Genetic Correlations between Days to Calving across Joinings and Lactation Status in a Tropically Adapted Composite Beef Herd

Abstract

Female fertility is essential to any beef breeding program. However, little genetic gain has been made due to long generation intervals and low levels of phenotyping. Days to calving (DC) is a fertility trait that may provide genetic gain and lead to an increased weaning rate. Genetic parameters and correlations were estimated and compared for DC across multiple joinings (first, second and third+) and lactation status (lactating and non-lactating) for a tropical composite cattle population where cattle were first mated as yearlings. The genetic correlation between first joining DC and mature joining DC (third+) was moderate–high (0.55–0.83). DC was uncorrelated between multiparous lactating and non-lactating cows (r_G = −0.10). Mature joining DC was more strongly correlated with second joining lactating DC (0.41–0.69) than with second joining non-lactating DC (−0.14 to −0.16). Thus, first joining DC, second joining DC and mature joining DC should be treated as different traits to maximise genetic gain. Further, for multi-parous cows, lactating and non-lactating DC should be treated as different traits. Three traits were developed to report back to the breeding programs to maximise genetic gain: the first joining days to calving, the second joining days to calving lactating and mature days to calving lactating.

1. Introduction

Fertility traits are often treated with low priority in beef breeding programs worldwide, as many female fertility traits have a low heritability, are difficult to measure and the long generation interval of cattle dissuade phenotype recording [1]. Despite this, in Northern Australia female reproductive performance has been identified as a major economic issue in beef production [1,2]. An Australian beef industry study reported that an increase in weaning rate of 5% for tropically adapted cattle would lead to a 20% increase in average annual net profit, identifying fertility as a key performance driver in northern production systems [2].

In Northern Australia, low reproductive performance tends to be a consequence of late puberty attainment in heifers and extended post-partum anoestrous periods in cows [3,4]; these issues are particularly predominant in lactating first-calf heifers [5]. Cattle are required to adapt to the extreme heat, disease, pests, varying nutrition qualities and quantities as well as be reproductively successful [3,4,5]. These factors highlight the difficultly in improving reproductive performance in Northern Australia; however, ignoring fertility traits is extremely detrimental to any breeding program [6,7,8].

Days to calving is defined as the number of days from the start of joining (the day the bull goes into the same paddock) to subsequent calving, as described by Meyer et al. [9]. Days to calving is a trait that can be measured multiple times over a cow’s lifetime (each joining) and evaluated as a repeated measure trait [10]. A joining includes any cow given an opportunity to conceive over a period from the bull-in date to the bull-out date. Days to calving is often treated as a repeated trait; however, due to the complexity of the trait, earlier in life joining’s should possibly be evaluated separately to mature joinings due to different biological mechanisms.

Days to calving is a potential female fertility trait that can be measured to account for the attainment of puberty and extended post-partum anoestrous periods. Days to calving is a composite trait that is associated with age of puberty in heifers, measuring dam effects such as post-partum anoestrus, conception rate, gestation length and how early they conceive [11,12]. Days to calving has previously been reported to have a high correlation with lifetime weaning rate in both Bos taurus taurus and Bos taurus indicus breeds, an essential economic driver in breeding programs [1,13]. Incorporating days to calving in a breeding program has the potential to improve female fertility while maintaining adaption to the harsh environment of Northern Australia.

The present study investigates days to calving to enable the greatest genetic gain in breeding programs. This was done through testing different penalty values placed on non-pregnant cows, investigating the effect of joining and lactation status (lactating and non-lactating) and finally using selection index theory was to evaluate the best way to report days to calving to breeding programs. The study models the days to calving traits to estimate variance components, breeding values, response to selection and genetic and phenotypic correlations.

2. Materials and Methods

2.1. Breeding Program

Popplewell Composites, a bull breeding program focused on breeding composite bulls adapted to the semi-arid tropics in Northern Australia, provided the dataset. This breeding program is predominantly situated in southeast Queensland, with bulls sold across Northern Australia. The breeding program started in 2008 and involved four main breeds: Angus, Senepol, Africander and Brahman, to produce four composite products, Transition, Pathfinder, Eureka and Indiplus. Popplewell composites use the four composite products to change existing cow bases in commercial herds from their original breeds (often high content Brahmans) into composite herds of a consistent breed type. The main objective of Popplewell composites is to increase weaning rate through retained heterosis and intense selection pressure for reduced age at puberty and post-partum anoestrus interval. In addition, there is an emphasis on good growth, carcass traits and naturally polled red cattle that are well adapted for tropical environments such as Northern Australia.

2.2. Genotype Data

Genotype data were provided from 2613 composite cattle. Genotyping was conducted over the breeding program’s duration, resulting in multiple SNP chips being used (Illumina 777k, Illumina GGPLD V3 30K, Illumina GGPLD V4 30K, Illumina ICB 50K and Weatherby’s Scientific Versa50K). A total of 10,830 SNPs overlapped on all SNP chips. All genotypes were imputed from the common SNPs to GGPLD30K (27,755 SNPs) using FImpute 2.1 [14]. The genotype data were then filtered, and all SNPs with <1% minor allele frequency and duplicate animals were removed. After filtering, there were 2609 animals and 27,638 SNPs for constructing the genomic relationship matrix (GRM; see below). The GRM was built using VanRaden’s first method [15].

The heterozygosity fraction (Het) was calculated on imputed data, as the proportion (%) of heterozygous SNPs for each individual animal. Heterozygosity fraction is an indicator of heterosis, which is especially important in a composite population. All models included the heterozygosity fraction as a co-variate to account for heterozygosity when estimating breeding values [16].

2.3. Phenotype Data

Days to calving is the time from the day the bull goes in with the cow to the day the cow gives birth [9]. Days to calving includes every joining for a cow over its lifetime, thus providing multiple records. Days to calving was estimated using the bull-in date, bull-out date (i.e., in the same paddock as cow), pregnancy test results (fetal age) and calf date of birth. Typically, days to calving is treated as one trait, including all joinings; however, the dataset used herein routinely evaluates heifer (first joining) days to calving separately from all other joinings.

There were 2242 days to calving records from 903 unique animals. Of the 903 unique animals, there was 366 animals that had a first, second and third joining. The number of records and summary statistics at each joining are presented (

Table 1. Summary (min, max, mean, SD) of adjusted ¹ days to calving over joinings.

Joining Number	Total No. of Cows	No. of Lactating Cows	No of Non-Lactating Cows	No. of Empty 2 Cows	No. of Pregnant Cows	3 Min days	4 Max days	Mean Days	5 SD Days
1	649	-	-	214	435	269	409	340.0	38.0
2 6	636	326	287	472	164	271	406	335.0	38.5
3	494	406	88	325	169	260	409	343.6	38.0
4	249	225	24	166	83	272	400	340.8	36.9
5+	214	197	17	166	48	283	400	332.2	34.4

¹ Adjusted phenotypes have a penalty of 31 days added for empty cows. ² Empty cows refers to non-pregnant cows. ³ Min is the minimum. ⁴ Max is the maximum. ⁵ SD is the standard deviation. ⁶ There are 23 animals with no lactation status for second joining.

