ajout recommendation pierre

rapport/abstract.tex

@@ -0,0 +1,17 @@
+% Abstract
+\abstract{
+    Networks are versatile objects able to represent various types of
+    interactions and bipartite networks are particularly useful in ecological
+    context for interaction between different entities (e.g. plant-pollinator). As the networks grow in size, reliable metrics, models and methods are needed to detect structure and perform analysis.
+    Those methods exist and are pretty robust for single network analyses
+    but we have motivation to consider a collection of network,
+    in order to compare their structure or partition them.
+    For collection of simple networks a colSBM (collection Stochastic Block Model~\cite{chabert-liddellLearningCommonStructures2024a}) has been proposed.
+    We adapt this model to the bipartite case with a variational
+    Expectation-Maximization algorithm for inference, a clever parameter space
+    exploration and a BIC-like criterion for model selection. Building on this
+    method we present a partitioning algorithm to gather networks based
+    on their shared structures. We perform simulation studies to assess
+    performance of our models and algorithm. Finally, we apply our clustering
+    algorithm on ecological networks.
+}

rapport/chapter2-context.tex

@@ -1,168 +1,36 @@
 \addtocounter{customchapter}{1}
 \chapter{Introduction}
 
-\section{Usage and importance of bipartite graphs}\label{sec:usage-and-importance-of-bipartite-graphs}
+\input{abstract}
-Bipartite graphs, denoted as $G = (U,V,E)$ with $U$ and $V$ two disjoint and
-independent sets of vertices and $E$ the set of edges connecting $U$ vertices to
-$V$ vertices.
 
-\begin{minipage}{0.5\linewidth}
+A common usage of bipartite graphs in ecology is the representation of ecological
-    \centering
+interactions like
-    Bipartite network\\
-    \begin{tikzpicture}[scale=.6]
-        \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt]
-        \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape]
-        \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape]
-        \tikzstyle{every node}=[fill=blueind]
-
-        \node[state, draw=black!50] (A1) at (0,5) {\textbf{R1}};
-        \node[state, draw=black!50] (A2) at (2.5,5) {\textbf{R2}};
-        \node[state, draw=black!50] (A3) at (5,5) {\textbf{R3}};
-
-        \tikzstyle{every node}=[fill=greenind, shape=rectangle]
-        \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle]
-        \node[state, draw=black!50] (B1) at (0,0) {\textbf{C1}};
-        \node[state, draw=black!50] (B2) at (1.25,0) {\textbf{C2}};
-        \node[state, draw=black!50] (B3) at (2.5,0) {\textbf{C3}};
-        \node[state, draw=black!50] (B4) at (3.75,0) {\textbf{C4}};
-        \node[state, draw=black!50] (B5) at (5,0) {\textbf{C5}};
-        \path (A1) edge [] (B1);
-        \path (A1) edge  (B2);
-        \path (A1) edge  (B3);
-        \path (A1) edge  (B4);
-        \path (A2) edge  (B3);
-        \path (A2) edge  (B4);
-        \path (A3) edge  (B5);
-        \path (A2) edge  (B5);
-    \end{tikzpicture}
-\end{minipage}
-\begin{minipage}{0.5\linewidth}
-    \begin{center}
-        $X=
-            \begin{pmatrix}
-                1 & 1 & 1 & 1 & 0 \\
-                0 & 0 & 1 & 1 & 1 \\
-                0 & 0 & 0 & 0 & 1 \\
-            \end{pmatrix}
-        $\\
-        \vspace*{\baselineskip}
-        Incidence matrix
-    \end{center}
-\end{minipage}
-
-\vspace*{\baselineskip}
-$X$ is the \emph{incidence matrix} and is the mathematical object on which
-computations are performed. It is filled with the following rule:
-\begin{equation*}
-    \begin{cases}
-        X_{ij} = 0    & \text{if no interaction is observed between species }i\text{ and }j \\
-        X_{ij} \neq 0 & \text{otherwise}
-    \end{cases}
-\end{equation*}
-If the network represents binary observations (like presence-absence) then
-$X_{ij}\in\mathcal{K}=\{0,1\},\forall(i,j)$; if the interactions are weighted
-(like an abundance count), $X_{ij}\in\mathcal{K}=\mathbb{N},\forall(i,j)$.
-
-This representation can be used to represent various forms of interactions were
-two kinds of ``actors`` interact. Those interactions can be binary or valued
-and a numeric representation is the incidence matrix, in the above example
-$X$.\\
-
-Among the use case of bipartite graphs one can find the Netflix Problem, which
-was a prize organized by Netflix to improve its Recommender system. The row
-nodes are the movies and the columns are the user, at the intersection the
-value is the review of the user $j$ for the movie $i$.\\
-
-Another use is the representation of ecological interactions like
 plant-pollinator \parencite{ramos-jilibertoTopologicalChangeAndean2010},
 birds-seed dispersion, prey-predator or host-parasite
 \parencite{kaszewska-gilasGlobalStudiesHostParasite2021}. For plant-pollinator
-interactions, the rows are pollinator species and the columns are plant species,
+interactions, the rows are pollinator species and the columns are plant
+species,
 and the intersection is a value, binary if it is a presence/absence or a value
 if it is an abundance count.
 
