supplement-ichthyosaur_macroevolution.tex

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\title{Supplementary material for `Early high rates and disparity in the
evolution of ichthyosaurs'} 
\author{Benjamin C.\ Moon \and Thomas L.\ Stubbs}
\date{\today~\version}

\begin{document}

\maketitle

\tableofcontents


\section{Supplementary figures}\label{sec:supplemental-figures}

\listoffigures

\vspace{2em}
\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Per-bin discrete skeletal disparity of Ichthyosauriformes though
        the Mesozoic]{(following page) \textbf{Per-bin discrete skeletal disparity
        of Ichthyosauriformes though the Mesozoic.} Pairwise and weighted
        pairwise dissimilarity measured from raw Euclidean (RAW), generalised
        Euclidean (GED), Gower (GOW), and maximum observed rescaled (MAX)
        distances between taxa in the cladistic dataset of \textcite{Moon2018JSP}
        binned into epochs and equal 10-million-year bins. Also, pairwise number
        of comparable characters between taxa (CHAR) indicating the variation in
        completeness and comparability in each bin. Mean values and 95\%
        confidence intervals are shown from 500 bootstrap
        replicates.\label{fig:pairwise-disparity}}
\end{minipage}
\includepdf[pages = -, fitpaper = true]{supp_figures/figS3-pairwise_all.pdf}

\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Per-bin rarefaction curves for each disparity-time curve
        shown in \cref{fig:pairwise-disparity}]{(following pages) \textbf{Per-bin
        rarefaction curves for each disparity-time curve shown in
        \cref{fig:pairwise-disparity}.} Disparity for each pin is sequentiall
        rarefied on taxon occurrnece. Error polygon gives 95\% confidence interval
        from 500 replicates.\label{fig:pd-rarefaction-curves}}
\end{minipage}
\includepdf[pages = -, fitpaper = true]{supp_figures/figS5-pdrarefaction_curves.pdf}

\begin{figure}[h]
    \caption[Cumulative variance described by axes of the ordinated data
        and the correlation of these axes with the original data
        set]{\textbf{Cumulative variance described by axes of the ordinated data and
        the correlation of these axes with the original data.} Axes from principal
        coordinates analysis of the four distance matrices used here derived from
        the cladistic data set of
        \textcite{Moon2018JSP}.\label{fig:ordination-correlation}}
    \includegraphics[width = \textwidth]{supp_figures/figS4-scree_plot.pdf}
\end{figure}

\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Per-bin discrete skeletal disparity of Ichthyosauriformes through
        the Mesozoic from ordinated data]{(following pages) \textbf{Per-bin discrete
        skeletal disparity of Ichthyosauriformes through the Mesozoic from ordinated
        data.} Ichthyosaur disparity represented by mean sum of variances, mean sum
        of ranges, and mean centroid distance from each of eight PCA (four distance
        matrices: RAW, GED, GOW, MAX\@; with and without negative eigenvalue correction)
        on the cladistic matrix of \textcite{Moon2018JSP}. Error bars show 95\% confidence
        intervals from 500 bootstrap replicates.\label{fig:ordinated-disparity}}
\end{minipage}
\includepdf[pages=-, fitpaper = true]{supp_figures/figS5-disparity_time.pdf}

\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Per-bin rarefaction curves for each disparity-time curve shown in
        \cref{fig:ordinated-disparity}]{(following pages) \textbf{Per-bin
        rarefaction curves for each disparity-time curve shown in
        \cref{fig:ordinated-disparity}} Disparity for each bin is sequentially
        rarefied on taxon occurrences. Error polygon gives 95\% confidence interval from
        500 replicates.\label{fig:rarefaction-curves}}
\end{minipage}
\includepdf[pages = -, fitpaper = true]{supp_figures/figS6-rarefaction_curves.pdf}

\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Morphospace occupation of Ichthyosauriformes through the
        Mesozoic]{(following pages) \textbf{Morphospace occupation of
        Ichthyosauriformes through the Mesozoic.} Principal coordinate axis 1
        against axes 2 (top row) and 3 (bottom row) from each of eight PCA (four
        distance matrices: RAW, GED, GOW, MAX\@; with and without negative eigenvalue
        correction) on the cladistic matrix of \textcite{Moon2018JSP} binned into
        epochs.\label{fig:morphospace-plots}}
\end{minipage}
\includepdf[pages = -, fitpaper = true]{supp_figures/figS7-all_morphospace.pdf}

\begin{figure}[h]
    \includegraphics[width = \textwidth, center]{supp_figures/figS8-rates_MBLspaghetti}
    \caption[Rates of discrete skeletal character evolution in
    Ichthyosauriformes]{\textbf{Rates of discrete skeletal character evolution in
    Ichthyosauriformes.} Calculated from the matrix of \textcite{Moon2018JSP} using
    1000 time-scaled trees from the minimum branch length method. Rates of evolution
    are plotted in \textbf{a}, epoch-bins and \textbf{b}, equal-length
    10-million-year bins.\label{fig:mbl-discrete-rates}}
\end{figure}