). The cattle are first joined at 12–15 months of age (12 months earlier than most tropically adapted cattle programs), with subsequent joinings every year. Pregnancy results represent if the cow got pregnant during the joining period; however, lactation status represents if the cow weaned a calf during the mating period.

Correcting days to calving values by adding a constant penalty (21 days = 1 oestrus cycle) to cows that have not calved is standard practice [10]. However, a longer period was used herein to allow for low-quality sub-tropical pasture as the breeder felt it was too “generous” to assume open heifers and cows would have conceived in a single additional cycle. Those animals that did not conceive during the joining period received an adjusted value of 32 days (1.5 oestrus cycles) added to the maximum value of the animals joining management group. This penalty assumes they would have conceived in the next cycle and a half if given the opportunity. The impact of the penalty was tested herein, with several different penalty values investigated. These values were no-penalty, 21, 32, 43, 63 and 252 days. The breeding values, variance components, heritability and heterozygosity coefficient slope were estimated and compared.

Contemporary groups were defined as management groups plus birth groups. Throughout their lifetime, management groups were recorded. The birth group was defined by year and time of birth, early (1 June to the 4 September, 75% of cattle), mid (5 September to the 30 November, 6% of cattle) and late (1 December to the end of calving season, 19% of cattle). Breed group was partially confounded with contemporary group.

2.4. Genomic Model

A linear mixed model to estimate breeding values can be written as,

$$\mathit{y}=\mathit{X}\mathit{\beta }+{\mathit{Z}}_{\mathit{a}}{\mathit{u}}_{\mathit{a}}+{\mathit{Z}}_{\mathit{r}}{\mathit{u}}_{\mathit{r}}+\mathit{e}$$

where $\mathit{y}$ is the vector of phenotypic values for days to calving; $\mathit{\beta }$ represents fixed effects with the design matrix $\mathit{X}$; the fixed effects included in all models are contemporary group, joining number, lactation status, days to calving management group and heterozygosity fraction (fit as a linear co-variate); ${\mathit{Z}}_{\mathit{a}}$ is the design matrix for additive effects ${\mathit{u}}_{\mathit{a}}$, with ${\mathit{u}}_{\mathit{a}}~\mathit{N}\left(\mathbf{0},{\sigma }_A^2{\mathit{G}}_{\mathit{A}}\right)$; ${\mathit{Z}}_{\mathit{r}}$ is the design matrix for the repeated environmental effects ${\mathit{u}}_{\mathit{r}}$ and $\mathit{e}$ is the residual effects.

The genomic relationship matrix (GRM) is calculated as follows [15]:

$${\mathit{G}}_{\mathit{A}}=\frac{\mathit{Z}\mathit{Z}\prime }{2{{\displaystyle \sum }}_{i=1}^m{p}_i{q}_i}$$

where the matrix $\mathit{Z}$ has dimensions of $n\mathrm{x}m$, $n$ is the number of individuals and $m$ is the number of markers. Matrix $\mathit{Z}$ has the elements $z_{ij}$ for the $j^{th}$ individual at the $i^{th}$ marker is,

$$z_{ij}=\left\{\begin{array}{c}\left(2-2p_i\right)\\ \left(1-2p_i\right)\\ -2p_i\end{array} for Genotypes \left\{\begin{array}{c}AA\\ AB\\ BB\end{array}\right.\right.$$

and $p_i$ is the allele frequency of the most frequent (major) allele at Marker $i$, and $q_i=1-p_i$

2.5. Days to Calving Models

Days to calving was modelled to estimate the variance components, heritability, repeatability and best linear unbiased predictions (BLUPs) or estimated breeding values (EBVs). Overall days to calving (DC) was run as a repeatability model to adjust for multiple records on the same cow over different years. Two models (

Table 2. Description of models run for days to calving.

Model	Description	Fixed	Random 1
Model_1	Overall days to calving, with a separate variance component for five joining categories	Join management group, heterozygosity fraction and Contemporary group:DPP	diag(Joining Number):vm(ID, GRM)
Model_2	Overall days to calving, fitted models with a separate variance component for each joining but estimation of the correlation between two joining at a time (due to computational limitations) with a total of 15 components	Join management group, heterozygosity fraction and Contemporary group:DPP	us(Joining Number):vm(ID, GRM)

¹ describes ASReml-R model terms, diag() = diagonal variance model, vm() = known variance structure allows the use of either a relationship or inverse relationship matrix, us() = unstructured general covariance matrix.

) were fitted in RStudio version 4.1.1 [17] using the package ASReml-R v4 [18]. A description of each model are listed in Table 2. Days post-partum (DPP) was calculated as the number of days between bull-in date and last calf date of birth, and it was included in the model to be compared within the contemporary group.

The differences and similarities between the joining numbers was explored. Two models were run, Model_1 to estimate separate variance components for each joining, assuming joining numbers were uncorrelated with each other and Model_2 to estimate separate variance components between each joining number and estimate the correlation between each joining number. In Model_2 the correlation between joining numbers were estimated two at a time due to computational limitations. These models were used to calculate the genetic correlation between joining numbers.

As, by definition, maiden joinings can only have a non-lactating lactation status, a further analysis was run with second joining onwards (DC2+), splitting up lactating (DC2+_Wet) and non-lactating (DC2+_Dry) cattle to estimate the genetic correlation between lactating status. The fixed and random effects for these models are listed in

Table 3. Description of the fixed effects included first joining days to calving (DC1), second joining days to calving (DC2) and mature joining days to calving (DC3+).

