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\begin{document}

\title{New deep learning-based methods for visualizing ecosystem properties
using environmental DNA metabarcoding data}



\author[1]{Letizia Lamperti}%
\author[2]{Théophile Sanchez}%
\author[3]{Sara Si Moussi}%
\author[4]{David Mouillot}%
\author[2]{Camille Albouy}%
\author[2]{Benjamin Flück}%
\author[5]{Morgane Bruno}%
\author[6]{Alice Valentini}%
\author[7]{Loïc Pellissier}%
\author[8]{Stéphanie Manel}%
\affil[1]{EPHE PSL}%
\affil[2]{ETH Zurich}%
\affil[3]{TIMC-IMAG}%
\affil[4]{MARBEC}%
\affil[5]{CEFE}%
\affil[6]{SPYGEN}%
\affil[7]{ETH Zürich}%
\affil[8]{CNRS}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\selectlanguage{english}
\begin{abstract}
1. Metabarcoding of environmental DNA (eDNA) has recently improved our
understanding of biodiversity patterns in marine and terrestrial
ecosystems. However, the complexity of these data prevents current
methods to extract and analyze all the relevant ecological information
they contain. Therefore, ecological modeling could greatly benefit from
new methods providing better dimensionality reduction and clustering. 2.
Here we present two new deep learning-based methods that combine
different types of neural networks to ordinate eDNA samples and
visualize ecosystem properties in a two-dimensional space: the first is
based on variational autoencoders (VAEs) and the second on deep metric
learning (DML). The strength of our new methods lies in the combination
of several inputs: the number of sequences found for each molecular
operational taxonomic unit (MOTU), together with the genetic sequence
information of each detected MOTU within an eDNA sample. 3. Using three
different datasets, we show that our methods represent well three
different ecological indicators in a two-dimensional latent space: MOTU
richness per sample, sequence \selectlanguage{greek}α-\selectlanguage{english}diversity per sample, and sequence
ꞵ-diversity between samples. We show that our nonlinear methods are
better at extracting features from eDNA datasets while avoiding the
major biases associated with eDNA. Our methods outperform traditional
dimension reduction methods such as Principal Component Analysis,
t-distributed Stochastic Neighbour Embedding, and Uniform Manifold
Approximation and Projection for dimension reduction. 4. Our results
suggest that neural networks provide a more efficient way of extracting
structure from eDNA metabarcoding data, thereby improving their
ecological interpretation and thus biodiversity monitoring.%
\end{abstract}%



\sloppy


\textbf{New deep learning-based methods for visualizing ecosystem
properties using environmental DNA metabarcoding data}Letizia
Lamperti\textsuperscript{a,b}, Th\selectlanguage{ngerman}éophile Sanchez\textsuperscript{b},
Sara Si Moussi\textsuperscript{e} , David Mouillot\textsuperscript{c,d},
Camille Albouy\textsuperscript{b}, Benjamin Flück\textsuperscript{b},
Morgane Bruno\textsuperscript{a}, Alice Valentini\textsuperscript{f},
Loi\selectlanguage{english}c Pellissier\textsuperscript{b}*, Ste\selectlanguage{english}phanie
Manel\textsuperscript{a,d} \textbf{*}\textsuperscript{a} CEFE, Univ
Montpellier, CNRS, \textbf{EPHE-PSL University}, IRD, Montpellier,
France~\textsuperscript{b} Landscape Ecology, Inst. of Terrestrial
Ecosystems, ETH Zu\selectlanguage{english}rich, Zu\selectlanguage{english}rich, Switzerland and Swiss Federal Research
Inst. WSL, Birmensdorf, Switzerland\textsuperscript{c} MARBEC, Univ
Montpellier, CNRS, IFREMER, IRD, Montpellier, France~\textsuperscript{d}
Institut Universitaire de France, Paris, France\textsuperscript{e}
TIMC-IMAG, LECA, Grenoble, France\textsuperscript{f} SPYGEN, Savoie
Technolac *Co-senior authors\textbf{Correspondence:} Letizia Lamperti,
e-mail: letizia.lamperti@ephe.psl.eu\textbf{Abstract}Metabarcoding of
environmental DNA (eDNA) has recently improved our understanding of
biodiversity patterns in marine and terrestrial ecosystems. However, the
complexity of these data prevents current methods to extract and analyze
all the relevant ecological information they contain. Therefore,
