathrm{\sigma }}_a^2}{{\mathrm{\sigma }}_p^2},h_m^2=\frac{{\mathrm{\sigma }}_m^2}{{\mathrm{\sigma }}_p^2},c^2=\frac{{\mathrm{\sigma }}_c^2}{{\mathrm{\sigma }}_p^2}}\end{array}}$$

and

$${\displaystyle \begin{array}{l}{\displaystyle r_{am}=\frac{{\mathrm{\sigma }}_{am}}{\sqrt{{\mathrm{\sigma }}_a^2\times {\mathrm{\sigma }}_m^2}},}\end{array}}$$

where, ${\sigma }_a^2$, ${\mathrm{\sigma }}_m^2$, ${\mathrm{\sigma }}_c^2$, and ${\mathrm{\sigma }}_p^2$ are direct genetic, maternal genetic, maternal permanent environmental, and phenotypic variances, respectively, and ${\mathrm{\sigma }}_{am}$ is the direct maternal genetic covariance.

Single-trait model evaluation based on the Akaike’s information criterion (AIC; Akaike, 1973) and on a likelihood ratio test (LRT). The LRT was performed as follows:

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{L}\mathrm{R}\mathrm{T}=-2(\mathrm{l}\mathrm{o}\mathrm{g}{L}_{\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}-\mathrm{l}\mathrm{o}\mathrm{g}{L}_{\mathrm{f}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}})}\end{array}}$$

where $\mathrm{l}\mathrm{o}\mathrm{g}{L}_{\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{u}\mathrm{c}\mathrm{e}\mathrm{d}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}$ is the log-likelihood from model 1, 2, 3, or 4, and $\mathrm{l}\mathrm{o}\mathrm{g}{L}_{\mathrm{f}\mathrm{u}\mathrm{l}\mathrm{l}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}}$ is the log-likelihood from the most complete model 5. Differences in Log L between models were tested at P < 0.05 with values following a chi-square distribution. Degrees of freedom were equal to the differences in the number of (co)variance components fitted for the 2 models. Model evaluation criteria –2 log L, AIC, and the LRT are given in Table 3.

Table 3.

Model evaluation of the 5 single-trait animal models (as described in the text) considering –2LOGL, AIC, and LRT (as described in the Materials and methods)

Trait	Model1	No. of parameters	–2log L	AIC	LRT
T-LEN	Model 1	2	1,607.91	1,611.91	24,031.73*
	Model 2	3	––22,422.30	–22,416.30	1.5208ns
	Model 3	4	–22,423.72	–22,415.72	0.0978ns
	Model 4	4	–22,423.92	–22,415.92	–0.1016ns
	Model 5	5	–22,423.82	–22,413.82
BW	Model 1	2	1,060.90	1,064.90	24,054.55*
	Model 2	3	–22,993.71	–22,987.71	–0.0516ns
	Model 3	4	–22,993.63	–22,985.63	0.0253ns
	Model 4	4	–22,993.50	–22,985.50	0.155ns
	Model 5	5	–22,993.66	–22,983.66
WW	Model 1	2	4,200.11	4,204.11	24,032.09*
	Model 2	3	–19,831.53	–19,825.53	0.4459ns
	Model 3	4	–19,831.85	–19,823.85	0.1326ns
	Model 4	4	–19,831.96	–19,823.96	0.0228ns
	Model 5	5	–19,831.98	–19,821.98
PWW	Model 1	2	589.73	593.73	24,031.13*
	Model 2	3	–23,441.56	–23,435.56	–0.1594ns
	Model 3	4	–23,441.55	–23,433.55	–0.1498ns
	Model 4	4	–23,441.49	–23,433.49	–0.0943ns
	Model 5	5	–23,441.40	–23,431.40
ADG	Model 1	2	–31,078.03	–31,074.03	24,102.14*
	Model 2	3	–55,161.59	–55,155.59	18.5799*
	Model 3	4	–55,164.52	–55,156.52	15.6477*
	Model 4	4	–55,179.31	–55,171.31	0.8562ns
	Model 5	5	–55,180.17	–55,170.17

1Values from the best model are highlighted in bold. * = P ≤ 0.05; ns, non significant, P > 0.05.

The LRT for the full model 5 did not significantly differ from the remaining models. Hence, we used model 5 for the ongoing multiple-trait analyses, aiming at the estimation of all possible direct and maternal genetic (co)variance components. Model 5 considering all 5 traits simultaneously is:

$${\displaystyle \begin{array}{l}{\displaystyle \begin{array}{lll}& {\displaystyle \left[\begin{array}{c}{y}_1\\ ⋮\\ y_5\end{array}\right]=}& {\displaystyle \left[\begin{array}{ccc}{\mathit{X}}_{\mathbf{1}}& {\displaystyle \dots }& {\displaystyle \mathbf{0}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \mathbf{0}& {\displaystyle \dots }& {\displaystyle {\mathit{X}}_{\mathbf{5}}}\end{array}\right]\left[\begin{array}{c}{b}_1\\ ⋮\\ b_5\end{array}\right]+\left[\begin{array}{ccc}{\mathit{Z}}_{\mathit{a}\mathbf{1}}& {\displaystyle \dots }& {\displaystyle \mathbf{0}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \mathbf{0}& {\displaystyle \dots }& {\displaystyle {\mathit{Z}}_{\mathit{a}\mathbf{5}}}\end{array}\right]\left[\begin{array}{c}{a}_1\\ ⋮\\ a_5\end{array}\right]}\\ & & {\displaystyle +\left[\begin{array}{ccc}{\mathit{Z}}_{\mathit{m}\mathbf{1}}& {\displaystyle \dots }& {\displaystyle \mathbf{0}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \mathbf{0}& {\displaystyle \dots }& {\displaystyle {\mathit{Z}}_{\mathit{m}\mathbf{5}}}\end{array}\right]\left[\begin{array}{c}{m}_1\\ ⋮\\ m_5\end{array}\right]+\left[\begin{array}{ccc}{\mathit{Z}}_{\mathit{c}\mathbf{1}}& {\displaystyle \dots }& {\displaystyle \mathbf{0}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \mathbf{0}& {\displaystyle \dots }& {\displaystyle {\mathit{Z}}_{\mathit{c}\mathbf{5}}}\end{array}\right]\left[\begin{array}{c}{c}_1\\ ⋮\\ c_5\end{array}\right]+\left[\begin{array}{c}{e}_1\\ ⋮\\ e_5\end{array}\right]}\end{array}}\end{array}}$$

For the multiple-trait analysis, the (co)variance structure for random effects is:

$${\displaystyle \begin{array}{l}{\displaystyle \mathrm{v}\mathrm{a}\mathrm{r}\left[\begin{array}{c}\begin{array}{c}{a}_1\\ ⋮\\ a_5\end{array}\\ \begin{array}{c}\begin{array}{c}{m}_1\\ ⋮\\ m_5\end{array}\\ \begin{array}{c}{c}_1\\ ⋮\\ c_5\end{array}\\ \begin{array}{c}{e}_1\\ ⋮\\ e_5\end{array}\end{array}\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{ccc}A{\mathrm{\sigma }}_{a1}^2& {\displaystyle \dots }& {\displaystyle A{\mathrm{\sigma }}_{a1,m5}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ A{\mathrm{\sigma }}_{m5,a1}& {\displaystyle \dots }& {\displaystyle A{\mathrm{\sigma }}_{m5}^2}\end{array}& {\displaystyle \begin{array}{ccc}0& {\displaystyle \dots }& {\displaystyle 0}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ 0& {\displaystyle \dots }& {\displaystyle 0}\end{array}}& {\displaystyle \begin{array}{ccc}\begin{array}{c}\\ 0\end{array}& {\displaystyle \dots }& {\displaystyle \begin{array}{c}\\ 0\end{array}}\\ & {\displaystyle }& {\displaystyle }\\ & {\displaystyle }& {\displaystyle }\end{array}}\\ \begin{array}{ccc}\begin{array}{c}\\ 0\end{array}& {\displaystyle \dots }& {\displaystyle \begin{array}{c}\\ 0\end{array}}\\ & {\displaystyle }& {\displaystyle }\\ & {\displaystyle }& {\displaystyle }\end{array}& {\displaystyle \begin{array}{ccc}{I}_c{\mathrm{\sigma }}_{c1}^2& {\displaystyle \dots }& {\displaystyle I_c{\mathrm{\sigma }}_{c1,c5}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ I_c{\mathrm{\sigma }}_{c5,c1}& {\displaystyle \dots }& {\displaystyle I_c{\mathrm{\sigma }}_{c5}^2}\end{array}}& {\displaystyle \begin{array}{ccc}⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \begin{array}{c}\\ \end{array}& {\displaystyle }& {\displaystyle \begin{array}{c}\\ \end{array}\begin{array}{c}\\ \end{array}}\\ 0& {\displaystyle \dots }& {\displaystyle 0}\end{array}}\\ \begin{array}{ccc}⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ \begin{array}{c}\\ \end{array}& {\displaystyle }& {\displaystyle \begin{array}{c}\\ \end{array}\begin{array}{c}\\ \end{array}}\\ 0& {\displaystyle \dots }& {\displaystyle 0}\end{array}& {\displaystyle \begin{array}{ccc}0& {\displaystyle \dots }& {\displaystyle 0}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ 0& {\displaystyle \dots }& {\displaystyle 0}\end{array}}& {\displaystyle \begin{array}{ccc}{I}_n{\mathrm{\sigma }}_{e1}^2& {\displaystyle \dots }& {\displaystyle I_n{\mathrm{\sigma }}_{e1,e5}}\\ ⋮& {\displaystyle \ddots }& {\displaystyle ⋮}\\ I_n{\mathrm{\sigma }}_{e5,e1}& {\displaystyle \dots }& {\displaystyle I_n{\mathrm{\sigma }}_{e5}^2}\end{array}}\end{array}\right],}\end{array}}$$

