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ThesisItem Open Access Study of genetic correlations under full -SIB mating system (Two loci case)(Department of Statistics, College of veterinary and animal sciences Mannuthy, Thrissur, 1985) Khin Moe Moe; KAU; George, K CA purely theoretical investigation entitled ,JA Study of Genetic Correlations under Fu ll-s ib Mating System (two lo c i case)*1 was carried out with the following objectives, i ) to derive the joint distribution (correlation table) and to find the correlation between fu ll -s ib pairs under fu l l -s ib mating system in the case of two lo c i when there i s no linkage as well as when there i s complete linkage. l i ) to derive the joint distribution (correlation table) and to find the correlation between parent-offspring pair© under fu l l -s ib mating system in the case of two loci when there is no linkage as well as when there is complete linkage, i i i ) to derive the joint distribution (correlation table) and to find the correlation between fu l l -s ib pairs under paront-offspring mating system in the case of two lo c i when there is no linkage as well as when there is complete linkage, iv) to derive the joint distribution (correlation table) and to find the correlation between parent-offspring pairs under parent-offspring mating system in the case of two lo c i when there is no linkage as well as when there is complete linkage. 2 Th© joint distributions of fu ll -s ib pairs and parent- ©Ffspring pairs undor fu ll-s ib gating system wore derived with the help of generation matrix technique and th© correlations wore worked out therefrom, assuming additive genie e ffec ts and using the product-momeni correlation coefficient formula. The correlations were worked out for tho f i r s t ten generations of fu ll -s ib mating in both cases of no linkage and complete linkage, & comparative study of fu ll -s ib correlations and parent-offspring correlationsf conducted both numerically and graphically, revealed that £i) evonthough fu ll -s ib correlation was greater than parent-offspring correlation in in i t ia l generation (random mating) when there was complete linkage, the la tte r increased more rapidly than the former from in it ia l generation to f ir s t generation and ( i i ) from the second generation onwards, the rate of increase in both o f correlations were nearly the same upto tenth generation. I t was interesting to note that the parent-offspring correlations wore of comparatively higher order than th© fu ll-s ib correlations in both cases of complete linkage and no linkage. Similarly, th© joint distributions (correlation tables) for fu ll-s ib pairs and parent-offspring pairs under parentoffspring mating system were derived employing generation matrix approach and the correlations for the f i r s t ten 3 generations of parent—offspring mating in both cases of no linkage and complete linkage were worked out therefrom. A comparative study of those correlations was carried out both numerically and graphically. It was found that the trend in both correlation curves remain the same, but the value of parent-offspring correlation was always greater than that of full-sib correlation in case of no linkage as well as in caso of complete linkage. In comparison of all these correlations, it was found that the correlations increased as the number of generation increased and ultimately reached the limit unity when the number of generations increased indefinitely large. It was also observed that the magnitude of correlation in case of complete linkage was more than that of correlation In case of no linkage even under the same system of mating*ThesisItem Open Access Designs balanced for residual effects(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1984) Sathianandan, T V; KAU; George, K CThe usual problem in long term experiments is that due to residual effects of treatments. The effect of a treatment that persists for a period after the application of the treatment is referred to as residual effect of that treatment. In the present study an attempt is made to construct designs which will balance for first order residual effects to suit the above mentioned situations. By definition a design is said to be balanced if every treatment follows every other treatment equally frequently. We have established three different methods of construction of such type of designs. The first method of construction is by using cyclic latin squares as in the line of Amble (1977) and we have shown that such an arrangement is balanced for first order residual effects. The second method of construction is based on the set of (v-1) orthogonal latin squares of order v in the case of v treatments. A third method of construction of designs balanced for first order residual effects is also given. This is based on the procedure given by Nair (1967) for the construction of designs balanced for pairs of residual effects. A general intuitive method of analysis is also given.ThesisItem Open Access Influence of weather parameters on yield of coconut(Department of Statistics, College of Veterinary & Animal Sciences, Mannuthy, 1985) Pankajakshan Nair, B; KAU; Gopinathan Unnithan, V KInfluence of eighteen climatic factors for a period ranging from 10-45 months before harvest of coconut, were studied on monthly and annual coconut yield. Monthly climatic factors showed a seasonal relationship with monthly yield changing sign