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  <front>
    <journal-meta>
      <journal-id/>
      <journal-title-group>
        <journal-title xml:lang="en">Tourism and Hospitality Management </journal-title>
      </journal-title-group>
      <issn pub-type="ppub">1330-7533</issn>
      <issn pub-type="epub">1847-3377</issn>
      <publisher>
        <publisher-name xml:lang="hr">Sveučilište u Rijeci, Fakultet za menadžment u turizmu i
          ugostiteljstvu, Opatija</publisher-name>
        <publisher-name xml:lang="en">University of Rijeka, Faculty of Tourism and Hospitality
          Management, Opatija</publisher-name>
        <publisher-loc>Naselje Ika, Primorska 42, PP 97, 51410 Opatija <email
            xlink:href="thm@fthm.hr">thm@fthm.hr</email>
          <ext-link xlink:href="http://thm.fthm.hr/">http://thm.fthm.hr/</ext-link>
        </publisher-loc>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.20867/thm.27.3.6</article-id>
      <article-categories>
        <subj-group subj-group-type="heading" xml:lang="hr">
          <subject>Originalni znanstveni rad</subject>
        </subj-group>
        <subj-group subj-group-type="heading" xml:lang="en">
          <subject>Original scientific paper</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en"><bold>SHORT-TERM RENTALS: HOW MUCH IS TOO MUCH – SPATIAL
            PATTERNS IN PORTUGAL AND LISBON</bold></article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Antunes</surname>
            <given-names>Gonçalo</given-names>
          </name>
          <email xlink:href="goncalo.antunes@fcsh.unl.pt">goncalo.antunes@fcsh.unl.pt</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        
        <contrib contrib-type="author">
          <name>
            <surname>Ferreira</surname>
            <given-names>Jorge</given-names>
          </name>
          <email xlink:href="fjrc@fcsh.unl.pt">fjrc@fcsh.unl.pt</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff1">
          <label>1</label>
          <institution xml:lang="en"> Interdisciplinary Centre of Social Sciences (CICS.NOVA), Faculty of Social Sciences and Humanities (FCSH/NOVA)
          </institution>
          <addr-line>Avenida de Berna, 26-C / 1069-061 Lisboa, Portugal</addr-line>
        </aff> 
        
        <aff id="aff2">
          <label>2</label>
          <institution xml:lang="en">Interdisciplinary Centre of Social Sciences (CICS.NOVA), Faculty of Social Sciences and Humanities (FCSH/NOVA)</institution>
          <addr-line>Avenida de Berna, 26-C / 1069-061 Lisboa, Portugal</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <month>11</month>
        <year>2021</year>
      </pub-date>
      <volume>27</volume>
      <issue>3</issue>
      <fpage>581</fpage>
      <lpage>603</lpage>
      <history>
        <date date-type="received">
          <day>31</day>
          <month>05</month>
          <year>2021</year>
        </date>
        <date date-type="revised">
          <day>29</day>
          <month>08</month>
          <year>2021</year>
        </date>
        <date date-type="revised">
          <day>23</day>
          <month>Autumn</month>
          <year>2021</year>
        </date>
        <date date-type="accepted">
          <day>03</day>
          <month>10</month>
          <year>2021</year>
        </date>
      </history>
      <permissions>
        <license license-type="open-access">
          <license-p>CC BY-NC-SA 4.0</license-p>
        </license>
        <license license-type="open-access" xml:lang="hr">
          <license-p>Puni tekst radova ovog časopisa besplatno se smije koristiti za osobne,
            edukacijske ili istraživačke svrhe uz poštivanje autorskih prava autora i izdavača.
