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{{Inappropriate tone|date=April 2010}}
{{Inappropriate tone|date=April 2010}}
'''Inclusive composite interval mapping (ICIM) '''


In the last twenty years, rapid increase in the availability of fine-scale genetic marker maps makes possible the dissection of single quantitative trait gene. Based on genetic linkage map and phenotypic data, [[QTL mapping|QTL (quantitative trait locus) mapping]] was proposed to locate individual genetic factors on chromosomes and estimate their genetic effects. Composite interval mapping (CIM), proposed by Zeng (1994), is one of the most commonly used methods for mapping QTL with populations derived from bi-parental crosses. Inclusive composite interval mapping (ICIM) was proposed by [http://www.isbreeding.net/ Dr. Jiankang Wang’s group] to deal with the problems of CIM while retaining other advantages related to CIM. The details of ICIM are described below.
In the last twenty years, rapid increase in the availability of fine-scale genetic marker maps makes possible the dissection of single quantitative trait gene. Based on genetic linkage map and phenotypic data, [[QTL mapping|QTL (quantitative trait locus) mapping]] was proposed to locate individual genetic factors on chromosomes and estimate their genetic effects. Inclusive composite interval mapping (ICIM) was proposed by [http://www.isbreeding.net/ Dr. Jiankang Wang’s group] to mapping QTL with populations derived from bi-parental crosses. The details of ICIM are described below.

