Temporal fractals in seabird foraging behaviour: diving through the scales of time
Identifieur interne : 001858 ( Pmc/Checkpoint ); précédent : 001857; suivant : 001859Temporal fractals in seabird foraging behaviour: diving through the scales of time
Auteurs : Andrew J. J. Macintosh ; Laure Pelletier [France] ; Andre Chiaradia ; Akiko Kato [France] ; Yan Ropert-Coudert [France]Source :
- Scientific Reports [ 2045-2322 ] ; 2013.
Abstract
Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (
Url:
DOI: 10.1038/srep01884
PubMed: 23703258
PubMed Central: 3662970
Affiliations:
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PMC:3662970Le document en format XML
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<front><div type="abstract" xml:lang="en"><p>Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (<italic>Eudyptula minor</italic>
) across full-day foraging trips (2<sup>16</sup>
data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.</p>
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<pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Sci Rep</journal-id>
<journal-id journal-id-type="iso-abbrev">Sci Rep</journal-id>
<journal-title-group><journal-title>Scientific Reports</journal-title>
</journal-title-group>
<issn pub-type="epub">2045-2322</issn>
<publisher><publisher-name>Nature Publishing Group</publisher-name>
</publisher>
</journal-meta>
<article-meta><article-id pub-id-type="pmid">23703258</article-id>
<article-id pub-id-type="pmc">3662970</article-id>
<article-id pub-id-type="pii">srep01884</article-id>
<article-id pub-id-type="doi">10.1038/srep01884</article-id>
<article-categories><subj-group subj-group-type="heading"><subject>Article</subject>
</subj-group>
</article-categories>
<title-group><article-title>Temporal fractals in seabird foraging behaviour: diving through the scales of time</article-title>
</title-group>
<contrib-group><contrib contrib-type="author"><name><surname>MacIntosh</surname>
<given-names>Andrew J. J.</given-names>
</name>
<xref ref-type="corresp" rid="c1">a</xref>
<xref ref-type="aff" rid="a1">1</xref>
<xref ref-type="aff" rid="a5">5</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Pelletier</surname>
<given-names>Laure</given-names>
</name>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="aff" rid="a3">3</xref>
<xref ref-type="aff" rid="a5">5</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Chiaradia</surname>
<given-names>Andre</given-names>
</name>
<xref ref-type="aff" rid="a4">4</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Kato</surname>
<given-names>Akiko</given-names>
</name>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="aff" rid="a3">3</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Ropert-Coudert</surname>
<given-names>Yan</given-names>
</name>
<xref ref-type="aff" rid="a2">2</xref>
<xref ref-type="aff" rid="a3">3</xref>
</contrib>
<aff id="a1"><label>1</label>
<institution>Kyoto University Primate Research Institute, Center for International Collaboration and Advanced Studies in Primatology Kanrin 41-2</institution>
, Inuyama, Aichi, Japan 484-8506</aff>
<aff id="a2"><label>2</label>
<institution>Universite de Strasbourg</institution>
, IPHC, 23 rue Becquerel, 67087 Strasbourg, France</aff>
<aff id="a3"><label>3</label>
<institution>CNRS</institution>
, UMR7178, 67037 Strasbourg, France</aff>
<aff id="a4"><label>4</label>
<institution>Phillip Island Nature Parks, Research Department</institution>
, P. O. Box 97 Cowes, Victoria Australia 3922</aff>
<aff id="a5"><label>5</label>
These authors contributed equally to this work.</aff>
</contrib-group>
<author-notes><corresp id="c1"><label>a</label>
<email>macintosh.andrew.7r@kyoto-u.ac.jp</email>
</corresp>
</author-notes>
<pub-date pub-type="epub"><day>24</day>
<month>05</month>
<year>2013</year>
</pub-date>
<pub-date pub-type="collection"><year>2013</year>
</pub-date>
<volume>3</volume>
<elocation-id>1884</elocation-id>
<history><date date-type="received"><day>15</day>
<month>03</month>
<year>2013</year>
</date>
<date date-type="accepted"><day>09</day>
<month>05</month>
<year>2013</year>
</date>
</history>
<permissions><copyright-statement>Copyright © 2013, Macmillan Publishers Limited. All rights reserved</copyright-statement>
<copyright-year>2013</copyright-year>
<copyright-holder>Macmillan Publishers Limited. All rights reserved</copyright-holder>
<license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><pmc-comment>author-paid</pmc-comment>
<license-p>This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by-nc-nd/3.0/">http://creativecommons.org/licenses/by-nc-nd/3.0/</ext-link>
</license-p>
</license>
</permissions>
<abstract><p>Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (<italic>Eudyptula minor</italic>
) across full-day foraging trips (2<sup>16</sup>
data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.</p>
</abstract>
</article-meta>
</front>
<floats-group><fig id="f1"><label>Figure 1</label>
<caption><title>Correlations between diving parameters for both (a) frequency-based and (b) fractal measures.</title>
<p>Lower-left panels show correlation scatterplots while upper-right panels give Pearson's correlation coefficients along with their respective confidence intervals. Measurement types are shown diagonally between these panel blocks.</p>
</caption>
<graphic xlink:href="srep01884-f1"></graphic>
</fig>
<fig id="f2"><label>Figure 2</label>
<caption><title>Example of (a) a single little penguin female's binary foraging sequence denoted 1 for diving and −1 for lags between successive dives and (b) integrated (cumulatively summed) dive sequences from 5 different little penguin females showing variation in foraging patterns and resultant changes in <italic>α<sub>DFA</sub>