            Radovi su dostupni pod uvjetima licence CC BY-NC-SA 4.0 International. Tourism and
            hospitality management je plavi Sherpa/RoMEO časopis.</license-p>
        </license>
        <license license-type="open-access" xml:lang="en">
          <license-p>The papers can be used for personal, scientific, educational and research
            purposes, provided that the credit is given. The papers are licensed under CC BY-NC-SA
            4.0 International license. Tourism and hospitality management is a Sherpa/RoMEO blue
            journal. </license-p>
        </license>
      </permissions>
      <abstract>
        <p> Purpose - This paper analyses the growth of tourism in Portugal and in the municipality
          of Lisbon, with a focus on short-term rentals. </p>
        <p>Design - The paper begins with the statistical background of the tourism boom that
          occurred in Portugal in the 2010s. The central part of the paper concentrates on an
          analysis of the spatial distribution of short-term rental properties, consisting of two
          parts: i) observation of spatial patterns in Portugal, by NUTS II region; ii) analysis of
          the municipality of Lisbon, which accounts for 22% of all short-term rentals units
          registered in Portugal. </p>
        <p>Methodology - The spatial analysis was carried out within GIS, using an approach based on
          spatial statistics, with research that involves geographic data and big data. </p>
        <p>Approach - This study combines a qualitative and quantitative approach. It begins with a
          theoretical review on the growth of tourism and short-term rental in the last decade,
          followed by a quantitative-spatial analysis to the case of Portugal and the municipality
          of Lisbon, and ending with reflections that combine the results of the practical analysis
          with the most recent literature on the impacts of tourism in Lisbon </p>
        <p>Findings - The paper ends with some reflections on the excessive concentration of
          short-term rentals in urban areas and their positive and negative externalities on urban
          life. The results suggest that the city center presents the highest concentration of
          short-time rentals, but not the highest concentration of beds. It also shows that the
          excessive concentration of short-term rentals units may cause serious negative
          externalities that affect the quality of life in its multiple dimensions. </p>
        <p>Originality - The results and the final discussion of this paper contributes to a greater
          knowledge of the spatial distribution of short-term rentals in Portugal and Lisbon and to
          debate the future of short-term rentals in cities that are among the world’s leading
          tourism destinations.  </p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>Tourism</kwd>
        <kwd>urban tourism</kwd>
        <kwd>short-term rentals</kwd>
        <kwd>Portugal</kwd>
        <kwd>Lisbon</kwd>
        <kwd>overtourism</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec sec-type="intro">
      <label>1. INTRODUCTION</label>
      <p>Over the past few years, the issue of urban tourism has gained prominence in political,
        academic and civil society debate, in particular, due to the explosive growth of short-term
        rentals in many major European and North American cities (<xref ref-type="bibr" rid="Ashworth">Ashworth and Page
          2011</xref>; <xref ref-type="bibr" rid="Davidson">Davidson and Lees 2010</xref>; <xref ref-type="bibr" rid="Guttentag">Guttentag 2015</xref>;
        <xref ref-type="bibr" rid="Crommelin">Crommelin et al. 2018</xref>; <xref ref-type="bibr" rid="Adamiak2018">Adamiak 2018</xref>, <xref ref-type="bibr" rid="Adamiak2019">2019</xref>;
        <xref ref-type="bibr" rid="Oskam">Oskam 2020</xref>). According to <xref ref-type="bibr" rid="Pereira2020">Pereira (2020)</xref>, although Lisbon
        quantitatively stands out in the global short-term rentals expansion, both in absolute and
        relative numbers (<xref ref-type="bibr" rid="Adamiak2018">Adamiak 2018</xref>, <xref ref-type="bibr" rid="Adamiak2019">2019</xref>), the discussion about the
        impacts of the excessive concentration of short-term rental is dominated by some specific
        North America and European cities (<xref ref-type="bibr" rid="Schäfer">e.g. Schäfer and Braun 2016</xref>; <xref ref-type="bibr" rid="Hughes">Hughes
          2018</xref>; <xref ref-type="bibr" rid="Crommelin">Crommelin et al. 2018</xref>; <xref ref-type="bibr" rid="Ferreri">Ferreri and Sanyal 2018</xref>;
        <xref ref-type="bibr" rid="Freytag">Freytag and Bauder 2018</xref>; <xref ref-type="bibr" rid="Aznar">Aznar et al. 2018</xref>; <xref ref-type="bibr" rid="Aguilera">Aguilera et
          al. 2019</xref>; <xref ref-type="bibr" rid="Jiao">Jiao and Bai 2020</xref>; <xref ref-type="bibr" rid="Miquel-Àngel">Miquel-Àngel et al. 2020</xref>;
        <xref ref-type="bibr" rid="Celata">Celata and Romano 2020</xref>; <xref ref-type="bibr" rid="Mikulić">Mikulić et al. 2021</xref>). Despite Lisbon is
        an important European urban destination, the Portuguese capital has gone unnoticed by the
        international literature, although this issue has been subjected to numerous scientific
        studies in Portugal itself (see section 4). </p>
      <p> The objective of this paper is to analyse the growth of tourism in Portugal, with a focus
        on short-term rentals. The paper is organised in the following way: a) section 1,
        documenting growth trends in tourism at the global level and focussing on the case of
        Portugal; c) section 2, looking at growth in the short-term rentals market and its
        multidimensional impact; d) section 3, undertaking a spatial analysis <fn>
          <p>The methodology is indicated in section 3.1.</p>
        </fn> of the distribution of short-term rental units, with first a national analysis by NUTS <fn>
          <p>NUTS: Nomenclature of Territorial Units for Statistics (NUTS).</p>
        </fn>. II region and then an analysis of the municipality of Lisbon; e) section 4, seeking
        to interpret the possible consequences of the excessive concentration of short-term rentals
        in urban areas</p>
      <p>The spatial analysis (section 3) and the discussion (sections 4 and 5) aspires to
        contribute to a greater knowledge of the spatial patterns of short-term rental units in
        Portugal and in the municipality of Lisbon and to illustrate how the excessive concentration
        of short-term rentals produces multidimensional and non-linear externalities that need to be
        analysed and recognised.</p>
    </sec>
    <sec sec-type="methods">
