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 \section{Introduction}\label{introduction}
 In the vast North Atlantic and subarctic region, the Icelandic area and its surrounding waters offer fascinating ecological interest \citep{schnurr_composition_2014, uhlir_adding_2021}. The waters surrounding Iceland contain a significant diversity of water bodies from various sources \citep{brix_iceage_2014}. These specific oceanographic and hydrographic characteristics shape benthic habitats through various parameters such as depth gradients, water mass indicators, and specific arrangement of habitats (\citep{meisner_benthic_2014, uhlir_adding_2021}). Therefore, research in these areas enhances our understanding of deep-sea ecosystems and the patterns of biodiversity patterns found within them (\citep{rogers2007corals, meisner_prefacebiodiversity_2018}).
 
-Biological and environmental baseline data collected in these regions the IceAGE project, as well as its predecessors BIOFAR and BIOICE, which studied the biodiversity of the Faroe Islands and Iceland \citep{meisner_prefacebiodiversity_2018} are invaluable resources. They provide a crucial source of information for understanding two major issues facing present and future generations: the impact of climate change and mining on the seabed. The North Atlantic region around Iceland has been recognized for decades as a critical region for the regulation of global thermohaline (\citep{meisner_prefacebiodiversity_2018}). The Greenland, Iceland and Norwegian (GIN) seas, as well as the high-latitude North Atlantic, play a crucial role in modern deep-sea ventilation. The surface waters of these regions are essential source regions for global deep-sea renewal, and are essentials for the circulation of thermohaline (\citep{johannessen_relationship_1994}). One of the most important of these changes is the formation of cold, deep water (\citep{meisner_prefacebiodiversity_2018}). With the loss of Arctic sea ice, the deep-sea formation process slowed down, likely impacting the flow dynamic and chemistry in the region studied during the IceAGE expedition (\citep{meisner_prefacebiodiversity_2018}).
+Biological and environmental baseline data collected in these regions the IceAGE project, as well as its predecessors BIOFAR and BIOICE, which studied the biodiversity of the Faroe Islands and Iceland \citep{meisner_prefacebiodiversity_2018} are invaluable resources. They provide a crucial source of information for understanding two major issues facing present and future generations: the impact of climate change and mining on the seabed. The North Atlantic region around Iceland has been recognized for decades as a critical region for the regulation of global thermohaline \citep{meisner_prefacebiodiversity_2018}. The Greenland, Iceland and Norwegian (GIN) seas, as well as the high-latitude North Atlantic, play a crucial role in modern deep-sea ventilation. The surface waters of these regions are essential source regions for global deep-sea renewal, and are essentials for the circulation of thermohaline \citep{johannessen_relationship_1994}. One of the most important of these changes is the formation of cold, deep water \citep{meisner_prefacebiodiversity_2018}. With the loss of Arctic sea ice, the deep-sea formation process slowed down, likely impacting the flow dynamic and chemistry in the region studied during the IceAGE expedition \citep{meisner_prefacebiodiversity_2018}.
 
-There is a growing international interest in deep-sea resource extraction (\citep{mengerink_call_2014}). These operations target in particular mid-ocean ridges and other active geothermal areas. The ridges around Iceland include these types of areas, such as the Reykjanes Ridge, which is home to hydrothermal vent sites. Accurately and rigorously assessing the extent of damage and loss of ecosystem services caused by mining activities is difficult without robust baseline data (\citep{meisner_prefacebiodiversity_2018}).
+There is a growing international interest in deep-sea resource extraction (\citep{mengerink_call_2014}). These operations target in particular mid-ocean ridges and other active geothermal areas. The ridges around Iceland include these types of areas, such as the Reykjanes Ridge, which is home to hydrothermal vent sites. Accurately and rigorously assessing the extent of damage and loss of ecosystem services caused by mining activities is difficult without robust baseline data \citep{meisner_prefacebiodiversity_2018}.
 
-Crustaceans of the taxon Peracarida Calman, 1904, often constitute a significant portion of macrobenthic communities in Arctic and subarctic waters. They are widely dispersed across the continental shelf and slope of northern seas (\citep{stransky_diversity_2010}). In this study, we focus on the peracarid taxon Cumacea Krøyer, 1846, which not only contribute to food webs, but are also essentials as indicators of marine habitat health (\citep{stransky_diversity_2010}). The latter are mainly bottom-dwelling marine benthic crustaceans, spending a large part of their lives buried in or near sediments. Thus, Cumacea are presumed to have limited dispersal abilities and are unlikely to be able to move great distances (\citep{uhlir_adding_2021}).
+Crustaceans of the taxon Peracarida Calman, 1904, often constitute a significant portion of macrobenthic communities in Arctic and subarctic waters. They are widely dispersed across the continental shelf and slope of northern seas \citep{stransky_diversity_2010}. In this study, we focus on the peracarid taxon Cumacea Krøyer, 1846, which not only contribute to food webs, but are also essentials as indicators of marine habitat health (\citep{stransky_diversity_2010}). The latter are mainly bottom-dwelling marine benthic crustaceans, spending a large part of their lives buried in or near sediments. Thus, Cumacea are presumed to have limited dispersal abilities and are unlikely to be able to move great distances \citep{uhlir_adding_2021}.
 
