Genetic Control of Canalization for Twinning Rates in Polypay and Rambouillet Sheep Using Threshold or Double Hierarchical Generalized Linear Models

ABSTRACT

In most sheep production systems, the ideal scenario is for every ewe to lamb and successfully raise twins. However, selection for increased number of lambs born (NLB) is often accompanied by a higher incidence of triplet and higher‐order births, which increases management challenges and producer reluctance to intensify selection for this trait. Therefore, there is a need to identify animals who not only exhibit a high twinning rate, but also canalized reproductive performance, characterized by consistent expression of twin births and reduced variability toward extreme litter sizes. In this context, the double hierarchical generalized linear model (DHGLM) provides a mechanism to evaluate both the mean and the dispersion components of a trait, enabling the evaluation of the heteroskedastic residual variance for each animal, and thereby select animals with lower residual variances. Therefore, the main objectives of this study were to estimate (co)variance components and genetic parameters for the mean and dispersion traits related to number of lambs born and twinning rate and to develop a strategy to identify rams whose daughters consistently produce twins. Data from the US Sheep Experiment Station (USSES; Dubois, ID, USA) Polypay flock recorded from 1999 to 2025 included 8061 litters (3115 dams; 293 sires) and the Rambouillet flock included 5948 litters (2333 dams; 228 sires) recorded from 2005 to 2025. The proportion of twin litters have significantly decreased in the Polypay flock while remaining unchanged (p = 0.13) in the Rambouillet flock. For both breeds, the proportion of single lamb litters have decreased while triplets have increased. For sires with a minimum of 15 daughter litters, the average litter size was 1.53 ± 0.55 for 1‐year‐old ewes and 2.29 ± 0.75 for mature ewes for the Polypay and 1.24 ± 0.43 for 1‐year‐old ewes and 1.93 ± 0.64 for mature ewes for the Rambouillet. A DHGLM was used to estimate both the mean and dispersion of the NLB3 considering 3 classes (1, 2 or 3+) and NLB for all classes (1 to 5 for Polypay and 1 to 4 for Rambouillet) traits using the DHGLMF90 package. A bivariate animal model was fitted each for NLB3 and NLB, and their associated dispersions (vNLB3 and vNLB) with contemporary group as a concatenation of ewe age category and birth year fitted as a categorical fixed effect and animal (ewe), permanent environment, and the residual as random effects for a model including data from all ewes (ALL) and excluding phenotypic records from 1‐year‐old ewes (MATURE). The same mean traits and twinning (TWIN; 1 for non‐twins and 2 for twins) were evaluated using a threshold model with the THRGIBBSF90 package. Heritability estimates ranged from 0.024 ± 0.012 for vNLB3 analysed using the DHGLM model to 0.110 ± 0.020 for NLB3 analysed using the threshold model for the ALL Polypay dataset and from 0.016 ± 0.014 for vNLB3 analysed using the DHGLM model to 0.094 ± 0.022 for NLB3 analysed using the threshold model for the MATURE Polypay dataset. For the Rambouillet, heritability estimates ranged from 0.020 ± 0.013 for TWIN analysed using the threshold model to 0.150 ± 0.022 for NLB analysed using the threshold model for the ALL dataset and from 0.021 ± 0.012 for vNLB3 analysed using the DHGLM model to 0.151 ± 0.023 for NLB analysed using the threshold model for the MATURE dataset. The estimated breeding values (EBV) were filtered if lower than the square root of heritability, or the equivalent of a single phenotypic record and correlations of EBV among animals were compared. Correlations among all NLB approaches were high (0.80 to 1.00) for both breeds, indicating high agreement between NLB considering differing numbers of classes and also for different models (DHGLM and threshold). Theoretical accuracies were evaluated for all animals and sires with more than 15 daughter litters. The TWIN trait analysed using a threshold model and the vNLB trait analysed using the DHGLM model were selected to represent twinning rate using the MATURE dataset for both breeds. Of the sires, 9.9% of Polypay and 32.1% of Rambouillet had both positive TWIN EBV and negative vNLB EBV, suggesting that progress can be achieved for both increased twins and canalization of number of lambs born. Extension of twinning rate to national genetic evaluation is warranted to meet the needs of US sheep producers.

1. Introduction

In sheep production systems that rely on the natural rearing of lambs, the economic optimum is for every ewe to lamb and successfully raise twins (SanCristobal‐Gaudy et al. ²⁰⁰¹). This is not the same as selecting for a 200% lamb crop, which could be achieved without any twins at all. Rather than a 200% lamb crop, the production of exactly two lambs per ewe is ideal (SanCristobal‐Gaudy et al. ²⁰⁰¹; Cottle et al. ²⁰¹⁶). However, selection for an increased number of lambs born inherently results in an increased number of triplet and higher‐order births (Amer et al. 1999), creating management and animal welfare concerns for sheep breeders, particularly those with extensive management practices with no opportunity to artificially raise extra lambs. Indeed, because of these concerns, the lambing percentage across US flocks is persistently low, averaging only 106% across all breeds in 2024 (USDA‐NASS ²⁰²⁵).

Within the livestock industry, there has been an increased emphasis on production of a uniform and consistent product, and this has resulted in moving beyond traditional genetic models to more complex ones, including reaction norm models (Scheiner 1993) and canalization models (Waddington 1942). The identification of animals whose phenotype, twinning rate in this instance, is robust to changes in genotype and environment (Siegal and Bergman 2002) is critical to achieving a twinning flock. The double hierarchical generalized linear model (DHGLM) provides a mechanism to evaluate both the mean and the dispersion component of a trait, enabling the modelling of the heteroskedastic residual variance for each animal (Lee and Nelder 2006) and the identification of those with an increased propensity for twinning. Advancements in the computational efficiency of the algorithm, implemented in the DHGLMF90 software as part of the BLUPF90 suite of programs, allow us to evaluate these traits on a large scale (Misztal et al. 2002; Munera et al. ²⁰²⁴).

The number of lambs born (NLB) to each ewe is determined by a combination of ovulation rate, fertilization rate and embryonic mortality, all of which have a genetic component (Schoenian and Burfening 1990; Amer and Bodin ²⁰⁰⁶). Breed variation has also been reported for each of these traits (J. P. Hanrahan ¹⁹⁸⁷). Selection for animals with reduced variation for NLB, or for twinning rate, is presumably selecting for less variation in these contributing traits (Young 2007). As many as 43% of potential offspring are lost between ovulation and parturition (Dixon et al. 2007), which is not only an astonishing economic loss but also contributes to the variability in NLB.

