Parentage analysis with few contributing breeders: validation and improvement

Validation of parental allocation using PAPA software (Duchesne P, Godbout MH, Bernatchez L. 2002. PAPA (package for the analysis of parental allocation): a computer program for simulated and real parental allocation. Mol Ecol Notes. 2:191-193.) was investigated under the assumption that only a small proportion of potential breeders contributed to the offspring sample. Inbreeding levels proved to have a large impact on allocation error rate. Consequently, simulations from artificial, unrelated parents may strongly underestimate allocation error, and so, whenever possible, simulations based on the actual parental genotypes should be run. An unexpected and interesting finding was that ambiguity (the highest likelihood is shared by several parental pairs) rates below 10% stood very close to exact allocation error rates (true proportions of wrong allocations). Hence, the ambiguity rate statistic may be viewed as a ready-made indicator of the resolution power of a specific parental allocation run and, if not exceeding 10%, used as an estimate of allocation error rate. It was found that the PAPA simulator, even with few contributing breeders, can be trusted to output reasonably accurate estimates of allocation error as long as those estimates do not exceed 15%. Indeed, most discrepancies between exact and estimated error then stood below 3%. Reproductive success variance had little impact on error estimate discrepancies within the same range. Finally, a (focal set) method was described to correct the estimated family sizes computed directly from parental allocations. Essentially, this method makes use of the detailed structure of the allocation probabilities associated with each parental pair with at least 1 allocated offspring. The allocation probabilities are expressed in matrix form, and the subsequent calculations are run based on standard matrix algebra. On average, this method provided better estimates of family sizes for each investigated combination of parameter values. As the size of offspring samples increased, the corrections improved until a plateau was finally reached. Typically, samples comprising 250, 500, and 1000 offspring would bring corrections in the order of 10-20%, 20-30%, and 30-40%, respectively.