where ${\mathrm{\sigma }}_{ai}^2$ and ${\mathrm{\sigma }}_{mi}^2$ are direct and maternal genetic variances, respectively, for trait i (i = 1 to 5); ${\mathrm{\sigma }}_{ai,mj}$ is the covariance between the direct genetic effect for trait i and the maternal genetic effect for trait j (j = 1 to 5); ${\mathrm{\sigma }}_{ci}^2$ is the maternal permanent environmental variance for trait i; ${\mathrm{\sigma }}_{ci,cj}$ is the maternal environmental covariance between traits i and j; and ${\mathrm{\sigma }}_{e\mathrm{i}}^2$ and ${\mathrm{\sigma }}_{e\mathrm{i},e\mathrm{j}}$ are residual variances and covariances, respectively; A is the numerator relationship matrix among animals; I_c and I_n are identity matrices for maternal permanent environmental effects considering c sows and for residual effects considering n records, respectively.

In the multiple-trait analysis, genetic correlations between the direct genetic effect for trait i and the maternal genetic effect for trait j, or vice versa, are calculated as follows:

$${\displaystyle \begin{array}{l}{\displaystyle r_{ai,mj}=\frac{{\mathrm{\sigma }}_{ai,mj}}{\sqrt{{\mathrm{\sigma }}_{ai}^2\times {\mathrm{\sigma }}_{mj}^2}},}\end{array}}$$

where ${\mathrm{\sigma }}_{ai,mj}$ is the covariance between the direct genetic effects for trait i and the maternal genetic effect for trait j; ${\mathrm{\sigma }}_{ai}^2$ and ${\mathrm{\sigma }}_{mj}^2$ are the direct genetic variance for trait i and the maternal genetic variance for trait j, respectively.

Genetic (co)variance components were estimated via REML, and using the REMLF90 software package (Misztal et al., 2002).

Dataset 2. Single-trait animal models were applied to estimate genetic parameters for binary T-LES-1, T-LES-2, and T-LES-3 in consecutive runs. In a further model for repeated measurements, T-LES-1, T-LES-2, and T-LES-3 were considered simultaneously. All analyses were performed using generalized linear mixed models with an identity link function (i.e., depicting a typical linear model (LIN)) and with a logit link function (i.e., to account for the binary trait structure in threshold models (TH)). Repeatability model 6 is as follows:

$${\displaystyle \begin{array}{l}{\displaystyle \begin{array}{lll}& {\displaystyle y_{ijklmn}|\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{k}\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}(y_{ijklmn})=}& {\displaystyle \mu +\mathrm{P}\mathrm{E}{\mathrm{N}}_i+\mathrm{P}{\mathrm{S}}_j}\\ & & {\displaystyle +\mathrm{I}{\mathrm{A}}_k+a_l+\mathrm{G}\mathrm{r}\mathrm{o}\mathrm{u}{\mathrm{p}}_m+\mathrm{p}{\mathrm{e}}_n+e_{ijklmn}}\end{array}}\end{array}}$$ (6)

where $y_{ijklmn}$ is the observations for T-LES, RFB_i is the fixed effect for rearing and/or fattening bay, PS_j is the fixed effect for piglet supplier, IA_k is the fixed effect for initial tail assessment at entry for rearing, a_l is the random additive genetic animal effect; Group_m is the random genetic group effect for either crossbreeds or German Landrace pigs, pe_n is the random permanent environment effect in the repeatability models, and $e_{ijklmn}$ is the random residual effect for the LIN applications. For the TH with the logit link function, the residual was fixed to π ²/3 (Southey et al., 2003).

Genetic analyses were performed using the REML algorithm, and applying the software package DMUV6 (Madsen and Jensen, 2013).

Results

Genetic parameters for tail length and growth traits

Variance components and variance ratios for T-LEN, BW, WW, PWW, and ADG from the single-trait model 5 are given in Table 4. Interestingly, among all traits, the largest direct heritability with 0.42 (±0.03) was estimated for T-LEN. The direct heritability for PWW was moderate with 0.22 (±0.04), but smaller for BW (0.07 ± 0.01), WW (0.12 ± 0.03), and ADG (0.15 ± 0.04). The maternal heritabilities for all traits were small and in a narrow range from 0.05 (±0.02) for T-LEN to 0.10 (±0.03) for BW. The maternal permanent environmental effect reflecting the common litter environment contributed to <5% of the phenotypic variations. Pronounced negative and antagonistic relationships were estimated between direct and maternal genetic effects in the range from –0.35 (±0.13) for T-LEN to –0.90 (±0.19) for PWW. Estimated direct heritabilities, maternal heritabilities, and correlations between direct and maternal genetic effects for T-LEN from the different single-trait animal models 1 to 5 reflect the results from the multiple-trait model (Supplementary Table 1A). Also alternative single-trait animal models 1 to 5 with BW as covariate confirmed the quite large direct heritability estimates, which were in a range from 0.36 (±0.01) to 0.46 (±0.03) (Supplementary Table 1B). The alternative single-trait animal models with BW as covariate generally contributed to slightly smaller residual and additive-genetic variances.

