Visualizing Results
plot_sumz() and plot_sumz_density()
The community-level output may be viewed using the
plot_sumz() or plot_sumz_density() functions.
The plot_sumz_density() function is new to this version of
TITAN2. We recommend its use because we think it will
be both easier to understand than previous output and encourage
appropriate interpretation of results.
There are many options for changing the look of the graphs; see their
full documentations with ?plot_sumz or
?plot_sumz_density. An abbreviated version is presented
below. To begin, here’s how you use
plot_sumz_density():
plot_sumz_density(glades.titan)
# Warning: The `guide` argument in `scale_*()` cannot be `FALSE`. This was deprecated in
# ggplot2 3.3.4.
# ℹ Please use "none" instead.
# ℹ The deprecated feature was likely used in the TITAN2 package.
# Please report the issue to the authors.
# This warning is displayed once every 8 hours.
# Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
# generated.
plot_sumz_density() plots community level change
identified with TITAN2. There are three component
panels in the default output and we will consider them from the bottom
to the top. The first plot is a slight modification of the original
sum(z) plot first presented by Baker and King (2010). It shows the
magnitude of change among taxa declining along the gradient (z-) and
those increasing along the gradient. Peaks in the values indicate points
along the environmental gradient that produce large amounts of change in
community composition and/or structure. These are the nominal community
change points. Plateaus denote regions of similar change. The sums are
converted to areas using the logical argument ribbon, a
line plot can be obtained by setting ribbon to FALSE, and
the original point plot can be obtained by setting the logical argument
points to TRUE.
The second change from earlier versions of TITAN2 is
that the logical argument filter defaults to TRUE. This
argument ensures that the only taxa contributing to patterns in the
sum(z) are pure and reliable taxa identified by the bootstrap results
rather than all taxa. Setting filter to FALSE allows impure
or unreliable taxa to contribute to apparent patterns of commuity
change. In general, the filtered scores should show a similar pattern
but be somewhat lower in magnitude depending on contributions from
impure or unreliable taxa.
The middle panel shows the estimated probability density of the sum(z) across all bootstrap replicates. Previously these distributions were represented by cumulative frequency distributions of the sum(z) maxima. A narrow spread indicates a high degree of precison regarding the location of the community change point.
The top panel shows the observed sum(z-) and sum(z+) maxima as circles with the 95th percentile of their distributions as horzontal lines. The primary reason for this plot is to illustrate how much information is hidden by this technique relative to the probability density functions.
There are several additional plotting options in
plot_sumz_density(). First, any of the three panels can be
dropped by setting logical agruments sumz,
density, or change_points to FALSE. Second, it
is possible to display only the z- or z+ taxa through the use of the
logical arguments sumz1 and sumz2. Finally,
the x axis label can be edited using the xlabel
aregument.
plot_sumz_density(glades.titan,
ribbon = TRUE, points = FALSE, sumz1 = FALSE, change_points = FALSE,
xlabel = expression(paste("Surface Water Total Phosphorus ("*mu*"g/l)"))
)
Besides the mandatory titan object, arguments include:
filter- controls whether filtered (default) or unfiltered sum(z) scores are plottedsumz- logical whether sum(z) values are plottedpoints- logical whether point values of the sum(z) should be plottedribbon- logical whether values of sum(z) should be plotted as a ribbondensity- logical whether estimated probability densities should be plottedchange_points- logical whether community change points should be plottedsumz1- logical whether sum(z) formaxgrp = 1should be plottedsumz2- logical whether sum(z) formaxgrp = 2should be plottedxmin- controls the x-axis minimumxmax- controls the x-axis maximumxlabel- text string for x-axis labely1label- text string for sum(z) y-axis, default labels are providedy2label- text string for density plotalpha1- controls the transparancy of sum(z-)alpha2- controls the transparancy of sum(z+)col1- color for `maxgrp = 1col2- color for `maxgrp = 2axis_lab_size- controls size of axis labelslegend.position- controls location of legend
For plot_sumz, the older plotting function in
TITAN2, filled and hollow symbols denote the magnitude
of summed z scores of increasing (z+) or decreasing (z-) taxa. Peaks in
the values indicate points along the environmental gradient that produce
large amounts of change in community composition and/or structure. Solid
and dashed lines are cumulative frequency distributions of sum(z-) and
sum(z+) maxima (respectively) across bootstrap replicates. Vertical CFDs
indicate narrow uncertainty about where the maximum chnage occurs,
sloping or stair-step CFDs suggest broad uncertainty regarding the
location of maximum change.