Trait	Description	Number of Records	Number of Contemporary Groups	Fixed Effects	Random Effects
DC1	First joining days to calving	649	45	Birth group, Join group, Dam age, Het, contemporary group	GRM
DC2	Second joining days to calving with all records (wet 1 and dry 2)	636	54	Birth group, Dam age, Het, contemporary group:DPP:Lactation Status	GRM
DC2_Dry	Second joining days to calving with dry 2 records only	287	44	Birth group, Dam age, Het, contemporary group:DPP	GRM
DC2_Wet	Second joining days to calving with wet 1 records only	326	45	Birth group, Dam age, Het, contemporary group:DPP	GRM
DC2+	Days to calving that include records from the second joining, third joining, fourth joining and joining five + with both wet 1 and dry 2 records	1534	213	Joining number, Het, contemporary group:DPP:Lactation Status	GRM, ID
DC2+_Dry	Days to calving that include records from the second joining, third joining, fourth joining and joining five + with dry 2 records only	431	82	Joining number, Het, contemporary group:DPP	GRM, ID
DC2+_Wet	Days to calving that include records from the second joining, third joining, fourth joining and joining five + with wet 1 records only	1103	189	Joining number, Het, contemporary group:DPP	GRM, ID
DC3+	Days to calving that include records from the third joining, fourth joining and joining five + with both wet 1 and dry 2 records	898	162	Joining number, Het, contemporary group:DPP:Lactation Status	GRM, ID
DC3+_Wet	Days to calving that include records from the third joining, fourth joining and joining five + with wet 1 records only	796	143	Joining number, Het, contemporary group:DPP	GRM, ID
DC	All days to calving records, including both wet 1 and dry 2 records	2242	270	Joining number, join group, Hey, contemporary group:DPP	GRM, ID

ID is the unique animal tag, GRM is the genomic relationship matrix. ¹ Wet refers to lactating cows. ² Dry refers to non-lactating cows.

.

2.6. Univariate Models

Further univariate models were run based on the results from the above Days to calving models; these included first joining days to calving (DC1), second joining days to calving (DC2) and mature joinings (J3+) days to calving (DC3+). These models were further split into lactating (wet) and non-lactating (dry) for DC2, DC2+ and DC3+. Variance components, heritability and estimated breeding values were estimated for all traits. The fixed and random effects are listed in Table 3, and the GRM was included as a random effect for all models. For repeatability models, a unique animal tag (ID) was fit alongside the genomic relationship matrix as a random term to account for multiple records on the same animals, estimating the repeatable environmental variance in addition to the residual.

2.7. Response to Selection

A simple breeding objective of five consecutive pregnancies was assumed and selection index theory used to test what trait combination would maximise response. The index followed standard selection index theory [19,20], and three matrices were calculated ($\mathit{P}, \mathit{G}, \mathit{C}$). The $\mathit{P}$ matrix is a square matrix of phenotypic (co)variances among the traits used as selection criteria, in this instance each individual joining was used. The $\mathit{G}$ matrix consists of genetic (co)variances between the selection criteria and breeding objective. The $\mathit{C}$ matrix is a square matrix with genetic (co)variance among the traits in the breeding objective. The selection index for three different scenarios were calculated (

Table 4. Description of the different scenarios used in the index (description in Table 3).

Index One	Index Two	Index Three
DC	DC1	DC1
	DC2+_Wet	DC2_Wet
		DC3+_Wet

). The (co)variance estimates for each index were estimated as a univariate model (index one), bivariate model (index two) and tri-variate model (index three).

The standard deviation of the breeding objective was calculated by,

$${\sigma }_H=\sqrt{\mathit{a}\prime \mathit{C}\mathit{a}}$$

where $\mathit{a}$ is a vector of five economic weights, in these calculations the weighting used was dependent on weaning rate over five joinings. For example, in Index three the DC1 value was 0.2, the DC2_Wet value was 0.2, and the DC3+ value was 0.6 for $\mathit{a}$, representing how many calves can be produced in each trait, with the aim for five calves from five joinings.

A vector of index weights ($\mathit{b}$) was calculated by,

$$\mathit{b}={\mathit{P}}^{-1}\mathit{G}\mathit{a}$$

The standard deviation of the index was calculated by,

$${\sigma }_I=\sqrt{\mathit{b}\prime \mathit{P}\mathit{b}}$$

The accuracy of selection was calculated by,

$$r_{I,H}=\frac{{\sigma }_I}{{\sigma }_H}$$

The selection response was calculated for each trait reported. The response was calculated in two ways, first for the individual traits by the additive genetic standard deviation multiplied by accuracy (${\sigma }_A\sqrt{h^2}$), which is equivalent to the accuracy based on a single measure. Second for the index values, the standard deviation of the breeding objective multiplied by the accuracy of selection (${\sigma }_H{r}_{I,H}$). The response calculations are over one generation with an assumed selection intensity of one and with units of days/generation.

2.8. Multi-Variate Models

Multi-variate models were run between the different days to calving traits to estimate genetic and phenotypic correlation. DC2 and DC3+ were further partitioned into lactating and non-lactating. An average DC3+ (DC3+_Ave) was used to estimate phenotypic correlations between DC3+ and other days to calving traits. The mixed model for bivariate is now written as,

$$\mathit{y}={\mathit{X}}^{*}\mathit{b}+{\mathit{Z}}_{\mathit{a}}^{*}{\mathit{u}}_{\mathit{a}}+{\mathit{Z}}_{\mathit{r}}{\mathit{u}}_{\mathit{r}}+\mathit{e}$$

where $\mathit{y}={\left({\mathit{y}}_{\mathbf{1}}^{\prime },{\mathit{y}}_{\mathbf{2}}^{\prime }\right)}^{\prime },$ is the combined vector of data between two traits; $\mathit{b}={\left({\mathit{b}}_{\mathbf{1}}^{\prime },{\mathit{b}}_{\mathbf{2}}^{\prime }\right)}^{\prime }$ is the 2m x 1 vector of fixed effect with ${\mathit{X}}^{*}={\mathit{I}}_{\mathbf{2}}\otimes \mathit{X}$ the associated design matrix; ${\mathit{u}}_{\mathit{a}}={\left({\mathit{u}}_1^{\prime },{\mathit{u}}_2^{\prime }\right)}^{\prime }$ is the 2n x 1 vector of random effects with ${\mathit{Z}}_{\mathit{a}}^{*}={\mathit{I}}_{\mathbf{2}}\otimes \mathit{Z}$ the associated design matrix, ${\mathit{Z}}_{\mathit{r}}$ is the design matrix for the repeated environmental effects ${\mathit{u}}_{\mathit{r}}$ and $\mathit{e}={\left({\mathit{e}}_{\mathbf{1}}^{\prime },{\mathit{e}}_{\mathbf{2}}^{\prime }\right)}^{\prime }$ the vector of residual variance, where $\prime$ is the transpose. The variance components estimates from this multi-variate an additive genetic variance (${\sigma }_{A1}^2$, ${\sigma }_{A2}^2)$ for each trait, an additive covariance between two traits $\left({\sigma }_{A12}^2\right)$, one repeatability variance (${\sigma }_R^2$), a separate residual variances (${\sigma }_{\epsilon 1}^2,{\sigma }_{\epsilon 2}^2$) for each trait and the correlation between residual variances (${\sigma }_{\epsilon 12}^2)$. All bivariate models were fitted for all traits utilising a genomic relationship matrix with heritability, genetic and phenotypic correlations estimated.