ecological modeling could greatly benefit from new methods providing
better dimensionality reduction and clustering. Here we present two new
deep learning-based methods that combine different types of neural
networks to ordinate eDNA samples and visualize ecosystem properties in
a two-dimensional space: the first is based on variational autoencoders
(VAEs) and the second on deep metric learning (DML). The strength of our
new methods lies in the combination of several inputs: the number of
sequences found for each molecular operational taxonomic unit (MOTU),
together with the genetic sequence information of each detected MOTU
within an eDNA sample. Using three different datasets, we show that our
methods represent well three different ecological indicators in a
two-dimensional latent space: MOTU richness per sample, sequence
\selectlanguage{greek}α-\selectlanguage{english}diversity per sample, and sequence \selectlanguage{greek}β-\selectlanguage{english}diversity between samples. We
show that our nonlinear methods are better at extracting features from
eDNA datasets while avoiding the major biases associated with eDNA. Our
methods outperform traditional dimension reduction methods such as
Principal Component Analysis, t-distributed Stochastic Neighbour
Embedding, and Uniform Manifold Approximation and Projection for
dimension reduction. Our results suggest that neural networks provide a
more efficient way of extracting structure from eDNA metabarcoding data,
thereby improving their ecological interpretation and thus biodiversity
monitoring.\textbf{Keywords:} biodiversity monitoring; deep learning;
deep metric learning; data visualization; environmental DNA; machine
learning; neural networks; variational autoencoder~\textbf{1
INTRODUCTION}Human-induced disturbances affect most of the Earth's
ecosystems, which are suffering from the accelerating impacts of climate
change and overexploitation (Johnston et al., 2022; Jouffray et al.,
2020). These threats alter species assemblages and lead to escalating
perturbations in ecosystem processes (Frainer et al., 2017, McLean et
al., 2019), ultimately altering ecosystem services and thus humanity
(Cinner et al., 2020; Tigchelaar et al., 2022). In the context of global
change, it is crucial to capture the spatio-temporal dynamics of species
assemblages and better understand their responses in order to design
appropriate management and mitigation measures (Makiola et al., 2020).
Recently, our ability to rapidly generate comprehensive biodiversity
inventories has been enhanced by the development of environmental DNA
(eDNA) metabarcoding, which allows the retrieval and analysis of DNA
naturally shed by organisms in their environment (Miya 2022; Deiner et
al., 2017). eDNA metabarcoding is now operational in many ecosystems for
a wide range of micro- and macroorganisms (Cantera et al., 2022; Kj\selectlanguage{ngerman}ær et
al., 2022; Mathon et al., 2022; Cordier et al., 2021), providing
information on their taxonomic, functional, but also phylogenetic
affiliations (Marques et al., 2021; Rozanski et al., 2022). Given the
low field effort and disturbance (Muff et al., 2022), even in the most
remote locations, and the decrease in sequencing costs in recent years,
this approach can be scaled up to monitor many sites at high temporal
frequency (Agersnap et al., 2022). eDNA metabarcoding produces massive
sequencing data (i.e., a high number of short DNA sequences), that
represent complex and high-dimensional information. Typically, these
sequences are assigned to known taxonomic units stored in a genetic
reference database. The incompleteness of genetic reference databases
(Marques et al., 2020) precludes the identification of many species,
thus working with Molecular Operational Taxonomic Units (MOTUs)
representing a cluster of similar sequences may be required (Deiner et
al., 2017; Mathon et al., 2022). MOTUs are then defined by a consensus
sequence. The attribute attached to an eDNA MOTU is the relative
frequency of the sequences in each MOTU and the genetic sequence itself.