alternatively. Month-wise and season-wise climate and their influence on monthly and annual yield was also studied. The influence of climatic factors were more in evidence during pre and post monsoon seasons. RH, SSH and EV are frequently showed significant relationship with monthly yield than the rest. Seasonal grouping of climate showed stronger relationship on annual yield than month-wise climate. May, September, October and December months of yester years showed explicit association with annual yield.ThesisItem Open Access Confounded asymetrical factorial designs construction and analysis(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1984) Santy George; KAU; George, K CExperiments in agriculture require several types of designs. Situations in which treatments are combinations of factors with asymetrical factors are many. When the total number of treatment combinations is large, confounding is practised In order to get more precise estimates. Confounding is inextricable mixing up interaction effects with block effects. In the present study four different methods of construction of asymmetrical designs are attempted. In the first method polynomials In Galois field ore used for construction. These polynomials ore devised on the basis of two lemmas and following the line of Kichen end Srivastava (1959).ThesisItem Open Access Pattern of occurrence of rainfall and estimation of rainfall probabilities in northern districts of Kerala(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1987) Santhoh, K; KAU; Prabhakaran, P VA study was undertaken with a view to characterize the pattern of occurrence of rainfall and to estimate the rainfall probabilities and confidence limits at six reporting stations of the northern districts of Kerala viz, Kasaragod, Irikkur, Cannanore, Kozhikode, Quilandy and Mananthody, Daily rainfall data of the past 30 years were used to investigate the pattern of fortnightly and seasonal rainfall occurrence by fitting a first order Markov chain model to the sequence of wet and dry days. The rainfall probabilities and confidence limits were computed by fitting appropriate probability distributions to fortnightly rainfall amounts. The results of the analysis showed that at all the centres, there were more chances for a wet day to be preceded by a wet day than by a dryday. The maximum expected length of wet spell at different centres was observed during 12th to 14th fortnight of the year. The state occupation probability at equillibrium for a wet day was also foundmaximum during the same period. It could be seen that at all the centres, the likely commencement of southwest monsoon would be in the 11th fortnight. Suitable probability distributions from among normal, root normal, log normal and gamma distribution were selected and fitted to fortnightly amounts of rainfall. Rainfall probabilities of getting a fixed amount or less of rainfall wore worked out together with the 80% and 90% confidence limits of the mean fortnightly rainfall. The 3rd fortnight of the year all over the centres was found to be the driest fortnight and the 12th or 13th fortnight was found to be the wettest fortnight of the year.ThesisItem Open Access Standardisation of techniques of clustering genotypes using mahalanobis D2 and wilks ^ criterion(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1986) Suresh, K M; KAU; Gopinathan Unnithan, V KTwo major drawbacks of Tocher's method of clustering genotypes using Mahalanobls D were pointed out and animprovement over Tocher's method was suggested. The cluster configuration obtained by these two methods were compared with those obtained by canonical analysis method. A new computer oriented iterative algorithm for clustering using Mahalanobis D values was proposed. A procedure for formation of clusters statistically, using O V Mahalanobls Er was suggested to form maximum nonsignificant subsets of genotypes. A new measure of dissimilarity which does not require any assumption on distribution of the population, viz., the determinant of the pairwise scatter matrix was proposed in the study. Minimum /W/ criterion of Friedman and Rubin (1967) was also used for clustering. The clustering obtained by the new iterative algorithm using either Mahalanobls or determinant of pairwise scatter matrix or both could be used as the initial solution for it A graphical method for determining the optimum number of clusters was suggested The different methods were illustrated in two sets of dataThesisItem Open Access Selection indices on goats- a comparative study(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1985) Rema, T P; KAU; Sunny, K LRecords on birth weight, age at first kidding, body weight at first kidding and first lactation milk yield of Malabari, Sannon % tnalabari (SM) , Alpine X Malabari (AM) and AM X AM (F2 A) goats from 1974- 1984 were examined to make a comparative study of selection indices constructed by employing different methods. The relative economic value of each trait in rupees was calculated as 29,96 for birth weight, 0.67 for age at first kidding, 20.83 for body weight at first kidding and 18 for first lactation milk yield. Simultaneous selection indices wore constructed by incorporating all tho traits together for each breed and on finding the percent gain in efficiency of each index over that due to straight selection, the efficiency of index selection was proved. Out of the seven restricted selection indices constructed