Although milk production is considered as the single most important trait in dairy farming, cattle breeding programmes are changing their breeding objectives to include longevity and other traits (type and functional) [1], so that cows can meet the challenges associated with high milk production. Direct selection for longevity results in improved health and fitness [3] and even milk production of cows [4]. Longevity is also associated with decreased cases of involuntary culling due to reproduction, udder health, and workability [5]. Decrease in involuntary culling is accompanied by an increase in voluntary culling due to low production. Therefore, breeding for longevity is considered to have ethical and economic benefits since it results in favorable response in profitability of beef and dairy cattle enterprises [3].

However, inclusion of longevity in the breeding objective is hampered because the trait is low heritable [4] [6]. Estimates of heritability for longevity are defined variously based on the length of time interval for survival after first calving range from 0.002 to 0.031 [6]. When defined as total milk production over all lactations, number of lactations initiated, total number of days in lactation over all lactations, the time between birth and last milk recording in months; and time from first calving to last milk recording in months, the estimates ranged from 0.05 to 0.18 [4]. Thus, heritability estimates for longevity regardless of how the trait is defined or analyzed are low, implying that direct selection may not yield significant gains [4].

Another limitation of selecting directly for longevity is the delay in availability of phenotypic information [7], which may lead to increase in generation interval [8]. The age at exit from a herd has been reported to be around 80 months from birth or 54 months from first calving [4], delaying the time in which information on exit from the herd is obtained. Information on other measures of longevity such as lifetime milk production, number of lactations initiated, total days in milk is also available once a cow exits the herd. Availability of traits expressed early in life and which are favorably correlated to longevity can be useful in selecting for this trait. Genetic correlations between longevity and linear and fertility traits have been reported to be low to moderately positive [4] [9] [10]. Such traits can be used in breeding programmes to indirectly select for longevity early in an animal’s life, leading to improvement in longevity and reduction in generation interval.

Reproductive performance is a crucial component of culling criteria and therefore influences longevity in cattle herds and is regarded as the single most economically important trait in cattle [11]. Poor reproductive performance leads to increased involuntary culling, fewer lactations initiated and calves born and less milk in a cow’s lifetime, as well as increased cost of replacement. Therefore, since productive longevity is closely related to fertility, it is important to consider the genetic effects of both traits simultaneously. Other traits which influence culling decisions such as body conformation type traits have also been considered as proxy for longevity [4] [12]. Despite its importance in cattle, longevity has not been studied in the Sahiwal cattle and has not been recommended for inclusion in the breed’s breeding objective [13] [14] [15].

Since direct selection for longevity is not feasible partly due to delay in acquisition of data, correlated response due to selection on traits that are genetically correlated with longevity should be explored. Favorable associations between longevity and linear type traits have been reported, indicating selecting for these traits would improve longevity [4]. Based on phenotypic relationships, [12] found those type traits were not a good indirect indicator for a productive life. However, there seems to be an important influence of the definition of longevity on the associations reported [4]. Fertility traits such as number of services per conception, difficulties in calving, days open and other fertility traits were reported to influence longevity significantly [11]. Estimates of genetic correlations between longevity and other performance traits, which can be used as selection criteria for longevity in the Sahiwal breed in Kenya are lacking.

Whereas the current quest is to improve longevity, the trait and other correlated traits are negatively affected by inbreeding in livestock populations. Longevity and reproductive performance have been shown to decrease while, rate of disposal or loss of replacement heifers before first calving, age at puberty increased due to inbreeding through reduced growth [16]. Studies of inbreeding depression on longevity are rare. However, for every increase of 1% in inbreeding, productive life has been reported to decrease by about 13 days according to the Canadian Dairy Network [17]. Cows with high inbreeding levels have also been reported to have a higher risk of being culled [18]. Effects of inbreeding on non-production traits include decreased reproductive efficiency and decreased stay ability. The negative effects on traits related to fitness have been attributed to reduced heterozygosity as inbreeding accumulates [19].