Research at the US Sheep Experiment Station (USSES) near Dubois, Idaho (USA) is representative of large, extensive range flocks throughout the US West. Incorporation of industry sires into the research program creates genetic linkages throughout the nation, making the research directly applicable to other sheep producers (Wilson et al. 2024, 2025). Breeds included in this study were the Polypay, a semi‐prolific breed and the Rambouillet, which is the foundation of ‘Western white‐face’ sheep flocks. The Polypay breed was developed at the USSES in the 1970s to improve the productivity of US Western range flocks and included equal contributions from Rambouillet, Targhee, Finnsheep and Dorset (Hulet et al. 1984). The development of the Polypay breed had five main selection objectives that included high lifetime prolificacy, first lambing at 1 year of age, more than one lambing event per year, rapid lamb growth and high carcass quality. The Polypay has proven itself to be a versatile breed and is used extensively in range sheep operations as well as accelerated lambing flocks throughout the US (Vanimisetti and Notter 2012; Hulet and Stellflug ²⁰¹⁹). The Rambouillet is an international breed with a long history that started in France from the Spanish Merino. The Rambouillet has been a foundational flock at the USSES for more than 100 years and is well known for both lamb production and a high‐quality fleece. The Rambouillet is adaptable to a wide variety of climates ranging from the hot, arid areas of Texas to the cold, mountainous regions in the US West. The breed is particularly gregarious, making it a popular choice for extensive range flocks where grazing is often unfenced and the flock is monitored by a single herder. Rambouillet sheep from the USSES, used for continuation of the breed and for development of the Polypay breed, were a specific type of Rambouillet that were somewhat differentiated from what was popular at the time and has had an enduring impact throughout the United States.

The main objectives of this research were to estimate variance components for both the mean and dispersion traits related to twinning rate and to develop a strategy to identify rams whose daughters consistently produce twins.

2. Material and Methods

2.1. Data Source

The Polypay and Rambouillet flocks are managed together with other maternal breeds at the USSES. The USSES flock is similar to other extensively managed range flocks throughout the US West. Lambing occurs in the spring in a shed lambing system, where the ewe lambs in a drylot followed by moving the ewes and lambs to a lambing jug for a 36‐ to 48‐h period of bonding. They are then turned out into consecutively larger pens. At an average lamb age of approximately 35 days, the ewes and lambs are turned out for grazing in bands of up to 1000 sheep. The sheep follow a traditional system of transhumance where they are moved by a herder up in elevation as the temperatures increase throughout the spring and summer and return to the lower elevations in late summer for weaning. Grazing occurs on a combination of public and private lands and there is a continuous herder presence to monitor and move the sheep. Ewes and lambs are estimated to travel 200 km during this period. A detailed explanation of the system was provided by Wilmer et al. (2024).

For the Polypay analyses, data from 1999 to 2025 were used and included 8061 litter records (ALL) after removing litters with unknown or non‐Polypay sires. The analyses included 3115 ewes and 293 rams. Pedigree records were traced back three generations from animals with phenotypic records and included 3443 animals. Of the rams, there were 192 with daughters totalling at least 15 litters with an average of 39.7 ± 22.8 litters and a maximum of 121 litters. An additional analysis (MATURE) excluded data from 1‐year‐old ewes (n = 1805 litters), leaving 6256 litters from 2600 mature ewes and 241 rams. For the ALL dataset, there were 1700 single (21.1%), 3995 twin (49.6%), 2075 triplet (25.7%), 278 quadruplet (3.4%) and 13 quintuplet (0.2%) litters for the NLB trait with triplets, quadruplets and quintuplets combined for the NLB3 trait. There were 997 ewes with only one record and 2118 ewes with repeated records. For the MATURE dataset, there were 809 single (12.9%), 3131 twin (50.0%), 2025 triplet (32.4%), 278 quadruplet (4.4%) and 13 quintuplet (0.2%) litters for NLB, with the latter three categories combined in the NLB3 trait. There were 848 ewes with one record and 1752 ewes with repeated records. There were no ewes with missing phenotypic records.

For the Rambouillet analyses, data from 2005 to 2025 were used and included 5948 litter records (ALL) after removing records from litters with unknown or non‐Rambouillet sires. Pedigree records were traced back three generations from the animals with phenotypic records and included 2921 animals. There were 2333 ewes and 228 rams included in the analyses. Of the rams, 134 had daughters totalling at least 15 litters with an average of 35.9 ± 20.0 daughter litters and a maximum of 113 litters. An additional analysis (MATURE) excluded 1‐year‐old ewe records (n = 553 litters), leaving 5395 litters from 2150 mature ewes and 209 rams. There were 1702 single (28.6%), 3404 twin (57.2%), 808 triplet (13.6%) and 34 quadruplet (0.6%) litters in the ALL dataset for the NLB trait with the last two categories combined for the NLB3 trait. There were 752 ewes with one record and 1581 ewes with repeated records. There were 1280 single (23.7%), 3273 twin (60.7%), 808 triplet (15.0%) and 34 quadruplet (0.6%) litters in the MATURE dataset for NLB with the last two categories combined for NLB3. There were 748 ewes with one record and 1402 ewes with repeated records. There were no ewes with missing phenotypic records.

2.2. Data Analyses

The DHGLMF90 software (Munera et al. 2024) was used to perform the analyses. The software applies a DHGLM to estimate the direct additive genetic effect of a trait in addition to the heteroskedastic additive genetic effect of the environmental (residual) variance. In other words, it jointly estimates genetic effects and variance–covariance components for both the mean and dispersion components of the trait. The DHGLM algorithm iterates between two sets of mixed model equations, one for the main trait (mean) and one for the variances using iterative reweighted least squares (IRWLS) until convergence, where the convergence criteria were set to 1 × 10⁻¹². The DHGLM was developed by Lee and Nelder (2006) and expanded to variance component estimation in animal breeding by Rönnegård et al. (2010) and Felleki et al. (2012). With the DHGLMF90 software, the dispersion component was approximated using a linear normal framework, which is equivalent to a Gamma generalized linear model (GLM) (Felleki et al. 2012). The DHGLMF90 software uses the Restricted Maximum Likelihood (REML) method implemented in the BLUPF90+ software for variance component estimation (Misztal et al. 2002; Munera et al. ²⁰²⁴).