Table 4.

Estimates of (co)variance components and variance ratios from the multiple-trait animal model application

	Variance components and genetic parameters1
Traits	${\mathrm{\sigma }}_{\mathrm{p}}^2$	${\mathrm{\sigma }}_{\mathrm{e}}^2$	${\mathrm{\sigma }}_{\mathrm{a}}^2$	${\mathrm{\sigma }}_{\mathrm{m}}^2$	${\mathrm{\sigma }}_{\mathrm{c}}^2$	${\mathrm{\sigma }}_{\mathrm{a}\mathrm{m}}$	$r_{\mathrm{a}\mathrm{m}}$	$h_{\mathrm{d}}^2$	$h_{\mathrm{m}}^2$	$c^2$
T-LEN	1.57	0.79	0.66	0.07	0.05	–0.08	–0.35	0.42	0.05	0.03
BW	0.13	0.11	0.01	0.01	0.00	0.01	–0.49	0.07	0.10	0.02
WW	2.39	1.84	0.29	0.17	0.09	–0.10	–0.44	0.12	0.07	0.04
PWW	21.95	14.60	4.82	1.85	0.69	–2.67	–0.90	0.22	0.08	0.03
ADG2	3.24	2.37	0.50	0.21	0.17	–0.17	–0.54	0.15	0.07	0.05

¹ ${\mathrm{\sigma }}_{\mathrm{p}}^2$, phenotypic variance, ${\mathrm{\sigma }}_{\mathrm{e}}^2$, residual variance, ${\mathrm{\sigma }}_a^2$, direct genetic variance, ${\mathrm{\sigma }}_{\mathrm{m}}^2$, maternal genetic variance, ${\mathrm{\sigma }}_{\mathrm{c}}^2$, permanent environmental variance, ${\mathrm{\sigma }}_{\mathrm{a}\mathrm{m}}$, covariance between direct and maternal genetic effects, ${\mathrm{r}}_{\mathrm{a}\mathrm{m}}$, correlation between direct and maternal genetic effects, ${\mathrm{h}}_{\mathrm{d}}^2$, direct heritability, ${\mathrm{h}}_{\mathrm{m}}^2$, maternal heritability, ${\mathrm{c}}^2$, common litter environment.

²(co)variance components: multiplication of given values with10³.

Standard errors for $h_{\mathrm{d}}^2$ and $h_{\mathrm{m}}^2$ ranged from 0.01 to 0.04; standard errors for $r_{\mathrm{a}\mathrm{m}}$ ranged from 0.11 to 0.19.

Genetic correlations between tail length and growth traits

Estimates of genetic covariances and genetic correlations among traits considering direct and maternal genetic effects are given in Table 5. The genetic correlation for direct genetic effects between T-LEN with BW was moderate (0.40 ± 0.03). Both traits T-LEN and BW were recorded on the same date. Further genes and environmental effects might influence the remaining growth traits recorded with pig aging. Hence, the direct genetic correlations with T-LEN altered, and were close to zero in the range from 0.02 ± 0.01 (PWW) to 0.03 ± 0.01 (WW and ADG). The correlations between the direct genetic effects for T-LEN with the maternal genetic effects for the breeding goal traits BW, WW, and ADG were quite large in the range from 0.55 ± 0.21 (ADG) to 0.73 ± 0.26 (WW), but close to zero with the maternal genetic effect for PWW (0.13 ± 0.19). Accordingly, positive but weak correlations were estimated between maternal genetic effects for T-LEN with direct genetic effects for all other breeding goal traits in the range from 0.10 ± 0.10 (ADG) to 0.27 ± 0.16 (PWW). The correlations between maternal genetic effects for T-LEN with maternal genetic effects for BW, WW, PPW, and ADG were in a narrow range and close to zero, i.e., 0.09 (±0.06), 0.08 (±0.06), 0.09 (±0.06), and 0.06 (±0.09), respectively. From an antagonistic across-trait perspective, and with a focus on direct-maternal genetic associations, negative correlations were estimated among BW, WW, PWW, and ADG.

Table 5.

