Markov chains as a shortcut method to estimate age distributions in herds of beef cattle under different culling...

Markov chains were used to estimate the age distribution at equilibrium and average age in herds of beef cattle and the age distribution and average age of culled cows. These estimates are essential in systems simulation and economic analyses of beef production alternatives because the biological input and output from a beef production system depend on the age structure of the cows in the system. Ten sets of data on age-specific probabilities of culling for different reasons were found in the literature and used in simulation of different culling strategies. Three different culling strategies were simulated using these data. In addition to culling on maximum age, culling was either based on health alone, health and reproductive failure in one year (not pregnant) or health and reproductive failure in two consecutive years (not pregnant twice). The average herd age in the data sets reviewed under the actual culling strategies ranged from 4.58 to 6.73 yr and the average age of culled cows ranged from 5.41 to 9.94 yr. Description of the culling process as a Markov chain enables calculations of the age distribution at equilibrium by simple matrix operations, an advantage over the methods presently used. The scarcity of estimated age-specific probabilities of health and reproductive failure points to the need for more population analyses of beef cattle.