Inbreeding level and rate of inbreeding in the Sahiwal cattle population in Kenya has been found to be on an upward trend and is above 1% [20]. It is therefore expected that there will be depression in production and functional traits such as fertility and longevity. Inbreeding depression depends not only on actual level of inbreeding but also on the rate of inbreeding. At a slow rate of inbreeding per generation, natural selection counteracts the effects of inbreeding by removing the less adapted inbred animal [21]. Therefore, animals with the same level of inbreeding may have different inbreeding depression effects depending on the completeness of their respective pedigrees [22]. The quality of pedigree can be accounted for by estimating the rate of inbreeding [22]. Estimated this way, the estimated coefficient corrects for depth of the pedigree depth of an individual and indicates the increment in inbreeding regardless of number of known generations in its pedigree [22].

Inclusion of longevity in breeding objective of cattle is hampered by the delayed availability of phenotypic information. Genetic correlations between longevity and traits expressed early in an animals’ life which can be useful in selecting for longevity have not been estimated [23]. Further, though inbreeding levels for Kenyan Sahiwal breed have been on an upward trend due to selection in a closed nucleus with small effective population size, inbreeding depression for longevity and fertility traits in the Sahiwal population in Kenya has not been assessed. Consequently, the long-term sustainability of the Sahiwal breeding programme is threatened due to reduced viability of the population and variance of genetic gains across generations [23].

Sahiwal is humped zebu cattle that originated from India and Pakistan. The breed was imported into Kenya between 1939 and 1963 to improve the performance of the local East African zebu [24]. The founding population consisted of 60 bulls and 20 cows which were introduced in Livestock Improvement Centres (LICs) across the country. After some basic performance evaluation, the best animals from the LICs were taken to Naivasha to establish the National Sahiwal Stud (NSS) in 1963. Breeding of this population followed a closed nucleus after the recommendation for genetic improvement of milk and growth rate [98]. To date breeding of the Sahiwal has been under a closed nucleus breeding programme except for the introduction of semen from Pakistan in 1992 [25].

In Kenya, the breed is favored by the Maasai pastoralists due to its high milk production and growth as well as good reproductive ability compared to the local zebu [14] [25]. Therefore, the breed is a very important dual-purpose cattle breed for pastoral and mixed farming communities in the Eastern African region [24]. The breed fits well within the harsh rangelands of East Africa because the agro-climatic conditions of these rangelands are similar to the breed’s original habitat in the Punjab region of India and Pakistan [24].

The Sahiwal cattle in Kenya are mainly raised by Maasai pastoralists in the Arid and semi-arid areas of Kenya. However, pure Sahiwal cattle are found in government and private ranches [13]. The government and private ranches form the nucleus of the Sahiwal cattle breeding programme in Kenya. The breeding strategies adopted are pure breeding by the nucleus herds and crossbreeding among the pastoralists. The nucleus herds, therefore, produce bulls for pure breeding and crossbreeding in the pastoral herds. Breeding takes place under a closed nucleus, where movement of genes is unidirectional, from the nucleus to the pastoral herds, which form the commercial population. Cattle in the pastoral herds as well as those in government and private herds are raised under low input production systems where the purpose is for tangible and intangible benefits [13]. The main aim of Sahiwal farmers in the different production systems is to increase milk yield, body size and mature weight. Good fertility and adaptation to local production conditions are also considered [14].

Before any genetic improvement programme is implemented, the breeding objective must be defined [26]. The breeding objective comprises traits which the producer attempts to improve genetically because they influence returns and costs. Development of breeding objectives involves specification of the breeding, production and marketing systems, identification of sources of income and expense, identification of biological traits influencing revenue and costs, derivation of economic and biological values, estimation of genetic and phenotypic parameters and prediction of genetic gain. For the Kenyan Sahiwal, these steps have been covered in recent studies [13] [14].