Genetic covariances (above the diagonal) and genetic correlations (below the diagonal) for direct genetic (a), maternal genetic (m), and direct–maternal genetic associations1

		a				m
	Traits	T-LEN	BW	WW	PWW	ADG	T-LEN	BW	WW	PWW	ADG
a	T-LEN		0.66	0.03	0.01	0.04		0.08	0.06	0.25	0.03
	BW	0.40 (0.03)		0.01	0.00	0.06	0.14 (0.10)		–0.01	–0.01	–0.01
	WW	0.03 (0.01)	0.08 (0.02)		0.29	0.34	0.11 (0.10)	–0.05 (0.06)		–0.10	–0.09
	PWW	0.02 (0.01)	0.27 (0.05)	0.29 (0.05)		4.82	0.27 (0.16)	–0.09 (0.10)	–0.04 (0.10)		–2.67
	ADG	0.03 (0.01)	0.04 (0.01)	0.96 (0.11)	0.07 (0.04)		0.10 (0.10)	–0.01 (0.07)	–0.00 (0.08)	–0.01 (0.06)
m	T-LEN		0.51	0.37	0.15	0.40		0.07	0.01	0.07	0.03
	BW	0.65 (0.21)		–0.29	–0.18	–0.16	0.09 (0.06)		0.01	0.02	0.00
	WW	0.73 (0.26)	–0.37 (0.24)		–0.14	–0.41	0.08 (0.06)	0.32 (0.07)		0.17	0.13
	PWW	0.13 (0.19)	–0.07 (0.16)	–0.12 (0.17)		–0.05	0.09 (0.06)	0.02 (0.05)	0.23 (0.06)		1.85
	ADG	0.55 (0.20)	–0.25 (0.19)	–0.56 (0.36)	–0.05 (0.19)		0.06 (0.09)	0.08 (0.10)	0.91 (0.18)	0.11 (0.11)

1Standard errors of correlation estimates in parentheses.

Genetic parameters for T-LES at different ages

For T-LES-1, TLES-2, and T-LES-3, heritabilities and corresponding SE were larger from linear than from TH (Table 6). Nevertheless, heritabilities from the TH were estimated on the underlying liability scale, and from LIN on the observed scale. According to the theory of TH (Dempster and Lerner, 1950), heritabilities in either liability or observed scales may differ, especially in the case of low disease incidences.

Table 6.

Genetic parameters¹ for T-LES from different ages, and for LIN and TH applications considering single trait or repeated measurements

Trait2	Model	h 2 ± SE	${\mathrm{\sigma }}_{\mathrm{a}}^2$	${\mathrm{\sigma }}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}}^2$	${\mathrm{\sigma }}_{\mathrm{e}}^2$
T-LES-1	LIN/single trait	0.18 ± 0.14	0.041	0.088	0.102
T-LES-1	TH/single trait	0.01 ± 0.07	0.062	4.105	3.290
T-LES-2	LIN/single trait	0.46 ± 0.15	0.112	0.059	0.073
T-LES-2	TH/single trait	0.11 ± 0.06	0.714	2.455	3.290
T-LES-3	LIN/single trait	0.39 ± 0.19	0.084	0.048	0.083
T-LES-3	TH /single trait	0.10 ± 0.09	0.587	2.257	3.290
T-LES3	LIN/repeatability	0.23 ± 0.04	0.044	0.026	0.120
T-LES3	TH/repeatability	0.21 ± 0.06	1.646	2.898	3.290

¹ h ², heritability$(\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{a}\mathrm{r}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{s}$ on the underlying liability scale), ${\mathrm{\sigma }}_a^2,\mathrm{a}\mathrm{d}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$, ${\mathrm{\sigma }}_{\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}}^2,\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{g}\mathrm{e}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}\mathrm{e}\mathrm{f}\mathrm{f}\mathrm{e}\mathrm{c}\mathrm{t}$, ${\mathrm{\sigma }}_{\mathrm{e}}^2,\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{v}\mathrm{a}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e}$.

²T-LES-1, 30 ± 7 d after entry for rearing; T-LES-2, 50 ± 7 d after entry for rearing (end of rearing period); T-LES-3, 130 ± 20 d after entry for rearing (end of fattening period); T-LES, repeated measurements for T-LES as used for the repeatability model.

³The repeatability from the LIN was 0.30, and from the TH 0.29.

In repeatability models, heritabilities from both modeling approaches were very similar (0.23 ± 0.04 for LIN and 0.21 ± 0.06 for TH), and SE were smaller than from the single-trait models. All estimated variance components were larger than the TH. The largest additive genetic variance for T-LES with 1.65 was estimated with the threshold repeatability model. Accordingly, the group variances were larger than the TH for all T-LES definitions. Especially, the fixation of the residual variances (value π ²/3, Southey et al., 2003) contributed to the smaller heritabilities for T-LES from the TH.

Breeding value correlations for T-LES at different ages

Breeding value correlations between T-LES from different ages (Figure 1) indicate that T-LES or tail abnormalities during rearing are genetically different traits. The lowest breeding value correlation was 0.13 between T-LES-3 from the TH with T-LES-1 from the LIN. Generally, correlations between breeding values from the early diagnosis date (T-LES-1) with breeding values from the latest diagnosis date (T-LES-3) were quite low, for threshold as well as for LIN applications. For the same trait definitions, correlations between breeding values from linear and TH were throughout larger than 0.90, i.e., 0.92 for T-LES-1, 0.94 for TLES-2, 0.98 for T-LES-3, and 0.90 when considering the repeated measurement data structure. The breeding values correlations from both repeatability models (LIN and TH) with T-LES from both early diagnosis dates were quite large in the range from 0.68 to 0.90, but only moderate with breeding values for T-LES-3 (0.31 to 0.32).