for each breed, imposing restriction on birth weight was found effective for Malabari, SM and F2A breeds and restriction on body weight at first kidding was effective for both f 2 a and AM breeds. But all these effective restricted selection indices, except the one for Malabari breed (when birth weight was restricted) were increasing the age at first kidding. Seven phenotypic selection indices were constructed for each breed. But none of them was found improving the first lactation milk yield of Kalahari and F2A goats. For SM breed, the best index was the one constructed between the main trait first lactation milk yield and the auxiliary trait age at first kidding. Relative efficiency was the largest, when all the auxiliary traits were considered simultaneously for improving the first lactation milk yield of AM goats.ThesisItem Open Access Optimum size of plots in cocoa (Theobroma cacoa L.) a multivariate case(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1987) Sheela, M A; KAU; Gopinathan Unnithan, V KA procedure to determine optimum size of experimental units in the multivariate case was proposed. For the purpose, the matrix of relative dispersion was defined and its determinant was used as the measure of variation for comparison of plots of different sizes. This procedure was illustrated with the help of observations on three characters of 738 trees of 'Forastero1 variety of cocoa raised in the' KADP farm of the Kerala Agricultural University, Vellanikkara. Optimum plot size also was obtained in the univariate case. The following three different methods of plot formation were used in this investigation. Method I The whole set of trees were divided into compact blocks of different sizes and plots of one to fifteen trees were formed by combining adjacent trees in the field. Method II All trees were arranged in descending order of magnitude of trunk girth and of the canopy spread separately and were divided into blocks of required size. Plots of one to fifteen trees were formed by combining adjacent trees in the list in each block for each arrangement. Method III The trees were first arranged in descending order of magnitude of each character and they were divided into blocks of required size. Plots of different sizes were formed within each block by the following procedure, let there be 'nk* trees in a block. The nk trees were divided into 1 n 1 groups of 'It* trees each bearing continuous serial numbers * When 'n' is even, the 1st plot was formed by combining 1th tree from each of the first 'n/2* groups and (k-i+j)st tree from each of the remaining 'n/2' groups, where i=1,2,....n. When 'n1 is odd, ith plot was formed by combining the i^h tree from each of the first (J[n+iy2) groups and (k-i+fy9^ tree from each of the remaining [(n-lj/2) groups, whore 1=1,2, n. Of the three methods of plot formation Method III, which was proposed in this study was found to be superior to Methods I and II for experiments in established gardens and Method I for experiments for which fresh planting is required Optimum size of plots were al so determined by three different methods viz., (a) that which requires minimum experimental material for a specified precision (b) that which has maximum efficiency and (c) that for which the best fitting model has maximum curvature.ThesisItem Open Access Forecasting models for the yield of coconut(Department of Statistics, College of Veterinary and Animal Sciences, Mannuthy, 1985) Myint Swe; KAU; George, K CAn analysis of the yield data of 91 coconut palms, maintained at Coconut Research Station (Nileshwar I), Regional Agricultural Research Station, Pilicode, under Kerala Agricultural University and the weather data for the region of Pilicode, collected from Central Plantation Crops Research Institute (CPCRI), Kasaragod District, Kerala was carried out with the following views and objectives. 1) To develop a suitable and reliable statistical methodology for the pre-harvest forecast of coconut crop yields by evolving different empirical-statistical crop- weather models using the original and generated weather variables as predictor variables. 2) To perform a comparative study of relative efficiency, adequacy and performance of each of these crop- forecasting models evolved and to select the 'best1, most promising and plausible crop forecasting models for the purpose of future use in predicting the coconut crop yields reliably in advance of harvest, 3) To investigate the effect and influence of changes in weather variables on the yield of coconut crop, based on the crop forecasting models selected as the 'best' fitted models. 4) To render suggestion and guidelines for further development of statistical crop-weather models, criteria for their selection, and relevant statistical analysis, In this study, the twelve crop forecasting models for the yields of coconut were developed and fitted under the effective crop season of 3 years (i.e., as far back as 36 months from the first month just before a half-year harvest) with 3-month and 6-month period (season), using the generated weather predictor variables. The response variable was taken as average yield of nuts per bearing tree per half year, and the original weather variables were total rainfall, duration of bright sunshine hours, wind velocity, relative humidity and maximum temperature. Since the relative humidity is expressed in percentages, the datawere transformed into arc—sine root proportion.
