Quantifying the sources of variation in eosinophilia among Scottish blackface lambs with mixed, predominantly Teladorsagia circumcincta nematode infection

Eosinophils play a key role in defence against gastrointestinal nematodes. There is considerable variation among animals in the intensity of eosinophilia following nematode infection. However, the statistical distribution of eosinophils among animals has still to be determined. A better description of the variation among animals could provide biological insight and determine the most appropriate way to analyse the effect of eosinophils. We estimated blood eosinophil numbers in a flock of Scottish Blackface sheep that were naturally exposed to mixed, predominantly Teladorsagia circumcincta infection. Three of the four eosinophil counts were better described by a gamma distribution than by a lognormal distribution. The scale and shape parameters of the gamma distribution varied over time. Eosinophil counts differed among animals kept on separate fields before weaning and between singletons and twins but were not significantly different between years and genders. Eosinophil counts also differed among offspring from different sires and dams. The parameters of the gamma distribution were used to enable a power analysis. Large numbers of animals were required to reliably detect even large differences between two groups. These results indicate that methods appropriate for gamma distributions, such as generalized linear mixed models, will provide more reliable inferences than traditional methods of analysis and experimental design.