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\title{Representing SSR Molecular Marker Profiles Using Concepts from Andean Khipus - submssion to PeerJ}



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\section{Authors and Affiliations}

Authors:

Reinhard Simon[1], Pablo Carhuapoma[1], Vilma Hualla[1], Marc Ghislain[1], Felipe de Mendiburu[1, 2], Rene Gomez[1], Cinthya Zorrilla[1,2], William Roca[1], Stef de Haan[1], Merideth Bonierbale[1]



[1] International Potato Center (CIP)International Potato Center (CIP)

[2] Universidad Agraria La Molina (UNALM)


\section*{Introduction}
Genebanks increasingly use molecular markers for routine characterization of ex-situ collections and farmer managed diversity. CIPs genebank presently uses a SSR marker-kit \cite{Ghislain2008} to assist cultivar or genotype identification through molecular profiling. Applications include the comparison of ex-situ and in-situ collections to assess effectiveness and orient  conservation strategies \cite{Haan2013} or to document provenance and attribution as in an in-situ catalog \cite{Haan2006}. A primary motivation came from Andean potato growing communities that are in a working relationship with CIP: farmers called for support to aid in registry and identification of landraces and protect native varieties against 'biopiracy'. As a visual aid to compare SSR marker profiles between accessions in these contexts we identified the need for a compact graphical presentation similar to a 'bar-code'. 

A first set of criteria included:
\begin{itemize}
  \item Amenable to standardization using bioinformatics tools
  \item compact presentation (e.g. a chart of maximum 2.5cm x 2cm width by height)
  \item all SSR marker information for a given land-race
  \item Convey the individuality of a genotype in comparison to diversity in a group
  \item Recognize the contribution of Andean farmers to the development of the potato crop
\end{itemize}

To our knowledge no tool exists that would have allowed us to produce such compact graphs based on a set of informative SSR marker. 
In the context of the production of the first in-situ catalog (\cite{Haan2006} and \cite{Scurrah2013}) of Andean potato landraces it seemed worthwhile to consider the use or adaptation of the traditional Andean information communication tool - the khipu (see Figure~\ref{fig:khipu_orig}). 

Khipus consisted of a set of chords organized as a set of pendants hanging from a backbone chord. They used colors and knots to store a wide variety of information from tribute statistics (see Figure~\ref{fig:khipu_count}) to state history \cite{Ascher1983} to sins \cite{Beyersdorff2005}. Numbers apparently were represented as groups of knots and in a top-down order from 1000s to 100s to 10s and ones \cite{Urton2012}. Currently, khipus are not any more read by local people but some are still used for ceremonial purposes \cite{wp2014quipu}. The interpretation and usage of khipus is still not fully understood ~\cite{Urton2012}, so we did not aim to replicate a historically accurate way of coding SSR marker information. We rather used the khipu as an inspiration to design our own version. In this paper we summarize the process, design elements and evolution, implementation, use and reception. Details on usage can be obtained from the tutorial \cite{Simon2014b} available together with the software.



\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{Inca_Quipu.PNG}
\caption{An example of a traditional khipu. Source: wikipedia (\cite{Ableiter2007})}
\label{fig:khipu_orig}
\end{figure}



\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{khipu-orig.png}
\caption{An example of a khipucamayoc (khipu keepers) managing apparently statistical information. Source: \cite{AyalaPomade1612}.. In the lower left corner apparently a simple counting system is shown based on pebbles or seeds to collect data. The cumulative results are summarized in a khipu.}
\label{fig:khipu_count}
\end{figure}


\section*{Methods}



\subsection*{Process}
The first idea of using the khipu concept was refined by matching the properties of a set of molecular markers against the generic properties of a khipu (see details below). Then, in a first round, design criteria were consolidated and several draft designs tested on real data. Subsequently, the molecular khipu idea was presented to the general public through posters at CIP's genebank foyer, to scientists and breeders through journals \cite{Stapleton2006}, at conferences (\cite{Simon2006} and \cite{Simon2007}),  and through web sites (\cite{CIP2013}) as well as to farmers (\cite{Haan2006} and \cite{Scurrah2013}) to solicit feedback over the course of several years. Recently, the molecular khipu idea was consolidated in a publicly available open source software (\cite{Simon2014a} and \cite{Simon2014b}).