3. Results

3.1. Effect of Changing the Penalty Value of Days to Calving

Varying penalty values were assessed for DC1 and DC2+ to determine how the penalty value affected the variance components, breeding values and heritability. For DC1, the heritability increased by including the non-pregnant animals across all the penalty values used. The variance components and the absolute heterozygosity coefficients increased as the penalty increased; however, there was little change in the heritability, which is a ratio of variances (

Table 5. Variance Components, heritability and heterozygosity (het) coefficient of DC1 with different penalty values with standard error in parenthesis.

Model	Number of Records	Additive Variance	Residual Variance	Heritability	Het Coefficient (Day/%)
No penalty	435	25.9 (44)	394 (47)	0.06 (0.10)	−0.29
21 Days	634	195 (95)	827 (86)	0.19 (0.09)	−1.59
32 Days	634	257 (121)	1049 (110)	0.20 (0.09)	−1.90
43 Days	634	309 (150)	1290 (136)	0.19 (0.09)	−2.16
63 Days	634	446 (221)	1903 (201)	0.19 (0.09)	−2.73
252 Days	634	2693 (1552)	141,213 (1457)	0.16 (0.09)	−7.93

). A one percent increase in heterozygosity results in fewer days to calving, therefore a negative heterozygosity fraction is advantageous.

Similar results were observed for DC2+; as the penalty value increased, total variance and the absolute heterozygosity coefficient increased. When no penalty was applied, the heritability was 0.17, compared with 0.09 when a 21-day penalty was applied. The heritability for DC2+ seems to have a direct scale effect, resulting in slight decreases as the penalty value increases (

Table 6. Variance Components, heritability and heterozygosity (Het) coefficient of DC2+ (including J2) with different penalty values with standard error in parenthesis.

Model	Number Records	Additive Variance	Repeatability Variance	Residual Variance	Heritability	Het Coefficient (Day/%)
No penalty	1122	78 (31)	53 (30)	318 (23)	0.17 (0.06)	−0.62
21 Days	1550	81 (30)	0 1	783 (37)	0.09 (0.03)	−1.81
32 Days	1550	86 (36)	0 1	998 (46)	0.08 (0.03)	−2.05
43 Days	1550	92 (48)	0 1	1227 (68)	0.07 (0.04)	−2.26
63 Days	1550	106 (65)	0 1	1810 (99)	0.06 (0.03)	−2.71
252 Days	1550	371 (333)	0 1	13,267 (584)	0.03 (0.02)	−6.87

¹ Converged to zero.

). The correlation between the BLUPs was high (>0.99; data not shown) for both DC1 and DC2+ for the different penalty values, indicating no re-ranking of the animals.

3.2. Variance Components and Genetic Correlation of the Different Joining Number

When estimating the variance for each joining separately (Model 1), the first joining had the largest variance of 563 days squared and joining 5+ had the lowest variance of 104 days squared (

Table 7. Genetic variance component of each joining for Model_1 model with standard error in parenthesis.

Joining Number	Variance
1	563 (107)
2	280 (79)
3	215 (77)
4	125 (98)
5+	104 (104)

). The estimated genetic variance decreased with joining number.

Model_2 (Table 2) was run to estimate the genetic correlation and covariances between joinings with an unstructured covariance matrix. There were many variance components (15), estimated with large standard errors. The correlation between J1 and J2 was −0.12, which is extremely low (

Table 8. Correlation matrix for days to calving with genetic correlation below for each joining number with standard error in parenthesis.

	1	2	3	4	5+
1	1
2	−0.12 (0.19)	1
3	0.73 (0.17)	0.22 (0.25)	1
4	0.36 (0.35)	−0.11 (0.39)	0.79 (0.37)	1
5+	0.64 (0.39)	−0.64 (0.54)	−0.03 (0.61)	0.99 (0.62)	1

). However, correlations between J1 and J3, J4 and J5+ were higher at 0.73, 0.36 and 0.64, respectively. The correlation between J2 and J3 was low (0.22), and the correlation between J2 and J4 and J5+ was negative, with values of −0.11 and −0.64, respectively. The correlations between J3, J4 and J5+ were all high, except for J3 and J5, which was −0.03 correlation. The correlation matrix was not positive definite, possibly due to the lower number of records for J4 and J5+. The large standard errors on the estimates of correlations were due to the lower number of records in the older ages (4 and 5+). Based on the high correlation between later joining, the decision was made to combine and treat them as a single trait (DC3+), reducing standard error and maximise response to selection.

3.3. Days to Calving Separated by Lactation Status

A further analysis was run, splitting days to calving into individual traits based on lactation status for cows on their second and subsequent lactations. There were 1103 records for DC2+_Wet and 431 records for DC2+_Dry. The heritability of DC2+_Dry and DC2+_Wet which are mature joining from joining 2 onward and non-lactating and lactating individuals respectively had similar heritability estimates of 0.22 and 0.17 (

Table 9. Variance components, heritability and heterozygosity coefficient of days to calving (J2+) split into lactation status (lactating/non-lactating) with standard errors in parenthesis.

Models	Number of Records	Additive Variance	Repeatability Variance	Residual Variance	Heritability	Repeatability 1	Het Coefficient	Response to Selection
DC2+_Dry	431	217 (90)	NA	775 (88)	0.22 (0.09)	0	−2.38	6.92
DC2+_Wet	1103	144 (53)	166 (58)	538 (42)	0.17 (0.06)	0.37 (0.07)	−2.80	4.92

¹ Repeatability is the additive and repeatable variance divided by the total variance.

). The residual variance was smaller for DC2+_Wet at (537 days squared) then DC2_Dry (775 days squared). The repeatability of DC2+_Dry could not be estimated as non-lactating cows were not retained for more than two joinings, whereas DC2+_Wet had a repeatability estimate of 0.37. The genetic correlation between DC2+_Dry and DC2+_Wet was −0.10. The correlation between BLUPs was 0.32 (Figure 1). As expected, the animals with phenotypes re-ranked more than those animals without phenotypes (Figure 1).

3.4. Univariate Models of Days to Calving

The heritability for the seven different days to calving traits is presented (

Table 10. Variance components, repeatability, heritability and heterozygosity (Het) coefficient of days to calving traits with standard error in parenthesis.