      <label>2. TOURISM AND DOMINANT TRENDS</label>
      <p>In the 21st century, tourism has become one of the most important economic activities
        (<xref ref-type="bibr" rid="Becker">Becker 2013</xref>; <xref ref-type="bibr" rid="Page">Page and Connel 2020</xref>; <xref ref-type="bibr" rid="Oskam">Oskam 2020</xref>). In
        recent decades, various cities, regions and even countries have relied on the tourism sector
        as the big opportunity for economic growth. At present, tourism is important for job
        creation and territorial development and is a major component of gross domestic product
        (GDP) in countries that have invested in this sector.</p>
      <p>The factors that have fostered the growth of tourism are well known and include the opening
        of frontiers, the expansion of air travel (especially low-cost flights), the emergence of
        online accommodation booking platforms, among other factors that are related to
        globalisation and the free movement of people across borders.</p>
      <p>According to the World Travel &amp; Tourism Council (WTTC), the tourism sector in 2019
        accounted for 10.3% of global GDP. Also, at global level, it should be noted that the
        tourism sector growth of 3.5% at the same year, slightly faster than the overall growth in
        the global economy, which was 2.5% (<xref ref-type="bibr" rid="WTTC2020a">WTTC 2020a</xref>).</p>
      <p> Europe is the world’s top tourist destination (<xref ref-type="bibr" rid="WTTC2020a">WTTC
          2020a</xref>). The tourism sector plays a very important role in the economy of several
        European countries, above all in Central and Mediterranean Europe (<xref ref-type="bibr"
          rid="Williams">Williams and Lew 2014</xref>; <xref ref-type="bibr" rid="Silva2018">Silva
          et al. 2018</xref>; <xref ref-type="bibr" rid="WTTC2020a">WTTC 2020a</xref>). Looking
        specifically at some indicators at the European Union level <fn>
          <p>Amounts relate to European Union with the current 27 member states.</p>
        </fn>, the number of “establishments and bed-places” <fn>
          <p>Source: Eurostat, ‘Number of establishments, bedrooms and bed-places’ (online data
            code: TIN00181).</p>
        </fn> grew by around 355,000 in 2008, to approximately 620,000 in 2019 (growth of 74%). In
        the case of Portugal, the growth was still faster, with the number of tourist accommodation
        establishments rising from 2,351 in 2008 to more than 7,000 in 2019 (growth of 198%). </p>
      <p> Another indicator of how the tourism trade has grown in Europe is the “arrivals of
        residents/non-residents at tourist accommodation establishments”<fn>
          <p>Source: Eurostat, ‘Arrivals of residents/non-residents at tourist accommodation
            establishments’ (online data code: TIN00174).</p>
        </fn>, with an estimate for the European Union in 2018 of 253,267,989 arrivals, rising in
        2019 to 406,907,066 (growth of 60%). Looking again at Portugal, it can easily be understood
        that the Portuguese economy became increasingly reliant on the tourist trade during the
        2010s, with the estimated number of arrivals fewer than 7 million in 2008 but rising to 16
        million a decade later. </p>
      <p><bold>2.1. Tourism trends in Portugal</bold></p>
      <p>Like many other countries, Portugal has experienced a tourism boom in recent times. In a
        global study carried out by the WTTC, the section on Europe includes a part dedicated to
        Portugal, in which it is stated that the tourism sector in 2019 generated 16.5% of national
        GDP (one of the highest percentages in Europe, and well above the global average of 10%)
        (<xref ref-type="bibr" rid="WTTC2020a">WTTC 2020a</xref>).</p>
      <p> According to the same organisation, the Portuguese tourism sector in 2019 grew by more
        than 4% (versus 1.6% real GDP growth) and it accounted for 900,000 jobs (18.6% of total employment)<fn>
          <p>In the previous year’s report, the same institution indicated that tourism accounted
            for 60% of the jobs created in 2018 (<xref ref-type="bibr" rid="WTTC2019">WTTC
              2019</xref>). </p>
        </fn> (<xref ref-type="bibr" rid="WTTC2020a">WTTC 2020a</xref>, <xref ref-type="bibr"
          rid="WTTC2020b">2020b</xref>). Meanwhile, according to Statistics Portugal, the total
        number of tourists has been increasing continuously in the 2010s, with new record highs for
        arrivals and overnight stays year after year (<xref ref-type="bibr" rid="INE">INE
          2019</xref>). However, there was a clear deceleration in 2018, which could indicate a new
        period of stabilisation (<xref ref-type="bibr" rid="INE">INE 2019</xref>). </p>
      <p>Tourism in Portugal is related to leisure spending (85%) and dominated by foreign tourists
        (70%), notably from the United Kingdom (14%), Spain (14%), France (12%), Germany (11%) and
        Brazil (6%) (<xref ref-type="bibr" rid="WTTC2020a">WTTC 2020a</xref>, <xref ref-type="bibr" rid="WTTC2020b">2020b</xref>). Indeed, it was foreign tourists
        who drove growth in Portuguese tourism in the 2010s (<xref ref-type="bibr" rid="INE">INE 2019</xref>). It is also
        necessary to highlight that in recent years, Portugal has often been cited as a case study
        in global reviews of tourism (<xref ref-type="bibr" rid="WTTC2018">e.g. WTTC 2018</xref>, <xref ref-type="bibr" rid="WTTC2019">2019</xref>,
        <xref ref-type="bibr" rid="WTTC2020a">2020a</xref>).</p>
      <p>Along with the growth in tourism, other related sectors also showed an increase in
        activity, such as hospitality, transports, golf, arts and culture, and also the
        rehabilitation of existing buildings (e.g. turning them into short-term rentals), which
        contributed to turnover in the civil construction and property sectors (<xref ref-type="bibr" rid="Cachinho">Cachinho
          2019</xref>; <xref ref-type="bibr" rid="Cabral">Cabral 2019</xref>).</p>
      <p>From a qualitative point of view, the growth in tourism in Portugal is related a
        well-defined political strategy that in the last decade has sought to replace traditional
        seasonal tourism (above all in the Algarve region) (<xref ref-type="bibr" rid="Silva2018">Silva et al. 2018</xref>) with an
        activity that is spread over the whole year and is not so dependent on sun/beach
        tourism.</p>
      <p>In recent years, international macroeconomic studies (<xref ref-type="bibr" rid="OECD">e.g. OECD 2019</xref>) and
        specific analyses of the tourism sector have stressed the importance of this activity for
        the economic recovery that followed the financial bailout that Portugal exited in 2014.
