Sample size for collecting germplasms--a polyploid model with mixed mating system.

The present paper discusses a general expression for determining the minimum sample size (plants) for a given number of seeds or vice versa for capturing multiple allelic diversity. The model considers sampling from a large 2 k-ploid population under a broad range of mating systems. Numerous expressions/results developed for germplasm collection/regeneration for diploid populations by earlier workers can be directly deduced from our general expression by assigning appropriate values of the corresponding parameters. A seed factor which influences the plant sample size has also been isolated to aid the collectors in selecting the appropriate combination of number of plants and seeds per plant. When genotypic multiplicity of seeds is taken into consideration, a sample size of even less than 172 plants can conserve diversity of 20 alleles from 50,000 polymorphic loci with a very large probability of conservation (0.9999) in most of the cases.

A general model for sample size determination for collecting germplasm.

The paper develops a general model for determining the minimum sample size for collecting germplasm for genetic conservation with an overall objective of retaining at least one copy of each allele with preassigned probability. It considers sampling from a large heterogeneous 2k-ploid population under a broad range of mating systems leading to a general formula applicable to a fairly large number of populations. It is found that the sample size decreases as ploidy levels increase, but increases with the increase in inbreeding. Under exclusive selfing the sample size is the same, irrespective of the ploidy level, when other parameters are held constant. Minimum sample sizes obtained for diploids by this general formula agree with those already reported by earlier workers. The model confirms the conservative characteristics of genetic variability of polysomic inheritance under chromosomal segregation.