<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">OJS</journal-id><journal-title-group><journal-title>Open Journal of Statistics</journal-title></journal-title-group><issn pub-type="epub">2161-718X</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/ojs.2019.94032</article-id><article-id pub-id-type="publisher-id">OJS-94298</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Demographic Expansion and Contraction in a Neotropical Fish during the Late Pleistocene-Holocene
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Carolina</surname><given-names>L. N. Costa</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>S.</surname><given-names>Ivan Perez</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>José</surname><given-names>Louvise</given-names></name><xref ref-type="aff" rid="aff3"><sup>3</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Carlos</surname><given-names>H. Tonhatti</given-names></name><xref ref-type="aff" rid="aff4"><sup>4</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Rute</surname><given-names>B. G. Clemente-Carvalho</given-names></name><xref ref-type="aff" rid="aff5"><sup>5</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ana</surname><given-names>C. Petry</given-names></name><xref ref-type="aff" rid="aff6"><sup>6</sup></xref></contrib><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>S.</surname><given-names>F. dos Reis</given-names></name><xref ref-type="aff" rid="aff7"><sup>7</sup></xref></contrib></contrib-group><aff id="aff2"><addr-line>División Antropología, Facultad de Ciencias Naturales y Museo, Universidad Nacional de La Plata, CONICET, La Plata, Argentina</addr-line></aff><aff id="aff6"><addr-line>Núcleo em Ecologia e Desenvolvimento Sócio-Ambiental de Macaé, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil</addr-line></aff><aff id="aff1"><addr-line>Programa de Pós-Graduacao em Ecologia, Universidade Estadual de Campinas, Sao Paulo, Brazil</addr-line></aff><aff id="aff5"><addr-line>Deparment of Biology, Queen’s University, Ontario, Canada</addr-line></aff><aff id="aff3"><addr-line>Faculdade do Vale do Jaguaribe, Ceará, Brazil</addr-line></aff><aff id="aff4"><addr-line>Programa de Pós-Graduacao em Genética, Universidade Estadual de Campinas, Sao Paulo, Brazil</addr-line></aff><aff id="aff7"><addr-line>Departamento de Biologia Animal, Universidade Estadual de Campinas, Sao Paulo, Brazil</addr-line></aff><pub-date pub-type="epub"><day>05</day><month>08</month><year>2019</year></pub-date><volume>09</volume><issue>04</issue><fpage>470</fpage><lpage>483</lpage><history><date date-type="received"><day>12,</day>	<month>June</month>	<year>2019</year></date><date date-type="rev-recd"><day>10,</day>	<month>August</month>	<year>2019</year>	</date><date date-type="accepted"><day>13,</day>	<month>August</month>	<year>2019</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p>
 
 
  Demographic changes during the late Pleistocene-Holocene left signatures in the DNA of contemporary populations. These signatures reveal demographic phenomena like the increase or decrease in effective population size. In this paper we searched for signatures of demographic change in the DNA of the Neotropical freshwater fish 
  Poecilia vivipara
  . Also, we investigated whether demographic changes are correlated with palaeoclimatic events of the late Pleistocene-Holocene
  ,
   in particular, if changes in effective population size are correlated with expansion and contraction of available habitats, induced by global ice-volume changes and sea-level fluctuations. We used Bayesian Skyline Plot (BSP) analysis with sequences from the mitochondrial gene cytochrome b to estimate the ancestral demography of the Neotropical freshwater fish P. vivipara. To test the assumptions of neutrality and absence of population structure we used Tajima’s D and Spatial Analysis of Molecular Variance (SAMOVA), respectively. Effective population size of P. vivipara remained stable until 75,000 years ago, increased by 10-fold reaching a maximum at approximately 25,000 years ago, then suddenly declined at the Pleistocene-Holocene boundary. Variation in effective population size in P. vivipara correlates with expansion and contraction of habitats induced by sea-level fluctuations, caused by the advance and retreat of ice sheets during the Last Glacial Maximum (LGM).