</italic>
values.</title>
<p>The bold solid line indicates the integrated dive sequence corresponding to the binary sequence shown above.</p>
</caption>
<graphic xlink:href="srep01884-f2"></graphic>
</fig>
<fig id="f3"><label>Figure 3</label>
<caption><title>Validation of scaling regions in sequences of diving behaviour from little penguins.</title>
<p>(A) The R<sup>2</sup>
– SSR procedure determines the values of log(scale) that maximize the coefficient of determination and minimize the sum of squared residuals (*), corresponding to the range of scales across which the data reflect strong scaling behaviour (filled circles shown in (B)). Note that when all scales are used (+) the coefficient of determination remains comparable to that of the best scaling region, indeed all regression fits produced R<sup>2</sup>
values greater than 0.997, but the sum of squared residuals increases dramatically. In this case, the estimates of <italic>α</italic>
<sub>DFA</sub>
for the best scaling region and the full range of scales are also comparable at 0.877 and 0.865, respectively. (C) The compensated slope procedure allows testing the effect that varying the scaling exponent has on dispersion around a “zero-slope” (solid line), the point at which the scaling exponent is a true representation of the sequence. The scaling exponent derived from the best scaling region produces values that best approximate a zero-slope (Δ), with all points examined falling within the 95% confidence intervals (dotted lines) generated by 1000 simulations of random variation around a zero-slope. Therefore, these observed sequences do exhibit fractal structure with power-law scaling behaviour, i.e. strong linearity in the log-log plot of fluctuation as a function of scale, at least across the scales outlined in (B).</p>
</caption>
<graphic xlink:href="srep01884-f3"></graphic>
</fig>
<table-wrap position="float" id="t1"><label>Table 1</label>
<caption><title>Results of linear mixed-effects models examining influence of individual traits on variation in scaling exponents from little penguin foraging sequences</title>
</caption>
<table frame="hsides" rules="groups" border="1"><colgroup><col align="left"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
</colgroup>
<thead valign="bottom"><tr><th align="left" valign="top" charoff="50">Model</th>
<th align="left" valign="top" charoff="50">Predictor</th>
<th align="center" valign="top" charoff="50">est.</th>
<th align="center" valign="top" charoff="50">s.e.m.</th>
<th align="center" valign="top" charoff="50">df</th>
<th align="center" valign="top" charoff="50"><italic>t</italic>
</th>
<th align="center" valign="top" charoff="50">Pr(>|<italic>t</italic>
|)</th>
</tr>
</thead>
<tbody valign="top"><tr><td align="center" valign="top" charoff="50">DFA</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">0.652</td>
<td align="char" valign="top" char="." charoff="50">0.168</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">3.884</td>
<td align="center" valign="top" charoff="50">0.002</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">−0.001</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.604</td>
<td align="center" valign="top" charoff="50">0.560</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">−0.046</td>
<td align="char" valign="top" char="." charoff="50">0.027</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.677</td>
<td align="center" valign="top" charoff="50">0.125</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">0.0002</td>
<td align="char" valign="top" char="." charoff="50">0.0001</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.750</td>
<td align="center" valign="top" charoff="50">0.111</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">−0.003</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.829</td>
<td align="center" valign="top" charoff="50">0.426</td>
</tr>
<tr><td align="center" valign="top" charoff="50">DFA<sub>b</sub>
</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">1.611</td>
<td align="char" valign="top" char="." charoff="50">0.145</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">11.124</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">0.000</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.188</td>
<td align="center" valign="top" charoff="50">0.855</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">−0.040</td>
<td align="char" valign="top" char="." charoff="50">0.023</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.730</td>
<td align="center" valign="top" charoff="50">0.114</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">0.0003</td>
<td align="char" valign="top" char="." charoff="50">0.0001</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">2.238</td>
<td align="center" valign="top" charoff="50">0.049</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">−0.001</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.442</td>
<td align="center" valign="top" charoff="50">0.668</td>
</tr>
<tr><td align="center" valign="top" charoff="50">H<sub>AV</sub>
</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">0.530</td>
<td align="char" valign="top" char="." charoff="50">0.171</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">3.100</td>
<td align="center" valign="top" charoff="50">0.008</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">0.0001</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.026</td>
<td align="center" valign="top" charoff="50">0.979</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">−0.037</td>
