I. Simple Interval Mapping

When to use

For quick scanning of the entire genome (all chromosomes) to find best possible QTLs and identify missing (or incorrectly formatted) data. Use single-marker analysis first to ensure your data file is clean; then move on more sophisticated analysis methods, such as Interval Mapping and Composite Interval Mapping.

How it works

Single-marker analysis is based on the idea that if there is an association between a marker genotype and trait value, it is likely that a QTL is close to that marker locus.

Comments

Single-marker analysis can be somewhat useful for a quick look at data, but it has been superceded by Interval Mapping and Composite Interval Mapping. IM and CIM are more thorough and accurate indicators of QTL. The prime value of WinQTLCart's single-marker analysis is its identification of missing data that could affect later analysis.

Running a single-marker analysis

1. Open a mapping source data file (an .MCD file) into the WinQTLCart main window.

2. Select Method>Single-Marker Analysis. WinQTLCart analyzes the data and displays the single-marker analysis controls in the form pane. The information pane on the right includes the analysis results.

 

3. Select a trait for display from the Trait Selection pull-down list. All the traits present in the file will be on the list.

4. For each trait, the information pane on the right displays WinQTLCart's statistical summary of the file. (You can view this summary in a larger window by clicking the Result button in the Statistical Summary group box, just to the left of the information pane.)

5. In the Single Marker Analysis group box, click Result to view the analysis result for the selected trait. You can change the font used by the display window to make the results easier to read. Click the Save… button in this group to save the marker analysis results to a text file.

6. In the Statistical Summary group box, click Result to view the summary in a larger display window. Click the Save… button to save the statistical results to a text file.

The statistical summary includes:

· Basic summary of the data
· A histogram for the quantitative trait
· WinQTLCart's summary of missing individuals that should be present, as indicated by the data. If markers show 0% data, there was likely an import problem.
· Summary of marker segregation
· Combines LR map QTL and Q stats

7. Click the Graphic File… button to save the results to a QTL mapping result file (*.QRT). You can open this .QRT file later to view the results as a graph.

8. Click Close to end the single-marker analysis session and return to the Form View of Source Data.

Qstats show some important results:

· Tells you that the data were imported correctly. If a marker has 0% data, that indicates a problem (likely an import problem). For example, the original marker may be *Marker_1, but QTL sees that as *Marker-1, and the values won't match.
· Tests for segregation distortion

 

Simple Interval Mapping

This analysis occurs before you start the QTL analysis.
Use this procedure to set the threshold for each trait manually. This is useful if you know the value for each trait. Alternatively, select All Traits and apply this threshold setting to all the traits.

1. From the Trait Selection pull-down, select a trait to find the threshold value for that trait. (The All Traits selection is available for permutations only.)
2. Click the By Manual Input option.
3. Input a threshold value into the box.
4. Optional: Click Set as Default if you want to assign the threshold value you entered to all traits.

Both Interval Mapping and Composite Interval Mapping use threshold values to determine QTLs. If you don't know the threshold value for a trait, you can have WinQTLCart find them out and use them as inputs for the QTL search.

The threshold levels control the rate of Type 1 errors (false positives). A lower threshold value means more false positives; but a higher value means you may miss more QTLs.

When you look at a result graph, the horizontal line you see running across the graph is the threshold level. When the graph peaks over the threshold level, that is good evidence for a QTL. So, setting the threshold level in this form controls how high or low that line will sit on the graph. Too high and you'll see no QTLs; too low and you'll see too many. (The threshold value can be changed later in the Graph window.)

Getting a very accurate threshold level may take a long time. Recommendations are included in the threshold procedures.

1. Follow the instructions for the form you're working with (either IM or CIM). Be sure to select a trait or all traits for which you want to set a threshold level.

2. The Threshold group box on the right of the form controls inputting or obtaining mapping threshold values for each trait. Select a different trait number to see the threshold value of that trait.

3. Select whether you want to set the threshold levels manually or have WinQTLCart determine the threshold via permutations.

If you... Do this... Comments
Know the threshold values you want to use Input them into the Manual Input box
Don't know the threshold values you want to use Select By Permutations to have WinQTLCart calculate them. Permutations take a long time to run. If 1 permutation runs for 10 seconds, than 1000 permutations will take 2-3 hours.