The breeding objective for the Sahiwal cattle, which targets traditional markets, includes sale weight (kg), lactation milk yield, feed intake, age at first calving, cow weight, calving interval, pre-weaning survival, post-weaning survival and productive lifetime. The breeding objective as presently defined [14] [15] includes a measure of longevity, but it is important to note that genetic parameters of longevity for the population are lacking. Use of parameters from other livestock populations, albeit being raised under the same production system or climatic conditions as the Sahiwal cattle, as in any other improvement programme implies that the trait may be influenced by other traits indirectly, resulting either in a favorable or unfavorable genetic change [4]. Therefore it is important to estimate genetic parameters for the Sahiwal cattle in Kenya and its relationship with other breeding goal traits.

Longevity traces time from a defined starting point up to the occurrence of an event [27] [28] [29]. In the context of this paper, the defined starting point can be the time of birth or first calving up to the last test day record or last day in milk, or the time when an animal exits a herd. Longevity can be true or functional longevity. Functional longevity is the ability of a cow to delay culling on whatever basis, other than milk production. The implication in this case is that the animal has above average health, fitness and fertility [30] [31]. Measures of functional longevity include number of lactations, age from first calving to last day in milk, length of productive life and lifetime production [27]. The uncensored definitions of longevity are based on age at the exit, either through culling or death.

Censored definitions of longevity are related to survival to a pre-determined age within or across lactations [32] [33]. Defined this way, longevity can be scored as a binary trait, where animals are scored as to whether they survived to a given age or not [34] [35]. The trait can be analyzed using linear regression models [36] [37] or threshold models [34]. The period can be limited to within lactation [34] or across all lactations [6]. This definition is limited by the fact that only animals that survive to a given age are included in the genetic analysis, while those which are still surviving are left out [38]. Further, animals that left before the specified period are excluded since they are considered missing [36]. Longevity can also be regarded as stay ability, which is the probability that a cow will survive to a certain age if it is given the opportunity to attain that age [39]. Another definition is the time in days between calving’s, or from one calving to death or culling [40]. Other definitions of longevity include number of days from calving to culling, death, censoring, or second calving (herd life in the first lactation) and number of days from calving to culling, death, censoring, or sixth lactation (herd life in the first five lactations). Survival scores for the first five lactations or survival to 365 days (0 if a cow was culled before 365 days or 1 if it reached at least 365 days) [34] have also been used to define longevity.

Removal of a cow from the herd occurs primarily due to reproductive failure, production of poor-quality calves, or low milk production. The importance of longevity is clearly understood when viewed against the value of removal and the cost of replacement. In beef cattle, a cow’s peak performance and profitability are about 9 years of age. From a production perspective, the optimal age of exit from a herd has also been found to be about 9 years of age [3]. From an economics perspective, selecting for increased longevity has a positive impact on profitability of cattle enterprises [3] through lowered costs of replacement. Despite its importance in cattle breeding, longevity is not considered in routine genetic evaluation of Sahiwal cattle and its genetic parameters have not been estimated [14] [15]. Recently, higher production costs have led to an increase in prices of calves, cattle, and beef prices are pushing the costs of purchasing replacement cows and heifers up. To counter this trend cows can be selected for a longer productive life. Selecting for longer productive life leads to a positive economic impact [3].

As a trait, longevity has many definitions, all of which aims at describing the importance of an animal’s lifespan in relation to its contribution to profitability of a herd [41]. Regardless of the definition adopted, it is generally agreed that longevity is a trait of major economic importance in cattle and greatly influences herd profitability [42] [43] [44]. Longer longevity is an indication of lower incidences of involuntary culling and implies an increased proportion of higher producing mature cows in the herd leading to improved herd production [45]. A positive consequence of this herd structure is that replacement requirements are lowered, meaning more surplus heifers are available for sale. Cow maintenance costs are also spread over a large number of offspring [46]. The higher selection intensity among cows is possible since involuntary culling and replacement requirements are reduced.