==Background==
In the algorithm of CIM implemented in QTL Cartographer software, QTL effects at the current testing position and regression coefficients of the marker variables used to control genetic background were estimated simultaneously in an [http://en.wikipedia.org/wiki/EM_algorithm expectation and conditional maximum likelihood (EM) algorithm]. Thus, the same marker variable may have different coefficient estimates as the testing position moves along the chromosomes. The algorithm used cannot completely ensure that the effect of QTL at current testing interval is not absorbed by the background marker variables, and may result in biased estimation of the QTL effect. In addition, different background marker selection methods may give very different mapping results, and CIM cannot be extended for mapping epistasis. CIM’s problem motivated [http://www.isbreeding.net/ Wang’s group] to modify its algorithm.
==ICIM of additive and dominance QTL mapping==
==ICIM of additive and dominance QTL mapping==
Two genetic assumptions used in ICIM are (1) the genotypic value of an individual is the summation of effects from all genes affecting the trait of interest; and (2) linked QTL are separated by at least one blank marker interval. Under the two assumptions, they proved that additive effect of the QTL located in a marker interval can be completely absorbed by the regression coefficients of the two flanking markers, while the QTL dominance effect causes marker dominance effects, as well as additive by additive and dominance by dominance interactions between the two flanking markers. By including two multiplication variables between flanking markers, the additive and dominance effects of one QTL can be completely absorbed. As a consequence, an inclusive linear model of phenotype regressing on all genetic markers (and marker multiplications) can be used to fit the positions, and additive (and dominance) effects of all QTL in the genome.<ref name="Li">{{cite journal |author= Li, H., G. Ye and J. Wang |year= 2007 |title= A modified algorithm for the improvement of composite interval mapping|journal=Genetics |volume=175|pages=361–374|url= http://www.genetics.org/cgi/reprint/175/1/361?maxtoshow=&hits=10&RESULTFORMAT=&fulltext=A+modified+algorithm&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT }}</ref><ref name="Wang">{{cite journal |author= Wang J.|year= 2009 |title= Inclusive composite interval mapping of quantitative trait genes|journal= Acta. Agron. Sin. |volume=35|pages=3239–245 }}</ref><ref name="Zhang">{{cite journal |author= Zhang, L., H. Li, Z. Li, and J. Wang|year= 2008 |title= Interactions between markers can be caused by the dominance effect of QTL|journal= Genetics |volume=180|pages=1177–1190|url= http://www.genetics.org/cgi/content/abstract/genetics.108.092122v1}}</ref> A two-step strategy was adopted in ICIM for additive and dominance QTL mapping. In the first step, stepwise regression was applied to identify the most significant marker variables in the linear model. In the second step, one-dimensional scanning or interval mapping was conducted for detecting QTL and estimating its additive and dominance effects, based on the phenotypic values adjusted by the regression model in the first step.
Two genetic assumptions used in ICIM are (1) the genotypic value of an individual is the summation of effects from all genes affecting the trait of interest; and (2) linked QTL are separated by at least one blank marker interval. Under the two assumptions, they proved that additive effect of the QTL located in a marker interval can be completely absorbed by the regression coefficients of the two flanking markers, while the QTL dominance effect causes marker dominance effects, as well as additive by additive and dominance by dominance interactions between the two flanking markers. By including two multiplication variables between flanking markers, the additive and dominance effects of one QTL can be completely absorbed. As a consequence, an inclusive linear model of phenotype regressing on all genetic markers (and marker multiplications) can be used to fit the positions, and additive (and dominance) effects of all QTL in the genome.<ref name="Li">{{cite journal |author= Li, H., G. Ye and J. Wang |year= 2007 |title= A modified algorithm for the improvement of composite interval mapping|journal=Genetics |volume=175|pages=361–374|url= http://www.genetics.org/cgi/reprint/175/1/361?maxtoshow=&hits=10&RESULTFORMAT=&fulltext=A+modified+algorithm&andorexactfulltext=and&searchid=1&FIRSTINDEX=0&sortspec=relevance&resourcetype=HWCIT }}</ref><ref name="Wang">{{cite journal |author= Wang J.|year= 2009 |title= Inclusive composite interval mapping of quantitative trait genes|journal= Acta. Agron. Sin. |volume=35|pages=3239–245 }}</ref><ref name="Zhang">{{cite journal |author= Zhang, L., H. Li, Z. Li, and J. Wang|year= 2008 |title= Interactions between markers can be caused by the dominance effect of QTL|journal= Genetics |volume=180|pages=1177–1190|url= http://www.genetics.org/cgi/content/abstract/genetics.108.092122v1}}</ref> A two-step strategy was adopted in ICIM for additive and dominance QTL mapping. In the first step, stepwise regression was applied to identify the most significant marker variables in the linear model. In the second step, one-dimensional scanning or interval mapping was conducted for detecting QTL and estimating its additive and dominance effects, based on the phenotypic values adjusted by the regression model in the first step.
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Under the same assumptions in additive and dominance QTL mapping of ICIM, additive by additive epistatic effect between two interacting QTL can be completely absorbed by the four marker interaction variables between the two pairs of flanking markers [5]. That is to say, the coefficients of four marker interactions of two pairs of flanking markers contain the genetic information of the additive by additive epistasis between the two marker intervals.<ref name="Li2">{{cite journal |author= Li, H., Z. Li and J. Wang
Under the same assumptions in additive and dominance QTL mapping of ICIM, additive by additive epistatic effect between two interacting QTL can be completely absorbed by the four marker interaction variables between the two pairs of flanking markers [5]. That is to say, the coefficients of four marker interactions of two pairs of flanking markers contain the genetic information of the additive by additive epistasis between the two marker intervals.<ref name="Li2">{{cite journal |author= Li, H., Z. Li and J. Wang
|year= 2008 |title= Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations|journal= Theor. Appl. Genet. |volume=116|pages=243–260 |url=http://www.springerlink.com/content/r2m7hu812j9l12w2/}}</ref> As a consequence, a linear model of phenotype regressing on both markers and marker multiplications can fit the positions and effects of all QTL and their digenic interactions. Similar to the additive QTL mapping of ICIM, two-step strategy was also adopted in additive by additive epistasis mapping. In the first step, stepwise regression was applied to identify the most significant marker and marker interactions. In the second step, two-dimensional scanning was conducted for detecting additive by additive QTL and estimating the genetic effects, based on the phenotypic values adjusted by the regression model in the first step.
|year= 2008 |title= Inclusive composite interval mapping (ICIM) for digenic epistasis of quantitative traits in biparental populations|journal= Theor. Appl. Genet. |volume=116|pages=243–260 |url=http://www.springerlink.com/content/r2m7hu812j9l12w2/}}</ref> As a consequence, a linear model of phenotype regressing on both markers and marker multiplications can fit the positions and effects of all QTL and their digenic interactions. Similar to the additive QTL mapping of ICIM, two-step strategy was also adopted in additive by additive epistasis mapping. In the first step, stepwise regression was applied to identify the most significant marker and marker interactions. In the second step, two-dimensional scanning was conducted for detecting additive by additive QTL and estimating the genetic effects, based on the phenotypic values adjusted by the regression model in the first step.
[[Image:ICIM_Fig3.jpg|frame| Fig. 3 Two-dimensional average LOD contour profiles testing the significance of additive and epistasis (A) and epistasis only (B), and average epistatic effect profile (C) for genome consisted of four 100 cM chromosomes. Eleven markers on each chromosome were positioned as shown at the numerical labels of the horizontal axis of Fig. 3 in Yi et al. (2003). Seven QTL (represented by QY1 to QY7) with epistatic patterns controlled the expression of a quantitative trait of interest (for details see Table 1 in Yi et al. (2003)). Similar to Yi et al. (2003), the residual variance was adjusted to 1, and one hundred backcross populations each of 300 individuals were simulated.The number of simulation runs is 100. On the coordinate axes of the two-dimensional average LOD contour profiles are the one-dimension average LOD profiles testing the significance of the additive effects. On the coordinate axes of the two-dimensional average epistatic effect profiles are the one-dimensional average additive effect profiles. The size and direction of each arrow approximately represent the effect size and direction of the pointed QTL, respectively. QTL without arrows have no additive effects. Predefined digenic epistasis are indicated by text boxes. LOD score testing the significance of either additive and epistasis (A) or epistasis (B), or estimated additive by additive epistatic effect (C) was shown in each box. True epistatic effect was given in parentheses.]]
[[Image:ICIM_Fig3.jpg|frame| Fig. 3 Two-dimensional average LOD contour profiles testing the significance of additive and epistasis (A) and epistasis only (B), and average epistatic effect profile (C) for genome consisted of four 100 cM chromosomes. Eleven markers on each chromosome were positioned as shown at the numerical labels of the horizontal axis of Fig. 3 in Yi et al. (2003). Seven QTL (represented by QY1 to QY7) with epistatic patterns controlled the expression of a quantitative trait of interest (for details see Table 1 in Yi et al. (2003)). Similar to Yi et al. (2003), the residual variance was adjusted to 1, and one hundred backcross populations each of 300 individuals were simulated. The number of simulation runs is 100. On the coordinate axes of the two-dimensional average LOD contour profiles are the one-dimension average LOD profiles testing the significance of the additive effects. On the coordinate axes of the two-dimensional average epistatic effect profiles are the one-dimensional average additive effect profiles. The size and direction of each arrow approximately represent the effect size and direction of the pointed QTL, respectively. QTL without arrows have no additive effects. Predefined digenic epistasis are indicated by text boxes. LOD score testing the significance of either additive and epistasis (A) or epistasis (B), or estimated additive by additive epistatic effect (C) was shown in each box. True epistatic effect was given in parentheses.]]