<td align="char" valign="top" char="." charoff="50">0.028</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.302</td>
<td align="center" valign="top" charoff="50">0.222</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">0.0002</td>
<td align="char" valign="top" char="." charoff="50">0.0001</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.588</td>
<td align="center" valign="top" charoff="50">0.143</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">−0.002</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.516</td>
<td align="center" valign="top" charoff="50">0.617</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Box Count</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">1.354</td>
<td align="char" valign="top" char="." charoff="50">0.163</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">8.320</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">−0.001</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.374</td>
<td align="center" valign="top" charoff="50">0.716</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">0.030</td>
<td align="char" valign="top" char="." charoff="50">0.027</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.120</td>
<td align="center" valign="top" charoff="50">0.289</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">−0.0002</td>
<td align="char" valign="top" char="." charoff="50">0.0001</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.615</td>
<td align="center" valign="top" charoff="50">0.137</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.743</td>
<td align="center" valign="top" charoff="50">0.475</td>
</tr>
</tbody>
</table>
<table-wrap-foot><fn id="t1-fn1"><p>BM refers to initial body mass at time of logger deployment.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="t2"><label>Table 2</label>
<caption><title>Results of linear mixed-effects models examining influence of individual traits on variation in frequency-based dive parameters from little penguin foraging sequences</title>
</caption>
<table frame="hsides" rules="groups" border="1"><colgroup><col align="left"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
</colgroup>
<thead valign="bottom"><tr><th align="left" valign="top" charoff="50">Model</th>
<th align="left" valign="top" charoff="50">Predictor</th>
<th align="center" valign="top" charoff="50">est.</th>
<th align="center" valign="top" charoff="50">s.e.m.</th>
<th align="center" valign="top" charoff="50">df</th>
<th align="center" valign="top" charoff="50"><italic>t</italic>
</th>
<th align="center" valign="top" charoff="50">Pr(>|<italic>t</italic>
|)</th>
</tr>
</thead>
<tbody valign="top"><tr><td align="center" valign="top" charoff="50">Dive</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">52915.520</td>
<td align="char" valign="top" char="." charoff="50">7613.679</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">6.950</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Trip</td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">46.980</td>
<td align="char" valign="top" char="." charoff="50">91.300</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.515</td>
<td align="center" valign="top" charoff="50">0.618</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Duration</td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">−980.990</td>
<td align="char" valign="top" char="." charoff="50">1264.637</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.776</td>
<td align="center" valign="top" charoff="50">0.456</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">1.400</td>
<td align="char" valign="top" char="." charoff="50">6.408</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.219</td>
<td align="center" valign="top" charoff="50">0.831</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">−99.560</td>
<td align="char" valign="top" char="." charoff="50">138.918</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.717</td>
<td align="center" valign="top" charoff="50">0.490</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Dive</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">36.188</td>
<td align="char" valign="top" char="." charoff="50">18.474</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">1.959</td>
<td align="center" valign="top" charoff="50">0.072</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Duration</td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">0.195</td>
<td align="char" valign="top" char="." charoff="50">0.227</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.861</td>
<td align="center" valign="top" charoff="50">0.409</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">0.793</td>
<td align="char" valign="top" char="." charoff="50">2.962</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.268</td>
<td align="center" valign="top" charoff="50">0.794</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">−0.009</td>
<td align="char" valign="top" char="." charoff="50">0.015</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.592</td>
<td align="center" valign="top" charoff="50">0.567</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">0.249</td>
<td align="char" valign="top" char="." charoff="50">0.334</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.746</td>
<td align="center" valign="top" charoff="50">0.473</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Dive</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">16.067</td>
<td align="char" valign="top" char="." charoff="50">9.085</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">1.768</td>
