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Hey, welcome. Double click anywhere on \documentclass[11pt]{article}  \usepackage{graphicx,amsmath,amsfonts,amssymb,amsxtra,setspace,lineno}  \usepackage[usenames,dvipsnames]{xcolor}  \usepackage[protrusion=true,expansion=true]{microtype}  \usepackage[font={small},bf]{caption}  \usepackage[T1]{fontenc}  \usepackage[utf8]{inputenc}  \usepackage[letterpaper,margin=1in]{geometry}  \usepackage{lmodern}  \usepackage{verbatim}  \usepackage{siunitx}  \newcommand{\ud}{\text{d}}  \newcommand{\rem}[1]{\textcolor{red}{#1}}  %\newcommand{\citeapos}[1]{\citeauthor{#1}'s (\citeyear{#1})}  \let\originalleft\left  \let\originalright\right  \renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft}  \renewcommand{\right}{\aftergroup\egroup\originalright}  %\bibpunct{(}{)}{,}{a}{}{,}  %\DeclareMathAlphabet{\mathcal}{OMS}{txsy}{m}{n}  \clubpenalty = 10000  \widowpenalty = 10000  \begin{document}  \title{Trait patterns in alpine grasslands}  \author{Rafael D'Andrea$^{1, \ast}$, John Guittar$^{1, \dag}$, Deborah Goldberg$^{1,\ddag}$ \& Annette Ostling$^{1,\P}$ \\   $^1${\small Dept.~Ecology \& Evolutionary Biology, University of Michigan, Ann Arbor, MI, USA}\\ $^{\ast}${\small \texttt{[email protected]}}  $^{\dag}${\small \texttt{[email protected]}} $^{\ddag}${\small \texttt{[email protected]}} $^{\P}${\small \texttt{[email protected]}}  }  \date{}  \maketitle  \doublespacing  \linenumbers  \begin{abstract}  If deterministic forces drive community assembly, locally co-occurring species will comprise a nonrandom sample of surrounding species pools. In addition, species traits should determine  the text degree  to start writing. which they thrive in local environments. Specific types of nonrandom trait structure may suggest particular community assembly mechanisms such as environmental filtering and niche differentiation. Here we test alpine grass communities for functional overdispersion, regularity in trait differences, and the presence of species clusters in trait space. Our field sites follow a temperature gradient, which allows us to test for strength of trait pattern against local temperature. We find that ...  \end{abstract}  \section*{Introduction}  \section*{Methods}  \subsection*{Data}  \rem{Explain sampling design}  \subsection*{Null model}  In addition order  to simple text you can create null communities against which to compare our data, we used a mainland-island approach, where each site undergoes zero-sum birth-death neutral dynamics and immigration from a fixed regional species pool \cite{Hubbell2001}. For each site, the regional pool includes all species falling within the observed trait range, with the regional abundance of each species calculated as the mean across all sites. For each site we estimated immigration rates by fitting a neutral model to the observed relative species cover, and estimated community size by matching the neutral simulated communities to observed species richness. Estimated community size ranged from 215 individuals for Fauske to 567 for Gudmedalen, and immigration rate ranged from 0.03 for Ovstedal to 0.53 for Lavisdalen. For each site we simulated 1,000 neutral communities.  \subsection*{Metrics}  For each site we calculate its Rao quadratic entropy, defined as $Q=\sum_i^{S-1}\sum_{j=i+1}^S d_{ij}p_i p_j$, where $p_i$ and $p_j$ are the relative abundance of species $i$ and $j$, $d_{ij}$ is the absolute trait difference between them, and the sum is over all species pairs. It corresponds to the expected trait difference between two individuals randomly sampled (with replacement) from the community. We  also add text formatted used the functional dispersion metric proposed  in \textbf{boldface}, \textit{italic}, \cite{Laliberte2010}, defined as the abundance-weighted mean distance between each species  and yes, math too: $E = mc^{2}$! Add images the community trait centroid. In one dimension, it reduces to $\text{FDis}=\sum_i p_i |x_i-\sum_j p_j x_j|$, where $x_i$ is the trait value of species $i$. Both indices have been used to quantify community functional diversity \cite{Botta-Dukat2005, Laliberte2010, Ricotta2011}. A high value indicates trait overdispersion, i.e. species cover a wider region of trait space than expected by chance. In contrast, a low value suggests that species are being filtered toward a particular trait value, possibly due to selection for optimal tolerance to local environmental conditions \cite{Keddy1992}.  In addition to test statistics based on trait dispersion, we also used a measure of the degree of even spacing between adjacent species on the trait axis. Even spacing has been proposed as indicative of niche differentiation, as it maximizes exploration of niche space \cite{Mason2005}, and minimizes competitive interactions caused by trait similarity \cite{MacArthur1967}. If species are ordered by trait value, the metric is defined as $\text{CV}=\sigma/\mu$, where $\mu$ and $\sigma$ are respectively the mean and standard deviation of the distance vector $d_i=|x_i-x_{i+1}|$ between adjacent species $i$ and $i+1$. A low CV indicates even spacing.  On the other hand, recent work has raised the possibility that resource partitioning may actually lead to species clustering on the trait axis \cite{Scheffer2006}. In particular, clusters in trait space are expected if competitive exclusion is slow or if immigration replenishes species that are not niche-differentiated \cite{DAndrea2016}. Given this possibility, the coefficient of variation may actually be higher than expected by chance.  %as exclusion is actually faster in the gaps between niches than in their immediate vicinity  Although species may be clustered, they may still sort into niches that in turn are evenly spaced. This could occur if competition is caused by trait similarity \cite{Scheffer2006, DAndrea2017}. In that case, the most abundant species in the community might be expected to be evenly spaced even though the community as a whole is clustered. Based on these considerations, we used the CV in two metrics. First, we considered all species in the community without regard for abundance. A similar test statistic, the variance divided by the range, is commonly used to quantify evenness \cite{Stubbs2004, Kraft2008, Ingram2009}. Second, we gradually remove species from the community in increasing order of abundance, at each step calculating the CV among the remaining species. A negative trend in CV as the community is progressively trimmed towards only the most abundant species suggests even spacing between niches concomitant with clustering between species.   %To our knowledge, this is the first use of this metric to describe trait pattern in species assemblages.  Finally, we test for the presence of clusters directly  by drag'n'drop applying a cluster-finding method. Our metric uses a k-medoid clustering algorithm: for a given number of clusters, it decides which species belong in which cluster by minimizing the trait distance between the center of each cluster and the individuals belonging to that cluster \cite{Kaufman1990}. We implement the algorithm using the function \textit{clara} in R package \textit{cluster} \cite{Maechler2016}. The number of clusters that best fits the data is found using R's \textit{optim} function for Markov chain Monte Carlo optimization \cite{RCoreTeam2015}. For each community-year, we search for the best fit between two clusters and half the number of species  or click forty clusters, whichever is smaller. The test statistic is the average silhouette width, a measure of how similar individuals are to their own cluster compared to neighboring clusters --- thus providing the goodness of fit of the k-medoid algorithm \cite{Kaufman1990}.  %To determine whether species are arranged into clusters, we used the k-means clustering method \cite{Tibshirani2001}. The algorithm partitions species into $k$ clusters based  on proximity to the centroid of the nearest cluster on the trait axis. The process is repeated until the centroids are found which minimize total within-cluster distance $W(k)$, called dispersion. The same process is applied to randomizations of the data, and the difference in dispersion $\Delta W(k)=\bar{W_r}(k)-W(k)$ is reported, where $\bar{W}_r(k)$ is the mean dispersion across randomizations. As the true number of clusters is unknown, we perform this for $k$ ranging between 1 and half of the number of species in the data, and find the value $\hat{k}$ that maximizes $\Delta W$. The estimated number of clusters is then $\hat{k}$, and $\Delta W(\hat{k})$ quantifies the strength of the clustering. We consider the data to be significantly clustered if $\Delta W(\hat{k})$ falls outside the 95\% percentile of the neutral runs. We adapted code from   %The peak-flanker correlation index (Cor) determines whether the abundances of the most abundant species in each cluster (``peak'') is significantly correlated with that of its closest species on the trait axis (``flanker''). A positive correlation denotes abundance trends   %The relative flanker abundance index (ReFA) compares the abundance of each flanker to that of all other species in its cluster, excluding the peak. A low index indicates competitive suppression caused by proximity to the peak species, while a high index indicates a positive abundance trend toward the peak, which could be caused by local filtering, i.e. selection towards a locally optimal trait.  To test for significance, for each of our sites in a given year we compare the metric value to the $(1-\alpha)$-quantile of the corresponding set of null communities. Of our five metrics, three (Rao, FDis, CV) are two-tailed, as both low and high values can be interpreted to suggest specific community assembly processes, while the other two (CVtrend, Clara) are one-tailed. We use significance level $\alpha=0.025$ for the two-tailed tests and $\alpha=0.05$ for the one-tailed tests.   \section*{Results}  \section*{Discussion}  \bibliography{AllRefs}  \bibliographystyle{ieeetr}  \newpage  \section*{Figures}  \begin{figure}[h]  \label{fig:Fig1}  \caption{Example data from the site of Lavsdalen from the 2009 census. Species are arranged by trait value on the x-axis, and species percentage cover is shown on the y-axis. Trait values are logged and then normalized to range between 0 and 1. Maximum height values are jittered to show species sharing same binned value. PC1: first principal component.}  \includegraphics[width=1\textwidth,angle=0]{Fig1}  \centering  \end{figure}  \begin{figure}[h]  \label{fig:Fig2}  \caption{Summary of metric results across sites from the 2009 census. For each test, percentage of sites with statistically significant results are shown for leaf area (LFA), specific leaf area (SLA), maximum plant height (MXH), seed mass (SDM), and the first principal component (PC1). Rao, FDis, and CV are two-tailed: bars show the percentage of sites, out of 12, whose metric values were lower than the 2.5\% null percentile (red bars) or higher than 97.5\% null percentile (blue bars). CV trend and Clara are one-tailed: bars show the percentage of sites with metric values exceeding the 95\% null percentile.}   \includegraphics[width=1\textwidth,angle=0]{Fig2}  \centering  \end{figure}  \begin{figure}[h]  \label{fig:Fig3}  \caption{Standard scores of the Rao metric for each site, plotted against the site's mean summer temperature. Significant negative trends were observed for SLA, maximum plant height, and  the "Insert Figure" button. first principal component.}   \includegraphics[width=1\textwidth,angle=0]{Fig3}  \centering  \end{figure}  \end{document}