Both attributes can be directly related to ecosystem states and
properties (Shelton et al., 2019; Bakker et al., 2017).~ Therefore, eDNA
data are potentially relevant for revealing ecological patterns that
distinguish sampled sites along environmental or human pressure
gradients (Marques et al., 2020). Such patterns are expected to emerge
from the interaction and nonlinear combination of both abundance and
phylogenetic information. However, the dimensionality of the massive
amount of sequence information must be reduced to extract relevant
features. Dimensionality reduction is the transformation of
high-dimensional data into a meaningful representation of reduced
dimensionality (Van Der Maaten et al., 2009; Nguyen and Holmes, 2019).
Traditionally, dimensionality reduction is performed using linear
techniques such as Principal Component Analysis (PCA; Pearson, 1901),
Factor Analysis (Spearman, 1904), and classical scaling (Torgerson,
1952). However, due to their hypotheses, these linear techniques cannot
adequately deal with complex non-linear relationships in data such as
eDNA. In the last decade, many nonlinear techniques have been proposed
for dimensionality reduction (Nguyen et al., 2019; Facco et al., 2017).
Recently, two machine learning techniques - the t-distributed stochastic
neighbour embedding (t-SNE; van der Maaten and Hinton, 2008) and the
Uniform Manifold Approximation and Projection (UMAP; McInnes et al.,
2018) - have shown promising results in generating two-dimensional
visualisations of high-dimensional biological data (Diaz-Papkovich et
al., 2019). However, the interpretation of t-SNE and UMAP plots remains
challenging due to the lack of global structure in the reduced space
representation (Battey et al., 2019). Although these methods perform
well in clustering similar samples, distances between clusters are not
always meaningful (Becht et al., 2019). However, neural networks (NN)
have been shown to have a good representation of learning capacity (Sze
et al., 2017). NN are complex mathematical models consisting of many
operators called neurons, organized in a network of interconnected
nodes. UMAP and t-SNE learn features by satisfying distances between
observations, i.e., in contrast. Other methods instead use generative
latent variable models, where prior distributions are specified for the
unobserved structure in the data so that these unknown properties can be
inferred by posterior inference. Examples include factor analysis,
probabilistic PCA, and Variational Autoencoders (VAEs). VAEs combine two
deep neural networks, where the first network (the encoder) encodes
input data (e.g., the number of sequences per MOTU detected in each
sample) as a probability distribution in a latent space, and the second
network (the decoder) attempts to reconstruct the input data given a set
of latent coordinates. VAEs have been used extensively in image
generation (e.g., Larsen et al., 2015; Gulrajani et al., 2016; Hou et
al., 2016), and several recent studies have applied them to
dimensionality reduction and classification of single-cell RNAseq data
(Grønbech et al., 2018; Lafarge et al., 2019; Wang and Gu 2018; Battey
et al., 2019). Thanks to the design flexibility of artificial neural
networks in general, they also have the advantage of being able to
encode and mix information from different data types. Deep metric
learning (DML) lies between contrastive and generative latent variable
models. Metric learning is an approach directly based on a distance
metric that aims to establish similarity or dissimilarity between
objects (Kulis, 2013). Although metric learning aims to reduce the
distance between similar objects, it also aims to increase the distance
between dissimilar objects (Duffner et al., 2021). Through DML, it is
possible to use a distance measure relevant to the case study as a
contrastive model but also to encode different inputs via neural
networks. VAE and DML have not yet demonstrated their potential to
ordinate eDNA samples in a low-dimensional space. In this study, we
present two new methods, one based on VAE and the other on DML, to
perform data visualisation. In our methods, we assemble, modify, and
adapt these neural networks with others to work best with eDNA data. We
tested our methods on three different published eDNA datasets: a fish
eDNA dataset collected in the Mediterranean Sea (Boulanger et al. 2020),
and two eukaryotic plankton eDNA datasets from the Tara Ocean expedition
(de Vargas et al. 2015). We used both the number of sequences per
detected MOTU and the genetic sequence information of each MOTU detected
in each sample as input data. To validate these two new methods, we
compare them with three classical methods: PCA, t-SNE, and UMAP.
