Strategies for Developing Core Collections of Safflower (Carthamus tinctorius L.) Germplasm – Part II. Using an Information Measure for Obtaining a Core Sample with Pre-determined Diversity Levels for Several Descriptors Simultaneously

A new technique for establishing a core sample from a large germplasm collection based on an information measure is proposed. The procedure is viewed as a classification scheme having two groups, viz., the core sample group and the non-core group with pre-assigned properties in terms of group sizes and the density distributions of several descriptors. That is, for a known or fixed core sample size, the proportion p[m,d,t] of each state m for each multistate qualitative descriptor d is pre-assigned within each group t. Similarly, for each continuous or quantitative descriptor d, the mean μ[d,t] and standard deviation σ[d,t] are pre-assigned. The probability of finding an accession with a given set of attributes or values in the vicinity of either of the two groups is estimated from the density of the pre-assigned composite model for each group. Then, based on an information measure a group is identified that has the highest density in the neighbourhood of any accession in the measurement space and each accession in the collection is assigned to that group i.e. the eore sample or the non-core group. The information measure that is used is the length of the message that can optimally convey the description of the measurements, which equals the negative value of the logarithm of the probability of obtaining the given set of measurements in the neighbourhood of anyone of the two groups. An accession that has the least length with regard to any group is assigned that group. The method is illustrated with a data set of safflower germplasm described by Balakrishnan and Suresh (2000) and Part I of this article. A scheme by which the accessions are stratified as per their geographical origin is also considered. The diversity indices of the core samples constituted by using various options in the proposed mcthod are compared with thosc of the whole collection as wcll as those obtained through simple or stratified random sampling.