The main (mean) traits included number of lambs born with triplets and higher order litters combined (NLB3; 1, 2, 3+), number of lambs born including all classes (NLB; 1 to 5 for Polypay and 1 to 4 for Rambouillet), and their associated dispersions (vNLB3 and vNLB). The traits included lambs that were born either dead or alive, but ewes that were exposed but did not lamb were excluded from the analyses. The contemporary group (CG) was included as a categorical fixed effect and consisted of the lamb birth year and age of the ewe (1, 2 or 3+ year). Since there was only a single flock with a single lambing season, flock and season were not included in the CG. There were 74 and 54 CG for the Polypay ALL and MATURE datasets, respectively, and 52 and 42 CG for Rambouillet ALL and MATURE datasets, respectively. Random effects included animal (ewe), permanent environment and the residual. The mean traits and twinning (TWIN; 1 for non‐twins and 2 for twins) were also evaluated using a threshold model with the THRGIBBSF90 package (Misztal et al. 2002). The direct heritability estimate (h ²) for each mean trait was computed as $h^2={\sigma }_a^2/{\sigma }_p^2$, where ${\sigma }_a^2$ is the direct additive variance and ${\sigma }_p^2$ is the phenotypic variance. The heritability estimate ($h_v^2$) for each dispersion trait was computed as ${\sigma }_a^2/\left(2{\sigma }_p^4+3{\sigma }_a^2\right)$ (Mulder et al. 2007). The genetic coefficient of variation for environmental variance (GCV_E) was computed as ${\sigma }_a/{\sigma }_e^2$, where ${\sigma }_a$ was the direct additive standard deviation and ${\sigma }_e^2$ was the residual variance (Houle 1992; Mulder et al. ²⁰⁰⁷).

Theoretical accuracies were calculated as $\mathrm{ACC}=\sqrt{1-\left(\mathrm{PEV}/{\sigma }_a^2(1+F\right))}$, using the squared standard error as the prediction error variance (PEV), ${\sigma }_a^2$ as the additive variance for each trait, and F as the pedigree inbreeding coefficient. Accuracies were compared for each trait for all animals and for sires with at least 15 daughter litters. The EBV for the vNLB trait analysed with the DHGLM model and the TWIN EBV from the threshold model for sires with at least 15 daughter litters were plotted and the percentage of sires that were favourable for each trait were reported. Next, the EBV for each trait were filtered if the accuracy value was less than the square root of the heritability for each trait, which is the expected accuracy of an animal with a single phenotypic record. The Pearson correlations of the EBV were compared between traits and models for each dataset.

3. Results

3.1. Phenotypic Data

The percentage of singles, twins and triplets and higher‐order births was plotted over time for both Polypay (Figure 1a) and Rambouillet (Figure 1b). Although twin litters are preferred for both breeds, twin litters decreased in the Polypay breed (p = 0.05) and remained statistically unchanged (p = 0.13) in the Rambouillet flock. Singles decreased in both breeds (Polypay: p = 0.07; Rambouillet: p < 0.001) while triplets increased (Polypay: p = 0.02; Rambouillet: p < 0.001). The birth type for the contributing Polypay sires with at least 15 daughter litters was 2% singles, 51% twins, 43% triplets and 4% quadruplets. For Rambouillet, the birth type of the sires with at least 15 daughter litters was 21% singles, 66% twins, 13% triplets and 0% quadruplets. The percentage of twin litters for each sire ranged from 7 to 80 for the Polypay (Figure 2a) and 30 to 89 for the Rambouillet (Figure 2b). For Polypay sires with a minimum of 15 daughter litters, the average litter size was 1.53 ± 0.55 for 1‐year‐old ewes and 2.29 ± 0.75 for mature ewes (Figure 3a). For Rambouillet sires with at least 15 mature daughter litters, the average litter size was 1.24 ± 0.43 for 1‐year‐old ewes and 1.93 ± 0.64 for mature ewes (Figure 3b).

FIGURE 1.

Litter size trend from 1999 to 2025 for the US Sheep Experiment Station (USSES) Polypay flock (a) and from 2005 to 2025 for the USSES Rambouillet flock (b). [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 2.

The percentage of twin litters for Polypay (a) and Rambouillet (b) sires with a minimum of 15 daughter litters for all ewes and mature ewes (2+ year). [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3.

The average number of lambs born (NLB) for Polypay (a) and Rambouillet (b) sires with a minimum of 15 daughter litters for all ewes and mature ewes (2+ year). [Colour figure can be viewed at wileyonlinelibrary.com]

3.2. Estimates of Variance Components and Genetic Parameters

For the Polypay, the heritability estimates for all traits were low, with the highest estimates for NLB and NLB3 analysed using a threshold model (Table 1). When comparing the traits analysed with the DHGLM approach, NLB and vNLB had more additive genetic variation and higher heritability estimates than NLB3 and vNLB3 for both the ALL and MATURE datasets. The vNLB also had a higher GCV_E than vNLB3. The TWIN heritability estimates were higher for the MATURE dataset than for the ALL dataset (Table 1).

TABLE 1.

Estimates and standard errors for the additive genetic variance (${\sigma }_a^2$), permanent environmental variance (${\sigma }_{\mathit{pe}}^2$), phenotypic variance (${\sigma }_p^2$), direct heritability (h ²) ^a or ($h_v^2$) ^b , and genetic coefficient of variation for environmental variance (GCV_E) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 5 classes (NLB; 1, 2, 3, 4 and 5 lambs) and number of lambs born dispersion for 3 classes (vNLB3) and 5 classes (NLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for threshold (liability scale) models for all (ALL) and mature (age 2+ year; MATURE) Polypay ewes.

