IOSR Journal of Agriculture and Veterinary Science (IOSR-JAVS) e-ISSN: 2319-2380, p-ISSN: 2319-2372. Volume 11, Issue 7 Ver. II (July 2018), PP 16-36 www.iosrjournals.org DOI: 10.9790/2380-1107021636 www.iosrjournals.org 16 | Page Common Mating Designs in Agricultural Research and Their Reliability in Estimation of Genetic Parameters Luka A.O. Awata 1 ; Beatrice E. Ifie 2 ; Pangirayi Tongoona 2 ; Eric Danquah 2 ; Philip W. Marchelo-Dragga 3 1 Directorate of Research, Ministry of Agriculture and Food Security, Ministries Complex, Parliament Road, P.O.Box 33, Juba, South Sudan, 2 West Africa Centre for Crop Improvement (WACCI), Collage of Basic and Applied Sciences, University of Ghana, PMB 30, Legon, Ghana; 3 Department of Agricultural Sciences, Collage of Natural Resources and Environmental Studies, University of Juba, P.O.Box 82 Juba, South Sudan. Corresponding Author: Luka A.O. Awata Abstract: Population development and hybridization are important for improvement of both quantitative and qualitative traits of different crops and are determined by proper selection of mating designs as well as the parents to be mated. Mating design refers to schematic cross between the groups or strains of plants and has been extensively used in agriculture and biological sciences. The mating design in plant breeding has two main objectives: (1) to obtain information and understand the genetic control of a trait or behavior that is observed, and (2) to get the base population for the development of plant cultivars. Analysis of variance in offspring plants resulting from mating designs is used to understand the additive and dominant effects, epistasis and heritability. Various mating designs are available and have been effectively utilized to create different kinds of relatives and to estimate the additive as well as other genetic variance components. Choice of a mating design is based on the breeding objectives and the available capacity such as time, space and cost. It is assumed that individuals used in a mating design are selected at random and crossed to form progenies that are related to each other as half- sibs or full-sibs. Variations among the progenies (sibs) can be assessed using analysis of variance procedures. Mating designs most used are those that can be easily analyzed by normal statistical procedures and provide components of variance that can be translated into covariance of relatives. Although various mating schemes have been introduced, very few of them have been maximized in crop improvement. This is because majority of breeders and geneticists are disadvantaged by inadequate knowledge about the specificity of value each scheme could offer to crop improvement. The objective of this review was to underscore the different forms of mating designs and to shed some light on their implications in plant breeding and genetic studies. The review may provide easy and quick insight of the different forms of mating designs and some statistical components involved for successful plant breeding. Keywords: Sib mating, genetic variance, crosses, statistics, progeny, population --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 16-07-2018 Date of acceptance: 30-07-2018 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction Various experimental mating designs are developed for the purpose of estimating genetic variance, based on correlation between relatives and how they are used to partition the variations into different genetic components using second degree statistics [1], [2]. Major roles of mating designs are: (1) to provide information on the genetics of the character under investigation; (2) to generate a breeding population to be used as a basis for selection and development of potential varieties; (3) to provide estimates of genetic gain and; (4) to provide information for evaluating the parents used in the breeding program [3]. Various levels of relatedness among relative progenies are determined by making series of crosses among individuals of random mating population. These generate different statistical components of variation from which genetic variances can be estimated. The genetic components of the variance are used to estimate relationships among the relatives [1]. Evaluation of the progenies in multi environments using appropriate experimental designs and statistical analyses provides good understanding of genotype, environment and genotype x environment interaction effects and reduces error. In addition, the additive model allows estimation of components of variance. Precision of estimates of genetic variance for any mating design depends on number of replications and environments, level of inbreeding of the parents and number of progenies involved [1], [4]. Experiments are analyzed to estimate experimental error in which expectations of expected mean squares (EMS) are expressed in terms of components of variance. These components of variance are then translated into covariance of relatives
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IOSR Journal of Agriculture and Veterinary Science (IOSR-JAVS)
Since the lines are pure, they can be multiplied without changes in their genetic compositions and thus
are the best materilas to be considered for biological studies aimed at estimation of genetic variances [23].
