Mesquite's Charts
Charts compile and display values for a series of objects or
items, whether taxa, trees, characters, or matrices. Mesquite
has two primary styles of charts:
- Bar & Line Charts - a bar or linechart
summarizing values for each of many objects; includes histograms
to show frequencies of values. (Called "Histogram"
in earlier versions of Mesquite.)
- Scattergram - a plot showing each object's
value in two variables
Most of Mesquite's charts are available through the first few
submenus of the Analysis menu.
We suspect the greatest challenge to the user will be learning
what chart to choose and how to set it up. For instance, how can
one create a chart summarizing the estimated rate of a character's
evolution according to each of a series of trees? Does one choose
New Bar
& Line Chart For>Characters because the value
concerns a character? No, one chooses New
Bar & Line Chart For>Trees because the numerous
objects being summarized are trees, as the question concerns just
one character but many trees. For each tree, what is being calculated
is a value that relates to a character.
Contents
Chart Wizard
The first item in the Analysis window, Chart Wizard, helps you
make charts. It asks you a series of questions to determine what
type of chart you want. We provide this because it is sometimes
difficult to decide how to start building a chart. Alternatively,
you can use the New Bar & Line Chart for
and New Scattergram for submenus
to build a chart.
Selection of objects in charts
Most bar & line charts and scattergrams depict the values
of objects— characters, taxa, trees — that can be
selected. If you select these objects elsewhere in Mesquite, for
example by selecting a column (character) in the Character Matrix
Editor, then this selected objects will be highlighted in the
chart. You can select the objects directly in the chart by clicking
and dragging with the arrow cursor.
When objects are selected in the chart, and Copy is selected,
then a list of the selected data points is copied to the clipboard.
Otherwise if no objects are selected, then Copy puts the list
of all data points into the clipboard.
Auto-recalculation
By default, charts are recalculated whenever Mesquite detects
that the data or assumptions underlying the chart have changed.
If the chart calculation takes a long time, then this can lead
to many delays if you need to make many changes in the data or
assumptions. You can temporarily turn off the automatic chart
recalculation by deselecting the Auto-recalculate menu item in
the Chart or Scattergram menu. You can also request to Force Recalculation
in the Chart menu.
Bar & Line Charts
The bar & line charts available via the Analysis menu are:
- Characters — the items whose values
are summarized are characters. These could be all of the characters
of a matrix, or a series of simulated or randomized characters.
- Character Matrices — the items whose
values are summarized are whole character matrices. These could
be all of the matrices stored in a file, or a series of simulated
or randomized matrices.
- Taxa — the items whose values are summarized
are taxa within a taxa block.
- Tree blocks —the items whose values
are summarized are blocks of multiple trees. That is, each item
is a block of several trees. These could be all of the tree
blocks stored in a file, or a series of simulated or randomized
tree blocks.
- Trees — the items whose values are
summarized are trees. These could be all of the trees within
a tree block, or a series of simulated or randomized trees.
Tables as output
In addition to the graphical chart, you can obtain a text table
representation of the chart in several ways:
- Select Copy in the Edit menu of the chart to copy a list
of point values to the clipboard; you can then copy it in
to your favorite text or spreadsheet program
- Select Save Window as Text from the File menu to save a
full text representation of the chart
- If Record Table to File in the Chart menu
is selected, then a text file of the results will be saved
each time a chart is recalculated. This is particularly useful
for some calculations that result in more than just a single
value per item charted; in this case you will be asked when
you start the chart whether you want to save the record.
Examples
Robustness of estimated bias
in character evolution — Suppose a biologist estimated
the bias in the rates of gains versus losses in a character's
evolution on a given tree. How might the estimate depend on accuracy
of the tree's branch lengths? To answer this, one could see how
the estimate varies when noise is added to the branch lengths
of the given tree. First have a tree window available with the
given tree showing. Then:
- Select the menu item Analysis>New
Bar & Line Chart For>Trees
- A dialog box with heading "Source of trees (Trees chart)"
should appear. Choose Randomly Modify Current Tree.
- In the dialog box "Random modifier of tree", choose
Add Noise to branch lengths. You will then
be asked to indicate the variance of the noise, and the number
of trees to chart.
- In the dialog box "Value to calculate for trees"
should appear. If you see "Forward/Backward Rates" as a choice under Tree Value using character, choose it. If you don't see Forward/Backward Rates, choose Tree Value using character,
because the desired value depends on the tree and a character. and in the next dialog box "Value to calculate for tree with character",
ask to show secondary choices then choose Forward/Backward
rates
- In the dialog box "Source of characters (for Forward/Backward
rates)", choose Stored Characters (presuming
you already have your character of interest entered in a data
matrix). If you have "Use Stored Characters/Matrices by Default" turned on in the Defaults submenu if the File menu, Mesquite won't ask you and will simply use Stored Characters.