<td align="center" valign="top" charoff="50">0.100</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Depth</td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">0.022</td>
<td align="char" valign="top" char="." charoff="50">0.111</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.202</td>
<td align="center" valign="top" charoff="50">0.844</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">0.618</td>
<td align="char" valign="top" char="." charoff="50">1.459</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.424</td>
<td align="center" valign="top" charoff="50">0.681</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">−0.005</td>
<td align="char" valign="top" char="." charoff="50">0.008</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.651</td>
<td align="center" valign="top" charoff="50">0.530</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">0.184</td>
<td align="char" valign="top" char="." charoff="50">0.164</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.124</td>
<td align="center" valign="top" charoff="50">0.287</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Underwater</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">0.482</td>
<td align="char" valign="top" char="." charoff="50">0.228</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">2.111</td>
<td align="center" valign="top" charoff="50">0.055</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Time</td>
<td align="left" valign="top" charoff="50">Age</td>
<td align="char" valign="top" char="." charoff="50">−0.001</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.348</td>
<td align="center" valign="top" charoff="50">0.735</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Sex (male)</td>
<td align="char" valign="top" char="." charoff="50">0.054</td>
<td align="char" valign="top" char="." charoff="50">0.038</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.413</td>
<td align="center" valign="top" charoff="50">0.188</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">BM</td>
<td align="char" valign="top" char="." charoff="50">−0.0002</td>
<td align="char" valign="top" char="." charoff="50">0.0002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−0.783</td>
<td align="center" valign="top" charoff="50">0.452</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Chick Age</td>
<td align="char" valign="top" char="." charoff="50">0.005</td>
<td align="char" valign="top" char="." charoff="50">0.004</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.244</td>
<td align="center" valign="top" charoff="50">0.242</td>
</tr>
</tbody>
</table>
<table-wrap-foot><fn id="t2-fn1"><p>BM refers to initial body mass at time of logger deployment.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="t3"><label>Table 3</label>
<caption><title>Results of linear mixed-effects models examining relationship between scaling exponents and frequency-based dive parameters from little penguin foraging sequences</title>
</caption>
<table frame="hsides" rules="groups" border="1"><colgroup><col align="left"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
<col align="center"></col>
</colgroup>
<thead valign="bottom"><tr><th align="left" valign="top" charoff="50">Model</th>
<th align="left" valign="top" charoff="50">Predictor</th>
<th align="center" valign="top" charoff="50">est.</th>
<th align="center" valign="top" charoff="50">s.e.m.</th>
<th align="center" valign="top" charoff="50">df</th>
<th align="center" valign="top" charoff="50"><italic>t</italic>
</th>
<th align="center" valign="top" charoff="50">Pr(>|<italic>t</italic>
|)</th>
</tr>
</thead>
<tbody valign="top"><tr><td align="center" valign="top" charoff="50">DFA</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">0.796</td>
<td align="char" valign="top" char="." charoff="50">0.156</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">5.093</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Trip Duration</td>
<td align="char" valign="top" char="." charoff="50">5.2E-06</td>
<td align="char" valign="top" char="." charoff="50">2.8E-06</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.865</td>
<td align="center" valign="top" charoff="50">0.092</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Underwater Time</td>
<td align="char" valign="top" char="." charoff="50">−0.396</td>
<td align="char" valign="top" char="." charoff="50">0.111</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−3.568</td>
<td align="center" valign="top" charoff="50">0.005</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Duration</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.830</td>
<td align="center" valign="top" charoff="50">0.426</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Depth</td>
<td align="char" valign="top" char="." charoff="50">−0.010</td>
<td align="char" valign="top" char="." charoff="50">0.007</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.482</td>
<td align="center" valign="top" charoff="50">0.169</td>
</tr>
<tr><td align="center" valign="top" charoff="50">DFA<sub>b</sub>
</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">1.810</td>
<td align="char" valign="top" char="." charoff="50">0.104</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">17.480</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Trip Duration</td>
<td align="char" valign="top" char="." charoff="50">5.0E-06</td>
<td align="char" valign="top" char="." charoff="50">1.8E-06</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">2.716</td>
<td align="center" valign="top" charoff="50">0.022</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Underwater Time</td>