Figure 1.

Breeding value correlations between T-LES considering pigs with more than 6 offspring from different ages. T-LES-1: 30 ± 7 d after entry for rearing; T-LES-2: 50 ± 7 d after entry for rearing (end of rearing period); T-LES-3: 130 ± 20 d after entry for rearing (end of fattening period); T-LES: repeated measurements for T-LES as used for the repeatability model; *_LIN = linear model applications; *_TH = threshold model applications.

Discussion

Genetic parameters for tail length and breeding goal traits

The direct heritability for T-LEN with 0.42 was quite large and significantly larger than for the breeding goal traits from the present study reflecting piglets’ weights and growth. The substantial genetic variation for T-LEN indicates that selection on short tails may reduce the tail length in the pig populations within a few generations. Successful breeding on short tails was reported for several sheep breeds, which was possible in short time due to the large direct heritabilities ranging from 0.40 to 0.80 (Scobie and O’Connell, 2002). Regarding interpretations, it should be kept in mind that several breeds were considered simultaneously in the present study for the estimation of genetic parameters. From the strict theoretical background, a heritability is a population parameter. Nevertheless, several multibreed studies have been conducted, but mostly based on genomic data enabling connectedness among breeds through the genomic relationship matrix (Yin et al., 2019). Additionally, we run breed-specific analyses, but the complex models did not properly converge. When including all breeds together, we had quite stable estimates from different models 1 to 5 (Supplementary Table 1). To account for the breed impact, we included breed as a fixed effect in the statistical model 1. Accordingly, Lo et al. (1992) defined a statistical model with a fixed breed effect, and estimated heritabilities for growth, backfat thickness, carcass, and meat quality traits in a mixed population including Landrace, Duroc, and their reciprocal crosses. Meyer et al. (1993) estimated genetic parameters in a multibreed beef cattle population. In their pedigree-based modeling approach, they did not include any effect reflecting the breed or genetic compositions.

BW is a trait of increasing importance in pig breeding, because BW is strongly associated with piglet vitality, survival, growth performance, and weight gain (Gondret et al., 2005; Muns et al., 2013; Klein et al., 2018). The direct heritabilities for BW from single-trait models 2 to 5 were in a narrow range from 0.05 to 0.09, confirming the direct heritability from the multiple-trait model (0.09) and heritability estimates from previous studies (Arango et al., 2006; Tomiyama et al., 2010, Alves et al., 2018). Dufrasne et al. (2013) reported a larger BW heritability of 0.25, but the recording date was time-lagged with at least 4 d after birth. Accordingly, Edwards (2006) reported increasing body weight heritabilities in piglets with aging. The direct body weight heritabilities from the present study gradually increased with age up to 0.22 for PWW. Accordingly, Alves et al. (2018) found an increase of direct heritability estimates with age, due to the decreasing maternal influence. Substantial differences in direct heritabilities for BW from single-trait (0.51) and multiple-trait model applications (0.05) were identified by Banville et al. (2015) in Chinese–European Tai Zumu pigs. A tendency for slightly smaller heritabilities for growth traits from multiple-trait model applications was also found in the present study.

The maternal genetic effect was considered in models 2, 3, 4, and 5. Ignoring the maternal genetic component contributed to biased genetic evaluations and lowered response to selection (Näsholm and Danell, 1994; Solanes et al. 2004). For all traits in our study, we estimated similar direct heritabilities from the single-trait models 2 to 5 and from the multiple-trait model, but the direct heritability increased for all traits when ignoring the maternal genetic impact in model 1. This is exemplarily shown in Supplementary Table 1 for TL. From a statistical model perspective, it seems to be imperative to separate the maternal component into a maternal genetic and a maternal permanent environmental effect, and to consider a covariance structure between direct genetic and maternal genetic effects. Also from a physiological perspective, the impact of uterus characteristics on morphological and growth traits in offspring suggests consideration of maternal genetic effects. In pigs and other species, uterus size was related with improved nutrient transport from the mother to the fetus, initiating larger body size of offspring (Fowden et al., 2006). Yuan et al. (2015) reported associations between uterine characteristics with the efficiency of placental transports of nutrients, with further impact on piglet BW. Maternal genetic influence through uterine nutrition status and supply levels, uterus capacity and milk production was detected for piglet weights and weight gains (Kaufmann et al., 2000; Alves et al., 2018). In a long-term selection experiment in pigs (Freking et al., 2007), increasing uterus capacity was associated with offspring performance and fertility traits. Matheson et al. (2018) defined the percentage of piglets with delayed growth as a maternal uterus indicator trait and estimated negative genetic correlations with BW.

Interestingly, the maternal genetic component explained 5% of the phenotypic variation for T-LEN, indicating uterine influence on tail characteristics. Consequently, we assume uterine impact on piglet conformation traits including vertebrae characteristics (e.g., the number of dorsal vertebras). In this regard, Haverkamp et al. (2015) proved associations between the number of dorsal vertebras and tail length in a Merino sheep population. In mice, Cowley et al. (1989) proved the impact of the maternal uterine genotype on growth parameters, body size, and tail length in offspring.