Model	Dataset	DHGLM		DHGLM		Threshold	Threshold	Threshold
Parameter		NLB3	vNLB3	NLB	vNLB	NLB3	NLB	TWIN
${\sigma }_a^2$	ALL	0.035 ± 0.006	0.026 ± 0.014	0.046 ± 0.007	0.156 ± 0.025	0.046 ± 0.009	0.025 ± 0.005	0.036 ± 0.014
	MATURE	0.042 ± 0.007	0.026 ± 0.023	0.050 ± 0.008	0.163 ± 0.034	0.043 ± 0.010	0.021 ± 0.005	0.018 ± 0.004
${\sigma }_{\mathit{pe}}^2$	ALL	0.034 ± 0.006	0.165 ± 0.021	0.013 ± 0.006	0.012 ± 0.024	0.034 ± 0.009	0.019 ± 0.005	0.017 ± 0.014
	MATURE	0.039 ± 0.007	0.396 ± 0.034	0.016 ± 0.009	0.061 ± 0.035	0.049 ± 0.012	0.023 ± 0.006	0.003 ± 0.003
${\sigma }_p^2$	ALL	1.068 ± 0.010	0.704 ± 0.018	1.060 ± 0.011	0.841 ± 0.021	0.418 ± 0.012	0.225 ± 0.024	1.062 ± 0.028
	MATURE	1.081 ± 0.012	0.883 ± 0.026	1.066 ± 0.013	0.948 ± 0.027	0.455 ± 0.014	0.223 ± 0.027	0.245 ± 0.005
h 2 or $h_v^2$	ALL	0.032 ± 0.005	0.024 ± 0.012	0.044 ± 0.006	0.083 ± 0.009	0.110 ± 0.020	0.110 ± 0.022	0.034 ± 0.013
	MATURE	0.039 ± 0.007	0.016 ± 0.014	0.047 ± 0.008	0.071 ± 0.011	0.094 ± 0.022	0.094 ± 0.023	0.074 ± 0.014
GCVE	ALL	N/A	0.313 ± 0.100	N/A	0.588 ± 0.051	N/A	N/A	N/A
	MATURE	N/A	0.351 ± 0.169	N/A	0.556 ± 0.062	N/A	N/A	N/A

^a

$h^2={\sigma }_a^2/{\sigma }_p^2.$

^b $h_v^2={\sigma }_a^2/\left(2{\sigma }_p^4+3{\sigma }_a^2\right)$.

The Rambouillet heritability estimates were also low, with the highest estimates for NLB3 and NLB analysed using a threshold model (Table 2). The additive genetic variance and heritability estimates were higher for the NLB and vNLB traits than the NLB3 and vNLB3 traits for both the ALL and MATURE datasets. Additionally, the GCV_E was higher for vNLB than vNLB3. The heritability estimates for TWIN were low, with TWIN for the MATURE dataset being the highest (0.042 ± 0.017).

TABLE 2.

Estimates and standard errors for the additive genetic variance (${\sigma }_a^2$), permanent environmental variance (${\sigma }_{\mathit{pe}}^2$), phenotypic variance (${\sigma }_p^2$), direct heritability (h ²) ^a or ($h_v^2$) ^b , and genetic coefficient of variation for environmental variance (GCV_E) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 4 classes (NLB; 1, 2, 3 and 4 lambs) and number of lambs born dispersion for 3 classes (vNLB3) and 4 classes (NLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for threshold (liability scale) models for all (ALL) and mature (age 2+ year; MATURE) Rambouillet ewes.

Model	Dataset	DHGLM		DHGLM		Threshold	Threshold	Threshold
Parameter		NLB3	vNLB3	NLB	vNLB	NLB	NLB	TWIN
${\sigma }_a^2$	ALL	0.028 ± 0.005	0.070 ± 0.021	0.029 ± 0.005	0.099 ± 0.025	0.039 ± 0.006	0.035 ± 0.005	0.021 ± 0.014
	MATURE	0.034 ± 0.006	0.032 ± 0.019	0.036 ± 0.006	0.051 ± 0.023	0.042 ± 0.006	0.035 ± 0.006	0.046 ± 0.019
${\sigma }_{\mathit{pe}}^2$	ALL	0.001 ± 0.005	0.036 ± 0.026	0.0002 ± 0.005	0.037 ± 0.028	0.005 ± 0.004	0.006 ± 0.004	0.023 ± 0.017
	MATURE	0.007 ± 0.006	0.103 ± 0.029	0.005 ± 0.006	0.102 ± 0.031	0.007 ± 0.005	0.005 ± 0.004	0.026 ± 0.020
${\sigma }_p^2$	ALL	1.029 ± 0.011	0.846 ± 0.024	1.029 ± 0.011	0.903 ± 0.026	0.341 ± 0.007	0.234 ± 0.018	1.054 ± 0.032
	MATURE	1.041 ± 0.012	0.844 ± 0.025	1.041 ± 0.012	0.900 ± 0.027	0.358 ± 0.007	0.235 ± 0.019	1.081 ± 0.035
h 2 or $h_v^2$	ALL	0.027 ± 0.005	0.043 ± 0.011	0.028 ± 0.005	0.051 ± 0.011	0.115 ± 0.016	0.150 ± 0.022	0.020 ± 0.013
	MATURE	0.033 ± 0.006	0.021 ± 0.012	0.035 ± 0.006	0.029 ± 0.012	0.116 ± 0.017	0.151 ± 0.023	0.042 ± 0.017
GCVE	ALL	N/A	0.358 ± 0.059	N/A	0.409 ± 0.056	N/A	N/A	N/A
	MATURE	N/A	0.253 ± 0.091	N/A	0.303 ± 0.078	N/A	N/A	N/A

^a $h^2={\sigma }_a^2/{\sigma }_p^2$.

^b $h_v^2={\sigma }_a^2/\left(2{\sigma }_p^4+3{\sigma }_a^2\right)$.

3.3. Correlations Between EBV

The Pearson correlations of EBV among the NLB traits within the ALL Polypay dataset were high (0.80 ± 0.01 to 0.99 ± 0.02; Table 3). The correlations of EBV between the NLB and vNLB traits ranged from 0.67 ± 0.01 to 0.99 ± 0.02. The correlations of EBV between the NLB traits and the TWIN trait were moderately negative. For the MATURE Polypay dataset, the correlations among the NLB traits were also high and ranged from 0.80 ± 0.02 to 0.99 ± 0.02 (Table 4). Correlations between the NLB and vNLB traits were moderate to high. Correlations between the NLB traits and TWIN were moderately to highly positive.

