Degree Type


Date of Award


Degree Name

Master of Science




Applied Mathematics


The twinning rate of North American Holsteins was analyzed using a linear sire model (LM) and a threshold sire model (TM) to estimate fixed effects and predict sire predicted transmitting abilities (PTAs). The data were 1,324,678 births of 37,174 sires of dams collected from the National Association of Animal Breeders (NAAB) calving ease database. Due to small numbers of triplets, they were not included in the analysis. The twinning rate was 5.02%. No differentiation between monozygotic and dizygotic twins was available, so all twins were assumed to be dizygotic. The sire model included relationships among sires and fixed effects of herd-year, season, parity, and sire groups. Heritabilities for the sire of the dam effect were estimated to be 2.10% for the LM analysis and 8.71% for the TM analysis.The sire evaluations ranged from 1.56% to 7.95%. The parity effect show a marked increase between first and second parities (1.17% vs. 3.95%), but this trend leveled off in parities 3, 4, and 5 or more (5-11%, 5.54%, and 5.54%, resp.). The season effect showed a peak in the spring and a valley in the fall (4.48% vs. 3.17%). Sire group effects were found to show sires born after 1990 to be more likely to cause twinning. The mean twinning rate for sires born before 1980 was 3.42% compared to mean of 4.25% for sires born after 1991. The highest sire evaluation for twinning rate had an estimated PTA of 7.95%. His observed frequency of twinning was 16.2%. The lowest sire PTA was 1,56%, while his observed frequency was 0.7%.


Copyright Owner

James Matthew Johanson



OCLC Number


File Format


File Size

67 pages

Included in

Mathematics Commons