        According to these studies, the tourism sector played a very important role boosting
        Portugal’s economy and exports in the wake of the financial crisis (<xref ref-type="bibr" rid="Bento">Bento 2016</xref>;
        <xref ref-type="bibr" rid="Pereira2017">Pereira and Teixeira 2017</xref>; <xref ref-type="bibr" rid="Araújo">Araújo 2017</xref>; <xref ref-type="bibr" rid="Silva2019">Silva 2019</xref>;
        <xref ref-type="bibr" rid="OECD">OECD 2019</xref>).</p>
      <p>However, as we shall see in the next few sections, the public debate (political, academic
        and in civil society) on the multidimensional impacts of tourism has grown significantly,
        above all where the impacts of the excessive concentration of short-term rentals in the
        historic centres of the cities are concerned. And the question now arising is: how much is
        too much?</p>
      <p><bold>2.2. Short-term rentals: growth and concerns</bold></p>
      <p>Short-term rentals have emerged of late as a new area for investment and business, becoming
        one of the main engines of contemporary tourism (<xref ref-type="bibr" rid="Ashworth">Ashworth and Page 2011</xref>;
        <xref ref-type="bibr" rid="Davidson">Davidson and Lees 2010</xref>; <xref ref-type="bibr" rid="Guttentag">Guttentag 2015</xref>; <xref ref-type="bibr" rid="Crommelin">Crommelin et al.
          2018</xref>). Short-term rentals are aimed at tourists who want to avoid conventional
        hotel accommodation and seek a more informal tourism experience that is closer to that of
        locals. At the same time, short-term rentals are associated with the emergence of new
        concepts such as the ‘sharing economy’, ‘city branding’ and the use of online platforms,
        which are particularly popular with a younger generation (millennials), not only to reserve
        accommodation (e.g. Booking.com, Airbnb) but also to share their leisure experiences on
        social networks (e.g. Facebook, Instagram) (<xref ref-type="bibr" rid="Botsman">Botsman and Rogers 2010</xref>; <xref ref-type="bibr" rid="Belk">Belk
          2014</xref>; <xref ref-type="bibr" rid="Zervas">Zervas et al. 2017</xref>; <xref ref-type="bibr" rid="Hamari">Hamari et al. 2016</xref>).</p>
      <p>The boom in short-term rentals has triggered various criticisms, especially in major cities
        in Europe and North America (<xref ref-type="bibr" rid="Ashworth">Ashworth and Page 2011</xref>; <xref ref-type="bibr" rid="Davidson">Davidson and Lees
          2010</xref>; <xref ref-type="bibr" rid="Guttentag">Guttentag 2015</xref>; <xref ref-type="bibr" rid="Crommelin">Crommelin et al. 2018</xref>;
        <xref ref-type="bibr" rid="Adamiak2018">Adamiak 2018</xref>, <xref ref-type="bibr" rid="Adamiak2019">2019</xref>). These analyses note that the excessive
        spatial concentration of short-term rentals may be associated with classical urban phenomena
        such as gentrification, the financialisation of housing and touristification (<xref ref-type="bibr" rid="Brenner">Brenner
          et al. 2012</xref>; <xref ref-type="bibr" rid="Aalbers">Aalbers 2016</xref>; <xref ref-type="bibr" rid="Lees2016">Lees et al. 2016</xref>; <xref ref-type="bibr" rid="Lees2018">Lees
            and Phillips 2018</xref>; <xref ref-type="bibr" rid="Oskam">Oskam 2020</xref>; <xref ref-type="bibr" rid="Van">Van Heerden et al. 2020</xref>;
        <xref ref-type="bibr" rid="Mikulić">Mikulić et al. 2021</xref>). Also, studies identifying negative externalities
        arising from short-term rentals have looked at the saturation of local infrastructure and
        implications for the property market (<xref ref-type="bibr" rid="Hoffman">Hoffman and Heisler 2020</xref>; <xref ref-type="bibr" rid="Nieuwland">Nieuwland
          and Melik 2020</xref>; <xref ref-type="bibr" rid="Miquel-Àngel">Miquel-Àngel et al. 2020</xref>; <xref ref-type="bibr" rid="Celata">Celata and Romano
          2020</xref>). Meanwhile, social perceptions of excessive concentration and intensification
        of short-term rentals have triggered various urban tensions and protests on the part social
        movements against the ‘tourist city’ (<xref ref-type="bibr" rid="Colomb">Colomb and Novy 2016</xref>; <xref ref-type="bibr" rid="Hughes">Hughes
          2018</xref>; <xref ref-type="bibr" rid="Chin">Chin and Hampton 2020</xref>; <xref ref-type="bibr" rid="Vodeb">Vodeb et al. 2021</xref>).</p>
