Inbreeding effective population size and parentage analysis without parents

Authors

Robin S. Waples, NOAA FisheriesFollow
Ryan K. Waples, Casa Azul

Date of this Version

2011

Comments

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

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_i 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_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 (k²_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_i values and estimate N_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 (k²_i) can be estimated directly.