 
</p></abstract><kwd-group><kwd>Ancestral Population Dynamics</kwd><kwd> Coalescence</kwd><kwd> Bayesian Skyline Plot</kwd><kwd> Mitochondrial DNA</kwd><kwd> Last Glacial Maximum</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>1. Introduction</title><p>Late Pleistocene-Holocene global climatic oscillations markedly influenced the demographic history of Earth’s biota [<xref ref-type="bibr" rid="scirp.94298-ref1">1</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref2">2</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref3">3</xref>]. From the standpoint of demography, departures from stability, experienced as expansion or contraction in population size, are relevant events [<xref ref-type="bibr" rid="scirp.94298-ref4">4</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref5">5</xref>]. Signatures of changes in effective population size are written in the DNA of contemporary populations because of ancestor-descendant transmission of genetic material and the processes of mutation and substitution [<xref ref-type="bibr" rid="scirp.94298-ref6">6</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref7">7</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref8">8</xref>]. Consequently, from evolutionary and ecological perspectives, it is important to assess whether temporal changes in effective population size are correlated with episodic palaeoclimatic events [<xref ref-type="bibr" rid="scirp.94298-ref9">9</xref>]. Of the several known cases, the steppe bison is probably one of the richest for the complexity of its demographic response to the Pleistocene-Holocene climate changes [<xref ref-type="bibr" rid="scirp.94298-ref10">10</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref12">12</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref13">13</xref>]. Bison effective population size increased from 150 thousand years before present (ka BP), reaching a maximum between 30 - 45 ka BP [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. After the maximum, effective population size declined precipitously, reaching a minimum at approximately 10 ka BP [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. Following the minimum, effective population size increased and levelled off, and then decreased again [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. Minimum and maximum effective population sizes in the bison correlate, among other factors, with the contraction and expansion of available habitat, driven by the advance and retreat of ice sheets during the Last Glacial Maximum (LGM) and Holocene, respectively [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. As demonstrated by coalescent simulation, effective population size correlates with the amount of habitat available [<xref ref-type="bibr" rid="scirp.94298-ref14">14</xref>]. Therefore, a causal association between demographic expansion and contraction and palaeoclimatic cyclic events is tenable.</p><p>The expansion and contraction of habitats in continental areas in the Northern hemisphere is primarily a consequence of the cyclical retreat and advance of ice sheets [<xref ref-type="bibr" rid="scirp.94298-ref15">15</xref>]. In non-glaciated regions, however, the dynamics of habitat availability is locally induced by glacio-eustatic sea-level changes [<xref ref-type="bibr" rid="scirp.94298-ref16">16</xref>]. Sea-level low stands, caused by the advance of ice sheets, expose the continental shelf increasing habitat availability. Conversely, in non-glaciated regions the retreat of ice sheets induces an inverse effect on habitat availability. Such glacio-eustatic sea-level changes did have a major impact on coastal areas of South America [<xref ref-type="bibr" rid="scirp.94298-ref17">17</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref18">18</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref19">19</xref>]. Here, we investigate the potential consequences of the late Pleistocene-Holocene climatic oscillations for the historical demography of a poeciliid fish, Poecilia vivipara, inhabiting a non-glaciated region in South America. Poeciliids are well-known model organisms [<xref ref-type="bibr" rid="scirp.94298-ref20">20</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref21">21</xref>] , and P. vivipara is a freshwater species that also colonizes brackish and salt-water environments near