==Applications of ICIM in real mapping populations==
==Applications of ICIM in real mapping populations==
Take a barley doubled haploid population <ref name="Tinker">{{cite journal |author= Tinker, N. A., D. E. Mather, B. G. Rossnagel, K. J. Kasha, A. Kleinhofs, P. M. Hayes, D. E. Falk, T. Ferguson, L. P. Shugar, W. G. Legge, R. B. Irvine, T. M. Choo, K. G. Briggs, S. E. Ullrich, J. D. Franckowiak, T. K. Blake, R. J. Graf, S. M. Dofing, M. A. Saghai Maroof, G. J. Scoles, D. Hoffman, L. S. Dahleen, A. Kilian, F. Chen, R. M. Biyashev, D. A. Kudrna, and B. J. Steffenson|year= 1996 |title= Regions of the genome that affect agronomic performance in two-row barley|journal= Crop Science |volume=36|pages=1053–1062|url= http://147.49.50.65/ggpages/HxT/1996%20tinker_mather_96_hxt_agron.pdf}}</ref> as an example, nine additive QTL affecting kernel weight were identified to be distributed on five out of the seven chromosomes, explaining 81% of the phenotypic variance. In this population additive effects have explained most of the phenotypic variance, approximating the estimated heritability in the broad sense, which indicates that most of the genetic variance was caused by additive QTL.
Take a barley doubled haploid population <ref name="Tinker">{{cite journal |author= Tinker, N. A., D. E. Mather, B. G. Rossnagel, K. J. Kasha, A. Kleinhofs, P. M. Hayes, D. E. Falk, T. Ferguson, L. P. Shugar, W. G. Legge, R. B. Irvine, T. M. Choo, K. G. Briggs, S. E. Ullrich, J. D. Franckowiak, T. K. Blake, R. J. Graf, S. M. Dofing, M. A. Saghai Maroof, G. J. Scoles, D. Hoffman, L. S. Dahleen, A. Kilian, F. Chen, R. M. Biyashev, D. A. Kudrna, and B. J. Steffenson|year= 1996 |title= Regions of the genome that affect agronomic performance in two-row barley|journal= Crop Science |volume=36|pages=1053–1062|url= http://147.49.50.65/ggpages/HxT/1996%20tinker_mather_96_hxt_agron.pdf}}</ref> as an example, nine additive QTL affecting kernel weight were identified to be distributed on five out of the seven chromosomes, explaining 81% of the phenotypic variance. In this population additive effects have explained most of the phenotypic variance, approximating the estimated heritability in the broad sense, which indicates that most of the genetic variance was caused by additive QTL.
[[Image:ICIM_Fig4.jpg|frame| Fig. 4 Mapping results from ICIM for additive QTL affecting kernel weight (KWT) in the barley population consisting of 145 DH lines. Three probabilities for entering variables and removing variables were set as 0.05 and 0.10, respectively. The scanning step is 1 cM and 1H to 7H represent the seven barley chromosomes.]]
[[Image:ICIM_Fig4.jpg|frame| Fig. 4 Mapping results from ICIM for additive QTL affecting kernel weight (KWT) in the barley population consisting of 145 DH lines. Three probabilities for entering variables and removing variables were set as 0.05 and 0.10, respectively. The scanning step is 1 cM and 1H to 7H represent the seven barley chromosomes.]]