Frequency of alleles at heterozygous locus at F2 is given p=q=0.5. However, the genetic coefficient for
convariances of relatives F ≈ 1 at the later inbreeding stage [5]. Similarly, variance component (σ2g) is
equivalent to additive component (σ2
A). Therefore, heterosis within pure line is not important because at the
advanced inbreeding stage, dominance (difference in allele frequency between loci) is minimized or lost [24].
Seed of selected homozygous (pure) lines can be multiplied without alteration and evaluated in replicated
experiments across locations (Table 2).
Table 2. The analysis of variance for pure line progenies tested in replicated trials across locations Source of variation Df Mean Squares Expected Mean Squares
phase linkages are overestimated [5]. A reference population (F2) is used to develop progenies by backcrossing
randomly chosen males (S0) from the F2 population to each of the parents (females) of the F2 (Figure 5).
Figure 5. Diagram for generation of progenies using NC Design III
The focus on expected mean squares is based on the component of variance among males and the one
for the interaction of males and inbred parents [29], [30]. The design provides exact F-tests of two hypotheses
concerning the relative importance of dominance effects: (1) that dominance is not present (this can be tested by
comparison of the M1 and M2 mean squares (Table 7); and (2) that dominance is complete. Sufficient sampling
of the F2 population is required so as to obtain valid estimates of components of variance to determine average
level of dominance. However, to make proper sampling the number of progenies produced may get huge.
Therefore, local control of error can be done by grouping the pairs of progenies into sets. Analysis is done for
each set and the sums of squares and degrees of freedom across sets are pooled to estimates the variance
components. These components are important for estimating narrow-sense heritability in the F2 populations.
Estimate of narrow-sense heritability based on the mean of r plots in one environment can be determined as
follows:
h2 = (4σ
2m) / (σ
2/r + σ
2mp + 4σ
2m) (40)
Table 7. Analysis of variance for NC Design III progenies Source of variation Df Mean Squares Expected Mean Squares (Model II)
Replications r-1
Parents (p) 1 M4 σ2 + rσ2mp + rmK2
p Males (m) m-1 M3 σ2 + 2rσ2
m
m x p m-1 M2 σ2 + rσ2m
Error (m-1)(2m-1) M1 σ2 Total 2mr-1
r and m refer to number of replications and male parents respectively. Combined analyses across environments provide estimates of the interaction of the additive and
dominance effects with environments. Direct F-tests can be obtained for each mean square and components of
variance can be calculated directly from the mean squares with their appropriate standard errors (Table 10). In
addition to providing a measure of the dominance of genes for the expression of a trait, NC Design III also is an
excellent mating design for estimation of additive and dominance variances for F2 populations (assuming both
linkage and epistasis are absent) [29]. The estimate of narrow-sense heritability based on the mean of progenies
pooled over sets and across environments is given as:
h2 = (4σ
2m) / (σ
2/re + σ
2mpe/e + σ
2mp + 4σ
2me)/e + 4σ
2m) (41)
Normally, individual F2 plants are males crossed to both inbred (female) parents, and the differences among
male means are covariance of half-sib families. The heritability estimates based on half-sib family means are:
Heritability within environment = h2 = (σ
2m) / (σ
2/r + σ
2m) (42)
Heritability across environments = h2 = (σ
2m) / (σ
2/2re + σ
2mpe/2e + σ
2me/e + σ
2m) (43)
NC Design III is widely used in testing for presence of dominance effects, though linkage biases may
affect the estimation of additive and dominance variance for the F2 populations where effects of linkage are
expected to be maximum [31], [32]. However, linkage equilibrium can be reached by allowing F2 populations to
randomly mate without male and female selection; to develop first random mating population (e.g synthetic 1).
The synthetic 1 is then allowed to advance to successive synthetic generations (e.g synthetic 8) by random
Common Mating Designs in Agricultural Research and Their Reliability in Estimation of Genetic
mating where linkage disequilibrium is minimized. The attainment of linkage equilibrium state depends on the
rate of recombination, tightly linked genes may require many generations of random mating. The synthetic and
the original F2 populations are tested each in replicated trials so as to detect the effects of overdominance and
bias by linkage disequilibrium among loci in the populations [5]. The restriction in this design is that there may
be a situation where the gene frequencies are equal which is limiting. However, where the technique is
applicable, major advantage is that it provides estimates for additive and dominance components of variance
with equal precision compared to other designs [29], [32]. In addition, the ratio of the variance among
differences to the additive variance provides weighted estimte of the squatted degree of dominance, with
expectation identical to that of Design II. However, violation of the above assumptions results in inflated
estimates of the degree of dominance [18].
