## U.S. Department of Commerce

#### Date of this Version

2011

#### Abstract

An important use of genetic parentage analysis is the ability to directly calculate the number of offspring produced by each parent (*k _{i}*) and hence effective population size, N

_{e}. But what if parental genotypes are not available? In theory, given enough markers, it should be possible to reconstruct parental genotypes based entirely on a sample of progeny, and if so the vector of parental

*k*values. However, this would provide information only about parents that actually contributed offspring to the sample. How would ignoring the ‘null’ parents (those that produced no offspring) affect an estimate of N

_{i}_{e}? The surprising answer is that null parents have no effect at all. We show that: (i) The standard formula for inbreeding N

_{e}can be rewritten so that it is a function only of sample size and Σ (k

^{2}

_{i}); it is not necessary to know the total number of parents (N). This same relationship does not hold for variance N

_{e}. (ii) This novel formula provides an unbiased estimate of N

_{e}even if only a subset of progeny is available, provided the parental contributions are accurately determined, in which case precision is also high compared to other single-sample estimators of N

_{e}. (iii) It is not necessary to actually reconstruct parental genotypes; from a matrix of pairwise relationships (as can be estimated by some current software programs), it is possible to construct the vector of

*k*values and estimate N

_{i}_{e}. The new method based on parentage analysis without parents (PwoP) can potentially be useful as a single-sample estimator of contemporary N

_{e}, provided that either (i) relationships can be accurately determined, or (ii) Σ (k

^{2}

_{i}) can be estimated directly.

## Comments

Published in

Molecular Ecology Resources(2011) 11 (Suppl. 1), 162–171; doi: 10.1111/j.1755-0998.2010.02942.x