Among all traits, and with regard to the single-trait model 5 and the multiple-trait modeling approach, the largest maternal heritability was estimated for BW (0.10). Maternal heritabilities for BW in the range from 0.02 to 0.15 were reported by Kaufmann et al. (2000), Tomiyama et al. (2010), and Alves et al. (2018). As expected from a physiological perspective, maternal heritabilities for weight traits slightly decreased with aging (i.e., the maternal heritabilities for WW and PWW). The gradual decline of maternal heritabilities with aging was explored by Yin and König (2018), considering a dense longitudinal body weight data structure and random regression methodology. In contrast, Zhang et al. (2000) estimated a quite low direct heritability (0.03) but a larger maternal heritability (0.11) for piglet weights at the age of 28 d. Zhang et al. (2000) explained the larger maternal heritability with the strong impact of sow milk productivity and sow behavior. Nevertheless, with ongoing piglet aging from weeks 8 to 22, also Zhang et al. (2000) reported a substantial decline of the maternal genetic impact.

The estimates for the direct heritability of 0.12 and for the maternal heritability of 0.07 for WW from model 5 are very close to estimates as reported by Damgaard et al. (2003) and Tomiyama et al. (2010). Hermesch (2001), Kaufmann et al. (2000), and Alves et al. (2018) estimated slightly lower WW heritabilities. The direct heritability for PWW with 0.22 and the maternal heritability with 0.08 was very similar when comparing to estimates from Tomiyama et al. (2010) for weight gain at 60 d. Direct and maternal heritabilities for ADG (0.15 and 0.07, respectively) reflect genetic parameter estimates for weight gain in the period from birth to the weaning date (Banville et al., 2015). Larger direct and maternal genetic heritabilities for daily gains were reported for Chinese pig populations (Zhang et al., 2016), Landrace pigs in the United States (Jiao et al., 2014) and Yorkshire in the United States (Lopez et al., 2018).

The negative correlations between direct and maternal effects for weights and growth traits are in agreement with estimates in other species, e.g., in dairy cattle (Johanson et al., 2011), beef cattle (Chud et al., 2014), and sheep (Boujenane et al., 2015). Explanations addressed the antagonistic relationships between milk yield of the dam (maternal impact) in the suckling period and the direct genetic impact on growth. However, the mechanisms explaining the negative correlations between direct and maternal genetic effects for T-LEN are unclear, suggesting molecular, morphological, and physiological investigations.

Genetic correlations between tail length and growth traits

The direct genetic correlation between T-LEN and BW was positive (0.66), indicating that larger piglets have longer tails. Addressing tail biting, the heavy and large pigs from the same group displayed dominant behavior and were stronger involved in biting activities than the smaller group contemporaries (Andersen et al., 2011). Accordingly, Edwards (2006), Taylor et al. (2010), and Palander et al. (2013) associated tail biting with pig weights or pig growth. Hence, from a tail-biting perspective, the selection on lighter piglets contributes to shorter tails (as identified in the present study) and to fewer cases for tail necrosis. However, the positive genetic correlations between BW with other breeding goal traits reflecting piglet survival and piglet vitality (Klein et al., 2018) suggest selection on increasing individual piglet size. Furthermore, in the present study, we estimated positive (but weak) direct genetic correlations between BW and the other growth traits, as reported previously (Kerr and Cameron 1995; Kaufmann et al., 2000). The direct genetic correlation was largest (0.27) between BW and WW, but declined to 0.08 when correlating BW with PWW. The changing genetic correlations between BW with growth traits record later in life suggest consideration of repeated weight records during aging in body weight indices. The genetic correlation between BW and ADG was weak (0.04), but quite large between WW and ADG (0.96). Differences in body weight trait (co)variance components with aging indicate that different genes are switched on or off along the growth trajectory, as outlined by Schaeffer (2004) when introducing random regression models for animal breeding. Also within parity or lactations, body weight heritabilities and correlations among body weights from different measuring dates altered substantially (Yin and König, 2018).

To our knowledge, this is the first study addressing correlations between direct genetic effects for T-LEN with maternal genetic effects for growth traits, between maternal genetic effects for T-LEN with maternal-genetic effects for growth traits, and between maternal genetic effects for T-LEN with direct genetic effects for growth traits. All correlations with T-LEN when considering maternal effects of either T-LEN or of the growth traits were positive. Hence, from a practical breeding perspective, breeding on improved maternal abilities for body weights and growth traits contributes to longer tails in pig populations, and vice versa. Overall, the antagonistic (positive) correlations between T-LEN with all direct and maternal genetic components of body weight traits suggest the development of breeding goals or selection indices considering direct measurements for T-LEN. Especially in organic pig production, tail docking is under very critical focus, implying to raise long-tail pigs. The newly developed selection indices for organic pig production emphasizing larger BWs with an associated positive impact on piglet vitality (Klein et al., 2018) are counterproductive from a T-LEN breeding perspective. Direct-maternal and maternal-direct genetic correlations among the growth traits BW, WW, and PWW were negative, reflecting the antagonistic relationships between direct and maternal genetic effects within the same traits. Hence, also from a time-lagged body weight recording perspective, unfavorable direct-maternal genetic associations complicate breeding goal definitions and hamper selection efficiency. Direct-maternal associations close to zero among body weights from different ages were reported by Herring et al. (2010).