VII. Dialel mating designs Diallel mating design first presented by Schmidt (1919) became an important tool used to produce
crosses for evaluation of genetic variances [4], [33], [34]. Crosses are generated from parents ranging from
inbred lines to broad genetic base varieties where progenies are developed from all possible combinations of
parents involved. Analysis of diallel progenies allows inference about heterosis (Gardner & Eberhart, 1966),
estimation of general and specific combining ability (Griffing, 1956) and study of genetic control of traits [33],
[35], [36]. Two models designated as model I and model II by Eisenhart (1947) are available and have been
equally used in diallel mating with each having its own assumptions [37], [38]. Model I is a fixed model based
on the assumption that the parents used have undergone selection for a period of time and have become a
complete population. The model measures only GCA and SCA effects because the parents are fixed. Model II is
where parents are random, taken from a random mating population. It is assumed that the effects in the model u
are randomly distributed with mean zero and variance σ2θ where θ = b, g, s, r. As a result, model I is used for
selection of parents based on the GCA and SCA results. Model II is appropriate for estimating GCA and SCA
variances, and to compute the standard errors for differences between effects, considering epistatic is negligible
or absent. It is therefore, assumed that the error terms eijkl are normally distributed with mean zero and variance
σ2. Thus, expected mean squares are expressed in terms of genetic relationships of relatives, and translated from
the covariances of relatives to the genetic components of variance [4], [5].
Four main methods of diallel mating design (Table 8) have been developed by Griffing (1956) and they
include: (i) Full diallel where parents, one set of F1 and reciprocal F1 are included (number of crosses = p2 where
p is the number of parent lines); (ii ) Half diallel where only parents and one set of F1 are included (number of
crosses = 1/2p(p+1)); (iii) Full diallel where only one set of F1 and reciprocals are included (number of crosses =
p(p-1)); and (iv) Half diallel where only one set of F1 are included and the number of crosses = 1/2p(p-1).
Choice among the four methods depends on inbreeding depression of the parents. For pure inbred lines use of
parents in the crosses will not be necessary. However, if the parents are synthetics or a set of non-inbred (species
with less inbreeding depression) it is important to include the parents so that comparison between performances
of heterosis and mean is made [4], [28], [39].
Table 8. Schematic diagrams of 4 methods of diallel mating scheme showing crosses between 5 parents Method I - Full diallel crosses including parents and reciprocals:
number of crosses = p2 = 25
Method III - Full diallel crosses with no parents:
number of crosses = p(p-1) = 20
Male Male
Female 1 2 3 4 5 Female 1 2 3 4 5
1 1x1 1x2 1x3 1x4 1x5 1 - 1x2 1x3 1x4 1x5
2 2x1 2x2 2x3 2x4 2x5 2 2x1 - 2x3 2x4 2x5
3 3x1 3x2 3x3 3x4 3x5 3 3x1 3x2 - 3x4 3x5
4 4x1 4x2 4x3 4x4 4x5 4 4x1 4X2 4x3 - 4x5
5 5x1 5x2 5x3 5x4 5x5 5 5x1 5x2 5x3 5x4 -
Method II – Half diallel crosses including parents and no
reciprocals: number of crosses = p(p+1)/2 = 15
Method IV– Half diallel with no parents and no
reciprocals: number of crosses = p(p-1)/2 = 10
Male Male
Female 1 2 3 4 5 Female 1 2 3 4 5
1 1x1 - - - - 1 - - - - -
2 2x1 2x2 - - - 2 2x1 - - - -
3 3x1 3x2 3x3 - - 3 3x1 3x2 - - -
4 4x1 4X2 4x3 4x4 - 4 4x1 4X2 4x3 - -
5 5x1 5x2 5x3 5x4 5x5 5 5x1 5x2 5x3 5x4 -
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Luka A.O. Awata "Common Mating Designs in Agricultural Research and Their Reliability in
Estimation of Genetic Parameters." IOSR Journal of Agriculture and Veterinary Science