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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Conserv. Sci.</journal-id>
<journal-title>Frontiers in Conservation Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Conserv. Sci.</abbrev-journal-title>
<issn pub-type="epub">2673-611X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fcosc.2023.1118418</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Conservation Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Evaluating simple measures of spatial-temporal overlap as a proxy for encounter risk between a protected species and commercial fishery</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Hatch</surname>
<given-names>Joshua M.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>*</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2128076"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Murray</surname>
<given-names>Kimberly T.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1530585"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Patel</surname>
<given-names>Samir</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/352920"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Smolowitz</surname>
<given-names>Ronald</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Haas</surname>
<given-names>Heather L.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/385180"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>National Oceanic and Atmospheric Administration (NOAA) National Marine Fisheries Service, Northeast Fisheries Science Center (NEFSC)</institution>, <addr-line>Woods Hole, MA</addr-line>, <country>United States</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Coonamessett Farm Foundation</institution>, <addr-line>East Falmouth, MA</addr-line>, <country>United States</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>Edited by: Kristen Marie Hart, United States Department of the Interior, United States</p>
</fn>
<fn fn-type="edited-by">
<p>Reviewed by: Kelsey Roberts, Louisiana State University, United States; Allison M. Benscoter, United States Department of the Interior, United States</p>
</fn>
<fn fn-type="corresp" id="fn001">
<p>*Correspondence: Joshua M. Hatch, <email xlink:href="mailto:joshua.hatch@noaa.gov">joshua.hatch@noaa.gov</email>
</p>
</fn>
<fn fn-type="other" id="fn002">
<p>This article was submitted to Human-Wildlife Interactions, a section of the journal Frontiers in Conservation Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>29</day>
<month>03</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>4</volume>
<elocation-id>1118418</elocation-id>
<history>
<date date-type="received">
<day>07</day>
<month>12</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>02</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Hatch, Murray, Patel, Smolowitz and Haas</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Hatch, Murray, Patel, Smolowitz and Haas</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Spatial and temporal assessments of overlap are becoming increasingly popular as indicators of encounter risk. The overlap in distributions between protected species and commercial fishing effort is of interest for reducing bycatch. We explored overlap between the U.S. Atlantic sea scallop fishery and loggerhead turtles (<italic>Caretta caretta</italic>) using 2 metrics, and we assessed the ability of one of those metrics to track estimated fishery interactions over time. Moderate overlap occurred between June - September; mild overlap in the spring (May) and fall (October - November); and relatively little overlap from December to April. Qualitatively, there appeared to be some correspondence between the overlap values averaged across months for each calendar year and published annual loggerhead interaction estimates with fisheries, but the predictive performance of the overlap metric was low. When data on the relative distributions of commercial fishing effort and protected species are available, simple measures of spatial and temporal overlap can provide a quick and cost-effective way to identify when and where bycatch is likely to occur. In this case study, however, overlap was limited in helping to understand the relative susceptibility of protected species to commercial fishing (i.e., magnitude of interactions). We therefore caution against using overlap as a meaningful predictor of absolute risk unless there is direct evidence to suggest a relationship.</p>
</abstract>
<kwd-group>
<kwd>
<italic>Caretta caretta</italic>
</kwd>
<kwd>loggerhead turtles</kwd>
<kwd>overlap</kwd>
<kwd>U.S. Atlantic sea scallop fishery</kwd>
<kwd>interactions</kwd>
</kwd-group>
<counts>
<fig-count count="5"/>
<table-count count="0"/>
<equation-count count="7"/>
<ref-count count="55"/>
<page-count count="10"/>
<word-count count="4563"/>
</counts>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<title>Introduction</title>
<p>Spatial and temporal assessments of overlap are becoming increasingly popular as indicators of encounter risk (i.e., relative risk of interaction) between protected species and human activities. <xref ref-type="bibr" rid="B2">Bedri&#xf1;ana-Romano et&#xa0;al. (2021)</xref> identified priority areas for blue whale conservation by exploring overlap between the whales&#x2019; critical habitat and vessel traffic. <xref ref-type="bibr" rid="B3">Best and Halpin (2019)</xref> quantified tradeoffs in site selection and timing of offshore wind energy development by exploring overlap between the industry&#x2019;s profitability and sensitivities of several seabird and cetacean species. Numerous studies have explored the overlap between protected species&#x2019; distributions and commercial fishing to help inform discussions on bycatch mitigation (<xref ref-type="bibr" rid="B10">Cronin et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B20">Hatch et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B50">Stepanuk et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B1">Baird et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B35">Murray et&#xa0;al., 2021</xref>) and to prevent seasonal area closures (<xref ref-type="bibr" rid="B27">Howell et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B26">Howell et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B12">Eguchi et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B21">Hazen et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B37">Myers and Moore, 2020</xref>).</p>