- You may be asked other questions, depending on whether you
data file includes multiple matrices. Then, a chart should appear
to answer your query. (The calculation may take while.)
Compositional bias along a sequence
— A biologist with DNA sequence data wants to see how the
relative frequences of A, C, G and T vary along the length of
the sequence. To see this:
- Select the menu item Analysis>New
Bar & Line Chart For>Characters
- In the dialog asking for a source of characters, choose Stored
Characters (assuming you have your DNA matrix in the
file). If you have "Use Stored Characters/Matrices by Default" turned on in the Defaults submenu if the File menu, Mesquite won't ask you and will simply use Stored Characters.
- In the dialog "Value to calculate for characters (for
Character Values Chart)", ask to show secondary choices
then choose Character Compositional Bias
- The chart may initially appear uninteresting, but adjust as
follows:
- Select Chart>Orientation>Values
(Y) by Items (X) to cause the chart to show the
characters lined up, in sequence, along the X axis.
- The chart will probably be set to automatically group into
categories along the X axis. Try a moving window analysis
by selecting Chart>Grouping
on X>Moving Window..., and indicating the width
of the moving window and the offset between adjacent window
positions. The defaults are 5 and 1 respectively, but you
could also try 10 and 2 to smooth further.
Above is an example of how the chart may appear. Some sections
of the chart are red because those characters were indicated as
belonging to a distinct character
group or partition. In this chart, the introns (marked in
red) have a stronger AT bias.
Calculation and Formatting options
The following menu items can be found in the Chart menu:
- Orientation
- Number of Items (Y) by Values (X) —
This is the typical "histogram" where the vertical
axis shows how many items have the various values arrayed
along the X axis. Thus, the X axis represents the value, the
Y axis the number of items.
- Value (Y) by Items (X) — This displays
the data with items arrayed in sequence along the X axis,
and the Y axis representing the value for each item. This
may be appropriate for items, like characters (sites in a
DNA sequence), which have a natural ordering to them.
- Grouping on X — The X axis may be grouped
into categories, such that the values falling within a range
on the X axis are summarized in a single bar. This submenu controls
any grouping.
- Automatic — Mesquite chooses automatically
how to group on the X axis
- No grouping — The X axis is not
grouped, and thus each item or object (each character, tree,
etc.) is represented by a separate bar.
- Fixed number of groups — The X
axis is divided into a specified number of groups.
- Fixed Group width — The X axis
is divided into groups of a chosen width.
- Moving Window — The X axis is
divided into overlapping groups of a chosen width. This
serves to smooth the chart by averaging over adjacent values.
There are two parameters to set: the width of the moving
window, and its increment. The increment is the offset between
the starting edge of adjacent moving window positions.
- Analysis — In this submenu could be
various analytical tools. Two standard choices are Display Mean
and Percentiles..., which display the mean value and tails of
the distribution.
- Show Average For Group — When the chart
is in the orientation Values by Items, and there is grouping
along the X axis, then each bar may represent several objects
(characters, etc.). This menu item allows you to choose whether
the Y axis should show the sum of the values of those objects,
or their average value.
- Show Individual Points in Text — When
the chart has grouping along the X axis, then the text view
of the window by default hows sums or averages of the groups.
If instead you want the text view to give all of the values
for the original objects shown by the chart, then select this
menu item.
- Show as Bar Chart — By default, the
chart is shown as a bar chart. However, if this option is turned
off, the chart will be shown as a series of dots connected by
a thin line.
- Cumulative Mode — By default, the chart
is not shown in Cumulative mode. However, by choosing items
in the Cumulative submenu of the chart, Mesquite will present
the cumulative values at each point:
- Off — Not cumulative
- Simple Cumulative — The value of
each item is the sum of the values of all previous items
- Average Cumulative — The value
of each item is the average of the values of all previous
items
- Reverse Simple Cumulative — The
value of each item is the sum of the values of all following
items
- Reverse Average Cumulative — The
value of each item is the average of the values of all following
items
Scattergrams
The scattergrams available in the Analysis menu are:
- Characters — each point in the plot
represents a character. These could be all of the characters
of a matrix, or a series of simulated or randomized characters.
- Taxa — each point in the plot represents
a taxon within a taxa block.