the mouth of rivers [<xref ref-type="bibr" rid="scirp.94298-ref22">22</xref>]. Poecilia vivipara thus has the potential to track environmental changes such as the expansion or contraction of habitats associated with glacio-eustatic sea-level changes. Given the environmental changes of the late Pleistocene-Holocene and the ecological and life history attributes of P. vivipara, we expect contemporary populations of P. vivipara will harbour signatures of their historical demography. We used sequences of the mitochondrial gene cytochrome b (cyt-b), sampled from southeastern Brazil, and the coalescent-based Bayesian Skyline Plot (BSP) [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>] to explore an association between historical variation in effective population size in P. vivipara and climatic oscillations during the late Pleistocene-Holocene. We believe our results do contribute relevant information to the ongoing research on the interplay between late Pleistocene-Holocene climatic oscillations and ecological and evolutionary processes in South America.</p></sec><sec id="s2"><title>2. Methods</title><sec id="s2_1"><title>2.1. Study System</title><p>We sampled a total of 206 individuals of P. vivipara using a fine mesh net from 20 lagoons, which are hydrogeologically associated with the Para&#237;ba do Sul River in northern Rio de Janeiro state in southeastern Brazil (<xref ref-type="table" rid="table1">Table 1</xref>). These lagoons vary in salinity from freshwater to brackish and saltwater [<xref ref-type="bibr" rid="scirp.94298-ref22">22</xref>].</p></sec><sec id="s2_2"><title>2.2. DNA Processing</title><p>DNA was extracted from the caudal peduncle using the salting-out method [<xref ref-type="bibr" rid="scirp.94298-ref23">23</xref>]. The entire mitochondrial cyt-b (1140 base pairs) gene was amplified using primers and reaction parameters defined in Schories et al. [<xref ref-type="bibr" rid="scirp.94298-ref24">24</xref>]. Purified Polymerase Chain Reaction (PCR) products were outsourced to Macrogen Inc. (South Korea) for sequencing (using the BigDyeTM 158 terminator kit and run on an ABI 3730XL). PCR products were sequenced in both directions with the same primers used for PCR amplification and subjected to Basic Local Alignment Search Tool (BLAST) in GenBank to verify that the desired sequences had been amplified. The sequences were deposited in GenBank (accession numbers: MG266475-MG266680).</p></sec><sec id="s2_3"><title>2.3. Tests of Neutrality and Population Structure</title><p>We used Tajima’s D statistic [<xref ref-type="bibr" rid="scirp.94298-ref25">25</xref>] to test for the departure from the mutation-drift equilibrium and to evaluate whether the cyt-b gene conformed to neutral expectations using program DNA Sequence Polymorphism (DnaSP) v4.50.02 [<xref ref-type="bibr" rid="scirp.94298-ref26">26</xref>]. We estimated the genealogical relationships among haplotypes using the statistical parsimony method, developed by Templeton, Crandall and Sing (TCS) [<xref ref-type="bibr" rid="scirp.94298-ref27">27</xref>] , with a 95% probability that no multiple substitutions have occurred, as implement in the software TCS v1.21 [<xref ref-type="bibr" rid="scirp.94298-ref28">28</xref>]. The assumption of a panmictic population was tested with Spatial Analysis of Molecular Variance</p><table-wrap id="table1" ><label><xref ref-type="table" rid="table1">Table 1</xref></label><caption><title> Geographical locations of the 20 sampled populations of Poecilia vivipara. The number of individuals (n) analysed for cyt-b mitochondrial DNA (mtDNA) marker and the number of haplotypes (h) are given for each location</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >ID</th><th align="center" valign="middle" >Sample</th><th align="center" valign="middle" >Latitute S</th><th align="center" valign="middle" >Latitude W</th><th align="center" valign="middle" >n</th><th align="center" valign="middle" >h</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >A&#231;u</td><td align="center" valign="middle" >21.99416˚</td><td align="center" valign="middle" >41.00001˚</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >6</td></tr><tr><td align="center" valign="middle" >2</td><td align="center" valign="middle" >Atafona</td><td align="center" valign="middle" >21.62836˚</td><td