<p>Fisheries bycatch is often cited as a major source of mortality for protected species in the marine environment (<xref ref-type="bibr" rid="B45">Read et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B30">Lewison et&#xa0;al., 2009</xref>; <xref ref-type="bibr" rid="B52">Wallace et&#xa0;al., 2010</xref>) because many protected species exhibit life-history traits (e.g., long-lived, delayed sexual maturity) that make them particularly vulnerable (<xref ref-type="bibr" rid="B11">Crouse et&#xa0;al., 1987</xref>; <xref ref-type="bibr" rid="B23">Heppell et&#xa0;al., 1999</xref>; <xref ref-type="bibr" rid="B22">Heppell et&#xa0;al., 2000</xref>; <xref ref-type="bibr" rid="B15">Fujiwara and Caswell, 2001</xref>; <xref ref-type="bibr" rid="B24">Heppell et&#xa0;al., 2005</xref>, <xref ref-type="bibr" rid="B39">Niel and Lebreton, 2005</xref>, <xref ref-type="bibr" rid="B18">Gray and Kennelly, 2018</xref>; <xref ref-type="bibr" rid="B19">Hatch et&#xa0;al., 2019</xref>). Minimizing fisheries-related mortality and morbidity, then, can better position threatened populations to recover (<xref ref-type="bibr" rid="B29">Lewison et&#xa0;al., 2004</xref>; <xref ref-type="bibr" rid="B53">Warden et&#xa0;al., 2015</xref>). Interactions between fisheries and protected species can also pose an economic cost to fishers, possibly leading to depredation of catch (<xref ref-type="bibr" rid="B51">Tixier et&#xa0;al., 2021</xref>), damage to fishing gear (<xref ref-type="bibr" rid="B43">Panagopoulou et&#xa0;al., 2017</xref>), and loss of fishing opportunities through time-area closures or reductions in fishing effort if bycatch limits are exceeded (<xref ref-type="bibr" rid="B21">Hazen et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B37">Myers and Moore, 2020</xref>). Here, interaction refers to any direct or close contact between protected species and fishing gear, whereas bycatch refers to a subset of interactions that result in serious injury or mortality.</p>
<p>Mitigating bycatch of protected species often revolves around issues of when and where animals occur and how they interact with commercial fishing gear (<xref ref-type="bibr" rid="B47">Senko et&#xa0;al., 2014</xref>). This where, when, and how approach is often associated with implementing gear modifications and time-area closures as preferred management strategies to reduce fisheries bycatch. The U.S. Atlantic sea scallop fishery is an important commercial fishery (<xref ref-type="bibr" rid="B40">NMFS, 2021</xref>) that primarily extends from Georges Bank to the Mid-Atlantic and overlaps with the distribution of threatened loggerhead sea turtles requiring vessels to use gear modifications aimed at minimizing sea turtle bycatch. Those gear modifications have had an apparent conservation benefit (<xref ref-type="bibr" rid="B48">Smolowitz et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B49">Smolowitz et&#xa0;al., 2012</xref>), with reductions in serious injury and mortality rates of sea turtles since their implementation (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>). However, those same gear modifications complicate bycatch monitoring and increase interest in alternative monitoring approaches such as using overlap metrics as a proxy for encounter risk.</p>
<p>Assessing susceptibility of protected species to commercial fishing can be complicated, as most threatened populations are data-limited. Attributes that define a species susceptibility to fishing are often classified into four ordinal categories (<xref ref-type="bibr" rid="B25">Hobday et&#xa0;al., 2011</xref>): overlap (in geographic space [hereafter referred to as space] and time), encounterability (depth usage, given overlap), selectivity (caught and retained by the fishing gear, given overlap and encounterability), and post-interaction mortality (death, given overlap, encounterability, and selectivity). Ideally, each of these parameters should be quantified before defining a species&#x2019; risk to fishing activities (i.e., bycatch). But quantifying each of those attributes is difficult when available data are sparse, as is the case for most threatened populations. Using simple measures of spatial-temporal overlap may be useful (<xref ref-type="bibr" rid="B27">Howell et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B26">Howell et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B10">Cronin et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B20">Hatch et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B12">Eguchi et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B21">Hazen et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B50">Stepanuk et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B1">Baird et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B35">Murray et&#xa0;al., 2021</xref>), especially if the other attributes of susceptibility can be simplified or assumed known. For example, assuming high encounterability may be reasonable if turtles are known to be predominately benthic in a certain time and area that overlaps with bottom fishing.</p>
