Abstract: Phenotypic expression of a trait is a function of both the genotype of the animal and the environment that influences it. Connectedness among management units is of concern in genetic evaluation. In this study, for considering effect of genetic connectedness effect on the genetic evaluation, comparisons of estimated evaluations and genetic parameters in two cases lack and un-lack (GC) have been written in the C⁺⁺ language program by simulation method in sheep herds with consideration of natural conditions (fertility percent, mortality percent). It is argued that connectedness increases as the proportion of offspring from common sires. A high level of connections improved the accuracy of the genetic evaluation. Connectedness ratings were higher for highly heritable traits and lower for traits with low heritability.

INTRODUCTION

Phenotypic expression of a trait is a function of both the genotype of the animal and the environment that influences it. Connectedness can be defined as a measure of the relationships between herds or contemporary groups as they affect the accuracy of comparing the genetic values of animals from one herd or group to the other. The higher the connectedness, the more accurate the comparisons of EBVs across groups or herds. A simple approach to increase connectedness between paired herds is to use common sire by Artificial Insemination (AI). The magnitude of this increase depends upon the magnitude of their use in both herds. If there are few or no genetic connectedness between a herd and the reminder of the tested population, the EBVs of animals in that herd cannot be compared accurately to the EBVs estimated in other herds (Banos and Smith, 1991).

The concept of connectedness in experimental design was first defined by statisticians (Bose, 1947). To prevent lack of connectedness developed the use of reference sire progeny testing schemes (Hanocq et al., 1996; Kennedy and Turs, 1993).

Geneticists also developed methods to check for disconnection or to measure the degree of connectedness in a design (Peterson, 1978; Foulley et al., 1990, 1992). In this study for considering effect of genetic connectedness on the genetic evaluation, comparisons estimated evaluations and genetic parameters in two case lack and un-lack (GC) in herds with consideration of natural conditions have been written in C⁺⁺ language by Stochastic simulation method.

MATERIALS AND METHODS

First, a base population defined with parameters (additive genetic SD, environment SD) that before had reported in the research studies then divided to 10 herds (genetic groups) with equal number animals (500 ID) (Mathur et al., 1998; Radjabalizadeh, 2007).

The genetic groups defined in the situation of connectedness (common sire, son of sire, relative). The simulation program has been written in the C⁺⁺ language.

The Components of (Co) variance and genetic parameters for BW, WW and SL were estimated by DFREML software. With infinite loci additive genotypic values are normally distributed in large randomly mated populations in Hardy-Weinberg equilibrium. We assume that parents are unrelated and are sampled from an infinite base population in equilibrium. Additive genetic values can be simulated from a normal (0, 1) random number generator as follows (Kennedy, 1995):

Where:

If Phenotypic observations (P) are required, an Environmental term (E) simulated as:

Where, ESD = Environmental Standard Deviation, can be added to G. Offspring additive genetic values (A_o) can be simulated from parental additive genetic values plus a term for Mendelian Sampling (MS) as:

Where, A_p and A_m are the additive genetic values of the sire and dam, respectively. In a non-inbred population:

So, the MS term can be simulated as:

This process can be repeated over any number of generations. In general for each trait in next generation can be simulated as:

Where:

The genetic evaluation can be estimated for each animal by Animal model in single trait as:

Where:

In matrix notation, the model is:

Where:

The genetic evaluation can be estimated for each animal by Animal model in record repeated model as:

Where:

In matrix notation, the model is:

Where:

The high performance individuals in each generation base upon the selection method (phenotype or genotype) evaluated then selected for creation of next generation. The selected parents have been crossed in random case (Radjabalizadeh, 2004, 2007).

RESULTS AND DISCUSSION

Statistics analysis: From simulation data for estimating of variance components and genetic parameters by use of animal model (single trait and repeatability record) for BW, WW and SL traits in three case of connectedness are shown in Table 1 and 2.

Table 1:	Comparison of variance components and genetic parameters estimated for three case of GC
1: Repeatability; 2: Heritability; 3: Phenotypic variance; 4: Error variance; 5: Permanent environmental variance; 6: Additive genetic variance; 7: Birth weight; 8: Weaning weight; 9: Staple length

Table 2:	Comparison of variance components and genetic parameters estimated for the lack of GC and PBV

CONCLUSION

There is significant difference between average EBVs in lack and un-lack genetic connectedness between herds. The study shows that connectedness increases as the proportion of offspring from the common sire increases. It is very high if 100% of the offspring in both herds is from common sires.

If the proportion of offspring from the common sires is low in one of the herds, the other herd has to have a large proportion of offspring to reach a higher level of connectedness. If the sires have <25% of offspring in another herds, the maximum level of connectedness rating possible is about 15% even if >50% of the offspring in the original herd are produced from the common sires. However, if the sires have >75% of the offspring in the other herd, the connectedness rating increases with the percentage of offspring in the original herd. Connectedness ratings were higher for highly heritable traits and lower for traits with low heritability.