Numerous cattle breeding programmes have incorporated longevity in their breeding objectives due to their high economic importance [1] [41] [44]. As breeding programmes focused on increasing yield, there has been an associated decline in fitness traits such as longevity, udder health and fertility. This has necessitated inclusion of such traits in the breeding objectives for many cattle breeding programmes. Increase in longevity has been found to result in increased profits in various cattle breeding programmes [1] [47], although it was found to be breed dependent [1]. By definition, the economic value of a trait is the expected increase in profit due to a unit improvement in the genetic merit of a trait when all other traits in the breeding objective are held constant [48]. It can also be defined as the change in farm profit per cow per year due to a unit change in genetic merit of the trait of interest [49].

The global trend in cattle breeding is now to include all economically important traits in the breeding objective. Functional traits such as longevity, disease, fertility and type traits are now featuring prominently in the breeding objective of many breeding programmes [9] [66] [67]. This is because the economic value of longevity is reported to be up to half of that of production traits [68]. In the quest to include longevity in the breeding objective, the first step has been to come up with a definition of longevity. To date, longevity is variously defined as length of productive life, lifetime milk production, herd life, total number of lactations and survival from birth or first calving to a certain age [69] [70]. The second challenge has been the choice of an appropriate analysis procedure. Here the challenge is basically because factors affecting longevity change over time.

Characteristically, longevity is a threshold trait, and displays distinct categorical phenotypes. Threshold traits are influenced by an underlying continuous liability [19]. For longevity data, most animals in a herd are found in early lactation, hence the data is usually skewed to the left [71]. Factors that influence longevity differ over time depending on prevailing environmental conditions and are therefore time dependent [29] [72]. Survival data can be censored or uncensored. Events like death or culling may be known to have occurred and therefore will be uncensored. On the other hand, such events may not have been recorded because they are not known to have occurred. If animals are alive at the time of analysis, they will be included in the evaluation and are therefore regarded as censored [28]. These complex characteristics or features of survival data require careful consideration and choice of the appropriate modelling strategies in order to discover all phenotypic, additive and environmental variance [73]. Approaches used in the analysis of longevity include linear models [4] [35]. This method has been used for longevity measures defined quantitatively such as lifetime milk yield, age from birth or calving to last day in milk and total days in lactation. Other models include random regression [37], threshold, proportional hazard and random regression models [6].

This approach accounts for censored data or records of cows which are still alive at the time of analysis. Survival of an animal to a predefined age or time period is used. The time period or age t, is pre-determined on a time scale and the record of each animal is assigned a 1 or 0, for successful survival to that age or not, respectively. The model is as follows:

y i j ( t ) = μ + s i + e i j

where y i j ( t ) = 0 if the jth progeny of the ith sire did not survive to time t and 1 if it was alive at that time. μ is the overall popualtion mean, s i is the breeding value of the ith sire on the binary scale and e i j are random residuals. This approach to modelling longevity has been applied to Czech Fleckvieh [9], South African Jerseys [16] among other cattle populations [31] [74]. This approach is simple and can accommodate univariate as well as multivariate animal, sire or maternal grandsire models. The drawback of this model is that it makes unrealistic assumption that data are continuous and are normally distributed [75]. Animals at different ages before the pre-determined time point are treated the same way, leading to erroneous results [27]. Factors that influence longevity over the time period are not considered, since survival times are derived from a product [76].

Linear models are more appropriate in analyzing continuous traits such as milk yield rather than binary traits. This is the caution that was taken by [4]. In this study measure of longevity was continuous for example. lifetime milk yield, age from birth or first calving to last day in milk, total days in milk over all lactations were analyzed using linear models, while measures of longevity related to survival were analyzed using threshold models. This was necessary because the use of linear model BLUP was inappropriate because with categorical, data breeding values and residuals would not be independent of each other [77].