      <p>The issue of excessive concentration of short-term rentals does not necessarily arise
        because of the increase in the number of tourists, but rather to the implications that this
        business model has for Portugal’s residential market. As some studies note, the concept of
        the sharing economy hides a reality in which short-term rentals do not function merely as
        complementary income for the property owner, but as informal hotels all year round. In this
        sense, short-term rentals make use of housing units that are withdrawn from the property
        market, so reducing the number of homes available to buy or rent, which has direct
        implications for prices per square metre and which can lead to economic and social
        transformations in these urban areas under pressure (<xref ref-type="bibr" rid="Hoffman">Hoffman and Heisler
        2020</xref>).</p>
      <p>As we shall see, there has been strong growth in short-term rentals in the centres of
        Portugal’s main cities, in particular Lisbon and Porto, which has presented new urban
        challenges and had various economic and social repercussions (<xref ref-type="bibr" rid="Barata2017">Barata-Salgueiro et al.
          2017</xref>; <xref ref-type="bibr" rid="Carvalho">Carvalho et al. 2019</xref>; <xref ref-type="bibr" rid="Rio2018">Rio Fernandes et al. 2018</xref>,
        <xref ref-type="bibr" rid="Rio2019a">2019a</xref>, <xref ref-type="bibr" rid="Rio2019b">2019b</xref>; <xref ref-type="bibr" rid="Seixas2019a">Seixas 2019a</xref>, <xref ref-type="bibr" rid="Seixas2019b">2019b </xref>and
        <xref ref-type="bibr" rid="Seixas2019">Seixaset al. 2019</xref>). In the next section, official data is used to make
        observations on the spatial distribution of short-term rental units in Portugal and in the
        municipality of Lisbon.</p>
    </sec>
    <sec sec-type="results">
      <label>3. SHORT-TERM RENTALS – SPATIAL SCENARIOS</label>
      <p><bold>3.1. Methodology</bold></p>
      <p> Section 3 looks at the spatial distribution of short-term rentals in Portugal, in a
        geographical perspective that, by using a spatial and multiscale analysis, makes it possible
        to identify spatial patterns.   </p>
      <p>From a methodological point of view, it uses spatial data available in the ‘Registo
        Nacional de Turismo’ (RNT) and the ‘Sistema de Informação Geográfica do Turismo’ (SIGTUR),
        both managed by the national tourist board (‘Turismo de Portugal’) <fn>
          <p>This registry contains mandatory information provided by the owners of short-term
            rental properties. This study only uses official data provided by public entities, so
            illegal short-term rental units are not included. There is no data about the Madeira and
            Azores autonomous regions. </p>
        </fn> The information used relates to July 2019 and was explored using geographical
        information systems in ArcGIS software, employing spatial analysis tools such as ‘standard
        distance’, ‘standard deviational ellipse’, ‘central feature’ and ‘clustering hotspots’,
        among others. The observation encompasses around 85,000 geo-referenced points and
        differentiated items of alphanumeric information, as part of an approach based on statistics
        and spatial modelling that can be related to research that involves big data and geographic
        data (<xref ref-type="bibr" rid="Li">Li et al. 2018</xref>; <xref ref-type="bibr"
          rid="Encalada">Encalada-Abarca et al. 2021</xref>). </p>
      <p>The spatial distribution and analysis operate using spatial measurement tools as the “mean
        center” (<xref ref-type="fig" rid="f1">Figure 1</xref>), “standard distance” (<xref
          ref-type="fig" rid="f1">Figure 1</xref>) and “ellipsis distance” (<xref ref-type="fig"
          rid="f1">Figure 1</xref>), and (optimized) “hot spot analysis” (<xref ref-type="fig"
          rid="f4">Figures 4</xref> and <xref ref-type="fig" rid="f5">5</xref>). On other hand,
          <xref ref-type="fig" rid="f2">Figures 2</xref> and <xref ref-type="fig" rid="f2">3</xref>
        are based on a statistical-spatial approach.</p>
      <p>
        <list>
          <list-item>
            <p><italic>Mean center</italic>
            : determines the spatial position of the central point of a distribution, in X and Y.