align="center" valign="middle" >41.02417˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >5</td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >Cabiunas</td><td align="center" valign="middle" >22.30140˚</td><td align="center" valign="middle" >41.69300˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >1</td></tr><tr><td align="center" valign="middle" >4</td><td align="center" valign="middle" >Cacimba</td><td align="center" valign="middle" >21.63940˚</td><td align="center" valign="middle" >41.09540˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >4</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >Catingosa</td><td align="center" valign="middle" >22.18850˚</td><td align="center" valign="middle" >41.41540˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >4</td></tr><tr><td align="center" valign="middle" >6</td><td align="center" valign="middle" >Campelo</td><td align="center" valign="middle" >21.66463˚</td><td align="center" valign="middle" >41.20097˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >3</td></tr><tr><td align="center" valign="middle" >7</td><td align="center" valign="middle" >Cima</td><td align="center" valign="middle" >21.78693˚</td><td align="center" valign="middle" >41.51622˚</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >3</td></tr><tr><td align="center" valign="middle" >8</td><td align="center" valign="middle" >Comercio</td><td align="center" valign="middle" >21.57530˚</td><td align="center" valign="middle" >41.06740˚</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >7</td></tr><tr><td align="center" valign="middle" >9</td><td align="center" valign="middle" >Feia</td><td align="center" valign="middle" >21.94553˚</td><td align="center" valign="middle" >41.34551˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >7</td></tr><tr><td align="center" valign="middle" >10</td><td align="center" valign="middle" >Barra do Furado</td><td align="center" valign="middle" >22.08086˚</td><td align="center" valign="middle" >41.11850˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >5</td></tr><tr><td align="center" valign="middle" >11</td><td align="center" valign="middle" >Gar&#231;a</td><td align="center" valign="middle" >22.12140˚</td><td align="center" valign="middle" >41.49220˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >4</td></tr><tr><td align="center" valign="middle" >12</td><td align="center" valign="middle" >Grussa&#237;</td><td align="center" valign="middle" >21.71979˚</td><td align="center" valign="middle" >41.03783˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >7</td></tr><tr><td align="center" valign="middle" >13</td><td align="center" valign="middle" >Heliporto</td><td align="center" valign="middle" >22.03078˚</td><td align="center" valign="middle" >41.06392˚</td><td align="center" valign="middle" >11</td><td align="center" valign="middle" >8</td></tr><tr><td align="center" valign="middle" >14</td><td align="center" valign="middle" >Iquipari</td><td align="center" valign="middle" >21.80019˚</td><td align="center" valign="middle" >41.02122˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >8</td></tr><tr><td align="center" valign="middle" >15</td><td align="center" valign="middle" >Lagamar</td><td align="center" valign="middle" >22.06027˚</td><td align="center" valign="middle" >41.08317˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >7</td></tr><tr><td align="center" valign="middle" >16</td><td align="center" valign="middle" >Praia I</td><td align="center" valign="middle" >21.57534˚</td><td align="center" valign="middle" >41.06043˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >5</td></tr><tr><td align="center" valign="middle" >17</td><td align="center" valign="middle" >Praia II-Gargau</td><td align="center" valign="middle" >21.57440˚</td><td align="center" valign="middle" >41.05867˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >6</td></tr><tr><td align="center" valign="middle" >18</td><td align="center" valign="middle" >Santa Clara</td><td align="center" valign="middle" >21.52043˚</td><td align="center" valign="middle" >41.07912˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >4</td></tr><tr><td align="center" valign="middle" >19</td><td align="center" valign="middle" >Tai Pequeno</td><td align="center" valign="middle" >21.80620˚</td><td align="center" valign="middle" >41.12870˚</td><td align="center" valign="middle" >12</td><td