<p>Here, we explore the spatial and temporal overlap between the U.S. Atlantic sea scallop fishery and loggerhead turtles (<italic>Caretta caretta</italic>) using 2 overlap metrics (i.e., Bhattacharyya&#x2019;s coefficient and the Morisita-Horn index), and we assessed the ability of one of those metrics to track estimated interactions over time. We characterized the spatial and temporal distributions of loggerhead turtles using satellite tag data (<xref ref-type="bibr" rid="B55">Winton et&#xa0;al., 2018</xref>) and the U.S. Atlantic sea scallop fishery using data from the Vessel Monitoring System (VMS). The characterized distributions were combined to develop a time series of overlap measures that spanned roughly 18 years (i.e., 2003 - 2020). We then extracted estimates of fishery interactions from published reports over the same time frame and examined the relationship between overlap and interactions. We decided to focus on loggerhead turtles because they broadly overlap with the U.S. Atlantic sea scallop fishery where fisheries bycatch of marine turtles has historically been a conservation issue.</p>
</sec>
<sec id="s2" sec-type="materials|methods">
<title>Materials and methods</title>
<sec id="s2_1">
<title>Data</title>
<sec id="s2_1_1">
<title>Commercial fishing effort</title>
<p>Under current regulations (<xref ref-type="bibr" rid="B14">FR, 2021</xref>), commercial fishing vessels are required to submit electronic Vessel Trip Reports (VTRs) after each fishing trip documenting a variety of trip-level characteristics (e.g., a single location where most fishing occurred, gear fished, quantity of gear fished, etc.). Starting in 1998, to provide better resolution of fishing locations, vessel monitoring systems (VMS) were mandated for vessels fishing under limited-access permits<xref ref-type="fn" rid="fn1">
<sup>1</sup>
</xref> in the U.S. Atlantic sea scallop fishery. The VMS program was subsequently expanded in following years to cover more vessels and fleets, and can be considered a near census of locations for those vessels equipped with VMS (which now constitutes most vessels in the U.S. Atlantic sea scallop fishery).</p>
<p>We measured the spatial footprint of the U.S. Atlantic sea scallop fishery using data from the VMS. Fishing activity was determined using a speed rule approach, with vessel speeds between 2 and 5.5 knots being used to indicate fishing (<xref ref-type="supplementary-material" rid="SM1"><bold>Figure A1</bold></xref>). Vessels participating in the U.S. Atlantic sea scallop fishery were obliged to report positions at pre-specified intervals defined by the VMS requirement of the Fishery Management Plan (FMP), usually twice an hour with an increase in frequency if the vessel approached a closed area.</p>
<p>The VMS data for the U.S. Atlantic sea scallop fishery from fishing years 2003 - 2020 were aggregated onto a 10km &#xd7; 10km grid that spanned the Greater Atlantic Region (GAR). As part of the gridding process, VMS spatial coordinates were re-projected into an oblique Mercator projection with a central line that roughly coincided with the long axis of the U.S. Atlantic coast. The gridding process involved determining how much time was spent in each grid cell by a vessel transiting between 2 VMS polls. To do this, we assumed the vessel was transiting at a constant speed and in a straight line between polls, with the time spent in a grid cell being proportional to the distance traveled in that grid cell relative to the total distance fished. For example, if a vessel had 2 VMS polls an hour apart and traveled 4km during that time, with 1km in grid cell 1 and 3km in grid cell 2, then &#xbc; of an hour would be allocated to grid cell 1 and &#xbe; of an hour would be allocated to grid cell 2. The VMS data were then aggregated by month to produce monthly composites of commercial fishing effort (i.e., hours fished) for the U.S. Atlantic sea scallop fishery.</p>
<p>Temporal trends in commercial fishing effort (i.e., hours fished) were explored using a Bayesian generalized additive mixed model to partition out the seasonal and relatively, long-term signals (<xref ref-type="bibr" rid="B5">B&#xfc;rkner, 2017</xref>; <xref ref-type="bibr" rid="B6">B&#xfc;rkner, 2018</xref>). Hours fished (<italic>y<sub>t</sub>
</italic>) were summed by month for FYs 2003 - 2020 and were indexed by month (<italic>x<sub>t,1</sub>
</italic>) and the number of months that elapsed since the beginning of the time series (<italic>x<sub>t,2</sub>
</italic>). The mixed model can then be written as,</p>
<disp-formula>
<mml:math display="block" id="M1">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>=</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>+</mml:mo>
<mml:msub>
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<mml:mrow>
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<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
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<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mrow>
<mml:mi>t</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>+</mml:mo>
<mml:msub>
<mml:mi>&#x3f5;</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>&#x3f5;</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x223c;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mtext mathvariant="italic">Normal</mml:mtext>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mtext>&#x39b;</mml:mtext>
<mml:msup>
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<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<p>Here, <italic>t</italic> refers to a date (e.g., March, FY 2003). The correlation matrix, &#x39b;, was chosen to reflect a first-order autoregressive process (i.e., AR(1)) grouped by FY. Effectively, the mixed model is detrending the data and then applying an AR(1) process to the residuals. Flat priors were placed on all coefficients (except the intercept) and the correlation parameter, while Student-<italic>t</italic> priors were placed on the intercept and truncated Student-<italic>t</italic> priors were placed on the standard deviations. We used a posterior predictive check to compare simulations from the fitted model and the observed data to assess model adequacy.</p>