TABLE 3.

Pearson correlations ^a between estimated breeding values (EBV) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 5 classes (NLB; 1, 2, 3, 4 and 5 lambs), number of lambs born dispersion considering 3 classes (vNLB3) and 5 classes (vNLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for a threshold (liability scale) model for all Polypay ewes (ALL dataset).

	DHGLM vNLB3	DHGLM NLB	DHGLM vNLB	Threshold NLB3	Threshold NLB	Threshold TWIN
DHGLM NLB3	0.90 ± 0.02	0.93 ± 0.02	0.89 ± 0.02	0.92 ± 0.02	0.90 ± 0.02	−0.58 ± 0.01
DHGLM vNLB3		0.89 ± 0.02	0.91 ± 0.02	0.70 ± 0.01	0.67 ± 0.01	−0.67 ± 0.01
DHGLM NLB			0.99 ± 0.02	0.81 ± 0.01	0.80 ± 0.01	−0.55 ± 0.01
DHGLM vNLB				0.72 ± 0.01	0.71 ± 0.01	−0.58 ± 0.01
Threshold NLB3					0.99 ± 0.02	−0.49 ± 0.01
Threshold NLB						−0.38 ± 0.01

^a Pearson correlations were compared for animals with accuracies above $\sqrt{h^2}$.

TABLE 4.

Pearson correlations ^a between estimated breeding values (EBV) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 5 classes (NLB; 1, 2, 3, 4 and 5 lambs), number of lambs born dispersion considering 3 classes (vNLB3) and 5 classes (vNLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for a threshold (liability scale) model for mature (age 2+ year) Polypay ewes (MATURE dataset).

	DHGLM vNLB3	DHGLM NLB	DHGLM vNLB	Threshold NLB3	Threshold NLB	Threshold TWIN
DHGLM NLB3	0.61 ± 0.01	0.92 ± 0.02	0.85 ± 0.02	0.92 ± 0.02	0.89 ± 0.02	0.80 ± 0.01
DHGLM vNLB3		0.66 ± 0.01	0.75 ± 0.01	0.33 ± 0.01	0.29 ± 0.01	0.79 ± 0.01
DHGLM NLB			0.98 ± 0.02	0.82 ± 0.02	0.80 ± 0.02	0.81 ± 0.02
DHGLM vNLB				0.68 ± 0.01	0.67 ± 0.01	0.85 ± 0.02
Threshold NLB3					0.99 ± 0.02	0.59 ± 0.01
Threshold NLB						0.51 ± 0.01

^a Pearson correlations were compared for animals with accuracies above $\sqrt{h^2}$.

For the ALL Rambouillet dataset, the Pearson correlations of EBV among the NLB traits were high and ranged from 0.88 ± 0.02 to 0.99 ± 0.02 (Table 5). The correlations of EBV between the NLB traits and vNLB traits were high. The correlations of EBV between the NLB traits and TWIN ranged from lowly negative to slightly positive. The Pearson correlations of EBV for the NLB traits for the Rambouillet MATURE dataset were high and ranged from 0.94 ± 0.02 to 1.00 ± 0.02 (Table 6). The correlations of EBV between the NLB traits and vNLB traits were also high. The correlation of EBV between the NLB traits and TWIN was lowly to moderately negative.

TABLE 5.

Pearson correlations ^a between estimated breeding values (EBV) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 4 classes (NLB; 1, 2, 3 and 4 lambs), number of lambs born dispersion considering 3 classes (vNLB3) and 4 classes (vNLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for a threshold (liability scale) model for all Rambouillet ewes (ALL dataset).

	DHGLM vNLB3	DHGLM NLB	DHGLM vNLB	Threshold NLB3	Threshold NLB	Threshold TWIN
DHGLM NLB3	0.99 ± 0.02	0.99 ± 0.02	0.98 ± 0.02	0.90 ± 0.02	0.90 ± 0.02	−0.16 ± 0.003
DHGLM vNLB3		0.99 ± 0.02	0.99 ± 0.02	0.86 ± 0.02	0.85 ± 0.02	−0.24 ± 0.005
DHGLM NLB			0.99 ± 0.02	0.88 ± 0.02	0.88 ± 0.02	−0.18 ± 0.003
DHGLM vNLB				0.84 ± 0.02	0.84 ± 0.02	−0.25 ± 0.005
Threshold NLB3					1.00 ± 0.02	−0.002 ± 0.001
Threshold NLB						0.05 ± 0.001

^a Pearson correlations were compared for animals with accuracies above $\sqrt{h^2}$.

TABLE 6.

Pearson correlations ^a between estimated breeding values (EBV) for number of lambs born considering 3 classes (NLB3; 1, 2 and 3+ lambs) and 4 classes (NLB; 1, 2, 3 and 4 lambs), number of lambs born dispersion considering 3 classes (vNLB3) and 4 classes (vNLB) for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models and twinning (TWIN; 1 for non‐twin and 2 for twin) for a threshold (liability scale) model for mature (age 2+ year) Rambouillet ewes (MATURE dataset).

	DHGLM vNLB3	DHGLM NLB	DHGLM vNLB	Threshold NLB3	Threshold NLB	Threshold TWIN
DHGLM NLB3	1.00 ± 0.02	0.99 ± 0.02	0.99 ± 0.02	0.96 ± 0.02	0.95 ± 0.02	−0.25 ± 0.005
DHGLM vNLB3		0.99 ± 0.02	0.99 ± 0.02	0.94 ± 0.02	0.93 ± 0.02	−0.30 ± 0.01
DHGLM NLB			1.00 ± 0.02	0.95 ± 0.02	0.94 ± 0.02	−0.25 ± 0.005
DHGLM vNLB				0.92 ± 0.02	0.92 ± 0.02	−0.31 ± 0.01
Threshold NLB3					1.00 ± 0.02	−0.07 ± 0.001
Threshold NLB						−0.02 ± 0.001

^a Pearson correlations were compared for animals with accuracies above $\sqrt{h^2}$.

