A Sampling Strategy for Conserving Genetic Diversity when Forming Core Subsets

The grouping of accessions into clusters is achieved by a classification strategy that partitions the original colWhen forming core subsets, accessions from a collection are classilection into groups with maximum distances between fied into clusters, and then samples are drawn from the clusters with accessions located in different groups and minimum disthe aim of maintaining the diversity of the collection. In a stratified tances between accessions located in the same group. sampling strategy, the allocation method provides a criterion for determining the number of accessions to be selected from each cluster. Franco et al. (1998, 1999, 2002) and Franco and Crossa This paper proposes an allocation method (D method) and compares (2002) proposed a sequential Ward-Modified Location it with three other allocation methods (L, LD, and NY methods). In Method (MLM) strategy in which the Gower (1971) these allocation methods, the number of accessions sampled per clusdistance is used as a measure of similarity (or distance) ter is proportional to (i) the mean of the Gower’s distance between among accessions considering all continuous and cateaccessions within the cluster (D method), (ii) the logarithm of the gorical variables. The initial groups were formed by the cluster size (L method), (iii) the product of the cluster size times the Ward (1963) method, and then the MLM was used to mean Gower distance (NY method), and (iv) the product of the logaimprove those groups. The Ward-MLM strategy was rithm of the cluster size times the mean Gower distance (LD method). used for analyzing the Latin American Maize Project Five hundred independent stratified random samples with two sam(Taba et al., 1999) and Caribbean maize collections pling intensities (10 and 20%) were obtained from four datasets. The (Taba et al., 1998) with data from more than 10 countries allocation methods were compared on the basis of three criteria: diversity of the samples, recovery of the range of variables in the and with the number of observations per collection rangsample, and variances of the samples. Results showed that the D method ing from 100 to 1800 and a mixture of continuous and produced samples (i) with significantly more diversity than the other discrete variables. These studies demonstrated that the allocation methods, (ii) that recovered more of the range of the variWard-MLM formed compact and well separated clusters. ables, (iii) with higher variances for the continuous variables than the The reason for sampling accessions when forming other three methods, and (iv) with variances higher than the variance core subsets is to identify a strategy that will structure among accessions of the collection. A sampling intensity of 10% prea sample that recovers most of the diversity contained serves the same or more variability than a sampling intensity of 20%. in the original collection, while maximizing the variance and the distances between accessions in the sample. A sampling strategy involves defining a sampling intensity, G resources stored in gene banks are usually a sampling method, and an allocation method (Thompsampled to foster efficient evaluation and utilizason, 2002). tion of the collections as well as to study phenotypic and The sampling intensity defines the overall sample size, genotypic diversity, form core subsets, and eliminate and for core collections, several authors studied samredundant and duplicate accessions within a collection. pling intensities that ranged from 5 to 20% of the total The main purpose of these activities is to preserve in the number of accessions (Brown, 1989; Schoen and Brown, sample as much of the diversity present in the original 1993; Brown and Spillane, 1999; van Hintum, 1999; van collection as possible (Crossa et al., 1995a). For examHintum et al., 2000). For species such as perennial ryeple, the approach of forming core collections (core subgrass (Lolium perenne L.), Charmet and Balfourier sets) was introduced to increase the efficiency of de(1995) found that a sampling intensity of 5 to 10% is scribing and using collections stored in gene banks, while optimal for capturing 86 to 90% of the diversity. Howpreserving as much as possible the diversity of the entire ever, for forming core collection of Medicago species, collection (Frankel and Brown, 1984; Brown, 1989). Diwan et al. (1995) pointed out that sampling intensities The process of sampling genetic resources with the of 5 to 10% are insufficient to represent the original colobjective of forming core subsets starts with grouping lection. accessions to obtain homogeneous within and heteroA stratified sampling method partitions the collection geneous between clusters (or groups) and then using a into clusters or groups, and then accessions within each predetermined sampling strategy within each cluster. cluster are selected. Several authors have recommended stratified sampling strategies for managing genetic resources and forming core subsets (Peeters and MartiJ. Franco, Facultad de Agronomı́a, Universidad de la República, Av. nelli, 1989; Crossa et al., 1994, 1995a; Spagnoletti Zeuli Garzón 780 CP 12900, Montevideo, Uruguay; J. Crossa, Biometrics and Statistics Unit, CIMMYT, Apdo. Postal 6-641, 06600, Mexico DF, and Qualset, 1993; Charmet and Balfourier, 1995; RinMexico; S. Taba, Maize Genetic Resources Unit, CIMMYT, Mexico; con et al., 1996). Statistical methods for stratifying and H. Shands, National Center of Genetic Resources Preservation genetic resources using three-way data (accessions (NCGRP), USDA, ARS, Fort Collins, CO 80523. Received 12 May 2004. trait location), with the purpose of forming core subPlant Genetic Resources. *Corresponding author ([email protected]). Published in Crop Sci. 45:1035–1044 (2005). doi:10.2135/cropsci2004.0292 Abbreviations: DA, days to anthesis; DS, days to silking; EH, ear height; GM, grain moisture; MLM, Modified Location Model; PH, © Crop Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA plant height. 1035 Published online May 6, 2005