Random regression models model additive genetic values as a function of an observed dependent variable through a set of random coefficients. In modelling survival data using random regressions, animal records are assigned binary units (0 or 1) if it survived a lactation or a month after calving. A linear model with random regressions for additive animal effect as random effects is then fitted for genetic evaluation and breeding values generated for any point in the trajectory [6] [32]. A univariate random regression model is described as follows:

y i j k l m n o : t = ( Y S : H t ) i j + ( Y S A P : t ) i k l + r ( a , x m 1 ) n + r ( p e , x , m 2 ) k + e i j k l m n o : t

where y i j k l m n o : t is the n^th observation of the k^th animal at time t of the i^th fixed effect and j^th group, YS is the i^th year-season of first calving, H is the j^th herd, A is the k^th age at first calving class, P is the production level, y i j k l m n o : t = ∑ i = 0 m 1 a k l x i j k : l is notation for random regression, where a is the additive genetic effect for the kth animal, x are orthogonal polynomials of time t, after calving, a is the random regression coefficients for additive genetic effects for animal n, pe are the random regression coefficients for permanent environmental effects for animal n and e i j k l m n o : t are random residuals. Random regression models are more robust to effects of censoring data [78] and are closer to proportional hazard models and generalized linear models. They can also handle multiple traits [79].

Proportional hazard (PH) models model survival as the probability that an animal will survive past a specified time t, and the hazard function, which is the instantaneous rate of failure [80]. The survival function and the hazard functions in PH modelling differentiate between a cow that dies exactly at time t, and one that was last alive at time t, and may have survived on. PH models make the assumption that the hazard rate or risk is a function of time-dependent baseline hazard and an exponential function of a series of explanatory variables i.e. covariates [81]. PH models may not result in the best fit to data and therefore may not accurately estimate the performance of future offspring of an individual [82]. They also make the assumption that survival is the same trait throughout the lifetime, although correlations between parities 1 to 3 have been reported to be less than unity. Another limitation is their inability to account for non-random mating among animals [83] and cannot handle multiple traits [36] [82]. Despite these limitations they are able to handle censored data and can accommodate non-normal data distribution well and incorporate time-dependent environmental effects [27]. Common PH models include Weibull and Cox models, with the former being more popular.

In threshold modelling, survival is considered as a binary trait (0 = dead at time t and 1 = alive at time t). Threshold models include sequential threshold models, threshold repeatability models, and threshold cross-sectional models. Threshold models have been used to evaluate survival to weaning in pigs [84], survival in dairy cattle [82]. Threshold models have been used to analyze measures of longevity related to survival such as survival from birth or first calving to predetermined age [4]. The major limitation of threshold models is that heritability estimates are from an underlying continuous scale, and their effect on rate of genetic gain may be similar to that from linear models [83]. However, they are capable of handling multiple traits and can handle large datasets.

Linear, threshold and random regression models yield lower estimates of heritability, ranging from 0.01 to 0.18 [4] [37] than proportional hazard models (0.15 to 0.22) on the original scale. However, the former group of models is able to accommodate multiple traits and therefore can produce genetic correlations of longevity with other indicator traits [12]. [82] found that threshold models yielded higher heritability estimates (0.04) compared to those obtained from linear repeatability and cross-sectional models (0.02). In terms of accuracy of evaluations, the models were compared based on the correlation between true and estimated breeding values for proportion of sire’s daughters that survived to a specified age and sire ranking. The correlation for Weibull models remained constant over time, but increased over time for linear and random regression models, though they were lower than for the former models. The models also differed in terms of ranking of sires. For instance, linear models and Weibull models had similar sire rankings compared to proportional hazard models. Multi-trait models were also found to be superior in terms of predicting survival of daughters up to a certain age compared to Weibull models [32]. In this study, Weibull models showed poor prediction of proportion of daughters of sires in early cow lifetime than multiple trait models.

In general, linear and threshold models have been found to be superior to Weibull models when sire breeding values are estimated when predicting survival to 365 days from first calving [82]. Weibull models are better when predicting functional longevity while linear random regression and linear multiple trait models are the models of choice when predicting overall survival [32]. Linear models are however favored when studying the predictive ability of sire estimated breeding values of survival to a particular age, since this is better measured by average longevity instead of functional longevity. Threshold models are more appropriate for analyzing binary survival than linear models [83], while linear multiple traits and random regression models resulted in inferior statistical correctness (inferior model fit) [32]. Threshold sire models also result in higher heritability estimates than linear sire models