3.4. Theoretical Accuracies

Theoretical accuracies for all animals and sires with at least 15 daughter litters were compared across the ALL and MATURE datasets for all traits for both breeds (Table 7). For the Polypay, the main traits of NLB3 and NLB had higher accuracies for the DHGLM models than their threshold model counterparts. Within the DHGLM model, the NLB and vNLB traits had higher accuracies than the NLB3 and vNLB3 traits for all animals and sires. For the Rambouillet, accuracies for all animals and for sires with at least 15 daughter litters were similar between datasets for all NLB3 and NLB models.

TABLE 7.

Theoretical accuracies and standard deviations for number of lambs born estimated breeding values (EBV) for 3 classes (NLB3) and 4 (Rambouillet) or 5 (Polypay) classes (NLB), number of lambs born dispersion EBV for 3 classes (vNLB3) and 4 or 5 classes (vNLB), and twinning EBV (TWIN) for all (ALL) and mature (age 2+ year; MATURE) Polypay and Rambouillet for all animals and for sires with a minimum of 15 daughter litters for double hierarchical generalized linear models (DHGLM) and threshold (liability scale) models.

Model	Trait	Dataset	Polypay		Rambouillet
			All animals	Sires	All animals	Sires
DHGLM	NLB3	ALL	0.59 (0.10)	0.67 (0.12)	0.57 (0.16)	0.72 (0.08)
		MATURE	0.58 (0.10)	0.65 (0.12)	0.56 (0.16)	0.71 (0.07)
DHGLM	vNLB3	ALL	0.45 (0.08)	0.52 (0.10)	0.55 (0.15)	0.70 (0.07)
		MATURE	0.29 (0.07)	0.35 (0.09)	0.53 (0.15)	0.68 (0.07)
DHGLM	NLB	ALL	0.66 (0.10)	0.72 (0.12)	0.59 (0.15)	0.74 (0.07)
		MATURE	0.63 (0.10)	0.68 (0.12)	0.57 (0.16)	0.72 (0.07)
DHGLM	vNLB	ALL	0.65 (0.10)	0.72 (0.12)	0.58 (0.15)	0.72 (0.07)
		MATURE	0.62 (0.09)	0.68 (0.12)	0.55 (0.15)	0.69 (0.07)
Threshold	NLB3	ALL	0.52 (0.10)	0.62 (0.13)	0.55 (0.16)	0.71 (0.08)
		MATURE	0.48 (0.09)	0.56 (0.12)	0.55 (0.15)	0.70 (0.07)
Threshold	NLB	ALL	0.54 (0.09)	0.63 (0.12)	0.54 (0.15)	0.70 (0.08)
		MATURE	0.49 (0.09)	0.57 (0.12)	0.53 (0.16)	0.69 (0.08)
Threshold	TWIN	ALL	0.35 (0.09)	0.44 (0.11)	0.26 (0.09)	0.37 (0.08)
		MATURE	0.49 (0.10)	0.57 (0.13)	0.35 (0.11)	0.48 (0.08)

3.5. Trait Selection and Sire EBV Plots

Due to the generally higher additive genetic variance and heritability estimates of NLB over NLB3 for both breeds, the NLB trait analysed with the DHGLM model was selected as the best option to represent number of lambs born and variation of number of lambs born. To represent twinning rate, the TWIN trait was selected as the most appropriate option for both breeds. The vNLB and TWIN EBV for sires with at least 15 daughter litters were plotted for Polypay (Figure 4a) and Rambouillet (Figure 4b) for both datasets. For the Polypay sires, 37.5% and 9.9% were negative (favourable) for vNLB EBV and positive for TWIN EBV for the ALL and MATURE datasets, respectively, as represented by the upper left quadrant of the plot. For the Rambouillet sires, 27.6% and 32.1% were negative for vNLB EBV and positive for TWIN EBV for the ALL and MATURE datasets, respectively.

FIGURE 4.

Twinning estimated breeding values (TWIN EBV) and number of lambs born dispersion EBV (vNLB) for USSES Polypay (a) and Rambouillet (b) sires with daughters totaling at least 15 litters for the mature (age 2+ year; MATURE) dataset. [Colour figure can be viewed at wileyonlinelibrary.com]

4. Discussion

The ovulation rate at breeding determines the maximum reproductive capacity for each ewe for a given breeding cycle and is lower for peripubertal ewe lambs than mature ewes (Shorten et al. 2013, 2021; Edwards et al. ²⁰¹⁶; Reader and Juengel ²⁰²⁵). Willingham et al. (1986) reported that a one unit increase in the ovulation rate of Rambouillet ewes resulted in 0.52, 0.46 and 0.23 embryos surviving, lambs born and lambs weaned, respectively. Heritability estimates for ovulation rate in the Rambouillet breed range from 0.20 to 0.58 (Waldron and Thomas 1992; Matos et al. ¹⁹⁹⁷). Although heritable, Edwards et al. (2016) reported no successful selection for consistent ovulation rate. Juengel et al. (2013) reported mutations affecting ovulation rate, although only two genes [GDF9 (FecG) and Booroola (FecB)] have a positive impact on ovulation rate in the homozygous state while the others result in sterility. Because the effects on ovulation rate of FecG and FecB differ depending on their presence in the homozygous or heterozygous state, selection for major prolificacy genes would substantially impact variability of NLB. Importantly, functional mutations in fecundity genes have not been identified in US sheep breeds nor have they been introgressed from other breeds in any substantial way (Murphy et al. 2022).

In mature ewes, the fertilization failure rate is 1%–2% (O'Connell et al. ²⁰¹⁶). The majority of embryo loss occurs prior to maternal recognition of pregnancy (around day 13), allowing for rebreeding if the opportunity exists (Shorten et al. 2010; O'Connell et al. ²⁰¹⁶; Reader and Juengel ²⁰²⁵). For peripubertal ewe lambs, the fertilization failure rate is around 10% followed by higher embryo loss than for mature ewes (Edwards et al. 2016; Shorten et al. ²⁰²¹; Reader and Juengel ²⁰²⁵). Embryo loss is 20%–40% for ewes (Reader and Juengel 2025) and is influenced by both the quality of the embryo and the uterine environment provided by the dam. Higher embryo loss for peripubertal ewe lambs has been attributed to reduced ova quality and oviduct function (Quirke and Hanrahan 1977; Edwards et al. ²⁰¹⁶). For Coopworth, Romney, Texel and Perendale sheep in New Zealand, heritability estimates for embryo survival were low and reported as 0.008, 0.0447 and 0.085 for direct, maternal and permanent environment, respectively, suggesting the role of the dam is more influential than that of the embryo (Shorten et al. 2013). For ewes that ovulate two or three ova, the average NLB is 1.7 and 2.2, respectively, indicating more embryonic loss as the number of ova ovulated increases (J. Hanrahan ¹⁹⁸⁰). This associated increase in embryonic loss as the ovulation rate increases was identified by others (Quinlivan et al. 1966; Schoenian and Burfening ¹⁹⁹⁰; Dixon et al. ²⁰⁰⁷). Ewes with multiple embryos were more likely to lose one embryo rather than all (Dixon et al. 2007), where the reduction in NLB would typically go undetected and further contributing to variability in NLB. Both advantageous and deleterious gene mutations for embryo survival have been reported (Juengel et al. 2012, 2016; Edwards et al. ²⁰¹⁶).