+Some interesting results can arise when applying a tool widely used on a
+particular kind of interactions is used on another kind of interactions. In
+~\cite{desjardins-proulxEcologicalInteractionsNetflix2017} the authors use the
+\emph{K-nearest neighbour} (KNN) algorithm as a Recommender to predict missing
+preys for predators in a predator-prey network.\\
+
 Bipartite graphs are widely used in biology in general, in various fields, among
 which the previously cited ecological networks, but also in medicine with
 biomedical networks, biomolecular networks or epidemiological networks.
 \parencite{pavlopoulosBipartiteGraphsSystems2018}
 
-Some interesting results can arise when applying a tool widely used on a
+There is a need for comparison methods of bipartite networks in literature, and
-particular kind of interactions is used on another kind of interactions.
+it is being actively developed,
-Companies like Netflix or Amazon use recommender system, to recommend other
+e.g.~\cite{pichonTellingMutualisticAntagonistic2024} use structures at multiple
-products to consumers based on their previous interactions. In
+scales (species degree, motif frequency, nestedness \dots) to tell apart
-~\cite{desjardins-proulxEcologicalInteractionsNetflix2017} the authors use the
+mutualistic and antagonistic networks.
-\emph{K-nearest neighbour} (KNN) algorithm as a Recommender to predict missing
-preys for predators in a predator-prey network.
 
-\section{Latent Block Model}
+This motivates us to propose a model for structure detection in bipartite
-\label{sec:latent-block-model}
+collections.
-The Latent Block Model (LBM) introduced by ~\cite{govaertLatentBlockModel2010}
-adapts the Stochastic Block Model (SBM)
-\parencite{hollandStochasticBlockmodelsFirst1983, snijdersEstimationPredictionStochastic1997}
-to bipartite graphs.
-
-\textit{Note :}\begin{small}
-    Please note that we prefer the term \enquote{BiSBM} and will use both LBM and BiSBM to
-    designate the Stochastic Block Model adapted to bipartite networks.
-\end{small}
-
-This model supposes that:
-\begin{itemize}
-    \item Row nodes are members of row blocks and column nodes are members of column
-          blocks.
-    \item The connectivity of two individuals is determined by their block memberships.
-    \item An interaction can only occur between a row and a column node.
-\end{itemize}
-
-\begin{figure}[H]
-    \center
-    \begin{tikzpicture}[scale=.6]
-        \input{../tikz/lbm.tex}
-    \end{tikzpicture}
-    \caption{An LBM model visualization}
-    \label{fig:LBMvisu}
-\end{figure}
-
-\begin{itemize}
-    \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ \emph{given} blocks in rows
-    \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ \emph{given} blocks in columns
-\end{itemize}
-Parameters
-\begin{itemize}
-    \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ for rows and $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ for columns
-    \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$, parameter influencing the probability and value of a link knowing node
-          membership blocks.
-\end{itemize}
-
-On figure~\ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong
-to the row block of corresponding color, $\bm{\rho}$ are the probabilities for
-a column node to belong to the column block of corresponding color and
-$\bm{\alpha}$ is a matrix $Q_1 \times Q_2$ of the connectivity parameters
-between the row and column blocks. When we talk about the \enquote{structure}
-of the network we are referring to this connectivity matrix.
-
-This model can be used to easily generate bipartite graphs with complex and
-very varied structures. But when trying to determine the structure of a given
-network we need to find those parameters and as the row and column block
-memberships are \emph{latent} i.e.,\ they are not known, they must be inferred.
-
-For this a common approach is to use a \emph{variational} EM algorithm, proposed
-for SBM in~\cite{daudinMixtureModelRandom2008} and for LBM in
-~\cite{govaertEMAlgorithmBlock2005}. The groups and required parameters
-can be inferred by maximizing a lower bound of the likelihood.
-
-\section{colSBM model, a joint model for a collection of networks}
-\label{sec:colsbm-model-a-joint-model-for-a-collection-of-networks}
-The \emph{colSBM} model introduced by ~\cite{chabert-liddellLearningCommonStructures2024a}
-propose an extension of the SBM model to collections of simple (or unipartite)
-networks. A collection is a set of networks which nodes are not in common nor
-linked between different networks and the interactions have the same valuations.
-
-The model can retrieve the shared structure in a collection, indicate if
-networks should be grouped in a collection and in a large pool of networks,
-collections with common structures.
-
-The next step after designing this collection model for unipartite networks was
-to extend it to the bipartite case.
 