Note that users can adjust colors (e.g. col1 and fil1) and labels for
the left hand y-axis using the argument y1label or the
x-axis with xlabel. Setting filter = TRUE will
display the filtered sum(z) scores. In general, the filtered scores
should show a similar pattern but be somewhat lower in magnitude
depending on contributions from impure or unreliable taxa:
plot_taxa_ridges()
Pure (purity>=0.95 or higher) and reliable (reliability>=0.95
or higher) indicator taxa that contribute to the overall sum(z) scores
can be plotted using the function plot_taxa_ridges().
Taxa that meet purity (pur.cut) and reliability (rel.cut) criteria
are extracted from the full taxa output object
titan.out$sppmax, separated into two groups: z- (negative
responders, or decliners) and z+ (positive responders, or
increasers).
These two groups of negative and positive responders are arranged into separate, stacked panels for plotting. Within each panel, taxa change points (values of x resulting in the largest indicator z value) are visualized as a probability density function of the nBoot bootstrapped replicates (n=500 or however many nBoot replicates specified by the user).
Taxa names are arranged discretely along the y-axis based on the rank order of the central tendency of the probability density function for z- (negative, decliners) and z+ (positive, increasers), respectively.
There are many options for changing the look of the graph, so see the
full documentation with ?plot_taxa_ridges, but you can get
started by simply calling plot_taxa_ridges() on the output
of titan():
plot_taxa_ridges(glades.titan, axis.text.y = 8)
# There are 90 indicator taxa of 90 possible for plotting
# Number of Decreasers = 41
# Number of Increasers = 49
Optional arguments include:
z1- logical whethermaxgrp = 1taxa (z-, negative, decliners) should be plottedz2- logical whethermaxgrp = 2taxa (z-, negative, decliners) should be plottedz1_fill_low- low value of the color fill gradient for z- (negative) taxaz1_fill_high- high value of the color fill gradient for z- (negative) taxaz2_fill_low- low value of the color fill gradient for z+ (positive) taxaz2_fill_high- high value of the color fill gradient for z+ (positive) taxapur.cut- the purity value cutoff for selecting taxa for plotting (defaults to value selected in titan.out). We do not recommend selecting values less than 0.95 for purity; higher values up to 1.0 may be used to refine your selection to the purest responders in terms of direction.rel.cut- the reliability value cutoff for selecting taxa for plotting (defaults to value selected in titan.out). We do not recommend selecting values less than 0.95 for purity; higher values up to 1.0 may be used to refine your selection to the purest responders in terms of direction.xlabel- the x axis label; the default is “Environmental Gradient”n_ytaxa- the maximum number of taxa that can be plotted on the y-axes (combined between the two panels if both z1 and z2 = TRUE, or just for one panel if z1 or z2 = FALSE). If the total number of pure and reliable indicator taxa exceeds the value of n_ytaxa, then the function will select only the most pure and reliable taxa to match the value of n_ytaxa based on rank order of purity, reliability, and finally z.med (sequential sorting, respectively). The selection of n_ytaxa is independent of group membership, so that only the best indicators are displayed, regardless of z- or z+ grouping.ytxt.sz- size of the taxa labels on the y-axis. Defaults to ytxt.sz=10. Depending upon the height and width of the plot, labels may need to set to a smaller size to avoid overlap (e.g., see the plot above; here, ytxt.sz = 8).printspp- a logical determining whether the sppmax output for the plotted taxa is printed to the console; default = FALSE.grid- a logical determining whether gridlines are plotted; default=TRUExlim- the upper and lower limits of the x-axis, e.g., xlim=c(0,180). The default is computed internally based on the lower and upper limits of the x variable.bw- short for “bandwidth”, it controls the degree of smoothing of the probability density plots. This is computed internally but can be adjusted manually using this argument. We strongly advise against changing this parameter from the default.
Below is the same function with a user-specified x-label and n_ytaxa set to 50
plot_taxa_ridges(glades.titan,
xlabel = expression(paste("Surface water total phosphorus ("*mu*"g/l)")),
n_ytaxa = 50
)
# There are 90 indicator taxa of 50 possible for plotting
# Number of Decreasers = 41
# Number of Increasers = 49
There are a total of 90 pure and reliable indicator taxa in the
glades.titan output, thus 40 taxa were excluded from this
plot because we set n_ytaxa = 50. The 50 taxa plotted are
the top 50 out of 90 taxa based on descending rank order of
purity, reliability, and
z.median, respectively.This argument can be useful when
there are too many pure and reliable taxa to effectively visualize in
one plot.
