CHAPTER I

INTRODUCTION

The aim of study is to describe the genetic parameter for traits reproduction dairy Friesian Holstein. The effective amount of selection pressure, however, in both cases depends on the degree to which the phenotypic variation, on which the selection differential and the selection coefficients are based, is reflected by genetic variation. It seems rather obvious that the changes in the genetic composition of a population from generation to generation, changes of which the shifts in the phenotypic mean will be representative (under a constant environment), are thus a function of the accuracy with which either nature or man recognizes genetic differences on the basis of phenotypic differences between individuals or groups of individuals. Intimations of this fact were apparent to early geneticists. Many of them recognized that a phenotype represents a combination of genetic and environmental effects, of which only the first would contribute to changes in a population, which are attributable to selection. As a single example the viewpoint of Yule (1906) may be cited. In discussing ancestor-offspring correlation, he stated: “A complete theory of heredity should take into account, besides germinal processes, the effect of the environment in modifying the soma obtained from any given type of germ-cell-an effect which is hardly likely to be negligible in the case of such a character as stature.” As early as 1910 Weinberg (1909, 1910) suggested methods of separating genetic and environmental components of total phenotypic variability, but his contribution to the subject was overlooked for many years, sharing the fate of his independent discovery of what was subsequently referred to in genetic literature as Hardy’s binomial (Stern 1943). It was only several years later that Wright (1917 et seq.) and Fisher (1918), independently of each other and apparently unaware of Weiberg’s papers, developed comprehensive techniques of dealing with the problem. The first of Wright’s papers dealt with a case in which the genetic and the environmental types of variation were separated by experimental rather than statistical means.
Similarly the environmental variance of the underlying variate may be independent of the mean genotypic value (the level of incidence or p), but this property may be lost on the p scale. This is apparent from the fact that environmental variance on the p scale, which, of course, is the total variance for any given fixed genotype, is equal to pq, where q =1-p. For the range of genotypes with p values from, say, .35 to .65, the environmental variance is reasonably constant, but in the extreme ranges of p from 0 to 0.1 and from 0.9 to 1.0, it is nearly directly proportional to p and to q respectively. Finally, the categorical nature of the p scale may obscure the finer degrees of measurable variation (as for example age of death, where viability in a set period of time is considered). All of these circumstances vitiate to some extent the utility of the degree of heritability determined on the p scale. Lush, Lamoreux and Hazel (1948) held that probit transformation avoids some of the objections to the p scale. As in the previously noted work of Wright, the transformation is based on the concept of an underlying variate with a normal environmental distribution, whose variance is independent of the genotypic level. The heritability on the probit scale is independent of the threshold value, above which the character will be manifested in individuals whose underlying variate exceeds it, whereas on the p scale heritability viding the genetic variance is not too large compared to the environmental variance) varies approximately in proportion to Zz/(ptj), where is the ordinate of a unit standard normal curve cutting off an area equal to p. The p scale heritability then, in terms of the probability of an individual exhibiting the character, would be low for values of p near zero or unity and relatively high for intermediate values. Robertson and Lerner (1949) have shown that the situation is similar where there are a number of underlying variates, although the distribution of h2 is, of course, somewhat different in form.
The probit transformation may be a satisfactory one for the purpose of comparing heritability values but it is not apparent how it can be used for devising optimum selection indexes nor is it at all convenient in many situations for computing expected rates of gain. It appears useful therefore to investigate the conditions, if any, under which serious errors are likely to result from the use of the convenient p scale and the nature and magnitude of such errors. Such an investigation might disclose that the p scale can be used without hesitation in many situations and with some reservations or with corrections in others. The results of such a study might also suggest in a general way the degree to which a scale can deviate from the optimum one without leading to selection indexes that depart seriously from the optimum or to computations of gain that are much in error. Where calculations of the gain from mass selection based on the p scale lead to correct results there is good reason to conclude that calculations of the gain from family and combined selection will also be accurate, as well as that the usual methods for the computation of optimum indexes will also be applicable to a high degree of approximation. The converse of this statement is, however, not necessarily valid. The present investigation is chiefly concerned with a study of the gains that would result from mass selection on an all-or-none basis in comparison to estimates of gains whose computations are based on heritability determinations on the p scale, as well as with gains that would result could selection be based on direct observation of the underlying variate. The bearing of these findings on indexes for combined individual and family selection is discussed briefly.

The Mathematical Model
The first step in the proposed investigation involves the comparison of genetic gains computed on the basis of h2 determined from the p scale with those expected on the postulate of a normally distributed underlying variate. The assumptions involved are that: (1) There is an underlying variate whose value is the sum of a normally distributed environmental component and an independent normally distributed genetic component; (2) The character is present in all those individuals, and only those, in which the underlying variate exceeds a certain threshold value; and (3) Gene substitutions have individually small and strictly additive effects on the underlying variate.
There is no claim made here that these conditions actually describe the situation with respect to all characters of an all-or-none nature. It is, however, reasonable to believe that a model in which additiveness is the property of the underlying variate (on what will henceforth be referred to as the x scale) approaches actual situations more closely than one based on additive gene action on the p scale.
These traits are subjectively scored categorical traits, influenced by both direct (calf) and maternal effects and with generally low heritabilities reported in the literature (Koots et al., 1994a). Friesian Holstein calving records for purebred dairy calves have not previously been used in the genetic evaluation of dairy breeds. Review index Birth weight record previously has been used as an indicator trait to avoid calving difficulties. High genetic correlations between calving ease and birth weight have been different univariate and bivariate analyses for Friesian Holstein calves born at first and later parities ranged from 0.44 to 0.51 for direct effects and 0.06 to 0.15 for maternal effects. Reported in reviews by Meijering (1984) and Koots et al. (1994b). This relationship is unfavorable because birth weight is positively correlated to growth rate after birth (Mohiuddin, 1993; Koots et al., 1994b).

yI xi 0 bI Zmi 0 mi Zai 0 ai ei
= + + +
yj 0 xj bj 0 Zmj mj 0 Zmi aj ej

There seems to be an optimal value for birth weight with regard to calf viability (Meijering, 1984). Koots et al. (1994b) reported positive genetic correlations between birth weight and perinatal mortality, suggesting that in most studies, birth weight was larger than optimum. Calving difficulty and stillbirth generally have higher incidences in the first parity vs. later parities and have been suggested in some studies to be genetically different, but correlated, traits in first and second-parity cows (Weller et al., 1988; Luo et al., 2002; Steinbock et al., 2003). This information is needed to review genetic parameters via evaluate whether more direct measures of calving difficulty and birth weight should be considered in the genetic evaluation based on field data.