align="center" valign="middle" >6</td></tr><tr><td align="center" valign="middle" >20</td><td align="center" valign="middle" >Tr&#234;s Vendas</td><td align="center" valign="middle" >21.68240˚</td><td align="center" valign="middle" >41.33580˚</td><td align="center" valign="middle" >10</td><td align="center" valign="middle" >2</td></tr></tbody></table></table-wrap><p>(SAMOVA) [<xref ref-type="bibr" rid="scirp.94298-ref29">29</xref>] , which requires no a priori definition of groups of populations. SAMOVA iteratively searches for the partitions of K groups of populations that maximize the F<sub>CT</sub> index, which is the proportion of the total genetic variance due to difference between groups of populations for any number of putative groups. SAMOVA was performed with 18 partitions for the 20 population samples for K varying from two to 19 groups of population samples. The F<sub>CT</sub> index was computed for each partition. The cases in which all population samples belong to the same group (K = 1) or each population is itself a group (K = 20) were not included in the analysis. For each K value, 10,000 simulated annealing steps were executed starting from 200 sets of initial conditions.</p></sec><sec id="s2_4"><title>2.4. Demographic Analysis</title><p>We estimated historical variation in the effective population size of P. vivipara using sequences of the cyt-b gene and the BSP method, which is based on the variable population size coalescent model [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. Starting with a sequence alignment from a sample, the BSP method co-estimates the phylogeny and the effective population size through time [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. This method is based on assumptions that samples come from a panmictic population and that sequences are orthologous, non-recombining, and evolve neutrally [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. We used the software Bayesian Evolutionary Analysis Utility (BEAUti) [<xref ref-type="bibr" rid="scirp.94298-ref30">30</xref>] to generate the XML input files for the Bayesian Evolutionary Analysis Sampling Trees software (BEAST v.1.8.2) [<xref ref-type="bibr" rid="scirp.94298-ref30">30</xref>]. We used unlinked strict clock rates and the General Time Reversible (GTR) model of nucleotide of substitution, which best fitted the cyt-b sequences according to jModelTestv.2.1.10 [<xref ref-type="bibr" rid="scirp.94298-ref31">31</xref>]. We ran 400 million Markov chain Monte Carlo (MCMC) iterations, sampling every 40,000 runs. The first 10% runs were discarded as burn-in. We verified convergence to a stationary distribution with Tracer v.1.5 [<xref ref-type="bibr" rid="scirp.94298-ref32">32</xref>]. Effective sample size for parameter estimates was always &gt;200. Demographic history through time was reconstructed also using Tracer v.1.5 [<xref ref-type="bibr" rid="scirp.94298-ref32">32</xref>]. Estimation of absolute ages of demographic events was based on a substitution rate of 0.9 &#215; 10<sup>−8</sup> per site per year, which we calculated using estimates of absolute divergence times derived by Meredith et al. [<xref ref-type="bibr" rid="scirp.94298-ref33">33</xref>].</p></sec></sec><sec id="s3"><title>3. Results</title><p>The inference of ancestral effective population size using DNA sequences and the BSP technique require testing the assumptions of neutrality and absence of population structure [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>]. The assumption of neutrality was tested with Tajima’s D statistics [<xref ref-type="bibr" rid="scirp.94298-ref25">25</xref>] , which was not significantly different from zero (D = - 0.1523; P &gt; 0.10). This result indicates that the assumption of mutation-drift is not violated and that the cyt-b gene is evolving neutrally in the sampled populations of P. vivipara. We used the statistical parsimony network [<xref ref-type="bibr" rid="scirp.94298-ref27">27</xref>] and the spatial analysis of molecular variance [<xref ref-type="bibr" rid="scirp.94298-ref29">29</xref>] to test for population structure. Thirty-eight unique haplotypes were identified among the 206 cyt-b sequences analysed. All haplotypes were connected into a single network, which has an overall star-like pattern (<xref ref-type="fig" rid="fig1">Figure 1</xref>). The network is