 

 

What it is

Interval mapping (IM) is an extension of single-marker analysis. In single-marker analysis, only one marker is used in QTL mapping but effects are underestimated and the QTL position cannot be determined. Interval mapping provides a systematic way to scan the whole genome for evidence of QTL.

IM uses two observable flanking markers to construct an interval within which to search for QTL. A map function (either Haldane or Kosambi) is used to translate from recombination frequency to distance or vice visa. Then, a LOD score is calculated at each increment (walking step) in the interval. Finally, the LOD score profile is calculated for the whole genome. When a peak has exceeded the threshold value, we declare that a QTL have been found at that location.

When to use it

IM is a good general standard to use for all datasets.

Use it in combination with or as part of a process including

You may wish to start with a single-marker analysis and then run IM to further refine the analysis.

High-level process

Here's a quick overview of how to use WinQTLCart's IM implementation. The first few times you run this analysis, go with the WinQTLCart default values for the form's parameters. The defaults provide the best all-around parameter settings, especially for initial analysis sessions.

1. Select the IM analysis method.
2. Select the chromosome(s) and trait(s) you want to analyze.
3. Select a threshold level to apply to the selected trait(s). Select either By manual input (the WinQTLCart default) or By permutations (to have WinQTLCart determine an optimum threshold). See Setting the threshold level for more information on the impact of each of these choices.
4. Click OK to start the calculations for the threshold level.

5. Following threshold calculation, set IM form parameters. Select a walk speed in cM. It's recommended you use the same walk speed for your entire dataset. Don't reset the walk speed between runs or your results will not be comparable.

6. Click Start to begin the analysis.

WinQTLCart provides default values for the parameters in this form. The defaults provide the best all-around parameter settings, especially for initial analysis sessions.

Interval mapping analysis uses WinQTLCart mapping source data files (.MCD files). Use WinQTLCart's import commands to move your source data files from text to .MCD format.

1. Open a source data file into the WinQTLCart main window.

2. Select Method>Interval Mapping. WinQTLCart displays the interval mapping analysis controls in the form pane.

3. Click Result File… to select the location of and to name the .QRT file that will be created when the analysis is complete.

4. Click the OTraits… button to enter other trait numbers or number ranges. WinQTLCart will use these as a co-factor in the analysis. (WinQTLCart's default is no OTraits.)

Note OTraits is another term for "categorical traits." Use OTraits for background control as nuisance factors we want to account for.

5. The Walk speed (cM) is the genome scan interval. and the default is 2. Click the spin dial beside the Walk speed value to increase or decrease the walk speed by .5 increments.

· Increasing the walk speed (greater than 2) means less precision but the analysis takes less time.
· Decreasing the walk speed (less than 2) yields a more precise result but will take more time.

You should set the walk speed value once for the entire dataset. A single walk speed establishes a consistent norm against which the data can be graphed. If you change the walk speed between mapping runs, the graph displays will be skewed. (If you want to check your data against a different walk speed, create a separate directory for your data files, and then run the new walk speed against those files.)

6. Select one or all chromosomes to include in the analysis.

7. Select one or all traits to include in the analysis. The Traits you select may change the value of the Threshold controls on the right side of the form.

8. Set the threshold level via either manual input or permutations. For more information, see Setting threshold levels (IM & CIM).

9. Click Start to begin QTL mapping analysis.

Following the analysis, WinQTLCart will:

· Create a QTL mapping result file (*.QRT) and open it in the Graph window
· Create a QTL summary information file using the EQTL function.
· Display a confirmation box asking if you want to display QTL summary information in the Main window's Data pane.

Composite Interval Mapping

What it is

Composite interval mapping (CIM) adds background loci to simple interval mapping (IM). CIM fits parameters for a target QTL in one interval while simultaneously fitting partial regression coefficients for "background markers" to account for variance caused by non-target QTL.

"In theory, CIM gives more power and precision than simple IM because the effects of other QTL are not present as residual variance. Furthermore, CIM can remove the bias that would normally be caused by QTL that are linked to the position being tested."

Background markers are usually 20-40cM apart.

High-level workflow

Here's a quick overview of how to use WinQTLCart's CIM implementation. The first few times you run this analysis, go with the WinQTLCart default values for the form's parameters. The defaults provide the best all-around parameter settings, especially for initial analysis sessions.