</sec>
<sec id="s2_1_2">
<title>Loggerhead turtle distribution</title>
<p>Predicted monthly densities of tagged loggerhead turtles from <xref ref-type="bibr" rid="B55">Winton et&#xa0;al. (2018)</xref> were modified using cubic convolution from a 40&#xa0;km to 10&#xa0;km spatial resolution to match the gridded VMS data (<xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>). Briefly, <xref ref-type="bibr" rid="B55">Winton et&#xa0;al. (2018)</xref> predicted the monthly densities of aggregated daily locations with a space-time geostatistical mixed effects model using satellite data from 271 large juvenile and adult loggerhead turtles tagged in the northwest Atlantic between 2004 and 2016. Turtle satellite tracks were reconstructed using a continuous time correlated random walk movement model to account for satellite location error; reconstructed tracks were then interpolated to a daily time step to account for irregular transmissions (see <xref ref-type="bibr" rid="B55">Winton et&#xa0;al., 2018</xref> for more details).</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>Logged relative densities of tagged loggerhead locations from 2004 &#x2013; 2016 modified from <xref ref-type="bibr" rid="B55">Winton et&#xa0;al. (2018)</xref> upsampled to a 10km &#xd7; 10km grid using cubic convolution. The Georges Bank (GB) and Mid-Atlantic (MAB) regions are outlined and labeled on the first panel (<xref ref-type="bibr" rid="B38">NEFSC, 2021</xref>).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fcosc-04-1118418-g001.tif"/>
</fig>
</sec>
</sec>
<sec id="s2_2">
<title>Overlap metrics</title>
<p>Two commonly cited overlap metrics were explored to better understand the intersection between the distribution of loggerhead sea turtles and the U.S. Atlantic sea scallop fishery. The first overlap metric is Bhattacharyya&#x2019;s coefficient (Bc; <xref ref-type="bibr" rid="B4">Bhattacharyya, 1943</xref>) defined as:</p>
<disp-formula>
<mml:math display="block" id="M2">
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mi>c</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
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</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <bold>
<italic>p<sub>1</sub>
</italic>
</bold> and <bold>
<italic>p<sub>2</sub>
</italic>
</bold> are the normalized vectors of commercial fishing effort and tagged loggerhead turtle densities, respectively, and <italic>i</italic> refers to the grid cell. The second overlap metric is the Morisita-Horn (MH) index, which has been used previously to assess overlap between protected species and commercial fisheries (<xref ref-type="bibr" rid="B10">Cronin et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B35">Murray et&#xa0;al., 2021</xref>), defined as:</p>
<disp-formula>
<mml:math display="block" id="M3">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo>&#xa0;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="bold-italic">p</mml:mi>
<mml:mn mathvariant="bold">1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">p</mml:mi>
<mml:mn mathvariant="bold">2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>=</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
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<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
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</mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
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<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>+</mml:mo>
<mml:mstyle displaystyle="true">
<mml:msub>
<mml:mo>&#x2211;</mml:mo>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mrow>
<mml:msubsup>
<mml:mi>p</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
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</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msubsup>
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</mml:mstyle>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
<p>Both overlap metrics can range from 0 (no overlap) to 1 (complete overlap) and were calculated by month, the lowest temporal resolution possible. Monthly overlap metrics could then be summarized by either calendar (CY) or fishing year (FY), with the definition of a FY changing over time. Prior to 2017, a FY spanned March 1 to February 28 (or 29) of the following year. For example, FY 2016 ran from March 1, 2016 to February 28, 2017. In 2017, a FY spanned March 1 - March 31. And after 2017, a FY spanned April 1 - March 31.</p>
<p>Beyond seasonal comparisons, we focused on the Bc overlap measure because it is more robust to a higher amount of low values. We included the MH index when looking at seasonal patterns because it has been used previously (<xref ref-type="bibr" rid="B10">Cronin et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B35">Murray et&#xa0;al., 2021</xref>); however, the MH index is known to be sensitive when overlap is low for a majority of the area in a particular time (<xref ref-type="bibr" rid="B46">Rempala and Seweryn, 2013</xref>). Since the relative patterns between the 2 overlap measures were similar, we focused on the more suitable metric given our situation that included a large amount of low overlap. For years with observed interactions, we superimposed the location of the observed interactions on maps of the averaged overlap values by fishing year.</p>
</sec>
<sec id="s2_3">
<title>Estimated fishery interactions</title>