Alternatively, set z1 or z2 = FALSE.
plot_taxa_ridges(glades.titan,
xlabel = expression(paste("Surface water total phosphorus ("*mu*"g/l)")),
z2 = FALSE
)
# There are 90 indicator taxa of 90 possible for plotting
# Number of Decreasers = 41
# Number of Increasers = 49
Gridlines are set to TRUE as the default, but can be
removed if desired:
plot_taxa_ridges(glades.titan,
xlabel = expression(paste("Surface water total phosphorus ("*mu*"g/l)")),
z2 = FALSE, grid = FALSE
)
# There are 90 indicator taxa of 90 possible for plotting
# Number of Decreasers = 41
# Number of Increasers = 49
plot_taxa()
Pure and reliable indicator taxa change points can be plotted using
an older plotting function that was integral to the original TITAN2
release, plot_taxa(). We have replaced this plot with the
distributions in plot_taxa_ridges() because it tended to
empahsize the observed change points over the bootrap replicates. Again,
there are many options for changing the look of the graph, so see the
full documentation with ?plot_taxa, but you can get started
by simply calling plot_taxa() on the output of
titan():
Each plot includes robust declining taxa on the left axis, increasers
on the right. Each observed change point (or median of bootstrap
replicates if z.med = TRUE) is indicated by the circular
symbol; the horizontal lines suggest 5-95% quantiles from the
bootstrapped change point distribution.
Optional arguments include:
z1- logical whethermaxgrp = 1taxa change points should be plottedz2- logical whethermaxgrp = 2taxa change points should be plottedinterval- logical whether 5%-95% quantile intervals should be plottedprob95- controls whether change point symbols are plotted at observed value or at quantile extremes, the extremes are useful for thinking about change from a risk perspectivez.med- controls whether change point symbols are plotted at median of bootstrap replicates and using median \(z\) score instead of observed valuecex.taxa- controls size of taxon names in graph.
log, at, xmin,
xmax, xlabel, tck,
bty, ntick, prtty,
dig, leg.x, leg.y,
cex, cex.axis, cex.leg,
cex.lab, legend, col1,
fil1, col2, and fil2 are the same
as in plot_sumz() above.
Here is the same function with z.med = TRUE:
Alternatively, with prob95 = TRUE:
Importantly, some of the control over the plotting that was optional
in the original version has been internalized and warnings are issued
when users plot results without using the bootstrap results. Tables of
significant z- and z+ taxa used to make graph are automatically returned
but no longer automatically written as text files (these can be easily
extracted from the glades.titan$sppmax table).
plot_cps()
In TITAN2 2.0 and later, there are several plotting options; all contained within a single function centered on interpreting taxon-specific change points in the context of the results from the bootstrap resampling procedure.
taxa.dist- logical controls if taxon-specific change point distributions are plottedz.weights- logical controls if the median z-sore magnitude is used to weight the PDF from the distribution of resampled change pointstaxaID- if a number or name, creates a single taxon-specific abundance plotcp.med- logical controls if change point locations should be plotted using the median value across all bootstrap replicates instead of the observed valuecp.trace- logical controls if IndVal and zscores are plotted for all candidate change pointscp.hist- logical controls if histogram of change point PDF is plottedstacked- logical controls if change point PDFs for increasing and decreasing taxa are stacked or plotted separately
The remaining arguments: xlabel, xmin,
xmax, tck, bty,
ntick, cex, cex.axis,
cex.leg, cex.lab, leg.x,
leg.y and legend are the same as in the
previous plotting functions.
The default graphic from plot_cps() is a \(z\)-score weighted probability density
function derived from the empirical distribution of change points across
all bootstrap replicates plotted as a histogram for each pure and
reliable taxon (blue for decreasers and red for increasers). NOTE: When
you try to plot the matrix of plots consecutively you can generate an
error about “Figure margins too large”. This is easily addressed by
closing the plot window, or turning the graphics device off.