Traits	Number	Repeatability Variance	Additive Variance	Residual Variance	Repeatability	Heritability	Het Coefficient	Response to Selection (Days/Gen)
DC	2184	87 (43)	124 (43)	811 (38)	0.20 (0.05)	0.12 (0.04)	−2.45	4.0
DC1	634	-	257 (122)	1049 (110)	-	0.20 (0.09)	−1.90	7.2
DC2	621	-	192 (90)	886 (89)	-	0.18 (0.08)	−1.07	5.8
DC2_Wet	326	-	353 (180)	551 (143)	-	0.39 (0.12)	−0.97	11.8
DC2_Dry	287	-	211 (124)	736 (117)	-	0.22 (0.18)	−2.40	6.8
DC3+	929	101 (73)	264 (78)	714 (56)	0.34 (0.08)	0.25 (0.06)	−4.13	8.1
DC3+_Wet	841	159 (68)	150 (64)	539 (47)	0.36 (0.08)	0.17 (0.08)	−3.68	5.0

). DC1 had a heritability of 0.20, DC2 had a heritability of 0.18, and DC3+ had a heritability of 0.25. The repeatability for DC3+ is 0.34. DC1 and DC2 do not have repeated records, so they cannot have a repeatability estimate. The heterozygosity coefficient was the lowest for DC2 (−1.07 days/%), with DC3+ having the highest (−4.13 days/%) and the DC1 heterozygosity coefficient being −1.90 days/%. DC1 had the highest residual variance of 1049.22 days² and a total variance of 1306.74 days². Further models were run with lactating and non-lactating cattle being separated. DC2_Dry heritability 0.22, which is similar to DC2. However, DC2_Wet had a higher heritability (0.39). Conversely, the heterozygosity coefficient in DC2_Dry was higher at −2.40 days/%, whereas DC2_Wet was −0.97 days/%.

3.5. Response to Selection

The response to selection was calculated for each day to calving trait. The response was highest for second joining days to calving lactating (DC2_wet) at 11.84 days/generation (Table 10), indicating that selection for DC2_Wet in a breeding program will have the biggest impact compared with every other trait. The second highest response was for joining one days to calving (DC1) of 7.21 days/generation (Table 10). The lowest response to selection was for days to calving including all joinings (DC) of 4.00 days/generation. The response to selection for DC3+ was 8.13 days/generation, and DC3+_Wet was 5.03 days/generation (Table 10). The response for DC2+_Wet was 4.92 days/generation, which was lower than DC3+_Wet (Table 9).

Three selection indexes were calculated for three different scenarios (Table 4) using index selection theory. The variance components used for Index one are the DC variance components in Table 10; index two used variance components in

Table 11. Variance components estimates used to calculate Index two.

	DC1	DC2+_Wet
DC1	279	-
DC2+_Wet	115	156

and index three used variance components in

Table 12. Variance components estimates used to calculate Index three.

	DC1	DC2_Wet	DC3+_Wet
DC1	332	-	-
DC2_Wet	27	366	-
DC3+_Wet	244	169	250

. Index three had the highest accuracy and response to selection indicating this would be the best scenario to use (

Table 13. Index values were calculated for three different scenarios using index theory, including breeding objective, the variance of the index, accuracy and response to selection. The response units are days per generation.

	Index One	Index Two	Index Three
Standard deviation of the breeding objective	11.7	12.2	14.8
Standard deviation of the index	5.9	6.4	9.5
Accuracy	0.50	0.52	0.64
Response to selection (days/generation)	2.97	3.32	6.08

Index scenarios are described in Table 4. Variance components used for index calculations can be found in Table 10 for index one, Table 11 for index two and Table 12 for index three.

).

The effect of additional records was investigated (Figure 2), demonstrating that more records increases accuracy. Using the indexes, showed that treating days to calving as three traits (DC1, DC2_Wet and DC3_Wet) results in the greatest response of 6.08 (index three), with little difference between response for index one and index two (Table 13).

3.6. Bivariate Models for Days to Calving

The genetic correlation between DC1 and DC2 was only −0.06, whereas DC1 had a much higher genetic correlation with DC3+ of 0.83 (

Table 14. Correlations between days to calving traits. Genetic correlations below and phenotypic correlations above the diagonal with standard errors in parenthesis.

	DC1	DC2	DC2_Dry	DC2_Wet	DC3+	DC3+_Wet	DC3+_Ave	DC3+_Ave_Wet
DC1	-	−0.22 (0.07)	−0.33 (0.11)	−0.04 (0.10)	NA	NA	0.34 (0.06)	0.31 (0.06)
DC2	−0.06 (0.33)	-	NA	NA	NA	NA	−0.17 (0.06)	−0.03 (0.07)
DC2_Dry	0.13 (0.48)	NA	-	NA	NA	NA	−0.28 (0.07)	−0.23 (0.08)
DC2_Wet	−0.42 (0.37)	NA	NA	-	NA	NA	0.07 (0.10)	0.19 (0.10)
DC3+	0.83 (0.20)	−0.04 (0.24)	−0.16 (0.25)	0.41 (0.29)	-	NA	NA	NA
DC3+_Wet	0.66 (0.26)	−0.16 (0.27)	−0.14 (0.26)	0.69 (0.33)	NA	-	NA	NA
DC3+_Ave	0.57 (0.29)	0.27 (0.32)	−0.10 (0.37)	0.70 (0.34)	NA	NA	-	NA
DC3+_Ave_Wet	0.32 (0.36)	0.46 (0.32)	0.32 (0.40)	0.55 (0.35)	NA	NA	NA	-

). However, when DC2 was split based on lactation status (lactating or non-lactating), there was a stronger positive correlation of 0.13 between DC1 and DC2_Dry. Conversely, DC2_Wet and DC1 had a large negative genetic correlation of −0.42. Similar changes in genetic correlation occurred when DC3+ was spilt based on lactation status, with the genetic correlation being reduced for DC1 and DC3+_Wet to 0.65. There were insufficient DC3+_Dry records to be able to estimate any genetic correlations. The genetic correlation between DC2 and DC3+ was −0.17. However, when DC2 was split by lactation status, the genetic correlation between DC2_Dry and DC3+ was −0.16, but the genetic correlation was much higher for DC2_Wet at 0.41. The genetic correlation was further increased for DC2_Wet and DC3+_Wet at 0.69. An average of DC3+ was used to calculate phenotypic correlations; the trends were similar to genetic correlations (Table 14). The standard errors for the correlation in the bivariate analysis ranged from 0.20 to 0.48 (Table 14), despite that large standard errors for some DC traits particular between DC1 and DC2_Dry, of the important traits which are DC1, DC2_Wet and DC3+_Wet the standard errors are comparable to previous studies estimates [1,21,22].

3.7. Days to Calving Correlations between Final Traits (Tri-Variate Model)

A final model was run between the traits recommended for breeding programs as a tri-variate model between the final three traits: DC1, DC2_Wet and DC3+_Wet. The genetic correlation between DC1 and DC3+_Wet was 0.85 (

Table 15. Correlation matrix of days to calving traits to be utilised in a breeding program run as a tri-variate. Genetic correlations (below) and heritability estimates (diagonal) with standard error in parenthesis.