 % DONE Relu

rapport/chapter3-structure-detection.tex

@@ -1,7 +1,147 @@
 \addtocounter{customchapter}{1}
 \chapter[Structure detection in bipartite collection]{Structure detection in a collection of bipartite networks}
 \label{chap:struct-detection}
-\section{Definition of a collection}
+
+
+\section{Formalism of bipartite graphs}\label{sec:usage-and-importance-of-bipartite-graphs}
+Bipartite graphs, denoted as $G = (U,V,E)$ with $U$ and $V$ two disjoint and
+independent sets of vertices and $E$ the set of edges connecting $U$ vertices to
+$V$ vertices.
+
+\begin{minipage}{0.5\linewidth}
+    \centering
+    Bipartite network\\
+    \begin{tikzpicture}[scale=.6]
+        \tikzstyle{every edge}=[-,>=stealth',shorten >=1pt,auto,draw,line width=1.5pt]
+        \tikzstyle{every state}=[draw, text=black,scale=0.95, transform shape]
+        \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape]
+        \tikzstyle{every node}=[fill=blueind]
+
+        \node[state, draw=black!50] (A1) at (0,5) {\textbf{R1}};
+        \node[state, draw=black!50] (A2) at (2.5,5) {\textbf{R2}};
+        \node[state, draw=black!50] (A3) at (5,5) {\textbf{R3}};
+
+        \tikzstyle{every node}=[fill=greenind, shape=rectangle]
+        \tikzstyle{every state}=[draw=none,text=black,scale=0.75, transform shape, shape=rectangle]
+        \node[state, draw=black!50] (B1) at (0,0) {\textbf{C1}};
+        \node[state, draw=black!50] (B2) at (1.25,0) {\textbf{C2}};
+        \node[state, draw=black!50] (B3) at (2.5,0) {\textbf{C3}};
+        \node[state, draw=black!50] (B4) at (3.75,0) {\textbf{C4}};
+        \node[state, draw=black!50] (B5) at (5,0) {\textbf{C5}};
+        \path (A1) edge [] (B1);
+        \path (A1) edge  (B2);
+        \path (A1) edge  (B3);
+        \path (A1) edge  (B4);
+        \path (A2) edge  (B3);
+        \path (A2) edge  (B4);
+        \path (A3) edge  (B5);
+        \path (A2) edge  (B5);
+    \end{tikzpicture}
+\end{minipage}
+\begin{minipage}{0.5\linewidth}
+    \begin{center}
+        $X=
+            \begin{pmatrix}
+                1 & 1 & 1 & 1 & 0 \\
+                0 & 0 & 1 & 1 & 1 \\
+                0 & 0 & 0 & 0 & 1 \\
+            \end{pmatrix}
+        $\\
+        \vspace*{\baselineskip}
+        Incidence matrix
+    \end{center}
+\end{minipage}
+
+\vspace*{\baselineskip}
+$X$ is the \emph{incidence matrix} and is the mathematical object on which
+computations are performed. It is filled with the following rule:
+\begin{equation*}
+    \begin{cases}
+        X_{ij} = 0    & \text{if no interaction is observed between species }i\text{ and }j \\
+        X_{ij} \neq 0 & \text{otherwise}
+    \end{cases}
+\end{equation*}
+If the network represents binary observations (like presence-absence) then
+$X_{ij}\in\mathcal{K}=\{0,1\},\forall(i,j)$; if the interactions are weighted
+(like an abundance count), $X_{ij}\in\mathcal{K}=\mathbb{N},\forall(i,j)$.
+
+This representation can be used to represent various forms of interactions were
+two kinds of \enquote{actors} interact. Those interactions can be binary or valued
+and a numeric representation is the incidence matrix, in the above example
+$X$.\\
+
+\section{Latent Block Model}
+\label{sec:latent-block-model}
+The Latent Block Model (LBM) introduced by ~\cite{govaertLatentBlockModel2010}
+adapts the Stochastic Block Model (SBM)
+\parencite{hollandStochasticBlockmodelsFirst1983, snijdersEstimationPredictionStochastic1997}
