INTRODUCTION
Commercial hybrid plant has potential to increase the world’s agricultural productivity. The first step in hybrid program is the development of inbred lines for a hybrids parents. Inbred lines are a population of identical or nearly identical plants that are usually developed by selfpollination (Sleper and Poehlman, 2006) and breeders have been developing a large number of inbred lines and evaluating their performance in crosses (Guo et al., 2013). During the early inbred line development from base population, each plant possesses different combinations of genes, resulting in various combinations of traits that respond differently. At this point, the inbreds sort themselves into unique patterns as the offspring plants segregate from the parent lines. During the phases of inbred line development, researchers select the seeds from the best plants in the best rows and plant those seeds for the next generation of testing. For most hybrid breeding programs, only a small proportion of crosses can be evaluated in the field. An accurate prediction of hybrid performance prior to and after some field testing is of crucial importance in maize breeding (Guo et al., 2013). Extracting inbred lines from the base population takes time, so it will be interesting if, during the extraction, there is useful information that appears for breeders on whether it is valuable or not. In order to get valuable results for the development of elite inbred, we must know genetic parameter from the inbred lines.
An equilibrium population consists of inbred lines and hybrids. The hybrids do not know their superiority, so they need to be extracted. The process of extraction of an equilibrium population will form an inbreeding population. One consequence of inbreeding is changes in the distribution of genetic variance (LopezFanjul et al., 1989; Fernandez et al., 1995; Fowler and Whitlock, 1999; Whitlock and Fowler, 1999). Under the assumption of segregation generation starting from selfing heterozygous individuals in the base population can form the structure of the F_{ 2} genotypes (Falconer and Mackay, 1996; Kearsey and Pooni, 1996). If we look at the groups of heterozygous genotype in an equilibrium population, they are a form of group pairs of inbred lines which have the possibility of being good hybrids. One parameter that is often used to assess the inbreeding population is variance component. Theory has shown that genetic parameters are present in an inbreeding population (Robertson, 1952; Mather and Jinks, 1982; Kearsey and Pooni, 1996; Hallauer et al., 2010).
With respect to a quantitative trait, a random mating population consists of a mixture of homozygous and nonhomozygous individuals where the latter is at least heterozygous for one locus. When the population is in equilibrium, their frequency is the product of the frequency of the genes they possess. Information on dominance variance in the population and the average degree of dominance are the basis prior to starting a hybrid program: Inbred lineshomozygous individualsare extracted, crossed in pairs and evaluated for heterosis in replicated experiments. Extraction is time consuming but there is no guarantee that elite in breds may be obtained in the evaluation phase. Using a single locus model with an arbitrary number of alleles, similar parameters relevant to a hybrid program are developed. The parameters: Heterosis, additive and dominance variance refer to the mixture of F_{ 2}S populations derived from all possible pairs of the in breds. Thus they are weighted averages.
Here we discuss the genetic parameters for selfing population through variance estimating of segregation generation in S_{ 1} (F = 1/2) and S_{2} (F = 3/4) families. In response to the described useful information that appears for breeders, we formulate the concepts to estimate the value of the base population by genetic parameters.
METHODOLOGY
Development of the theory: Consider a given locus in an equilibrium population π_{0} where there exists allele A_{ i} (i = 1, 2, ..., s) with frequency p_{ i}. The genetic structure of π_{0} is:
The population mean is:
where, μ_{ ij} is genotypic value of A_{ i}A_{ j}. Modelling μ_{ ij }statistically as μ_{ ij} = μ_{0}+α_{ i}+α_{ j}+δ_{ ij} with α_{ i} and α_{ j} is additive effect of allele A_{ i} and A_{ j} and δ_{ ij} is the dominance deviation or the interaction effect of allele A_{ i} and A_{ j}, the genetic variance of the population is measured according to Kempthorne (1969), Steel and Torrie (1980) and Nyquist (1990):
Where:
Table 1:  Composition of population, frequency, mean and variance when the coefficient of inbreeding is F 

and:
Inbred population derived from π_{0} is with mean and genetic variance . However, if inbreeding is up to an inbreeding coefficient of F, the resulting inbreeding population is π_{ F} = (1F)π_{0}+Fπ_{ 1} and is depicted in Table 1. Note that π_{ F} is a mixture of π_{0} and π_{ 1} with frequency of (1F) and F, respectively. Therefore, the mean of π_{ F}, denoted by μ_{ F}, is the expected value of the mean:

(1) 
while the variance, denoted by is the sum of variance of the mean, (1F) (μ_{0}μ_{ F})^{ 2}+F(μ_{1}μ_{ F})^{ 2} = F(1 F) (μ_{0}μ_{1})^{ 2} and the mean of the variance. Thus:

(2) 
An equation that according to Crow and Kimura (1970), Jain (1982) and Nyquist (1990) it was formulated for the first time by Wright (1951).
With selfing (F = ½), the population structure, denoted by is:

(3) 
The population mean is:

(4) 
Where:
Where:
H* as weighted intra varietal heterosis or weighted average heterosis in HardyWeinberg population.
Note that the expression in parentheses in the second term in Eq. 3 is an F_{ 2} genotypic array derived from A_{ i}A_{ i}×A_{ j}A_{ j} cross (i≠j). Denote the variance of this F_{ 2} by .Then variance within the S_{ 1} family is that with a common S_{0} parent:

(5) 
Further selfing gives an S_{ 2 }population (F = ¾), the structure of which is:
Note that in the second term, the expression in parentheses is an F_{ 2} and those in brackets is an F_{ 3 }derived from A_{ i}A_{ i}×A_{ j}A_{ j} cross. The mean of S_{2} population is:

(6) 
Within the S_{2} family variance is the variance within S_{2} families having common S_{ 1} parent is a half of F_{ 2} variance. Denote this by then:

(7) 
while within the S_{2} family variance having a common S_{0} parent is an F_{3} variance. Denoting this by then:

(8) 
then using Eq. 7, 8 estimate of variance of F_{3} mean can be obtained:

(9) 
Estimation procedure: From theory development, some parameters are of interest: and H^{*}. For estimating these parameters, from an equilibrium population, self a random sample of n individuals to generate S_{ 1} families. After saving some seeds from each ear for a replicated experiment, plant the remaining seeds in eartorom. In the ith (i = 1, 2, ..., n_{ i}( row, self a random sample of n_{ i} individuals to generate S_{2} families. Evaluate these:
S_{2} families together with n S_{ 1} families.
For simplicity of discussion, let the evaluation be conducted in a randomized complete block with r blocks as replicates. Analysis is done as shown in Table 2.
Table 2:  Analysis of variance for S_{ 1} and S_{2} families 

Let the mean of the S_{ 1} family data be_{S1}. It is an estimate of μ_{ S1 }=μ_{1/2}. Similarly for the S_{2} family data: _{S2} is an estimate of μ_{ S2} = μ_{ 3/4} Using Eq. 1, estimate of μ_{0} and μ_{1} may be obtained. Using Eq. 4 and 6 give an estimate of H^{*}.
Plottoplot S_{ 1} error variance consists of two components: Within plot environment and genetic within S_{ 1} family. Thus:
and estimated by M_{ 1}. Similarly for plottoplot S_{2} error variance:
and estimated by M_{ 2}. Recalling Eq. 5 and 7, these two equations can be solved to give incorporating Eq. 9 will yield. Finally, as and using Eq. 2, they may be used to give and .
RESULTS AND DISCUSSION
Inbreeding population may result from any inbreeding process. If this is so, only μ_{0}, μ_{1}, H^{*}, and can be estimated. Inbreeding through selfing will produce an F_{ 2} population if the selfed individuals are heterozygous. This unique characteristic is exploited to get parameters similar to the ones in line cross. In line cross, the parameters refer to a single F_{ 2} while ours refer to a mixture of F_{ 2} populations, each weighted by its frequency; hence, the average weighted parameters.
H_{ ij} in Eq. 4 is exactly d in Fisher notation with a subscript to remind that it refers to F_{ 2} population derived from A_{ i}A_{ i}×A_{ j}A_{ j} cross. Being related to the difference of μ_{0} and μ_{ F}, H* measures inbreeding depression, considered the reverse of heterosis, disregarding the number of loci involved.
Estimation procedure discussed above is a general one in the sense that it applies also when S_{2} families being evaluated may be generated from selfing S_{ 1} ears not included in the replicated experiment as when the seed number is a constraint. However, when they are, additional information, i.e., (Mather and Jinks, 1982) they can be used together with Eq. 8 to get . The latter is better in the sense that the estimation procedure is a direct one; no need to estimate . Better still, all information is used and the estimate is obtained using the least square method.
Note that:
using a notation of Fisher. It shows a better way to obtain . As:
their similarity to those of F_{ 2} in a line cross see standard textbooks on Quantitative Genetics such as Falconer and Mackay (1996) and Hallauer and Filho (1981) is apparent. Thus they may be extended to a multilocus model if there is no epistasis. Model extension with epistasis being included has also been available (Nasrullah et al., 1995; Kempthorne, 1969). The only difference is that they are weighted by their frequencies as their coefficient, instead of 1 as in a line cross.
A final point is to be mentioned. Though homozygous individuals in π_{0} are inbreds regardless of the number of loci, nonhomozygous ones are a mixture F_{1} hybrids in a single locus model but a mixture of F_{1} hybrids for one locus or more in a multilocus model.
CONCLUSION
Genetic parameters can be constructed by inbreeding. Inbreeding through selfing will produce an F_{ 2} population if the selfed individuals are heterozygous. The selfing families as expression in parentheses derived from A_{ i}A_{ i}×A_{ j}A_{ j} cross (i≠j(, produce some parameters are of interest: and H^{*}. The genetic parameters will then allow assessment for proper or improper assessment of hybrid programs before extraction of inbred lines are done too much.