\noindent\begin{minipage}[c]{\textwidth}
    \captionof{figure}[Rates of skull size evolution in
        Ichthyosauriformes]{(following page) \textbf{Rates of skull size
        evolution in Ichthyosauriformes.} Evolutionary rate results from 100
        Hedman-dated phylogenies. Branches are scaled and branches and taxon
        names coloured to the rate of skull size change on that branch.} 
\end{minipage}
\includepdf[pages = -, fitpaper = true]{supp_figures/figS10-bayestraits_trees_rates.pdf}

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\section{Supplementary tables}\label{supplementary-tables}

\listoftables

\begin{table}[h]
    \caption[Bin boundaries of \SI{10}{\mega\annum} bins used in this
    study]{\textbf{Bin boundaries of \SI{10}{\mega\annum} bins used in this
    study.} Approximate age ranges are given as
    indicators.\label{tbl:ten-ma-bins}}
	\csvreader[%
		centered tabular = rSSl,
		table head = {\toprule {Bin} & {Start (\si{\mega\annum})} & {End (\si{\mega\annum})} & {Approximate age range} \\\midrule},
		table foot = \bottomrule]%
		{supp_tables/10ma-dates.csv}%
		{}%
		{\csvlinetotablerow}
\end{table}

\begin{table}[h]
    \caption[Occurrence dates of outgroup taxa used to date the tree of
    Ichthyosauriformes]{\textbf{Occurrence dates of outgroup taxa used to date
    the tree of Ichthyosauriformes.} Stratigraphic occurrence intervals are
    taken from the given references. Occurrences are converted to absolute ages
    using \textcite{Gradstein2012}. FAD, first appearance date; FAS, first
    appearance stratigraphy; LAD, last appearance date; LAS, last appearance
    stratigraphy.\label{tbl:outgroup-dates}}
    \small
    \csvreader[%
	    tabular = >{\itshape}lSSlll,
	    table head = \toprule \emph{Taxon} & {FAD (\si{\mega\annum})} & {LAD (\si{\mega\annum})} & FAS & LAS & Reference\\\midrule,
        late after last line = \\\bottomrule]%
        {supp_tables/outgroup_dates.csv}%
        {Taxon=\taxon,FAD=\fad,LAD=\lad,FAStrat=\fas,LAStrat=\las,Reference=\ref}%
        {\taxon & \fad & \lad & \fas & \las & \ref}
\end{table}

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{\small%\addfontfeatures{Numbers = Monospaced}
	\csvreader[longtable = {>{\itshape}lSS[table-format=1.3]l},
	    table head = {
                \caption[Skull lengths of Ichthyosauriformes included in the
                analyses]{{\normalsize\textbf{Skull lengths of
                Ichthyosauriformes included in the analyses.} Logarithm values
                are shown to 3~d.p.\label{tbl:ingroup-lengths}}}\\
	        \toprule
	        \emph{Taxon} & {Skull length (\si{\milli\metre})} & {log\textsubscript{10}~(Skull length (\si{\milli\metre}))} & {References}\\\midrule\endfirsthead
	        \caption*{Supplementary table~\thetable{} continued}\\
	        \toprule\emph{Taxon} & {Skull length (\si{\milli\metre})} & {log\textsubscript{10}~(Skull length (\si{\milli\metre}))} & {References}\\\midrule\endhead
	        \bottomrule\endfoot
	        \bottomrule\endlastfoot}]%
	    {supp_tables/ichthyosaur_lengths.csv}%
	    {Taxon=\taxon,sklen=\sklen,lsklen=\lsklen,refs=\refs}%
	    {\taxon & \sklen & \lsklen & \cite*{\refs}}
}


\section{Supplementary code}\label{supplemental-code}

\begin{enumerate}[label = \textbf{Code \arabic*}, align = left,
    ref = {Code \arabic*}]
    \item \textbf{R code implementing the disparity, principal coordinates,
        diversity, and discrete character rates analyses.} This set of five
        scripts contains the code used to run the main discrete character
        analyses in R. Outputs include time-scaled trees, discrete rates of
        evolution, stratigraphic congruence values; PDF files of all figures
        produced; CSV files of root ages from the time-scaled trees,
        stratigraphic congruence tests, and statistical tests (pairwise
        PERMANOVA between epochs for PCA data and pairwise \emph{t}-tests of
        per-bin disparity).\label{disparity-discrete-code}
    \item \textbf{Continuous rates analyses in BayesTraits and plotting in R.}
        Rates analyses were run individually on 100 time-scaled trees then
        combined into consensus trees with branch rates averaged across all
        runs. Also includes code to create the traitgram of
        Fig.~4.\label{bayestraits-code}
\end{enumerate}


