### Description of the study area

Holeta Cattle Genetic Improvement Center is located 33 km west of Addis Ababa, in West Shoa Zone of Oromia Regional state. The center lies at longitude 38º 30′ E and latitude 9º 3′ N and at about 2400 meters above sea level. The site is characterized by cool sub-tropical climate with mean maximum and minimum temperatures of 22.3°C and 6.16°C, respectively with mean relative humidity of 59%. The mean annual rainfall ranged from 818 to 1247 with an average of 1014 mm. The seasons are classified in to dry, short rainy, and long rainy which last from October to February, March to May and June to September, respectively (HARC Holeta Agricultural Research Center 2008).

### Herd management

Cows grazing on native pasture from 8:00 am to 3:00 pm during the rainy season and they are allowed to forage irrigated pasture from February to May. Milking cows were grouped according to their milk production classes as high (>14 liters), medium (8 to 14 liters) and low (< 8 liters) yielding and provided with additional 0.5 kg concentrate per liter of milk, while pregnant dry cows are supplied with 3 kg of concentrates per day in the last two months of pregnancy. The concentrate mix was composed of 30% wheat middling, 30% noug seed cake (*Guizeta abysinica*), 25% wheat bran, 10% corn, 4% limestone and 1% salt. All animals had free access to water.

Calves were separated from their dams after birth and allowed to receive colostrums for the first 5 days of their age. Bucket-feeding of whole milk continued until weaning at 120 days of age. They were given 5, 4, 3, and 2 liters of milk per day from 5 to 65; 66 to 85; 86 to 105; and 106 to 120 days of ages, respectively. Besides, some concentrates and hay starting from the age of 15 days were provided.

Most of the cows were served at first observed heat after calving. Heifers were inseminated after maintaining 280 kg of body weight. Heat detections were routinely followed three times in a day, i.e. early in the morning after milking; in the resting period in mid day; and in the afternoon before milking. Heat detections were carried out by herd attendants and AI technicians. Services were given after the AI technicians confirmed the heat status and then pregnancy diagnosis is conducted by manual rectal palpation after three months of last service.

Regular vaccinations against contagious bovine pleura-pneumonia, lumpy skin disease, anthrax, and blackleg, foot and mouth disease and pasteurellosis were given and treatments provided when incidence of cases observed. Culling was practiced as a result of fertility failures, chronic mastitis, tuberculosis, old ages, and emaciations and in some cases due to low daily milk production.

### Data description and analysis

Abnormal birth includes stillbirth and abortion. A calf born dead between 260 days and full term or calf died within 24 hrs after birth is designated as stillbirth while abortion the loss of the fetus between the age of 42 days and approximately 260 days.

Sex ratio is defined as the probability of a cow at a given lactation producing a live female calf. Mortality is the probability of a female calf died before reaching to the age at first caving. Culling is the probability of a female calf culled before reaching to the age at first caving. Replacement rate is defined as proportion of young females that become replacements to that of the total females born and of total pregnancies in particular year

A total of 3092 calving collected over 24 years from 1986 to 2010 from 105 Friesian sires were used. In this study only singleton births were considered. Twin births were few and removed from the analysis. The traits considered were abnormal and normal births, sex ratios, mortality, and culling and survival rate up to the age at first calving and replacement rates based on female calves born and total pregnancies. The fixed effects studied were parity, season and year of calving. Proportions were estimated for each trait and transformed to arcsine and analyzed using the SAS procedures of General Linear Model (SAS Statistical Agricultural System 2002).

{\mathbf{Y}}_{\mathbf{\text{ijkl}}}\mathbf{=}\mathbf{\mu}\mathbf{+}{\mathbf{P}}_{\mathbf{i}}\mathbf{+}{\mathbf{Q}}_{\mathbf{j}}\mathbf{+}{\mathbf{S}}_{\mathbf{k}}\mathbf{+}{\mathbf{e}}_{\mathbf{\text{eijkl}}}

Where,

Y_{ijkl} = i^{th} observation (replacement rate/component traits) from a cow belonging to k^{th} parity, calved in j^{th} season of i^{th} year;

μ = overall mean;

P_{i} = effect of i^{th} parity of lactation (1… 8^{+})

Q_{k} = effect of k^{th} year of calving (1… 24)

S_{j} = effect of j^{th} season of calving (1, 2, 3)

e_{ijkl} = random error specific to the particular observation and assumed to be normally and independently distributed with mean zero and variance σ^{2} ie.σ^{2} ~ NID(0, σ^{2}
_{e}).