characterized by three high-frequency haplotypes, several intermediate, and rare haplotypes. The haplotypes are divided in two main groups, with each group connected by a maximum of three mutational steps, whereas a minimum of nine steps separates each group. In SAMOVA, the F<sub>CT</sub> statistics estimates the total genetic variance due to differences between groups of samples for partitions of K groups of populations. F<sub>CT</sub> values decrease smoothly as K increases from 2 to 8 and then levels off for values of K from 9 through 19 (<xref ref-type="fig" rid="fig2">Figure 2</xref>). This result indicates that no single value of K is maximized, indicating a lack of population structure in the populations sampled. An example of group composition for K = 5 resulted from the simulated anealing steps is shown in <xref ref-type="table" rid="table2">Table 2</xref>.</p><p>Modelling the effective population size over time with the BSP using the cyt-b sequences revealed a complex demographic history for P. vivipara (<xref ref-type="fig" rid="fig3">Figure 3</xref>(a) ). In this plot, the y-axis is expressed as female effective population size (N<sub>e</sub>) &#215; generation time and the x-axis is calendar time in years. Effective population size remained stable approximately until 75 ka BP and is followed by a steep, approximately 10-fold increase reaching a maximum value at the LGM (approximately 25 ka BP). There follows a sharp and sudden decline in effective population size starting around the Pleistocene-Holocene boundary, a trend that persists to the present. A sample of the MCMC iterations is shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>. The trace is stable indicating good parameter mixing and convergence of the likelihood estimation (<xref ref-type="fig" rid="fig4">Figure 4</xref>(a)). Also the plot of the marginal density for the likelihood estimation shows a high degree of symmetry (<xref ref-type="fig" rid="fig4">Figure 4</xref>(b)).</p><table-wrap id="table2" ><label><xref ref-type="table" rid="table2">Table 2</xref></label><caption><title> Group composition of sampled populations of Poecilia vivipara in one of the 10,000 simulated annealing steps for K = 5 in SAMOVA analysis</title></caption><table><tbody><thead><tr><th align="center" valign="middle" >Group</th><th align="center" valign="middle" >Number of populations</th><th align="center" valign="middle" >Lagoons</th></tr></thead><tr><td align="center" valign="middle" >1</td><td align="center" valign="middle" >16</td><td align="center" valign="middle" >A&#231;u, Cacimba, Com&#233;rcio, Feia, Furado, Grussa&#237;, Heliporto, Iquipari, Lagamar, Praia I, Praia II, Santa Clara, Tai Pequeno Tr&#234;s Vendas, Catingosa, Gar&#231;a,</td></tr><tr><td align="center" valign="middle" >2</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >Cima</td></tr><tr><td align="center" valign="middle" >3</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >Campelo</td></tr><tr><td align="center" valign="middle" >4</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >Cabiunas</td></tr><tr><td align="center" valign="middle" >5</td><td align="center" valign="middle" >1</td><td align="center" valign="middle" >Atafona</td></tr></tbody></table></table-wrap></sec><sec id="s4"><title>4. Discussion</title><p>The cyt-b sequences of the sampled populations of P. vivipara do have variation, which allows the estimation of variation in ancestral effective population size over time. However, it is well established that population structure can influence the estimation of effective population size [<xref ref-type="bibr" rid="scirp.94298-ref34">34</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref35">35</xref>]. In our study, no evidence of geographic structure can be gleaned from the haplotype network, that is, no discernable association between haplotypes and locations is evident. Furthermore, the evidence from the spatial analysis of molecular variance points to the absence of structure in the populations of P. vivipara. Equally relevant, the sequences of the cyt-b gene appear to be evolving neutrally. Therefore, fundamental assumptions of the BSP method [<xref ref-type="bibr" rid="scirp.94298-ref11">11</xref>] appear not to be violated by our samples.