Genetic parameters for T-LES

Heritabilities for T-LES in the present study were in a broad range from 0.01 to 0.39, depending on the recording date and the genetic-statistical modeling approach. Heritabilities from the LIN were throughout larger than from the TH. Varona et al. (1999) made comprehensive evaluations and comparisons with regard to linear and TH applications. In the case of a typical binary data structure, they identified TH superiority accompanied with larger heritabilities. Larger heritabilities from threshold than from LIN are in line with the theory for the analysis of categorical data (Dempster and Lerner, 1950). Not only for the T-LES in the present study but also for piglet skin lesions (König von Borstel et al., 2018), the LIN heritabilities were larger than the heritabilities from the TH. The tail and skin lesions recording in both studies based on a scoring system comprising several classes. Afterward, for TH applications, data were transformed into a binary structure. It may be more appropriate to consider TH allowing more than 2 classes for such kind of data, but the frequencies for score 3 (severe T-LES) were extremely low. On the other hand, Pashmi et al. (2009) suggested transforming nonlinear health indicators into a binary data structure.

According to the moderate heritabilities for T-LES from both repeatability models, T-LES may be proper indicator traits for genetic selection on pig behavior. Nevertheless, the ultimate goal is to reduce tail biting not from a victim, but instead from an actor's perspective. Identification of biting pigs implies comprehensive video analyses (which are very difficult to analyze), or a combination of modern video techniques with complex machine learning algorithms (D’Eath et al., 2018). As an alternative, several recent studies suggested to focus on recordings of tail or skin lesions (Gentz et al., 2019), which might be a suitable database for genetic group selection or models with social interactions (Heidaritabar et al. 2019). Accordingly, Turner et al. (2008) estimated quite large genetic correlations between lesion scores and pig behavior traits, indicating that selection on lesion scores indirectly reduces pig aggressiveness. Furthermore, T-LES can be the major reason for the outbreak of tail biting in a pig group (Statham et al., 2009).

When considering T-LES as indicators for genetic selection on reduced tail biting, the optimal recording period has to be determined. Due to the stable heritabilities from linear repeatability and threshold repeatability models accompanied with smallest SE, we suggest to analyze a longitudinal data structure. On the other hand, from a practical perspective, trait recording implies tremendous efforts on logistics and on labor, suggesting only 1 observation per pig during aging. Based on the breeding value correlations from the present study, we suggest tail lesion scoring at an age of 50 d, i.e., at the end of the rearing period. Accordingly, other quantitative genetic studies focusing on skin lesion analyses suggested trait recording before moving the pigs to the finishing barn (König von Borstel et al., 2018). Genetic analyses of lesions from this period contributed to the best genetic differentiation (i.e., the largest additive genetic variances).

In conclusion, the moderate additive genetic variances and direct heritabilities for T-LEN indicate the possibilities for successful genetic selection on short tails in pigs. Such a breeding approach may be the most sustainable solution to improve pig welfare considering both aspects: tail biting and tail docking. Nevertheless, we also identified a small maternal genetic effect on T-LEN and antagonistic associations between direct and maternal genetic effects, which complicates the definition of breeding goals and selection strategies. As a further constraint from a practical perspective, breeding on short tails is genetically related to a decrease in body weights at different ages, especially with BW. T-LES from repeatability models had moderate heritabilities and could be used as indicators for pig behavior. When aiming at single-trait genetic evaluations, T-LES should be recorded at the end of the rearing period. In an ongoing study, to fully understand all trait associations genetically, we suggest the estimation of covariances between tail lengths with T-LES. For datasets 1 and 2 in the present study, pedigree genetic relationships larger than zero only were identified for German Landrace. Hence, we will focus on pig genotyping and on inferring genetic covariances between tail length and T-LES considering genomic relationships and multibreed genomic approaches as suggested and evaluated by Yin et al. (2019) and VanvanHossou et al. (2020). A second ongoing research objective should consider tail biting traits from an actor’s (biting) perspective.

Glossary

Abbreviations

ADG

average daily gain

AIC

Akaike’s information criterion

BW

birth weight

LIN

linear model

LRT

likelihood ratio test

PWW

postweaning weight

REML

restricted maximum likelihood

SINS

swine inflammation and necrosis syndrome

TH

threshold model

T-LEN

tail length

T-LES

tail lesions

WW

weaning weight

Conflict of interest statement

The authors declare no real or perceived conflicts of interest.