Finally, we show how the proposed methods outperform classical methods
in their representation of ecological indicators.\textbf{2 MATERIALS and
METHODS~2.1 VAE-based method applied to eDNA Data}The VAE-based method,
called VAESeq (Fig. 1), processes eDNA samples into a two-dimensional
latent space. The model consists of an autoencoder (AE) and a
variational autoencoder (VAE). The AE takes as input the genetic
sequence information and the presence/absence of each MOTU within each
sample to generate the first latent encoding\emph{zAE}. The VAE encoder
then receives the embedding generated by the genetic autoencoder and
analyses it in combination with the number of sequences found for each
MOTU detected in the sample under consideration. By mixing the two
inputs, it encodes the samples as points in a 2D latent space called
\emph{zVAE}. In the decoding part, the VAE decoder seeks to recreate the
two inputs from \emph{zVAE}. The decoder measures how much information
is lost from the input during the encoding, and optimizes the network
accordingly. To reduce the running time of the model, we separately
trained the AE to embed genetic sequences. Because we were interested in
the compression of the genetic information rather than its
representation, we decided to use an AE rather than a VAE. To encode the
DNA sequence information in the AE, the sequences are equalised to the
same length. We have chosen to keep the maximum length, adding
nucleotides X to equalise. Each canonical base (A, C, T, G) of the
sequence and the IUPAC ambiguity codes are translated into an
appropriate four-dimensional probability distribution over the four
canonical bases (A, T, C, G), including uncertain base sequences (e.g.,
W and S). For example, A becomes {[}1,0,0,0{]} or W becomes {[}0.5, 0,
0, 0.5{]} (Flück et al., 2022). Furthermore, X nucleotides added to
equalise the sequence length become {[}0.25, 0.25, 0.25, 0.25{]}. We
combine the genetic information with the presence/absence of each MOTU
in each sample. Therefore, each sample is represented by a tensor
containing the translated binary matrices of the detected MOTUs and,
alternatively, a zero matrix if the MOTU was not detected. The AE
component of the network uses the Adam optimiser and the binary
cross-entropy loss function to optimise the network. The AE encoder
consisted of seven fully connected layers with decreasing widths down to
100, rectified linear unit activations, and dropout regularization. A
mirror architecture was used as the decoder.~ The VAE component of the
network uses the Adam optimiser and two loss functions to reconstruct
the two inputs: the VAE loss function (Kullback-Leibler divergence +
reconstruction error) for the occurrence information and binary
cross-entropy for the genetic sequence information. After testing
different combinations, we set the loss function weights to 1 and 0.2
respectively. The VAE encoder consisted of three fully connected layers
with decreasing widths down to 2, rectified linear unit activations, and
dropout regularization. A mirror architecture to the encoder was used as
the decoder.~\selectlanguage{greek}\textbf{2.2 DML-based method on β-diversity as a
distance}\selectlanguage{english}The ENNBetaDist DML-based method (Fig. 2) trains the network
accordingly to the pairwise \selectlanguage{greek}β-\selectlanguage{english}diversity calculated between the samples.
The pairwise \selectlanguage{greek}β-\selectlanguage{english}diversity is used as a distance measure on each pair of
samples, to help the network distribute the points in the latent space.