<p>We used published estimates of interactions between loggerhead turtles and the U.S. Atlantic sea scallop fishery. Loggerhead interactions in the fishery were estimated from fishery observer (vessel-based) data using Generalized Additive Models (GAMs) and stratified-ratio estimators for the following periods: 2001 - 2008 (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>); 2009 - 2014 (<xref ref-type="bibr" rid="B33">Murray, 2015</xref>); and 2015 - 2019 (<xref ref-type="bibr" rid="B34">Murray, 2021</xref>). The estimated interactions from <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref> included those that could be observed, as well as those that occurred subsurface and out of view as a result of gear modifications (see <xref ref-type="bibr" rid="B54">Warden and Murray, 2011</xref> for more details on unobservable but quantifiable fishery interactions). Those gear modifications include turtle chain mats and Turtle Deflector Dredges (TDDs) (<xref ref-type="bibr" rid="B49">Smolowitz et&#xa0;al., 2012</xref>), both of which are required when fishing west of 71&#xb0;W from May - November (<xref ref-type="bibr" rid="B13">FR, 2015</xref>). For instance, fishery observers documented 47 loggerhead turtle interactions between 2001 - 2008 (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>) at 3% sampling coverage, while the use of chain mats and turtle deflector dredges reduced the number of reported interactions to 12 between 2009 - 2015 (<xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>) at 6% sampling coverage. More details can be found in <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref>.</p>
<p>
<xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref> constrained the annual estimates of turtle interactions to the fraction of the fleet fishing in the Mid-Atlantic, where all observed loggerhead interactions occurred. The definition of the Mid-Atlantic study region, however, has changed slightly over time. <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref> defined the Mid-Atlantic as the region west of 71&#xb0;W and south of 42&#xb0;N. <xref ref-type="bibr" rid="B34">Murray (2021)</xref> defined the Mid-Atlantic region as the boundaries of the Mid-Atlantic Ecological Production Unit (EPU; <xref ref-type="bibr" rid="B38">NEFSC, 2021</xref>). We used the same definitions (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>) for the Mid-Atlantic region when comparing overlap values to the interaction estimates produced by <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref>. For 2015 and later, we also limited the overlap values to be between May and December to align with <xref ref-type="bibr" rid="B34">Murray (2021)</xref>, whereas the full calendar year was considered prior to 2015 (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>).</p>
<p>The annual estimated fishery interactions (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>) were then related to the mean annual overlap values using a Bayesian regression model. The published, estimated fishery interactions were summarized on an annual basis preventing monthly comparisons (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>). Monthly overlap values were then averaged across a calendar year to compare with the estimated interactions. The Bayesian regression model took the form,</p>
<disp-formula>
<mml:math display="block" id="M4">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x223c;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>N</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>m</mml:mi>
<mml:mi>a</mml:mi>
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</disp-formula>
<disp-formula>
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<mml:mrow>
<mml:mtext>log</mml:mtext>
<mml:mrow>
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<mml:mn>0</mml:mn>
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<mml:msub>
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<mml:mn>1</mml:mn>
</mml:msub>
<mml:msub>
<mml:mi>x</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula>
<mml:math display="block" id="M6">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>0</mml:mn>
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<mml:mo>&#xa0;</mml:mo>
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<mml:mn>3</mml:mn>
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<mml:mo>&#xa0;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<disp-formula>
<mml:math display="block" id="M7">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
<mml:mo>&#x223c;</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mtext mathvariant="italic">Student&#x2013;</mml:mtext><mml:mi>t</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>3</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#xa0;</mml:mo>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
<p>where <italic>y<sub>i</sub>
</italic> refers to the interaction estimate in calendar year <italic>i</italic>, <italic>x<sub>i</sub>
</italic> refers to the mean annual overlap value, <italic>&#x3b2;</italic>
<sub>0</sub> is the intercept, <italic>&#x3b2;</italic>
<sub>1</sub> is the slope, and <italic>&#x3c3;<sub>i</sub>
</italic> is the standard error for the interaction estimate. A log link was used to ensure the predictions were non-negative, as interaction estimates cannot be less than 0. The Bayesian model was structured to include the known errors of the estimated interactions into the regression, thereby ensuring propagation of uncertainty. We used Bayesian <italic>R<sup>2</sup>
</italic> as a measure of predictive performance, which is a convenient summary statistic that ranges from 0 (no predictive performance) to 1 (perfect predictive performance).</p>
</sec>
</sec>
<sec id="s3" sec-type="results">
<title>Results</title>
<sec id="s3_1">
<title>Commercial fishing effort</title>