Consistent with the reproductive objectives of extensively grazing flocks throughout the world, ideally all ewes would produce twins through an optimized ovulation rate, increased embryo survival and increased lamb survivability (Martin et al. 2024). Production of twin litters among New Zealand Romney, Texel and Composite flocks has typically plateaued at 65% twins with increases in NLB resulting in fewer singles and more triplets (Amer and Bodin 2006; Martin et al. ²⁰²⁴). Genetic selection for an increased proportion of twins and decreased twinning variability has the potential to control all of these underlying contributing traits by indirectly controlling variability in ovulation rate and embryo survival.

Because ewe lambs are still growing, they have a tendency to have fewer NLB than mature ewes (Notter 2000; Kenyon et al. ²⁰¹⁴; Edwards et al. ²⁰¹⁶; Edwards and Juengel ²⁰¹⁷; Pettigrew et al. ²⁰²¹). Causes identified for reduced NLB in peripubertal ewe lambs include a lack of exhibited estrus, reduced ovulation rate, increased fertilization failure and increased embryo loss when compared to mature ewes (Edwards et al. 2016). O'Brien et al. (1996) reported mature oocytes from prepubertal sheep are different developmentally from those from mature ewes and may be associated with metabolic and ultrastructural anomalies. For the USSES Polypay flock, the average NLB for ewe lambs was 1.53 ± 0.55 compared to 2.29 ± 0.75 for mature ewes while the USSES Rambouillet ewes lambs averaged 1.24 ± 0.43 compared to 1.93 ± 0.64 for mature ewes. This confounding led us to compare results from analyses including (ALL) and excluding (MATURE) 1‐year‐old ewes. Exclusion of primiparous ewes from the analyses was reported by Amer and Bodin (2006) and Young (2007) in their twinning rate study. The disadvantage of excluding 1‐year‐old ewes is that it takes at least an additional year for a sire to generate enough daughter litters to evaluate his twinning ability. In the USSES flock, it is also possible for a sire to only be bred to ewe lambs, leaving him unevaluated altogether. However, including 1‐year‐olds with a different level of NLB adds complexity to disentangle the components of this lowly heritable, multifaceted trait.

In the USSES flock, the phenotypic trend for twin litters in the Polypay breed has decreased and for the Rambouillet has not changed over time. Triplet litters have significantly increased for both flocks. Selection within the flock has been effective in producing more lambs but has not realized the objective of producing almost exclusively twin litters. Selection of twin‐born rams as sires is a common practice in the sheep industry, but it has been reported as ineffective by others because the low heritability often masks the true genetic potential for twinning (Amer et al. 1999; Amer and Bodin ²⁰⁰⁶; Young ²⁰⁰⁷; Cottle et al. ²⁰¹⁶). In 2025, the average NLB for the USSES Polypay and Rambouillet was 2.34 ± 0.06 and 2.03 ± 0.04, respectively. Once the flock has met or exceeded an NLB of 2, the focus must shift to decreasing triplets and increasing twins. The Polypay has already exceeded this threshold, with sires with many daughters exhibiting a range of 7%–80% twins. Since the Rambouillet is closer to the threshold, there are sires that range from 30% to 89% twins. Differences for producing twins exist and canalized selection for increased twinning rate should be possible.

Similar to Cottle et al. (2016), who reported NLB heritability estimates of 0.10 ± 0.01 when analysed with a threshold model, our NLB3 and NLB heritability estimates when analysed with a threshold model on the liability scale were 0.094 ± 0.022 to 0.110 ± 0.020 for the Polypay and 0.115 ± 0.016 to 0.151 ± 0.023 for the Rambouillet. Cottle et al. (2016) also reported a heritability estimate based on threshold models for TWIN as 0.02 ± 0.01 and our estimates were in agreement or slightly higher (0.034 ± 0.013 to 0.074 ± 0.014 for Polypay and 0.020 ± 0.013 to 0.042 ± 0.017 for Rambouillet). Using linear methods, Amer and Bodin (2006) reported heritability estimates of 0.04 ± 0.01 to 0.14 ± 0.03 for NLB and 0.01 < 0.01 to 0.10 ± 0.03 for a triplet trait, where triplets were coded as 1 and non‐triplets were coded as 0. SanCristobal‐Gaudy et al. (2001) used Bayesian methods and reported heritability estimates of 0.34 ± 0.03 for NLB and 0.23 ± 0.027 for vNLB. Cottle et al. (2016) used a sire model within DHGLM and reported heritability estimates of 0.17 for NLB and 0.08 for vNLB. For our final selected model and the MATURE dataset, the NLB and vNLB heritability estimates with the DHGLM model were 0.047 ± 0.008 and 0.071 ± 0.011, respectively, for the Polypay and 0.035 ± 0.006 and 0.029 ± 0.012, respectively, for the Rambouillet. While the DHGLM for variance component estimation has been typically used to analyse continuous traits (Sonesson et al. 2013; Vandenplas et al. ²⁰¹³; Madsen et al. ²⁰²⁴) or count data with multiple categories (Sell‐Kubiak et al. ²⁰²²), the methodology was used as described above by Cottle et al. (2016) for litter size in sheep. As with other linear models, the similarity of results from linear and threshold models for categorically recorded traits are well documented and accepted in animal breeding as robust toward departures from normality (Weller et al. 1988; Varona et al. ¹⁹⁹⁹; Ramirez‐Valverde et al. ²⁰⁰¹; Koeck et al. ²⁰¹⁰; Cappelloni et al. ²⁰²²; Hidalgo et al. ²⁰²⁴). The DHGLMF90 software is based on REML, which is generally used to fit linear mixed models. In our analyses, NLB with more classes performed slightly better than NLB3 where triplets and higher‐order litters were combined.