We used pairwise Jaccard dissimilarity as a measure of \selectlanguage{greek}β-\selectlanguage{english}diversity,
using the 'betapart' library in R. The structure of ENNBetaDist consists
of two encoder neural networks. The encoders of ENNBetaDist are similar
to those of VAESeq, with differences in the number of hidden layers,
training, and optimisation. VAESeq reconstructs input from the latent
space, however, we want the latent space to respect the distances we
want to optimise. At each iteration, each encoder takes as input a
sample containing the number of sequences per MOTU and the genetic
latent encoding from the AE of that sample.Then, the two encoders
process the two samples, combining the number of sequences found for
each MOTU detected and the autoencoder embedding of the sequences into a
point in the two-dimensional latent space \emph{z1} and \emph{z2}. To
optimise the model, we calculate the Euclidean distance between the two
points in \emph{z1} and \emph{z2} and compare it with the pairwise
\selectlanguage{greek}β-\selectlanguage{english}diversity via a loss function (the mean square error (MSE)). In
\emph{z1} and \emph{z2} we find the visual representation of all data
points. Indeed, ENNBetaDist represents the distances related to the
species composition of the samples (i.e., the information provided by
Jaccard's \selectlanguage{greek}β-\selectlanguage{english}diversity) as distances between points in the 2D space. The
encoders consisted of 5 fully connected layers with decreasing widths
down to 2, rectified linear unit activations, and dropout
regularization.\textbf{2.3 Sensitivity~}To perform a cross-validation of
our two new methods, we set a global random seed to split 80\% of the
original dataset in the training set and 20\% in the validation set. We
repeated the tests until the results were stable, ensuring that we did
not overfit by monitoring the loss on the validation set. We implemented
the models in R (version 4.1.3 R Core Team, 2020) using TensorFlow
(Abadi et al., 2015) and Keras (Chollet, F. et al., 2015)
libraries.\textbf{2.4 Case study}2.4.1 Data sets We tested our methods
on three different published eDNA datasets: a fish eDNA dataset
collected in the western Mediterranean Sea (Boulanger et al. 2020) and
two eukaryotic plankton eDNA datasets from the Tara Ocean Campaign (de
Vargas et al. 2015). Details are given in Table 1. eDNA samples from the
Western Mediterranean Sea dataset were collected at 77 stations in six
marine regions covering the western Mediterranean, including fished and
no-take protected areas (Fig. S1) (Boulanger et al. 2020). eDNA
extraction and amplification were performed at the SPYGEN facility. PCR
amplification was performed using the teleo primer pair, targeting a 64
bp fragment of the mitochondrial DNA 12S rRNA gene specific for teleost
fishes and elasmobranchs, according to the protocol described in
(Valentini et al. 2016). Data collection and sample processing are
described in detail in Appendix 1 of the supplementary material. The
Tara Ocean datasets were obtained from the Tara Oceans V9 rDNA
metabarcoding dataset (De Vargas et al. 2015) collected across tropical
and temperate oceans during the circumglobal Tara Oceans expedition. The
analysis was based on metabarcoding data from 129 stations in various
oceanic provinces worldwide, using 18S~ribosomal DNA sequences across
the intermediate plankton-size spectrum. All details on data collection,
extraction, and sequencing can be found in the article by Vargas et al.
(2015). We selected the Dictyochophyceae and Telonemia subsets by
taxonomic identification, resulting in two smaller datasets of similar
sizes to the western Mediterranean one and whose specifications are
shown in Table 1.\textbf{2.5 Comparison and evaluation}We tested the
ability of the two new methods to better represent the distance between
samples based on their species and sequence composition. We compared the
2D representations of VAESeq and ENNBetaDist with three other classical
dimension reduction methods: PCA, which is linear, and t-SNE, UMAP,
which are non-linear. Furthermore, we analysed the genetic embedding
generated by the autoencoder using the PCA to evaluate the results of
the first part of the models. We also compared it with a simpler VAE,
i.e., to which the embedding of the sequence autoencoder has not been
given as input. The inputs to PCA, t-SNE and UMAP are the
presence/absence information of each MOTU in each sample and the number
of sequences found during eDNA extraction for each detected MOTU (Table
3). Our neural network-based methods also receive genetic information on
the sequences of the latent embedding of the autoencoder (Table 2). To
evaluate the performance of all the methods, we used both multiple
regressions on distance matrices (MRM) representing the sample in space
(Table 3). For MRM, we implemented two different tests and assessed the
statistical significance using permutations. TEST 1 performs a multiple
regression between the sample distances in the two-dimensional latent
spaces of each method and their Jaccard's \selectlanguage{greek}β-\selectlanguage{english}diversity (Table 3). TEST 2,
instead of using Jaccard's \selectlanguage{greek}β-\selectlanguage{english}diversity matrix, uses the distance matrix
calculated on the \selectlanguage{greek}β-\selectlanguage{english}diversity between sequences within the Hill number
framework (Table 3). The baseline methods were performed using R version
4.1.3 with the packages ''stats'' for PCA, ''umap'' (Konopka 2019) for
UMAP, ''Rtsne'' (Jesse Krijthe 2022) for t-SNE and ''TensorFlow'' with
''Keras'' for VAE. We used the \emph{MRM} function of the ''ecodist''
package to perform the tests. We computed the Euclidean distance matrix
between each pair of samples in the latent spaces using the function
\emph{dist} from the package ''stats'' and the Jaccard \selectlanguage{greek}β-\selectlanguage{english}diversity using
the library ''betapart''. We calculated the distance matrix of sequence
\selectlanguage{greek}β-\selectlanguage{english}diversity between each pair of samples using the Hill number framework
(Alberdi 2019). The genetic distance between each pair of sequences was
computed with the function\emph{dist.gene} from the package ''ape''.