Sex ratio is expected to be 1:1. The equality of observed overall sex ratio (percent male birth) with expected overall sex ratio was tested by Chi square (*χ*
^{2}) test.

Random model was used to study the effect of sires on the different threshold traits. Tomar et al. (1991) devised a method for genetic analysis of proportion data without transformation by conducting the analysis of variance using the following method.

\text{Total}\phantom{\rule{0.5em}{0ex}}\text{sum}\phantom{\rule{0.5em}{0ex}}\mathrm{of}\phantom{\rule{0.5em}{0ex}}\text{squares}=\mathrm{pN}\u2012{\mathrm{p}}^{2}\mathrm{N}=\text{pqN}

\text{Sire}\phantom{\rule{0.5em}{0ex}}\text{sum}\phantom{\rule{0.5em}{0ex}}\mathrm{of}\phantom{\rule{0.5em}{0ex}}\text{squares}={\displaystyle \sum {\mathrm{p}}_{\mathrm{i}}{}^{2}{\mathrm{n}}_{\mathrm{i}}\u2012{\mathrm{p}}^{2}\mathrm{N}=\text{pqN}\u2012{\displaystyle \sum {\mathrm{p}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{i}}}}

\text{Error}\phantom{\rule{0.5em}{0ex}}\text{sum}\phantom{\rule{0.5em}{0ex}}\mathrm{of}\phantom{\rule{0.5em}{0ex}}\text{squares}=\mathrm{pN}\u2012{\displaystyle \sum {\mathrm{p}}_{\mathrm{i}}{}^{2}{\mathrm{n}}_{\mathrm{i}}={\displaystyle \sum {\mathrm{p}}_{\mathrm{i}}{\mathrm{q}}_{\mathrm{i}}{\mathrm{n}}_{\mathrm{i}}}}

Where,

n_{i} = number of total progenies of i^{th} sire

a_{i} = number of affected progenies of i^{th} sire

N = ∑n_{i}

p_{i} = a_{i} / n_{i} = average incidence of the trait among progenies of i^{th} sire

q_{i} = 1- p_{i}

Sire component of variance (σ^{2}
_{s}) was estimated from the mean squares of between sire (MS_{s}) and within sire component of variance (σ^{2}
_{w}) using the following formula:

{\sigma}_{s}^{2}=\frac{\mathit{\text{MSs}}-\mathit{\text{MSw}}}{K}

Where,

\begin{array}{l}\mathrm{K}\left(\text{average}\phantom{\rule{0.5em}{0ex}}\text{number}\phantom{\rule{0.5em}{0ex}}\mathrm{of}\phantom{\rule{0.5em}{0ex}}\text{progenies}\phantom{\rule{0.5em}{0ex}}\text{per}\phantom{\rule{0.5em}{0ex}}\text{sire}\right)\\ \phantom{\rule{0.8em}{0ex}}=1/\mathrm{S}\u20121\left({\displaystyle \sum \mathrm{ni}\u2012{\displaystyle \sum {\mathrm{n}}_{\mathrm{i}}{}^{2}}}/{\displaystyle \sum {\mathrm{n}}_{\mathrm{i}}}\right)\end{array}

Where,

S = number of sires;

N = total number of observations;

n_{i} = number of observations for i^{th} sire.

Heritability was estimated using paternal half-sib correlation methods using least squares analysis of variance for different traits.

\text{The}\phantom{\rule{0.5em}{0ex}}\text{intraclass}\phantom{\rule{0.5em}{0ex}}\text{correlation}\phantom{\rule{0.5em}{0ex}}\left(\mathrm{t}\right)=\frac{\left({\sigma}^{2}s\right)}{\left({\sigma}^{2}s+{\sigma}^{2}w\right)}

And,

\text{heritability}\phantom{\rule{0.5em}{0ex}}\left({\mathrm{h}}^{2}\right)=4\mathrm{t}=\frac{4\left({\sigma}^{2}s\right)}{\left({\sigma}^{2}s+{\sigma}^{2}w\right)}

Where,

*σ*
^{2}
*s* = sire component of variance

*σ*
^{2}
*w* = *σ*
^{2}
*e* = error variance

Standard error of heritability estimated according to Tomar et al. (1991).