---
title: ProcMod Variance partitionning of vectorial data.
preprint: false
author: 
  - name: Christelle Melodelima
    affiliation: 1
    corresponding: true
    email: christelle.melodelima@metabarcoding.org
  - name: Eric Coissac
    email: eric.coissac@metabarcoding.org
    affiliation: 1
affiliation:
  - code: 1
    address: Cold Spring Harbor Laboratory, One Bungtown Road Cold Spring Harbor, NY 11724
  - code: 2
    address: Down House, Luxted Rd, Downe, Orpington BR6 7JT, UK
abstract: >
  With new high-throughput technologies, especially next generation sequencing platforms, ecologists are more and more faced with analysis of data sets in which a reasonable number of individuals or sites are characterized by several hundreds or even thousands of variables. Classical data analysis procedures are usually failing on such high-dimensional data sets and new techniques have to be envisaged to treat them. Metabarcoding is probably one of such new methodology providing such kind of data set. ProcMod is an R packages generalizing Procrustean analysis allows for partitioning variance of a multi-dimensional data set to be explained among several explanatory multi-dimensional data tables.
header-includes: >
  \usepackage{lipsum}
bibliography: ProcMod.bib
output: 
  rticles::peerj_article:
    base_format: rmarkdown::pdf_document # bookdown::pdf_document2 # for using \@ref()
---


# Introduction {-}

With new high-throughput technologies, especially next generation sequencing platforms, ecologists are more and more faced with analysis of data sets in which a reasonable number of individuals or sites are characterized by several hundreds or even thousands of variables. Classical data analysis procedures are usually failing on such high-dimensional data sets and new techniques have to be envisaged to treat them. Metabarcoding is probably one of such new methodology providing such kind of data set. ProcMod is an R packages generalizing Procrustean analysis allows for partitioning variance of a multi-dimensional data set to be explained among several explanatory multi-dimensional data tables.

## Procrustean Analysis {-}

The Procrustean analysis aims to compare two multidimensional data sets $X$ and $Y$, both characterizing $n$ points per $p$ and $q$ variables respectively. The comparison is made by superimposing the points as defined by the two data sets in order to minimize the sum of the distances between the corresponding points. Three operations are considered to achieve this superposition: a translation, a rotation and a scaling.

## About PeerJ {-}

PeerJ is an award-winning open access publisher covering the biological and medical sciences.  PeerJ provides authors with three publication venues: *PeerJ* and *PeerJ Computer Science* (peer-reviewed academic journals) and *PeerJ PrePrints* (a 'pre-print server'). See https://peerj.com/about/publications/ for more information.

The PeerJ model allows an author to publish articles in their peer-reviewed journal via the purchase of a lifetime Publication Plan. Prices start from just \$99 (a one-off payment) which entitles an author to the lifetime ability to publish 1 article per year for free. Publication in PeerJ PrePrints is entirely free.

# Some \LaTeX{} Examples {-}

Use section and subsection commands to organize your document. \LaTeX{} handles all the formatting and numbering automatically. Use ref and label commands for cross-references.

## Figures and Tables {-}

Use the table and tabular commands for basic tables --- see Table \@ref(tab:widgets), for example. You can upload a figure (JPEG, PNG or PDF) using the project menu. To include it in your document, use the includegraphics command as in the code for Figure \@ref(fig:view) below.

Standard \LaTeX references will work as well (e.g. Fig. \ref{fig:view}).

<!-- There are three ways to include figures: -->
<!-- 1. The LaTeX way -->
<!-- 

\begin{figure}[ht]
\centering
\includegraphics[width=\linewidth]{view}
\caption{An example image.}
\label{fig:view}
\end{figure} 

 -->

<!-- 2. The RMarkdown way -->

```{r view, out.width = "100%", fig.cap = "An example image.", echo = FALSE}
knitr::include_graphics("view.pdf")
```


<!-- 3. The pandoc way -->
<!-- 

![An example image. Text *can* be processed with markdown.](view.pdf){#view width = 100%}

 -->

<!-- 
\begin{table}[ht]
\centering
\begin{tabular}{l|r}
Item & Quantity \\\hline
Widgets & 42 \\
Gadgets & 13
\end{tabular}
\caption{\label{tab:widgets}An example table.}
\end{table}
-->

Item     Quantity
------- ---------
Widgets        42
Gadgets        13

Table: (\#tab:widgets) An Example Table.

## Citations {-}

LaTeX formats citations and references automatically using the bibliography records in your .bib file, which you can edit via the project menu. Use the cite command for an inline citation, like @Figueredo:2009dg, and the citep command for a citation in parentheses [@Figueredo:2009dg].

## Mathematics {-}

\LaTeX{} is great at typesetting mathematics. Let $X_1, X_2, \ldots, X_n$ be a sequence of independent and identically distributed random variables with $\text{E}[X_i] = \mu$ and $\text{Var}[X_i] = \sigma^2 < \infty$, and let
$$S_n = \frac{X_1 + X_2 + \cdots + X_n}{n}
      = \frac{1}{n}\sum_{i}^{n} X_i$$
denote their mean. Then as $n$ approaches infinity, the random variables $\sqrt{n}(S_n - \mu)$ converge in distribution to a normal $\mathcal{N}(0, \sigma^2)$.

## Lists {-}

You can make lists with automatic numbering \dots


1. Like this,
1. and like this.

or bullet points...

- Like this,
- and like this.

or with descriptions...

- **Word** Definition
- **Concept** Explanation
- **Idea** Text


We hope you find write\LaTeX\ useful for your PeerJ submission, and please let us know if you have any feedback. Further examples with dummy text are included in the following pages.

# Methods {-}

\lipsum[4] 

\begin{equation}
\cos^3 \theta =\frac{1}{4}\cos\theta+\frac{3}{4}\cos 3\theta
\label{eq:refname2}
\end{equation}

\lipsum[5] 

## Subsection {-}

\lipsum[6] 

\paragraph{Paragraph} \lipsum[7] 
\paragraph{Paragraph} \lipsum[8] 

## Subsection {-}

\lipsum[9] 

<!-- \begin{figure}[ht]\centering -->
<!-- \includegraphics[width=\linewidth]{results} -->
<!-- \caption{In-text Picture} -->
<!-- \label{fig:results} -->
<!-- \end{figure} -->

```{r results, fig.width = 5, fig.height = 4, out.width = "100%", fig.cap = "In-text Picture", echo = FALSE}
time = seq(1.5, 8, 0.1)
plot(time, sin(time), type = "l", xlab = "time [s]", ylab = "amplitude [m]", 
     cex.main = 2, col = "blue", lwd = 3, font = 2, font.main = 2)
```


Reference to Figure \@ref(fig:results).

# Results and Discussion {-}

\lipsum[10] 

## Subsection {-}

\lipsum[11] 

### Subsubsection {-}

\lipsum[12] 

### Subsubsection {-}

\lipsum[14] 

## Subsection {-}

\lipsum[15-20] 

# Acknowledgments {-}

So long and thanks for all the fish.

# References