The primary purpose of utilizing a model such as the DHGLM was to identify if there is a genetic basis for environmental variability that could be exploited to select for canalization of twinning rate. We want to simultaneously estimate parameters for the genetics that control the mean trait and those that control the variation when the environment changes (Gutiérrez et al. 2006). Canalization can be defined as the reduction in variability of a trait, and we are specifically interested in selecting for the genetic component of canalization while acknowledging our inability to control the environmental variables outside of controlled experiments (Waddington 1942; Gibson and Wagner ²⁰⁰⁰; Debat and David ²⁰⁰¹). In a multi‐generation divergent selection experiment for litter size in rabbits, Argente et al. (2010) concluded that there was a genetic component to response to environmental variance. A similar conclusion was reached by Gutiérrez et al. (2006) when evaluating mice for litter size, litter weight and birth weight. The GCV_E was described as the ability to evolve or respond to selection (Houle 1992) and was reported as 0.51 by Mulder et al. (2007) when evaluating the SanCristobal‐Gaudy et al. (2001) sheep litter size dataset. Cottle et al. (2016) also reported a GCV_E of 0.50 for their DHGLM model evaluating sheep litter size. Similarly, our GCV_E values were 0.556 ± 0.062 to 0.588 ± 0.051 for Polypay NLB and 0.303 ± 0.078 to 0.409 ± 0.056 for Rambouillet NLB. Other GCV_E values were summarized by Hill and Mulder (2010) and included 0.31 for litter size in pigs (Sorensen and Waagepetersen 2003) and 0.44 for litter size in mice (Gutiérrez et al. 2006). Reports of $h_v^2$ of litter size were also similar to our findings and ranged from 0.026 to 0.048 for pigs (Sorensen and Waagepetersen 2003), rabbits (Ibáñez‐Escriche et al. ²⁰⁰⁸), mice (Gutiérrez et al. 2006) and sheep (SanCristobal‐Gaudy et al. ²⁰⁰¹) while we reported 0.071 ± 0.011 for Polypay and 0.029 ± 0.012 for Rambouillet.

When considering datasets (ALL and MATURE) and traits (NLB and TWIN), the NLB trait is measured the same across datasets, but the expression of the TWIN trait is dependent on the proportion of singles and triplets, since they are both recorded as ‘1’. When using NLB EBV as a selection criterion for increasing twinning rate, the current level of NLB in the flock needs to be taken into consideration in order to determine how much selection pressure to place on the trait. For the TWIN trait, this same consideration is not needed. Therefore, the combination of TWIN analysed using a threshold model and vNLB analysed using a DHGLM model was selected to represent twinning rate.

For the Polypay breed, when comparing the ALL and MATURE datasets for the NLB traits and TWIN trait, only the TWIN heritability estimate was significantly higher for the MATURE dataset than the ALL dataset. For the Rambouillet, the heritability estimates were not significantly different although the NLB mean trait and TWIN favoured the MATURE dataset. Accuracies for all animals and sires were not significantly different between datasets for either breed but were higher for TWIN for the MATURE datasets over the ALL datasets for both breeds. The final dataset and traits to represent canalization of twinning rate for both breeds were vNLB analysed with a DHGLM model and TWIN analysed with a threshold model using the MATURE dataset. The correlations of EBV between these two traits were 0.85 ± 0.02 for the Polypay and −0.31 ± 0.01 for the Rambouillet.

Once the TWIN and vNLB traits are implemented to represent twinning rate in the USSES Polypay and Rambouillet flocks, further refinement should be considered, particularly as we move toward implementation on a national scale. Sheep Improvement Limited in New Zealand included a twinning rate EBV in their national evaluation (Young 2007), but has since moved toward Capped Reproduction (Amer and Quinton 2017; Newman ²⁰¹⁷), which does not directly select for twinning rate, but selects against excessive triplets. Additional considerations for trait refinement include fitting a sire effect, evaluating a multi‐trait model including NLB and TWIN and their associated dispersions, and removing lambs that were dead at birth from the NLB count.

Before fully committing to the twinning‐only model, it is worth considering the option to improve the ability to successfully raise triplets. In the USSES flock, it was determined that the lamb mortality overhead among triplet litters was 3.75 dead lambs for every additional lamb weaned, making the rearing of triplets a considerable animal welfare concern. Further, the ewes that weaned triplets did not wean more kilograms of lamb than ewes that weaned twins (Notter et al. 2018). For sheep producers who have found cost‐effective methods to artificially rear lambs in a nursery setting or other arrangement, selection for twinning may not be necessary. An additional consideration is selection for an increased number of functional teats to support less competition among triplet lambs, as was explored in previous years (Davies 1988; Maijala and Kyle ¹⁹⁸⁸).

5. Conclusions

Based on the available literature, this is the first evaluation of twinning rate in US sheep breeds and the first international analyses in almost a decade. Yet, sheep breeders indicate a strong desire to achieve an economic optimum of twin litters. To meet this need, we have estimated variance components for traits associated with twinning rate and identified vNLB analysed with a DHGLM model and TWIN analysed with a threshold model as the recommended traits to best meet the breeding objective of increased twins and canalization of twin litters. Rams have been identified that are both positive for TWIN and negative for vNLB, which are expected to improve twinning rate in the USSES Polypay and Rambouillet flocks. Based on the economic relevance of this trait, implementation on a national level is warranted.

Author Contributions

C.S.W.: conceptualization, formal analyses, interpretation of data, visualization, writing – original draft, writing – review and editing; L.F.B.: conceptualization, interpretation of data, writing – review and editing; J.B.T.: resources, writing – review and editing. All authors read, revised and approved the final manuscript.

Funding

The authors have nothing to report.

Ethics Statement

The USSES Institutional Animal Care and Use Committee (IACUC) approved all husbandry practices used in this study.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data presented in this study are available upon reasonable request from the corresponding author.