1. Select the CIM analysis method.
2. Select the chromosome(s) and trait(s) you want to analyze.
3. Select a threshold level to apply to the selected trait(s). Select either By manual input (the WinQTLCart default) or By permutations (to have WinQTLCart determine an optimum threshold). See the Setting the threshold level topic for more information on the impact of each of these choices.
4. Click OK to start the calculations for the threshold level. This may take from several minutes to several hours to run.

5. Following threshold calculation, set CIM form parameters. Select a walk speed in cM. It's recommended you use the same walk speed for your entire dataset. Don't reset the walk speed between runs or your results will not be comparable.
6. Click Start to begin the analysis. The analysis may take from 20 minutes to several hours to run.

WinQTLCart provides default values for the parameters in this form. The defaults provide the best all-around parameter settings, especially for initial analysis sessions.

Composite interval mapping analysis uses WinQTLCart source data mapping files (.MCD files). Use WinQTLCart's import commands to move your source data files from text to .MCD format.

1. Open a source data file into the WinQTLCart main window.

2. Select Method>Composite Interval Mapping. WinQTLCart displays the CIM analysis controls in the form pane.

3. Click Result File… to select the .QRT file you want to create.

4. Click the Control… button to display the Set CIM Control Parameters dialog.

4a. For the CIM Model field, specify the markers to be used as cofactors in the CIM analysis:

· Model 1: All Marker Control—Use all the markers to control for the genetic background.
· Model 2: Unlinked Marker Control—Use all unlinked markers to control for the genetic background.
· Model 4: One Marker Control—This is an ad-hoc model. One marker from each chromosome (except for the chromosome on which we are testing) is used to control for the genetic background. The results of LRmapqtl are scanned, and the marker that showed the highest test statistic from each chromosome is used.

· Model 5: Two Marker Control—Another ad-hoc model. Two markers from each chromosome are used to control for the genetic background. They are the top two markers as determined by LRmapqtl. In addition, all the other markers on the chromosome of the test position that are more than 10 cM away from the flanking markers are also thrown in. It may be ad-hoc, but tends to work best at this time. Selecting this model also requires you to fill in the Window size (cM) field (explained below).

· Model 6: Standard Model—The default model that selects certain markers as control markers by using additional parameters: control marker number and window size. Selecting this model requires you to fill in extra fields on the dialog: Control marker numbers, Window size (cM), and Regression method selection (all explained below).

4b. Click Set control markers manually if you do not want WinQTLCart to automatically select the control markers. This will display a dialog box after you start the analysis so that you can manually select the control markers. Skip to step 10 for a description of this dialog box.

The Background Controls group box specifies the number of background controls and regression type WinQTLCart should use in applying the selected CIM model.

4c. Control marker numbers—Enter the number of markers to control for the genetic background. WinQTLCart will use up to the number of markers entered here.

4d. Window size (cM)—Enter the window size in centiMorgans. The window size will block out a region of the genome on either side of the markers flanking the test site. Since these flanking regions are tightly linked to the testing site, if we were to use them as background markers we would then be eliminating the signal from the test site itself.

If the control marker number is… And if the window size is… This is the result
The total number of markers 0.0 Model 6 reduces to Model 1
The total number of markers Large (such as the size of the largest chromosome) Model 2
Zero N/a Model 3
Recommendations

· Model 6 is good for starting an analysis. Start with the default values of 5 for control markers and 10 for window size.
· Increasing the number of control markers will allow better resolution for mapping linked QTLs.

4e. Regression method selection—Select a method.

· 1: Forward Regression
· 2: Backward Regression
· 3: Forward & Backward

4f. Probability for into:, Probability for out:

4g. If the OTrait number field is enabled, enter other trait numbers and their ranges to be included in the model.

Note OTraits is another term for "categorical traits." Use QTraits for background control as nuisance factors we want to account for.

4h. Click OK to close the dialog and return to the CIM analysis form.

5. The Walk speed (cM) default is 2. The walk speed is the genome scan interval. Click the spin dial beside the Walk speed value to increase or decrease the walk speed by .5 increments.

· Increasing the walk speed (greater than 2) means less precision but the analysis takes less time.
· Decreasing the walk speed (less than 2) yields a more precise result but will take more time.