	DC1	DC2_Wet	DC3+_Wet
DC1	0.25 (0.09)
DC2_Wet	0.08 (0.27)	0.40 (0.17)
DC3+_Wet	0.85 (0.18)	0.56 (0.25)	0.30 (0.06)

), which is higher than when it was modelled as a bivariate (0.66, Table 14). Similarly, the genetic correlation between DC1 and DC2_Wet in the multi-variate was 0.08 (Table 15), in contrast to the bivariate model (−0.42, Table 14). The genetic correlation between DC2_Wet and DC3+_Wet was 0.56 (Table 15), similar to the bivariate analysis (Table 14). The heritability estimates for the multi-variate analysis were 0.25, 0.40 and 0.30 for DC1, DC2_Wet and DC3+, respectively (Table 15). All heritability estimates from the multi-variate analysis were higher than the univariate analysis (Table 10). A comparison between BLUPs was made between the three traits (DC1, DC2_Wet and DC3+_Wet) and DC (days to calving, including all joinings) (Figure 3). The correlation between DC1 and DC2_Wet BLUPs, was 0.04, indicating that these two traits are uncorrelated and do not have any impact on each other. The correlation between DC1 and DC3+_Wet BLUPs was 0.18, indicating significant re-ranking among the two traits. The correlation between BLUPs was higher between DC1 and DC at 0.55, with the plot showing much less re-ranking than DC3+_Wet BLUPs. The correlation between DC2_Wet and DC3+_Wet was 0.70, with minimal re-ranking of the BLUPs. DC2_Wet had a lower correlation with DC of 0.55, indicating more re-ranking of animals than DC3+_Wet. Finally, the highest correlation was between DC3+_Wet and DC BLUPs at 0.81, implying the lowest amount of re-ranking between traits.

4. Discussion

4.1. Heritability of Days to Calving

A primary breeding objective of Popplewell Composites is to increase lifetime weaning rate. However, it is a complex trait to measure because, by definition, it is only obtained at the end of a cow’s breeding life. Days to calving is a good indicator of lifetime weaning rate as it is genetically correlated with lifetime weaning rate and is heritable [1,9,13,23]. Days to calving is a female fertility measure that combines effects such as the age of puberty for first joining, conception rate, how early they conceive in the joining period and gestation length. Female fertility traits are expensive and difficult to measure, and challenging to include in breeding programs due to bias caused by culling cattle that do not conceive. In the breeding program described herein, the strategy is that cattle are expected to wean two calves within the first three matings; those failing to do so are culled from the herd, any further subsequent matings cows are culled if they fail to wean a calf. These culling methods result in missing data as there are many cows without lifetime weaning rate records.

Previous studies in the use of days to calving as a fertility trait proxy, commonly treat days to calving as a single trait including all joinings as a repeated measure. This is the first publication separating both the effect of joining number and lactation status on days to calving. Separating days to calving based on joining number and lactation status into different traits was shown to increase genetic gain over the repeated days to calving trait. The heritability was 0.20, 0.18 and 0.25 for first joining days to calving, second joining days to calving and mature days to calving, respectively (Table 10). It should be noted that mature days to calving includes joining 3, 4 and 5+. This was determined by the genetic correlation calculated from a model that includes a separate variance component for each joining but estimation of the correlation between two joining at a time (Model_2), correlations with the first two joinings were the lowest and joining 3, 4 and 5+ generally had high correlations and combining them reduced the standard error (Table 8). The heritability estimated for traits that separated out first and second joining were higher than the overall days to calving (0.12), demonstrating in this Tropical Composite population that separating joining number will increase the amount of additive variance estimated and reducing bias.

Further analysis was done separating non-lactating cattle; the heritability estimate for these traits was 0.39 for second joining days to calving lactating and 0.17 mature days to calving lactating (Table 9). There is an increase in heritability estimates when days to calving is treated as multiple traits compared with an overall repeatable trait (DC, 0.12), this will allow for greater genetic gain. These increases of heritability indicate modelling across joining number and lactation status is improved and allows for more genetic improvement in a breeding program. These improvements are particularly important to a breeding program for a low heritable and hard to measure trait of high economic value.

4.2. Heifer Days to Calving

The heritability estimate of heifer days to calving (DC1) herein (0.20, Table 10) was similar to those reported by Johnston et al. [1], who estimated the heritability of first joining days to calving to be 0.13 in Tropical Composites and 0.22 in Brahmans. Slightly lower heritability was estimated in Angus cattle at 0.10 [13] and Brahman cattle at 0.09 [24]. In this study, cattle were first joined at 12–15 months; however, in other studies with tropically adapted cattle, heifers were not joined until 24–28 months. Further, Brahman cattle reach puberty at a later age than tropical composites [2,25], further explaining the difference in heritability estimates reported by Johnston et al. [1]. The genetic correlation could explain the higher heritability estimates of DC1 with the age of puberty. Johnston et al. [21] found a genetic correlation between age of puberty and DC1 to be 0.79 in Brahmans, with Johnston et al. [21] estimating a much lower correlation found in tropical composites (0.10); however, this is likely due to the age of puberty difference between the two breed types. The high correlation in Brahmans indicates that DC1 and the age of puberty influencing each other which results from similar biological mechanisms. Johnston et al. [1] also estimated the genetic correlation between DC1 and lifetime weaning rate, which was −0.54 in Brahmans and −0.57 in Tropical Composites. These genetic correlations indicate that DC1 are genetically positively associated with each other. Heifer days to calving is an important trait in the breeding program that is both heritable and positively associated with the age of puberty and lifetime weaning rate.

4.3. Second Joining Days to Calving

Second joining days to calving (DC2) heritability estimates (0.18, Table 10) were similar to those reported by Johnston et al. [1], at 0.17 in Tropical composites and 0.20 in Brahmans. Lower heritability estimates were reported in Angus to be 0.11 [13] and in Brahmans to be 0.15 [24]. The difference in the heritability estimates could be due to breed and age differences. A further model was run for DC2, separating lactating and non-lactating cattle. The heritability estimate of second joining days to calving lactating (DC2_Wet) much higher (0.39) than for DC2 when dry cows were included (Table 10, 0.18). A previous study separated DC2 lactating cows, and the heritability estimates were 0.49 in Brahman and 0.35 in Tropical composites which is similar to results herein for DC2_Wet. [1]. It should be noted that Johnston et al. [1] reported heifers that were not joined until 24–28 months, whereas in this study, heifers were joined at 12–15 months. This increase in heritability when only lactating cattle were included indicates that days to calving should be analysed separately for lactating and non-lactating cattle. Johnston et al. [1] also concluded that heritability estimates for all female fertility traits associated with the second joining were higher in lactating cows than in all cows. Indicating that more genetic progress can be made when only lactating animals are included in female fertility traits.