+to bipartite graphs.
+
+\textit{Note :}\begin{small}
+    Please note that we prefer the term \enquote{BiSBM} and will use both LBM and BiSBM to
+    designate the Stochastic Block Model adapted to bipartite networks.
+\end{small}
+
+This model supposes that:
+\begin{itemize}
+    \item Row nodes are members of row blocks and column nodes are members of column
+          blocks.
+    \item The connectivity of two individuals is determined by their block memberships.
+    \item An interaction can only occur between a row and a column node.
+\end{itemize}
+
+\begin{figure}[H]
+    \center
+    \begin{tikzpicture}[scale=.6]
+        \input{../tikz/lbm.tex}
+    \end{tikzpicture}
+    \caption{An LBM model visualization}
+    \label{fig:LBMvisu}
+\end{figure}
+
+\begin{itemize}
+    \item $Q_1 = |\{{\color{blueind}\bullet},{\color{cyanind}\bullet},{\color{electricblue}\bullet}\}|$ \emph{given} blocks in rows
+    \item $Q_2 = |\{{\color{burntorange}\bullet},{\color{goldenyellow}\bullet},{\color{peach}\bullet}\}|$ \emph{given} blocks in columns
+\end{itemize}
+Parameters
+\begin{itemize}
+    \item $\pi_{\bullet} = \mathbb{P}(Z_i = \bullet)$ for rows and $\rho_{\bullet} = \mathbb{P}(W_j = \bullet)$ for columns
+    \item $\alpha_{{\color{blueind}\bullet}{\color{burntorange}\bullet}} = \mathbb{P}(X_{ij} = 1 | Z_i = {\color{blueind}\bullet}, W_j = {\color{burntorange}\bullet})$, parameter influencing the probability and value of a link knowing node
+          membership blocks.
+\end{itemize}
+
+On figure~\ref{fig:LBMvisu}, $\bm{\pi}$ are the probabilities for a row node to belong
+to the row block of corresponding color, $\bm{\rho}$ are the probabilities for
+a column node to belong to the column block of corresponding color and
+$\bm{\alpha}$ is a matrix $Q_1 \times Q_2$ of the connectivity parameters
+between the row and column blocks. When we talk about the \enquote{structure}
+of the network we are referring to this connectivity matrix.
+
+This model can be used to easily generate bipartite graphs with complex and
+very varied structures. But when trying to determine the structure of a given
+network we need to find those parameters and as the row and column block
+memberships are \emph{latent} i.e.,\ they are not known, they must be inferred.
+
+For this a common approach is to use a \emph{variational} EM algorithm, proposed
+for SBM in~\cite{daudinMixtureModelRandom2008} and for LBM in
+~\cite{govaertEMAlgorithmBlock2005}. The groups and required parameters
+can be inferred by maximizing a lower bound of the likelihood.
+
+\section{colSBM model, a joint model for a collection of networks}
+\label{sec:colsbm-model-a-joint-model-for-a-collection-of-networks}
+The \emph{colSBM} model introduced by ~\cite{chabert-liddellLearningCommonStructures2024a}
+propose an extension of the SBM model to collections of simple (or unipartite)
+networks. A collection is a set of networks which nodes are not in common nor
+linked between different networks and the interactions have the same valuations.
+
+The model can retrieve the shared structure in a collection, indicate if
+networks should be grouped in a collection and in a large pool of networks,
+collections with common structures.
+
+The next step after designing this collection model for unipartite networks was
+to extend it to the bipartite case.
+
+\section{Definition of a bipartite collection}
 \label{sec:definition-of-a-collection}
 