\section{Supplementary methods}\label{supplemental-methods}

\paragraph{Comparison of time-scaling methods}\label{comparison-of-time-scaling-methods}

To assess the effects of variation in the timing of ichthyosaur evolution on
discrete evolutionary rates, we further used the minimum branch length (MBL)
tree-scaling method \autocite{Bapst2012MEE, Laurin2004SB}. This scales the
tree according to occurrence dates, but ensures that each branch length is
greater than a given value, rescaling ancestral branches as necessary to ensure
this minimum length. Here, we used a MBL of \SI{1}{\mega\annum} as a reasonable
minimum between speciation events and to avoid forcing excessive branch lengths
where speciation may occur rapidly. We used the same sample of 120 phylogenetic
trees as the main analysis from the Bayesian phylogenetic posterior distribution
of \textcite{Moon2018JSP}. Trees were time-scaled in R \autocite{RCoreTeam2019} using the
function \texttt{timePaleoPhy} in the package paleotree \autocite{Bapst2012MEE}
with point ages sampled from a uniform distribution between their first and last
occurrences. Each tree was resampled 10 times to account for the occurrence
ranges for each taxon (100 tree topologies × 10 samples = 1000 time-scaled trees
total). These MBL time-scaled trees were then used for a further set of discrete
character evolutionary rates analyses using function
\texttt{DiscreteCharacterRate} of R package Claddis \autocite{Lloyd2016BJLS}. The
results of this were used to produce `spaghetti' plots for epoch-length bins and
equal-length bins using modified scripts from \textcite{Close2015CB}. Code for
all these analyses is included in \cref{disparity-discrete-code}.

\paragraph{Additional disparity metrics}

Our main results present ichthyosauriform disparity using per-bin pairwise
differences between taxa from a distance matrix calculated using maximum
observed rescaled distances \autocite{Lloyd2016BJLS}. Additionally, we compared
different distance conversion and disparity metrics.

\indent Claddis provides four distance metrics for discrete character data
\autocite{Lloyd2016BJLS}: raw Euclidean distances (RAW), generalized Euclidean
distances (GED) \autocite{Wills1994P}, Gower's coefficient (GOW)
\autocite{Gower1971B}, and maximum observable rescaled distances (MAX)
\autocite{Lloyd2016BJLS}. All four distance metrics were run through the same
disparity work flow. Recent studies have shown that GED as implemented in
Claddis is susceptible to the completeness of the original data matrix, which
may have a strong effect on the resulting disparity
\autocite{FlannerySutherland2019PRSBBS, Lehmann2019P}; therefore we prefer MAX\@.

Similarly, several different disparity metrics have been developed, each with
varying properties. Our main results present mean and weighted mean pairwise
distances on MAX as this comes directly from the original data matrix, but we
also calculated the pairwise distances for RAW, GED, and GOW distances matrices
\pcref{fig:pairwise-disparity}. We ordinated the data using Principal
Coordinates Analysis (PCA), both with and without applying a correction to
negative eigenvalues \autocite{Caillez1983P} and compared the correlation of the
PCA data with the original distance matrix. 

From the PCA data we used all the resultant axes to calculate per-bin sum of
variances, sum of ranges, and centroid distances. These metrics have been used
extensively in previous analyses \autocite{Wills1998BJLS, Thorne2011PNAS,
FlannerySutherland2019PRSBBS}, so we considered it pertinent to compare them.
Binning, bootstrap resampling with 500 replicates, and complete rarefaction
were completed using the functions \texttt{custom.subsets} and
\texttt{boot.matrix}, and disparity calculations used the function
\texttt{dispRity}, all from package dispRity \autocite{Guillerme2018MEE} in R.
Code for this is included in \cref{disparity-discrete-code}.


\section{Supplementary results}\label{sec:supplemental-results}

\paragraph{Pairwise disparity}\label{par:pairwise-disparity}

Broadly speaking, trends in disparity across all four distance matrices are
similar: disparity peaks in the Late Triassic then declines through the Jurassic
and Cretaceous \pcref{fig:pairwise-disparity}. The bins that preserve the most
completely coded taxa (\cref{fig:pairwise-disparity} CHAR\@: Early Jurassic;
\SIrange{201.3}{171.3}{\mega\annum}) also show relatively increased disparity in
RAW and GED distance matrices compared to GOW and MAX\@. Indeed, the earliest
Jurassic bins are the most disparate for the RAW distance metric with both
binning schemes, and for GED the earliest Jurassic bins have relatively higher
disparity than GOW and MAX distance matrices. This is most likely a further
effect of incompleteness degrading the disparity signal by averaging the
difference between taxa \autocite{FlannerySutherland2019PRSBBS, Lehmann2019P},
therefore we prefer the results given by GOW and MAX distance matrices.
Rarefying the data shows that maximum disparity is reach quickly with minimal
taxa included, and supports using the full taxon sample for each bin
\pcref{fig:pd-rarefaction-curves}.