Sequence \selectlanguage{greek}β-\selectlanguage{english}diversity was calculated with the function
\emph{beta.fd.hill} from package ''mFD'', with parameters q = 1 and =
''mean'' (Chao et al. 2019), using S\selectlanguage{ngerman}ørensen's \selectlanguage{greek}β-\selectlanguage{english}diversity.\textbf{3
RESULTS3.3 Comparison with other methods}We decide to test the
representations of the points in the 2D latent spaces of the three
different data sets with the methods shown in Table 3. We test the 2D
representations with the Jaccard \selectlanguage{greek}β-\selectlanguage{english}diversity matrix and the sequence
\selectlanguage{greek}β-\selectlanguage{english}diversity matrix (TEST 1 and 2). Out of the three datasets considered,
the highest R\textsuperscript{2} values are achieved by the neural
network-based methods. For our methods, the results of TEST 2 are better
than those of TEST 1. In TEST 1, using the matrix based on Jaccard's
\selectlanguage{greek}β-\selectlanguage{english}diversity, the R\textsuperscript{2} values in the latent space of the
autoencoder (AEgen+PCA) are 10\textsuperscript{2} times higher than
those of PCA, t-SNE, and UMAP. Furthermore, for all three datasets, the
R\textsuperscript{2} values increase in the case of VAEseq and
ENNBetaDist, that is, when the number of sequences is also given as
input. The best results for all three datasets are obtained with
ENNBetaDist, i.e., when the model is optimised in pairwise \selectlanguage{greek}β-\selectlanguage{english}diversity.
The worst-performing method is PCA, which is the only linear method
used. Furthermore, we have shown that VAE fails to extract information
for the three datasets when genetic sequence information is not added.
We describe below in more detail the results in the case of the
Mediterranean eDNA fish data set. The same results obtained on the
Dictyochophyceae and Telonemia data sets are shown in Figure S2 in the
supplementary material.\textbf{3.2 VA Latent spaces representations and
ecological interpretation on western Mediterranean eDNA fish data
set}The 2D latent space representations of the eDNA fish data samples
using two new methods (Fig. S3) reveal gradients both in terms of MOTU
richness (Figs. 3 a-c) and sequence \selectlanguage{greek}α-\selectlanguage{english}diversity (Figs. 3 b-d). The two
gradients were visible along both directions of the 2D latent space. For
simplicity, we report only the studies along the vertical direction,
where the correlations are the strongest. We performed correlation tests
to validate the relationship between the vertical direction of our 2D
latent space and the diversity metrics. For both methods, we found that
the latent variable along the second axis is significantly correlated
with the sequence~\selectlanguage{greek}α-\selectlanguage{english}diversity (Pearson's r = 0.80, p \textless{} 0.001
for VAESeq Fig. 3a; r =0.84, p \textless{} 0.001for ENNBetaDist Fig.