 We define a collection of bipartite networks as

rapport/chapter4-simulation-studies.tex

@@ -1,7 +1,7 @@
 \addtocounter{customchapter}{1}
 \chapter{Simulation studies}\label{chap:simulation-studies}
 
-The below simulations are meant to test the capacities of our models. We assess
+The simulations below are meant to test the capacities of our models. We assess
 the inference capacities of the algorithm and method, the model selection
 performances and the clustering capacities.
 

rapport/chapter4-simulations/inference.tex

@@ -78,18 +78,20 @@ use the following indicators:
           For each network, for the
           $\pi$-colBiSBM, $\rho$-colBiSBM,
           $\pi\rho$-colBiSBM we compare the inferred block memberships to
-          the real ones by computing the mean of the ARI per axis over the two
+          the real ones by computing the mean of the ARI per dimension over the two
           networks
           \begin{equation*}
               \overline{\text{ARI}}_d = \frac{1}{2} \big( \text{ARI}(\widehat{\bm{Z}^1_d},\bm{Z}^1_d) + \text{ARI}(\widehat{\bm{Z}^2_d},\bm{Z}^2_d) \big),
           \end{equation*}
-          where $d$ is the dimension or axis (i.e., rows, $d=1$, or columns, $d=2$) of
+          where $d$ is the dimension (i.e., rows, $d=1$, or columns, $d=2$) of
           the block memberships.
           And we compute the ARI of the whole set of nodes to account for block
           pairing between networks
           \begin{equation*}
               \text{ARI}_d = \text{ARI}\big((\widehat{\bm{Z}^1_d},\widehat{\bm{Z}^2_d}),(\bm{Z}^1_d,\bm{Z}^2_d) \big).
           \end{equation*}
+          The purpose of this metric is to verify that the block labels found
+          in one network match the block labels in the second network.
 \end{itemize}
 
 All these quality indicators are averaged over the 108 datasets. The results are

rapport/conclusions.tex

@@ -18,17 +18,16 @@ At the end of this internship we now have:
 
 \subsection{Difficulties encountered}
 \label{ssec:difficulties-encountered}
-\paragraph{Seed dependance} While using our clustering on data
+\paragraph{Local optima} While using our clustering on data
 from~\cite{doreRelativeEffectsAnthropogenic2021} we obtained quite interesting
 results but investigating further, we noticed that the clustering on such big
 collections ($M=123$) was not fully reproducible. It depends a lot on the random
 generator seed and as there is no possibility to merge back
-collections\footnote{
+collections
-    This is due to the need of having same sized $\bm{\alpha}$ to be able to compute
-    the distance. Meaning that the networks must have been fitted together
-    in the same collection.}
 the clustering dendrograms do not stabilize on large collections.
 This, currently, prevents us to clusterize large collections.
+We suspect that our model selection method gets stuck on local optima
+of the BIC-L.
 
 \paragraph{Large penalties with free mixture models}
 We observed while testing clustering with the different models that
@@ -42,9 +41,9 @@ the connectivity parameters.
 \section{Future work}
 \label{sec:future-work}
 
-\paragraph{Fixing seed dependance}
+\paragraph{Fixing local optima}
 We are currently investigating the procedure and code to see if reducing or
-escaping seed dependance is possible.
+escaping seed dependance is possible and would allow escaping the local optima.
 