              Such point is merely theoretical and its existence in the distribution is not
              required.</p>
            <p><disp-formula>
              <mml:math>
                <mml:mrow>
                  <mml:mover>
                    <mml:mi>X</mml:mi>
                    <mml:mo >¯</mml:mo>
                  </mml:mover>
                </mml:mrow>
                <mml:mo>=</mml:mo>
                <mml:mfrac>
                  <mml:mrow>
                    <mml:munderover>
                      <mml:mo>∑</mml:mo>
                      <mml:mrow>
                        <mml:mi>i</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>1</mml:mn>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mi>n</mml:mi>
                      </mml:mrow>
                    </mml:munderover>
                    <mml:msub>
                      <mml:mi>x</mml:mi>
                      <mml:mrow>
                        <mml:mn>1</mml:mn>
                      </mml:mrow>
                    </mml:msub>
                  </mml:mrow>
                  <mml:mi>n</mml:mi>
                </mml:mfrac>
                <mml:mo>,</mml:mo>
                <mml:mrow>
                  <mml:mover>
                    <mml:mi>Y</mml:mi>
                    <mml:mo>¯</mml:mo>
                  </mml:mover>
                </mml:mrow>
                <mml:mo>=</mml:mo>
                <mml:mfrac>
                  <mml:mrow>
                    <mml:munderover>
                      <mml:mo>∑</mml:mo>
                      <mml:mrow>
                        <mml:mi>i</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>1</mml:mn>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mi>n</mml:mi>
                      </mml:mrow>
                    </mml:munderover>
                    <mml:msub>
                      <mml:mi>y</mml:mi>
                      <mml:mrow>
                        <mml:mi>i</mml:mi>
                      </mml:mrow>
                    </mml:msub>
                  </mml:mrow>
                  <mml:mi>n</mml:mi>
                </mml:mfrac>
              </mml:math>
            </disp-formula></p>
            <p>
              <list list-type="bullet">
                <list-item>
                  <p>Where <italic>x</italic><sub>i</sub> and <italic>y</italic><sub>i</sub> are the
                    coordinates for feature <italic>i</italic>, and <italic>n</italic> is equal to
                    the total number of features.</p>
                </list-item>
              </list>
            </p>
          </list-item>
          <list-item>
            <p><italic> Standard distance</italic>
            : calculated to determine the probability of the spatial occurrence of points
              according to the calculated radius.</p>
            <p><disp-formula>
              <mml:math>
                <mml:mi>S</mml:mi>
                <mml:mi>D</mml:mi>
                <mml:mo>=</mml:mo>
                <mml:msqrt>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mo>(</mml:mo>
                          <mml:msub>
                            <mml:mi>x</mml:mi>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                          <mml:mo>−</mml:mo>
                          <mml:mrow>
                            <mml:mover>
                              <mml:mi>X</mml:mi>
                              <mml:mo>¯</mml:mo>
                            </mml:mover>
                          </mml:mrow>
                          <mml:mo>)</mml:mo>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
                <mml:mo>+</mml:mo>
                <mml:msqrt>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mo>(</mml:mo>
                          <mml:msub>
                            <mml:mi>y</mml:mi>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                          <mml:mo>−</mml:mo>
                          <mml:mrow>
                            <mml:mover>
                              <mml:mi>Y</mml:mi>
                              <mml:mo>¯</mml:mo>
                            </mml:mover>
                          </mml:mrow>
                          <mml:mo>)</mml:mo>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
              </mml:math>
            </disp-formula></p>
            <p>Where <italic>x</italic><sub>i</sub> and <italic>y</italic><sub>i</sub> are the
              coordinates for feature <italic>i</italic> represents the Mean Center for the
              features, and <italic>n</italic> is equal to the total numbers of features.</p>
            <p>The Weight Standard Distance (SDw) extends to the following: </p>
            <p><disp-formula>
                <mml:math>
                  <mml:mi>S</mml:mi>
                  <mml:mi>D</mml:mi>
                  <mml:mi>w</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:msqrt>
                    <mml:mfrac>
                      <mml:mrow>
                        <mml:munderover>
                          <mml:mo>∑</mml:mo>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>1</mml:mn>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mi>n</mml:mi>
                          </mml:mrow>
                        </mml:munderover>
                        <mml:msub>
                          <mml:mi>ω</mml:mi>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                          </mml:mrow>
                        </mml:msub>
                        <mml:msup>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:msub>
                              <mml:mi>x</mml:mi>
                              <mml:mrow>
                                <mml:mi>i</mml:mi>
                              </mml:mrow>
                            </mml:msub>
                            <mml:mo>−</mml:mo>
                            <mml:msub>
                              <mml:mrow>
                                <mml:mover>
                                  <mml:mi>X</mml:mi>
                                  <mml:mo>¯</mml:mo>
                                </mml:mover>
                              </mml:mrow>
                              <mml:mrow>
                                <mml:mi>ω</mml:mi>
                              </mml:mrow>
                            </mml:msub>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mn>2</mml:mn>
                          </mml:mrow>
                        </mml:msup>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:munderover>
                          <mml:mo>∑</mml:mo>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>1</mml:mn>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mi>n</mml:mi>