\paragraph{Correlation of ordinated data}\label{par:pco-correlation}

Negative eigenvalue correction notably decreased the variance described by the
first few principal coordinate axes \cref{fig:ordination-correlation}. The
highest correlations between the original and ordinated data were found when
including all ordinated axes \pcref{fig:ordination-correlation}. Without
negative eigenvalue correction RAW and GED had the highest correlation, whereas
GOW and MAX were reduced to \textasciitilde{}0.8. With negative eigenvalue
correction the pattern of correlations with increasing number of axes was more
complex: RAW gradually increased whereas GED strongly decreased, but both
rapidly increased to 1.0 with the last axes; GOW and MAX correlations both
immediately decreased, increased to a peak at \textasciitilde{}axis 60, then
rapidly increased again when including the last axes.

\paragraph{Disparity of ordinated data}\label{par:ordinated-disparity}

\textcite{Wills1998BJLS} asserted that variance based disparity metrics are more
suited to measuring overall dissimilarity whereas range-based metrics are
appropriate for disparity as they are affected by occurrence and thus show the
diversification of morphology. In this context, our results support our
conclusions that ichthyosaurs represent an early burst of evolution: both of
these metrics show initial high disparity from all distance matrices
(\cref{fig:ordinated-disparity}). Sum of variances also has a marked increase
between the Early to Middle Triassic and a substantial decline in disparity
between the Late Triassic–Early Jurassic in the combination of GOW/MAX distance
matrix and uncorrected PCO\@; otherwise all curves follow similar trends. Sum of
variances proves more resilient to sample size in rarefaction than either sum of
ranges or centroid distance (\cref{fig:rarefaction-curves}).

All sum of ranges curves display the same trends in disparity, differing only in
the magnitude. Similarly, we find early high disparity and an increase between
the Early–Middle Triassic (\cref{fig:ordinated-disparity}). Disparity decreases
substantially through the later Triassic, but broadly recovers in the Early
Jurassic before more log-term decline through to the extinction of the
ichthyosaurs. Particularly low disparity (e.g. Middle Jurassic;
\SIrange{171.3} {161.3}{\mega\annum}) are those bins represented by few taxa and
relative incompleteness.

In the case of centroid distance, although this has been shown to be especially
susceptible to issues of `centroid slippage'
\autocite{FlannerySutherland2019PRSBBS, Lehmann2019P}, our results show the same
trends as for sum of variances: high early disparity that is sustained through
to the Late Jurassic/Early Cretaceous before decline, with dips that are most
likely related to incompleteness of specimens (\cref{fig:ordinated-disparity}).

\paragraph{Morphospace occupation of ordinated data}\label{par:ordinated-morphospace}

Morphospace occupation between Triassic and post-Triassic Ichthyosauriformes is
separated in almost all cases (\cref{fig:morphospace-plots}; except RAW and GED
distances). Late Triassic taxa are also separated from earlier Triassic taxa in
GOW and MAX distance without negative eigenvalue correction, and are
consistently positioned more closely towards the Early Jurassic taxa. The
variation in Jurassic and Cretaceous taxa is markedly increased in RAW and GED
distances relative to GOW and MAX\@. Differences within Jurassic and Cretaceous
taxa are more represented in PCo axis 2 than axis 3 in the RAW and GED
morphospace plots, but in a combination of PCO axes 1 and 3 in GOW and MAX\@. All
RAW and GED morphospace plots show more points towards the origins of the plots
than GOW and MAX, a results of `centroid slippage'
\autocite{FlannerySutherland2019PRSBBS, Lehmann2019P}; in particular these represent
the least complete taxa.

\paragraph{Time-scaling and rates}\label{par:mbl-scaling-rates}

Using the MBL time-scaling method created trees with a root age of
\SIrange{253.8}{268.5}{\mega\annum}; older than the corresponding root ages from
the Hedman scaling method. Rates of discrete character evolution are relatively
lower for during the Early–Middle Triassic, but these earlier bins nonetheless
show significantly higher rates of evolution that subsequent bins
\pcref{fig:mbl-discrete-rates}. Trends across the whole of ichthyosaur evolution
remain similar, although there are increased peaks in the later Early Jurassic
and the Late Cretaceous bins. Significantly low rates of discrete character
evolution are reached in the Early Jurassic (epoch bins) or Late Triassic
(\SI{10}{\mega\annum} bins).

\printbibliography

\end{document}

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