The difference between DC2_Wet and DC2_Dry heritability representing lactating and non-lactating estimates respectively could be due to post-partum anoestrus from either the threshold energy balance effect or the suckling effect that occurs in Bos taurus indicus cattle [26,27]. This post-partum effect prevents the cattle from cycling while lactating, with a previous study stating that in Droughtmaster cattle weaning was required to break anoestrus [28]. Lactating cattle combine growth and lactation in their second joining, which imposes greater energy requirements compared with non-lactating cattle in their second joining. These energy requirements are often not fulfilled when cows graze low-quality pastures, such as in Northern Australia and have a greater detrimental effect on post-partum reproduction in first lactation cows [29]. Johnston et al. [1] estimated the genetic correlation between days to calving second joining and lactation anoestrous interval to be 0.70 in Brahmans and 0.67 in Tropical composites. These high genetic correlations indicate that similar genes control both days to calving second joining and lactation anoestrus interval. Further, Johnston et al. [1] estimated genetic correlations between second joining days to calving and lifetime weaning rate to be −0.96 in Brahmans and −0.76 in Tropical composites. The high genetic correlations indicate that second joining days to calving is a good indicator of lifetime fertility.

4.4. Difference between Lactating and Non-Lactating Cows in Days to Calving

Lactating cows will often lose more body condition than non-lactation cows due to the energy cost of lactation and the low digestibility of tropical pasture [30,31]. Neville [31] calculated that lactating beef cattle require 38–41% more energy for maintenance compared to non-lactating. In addition to the extra energy requirements, in Bos taurus indicus cattle, an additional post-partum anoestrus effect is associated with suckling or the close presence of offspring [26,27]. Consequently, a model was fitted for days to calving for the animals second joining onwards that treated days to calving in lactating and non-lactating cows as separate traits. There was a low negative correlation (−0.10) between wet and non-lactating cows, demonstrating that lactating and non-lactating days to calving records are genetically different, and they were, therefore, analysed as separate traits. The low correlations could be driven by post-partum anoestrus. The post-partum anoestrus effect could be due to the calf’s suckling effect and the threshold of energy balance.

Energy balance is important in lactating cattle and can affect their post-partum anoestrus interval, causing the genetic difference between lactating and non-lactating days to calving. Therefore, lactating cows that keep getting back into calf (lower days to calving records) also have a lower threshold energy balance meaning they start cycling earlier than the lactating cows that struggle to get pregnant (larger days to calving records). Wolcott et al. [32] found in tropical composite cows at their second joining, lactating cows had significantly lower weight and body condition than non-lactating cows. Therefore, lactating and non-lactating cows, particularly in their second joining, have different requirements affecting post-partum anoestrus, re-enforcing the importance of treating them as different traits. In addition to the energy threshold balance, a suckling effect also contributes to post-partum anoestrus in Bos indicus cattle [26,27]. As this composite population includes Bos taurus indicus cattle, post-partum anoestrus could be due both to energy balance and a suckling effect, causing lactating days to calving to be genetically different from non-lactating days to calving.

Cattle with longer post-partum anoestrus intervals spend longer periods not cycling, including when they are lactating, which results in the cattle not conceiving in the joining period. These cattle will then become non-lactating in the next joining season. However, the most profitable system is those with more cows lactating yearly. Post-partum anoestrus was highly heritable, with estimates ranging from 0.42–0.51 in Brahmans and 0.26–0.63 in tropical composites [1,33]. It has been reported to have a high genetic correlation with days to calving [33]. This demonstrates that the genetic difference between lactating and non-lactating cattle could be due to the post-partum anoestrus interval, providing further evidence that days to calving should be treated as separate traits for lactating (wet) and non-lactating (dry).

It is important to also look at the effect of the breeding values and the ranking of individual animals. A breeding value comparison between DC2+_Dry and DC2+Wet (Figure 1, r = 0.32), showed significant re-ranking of animals. These re-ranking of animals provide further evidence that lactating and non-lactating days to calving should be treated as separate traits, with lactating days to calving the main trait of interest.

Most breeding programs aim to improve the lifetime weaning rate, meaning more calves on the ground. Therefore, lactating days to calving is important in improving the breeding objective, representing lactating cows getting back into calf. Despite lactating days to calving being important, non-lactating days to calving does not provide information that would help improve the breeding objective. Treating lactating and non-lactating cows as two distinct traits would benefit the producer as the most profitable system will be those with more cows lactating yearly.

4.5. Genetic and Phenotypic Correlation for Days to Calving

4.5.1. DC1 and DC2 Correlations

The genetic and phenotypic correlation between DC1 and DC2 was −0.06 and −0.22, respectively (Table 14). Johnston et al. [1] estimated the genetic correlation between joining one and two for days to calving to be 0.55; however, these were mated at 24–28 months of age and will have different growth requirements compared to the current study. Here, further analysis was conducted by splitting DC2 based on lactation status (lactating/non-lactating). DC2_Dry had a positive low (0.13) genetic correlation and a negative phenotypic correlation with DC1 (Table 14). In contrast, DC2_Wet had a moderate negative genetic correlation of −0.42 and a phenotypic correlation of −0.04 (Table 14). There are two reasons for these genetic correlations, post-partum anoestrous in lactating cows and age of puberty in heifers. The genetic correlation between DC1 and DC2_Wet indicates that DC1 is both a measure of fertility and puberty whereas DC2_Wet is a measure of fertility and post-partum anoestrus. The genetic correlation estimates between DC1 and DC2 (including DC2_Wet and DC2_Dry) would suggest that treating them as distinct traits is essential.

4.5.2. DC1 and DC3+ Correlations

The genetic correlation between DC1 and DC3+_Wet was 0.65 (Table 14); thus, genetic gain in one trait would result in genetic gains in the other. As DC1 is an early in-life trait, selecting for DC1 would allow for genetic improvement in DC3+_Wet earlier, increasing the overall production of the breeding program. Indicating that DC1 is a good indicator of lifetime female fertility. The high genetic correlation could be caused by two factors, post-partum anoestrus in mature cows or the age of puberty in heifers [1,26,27]. Post-partum anoestrus has a greater effect on primiparous cows than in mature cows; hence, the genetic correlation is more favourable between DC1 and DC3+_Wet than with DC1 and DC2_Wet [29]. The genetic and phenotypic correlations would indicate that DC1 is a good indicator for DC3+_Wet and allows for selection earlier in life.

4.5.3. DC2 and DC3+ Correlations

The genetic correlation between DC2 and DC3+ was low and negative (Table 14); similar correlations were found between DC2_Dry with DC3+ and DC3+_Wet. These low negative correlations indicate that second joining non-lactating animals would not improve DC3+ and, therefore, are not a good measurement of lifetime fertility. Second joining non-lactating animals had lower days to calving values in the second joining compared with DC3+; this could be due to the effect of post-partum anoestrus. Therefore, DC2_Dry is not a good indicator of mature (joining three onwards) days to calving and thus cannot be used to increase genetic gain. Furthermore, DC2_Dry is not a trait of interest in the breeding program as the most profitable system is those with more lactating cows yearly.