                          </mml:mrow>
                        </mml:munderover>
                        <mml:msub>
                          <mml:mi>ω</mml:mi>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                          </mml:mrow>
                        </mml:msub>
                      </mml:mrow>
                    </mml:mfrac>
                    <mml:mo>+</mml:mo>
                    <mml:mfrac>
                      <mml:mrow>
                        <mml:munderover>
                          <mml:mo>∑</mml:mo>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>1</mml:mn>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mi>n</mml:mi>
                          </mml:mrow>
                        </mml:munderover>
                        <mml:msub>
                          <mml:mi>ω</mml:mi>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                          </mml:mrow>
                        </mml:msub>
                        <mml:msup>
                          <mml:mrow>
                            <mml:mo>(</mml:mo>
                            <mml:msub>
                              <mml:mi>γ</mml:mi>
                              <mml:mrow>
                                <mml:mi>i</mml:mi>
                              </mml:mrow>
                            </mml:msub>
                            <mml:mo>−</mml:mo>
                            <mml:msub>
                              <mml:mrow>
                                <mml:mover>
                                  <mml:mi>Y</mml:mi>
                                  <mml:mo>¯</mml:mo>
                                </mml:mover>
                              </mml:mrow>
                              <mml:mrow>
                                <mml:mi>ω</mml:mi>
                              </mml:mrow>
                            </mml:msub>
                            <mml:mo>)</mml:mo>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mn>2</mml:mn>
                          </mml:mrow>
                        </mml:msup>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:munderover>
                          <mml:mo>∑</mml:mo>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mn>1</mml:mn>
                          </mml:mrow>
                          <mml:mrow>
                            <mml:mi>n</mml:mi>
                          </mml:mrow>
                        </mml:munderover>
                        <mml:msub>
                          <mml:mi>ω</mml:mi>
                          <mml:mrow>
                            <mml:mi>i</mml:mi>
                          </mml:mrow>
                        </mml:msub>
                      </mml:mrow>
                    </mml:mfrac>
                  </mml:msqrt>
                </mml:math>
              </disp-formula></p>
            <p>Where ω<sub>i</sub> is the weight at feature i and {X ̅,Y ̅}{X ̅ω,Y ̅ω} represents
              the weighted Mean Center.</p>
          </list-item>
          <list-item>
            <p><italic>Ellipsis standard</italic>
            : calculated to determine the general direction of the points’ distribution. The
              Standard Deviational Ellipse is given as:</p>
            <p><disp-formula>
              <mml:math>
                <mml:mi>S</mml:mi>
                <mml:mi>D</mml:mi>
                <mml:msub>
                  <mml:mi>E</mml:mi>
                  <mml:mrow>
                    <mml:mi>x</mml:mi>
                  </mml:mrow>
                </mml:msub>
                <mml:mo>=</mml:mo>
                <mml:msqrt>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mo>(</mml:mo>
                          <mml:msub>
                            <mml:mi>x</mml:mi>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                          <mml:mo>−</mml:mo>
                          <mml:mrow>
                            <mml:mover>
                              <mml:mi>X</mml:mi>
                              <mml:mo>¯</mml:mo>
                            </mml:mover>
                          </mml:mrow>
                          <mml:mo>)</mml:mo>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
              </mml:math>
              
            </disp-formula></p>
            <p><disp-formula>
              <mml:math>
                <mml:mi>S</mml:mi>
                <mml:mi>D</mml:mi>
                <mml:msub>
                  <mml:mi>E</mml:mi>
                  <mml:mrow>
                    <mml:mi>y</mml:mi>
                  </mml:mrow>
                </mml:msub>
                <mml:mo>=</mml:mo>
                <mml:msqrt>
                  <mml:mfrac>
                    <mml:mrow>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msup>
                        <mml:mrow>
                          <mml:mo>(</mml:mo>
                          <mml:msub>
                            <mml:mi>x</mml:mi>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                          <mml:mo>−</mml:mo>
                          <mml:mrow>
                            <mml:mover>
                              <mml:mi>X</mml:mi>
                              <mml:mo>¯</mml:mo>
                            </mml:mover>
                          </mml:mrow>
                          <mml:mo>)</mml:mo>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
              </mml:math>
              
            </disp-formula></p>
            <p>Where x<sub>i</sub> and y<sub>i</sub> are the coordinates for feature i, {X ̅,Y ̅}
              represents the Mean Center for the features, and n is equal to the total numbers of
              features.</p>
            <p>The angle of rotation is calculated as:</p>
            <p><disp-formula><mml:math>
              <mml:mi>tan</mml:mi>
              <mml:mo>⁡</mml:mo>
              <mml:mi>θ</mml:mi>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>A</mml:mi>
                  <mml:mo>+</mml:mo>
                  <mml:mi>B</mml:mi>
                </mml:mrow>
                <mml:mi>C</mml:mi>
              </mml:mfrac>
            </mml:math></disp-formula></p>
            <p><disp-formula>
              
              <mml:math>
                <mml:mi>A</mml:mi>
                <mml:mo>=</mml:mo>
                <mml:mrow>
                  <mml:mo>(</mml:mo>
                  <mml:munderover>
                    <mml:mo>∑</mml:mo>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mi>n</mml:mi>
                    </mml:mrow>
                  </mml:munderover>