<p>According to VMS data, the hours fished in the U.S. Atlantic sea scallop fishery has declined steadily since 2003 (see <xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>), with an average decrease of roughly 61 hours fished per month over the 18-year time period. We also see a regional shift in commercial fishing, with the Mid-Atlantic comprising a smaller portion of effort in recent years (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>). The decline in commercial fishing effort, coupled with relatively high landings (<xref ref-type="bibr" rid="B41">NOAA Fisheries, 2023</xref>), suggests the footprint of the fishery is retracting. Seasonally, most commercial fishing occurred between May and June (<xref ref-type="fig" rid="f2">
<bold>Figure&#xa0;2</bold>
</xref>). The autocorrelation parameter was estimated to be 0.65 (95% CI: 0.54 - 0.77), suggesting moderate residual autocorrelation about the fitted trend.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>Proportion of commercial fishing effort for the U.S. Atlantic sea scallop fishery from VMS data for fishing years 2003 to 2020 found in the Mid-Atlantic and Georges Bank regions (<xref ref-type="bibr" rid="B38">NEFSC, 2021</xref>); hours fished by date (month, year) for the U.S. Atlantic sea scallop fishery from VMS data for fishing years 2003 to 2020 superimposed with fitted values (line) and 95% credible intervals (shaded region) from the Bayesian generalized additive mixed model (GAMM); smooths (line) for the effects of season and trend on hours fished from the Bayesian GAMM, with shaded regions representing 95% credible intervals.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fcosc-04-1118418-g002.tif"/>
</fig>
</sec>
<sec id="s3_2">
<title>Loggerhead turtle distribution</title>
<p>The relative densities of tagged loggerhead turtles were highest along the continental shelf, with lower densities farther offshore (<xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>). There was also an apparent seasonal shift in relative densities, reflecting the highly migratory behavior of loggerhead turtles (<xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>). This migration was characterized by northward movements into the GAR from March - May, followed by southward movements out of the GAR from October - December as loggerhead turtles search for overwintering areas off the coast of North Carolina or farther south (<xref ref-type="fig" rid="f1">
<bold>Figure&#xa0;1</bold>
</xref>). More details can be found in <xref ref-type="bibr" rid="B55">Winton et&#xa0;al. (2018)</xref>.</p>
</sec>
<sec id="s3_3">
<title>Overlap metrics</title>
<p>Looking at the average value by month, we see similar seasonal patterns for both overlap metrics (<xref ref-type="fig" rid="f3">
<bold>Figure&#xa0;3</bold>
</xref>). Qualitatively, we see moderate overlap between June - September, with high overlap occurring in August. Mild overlap occurred during the spring (May) and fall (October - November) migrations, as loggerhead turtles enter and leave the GAR respectively. For the rest of the year, from December to April, we see relatively little overlap between loggerhead turtle distribution and the U.S. Atlantic sea scallop fishery. Observed interactions occurred mostly in areas where the averaged overlap values were relatively higher (<xref ref-type="fig" rid="f4">
<bold>Figures&#xa0;4</bold>
</xref>, <xref ref-type="supplementary-material" rid="SM1">
<bold>C1</bold>
</xref>), with observer coverage that ranged between 2 - 6% (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>).</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>Monthly values of the overlap metrics for each calendar year (light grey dots and lines). Superimposed on the overlap metrics is the average value (black dots and lines). Horizontal bars define the seasonal range of observed loggerhead bycatch occurrence as documented by <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fcosc-04-1118418-g003.tif"/>
</fig>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>Maps of averaged overlap values across months by fishing year (FY) for years where observed interactions occurred. Superimposed, as black dots, are the corresponding observed interaction locations between loggerhead turtles and the U.S. Atlantic sea scallop fishery. The black, contour line corresponds to the lowest value of the averaged overlap metric associated with an observed location of loggerhead turtle interaction across all years. The observer coverage (Obs. Cov.) for the corresponding calendar year is listed in the lower, right-hand corner of the maps and were extracted from <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fcosc-04-1118418-g004.tif"/>
</fig>
</sec>
<sec id="s3_4">
<title>Estimated fishery interactions</title>
<p>Estimated interactions between loggerhead turtles and the U.S. Atlantic sea scallop fishery were relatively high until 2006, which coincides with the implementation of chain mats. Fishery interactions remained fairly low from 2006 until 2015, with a small potential uptick in 2009 - 2010. Between 2015 - 2019 we again find relatively high estimated fishery interactions (<xref ref-type="bibr" rid="B34">Murray, 2021</xref>; <xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5</bold>
</xref>).</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>Time series of overlap values averaged across months by calendar year, with grey = entire region and black = Mid-Atlantic region as defined by <xref ref-type="bibr" rid="B32">Murray (2011)</xref>; <xref ref-type="bibr" rid="B33">Murray (2015)</xref>; <xref ref-type="bibr" rid="B34">Murray (2021)</xref>, and published annual interaction estimates for loggerhead turtles in the U.S. Atlantic sea scallop dredge fishery. Years when gear modifications were implemented are noted, with chain mats being implemented since September 2006 and Turtle Deflector Dredges being implemented since May 2013. Both gear modifications are required when fishing for sea scallops between May and November in U.S. waters west of 71&#xb0;W.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fcosc-04-1118418-g005.tif"/>