\subsection*{Design principle}
The basic design principle is described in more detail in the legend of  Figure~\ref{fig:quipu_construct}. In summary, SSR marker data are generated in a molecular laboratory applying each marker separately to a batch of genotypyes. In the case of the molecular marker kit for potato \cite{Ghislain2008} also the set of SSR markers is defined. Therefore, the SSR data can be simply re-organized to form a molecular profile or molecular khipu. The principal equivalencies used in Figure~\ref{fig:quipu_construct} to turn the profile into a khipu are listed in Table~\ref{table_khipu}. An important assumption is that only single-copy SSR markers are used. A first prototype using real data is shown in Figure~\ref{fig:quipu_p1}.  


\begin{table}[h]
\caption{Comparison of Traditional and Molecular khipu Concepts}\label{table_khipu}
\begin{tabular}{l l}
\hline
\textbf{Traditional} & \textbf{Molecular}\\
\hline
Set of data & Set of SSR marker \\
Chord & Marker or Locus \\
Knot position & Allele size \\
Knot color or knot size & Allele frequencies \\
\hline
\end{tabular}
\end{table}


\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{quipu_construct.png}
\caption{How the khipu is constructed. In the upper part of the figure schematic representations of four SSR marker gels are drawn. Each vertical 'bar' represents the lane in a gel where a SSR marker has been visualized. Differently located circles correspond to different alleles of a SSR marker. The higher up the circle, the more base pairs it has. For each genotype there may be more than one allele per lane up to the number of chromosome copies (ploidy number); only single-copy SSR markers are considered. Typically, for each gel a set of genotypes is characterized with the same SSR marker. Therefore, in order to compile data for a profile of a genotpye we will need to simply extract the lane or SSR marker information from the original gel. E.g. for genotype number 3 (marked in dark gray) we can virtually re-assemble the lanes from each original as indicated. With three simple graphical means this is transformed into a 'molecular khipu': a) the reduction of the lane to a symbolic lane, b) the addition of a top line to indicate that these markers comprise part of a set (now each lane represents a distinct gel or marker), and c) the representation of dyed fragments as dots. As a technical note: In a gel the fragments would separate according to an inverse logarithmic relationship. A direct linear scale is used in the molecuarl khipu for simplicity.}
\label{fig:quipu_construct}
\end{figure}



\begin{figure}[ht]\centering
\includegraphics[width=\linewidth, totalheight=0.12\textheight, width=0.15\textwidth]{quipu_p1.png}
\caption{A first prototype of the molecular khipu. Each pendant or vertical line represents a SSR marker locus. Superimposed dots represent alleles of a given size. The concept of a set is symbolized by the top horizontal backbone line. Annotations, scales, and legend are omitted to enable more minute images for display in a catalog. However, close by alleles overlap and may not be easily noticed.}
\label{fig:quipu_p1}
\end{figure}


\subsection*{Design refinements}
The next principal idea was to include comparative elements into each molecular khipu: how does this genotype compare to a reference genepool? To this end, we used in the second prototype the size of an elliptic dot or 'node'.  Color was used to indicate to which chromosome a marker belongs as well as to indicate the range of allele sizes for each marker. See Figure~\ref{fig:quipu_p2}. This prototype also tried to more closely visualize the string structure of a physical original khipu. 

\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{quipu_p2.png}
\caption{A second prototype of the molecular khipu. This prototype has the same basic features as prototype I. Pendant lines represent marker loci, dots or ellipses alleles of a certain size and the horizontal top backbone highlights the set concept for this data. The most striking contrasts are the use of colors to distinguish the different chromosomes to which each marker belongs and the use of size variation of each allele according to its frequency. Both axes are labeled. The right hand side contains information about the population from which the allele frequencies were derived. Further embellishments include structuring the lines in a chord-like manner. }
\label{fig:quipu_p2}
\end{figure}

However, eventually some of these latter elements were removed following general design principles of favoring simplicity and avoiding to depend only on color to convey meaning \cite{TufteVD}.