A different trend was found in DC2_Wet, which was moderate to highly genetically correlated with DC3+ (0.41) and DC3+_Wet (0.69) (Table 14). The higher correlations between second joining lactating days to calving and mature joining traits indicate that DC2_Wet is a good representation of how an animal will perform over its lifetime. Wolcott et al. [32] found that cattle, particularly in their second joining, have different requirements due to post-partum anoestrus, which could explain the genetic correlation between DC2_Wet and DC3+_Wet. The genetic correlations estimated between DC2_Wet and DC3+_Wet indicate they are highly correlated; however, they should be treated as separate traits. This would enable early selection while improving lifetime fertility and maximising genetic gain. However, DC2_Dry and DC3+_Dry should be excluded from the analysis and values not be reported back to the breeder as these are not the traits of interest as it is more profitable to have more lactating cows every year.

4.6. Recommended Days to Calving Traits

Response to selection was calculated for each individual trait. The response to selection was calculated over one generation with a selection intensity of one. The trait that with the most negligible response to selection was the overall days to calving trait (Table 10), indicating that this is the least desirable days to calving trait. The trait with the smallest response to selection is the trait that will make the least amount of genetic gain. As the overall days to calving trait had the lowest response to selection, separating traits based on lactation status and joining number will increase genetic gain. Days to calving is a complex trait combining many different biological effects so consideration is needed for modelling this trait to maximise response to selection. Selection indexes are important to consider when developing traits as they will account for genetic correlations and how one trait will affect the other.

Three different indexes were calculated based on three different scenarios (Table 4). Index three (which included DC1, DC2_Wet and DC3+_Wet) had the greatest response of 6.08 days/generation, indicating that it is the best scenario or the scenario that will make the most genetic gain in this population. Index two (which included DC1, DC2+_Wet) had the second highest response to selection (3.32 days/generation); this demonstrates that separating the first joining will improve genetic gain. Unsurprisingly, the index with the lowest response to selection was index one or treating days to calving as one trait, further demonstrating that it is important to treat days to calving as separate traits based on lactation and joining to maximise genetic gain and productivity of the breeding program. These response calculations need to be taken into consideration when making recommendations on the breeding program.

Considering index theory and heritability estimates, treating days to calving as three separate traits (DC1, DC2_Wet and DC3+_Wet) compared to just one days to calving trait will result in the greatest genetic gain in this population (Table 13). A further multi-variate model was fitted with DC1, DC2_Wet and DC3+_Wet. The multi-variate model resulted in a different genetic correlation compared with the bivariate model between DC1 and DC2_Wet (Table 15). The heritability of these traits was 0.25, 0.40 and 0.30 from DC1, DC2_Wet and DC3+_Wet (Table 15). The genetic correlation between these traits also indicates that they should be treated as separate traits. Despite these results, treating days to calving as two traits still resulted in increased genetic gain compared with treating it as a single trait (Figure 2); therefore, if the dataset is small, it is recommended to use DC1 and DC2+_Wet to potentially reduce the amount of error. Implementing the separation of days to calving as three traits in this population will enable greater genetic improvement in female fertility, resulting in higher production.

4.7. Heterosis Effect on Days to Calving

Heterosis is the phenomenon that occurs when two genetically different breeds are crossed and produce offspring that outperforms the midpoint of their parents [34,35]. Heterosis tends to have a bigger impact on traits that are lowly heritable such as fertility [34,36]. Retained heterosis, is essential to the breeding program as composite breeding exploits heterosis without further crossing different breeds [34]. Herein heterosis as estimated from heterozygosity had a positive effect on fertility traits by decreasing days to calving in all models (−0.97 to −4.13 days/%, Table 10). It has been reported that heterozygosity fraction is positively and linearly related to cow fertility and lifetime productivity and can be used to optimise heterosis in a composite population [34,37]. The biggest impact of heterozygosity was on DC3+ where a 1% increase was associated with a 4.31 reduction in days to calving. Early in life days to calving measurements, DC1 and DC2 both had lower heterozygosity coefficient −1.90 and −1.07 days per percent increase in heterosis, respectively (Table 10). DC3+ having the highest heterosis coefficient could be due to the higher number of records (957) compared to DC1 and DC2 (648 and 636, respectively). Heterosis can increase the weight of calf weaned per cow exposed by 50% or more in Bos taurus taurus and Bos taurus indicus crosses, increasing the production of the breeding program [38]. Therefore, utilising heterozygosity coefficient estimates should improve the breeding program’s overall fertility in composite populations.

4.8. Comparison of the Penalty Value

The penalty value commonly used for days to calving is to add 21 days to the largest value in the join group [10]. However, due to the breed type of these composite cattle and their environment, 32 days was used as the penalty value. An additional analysis was conducted to see the effects of changing the penalty value on the days to calving model. DC1 and DC2+ models were run using no penalty value, 21, 32, 43, 63 and 252 days. In both DC1 and DC2+, not using a penalty value affected the heritability estimate (Table 5 and Table 6). DC1 with no penalty has a lower heritability compared to using any penalty value; this could be due to the smaller number of records. However, DC2+ with no penalty had a larger heritability compared to using any penalty value. This demonstrates the importance of including all joining data, as it will affect heritability estimates. Despite this, when a penalty value was applied to cows that were not pregnant (empty cows), there was little difference in the heritability estimate no matter the value for both DC1 and DC2+; however, there seemed to be a scaling effect due to the penalty value (Table 5 and Table 6). Furthermore, the BLUPs between the models were all highly correlated (>0.90). These results demonstrate that the penalty value chosen does not affect the heritability and BLUPs; therefore, the value chosen for the penalty is a matter of convenience.

5. Conclusions

Days to calving is a trait used for genetic improvement of weaning rate and calving time. For the breeding objective of minimising days to calving in five joinings, in this population it is essential to estimate breeding values for three component traits: first joining (heifer) days to calving, second joining days to calving lactating and mature days to calving lactating. The results for heterozygosity fraction supported this. Selecting these three traits will allow for greater genetic gain in fertility, thus increasing production. As a commercial dataset was used, most estimates have large standard errors and further investigation using a larger dataset are required to support the results herein for further use in the industry. Despite the large standard errors, the results are comparable with published literature. It is important to use a penalty value for cows that are not pregnant as it allows for more complete records; however, the actual value of the penalty added does not affect heritability or BLUP estimates. As this is the first-time days to calving has been modelled this way and a commercial dataset was used, further study is required to confirm the genetic and phenotypic correlations between days to calving (separated into three traits, DC1, DC2_Wet and DC3+_Wet), particularly in other breeds. The relationship with production and days to calving traits should be investigated in composite breeds to allow for no detrimental effects.