</fig>
<p>Qualitatively, there appears to be some correspondence between the overlap values averaged across months for each calendar year and published annual interaction estimates (<xref ref-type="fig" rid="f5">
<bold>Figure&#xa0;5</bold>
</xref>). This correspondence was further explored by regressing the annual estimated interactions against the averaged overlap values, accounting for the known errors of the interaction estimates (<xref ref-type="supplementary-material" rid="SM1">
<bold>Appendix B</bold>
</xref>) using a Bayesian approach. Inspection of posterior density plots, trace plots, and <inline-formula>
<mml:math display="inline" id="im1">
<mml:mover accent="true">
<mml:mi>R</mml:mi>
<mml:mo>^</mml:mo>
</mml:mover>
</mml:math>
</inline-formula> values suggested convergence of the Bayesian estimator. The estimated slope from the Bayesian regression model was significantly different from 0, with strong evidence in favor of the estimated slope being non-zero using Bayes factors (BF &#x22d9; 1; <xref ref-type="supplementary-material" rid="SM1"><bold>Figure B1</bold></xref>). The <italic>R<sup>2</sup>
</italic> for the Bayesian regression model was 0.296 (95% CI [0.226, 0.366]; <xref ref-type="bibr" rid="B16">Gelman et&#xa0;al., 2019</xref>), indicating relatively low predictive performance.</p>
</sec>
</sec>
<sec id="s4" sec-type="discussion">
<title>Discussion</title>
<p>While higher degrees of overlap were associated with more estimated interactions between loggerhead turtles and the U.S. Atlantic sea scallop fishery, we would not characterize that relationship as strong. The overlap between distributions of loggerhead turtles and the U.S. sea scallop fishery poorly reflected the estimated number of interactions (<italic>R<sup>2</sup>
</italic> = 0.296), yet the times and areas of higher risk aligned well with patterns in observed bycatch (<xref ref-type="fig" rid="f3">
<bold>Figures&#xa0;3</bold>
</xref>, <xref ref-type="fig" rid="f4">
<bold>4</bold>
</xref>, <xref ref-type="supplementary-material" rid="SM1">
<bold>C1</bold>
</xref>). This suggests that while overlap does not encode enough information to be indicative of the magnitude of interactions, it may still be a good indicator of when and where interactions are likely to occur. With overlap in space and time being a relatively limited measure of encounter risk and probability of interaction (<xref ref-type="bibr" rid="B36">Murua et&#xa0;al., 2021</xref>, as well as this case), further refinements would be necessary to use overlap as a measure of absolute risk between turtles and U.S. commercial fisheries (<xref ref-type="bibr" rid="B25">Hobday et&#xa0;al., 2011</xref>).</p>
<p>We might expect that overlap metrics and interaction estimates would correlate given their direct linkages to commercial fishing effort. Interaction estimates are produced by expanding observed bycatch rates to the entire fleet using fishing effort, most of which is not observed. The overlap metrics cited in this paper, by definition, include the relative intensity of fishing effort over space and time. While the data sources used to define commercial fishing effort differ between the two (VMS for overlap and VTR for interaction estimates), they should conceivably be tracking similar patterns. So it is not surprising that overlap and interactions would associate, at least to some degree. But the low <italic>R<sup>2</sup>
</italic> value suggests poor predictive performance in the ability of overlap to predict interactions, at least in our case, again reinforcing the complexity of the fine-scale dynamics that produce bycatch and the inability of simple overlap measures to capture that complexity (<xref ref-type="bibr" rid="B25">Hobday et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B36">Murua et&#xa0;al., 2021</xref>), as well as potential data issues that could influence the comparison between the two (discussed in more detail below).</p>
<p>Fisheries bycatch is the culmination of a complicated process that starts with overlap in space and time and ends with incidental mortality (<xref ref-type="bibr" rid="B25">Hobday et&#xa0;al., 2011</xref>). The progression through this complicated process may ultimately determine the strength of association between overlap and interaction. For example, scallop vessels can dredge around the clock and turtles are known to have diel patterns in behavior (<xref ref-type="bibr" rid="B42">Ogden et&#xa0;al., 1983</xref>; <xref ref-type="bibr" rid="B28">James et&#xa0;al., 2006</xref>; <xref ref-type="bibr" rid="B7">Casey et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B9">Christiansen et&#xa0;al., 2017</xref>). This context-dependent behavior may influence encounterability and hence the potential for a dredge to catch a turtle during daytime vs. nighttime operations. Overlap and gear selectivity, then, may be high in this example, but encounterability would vary depending on the time of day resulting in a continuum of encounter risk. This shows the multifaceted nature of interactions and the processes leading up to them, and it illustrates a need to better understand what variables could influence risk (e.g., animal behavior and abundance, fishery characteristics, spatial and temporal scale and extent, etc.) using a more integrated approach (<xref ref-type="bibr" rid="B17">Gilman et&#xa0;al., 2019</xref>).</p>