3d). The same latent variable axis 2 is also significantly correlated
with the MOTU richness (r =0.86, p \textless{} 0.001 for VAESeq Fig. 3b;
r= 0.95, p \textless{} 0.001 for ENNBetaDist Fig. 3e). We tested the
correlation between the 2D spatial representation of the two new methods
with the Jaccard's \selectlanguage{greek}β-\selectlanguage{english}diversity matrix and with the sequence \selectlanguage{greek}β-\selectlanguage{english}diversity
matrix (TEST 1 and 2; Table 3). We found that the two new methods
outperform traditional methods (i.e., PCA, t-SNE, UMAP, Fig. S4). The
R\textsuperscript{2} values of the VAESeq and ENNBetaDist are
10\textsuperscript{2} times higher than PCA, and more than twice that of
t-SNE and UMAP. The first principal component of the PC axes in the PCA
on the eDNA dataset explains only 2.9\% of the variance of the data, and
there is a nonsignificant correlation in both tests (Fig. S4 a, Table
3).~Among the non-linear methods, ENNBetaDist shows the best
results\textsuperscript{~}(TEST 2: R\textsuperscript{2} = 0.5041; p
\textless{} 0.001 for VAESeq and R\textsuperscript{2} = 0.7415; p
\textless{} 0.001 for ENNBetaDist; Table 3).\textbf{4 DISCUSSION}The
massive arrival of big data in ecology, facilitated by new technologies
(Farley et al. 2018; Besson et al. 2022), makes dimensionality
reduction, as well as data visualization, an important analytical tool.
In this study, we introduce two new deep learning-based methods that
combine different types of neural networks to ordinate eDNA samples and
visualize ecosystem properties in a two-dimensional space: the first is
based on variational autoencoder (VAE), and the second on deep metric
learning (DML). The strength of our new methods lies in their ability to
combine multiple inputs simultaneously, namely for eDNA the number of
sequences found for each molecular operational taxonomic unit (MOTU),
together with the genetic sequence information for each detected MOTU.
Using three different datasets - a fish eDNA dataset collected in the
Mediterranean Sea (Boulanger et al. 2020), and two eukaryotic plankton
eDNA datasets from the Tara Ocean expedition (de Vargas et al. 2015) -
we show that our methods well represent three different ecological
indicators in the two-dimensional latent space: (i) MOTU richness per
sample, (ii) sequence \selectlanguage{greek}α-\selectlanguage{english}diversity per sample, and (iii) sequence
\selectlanguage{greek}β-\selectlanguage{english}diversity between samples along a gradient in the latent space (Fig. 3
and Fig. S2, Table 3). Thus, the 2D representation obtained reveals the
ecological information underlying the study of communities.
Additionally, we have shown how our two new methods outperform the
representation of eDNA data compared to other dimensionality reduction
techniques such as PCA, t-SNE, UMAP, and even a simple VAE to which no
sequence information is added (Table 3). In contrast, linear methods
such as PCA result in poor dimensionality reduction to ordinate eDNA
samples (Table 3; Fig. S4 a). This is due to the complexity of eDNA data
(Miya 2022, Xiong et al., 2022). eDNA metabarcoding is defined as the
use of general or universal polymerase chain reaction (PCR) primers on
mixed DNA samples of any origin, followed by high-throughput
next-generation sequencing (NGS) to determine the species composition in
a given sample (see, e.g., Deiner et al., 2017). Despite its potential
in biodiversity monitoring (Pawlowski et al., 2022, V.d. Heyde et al.,
2022, Mathon et al., 2022), it can be limited by false reads due to
contamination, errors that can occur during the extraction, PCR, or
sequencing process (Bohmann et al., 2014; Ficetola et al., 2016; Creer
et al., 2016; Hering et al., 2018, Calder\selectlanguage{ngerman}ón-Sanou, et al., 2020).