- Trees — each point in the plot represents
a tree. These could be all of the trees within a tree block,
or a series of simulated or randomized trees.
- Nodes (Available under New Chart for Tree
when a tree window is foremost) — each point in the plot
represents a node in the tree of the tree window.
These scattergrams show the values of two variables for the objects
of concern. For some scattergrams, a choice is given as to whether
the Same or Different calculations
should be shown on the two axes. By "Same" is meant
that the same calculation is done but with a different parameter
value. For instance, if the scattegram is a Taxa scattergram,
it could show the character state in continuous character 1 on
the Y axis, and the state in character 2 on the X axis. These
represent the same calculation (continuous character state value),
differing only in the character used. By "Different"
is meant an entirely different calculation, such as the asymmetry
of a tree on the Y axis and its likelihood score for a character
on the X axis.
Examples
Canonical Variates Analysis
— For a sample of specimens measured for a series of variables,
how can the measurements be combined to best distinguish predefined
groups? Multivariate analyses such as these can be done using
modules in the Rhetenor package. Each specimen will be treated
as a taxon. A continuous data matrix of the measurements should
first be entered, and the taxa be assigned to groups.
Next:
- Select Analysis>New
Scattergram For>Taxa
- In response to the query about same or different calculations,
chose Same
- If asked, indicate you want to value for taxa to be Continuous
States of Taxon. Otherwise, in response to the dialog
box "Source of characters (for Continuous States of Taxon)",
ask to show secondary choices and choose "Characters
from Ordinations".
- In the dialog box "Source of matrices to be ordinated",
select Stored Matrices. (If you have "Use Stored Characters/Matrices by Default" turned on in the Defaults submenu of the File menu, Mesquite may not ask and will simply use Stored Matrices.)
- In the dialog box "Ordination (for Characer Source)",
select Canonical Variates Analysis. (You may
need to ask for secondary choices)
Correlation between variability
and hydrophobicity — Do amino acid positions in
proteins tend to evolve more quickly or more slowly depending
on how hydrophobic they typically are? Mesquite does not yet have
a direct way to estimate rates for protein characters, but we can
approximately compare relative rates by comparing the number of
parsimony steps for characters on a tree. First, begin with a
file containing a protein data matrix and an open tree window
showing a tree. Next:
- Select Analysis>New
Scattergram For>Characters
- In the dialog box "Source of characters (For Characters
scattergram)" choose Stored Characters.
- In response to the query about same or different calculations,
chose Different
- On the X axis we will put hydrophobicity. Thus, in the dialog
box "Values for X axis", ask for secondary choices
and choose Protein Site Property.
- In the dialog box "Property of Amino Acid" choose
Kyte & Doolittle Hydrophobicity.
- In the dialog box "Values for Y axis", choose Parsimony Character Steps if you see it. (Whether or not you see it depends on the setting "Show Subchoices in Module Dialogs" in the Defaults menu of the File menu.) If you don't see it, choose Character
Value with Current Tree, then in the dialog box "Value
to calculate for character" chose Parsimony Character
Steps. If Mesquite asks, indicate you want Current Parsimony
Models to be used in the parsimony calculations.
The following scattergram shows the results of such an analysis,
with two additions. First, the dots are colored by a third variable,
the mean molecular weight of amino acids at that site. This can
be done by selecting Color by Third Value from the Color menu,
and in the dialog box "Values by which to color spots in the scattergram"
asking for secondary choices.
Second, the analysis assistant Scattergram Regression Diagnostics
(part of the PDAP
package) is in use, and shows the regression line. The text view
of the window shows the details of the analysis. The correlation
is highly significant.
Calculating and formatting options
The following menu items can be found in the Scattergram menu:
- Marker Size — allows you to choose
the size of the dots of the scatterplot
- Analysis — In this submenu could be
various analytical tools. For instance, if PDAP
is installed, you can request regression and correlation analysis
under Scattergram>Analysis>.
- Special Effects
- Show Density — this shades the
background of the chart according to the density of points.
To see this, you may want to turn off "Show dots"
(see below). Here is an example:
- Join the Dots, Join Last to First, Thick Joints
— These control whether and how a line is drawn between
dots of the scattergram. These options are used to indicate
molecular structure as in the cytochrome B example in Mesquite_Folder/examples/Molecular/06-cytochromeB.nex
- Show dots — determines whether or
not the dots representing objects in the scatterplot are drawn
individually
In addition, if the scattergram is of characters, a Color
menu will appear that allows you to color the dots according to
a third value of the characters.