-Unlike the benthic invertebrates that inhabit the rocky intertidal environments of the Northwest and Northeast Atlantic, the available information on the evolutionary history and dynamics of deep-sea benthic invertebrates in the North Atlantic remains limited (\citep{jennings_phylogeographic_2014}). Although many studies reveal interesting patterns of genetic distribution of benthic invertebrates from the deep sea (e.g. \citep{wilson_historical_1998, havermans_genetic_2013}). However, it is fundamental to better understand the origin and demography of deep Atlantic biota in order to grasp its relationship with ongoing climate change which should be considered a factor in range expansion of deep-sea fauna (\citep{jennings_phylogeographic_2014}).
+Unlike the benthic invertebrates that inhabit the rocky intertidal environments of the Northwest and Northeast Atlantic, the available information on the evolutionary history and dynamics of deep-sea benthic invertebrates in the North Atlantic remains limited \citep{jennings_phylogeographic_2014}. Although many studies reveal interesting patterns of genetic distribution of benthic invertebrates from the deep sea (e.g. \citep{wilson_historical_1998, havermans_genetic_2013}). However, it is fundamental to better understand the origin and demography of deep Atlantic biota in order to grasp its relationship with ongoing climate change which should be considered a factor in range expansion of deep-sea fauna \citep{jennings_phylogeographic_2014}.
 
 In the context of the current climate emergency, this study aims to undertake an in-depth analysis of the influence of extreme climatic parameters and environmental peculiarities on Cumacea (crustaceans: Peracarida). Specifically, we wish to determine whether there is a correlation between the genetic information of regions of the mitochondrial 16S rRNA gene of Cumacea species sampled and the physical characteristics of their habitats. Our approach includes a comparative study to validate different phylogeographic models by comparing them with environmental factors found in the waters of the North Atlantic seas around Iceland. Additionally, we will update a Python package (in beta) to facilitate these complex analyses.
 
 \section{Related Works}\label{related-works}
-Many studies have investigated the relationship between genetics and the climatic conditions of their study region, showing how organisms acclimatize to their environnement over time. These studies have provided a better understanding of how organisms adapt to their habitat and evolve in it over time (\citep{fc_genomic_2012}). They have also helped develop conservation plans to maintain biodiversity and protect endangered species by designing how populations are adapted to their environment (\citep{balkenhol_identifying_2009}).
+Many studies have investigated the relationship between genetics and the climatic conditions of their study region, showing how organisms acclimatize to their environnement over time. These studies have provided a better understanding of how organisms adapt to their habitat and evolve in it over time (\citep{fc_genomic_2012}). They have also helped develop conservation plans to maintain biodiversity and protect endangered species by designing how populations are adapted to their environment \citep{balkenhol_identifying_2009}.
 
-\citep{koshkarov_phylogeography_2022} proposed a phylogeographic approach based on an algorithm called aPhyloGeo to study the correlation between Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants and their geographical characteristics. More recently, \citep{li_aphylogeo-covid_2023} have developed an interactive platform called aPhyloGeo-Covid to facilitate these analyses.  We elaborate on the aPhyloGeo software as well as its use in this study later in this article.
+\cite{koshkarov_phylogeography_2022} proposed a phylogeographic approach based on an algorithm called aPhyloGeo to study the correlation between Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants and their geographical characteristics. More recently, \cite{li_aphylogeo-covid_2023} have developed an interactive platform called aPhyloGeo-Covid to facilitate these analyses.  We elaborate on the aPhyloGeo software as well as its use in this study later in this article.
 
-The correlation between genetics and environmental parameters has been confirmed in studies of a variety of organisms, supporting the influence of habitat characteristics on genetic diversity (\citep{colosimo_widespread_2005}, \citep{cheviron_genomic_2012}). A study by \citep{ghalambor_adaptive_2007} has demonstrated that habitat characteristics, such as water temperature, can affect the genetics of guppy populations (\emph{Poecilla reticulata}) by shaping their phenotypic plasticity as well as by promoting rapid genetic adaptation. \citep{cheviron_genomic_2012} also concluded that there was a correlation between vertebrate genetics and habitat properties, particularly in extreme environments such as high altitudes. This correlation between genetics and environmental characteristics was also supported by the results of studies of Threespine Sticklebacks (\citep{colosimo_widespread_2005}). Those results are to be expected considering that species acclimatization to climate change is often the result of the interaction between genetic variation among populations and selection pressures caused by environmental changes (\citep{hoffmann_climate_2011}).
+The correlation between genetics and environmental parameters has been confirmed in studies of a variety of organisms, supporting the influence of habitat characteristics on genetic diversity (\citep{colosimo_widespread_2005}, \citep{cheviron_genomic_2012}). A study by \citep{ghalambor_adaptive_2007} has demonstrated that habitat characteristics, such as water temperature, can affect the genetics of guppy populations (\emph{Poecilla reticulata}) by shaping their phenotypic plasticity as well as by promoting rapid genetic adaptation. \citep{cheviron_genomic_2012} also concluded that there was a correlation between vertebrate genetics and habitat properties, particularly in extreme environments such as high altitudes. This correlation between genetics and environmental characteristics was also supported by the results of studies of Threespine Sticklebacks \citep{colosimo_widespread_2005}. Those results are to be expected considering that species acclimatization to climate change is often the result of the interaction between genetic variation among populations and selection pressures caused by environmental changes \citep{hoffmann_climate_2011}.
 
