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:
- Histogram - a bar chart summarizing freqencies
of values in different categories for each of many objects.
- 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
Histogram For>Characters because
the value concerns a character? No, one chooses New
Histogram 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
Selection of objects in charts
Most histograms 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 Histogram
or Scattergram menu.
Histograms
The histograms 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.
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
Histogram For>Trees
- A dialog box with heading "Value to calculate for trees"
should appear. Choose Tree
Value using character, because the desired value
depends on the tree and a character.
- In the 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).
- In the dialog box "Source of trees (Trees chart)", 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. You may be asked
other questions, depending on whether you data file includes
multiple matrices. Then, a histogram 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 Histogram For>Characters
- In the dialog "Value to calculate for characters (for Character
Values Chart)", ask to show secondary choices then choose
Character Compositional Bias
- Choose Stored Characters as the source of characters (assuming you
have your DNA matrix in the file).
- The chart may initially appear uninteresting, but adjust as follows:
- Select Histogram>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
Histogram>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 Histogram 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.
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.
- 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 direct way to estimate rate 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 Character
Value with Current Tree. In the dialog box "Value
to calculate for character" chose Parsimony
Character Steps. 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>Other Choices.
- 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.