Besides that, ICIM has been successfully used in wild and cultivated soybeans in mapping conserved salt tolerance QTL <ref name="Hamwieh">{{cite journal |author= Hamwieh, A., and D. Xu, |year= 2008 |title= Conserved salt tolerance quantitaive trait locus (QTL) in wild and cultivated soybeans.|journal= Breeding Science |volume=58|pages=355–359|url= http://www.jstage.jst.go.jp/article/jsbbs/58/4/58_355/_article }}</ref>, in rice mapping tiller angle QTL <ref name="Chen">{{cite journal |author= Chen, P., L. Jiang, C. Yu, W. Zhang, J. Wang, and J. Wan, |year= 2008 |title= The identification and mapping of a tiller angle QTL on rice chromosome 9.|journal=Crop Science |volume=48|pages=1799–1806|url= http://crop.scijournals.org/cgi/reprint/48/5/1799 }}</ref>, and grain length QTL <ref name="Wan">{{cite journal |author= Wan, X., J. Wan, L. Jiang, J. Wang, H. Zhai, J. Weng, H. Wang, C. Lei, J. Wang, X. Zhang, Z. Cheng, X. Guo,|year= 2006 |title= QTL analysis for rice grain length and fine mapping of an identified QTL with stable and major effects.|journal=Theoretical Applied Genetics |volume=112|pages=1258–1270|url= http://www.springerlink.com/index/0406R22612531316.pdf}}</ref>, in wheat mapping flour and noodle color components and yellow pigment content <ref name="Yelun">{{cite journal |author= Zhang, Y., Y. Wu, Y. Xiao, Z. He, Y. Zhang, J. Yan, Y. Zhang, X. Xia, and C. Ma, |year= 2009 |title= QTL mapping for flour and noodle colour components and yellow pigment content in common wheat.|journal=Euphytica |volume=165|pages=435–444|url= http://www.springerlink.com/content/h447512813888178/}}</ref>, and adult-plant resistance to stripe rust QTL <ref name="Lu">{{cite journal |author= Lu, Y., C. Lan, S. Liang, X. Zhou, D. Liu, G. Zhou, Q. Lu, J. Jing, M. Wang, X. Xia, and Z. He, |year= 2009 |title= QTL mapping for adult-plant resistance to stripe rust in Italian common wheat cultivars Libellula and Strampelli.|journal=Theoretical Applied Genetics |volume=119|pages=1349–1359|url= http://www.springerlink.com/index/P407600163837875.pdf }}</ref>, etc. Some of these detected QTL has been fine mapped.


==ICIM of joint QTL mapping in multiple families or populations==
==ICIM of joint QTL mapping in multiple families or populations==
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The software implementing ICIM additive and epistasis mapping called [http://www.isbreeding.net/software.html QTL IciMapping] was written in Fortran 90/95. The functions of QTL IciMapping were as follows: (1) implementation of mapping methods including single marker analysis, interval mapping, ICIM for additive and dominance, ICIM for digenic epistasis, selective phenotyping, etc; (2) QTL linkage analysis more than twenty mapping populations derived from bi-parental cross, including backcross, double haploid, recombinant inbred lines, etc; (3) Power analysis for simulated populations under the genetic models user defined; and (4) QTL mapping for non-idealized chromosome segment substitution lines .<ref name="Wang2">{{cite journal |author= Wang J, X. Wan, J. Crossa, J. Crouch, J. Weng, H. Zhai, J. Wan
The software implementing ICIM additive and epistasis mapping called [http://www.isbreeding.net/software.html QTL IciMapping] was written in Fortran 90/95. The functions of QTL IciMapping were as follows: (1) implementation of mapping methods including single marker analysis, interval mapping, ICIM for additive and dominance, ICIM for digenic epistasis, selective phenotyping, etc; (2) QTL linkage analysis more than twenty mapping populations derived from bi-parental cross, including backcross, double haploid, recombinant inbred lines, etc; (3) Power analysis for simulated populations under the genetic models user defined; and (4) QTL mapping for non-idealized chromosome segment substitution lines .<ref name="Wang2">{{cite journal |author= Wang J, X. Wan, J. Crossa, J. Crouch, J. Weng, H. Zhai, J. Wan
|year= 2006 |title= QTL mapping of grain length in rice (Oryza sativa L.) using chromosome segment substitution lines|journal= Genet. Res. |volume=88|pages=93–104 |url= http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=555120}}</ref>
|year= 2006 |title= QTL mapping of grain length in rice (Oryza sativa L.) using chromosome segment substitution lines|journal= Genet. Res. |volume=88|pages=93–104 |url= http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=555120}}</ref>
==Frequently asked questions in QTL linkage mapping==
===Questions related to statistical method of QTL mapping ===
What does LOD score mean?