</p><p>The BSP revealed a marked increase in the effective population size of P. vivipara, which reached a maximum at approximately 25 ka BP (<xref ref-type="fig" rid="fig3">Figure 3</xref>(a)). This demographic event coincides approximately with the LGM, which is dated between 26.5 ka BP and 19 - 20 ka BP [<xref ref-type="bibr" rid="scirp.94298-ref36">36</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref37">37</xref>]. During the LGM, the sea level of the coast of Brazil was ~120 meters below its current level [<xref ref-type="bibr" rid="scirp.94298-ref37">37</xref>] (<xref ref-type="fig" rid="fig3">Figure 3</xref>(b)) exposing, as a consequence, much of the continental shelf (<xref ref-type="fig" rid="fig5">Figure 5</xref>(a)), arguably increasing the availability of both freshwater and brackish habitats for P. vivipara. A second striking feature is the sharp demographic decrease after the maximum effective population size (<xref ref-type="fig" rid="fig3">Figure 3</xref>(a)). This demographic trend is conceivably associated with a sea-level rising after the LGM (<xref ref-type="fig" rid="fig3">Figure 3</xref>(b)), which probably induced a contraction of habitats previously available during the LGM (<xref ref-type="fig" rid="fig5">Figure 5</xref>(b)).</p><p>How might the ancestral demography of P. vivipara revealed by the Bayesian skyline plot be interpreted? Idiosyncrasies of the ecology and life history of contemporary populations of P. vivipara may shed light onto the dynamics of effective population size and the climatic-related fluctuations associated with the LGM. Poecilia vivipara successfully colonizes rivers and inland habitats varying in salinity from 0 to 36 parts per thousand [<xref ref-type="bibr" rid="scirp.94298-ref22">22</xref>] ; the latter figure actually being equal to the salinity of sea water. Populations of P. vivipara at either extreme of the salinity gradient differ significantly in traits such as body size and shape, fecundity, and reproductive allotment, which are likely determined genetically [<xref ref-type="bibr" rid="scirp.94298-ref38">38</xref>] [<xref ref-type="bibr" rid="scirp.94298-ref39">39</xref>]. Poecilia vivipara also varies markedly in personality traits including boldness, activity, and sociability/shoaling behaviour, which are modulated by environmental factors such as water transparency/visibility, salinity, and dissolved oxygen [<xref ref-type="bibr" rid="scirp.94298-ref40">40</xref>]. Variability in personality traits vanishes, however, under homogenous laboratory conditions, indicating that plasticity underlies the behavioural differences observed in nature [<xref ref-type="bibr" rid="scirp.94298-ref40">40</xref>]. The available data thus suggest that genetics and plasticity play fundamental roles in the distribution of ecological and behavioural traits of P. vivipara, which are potentially relevant for the colonization of heterogeneous environments subjected to climatic fluctuations. In particular, plasticity, a major factor in the adaptive process [<xref ref-type="bibr" rid="scirp.94298-ref41">41</xref>] , may be a key</p><p>mechanism underlying the increase (decrease) in effective population size associated with habitat expansion (contraction) driven by glacio-eustatic sea level oscillations during the LGM.</p><p>The ancestral demography of P. vivipara appears strongly correlated with environmental changes driven by the LGM. This is indeed the major task of historical demography, that is, to test for correlation between demographic phenomena, as revealed by variation in DNA sequences and palaeoclimatic episodic events [<xref ref-type="bibr" rid="scirp.94298-ref9">9</xref>]. However, a correlation between variation in effective population size and climatic oscillations does not always emerge. For example, in the Northern hemisphere effective population size increased monotonically in the lizard Podarcis filfolensis in the Maltese archipelago [<xref ref-type="bibr" rid="scirp.94298-ref42">42</xref>] , whereas effective population size increased and then levelled off in the tree frog Hylasarda in the Corsica-Sardinian island system [<xref ref-type="bibr" rid="scirp.94298-ref43">43</xref>]. For these systems, the observed demographic expansion is actually the reverse trend expected under the classic expansion-contraction model, which predicts demographic contraction during glaciations [<xref ref-type="bibr" rid="scirp.94298-ref42">42</xref>]. In