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Context In the present study we assessed the use of average relationship as a means to control future rates of inbreeding in small cattle closed nucleus and its effect on genetic gain for milk yield as a means of managing genetic variability in livestock improvement programs. Aim The aim was to strike an ideal balance between genetic gain and loss of genetic variability for Sahiwal population. Methods A total of 8452 milk yield records of Sahiwal cows from National Sahiwal Stud, Kenya, were used to estimate breeding values and 19315 records used to estimate average relatedness of all individuals. The estimated breeding values and genetic relationships were then used to optimise individual genetic contributions between the best two males and the top 210 females in 2000–2008-year group, as well as between the best four, six and eight males and top, 420, 630 and 840 females based on estimated breeding values for lactation milk yield. Weights on genetic merit and average relationship considered in this study were (1, 0), (1, −300), (1, −500), (1, −1000) and (0, −1). Key results When the best sires were selected and used for mating disregarding average relationship with their mates i.e. (0, –1), genetic gain of up to 213 kg was realised accompanied by a rate of inbreeding per generation of 4%. Restricting average relationship alone i.e. (0, –1), resulted in a future rate of inbreeding of 1.6% and average merit of 154 when top two sires were used for breeding. At the same restriction level but using eight top sires, the rate of inbreeding per generation was 0.9% accompanied by an average merit of 128.2 kg. Controlling average relationship between mates resulted in increased genetic variability i.e. lower rate of inbreeding though average merit declined. Conclusion A rate of inbreeding per generation of |