Answer: The [http://en.wikipedia.org/wiki/Lod_score LOD score] is the common logarithm of the ratio of the two likelihood functions under the null hypothesis of no segregation QTL and the alternative hypothesis of existing segregation QTL, respectively. LOD score is the test statistic used in interval test based methods, such as interval mapping, CIM and ICIM, etc, to declare the existence of QTL. The higher the LOD score is, the more likely there is a QTL.

What is the relationship between the reliability of detected QTL and the LOD threshold?

Answer: Higher LOD threshold is, more likely the false discovery rate can be controlled, while more likely the minor QTL cannot be detected. How to find a balance? This is not a pure statistical issue, but should be determined by the research objective as well. If you want to apply the QTL information to pyramid breeding or marker assisted selection, a low LOD threshold would be needed to avoid missing QTL information, while if you want to fine mapping some QTL, a high LOD threshold would be needed to avoid false positives.

How to evaluate different QTL mapping methods?

Answer: QTL mapping procedure usually includes complex statistical tests, which is difficult to find an analytic expression. Thus simulation experiment is generally conducted to evaluate the QTL detection power and false discovery rate. Method having high power and low false discovery rate can be viewed as a good method.

How to improve the QTL detection power?

Answer: Increase in population size, decrease in phenotypic error, construction of near introgression lines or chromosome segment substitution lines, increase in marker density in a large population, etc, are the effective approaches to improve QTL detection power.

===Questions related to genetic parameter estimation===
How to calculate the phenotypic variance explained by each detected QTL?

Answer: The phenotypic variance explained by each detected QTL (PVE), that is the statistics to evaluate the genetic contribution of each QTL, is the ratio of the genetic variance of each QTL and the phenotypic variance. Generally, there is no additivity for variance, so for PVE. The genetic variance of each QTL is determined not only by its genetic effect, but also by its genotypic frequency. So in a population with segregation distortion, it is likely that a large QTL effect with a small PVE.

How to determine the source of favorable alleles at detected QTL? How efficient is the selective genotyping?

Answer: Assuming one QTL locus with two alleles denoted as Q and q, QQ is from P1 and qq is from P2, the source of favorable alleles at detected QTL in recombinant inbred lines is determined by how you code QQ and qq. If the additive effect of QTL is positive, parent whose QTL genotypes were coded as 2 has alleles that can improve the trait of interest. On the contrary, parent whose genotypes were coded as 0 has alleles that can improve the trait of interest.

How efficient is the selective genotyping?

Answer: Selective genotyping of individuals from the two tails of the phenotypic distribution of a population provided a cost efficient alternative to analysis of the entire population for genetic mapping. QTL mapping based on selective genotyping is more powerful than interval mapping, but less powerful than ICIM. Selective genotyping can be used, along with pooled DNA analysis, to replace entire population genotyping, for mapping QTL with relatively small effects, as well as linked and interacting QTL. [10]

Can composite traits be used in QTL mapping?

Answer: Traits having their own measurements and used directly in QTL mapping are called individual traits throughout this paper; those derived from two or more individual traits and then used in QTL mapping are called composite traits. The use of composite traits in QTL mapping increases the gene number, causes higher-order gene interactions than observed in individual traits, and complicates the linkage relationship between QTL. The increased complexity of the genetic architecture of composite traits reduces QTL detection power and increases FDR. Composite-only QTL identified in actual genetic populations can be explained either as minor QTL not identified by individual traits or as false positives. Though composite traits should be used with caution in QTL mapping, this should not rule out their use in breeding since they have a great advantage when selecting all favorable genes simultaneously. [11]

===Questions related to linkage map and mapping populations===
Does the phenotype of a trait of interest have to follow a normal distribution?