the Southern hemisphere, in estuarine habitats of the coastal plains of southeastern Brazil four species of fishes experienced demographic stability, whereas three other species underwent demographic expansion followed by an asymptote in effective population size [<xref ref-type="bibr" rid="scirp.94298-ref44">44</xref>]. In none of these cases, however, the demographic changes did coincide with the LGM. Global climatic oscillations coupled with local geomorphological features are probably the major exogenous factors contributing to the origin of the observed diversity of demographic regimes. However, as pointed out by Ruzzante et al. [<xref ref-type="bibr" rid="scirp.94298-ref45">45</xref>] , the life history and ecology of individual species is doubtless a fundamental endogenous determinant of the spatiotemporal demographic dynamics of contemporary populations. In this connection, Ruzzante et al. [<xref ref-type="bibr" rid="scirp.94298-ref45">45</xref>] showed that two sympatric species of Patagonian freshwater fishes differ in their historical demography. Galaxias platei experienced a bottleneck during the LGM, whereas Percichthys truch experienced sustained growth in effective population size for the last 100ka BP. However, the two species differ in physiological traits, habitat preferences, feeding ecology, ability to colonize new habitats, and predation pressure [<xref ref-type="bibr" rid="scirp.94298-ref45">45</xref>] , which conceivably explain the observed demographic dynamics of current populations of G. platei and P. truch [<xref ref-type="bibr" rid="scirp.94298-ref45">45</xref>]. The diversity of factors potentially affecting the demography of populations in a variety of species possibly explain the complexity of outcomes as the cited above, with different factors playing a more important role in each system.</p></sec><sec id="s5"><title>5. Conclusion</title><p>The emerging complexity and diversity of demographic regimes in terrestrial and aquatic species during the late Pleistocene-Holocene both in the Northern and in Southern hemispheres, in particular regarding the LGM, is remarkable. The pattern of variation in effective population size we uncovered for P. vivipara, particularly with respect the role of the LGM, adds to the already known complexity. In this connection, comparative studies of species differing in life history and ecology, but sharing common environments, will be instrumental in uncovering the processes underlying the historical demography of contemporary populations. Such an approach might lead to the discovery of the factors that determine whether the demographic dynamics coincides or not with the episodic climatic events of the Late Pleistocene-Holocene.</p></sec><sec id="s6"><title>Acknowledgements</title><p>We are grateful to Diego Gobbo for helping with <xref ref-type="fig" rid="fig2">Figure 2</xref>. Jo&#227;o M. S. de Souza kindly helped with fieldwork. We are indebted to Mathias M. Pires for critically reviewing the manuscript. Carolina L. N. Costa was supported by a scholarship from Coordena&#231;&#227;o de Aperfei&#231;oamento de Pessoal de N&#237;vel Superior (CAPES, FinanceCode 001). Jos&#233; Louvise was supported by a fellowship from Conselho Nacional de Desenvolvimento Cient&#237;fico e Tecnol&#243;gico (CNPq). Carlos H.Tonhatti was supported by a scholarship from Funda&#231;&#227;o de Amparo &#224; Pesquisa do Estado de S&#227;o Paulo (FAPESP). Minist&#233;rio do Meio Ambiente (Sistema de Autoriza&#231;&#227;o e Informa&#231;&#227;o em Biodiversidade) issued collecting permits. Research supported by CNPq and FAPESP.</p></sec><sec id="s7"><title>Conflicts of Interest</title><p>The authors declare no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s8"><title>Cite this paper</title><p>Costa, C.L.N., Ivan Perez, S., Louvise, J., Tonhatti, C.H., Clemente-Carvalho, R.B.G., Petry, A.C. and dos Reis, S.F. (2019) Demographic Expansion and Contraction in a Neotropical Fish during the Late Pleistocene-Holocene. Open Journal of Statistics, 9, 470-483. https://doi.org/10.4236/ojs.2019.94032</p></sec></body><back><ref-list><title>References</title><ref id="scirp.94298-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Hewitt, G.M. (2004) Genetic Consequences of Climatic Oscillations in the Quaternary. 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