\subsection*{Software implementation and availability}
A first version was implemented using the programming language PHP; subsequently, the algorithm was transferred to the language R and ultimately organized as a reusable package along with a tutorial. The package can be found at: http://cran.r-project.org/web/packages/quipu/index.html.


\section*{Results}

\subsection*{Khipu features}

The current version of the molecular khipu or SSR marker graph is displayed and described in detail in Figure~\ref{fig:quipu3}. In short, the standard graph has been enriched in terms of annotation and interpretation while the more playful graphical elements were removed. Many features can be customized as described in more detail in \cite{Simon2014b}.

\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{quipu3.png}
\caption{The current version of the molecular khipu as created by the corresponding R package 'khipu'. The top 'backbone' line has been modified (compared to the prototype versions) to convey additional information: that is the running number of the SSR marker locus. The pendant lines represent an individual marker locus. Upon each locus the range of the allele sizes in the reference population is superimposed as a thicker gray line. Alleles are sorted by decreasing dot radius to minimize occultation. Loci or 'lines' belonging to the same chromosome are joined by an upper thicker gray line. Both dot size and dot color can be configured to show allele frequencies in up to four classes. Marker loci are ordered from left to right by chromosome or if that information is missing by order in the given table. Along the y-axis the base pair counts are given in increasing order from bottom to top in a custom range which defaults to values from CIPs experience. The legend on the right hand has three groups. The top group shows the chosen color and size symbols corresponding to the allele frequency classes. Class breaks can also be modified. The second box displays additional information for the underlying population. Lastly, an optional logo image can be inserted into the lower right part.}
\label{fig:quipu3}
\end{figure}



\begin{figure}[ht]\centering
\includegraphics[width=\linewidth]{quipu4.png}
\caption{The current compact version of the molecular khipu as created by the correspondent R package 'khipu'. The khipu concept of a set is marked by the upper black horizontal line. Marker loci are symbolized by pendant chords or vertical lines. This y-axis also represents allele sizes increasing from bottom to top. They are in a light gray while allele base pair range is superimposed by a thicker and darker gray line fragment. On top of this, alleles are shown as dots and colored according to a classification scheme. The color scheme should be supplied in a separate way as this format is meant for compact display in a catalog. For the same reason axes units and legends are omitted. This figure shows three molecular khipus of distinct genotypes to illustrate the use of the compact chart in a comparative setting.}
\label{fig:quipu4}
\end{figure}

The more compact version is shown and described in Figure~\ref{fig:quipu4}. Briefly, it remains close to prototype I in Figure~\ref{fig:quipu_p1} with a few enhancements regarding allele frequencies.

\section{Discussion}

\subsection*{Related statistical graphs}
Perhaps a similar graph could be constructed based on a set of boxplots each showing a summary of a molecular marker with superimposed dots for each allele of an individual genotype. This would have the advantage of showing more statistical information. However, for compact figures in a catalog setting it would probably appear overly congested. Another related graph is the 'graphical genotype' chart as proposed by \cite{Young1989}. This latter chart also shows the molecular marker pattern across a set of genotypes but with an emphasis on explicitly comparing genotypes side-by-side whereas the molecular khipu puts an emphasis on an individual genotype. Both charts can complement each other.

\subsection{Reception}

The tool has been useful for registry of molecular passports and as a communication tool for genebanks both in-situ \cite{Haan2006} and ex-situ  as well as for breeding materials \cite{CIP2013}: particularly, it added value to local Peruvian potato landraces, served as an example of participatory knowledge generation, and assisted in the creation of printed community potato inventories or catalogs. It was also conceived as a tool to orient conservation efforts and as an educational tool for local farmers communities and schools. However, as documented in \cite{Scurrah2013} this has only been partially fulfilled: while the scientists interviewed were overall comfortable with the molecular chart, farmers in general did not 'understand' it. A different strategy would be required if the molecular khipu were to be used in dialogue on diversity with the diverse communities originally targeted.

\subsection{Acknowledgements}

We are grateful for farmers communities in Huancavelica and in Cuzco ("Asociacion del Parque de la papa") for providing primary materials and data. Additional support came from the NGO ANDES.

 
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