You should set the walk speed value once for the entire dataset. A single walk speed establishes a consistent norm against which the data can be graphed. If you change the walk speed between runs, the graph displays will be skewed. (If you want to check your data against a different walk speed, create a separate directory for your data files, and then run the new walk speed against those files.)

6. Select one or all chromosomes to include in the analysis.

7. Select one or all traits to include in the analysis. The Traits you select may change the value of the Threshold controls on the right side of the form.

8. Set the threshold level via either manual input or permutations. For more information, see Setting threshold levels (IM & CIM).

9. Click Start to begin QTL mapping analysis. WinQTLCart will open a Save As dialog for you to save the result file that will be created.

10. If you selected Set control markers manually in step 4b, then WinQTLCart will display the Select CIM Control Markers dialog box. Enter or edit the marker numbers you want to using the text box; separate each number with a space. Click on the marker row's cells to toggle their display in the text box.

When the analysis is complete

WinQTLCart will

· Create a QTL mapping result file (*.QRT) and open it in the Graph window
· Create a QTL summary information file using the EQTL function.
· Display a confirmation box asking if you want to display QTL summary information in the Main window's Data pane.

Multiple Interval Mapping

What it is

Multiple interval mapping (MIM) uses multiple marker intervals simultaneously to fit multiple putative QTL directly in the model for mapping QTL. The MIM model is based on Cockerham's model for interpreting genetic parameters and the method of maximum likelihood for estimating genetic parameters. MIM is well suited to the identification and estimation of genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance.

High-level process

Here's a quick overview of how to use WinQTLCart's MIM implementation:

1. Select the MIM analysis method.
2. Pick a trait you want to work with. (MIM works with only one trait at a time.)
3. Decide if you want to create a model using WinQTLCart's default search procedures or an alternative (such as Forward, Backward, or CIM).
4. Run the analysis to generate the model.
5. Refine the model as needed by editing individual cells in the model, adding or deleting QTL, searching and testing QTLs or epistatics, and re-estimating. This part of the analysis can iterate for as long as you want to search for QTLs.

6. Save the model as a .MDS file (or as a result file using the Refine Model function).

From the Source Data form, open a source data file and select Multiple Interval Mapping as the analysis method. If there is more than one trait in the dataset, the Select Trait for MIM Analysis dialog appears. Select a trait from the drop down list and click OK.

The MIM form appears. Before you can use this form, you need to load or create a MIM analysis model. You can open existing files containing MIM model parameters or you can use WinQTLCart to create a model. The following screen shot shows the MIM form with a model loaded and analyzed.

Model drop down list. Contains the list of MIM models to be used for the analysis. You can create or load several different models for selection.

New Model. Have WinQTLCart create a new initial MIM model for analysis.

Load Model. Load an existing MIM model parameters file (.MDS). Click the button to display an Open dialog; navigate to the .MDS file containing the parameters and click OK.

Save Model. Save the model you've created or modified to an .MDS file.

Parameters for current model

QTLs. Number of QTLs in model

Epistasis. Number of epistatic genes in model

L(k). Likelihood of the mode.

BIC. Bayesian Information Criteria (BIC) value of the mode.

Testing All…. Click to test additive, dominant and epistatic effects. The data pane under the form will show the test results. You can select the text and then Edit>Copy to copy it to the clipboard.

Testing Effect… Click on a cell in the model to test the effect and result in a dialog.

Re-estimate Model. Click to re-estimate the model's parameters.

Refine Model…. Select an option and click OK to refine the model's parameters.

Add QTL. Adds a QTL to the model.

Del QTL. Select a QTL column and click Del QTL to delete that QTL from the model.

Cell editing box. Click on a cell in the model to select it and then update its value in this field. Click the Cell Update button to write the value to the cell.

Finish. Close the MIM form and return to the Source Data form. If you have not saved your work, you can save your work at this time.

The Model. Occupies the right half of the form. Click the blue <<QTL cell to expand the model so it fills the form pane; click the QTL>> cell to re-display the MIM form.

Creating the Initial MIM model

Click the New Model (or Add Model) button on the MIM form. The following Create New MIM Model dialog appears. At the Create New MIM Model dialog, select an enabled option from the Initial MIM model selection method group box.