-However, studies have highlighted the complexity of the relationships between genetics and the environment that can be influenced by many factors such as genotype-environment interaction and natural selection. This can make it difficult to identify unambiguous causal relationships between these two parameters (\citep{balkenhol_identifying_2009}). Other studies mention that it is difficult to distinguish between the direct and indirect effects of the environment on genetics (\citep{manel_perspectives_2010, balkenhol_landscape_2019}). Studies of the effect of the environment on the genetics of organisms may be limited by the methods available to measure genetic and environmental characteristics, as well as by logistical constraints related to data collection and generation (\citep{manel_perspectives_2010, shafer_widespread_2013}). To our knowledge, this last point must contribute in particular to the fact that research on the environment and genetics of Cumacea is little explored, but they remain importants for understanding how these organisms adapt to fluctuating environmental conditions. 
+However, studies have highlighted the complexity of the relationships between genetics and the environment that can be influenced by many factors such as genotype-environment interaction and natural selection. This can make it difficult to identify unambiguous causal relationships between these two parameters \citep{balkenhol_identifying_2009}. Other studies mention that it is difficult to distinguish between the direct and indirect effects of the environment on genetics \citep{manel_perspectives_2010, balkenhol_landscape_2019}. Studies of the effect of the environment on the genetics of organisms may be limited by the methods available to measure genetic and environmental characteristics, as well as by logistical constraints related to data collection and generation \citep{manel_perspectives_2010, shafer_widespread_2013}. To our knowledge, this last point must contribute in particular to the fact that research on the environment and genetics of Cumacea is little explored, but they remain importants for understanding how these organisms adapt to fluctuating environmental conditions. 
 
 As stipulated in hypothesis of Darwin, individuals best adapted to their environment are likely to survive, reproduce and evolve. The objective of this study is to deepen and strengthen the natural selection hypothesis by examining whether there are one or more locations within DNA sequence of Cumacea of the mitochondrial 16S rRNA gene that could correlate not only the portions of the sequence (windows), but the Cumacea to their environment.
 
 \section{Materials and Methods}\label{materials-methods}
 
 \subsection{Description of the data}
-The study area is located in a northern area of the North Atlantic, including the Icelandic Sea, the Denmark Strait, and the Norwegian Sea. The specimens included in this study were collected during the IceAGE project (Icelandic marine Animals: Genetic and Ecology; Cruise ship M85/3 in 2011; \citep{brix_iceage_2014}) that explored the deep continental slopes and abyssal waters around Iceland (\citep{meisner_prefacebiodiversity_2018}). The sampling period for the specimens included in this study is from August 30 to September 22, 2011, and they were collected in a depth range of 316-2568 m. A description of the sampling plan, sample processing, the steps of DNA extraction, PCR amplification and sequencing, as well as the extracted and aligned DNA sequences, are available in the article by (\citep{uhlir_adding_2021}).
+The study area is located in a northern area of the North Atlantic, including the Icelandic Sea, the Denmark Strait, and the Norwegian Sea. The specimens included in this study were collected during the IceAGE project (Icelandic marine Animals: Genetic and Ecology; Cruise ship M85/3 in 2011; \citep{brix_iceage_2014}) that explored the deep continental slopes and abyssal waters around Iceland \citep{meisner_prefacebiodiversity_2018}. The sampling period for the specimens included in this study is from August 30 to September 22, 2011, and they were collected in a depth range of 316-2568 m. A description of the sampling plan, sample processing, the steps of DNA extraction, PCR amplification and sequencing, as well as the extracted and aligned DNA sequences, are available in the article by (\citep{uhlir_adding_2021}).
 
 \subsection{Data pre-processing}
-We considered data from the IceAGE project as well as the derived data from the BOLD Systems database, both of which are available via the article by (\citep{uhlir_adding_2021}). Given the large scope of attributes from these databases, we made a succinct selection of the number of attributes and samples across them. Thus, we omitted attributes that were not relevant to the context of this study, that were completely or nearly invariable (non-numerical data) as well as those that had abundant missing data (> 95\%). We considered 62 specimens of the dataset available (495) from the IceAGE project.
+We considered data from the IceAGE project as well as the derived data from the BOLD Systems database, both of which are available via the article by \citep{uhlir_adding_2021}. Given the large scope of attributes from these databases, we made a succinct selection of the number of attributes and samples across them. Thus, we omitted attributes that were not relevant to the context of this study, that were completely or nearly invariable (non-numerical data) as well as those that had abundant missing data (> 95\%). We considered 62 specimens of the dataset available (495) from the IceAGE project.
 
 Subsequently, we calculated the variance for each of the selected numeric attributes in order to eliminate those with zero or low variance (cut-off ≥ 0.1):