Variance Effective Population Size for Two-Stage Sampling of Monoecious Species

During the process of collecting, storing, and regenerating germplasm, random changes in allele frequency due to sampling (genetic drift) occurs and affect the genetic representativeness of the population. Drift is quantified and predicted through the variance effective population size, Nₑ₍ᵥ₎. When sampling a population, drift may occur at two stages: (i) when parents are sampled (selected) for reproduction (ii) when gametes (offspring) are subsequently sampled from these parents. Hence, Nₑ₍ᵥ₎ measures should include drift due to sampling of zygotes, relative to the original population, and that due to gametic sampling, relative to the set of parents. In this paper, the variance of the number of contributed gametes, Vₖ and Nₑ₍ᵥ₎ were derived, under a two-stage sampling scheme for monoecious species. An alternative derivation, solely based on the theory of random sampling within finite populations, is also given for comparison with the previous result. Practical procedures involving full-sibs (FS), half-sibs (HS), and half-sibs stemming from a restricted set of parents (HS') for decreasing Vₖ, or increasing Nₑ₍ᵥ₎, for field collection of germplasm and accession regeneration are described. For germplasm collection, results showed the advantage of the HS scheme over a wide range of situations. In the HS system, collectors should take, from a random set of plants, an equal number of seeds from as many seed parents as possible. When the number of seed parent plants is small compared with the total number of plants, the FS system is always better than the HS'scheme. When the reference population is a germplasm accession, the FS is clearly superior to the HS and HS' alternatives. Under the proposed model, measures of Nₑ₍ᵥ₎ require clear definition of (i) the reference population and the proportion of effective parents, (ii) the mating scheme, (iii) the number of parents and offspring sampled, and (iv) the level of female and male gametic control. The combination of these factors will determine the final Nₑ₍ᵥ₎ value.