<p>The veracity, quality, and comprehensiveness of data are other sources of uncertainty in the comparison between overlap and interactions. First, both of the derived data products (commercial fishing effort and loggerhead turtle distribution) used in the overlap calculations have their limitations. The VMS data does not capture the type (net or dredge) or number of gear (1 or 2) used by a vessel and may not be compatible with the measure of commercial fishing effort used to estimate interactions derived from self-reported VTRs (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>). Similarly, a simple speed-rule approach was used to define fishing activity from the VMS polls for convenience, but there are other methods (<xref ref-type="bibr" rid="B31">Muench et&#xa0;al., 2018</xref>). In addition, the relative distribution of loggerhead turtles is based on a limited number of satellite-tagged animals compared to their population size (<xref ref-type="bibr" rid="B55">Winton et&#xa0;al., 2018</xref>) and assumed to be static over the 18-year study period; yet climate change may affect turtle distribution (<xref ref-type="bibr" rid="B44">Patel et&#xa0;al., 2021</xref>), especially in what appears to be a period of slow (or no) recovery for this threatened population (<xref ref-type="bibr" rid="B8">Ceriani et&#xa0;al., 2019</xref>). Second, the limited number of observed interactions has led to high uncertainty in the estimates and has prompted the adoption of different analytical methods for different time periods, possibly resulting in an inconsistent time series (<xref ref-type="bibr" rid="B32">Murray, 2011</xref>; <xref ref-type="bibr" rid="B33">Murray, 2015</xref>; <xref ref-type="bibr" rid="B34">Murray, 2021</xref>).</p>
<p>The ability of overlap to capture some of the observed patterns in bycatch is promising for certain aspects of mitigation. Simple measures of overlap may be useful in determining where and when more research is needed (<xref ref-type="bibr" rid="B20">Hatch et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B35">Murray et&#xa0;al., 2021</xref>) or the targeting of observer coverage when resources are limited (<xref ref-type="bibr" rid="B1">Baird et&#xa0;al., 2021</xref>). Examples exist where simple approaches of quantifying bycatch risk using overlap have been successful at providing near real-time information to fishers (<xref ref-type="bibr" rid="B27">Howell et&#xa0;al., 2008</xref>; <xref ref-type="bibr" rid="B26">Howell et&#xa0;al., 2015</xref>). Although, as pointed out by <xref ref-type="bibr" rid="B12">Eguchi et&#xa0;al. (2017)</xref>, the success of overlap as an indicator of bycatch risk might ultimately be context-specific and depend on the complexity of the ecosystem and the amount of data available to capture that complexity through statistical modeling.</p>
<p>In summary, we found that overlap can be loosely thought of as an indicator of relative but not absolute risk. Simple measures of spatial and temporal overlap can provide a way to identify when and where bycatch is likely to occur relative to other times and areas. However, those measures may be limited in their ability to determine the probability of interaction and subsequent interaction estimates needed for fisheries management. Simple overlap studies, then, might be best suited for informing prioritization of resources in a relative sense, like focusing research in certain times and areas, providing targeted observer coverage, or initiating management discussions to delineate where and when bycatch mitigation approaches should be implemented. While overlap may contain some information about the actual risk of an interaction, we would caution against using it as a meaningful predictor of absolute risk unless there is evidence to suggest otherwise.</p>
</sec>
<sec id="s5" sec-type="data-availability">
<title>Data availability statement</title>
<p>The datasets presented in this article are not readily available because they are confidential. Requests to access the datasets should be directed to <ext-link ext-link-type="uri" xlink:href="https://www.fisheries.noaa.gov/new-england-mid-atlantic/enforcement/vessel-monitoring-contacts">https://www.fisheries.noaa.gov/new-england-mid-atlantic/enforcement/vessel-monitoring-contacts</ext-link>.</p>
</sec>
<sec id="s6" sec-type="author-contributions">
<title>Author contributions</title>
<p>JH led the conceptualization, analysis, discussion, and writing with input from all authors. All authors contributed to the article and approved the submitted version.</p>
</sec>
</body>
<back>
<sec id="s7" sec-type="funding-information">
<title>Funding</title>
<p>This study was funded in part by the National Marine Fisheries Protected Species Toolbox Initiative, the United States Department of the Interior, Bureau of Ocean Energy Management through Interagency Agreements M14PG00005, M10PG00075, and M19PG00007 with the United States Department of the Commerce, National Oceanic and Atmospheric Administration (NOAA), National Marine Fisheries Service (NMFS), Northeast Fisheries Science Center (NEFSC), and the scallop industry Sea Scallop Research Set Aside program administered by the Northeast Fisheries Science Center.</p>
</sec>
<ack>
<title>Acknowledgments</title>
<p>We thank Kristin Precoda and 2 reviewers for helpful comments on earlier versions of the manuscript. We also thank Benjamin Galuardi, Travis Ford, Michael Palmer, and Burton Shank for helpful discussions about the VMS data and the U.S. Atlantic sea scallop fishery.</p>
</ack>
<sec id="s8" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="s9" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<sec id="s10" sec-type="supplementary-material">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fcosc.2023.1118418/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fcosc.2023.1118418/full#supplementary-material</ext-link>
</p>
<supplementary-material xlink:href="DataSheet_1.docx" id="SM1" mimetype="application/vnd.openxmlformats-officedocument.wordprocessingml.document"/>
</sec>
<fn-group>
<fn id="fn1">
<label>1</label>
<p>Vessels that participated in the Days-At-Sea program that limited the number of fishing days or the Access Area program that limited the amount of harvested scallops.</p>
</fn>
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