Answer: The assumption of normal distribution of phenotypic data is not a premise for the conclusions we made in our manuscript. Actually, in QTL mapping, it is not necessary for phenotype of the trait of interest to follow the normal distribution, but random error should follow normal distribution. Here is an example from an artificial genetic model. We simulated one QTL model and the heritability in broad sense was set at 0.80. One doubled haploid population with size of 200 was generated. The phenotypic distribution was shown in Fig. 6 with two obvious peaks. From the normality test, P-value from Shapiro-Wilk test based on the phenotype is smaller than 0.0001, which indicates that the phenotype of the trait of interest does NOT follow normal distribution (Fig. 6). The phenotypic non-normal distribution does not hamper the identification of the predefined QTL. This QTL can be nearly unbiased estimated by IM and ICIM (Fig. 7).

[[Image:ICIM_Fig6.jpg|frame| Fig. 6 Phenotype distribution of the trait of interest in a simulated double haploid population with size of 200.]]

[[Image:ICIM Fig7.jpg|frame| Fig. 7 Profiles of LOD score and additive effect estimates from IM and ICIM.]]
[[Image:ICIM_Fig7.jpg|frame| Fig. 7 Profiles of LOD score and additive effect estimates from IM and ICIM.]]

Does the increase in marker density greatly improve QTL mapping power?

The use of dense markers makes linked QTL isolated by empty marker intervals and thus improves mapping efficiency. However, only large-size populations can take advantage of densely distributed markers [4].

What effects will missing markers have in QTL mapping?

Answer: Detection power decreases with increasing levels of missing markers for plant height and maturity QTL, and the false discovery rate increases when more markers are missing. Missing markers have greater effects on smaller-effect QTL and smaller-size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate .

What effects will segregation distortion have in QTL mapping?


Answer: If the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, and the linkage distance between the distorted marker and QTL. Sometimes, the distortion results in a higher genetic variance than that of non-distortion, and therefore benefits the detection of the linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the SDM increases or decreases the QTL detection power. The effect of SDM decreases rapidly as the linkage relationship with QTL becomes loose. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effect can be ignored in large-size mapping populations.


==Reference==
==Reference==

Revision as of 08:13, 26 April 2010

In the last twenty years, rapid increase in the availability of fine-scale genetic marker maps makes possible the dissection of single quantitative trait gene. Based on genetic linkage map and phenotypic data, QTL (quantitative trait locus) mapping was proposed to locate individual genetic factors on chromosomes and estimate their genetic effects. Inclusive composite interval mapping (ICIM) was proposed by Dr. Jiankang Wang’s group to mapping QTL with populations derived from bi-parental crosses. The details of ICIM are described below.

ICIM of additive and dominance QTL mapping

Two genetic assumptions used in ICIM are (1) the genotypic value of an individual is the summation of effects from all genes affecting the trait of interest; and (2) linked QTL are separated by at least one blank marker interval. Under the two assumptions, they proved that additive effect of the QTL located in a marker interval can be completely absorbed by the regression coefficients of the two flanking markers, while the QTL dominance effect causes marker dominance effects, as well as additive by additive and dominance by dominance interactions between the two flanking markers. By including two multiplication variables between flanking markers, the additive and dominance effects of one QTL can be completely absorbed. As a consequence, an inclusive linear model of phenotype regressing on all genetic markers (and marker multiplications) can be used to fit the positions, and additive (and dominance) effects of all QTL in the genome.[1][2][3] A two-step strategy was adopted in ICIM for additive and dominance QTL mapping. In the first step, stepwise regression was applied to identify the most significant marker variables in the linear model. In the second step, one-dimensional scanning or interval mapping was conducted for detecting QTL and estimating its additive and dominance effects, based on the phenotypic values adjusted by the regression model in the first step.

File:ICIM Fig1.jpg
Fig. 1 Comparison of inclusive composite interval mapping, composite interval mapping and interval mapping in a simulated population with 200 doubled haploid lines. A genome with 6 chromosomes was assumed, each of 120 cM and evenly distributed with 13 markers. One QTL was located at 35 cM on chromosome 1, and two QTL were located at 35 and 68 cM on chromosomes 2, 3, and 4. Arrows pointed to the approximate QTL positions. Upward arrows indicated the QTL have positive effects, while downward arrows indicated the QTL have negative effects. The absolute genetic effect is 1 for all QTL.