Regression options

· Regression forward selection on markers. Enables the Criterion… button
· Regression backward selection on markers. Enables the Criterion… button
· Forward and backward selection on markers. Enables the Criterion… button

CIM search option

· Scan through composite interval mapping. Enables the Control… and From File… buttons. (From File… displays only after you select this option.)

MIM search option

· MIM forward search method. Enables the OK button

After finishing the initial model creation, the MIM form redisplays with the buttons enabled, the Parameters group fields populated, the new model available in the drop down list, and the model values on the right . The Parameters fields are now populated.

Note To see the entire model without scrolling, click the blue <<QTL cell. To return to the MIM form, click the blue QTL>> button.

Where to go from here

From here, you can refine the MIM model, manually edit the model by clicking the Add QTL and Del QTL buttons, or click in the model field to change the value of Position, Chromosome, Additive, or epistatic values. Click Save Model… to save the model as a .MDS file.

Related topics

About the MIM form

Refining the MIM model

Click the New Model (or Add Model) button on the MIM form. The following Create New MIM Model dialog appears. At the Create New MIM Model dialog, select an enabled option from the Initial MIM model selection method group box.

Regression options

· Regression forward selection on markers. Enables the Criterion… button
· Regression backward selection on markers. Enables the Criterion… button
· Forward and backward selection on markers. Enables the Criterion… button

CIM search option

· Scan through composite interval mapping. Enables the Control… and From File… buttons. (From File… displays only after you select this option.)

MIM search option

· MIM forward search method. Enables the OK button

After finishing the initial model creation, the MIM form redisplays with the buttons enabled, the Parameters group fields populated, the new model available in the drop down list, and the model values on the right . The Parameters fields are now populated.

Note To see the entire model without scrolling, click the blue <<QTL cell. To return to the MIM form, click the blue QTL>> button.

Where to go from here

From here, you can refine the MIM model, manually edit the model by clicking the Add QTL and Del QTL buttons, or click in the model field to change the value of Position, Chromosome, Additive, or epistatic values. Click Save Model… to save the model as a .MDS file.

Related topics

About the MIM form

Refining the MIM model

Bayesian Interval Mapping
WinQTLCart's Bayesian interval mapping (BIM) module is an implementation of the command-line BIM library, provided courtesy of the R Project for Statistical Computing.

What it is

Bayesian interval mapping library R/bim provides Bayesian analysis of multiple quantitative trait loci models. This includes posterior estimates of the number and location of QTL and of their effects.

Bayesian interval mapping for controlled experiment provides a nice complement to the classical analysis for mapping QTLs. It is recommended that the standard IM, CIM, MIM, etc. analyses be run first. The Bmapqtl implements Bayesian analysis for either a fixed or random number of QTLs. (WinQTLCart's default is random.)

The program generates a random sample from the joint posterior of QTL and effects. Note that the BIM estimates should generally agree with those of MIM, and should be similar to those from CIM.

BIM allows one to look deeper at the properties of those estimates, such as how effects estimates are related to loci estimates. It also provides handy tools to explore research questions, such as the posterior chance of multiple QTL in an interval.

How to use

The defaults are quite robust, and it is recommended you use them during your first BIM runs.

For more information on the BIM parameters

Please refer to the R implementation, particularly the function bmapqtl.options(). The best way to get library(bim) is to already have R 1.9.0 installed on your PC.

1. If you don't have R 1.9.0 installed on your computer, go to http://cran.r-project.org/
2. Download the precompiled binary distribution of R (Linux or Windows is preferred.) Follow instructions for installation and run R.
3. While connected to the Internet, select R's Packages menu and select Install packages from Bioconductor.
4. Scroll down to the "bim" package and click on it.
5. Use the R Help to get HTML Help.

6. Select Packages and click BIM from the list. There is an overview document but the options are explained in detail in bmapqtl.options.

Note Pre-1.9.0 releases of R can get the bmapqtl package from the CRAN website cited above.Bioconductor is a companion project to CRAN focused on biological applications. Brian

A quick summary of BIM implementation in a previous version of QTL Cartographer can be found at http://www.cs.wisc.edu/~yandell/qtl/software/Bmapqtl/Bmapqtl.pdf.

High-level workflow

The first few times you run this analysis, go with the WinQTLCart default values for the form's parameters. The defaults provide the best all-around parameter settings, especially for initial analysis sessions.

