IOSR Journal of Agriculture and Veterinary Science (IOSR-JAVS) e-ISSN: 2319-2380, p-ISSN: 2319-2372. Volume 11, Issue 4 Ver. I (April 2018), PP 01-06 www.iosrjournals.org DOI: 10.9790/2380-1104010106 www.iosrjournals.org 1 | Page A Non-Parametric Method of Assessing the Yield Stability Using Principal Coordinate Analysis Tufleuddin Biswas, P. Dinesh Kumar A.B.Mandal, G.S.Mandal, S.Dewanjee (Agril.Statistics) (Genetics and Plant Breeding) Bidhanchandra Krishiviswavidyalaya, Mohanpur, Nadia, W.Bengal Corresponding Author: Tufleuddin Biswas Abstract: The Westcott (1986) method of stability analysis based on principal co-ordinate analysis is a simply non parametric method.The method depends ultimately on the choice of a suitable measure of similarity between genotypes.In the present study, there are 19 bread wheat genotypes for yield per plot under six environments are taken and as a result, there are two genotypes namely K7903 and Sonalika came out as stable genotypes. Further HUW100 and H1784 are stable for low yielding environments and HD2233, HD2214, HD2285 and CPAN1798 are stable for high yielding environments. Most of the stability information appears in a sequence of plots, where genotypes are immediately highlighted as consistently more remote points. --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 22-03-2018 Date of acceptance: 07-04-2018 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction Most of the measures relating to stability appeared in the literature are based on parametric methodology. Among those methods the Ebarhart and Russell (1966) methods,Finley and Wilkinson (1963) methods etc. are widely used approaches, which have some limitations. However here is need to look into a method which is robust and consistent in the assessing the stability of varieties when either certain locations are omitted or when sub-sets of varieties are analyzed. One such method is discussed by Westcott (1986) based on principal co-ordinate analysis.as this method is non parametric then no certain assumptions is needed. Hence it is easy to handle for the researcher and the breeder. II. Materials and methods Nineteen diverse genotype of bread wheat were taken for the present study. These genotypes were sown in three subsequent years with each at with a high and very low top dressing of boron respectively, making 6 six environments in all. Natural sets of environments can also be partitioned into the high and very low boron environments in turn. The method of study which is presented here is based on suitable measure of similarity between genotypes. In a particular environment, if L and S denotes the largest and smallest genotypes yields, then the similarity between genotypes’ yields x i and x j is defined byS(x i ,x j )= (L-(x i +x j )/2)/(L-S) if i and j are unequal ,while (x i ,x j ) = 1.The higher yielding the genotypes, as measured by their means, the more dissimilar, they according to this measure. The similarity is standarised by dividing by the yield range for the environment. When a set of environments is being considered, the similarity between x and y is just the mean of the similarities at advantage of the similarity matrix defined here is that in its principal coordinates analysis (Gower, 1966), no negative eigenvalues are obtained.Coordinates of points in a Euclidean space thus result, referred to principal axes, such that the distance between two points represents the dissimilarity between the corresponding genotypes. Each analysis produces a two-dimensional picture, in which the first two principal coordinates are plotted for each genotype. If distances are adequately approximated in this representation for a particular set of environments, genotypes which are above average yielding over these environments will be more dissimilar to the lesser yielding genotypes than the latter will be to each other and so will be represented by points which are more remote. Such plots show their value when the stability assessment is best on the sequential accumulation of environments. Thus, for the low-yielding environments, the first cycle (called LI) involves the analysis of the lowest-yielding environment, the second cycle (L2) involves analysing the two lowest-yielding environments, the third cycle (L3) adds the next lowest yielding environment.The lowest- yielding environment of those remaining being added at each cycle. Similarly, cycles HI, H2 and H3 respectively involve the highest-yielding environment, two highest yielding and three highest yielding environments based on the sequential accumulation of environments. Similarity matrix was also calculated considering all environments (cycle ALL). The environments are first ranked in descending order of mean yield and the low- and high-yielding environments are then examined in cycles’ environment s. Analysing these cycles produces a succession of pictures, in each of which the first two principal coordinates are plotted for each