Although field and laboratory practices can mitigate some of this, the
risk of error cannot be eliminated and must be considered (Burian et
al., 2021). Furthermore, eDNA metabarcoding sampling produces large,
high-resolution datasets that are complex and high-dimensional, with a
single observation from the experimental system containing measurements
describing multiple traits (Hallam et al., 2021). For this reason,
application neural architectures such as VAESeq and ENNBetaDist provide
a better solution for clustering or understanding eDNA data. Neural
networks allow the integration of multiple inputs into a single model
(Cichy et al., 2019; LeCun et al., 2015; Schmidhuber, J. 2015). This is
particularly relevant for the analysis of eDNA metabarcoding data, which
are combinations of different types of information (Table 2). Our two
new methods combine the number of sequences found for each MOTU and the
genetic sequence of the detected MOTUs, which provide complementary
information about the rarity and dissimilarity of the sequences,
respectively. Our methods can then represent eDNA samples in 2D space,
placing samples in relation to each other according to their composition
(Fig. 3, Fig. S2). Due to the process of phylogenetic niche conservatism
(Wiens et al., 2010) and environmental filtering (Guimarães 2020),
species present in a particular habitat or under particular management
constraints may show some phylogenetic and trait clustering (Jarzyna et
al., 2021). In the context of eDNA, it is therefore expected that if two
MOTUs are present in the same habitat, their genetic sequence
similarity, even based on a short sequence, will be higher than for
MOTUs from different habitats. Therefore, this genetic 'proximity'
information, taken into account in our two methods, contributes to the
ordination of eDNA samples in a lower-dimensional space along
ecological, environmental, or management gradients. Furthermore, despite
the short length of the recovered sequence in metabarcoding (Teleo fish
dataset approximately 60 pb, Table 1), our results indicate that such
genetic information can inform species ecology. Here, the manipulation
of the genetic information of the sequences highlights the proximity of
the sequences where the respective MOTUs are present in the different
samples. Therefore, the composition of each MOTU together with its DNA
sequence improves the representation of fish diversity and its
indicators. In addition, we show that a simple VAE, using only the
information on the number of sequences present in each sample, gives a
poor representation of the data (Table 3). The sequences turn out to be
crucial for good information extraction. Instead of relying solely on
the number of sequences identified per MOTU or the genetic information
within the sequences as in Cordier et al., (2018) and Flück et al.
(2022), our methods combine both information (Table 2). VAESeq is based
on VAE that is optimised to reconstruct the input. ENNBetaDist is a DML
method that also uses the diversity information (here the \selectlanguage{greek}β-\selectlanguage{english}diversity)
as a distance metric between samples. Using VAESeq for data extraction
has the advantage of treating each data independently because it is not
relying on any pairwise distance between samples. In this case, the
model is free to discover connections and highlight possible new ones in
a fully unsupervised learning process. Alternately, ENNBetaDist helps to
represent samples in a latent space according to an input metric. In
addition, two new methods allow users to define the output
dimensionality while preserving the global geometry (i.e., relative
positions in the latent space) better than competing methods. Our
results demonstrate that neural networks provide a more efficient way of
extracting structure from eDNA metabarcoding data than traditional
dimension reduction methods, thereby improving future ecological
interpretation. The resulting diversity indices can be used in future
applications to improve our understanding of the processes behind
spatial patterns coming from other types of monitoring approaches and in
any other fields. Visualizing ecosystem complexity can improve our
understanding of biodiversity and ecosystems, and thus help stakeholders
manage ecosystems.\textbf{Acknowledgments}This work is part of the
Horizon 2020-Marie Skodowska-Curie Actions-COFUND project Artificial
Intelligence for the Sciences (AI4theSciences) and the ANR FISH-PREDICT
project. This project was partly funded by the WSL internal grant ''eDNA
Proof'' and the Swiss Data Science Centre ''DNai''.\textbf{Conflict of
Interest~}The authors declare no conflict of interest.\textbf{Authors'
Contributions}L. Lamperti, S. Si Moussi, B. Fl\selectlanguage{ngerman}ück, L. Pellissier, and S.
Manel conceived the ideas and designed the methodology; M. Bruno and A.
Valentini analyzed the eDNA fish data samples; L. Lamperti, C. Albouy,
D. Mouillot, T. Sanchez, S. Manel, and L. Pellissier led the writing of
the manuscript. All authors critically contributed to the drafts and
gave final approval for publication.\textbf{Data Availability}If the
paper is accepted for publication, all the eDNA data will be available
in a Dryad Digital Repository. Codes and scripts for reproducing
analyses in this manuscript are available
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