1. Select the BIM analysis method.
2. Select the chromosome(s) and trait(s) you want to analyze.
3. Click New Seed to select a new random seed.
4. Click Parameters… and set the BIM parameters of interest to you.
5. Click Start to begin the analysis.

Running Bayesian Interval Mapping

1. Open a source data file into the WinQTLCart main window.
2. Select Method>Bayesian Interval Mapping. WinQTLCart displays the BIM analysis controls in the form pane.

 

3. Click Result File… to name the .QRT file you want to create and to specify its location.
4. Click New Seed to generate a new random seed number.
5. Select one or all chromosomes from the Chromosome Selection drop down to include in the analysis.
6. Select one or all traits from the Trait Selection drop down to include in the analysis.

7. Click the Parameters… button to display the Set BIM Parameters dialog.

For more information on each of these parameters, please refer to the R bmapqtl documentation cited in the topic, "
Bayesian Interval Mapping".

8. Click Start to begin QTL mapping analysis.

Displaying Chromosomes

You may need to use chromosome graphics when it's time to write an article on your research. WinQTLCart displays all the source data file's chromosomes, including each chromosome's markers and intervals, in a single display window that you can copy to the Windows clipboard.

From the Main window, with a source data file loaded, select Tools>DrawChrom to show the Chromosome Graphic Display window.

This sample graphic shows you the chromosome names, the markers on the chromosomes, and their distances.

Displaying chromosome graphics

You may need to use chromosome graphics when it's time to write an article on your research. WinQTLCart displays all the source data file's chromosomes, including each chromosome's markers and intervals, in a single display window that you can copy to the Windows clipboard.

 

From the Main window, with a source data file loaded, select Tools>DrawChrom to show the Chromosome Graphic Display window.

 

 

 

This sample graphic shows you the chromosome names, the markers on the chromosomes, and their distances.

 

 

 

Chromosome Graphic Display menus
File menu
Command Function
Copy to Clipboard Copies the graphs to the Windows clipboard.
Print Graphic Print the graphic to a selected printer.
Exit Closes the window. If you have unsaved data, you'll be prompted to save it.

View menu
Command Function
Proportion of Marker Number Show length of chromosome graph in proportion of marker number
Proportion of Chromosome Len Show length of chromosome graph in proportion of chromosome length in cM
Next Page >> If there are lots of chromosomes, displays the next group of graphs
First Page If there are more than one screen of chromosomes, return to the first page.
Add QTL positions… Mark a QTL position on the chromosome. See Adding QTL positions to the chromosome graphics for more information.

Setting menu
Command Function
Select Chromosomes… Select the chromosomes you want displayed in the graphic.
Show Chromosome Name Toggle between showing the chromosome name or its label
Font Size >> Increase font size for graph
Font Size << Decrease font size for graph
Space Between >> Increase the space between markers (graph gets longer)
Space Between << Decrease the space between markers (graph gets shorter)
Chromosome Name>> Go to the next chromosome in the series
Chromosome Name<< Go to the previous chromosome in the series
Column Number >> Increase number of graphics displayed in a column
Column Number << Decrease number of graphics displayed in a column

Chromosome Graphic Display menus
File menu
Command Function
Copy to Clipboard Copies the graphs to the Windows clipboard.
Print Graphic Print the graphic to a selected printer.
Exit Closes the window. If you have unsaved data, you'll be prompted to save it.
View menu
Command Function
Proportion of Marker Number Show length of chromosome graph in proportion of marker number
Proportion of Chromosome Len Show length of chromosome graph in proportion of chromosome length in cM
Next Page >> If there are lots of chromosomes, displays the next group of graphs
First Page If there are more than one screen of chromosomes, return to the first page.
Add QTL positions… Mark a QTL position on the chromosome. See Adding QTL positions to the chromosome graphics for more information.
Setting menu
Command Function
Select Chromosomes… Select the chromosomes you want displayed in the graphic.
Show Chromosome Name Toggle between showing the chromosome name or its label
Font Size >> Increase font size for graph
Font Size << Decrease font size for graph
Space Between >> Increase the space between markers (graph gets longer)
Space Between << Decrease the space between markers (graph gets shorter)
Chromosome Name>> Go to the next chromosome in the series
Chromosome Name<< Go to the previous chromosome in the series
Column Number >> Increase number of graphics displayed in a column
Column Number << Decrease number of graphics displayed in a column