Typically, these histograms are visually scanned to distinguish those
taxa whose bootstrapped change point distributions are clearly unimodal
from those that are multimodal or more uniform. For any taxon of
interest, a closer inspection can be achieved by setting the argument
“taxaID” to a taxon ID number or label name. For example, in the plot
above, if the declining (i.e., maxgrp = 1) taxon
"ENALCIVI" is of interest, the user can set
taxaID = 57 or taxaID = "ENALCIVI" and either
will produce the plot below. Again, you may need to close the plotting
window or turn graphics off because we are switching plot margins.
The base plot is simply taxon-specific abundance (black circles)
along the environmental gradient. Overlaid near the top of the plot in
red is the observed change point, or if cp.med = TRUE, the
median change point across all bootstrap replicates. Overlaid on the
abundance plot is the \(z\)-weighted
(if z.weights = TRUE) probability density function of
change point locations across all bootstrap replicates (blue histogram).
Setting cp.hist = FALSE will remove the histogram. On the
other hand, setting cp.trace = TRUE will plot the observed
IndVal \(z\) scores (in red; what
TITAN2 uses by default if imax = FALSE)
and the observed IndVal scores (in grey) for every candidate change
point along the environmental gradient (see Baker and King
2013 for examples):
Below is an increasing taxon from the same data set with a conspicuously bimodal distribution of replicate change points:
Here it appears as if two potential change points were predominantly identified: one that kept nearly all of the abundance to the right, and another (the observed) than kept nearly all the absences to the left.
Finally, if taxa.dist = FALSE, instead of a
taxon-specific plot, plot_cps() will produce a plot of the
summed \(z\)-weighted (if
z.weights = TRUE) probability densities across increasing
(maxgrp = 1; blue) decreasing (maxgrp = 2;
red) and all pure and reliable taxa (filter>0; grey):
plot_cps(glades.titan, taxa.dist = FALSE, xlabel = "Surface Water TP (ug/l)")
# [1] "Summary of Summed Density Functions"
# uw.env uw.max zw.env zw.max
# Group 1 14.55 1.00 14.55 10.22
# Group 2 28.80 1.34 28.80 11.13
# P&R Taxa 28.80 2.01 28.80 17.14
The accompanying table summarizes the location of both the \(z\)-weighted and unweighted maxima along
the environmental gradient, as well as the magnitude of those maxima for
decreasing taxa (maxgrp = 1), increasing taxa
(maxgrp = 2), and all pure and reliable taxa combined. In
this case there appears to be good correspondence between the sum(z)
maxima and the summed \(z\)-weighted
PDF maxima. In other words, the points at which community change appears
to be greatest corresponds to where the sum of individual taxa changes
tend to occur, even when different sets of observations are used. In
practice, this is a desirable result we would expect to occur most of
the time, yet exceptions to this pattern can also be informative. For
example, in the plot above, there appears to be another candidate change
point closer to ~10 ug/l where declining taxa tend to change frequently,
and at both ~25 ug/l and ~40 ug/l there are large numbers of frequently
occurring change points across both decliners and increasers even though
they are not particularly large for either group by itself.
Alternatively, these different sums can be represented as a stacked
bar chart by setting stacked = TRUE:
plot_cps(glades.titan, taxa.dist = FALSE, xlabel = "Surface Water TP (ug/l)", stacked = TRUE)
# [1] "Summary of Summed Density Functions"
# uw.env uw.max zw.env zw.max
# Group 1 14.55 1.00 14.55 10.22
# Group 2 28.80 1.34 28.80 11.13
# P&R Taxa 28.80 2.01 28.80 17.14
Here the blue and red circles correspond to the location of the
respective maxima for decreasing and increasing taxa change points. In
either case, the summed PDFs are meant to provide complementarity to the
plot_sumz() graphic about where there are key values along
the environmental gradient where many coincident change points occur
regardless of the sample.
Citations:
Baker, M.E. and R. S. King. 2010. A new method for detecting and interpreting biodiversity and ecological community thresholds. Methods in Ecology and Evolution 1: 25-43.Z
Baker, M.E. and R. S. King. 2013. Of TITAN and strawmen: an appeal for greater understanding of community data. Freshwater Science 32(2):489-506.
King, R.S. and C. J. Richardson. 2003. Integrating bioassessment and ecological risk assessment: an approach to developing numerical water-quality criteria. Environmental Management 31(6):795-809.
Dufrene, M. and P. Legendre. 1997. Species assemblages and indicator species: the need for a flexible asymmetrical approach. Ecological Monographs. 67:345-366.