<td align="char" valign="top" char="." charoff="50">−0.357</td>
<td align="char" valign="top" char="." charoff="50">0.073</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−4.921</td>
<td align="center" valign="top" charoff="50">0.001</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Duration</td>
<td align="char" valign="top" char="." charoff="50">0.003</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">1.250</td>
<td align="center" valign="top" charoff="50">0.240</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Depth</td>
<td align="char" valign="top" char="." charoff="50">−0.011</td>
<td align="char" valign="top" char="." charoff="50">0.005</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−2.331</td>
<td align="center" valign="top" charoff="50">0.042</td>
</tr>
<tr><td align="center" valign="top" charoff="50">H<sub>AV</sub>
</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">0.299</td>
<td align="char" valign="top" char="." charoff="50">0.200</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">1.491</td>
<td align="center" valign="top" charoff="50">0.160</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Trip Duration</td>
<td align="char" valign="top" char="." charoff="50">1.1E-05</td>
<td align="char" valign="top" char="." charoff="50">3.6E-06</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">2.994</td>
<td align="center" valign="top" charoff="50">0.014</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Underwater Time</td>
<td align="char" valign="top" char="." charoff="50">0.016</td>
<td align="char" valign="top" char="." charoff="50">0.145</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.109</td>
<td align="center" valign="top" charoff="50">0.915</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Duration</td>
<td align="char" valign="top" char="." charoff="50">0.002</td>
<td align="char" valign="top" char="." charoff="50">0.004</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.486</td>
<td align="center" valign="top" charoff="50">0.638</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Depth</td>
<td align="char" valign="top" char="." charoff="50">−0.014</td>
<td align="char" valign="top" char="." charoff="50">0.009</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.597</td>
<td align="center" valign="top" charoff="50">0.141</td>
</tr>
<tr><td align="center" valign="top" charoff="50">Box Count</td>
<td align="left" valign="top" charoff="50">(Intercept)</td>
<td align="char" valign="top" char="." charoff="50">1.099</td>
<td align="char" valign="top" char="." charoff="50">0.125</td>
<td align="center" valign="top" charoff="50">13</td>
<td align="char" valign="top" char="." charoff="50">8.787</td>
<td align="center" valign="top" charoff="50">0.000</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Trip Duration</td>
<td align="char" valign="top" char="." charoff="50">3.9E-06</td>
<td align="char" valign="top" char="." charoff="50">2.3E-06</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">−1.736</td>
<td align="center" valign="top" charoff="50">0.113</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Underwater Time</td>
<td align="char" valign="top" char="." charoff="50">0.471</td>
<td align="char" valign="top" char="." charoff="50">0.095</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">4.974</td>
<td align="center" valign="top" charoff="50">0.001</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Duration</td>
<td align="char" valign="top" char="." charoff="50">3.0E-04</td>
<td align="char" valign="top" char="." charoff="50">2.4E-03</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.126</td>
<td align="center" valign="top" charoff="50">0.902</td>
</tr>
<tr><td align="left" valign="top" charoff="50"> </td>
<td align="left" valign="top" charoff="50">Dive Depth</td>
<td align="char" valign="top" char="." charoff="50">0.004</td>
<td align="char" valign="top" char="." charoff="50">0.005</td>
<td align="center" valign="top" charoff="50">10</td>
<td align="char" valign="top" char="." charoff="50">0.821</td>
<td align="center" valign="top" charoff="50">0.431</td>
</tr>
</tbody>
</table>
</table-wrap>
</floats-group>
</pmc>
<affiliations><list><country><li>France</li>
</country>
<region><li>Alsace (région administrative)</li>
<li>Grand Est</li>
</region>
<settlement><li>Strasbourg</li>
</settlement>
</list>
<tree><noCountry><name sortKey="Chiaradia, Andre" sort="Chiaradia, Andre" uniqKey="Chiaradia A" first="Andre" last="Chiaradia">Andre Chiaradia</name>
<name sortKey="Macintosh, Andrew J J" sort="Macintosh, Andrew J J" uniqKey="Macintosh A" first="Andrew J. J." last="Macintosh">Andrew J. J. Macintosh</name>
</noCountry>
<country name="France"><region name="Grand Est"><name sortKey="Pelletier, Laure" sort="Pelletier, Laure" uniqKey="Pelletier L" first="Laure" last="Pelletier">Laure Pelletier</name>
</region>
<name sortKey="Kato, Akiko" sort="Kato, Akiko" uniqKey="Kato A" first="Akiko" last="Kato">Akiko Kato</name>
<name sortKey="Kato, Akiko" sort="Kato, Akiko" uniqKey="Kato A" first="Akiko" last="Kato">Akiko Kato</name>
<name sortKey="Pelletier, Laure" sort="Pelletier, Laure" uniqKey="Pelletier L" first="Laure" last="Pelletier">Laure Pelletier</name>
<name sortKey="Ropert Coudert, Yan" sort="Ropert Coudert, Yan" uniqKey="Ropert Coudert Y" first="Yan" last="Ropert-Coudert">Yan Ropert-Coudert</name>
<name sortKey="Ropert Coudert, Yan" sort="Ropert Coudert, Yan" uniqKey="Ropert Coudert Y" first="Yan" last="Ropert-Coudert">Yan Ropert-Coudert</name>
</country>
</tree>
</affiliations>
</record>
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