 \paragraph{Identifiability}
 As stated in section~\ref{sec:model-identifiability}, we only have
@@ -78,5 +77,3 @@ Recent work have been comparing
 capabilities of the models and particularly focusing on networks clustering.
 We will reproduce and adapt the analysis to test other simulation settings that
 were not considered in this work.
-
-\section*{Thank you for reading this work}

rapport/rapport.tex

@@ -211,6 +211,15 @@ automata,positioning}
 \newcommand{\Tau}{\mathcal{T}}
 \newcommand{\eps}[1][]{\ensuremath{\epsilon_{#1}}}
 
+% Nouvelle environnement
+\renewenvironment{abstract}[1]{%
+% \begin{center}\normalfont\textbf{Abstract}\end{center}
+\begin{quotation} #1 \end{quotation}
+}{%
+\vspace{1cm}
+}
+
+
 
 % titre et auteur
 \title{Détection et comparaison de structures de réseaux écologiques}

references.bib

@@ -417,6 +417,24 @@
   file = {/home/polarolouis/Zotero/storage/49IKUHMA/s11222-014-9472-2.pdf.pdf;/home/polarolouis/Zotero/storage/VXKAK359/Keribin et al. - 2015 - Estimation and selection for the latent block mode.pdf}
 }
 
+@article{pichonTellingMutualisticAntagonistic2024,
+  title = {Telling Mutualistic and Antagonistic Ecological Networks Apart by Learning Their Multiscale Structure},
+  author = {Pichon, Benoît and Le Goff, Rémy and Morlon, Hélène and Perez-Lamarque, Benoît},
+  date = {2024},
+  journaltitle = {Methods in Ecology and Evolution},
+  volume = {15},
+  number = {6},
+  pages = {1113--1128},
+  issn = {2041-210X},
+  doi = {10.1111/2041-210X.14328},
+  url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/2041-210X.14328},
+  urldate = {2024-06-17},
+  abstract = {Characterizing and understanding the processes that shape the structure of ecological networks, which represent who interacts with whom in a community, has many implications in ecology, evolutionary biology and conservation. A highly debated question is whether and how the structure of a bipartite ecological network differs between antagonistic (e.g. herbivory) and mutualistic (e.g. pollination) interaction types. Here, we tackle this question by using a multiscale characterization of network structure, machine learning tools, and a large database of empirical and simulated bipartite networks. Contrary to previous studies focusing on global structural metrics, such as nestedness and modularity, which concluded that antagonistic and mutualistic networks cannot be told apart from only their structure, we find that they can be told apart by combining a meso-scale characterization of their structure and supervised machine learning. Motif frequencies appear particularly informative, with an over-representation of densely connected motifs in antagonistic networks and of motifs with asymmetrical specialization in mutualistic networks. These structural properties can be used to predict the type of interaction with relatively good confidence. Beyond this classical mutualism/antagonism dichotomy, we also find significant structural uniqueness linked to specific ecologies (e.g. pollination, parasitism). Our results clarify structural differences between antagonistic and mutualistic networks and suggest the investigation of the structural uniqueness of specific ecologies as a promising approach for characterizing interactions beyond the coarse antagonistic/mutualistic dichotomy.},
+  langid = {english},
+  keywords = {ecological interactions,interaction classification,machine learning,motif frequency,network structure},
+  file = {/home/polarolouis/Zotero/storage/9DFZFNV7/Pichon et al. - 2024 - Telling mutualistic and antagonistic ecological ne.pdf;/home/polarolouis/Zotero/storage/RZXQ6LCV/2041-210X.html}
+}
+
 @article{chabert-liddellLearningCommonStructures2024a,
   title = {Learning Common Structures in a Collection of Networks. {{An}} Application to Food Webs},
   author = {Chabert-Liddell, Saint-Clair and Barbillon, Pierre and Donnet, Sophie},
@@ -503,3 +521,40 @@
   abstract = {Semantic Scholar extracted view of "On random graphs. I." by P. Erdos et al.},
   file = {/home/polarolouis/Zotero/storage/WRSY3FZV/Erdős et Rényi - 2022 - On random graphs. I..pdf}
 }
+
+@article{devotoUnderstandingPlanningEcological2012,
+  title = {Understanding and Planning Ecological Restoration of Plant–Pollinator Networks},
+  author = {Devoto, Mariano and Bailey, Sallie and Craze, Paul and Memmott, Jane},
+  date = {2012},
+  journaltitle = {Ecology Letters},
+  volume = {15},
+  number = {4},
+  pages = {319--328},
+  issn = {1461-0248},
+  doi = {10.1111/j.1461-0248.2012.01740.x},