The genetic and statistical properties of ICIM in additive QTL mapping

Through computer simulations they studied the asymptotic properties of ICIM in additive QTL mapping as well. The test statistic LOD score linearly increases as the increase in population size. The larger of the QTL effect, the greater the corresponding LOD score increases. When population size is greater than 200, the position estimation of ICIM for QTL explaining more than 5% of the phenotypic variance is unbiased. For smaller population size, there is a tendency that the QTL was identified towards the center of the chromosome. When population size is greater than 200, the effect estimation of ICIM for QTL explaining more than 5% of phenotypic variance is unbiased. For smaller sample size, the QTL effect was always over-estimated.

File:ICIM Fig2.jpg
Fig. 2 Relationship of QTL detection power with marker density and mapping population size.

ICIM of digenic epistasis mapping

Under the same assumptions in additive and dominance QTL mapping of ICIM, additive by additive epistatic effect between two interacting QTL can be completely absorbed by the four marker interaction variables between the two pairs of flanking markers [5]. That is to say, the coefficients of four marker interactions of two pairs of flanking markers contain the genetic information of the additive by additive epistasis between the two marker intervals.[4] As a consequence, a linear model of phenotype regressing on both markers and marker multiplications can fit the positions and effects of all QTL and their digenic interactions. Similar to the additive QTL mapping of ICIM, two-step strategy was also adopted in additive by additive epistasis mapping. In the first step, stepwise regression was applied to identify the most significant marker and marker interactions. In the second step, two-dimensional scanning was conducted for detecting additive by additive QTL and estimating the genetic effects, based on the phenotypic values adjusted by the regression model in the first step.

File:ICIM Fig3.jpg
Fig. 3 Two-dimensional average LOD contour profiles testing the significance of additive and epistasis (A) and epistasis only (B), and average epistatic effect profile (C) for genome consisted of four 100 cM chromosomes. Eleven markers on each chromosome were positioned as shown at the numerical labels of the horizontal axis of Fig. 3 in Yi et al. (2003). Seven QTL (represented by QY1 to QY7) with epistatic patterns controlled the expression of a quantitative trait of interest (for details see Table 1 in Yi et al. (2003)). Similar to Yi et al. (2003), the residual variance was adjusted to 1, and one hundred backcross populations each of 300 individuals were simulated. The number of simulation runs is 100. On the coordinate axes of the two-dimensional average LOD contour profiles are the one-dimension average LOD profiles testing the significance of the additive effects. On the coordinate axes of the two-dimensional average epistatic effect profiles are the one-dimensional average additive effect profiles. The size and direction of each arrow approximately represent the effect size and direction of the pointed QTL, respectively. QTL without arrows have no additive effects. Predefined digenic epistasis are indicated by text boxes. LOD score testing the significance of either additive and epistasis (A) or epistasis (B), or estimated additive by additive epistatic effect (C) was shown in each box. True epistatic effect was given in parentheses.

Applications of ICIM in real mapping populations

Take a barley doubled haploid population [5] as an example, nine additive QTL affecting kernel weight were identified to be distributed on five out of the seven chromosomes, explaining 81% of the phenotypic variance. In this population additive effects have explained most of the phenotypic variance, approximating the estimated heritability in the broad sense, which indicates that most of the genetic variance was caused by additive QTL.

File:ICIM Fig4.jpg
Fig. 4 Mapping results from ICIM for additive QTL affecting kernel weight (KWT) in the barley population consisting of 145 DH lines. Three probabilities for entering variables and removing variables were set as 0.05 and 0.10, respectively. The scanning step is 1 cM and 1H to 7H represent the seven barley chromosomes.

Besides that, ICIM has been successfully used in wild and cultivated soybeans in mapping conserved salt tolerance QTL [6], in rice mapping tiller angle QTL [7], and grain length QTL [8], in wheat mapping flour and noodle color components and yellow pigment content [9], and adult-plant resistance to stripe rust QTL [10], etc. Some of these detected QTL has been fine mapped.

ICIM of joint QTL mapping in multiple families or populations

Bi-parental populations are mostly used in QTL linkage mapping. QTL not segregating between the two parents cannot be detected. To find most, if not all, genes controlling a trait of interest, multiple parents have to be used. Complex cross populations have been proposed in recent years for this purpose. These crosses allow a more powerful understanding of the genetic basis of quantitative traits in more relevant genetic backgrounds. They extended ICIM to map Maize Nested Association Mapping (NAM) [11] .[12] design recently proposed by the Buckler laboratory at Cornell University. QTL detection efficiency of ICIM in this design was investigated through extensive simulations. In the actual maize NAM population, ICIM detected a total of 52 additive QTL affecting the silk flowering time in maize. These QTL have explained 79% of the phenotypic variance in this population.

File:ICIM Fig5.jpg
Fig. 5 The whole genome scanning from ICIM for day to silk, day to anthesis, and anthesis-silking interval in maize NAM population.

