The assumption that observed values for litter size result from a set of thresholds which impose a discontinuity to the visible expression of a continuous underlying variate has been tested using data from the French sheep recording scheme: 629 724 natural lambings for 32 different pure breeds and 66 379 litters obtained after synchronization treatment in 15 breeds. Frequencies of single, twin, triplet and higher-order births varied regularly with litter size within each fecundation type. The coefficient of variation of litter size was remarkably constant from breed to breed under both natural (0·35 to 0·40) and induced lambings for which it was higher (0·40 to 0·45). The regression of the difference between the first two thresholds of an underlying normally distributed variate on prolificacy was slowly negative for natural fecundation, but not significant for induced fecundation. A significant effect of fecundation type was found, resulting in a lower incidence of induced than of natural twin litters for the same level of prolificacy. Multivariate polynomial regression of frequencies on natural and induced prolificacy was used to predict expected frequencies of litter size and the proportion of lambs of each birth type.