+  url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1461-0248.2012.01740.x},
+  urldate = {2024-08-20},
+  abstract = {Ecology Letters (2012) 15: 319–328 Abstract Theory developed from studying changes in the structure and function of communities during natural or managed succession can guide the restoration of particular communities. We constructed 30 quantitative plant–flower visitor networks along a managed successional gradient to identify the main drivers of change in network structure. We then applied two alternative restoration strategies in silico (restoring for functional complementarity or redundancy) to data from our early successional plots to examine whether different strategies affected the restoration trajectories. Changes in network structure were explained by a combination of age, tree density and variation in tree diameter, even when variance explained by undergrowth structure was accounted for first. A combination of field data, a network approach and numerical simulations helped to identify which species should be given restoration priority in the context of different restoration targets. This combined approach provides a powerful tool for directing management decisions, particularly when management seeks to restore or conserve ecosystem function.},
+  langid = {english},
+  keywords = {Ecosystem function,functional complementarity,functional redundancy,pine forest,plant–animal interaction,plant–pollinator network,redundancy analysis,restoration,restoration strategy,succession},
+  file = {/home/polarolouis/Zotero/storage/XY2INESI/Devoto et al. - 2012 - Understanding and planning ecological restoration of plant–pollinator networks.pdf;/home/polarolouis/Zotero/storage/MWCIJ5TW/j.1461-0248.2012.01740.html}
+}
+
+@article{boschPlantPollinatorNetworks2009,
+  title = {Plant–Pollinator Networks: Adding the Pollinator’s Perspective},
+  shorttitle = {Plant–Pollinator Networks},
+  author = {Bosch, Jordi and Martín González, Ana M. and Rodrigo, Anselm and Navarro, David},
+  date = {2009},
+  journaltitle = {Ecology Letters},
+  volume = {12},
+  number = {5},
+  pages = {409--419},
+  issn = {1461-0248},
+  doi = {10.1111/j.1461-0248.2009.01296.x},
+  url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1461-0248.2009.01296.x},
+  urldate = {2024-08-20},
+  abstract = {Pollination network studies are based on pollinator surveys conducted on focal plants. This plant-centred approach provides insufficient information on flower visitation habits of rare pollinator species, which are the majority in pollinator communities. As a result, pollination networks contain very high proportions of pollinator species linked to a single plant species (extreme specialists), a pattern that contrasts with the widely accepted view that plant–pollinator interactions are mostly generalized. In this study of a Mediterranean scrubland community in NE Spain we supplement data from an intensive field survey with the analysis of pollen loads carried by pollinators. We observed 4265 contacts corresponding to 19 plant and 122 pollinator species. The addition of pollen data unveiled a very significant number of interactions, resulting in important network structural changes. Connectance increased 1.43-fold, mean plant connectivity went from 18.5 to 26.4, and mean pollinator connectivity from 2.9 to 4.1. Extreme specialist pollinator species decreased 0.6-fold, suggesting that ecological specialization is often overestimated in plant–pollinator networks. We expected a greater connectivity increase in rare species, and consequently a decrease in the level of asymmetric specialization. However, new links preferentially attached to already highly connected nodes and, as a result, both nestedness and centralization increased. The addition of pollen data revealed the existence of four clearly defined modules that were not apparent when only field survey data were used. Three of these modules had a strong phenological component. In comparison to other pollination webs, our network had a high proportion of connector links and species. That is, although significant, the four modules were far from isolated.},
+  langid = {english},
+  keywords = {Apparent specialization,coevolution,generalization,modularity,nestedness,plant–pollinator interactions,pollen analysis,pollination web,sampling effort},
+  file = {/home/polarolouis/Zotero/storage/C5TQ6Y49/Bosch et al. - 2009 - Plant–pollinator networks adding the pollinator’s perspective.pdf;/home/polarolouis/Zotero/storage/BHMVU3DU/j.1461-0248.2009.01296.html}
+}