QTL IciMapping, an integrated software of QTL mapping

The software implementing ICIM additive and epistasis mapping called QTL IciMapping was written in Fortran 90/95. The functions of QTL IciMapping were as follows: (1) implementation of mapping methods including single marker analysis, interval mapping, ICIM for additive and dominance, ICIM for digenic epistasis, selective phenotyping, etc; (2) QTL linkage analysis more than twenty mapping populations derived from bi-parental cross, including backcross, double haploid, recombinant inbred lines, etc; (3) Power analysis for simulated populations under the genetic models user defined; and (4) QTL mapping for non-idealized chromosome segment substitution lines .[13]


Reference

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  6. ^ Hamwieh, A., and D. Xu, (2008). "Conserved salt tolerance quantitaive trait locus (QTL) in wild and cultivated soybeans". Breeding Science. 58: 355–359.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  7. ^ Chen, P., L. Jiang, C. Yu, W. Zhang, J. Wang, and J. Wan, (2008). "The identification and mapping of a tiller angle QTL on rice chromosome 9". Crop Science. 48: 1799–1806.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  8. ^ Wan, X., J. Wan, L. Jiang, J. Wang, H. Zhai, J. Weng, H. Wang, C. Lei, J. Wang, X. Zhang, Z. Cheng, X. Guo, (2006). "QTL analysis for rice grain length and fine mapping of an identified QTL with stable and major effects" (PDF). Theoretical Applied Genetics. 112: 1258–1270.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  9. ^ Zhang, Y., Y. Wu, Y. Xiao, Z. He, Y. Zhang, J. Yan, Y. Zhang, X. Xia, and C. Ma, (2009). "QTL mapping for flour and noodle colour components and yellow pigment content in common wheat". Euphytica. 165: 435–444.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  10. ^ Lu, Y., C. Lan, S. Liang, X. Zhou, D. Liu, G. Zhou, Q. Lu, J. Jing, M. Wang, X. Xia, and Z. He, (2009). "QTL mapping for adult-plant resistance to stripe rust in Italian common wheat cultivars Libellula and Strampelli" (PDF). Theoretical Applied Genetics. 119: 1349–1359.{{cite journal}}: CS1 maint: extra punctuation (link) CS1 maint: multiple names: authors list (link)
  11. ^ Michael D. McMullen, Stephen Kresovich, Hector Sanchez Villeda, Peter Bradbury, Huihui Li, Qi Sun, Sherry Flint-Garcia, Jeffry Thornsberry, Charlotte Acharya, Christopher Bottoms, Patrick Brown, Chris Browne, Magen Eller, Kate Guill, Carlos Harjes, Dallas Kroon, Nick Lepak, Sharon E. Mitchell, Brooke Peterson, Gael Pressoir, Susan Romero, Marco Oropeza Rosas, Stella Salvo, Heather Yates, Mark Hanson, Elizabeth Jones, Stephen Smith, Jeffrey C. Glaubitz, Major Goodman,Doreen Ware, James B. Holland, Edward S. Buckler (2009). "Genetic Properties of the Maize Nested Association Mapping Population". Science. 325 (737): 737–740. PMID 19661427.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  12. ^ Edward S. Buckler, James B. Holland,Peter J. Bradbury, Charlotte B. Acharya, Patrick J. Brown, Chris Browne, Elhan Ersoz, Sherry Flint-Garcia, Arturo Garcia, Jeffrey C. Glaubitz, Major M. Goodman, Carlos Harjes, Kate Guill, Dallas E. Kroon,Sara Larsson, Nicholas K. Lepak, Huihui Li, Sharon E. Mitchell, Gael Pressoir,Jason A. Peiffer, Marco Oropeza Rosas, Torbert R. Rocheford, M. Cinta Romay, Susan Romero, Stella Salvo, Hector Sanchez Villeda, H. Sofia da Silva, Qi Sun, Feng Tian, Narasimham Upadyayula, Doreen Ware, Heather Yates, Jianming Yu, Zhiwu Zhang, Stephen Kresovich, Michael D. McMullen (2009). "The Genetic Architecture of Maize Flowering Time". Science. 325: 714–718. PMID 19661422. {{cite journal}}: line feed character in |author= at position 474 (help)CS1 maint: multiple names: authors list (link)
  13. ^ Wang J, X. Wan, J. Crossa, J. Crouch, J. Weng, H. Zhai, J. Wan (2006). "QTL mapping of grain length in rice (Oryza sativa L.) using chromosome segment substitution lines". Genet. Res. 88: 93–104.{{cite journal}}: CS1 maint: multiple names: authors list (link)
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