                  <mml:msubsup>
                    <mml:mrow>
                      <mml:mover>
                        <mml:mi>x</mml:mi>
                        <mml:mo>~</mml:mo>
                      </mml:mover>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msubsup>
                  <mml:mo>−</mml:mo>
                  <mml:munderover>
                    <mml:mo>∑</mml:mo>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                      <mml:mo>=</mml:mo>
                      <mml:mn>1</mml:mn>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mi>n</mml:mi>
                    </mml:mrow>
                  </mml:munderover>
                  <mml:msubsup>
                    <mml:mrow>
                      <mml:mover>
                        <mml:mi>y</mml:mi>
                        <mml:mo>~</mml:mo>
                      </mml:mover>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mi>i</mml:mi>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msubsup>
                  <mml:mo>)</mml:mo>
                </mml:mrow>
              </mml:math>
            </disp-formula></p>
            <p><disp-formula>
              <mml:math>
                <mml:mi>B</mml:mi>
                <mml:mo>=</mml:mo>
                <mml:msqrt>
                  <mml:msup>
                    <mml:mrow>
                      <mml:mo></mml:mo>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msubsup>
                        <mml:mrow>
                          <mml:mover>
                            <mml:mi>x</mml:mi>
                            <mml:mo>~</mml:mo>
                          </mml:mover>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>−</mml:mo>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msubsup>
                        <mml:mrow>
                          <mml:mover>
                            <mml:mi>y</mml:mi>
                            <mml:mo>~</mml:mo>
                          </mml:mover>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msubsup>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msup>
                  <mml:mo>+</mml:mo>
                  <mml:mn>4</mml:mn>
                  <mml:msup>
                    <mml:mrow>
                      <mml:mo>(</mml:mo>
                      <mml:munderover>
                        <mml:mo>∑</mml:mo>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                          <mml:mo>=</mml:mo>
                          <mml:mn>1</mml:mn>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>n</mml:mi>
                        </mml:mrow>
                      </mml:munderover>
                      <mml:msub>
                        <mml:mrow>
                          <mml:mover>
                            <mml:mi>x</mml:mi>
                            <mml:mo>¯</mml:mo>
                          </mml:mover>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:msub>
                        <mml:mrow>
                          <mml:mover>
                            <mml:mi>y</mml:mi>
                            <mml:mo>¯</mml:mo>
                          </mml:mover>
                        </mml:mrow>
                        <mml:mrow>
                          <mml:mi>i</mml:mi>
                        </mml:mrow>
                      </mml:msub>
                      <mml:mo>)</mml:mo>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msup>
                </mml:msqrt>
              </mml:math>
            </disp-formula></p>
            <p><disp-formula>
              <mml:math>
                <mml:mi>C</mml:mi>
                <mml:mo>=</mml:mo>
                <mml:mn>2</mml:mn>
                <mml:munderover>
                  <mml:mo>∑</mml:mo>
                  <mml:mrow>
                    <mml:mi>i</mml:mi>
                    <mml:mo>=</mml:mo>
                    <mml:mn>1</mml:mn>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mrow>
                </mml:munderover>
                <mml:msub>
                  <mml:mrow>
                    <mml:mover>
                      <mml:mi>x</mml:mi>
                      <mml:mo>~</mml:mo>
                    </mml:mover>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:mi>i</mml:mi>
                  </mml:mrow>
                </mml:msub>
                <mml:msub>
                  <mml:mrow>
                    <mml:mover>
                      <mml:mi>y</mml:mi>
                      <mml:mo>~</mml:mo>
                    </mml:mover>
                  </mml:mrow>
                  <mml:mrow>
                    <mml:mi>i</mml:mi>
                  </mml:mrow>
                </mml:msub>
              </mml:math>
            </disp-formula></p>
            <p>The standard deviations for x-axis and y-axis are:</p>
            <p><disp-formula>
              <mml:math>
                <mml:msub>
                  <mml:mi>σ</mml:mi>
                  <mml:mrow>
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                      <mml:msup>
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                          <mml:mi>cos</mml:mi>
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                          <mml:mi>θ</mml:mi>
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                            <mml:mrow>
                              <mml:mi>i</mml:mi>
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                          </mml:msub>
                          <mml:mi>sin</mml:mi>
                          <mml:mo>⁡</mml:mo>
                          <mml:mi>θ</mml:mi>
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                        </mml:mrow>
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                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
              </mml:math>
            </disp-formula></p>
            <p><disp-formula>
              <mml:math>
                <mml:msub>
                  <mml:mi>σ</mml:mi>
                  <mml:mrow>
                    <mml:mi>y</mml:mi>
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                <mml:mo>=</mml:mo>
                <mml:msqrt>
                  <mml:mn>2</mml:mn>
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                        </mml:mrow>
                      </mml:munderover>
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                            </mml:mrow>
                            <mml:mrow>
                              <mml:mi>i</mml:mi>
                            </mml:mrow>
                          </mml:msub>
                          <mml:mi>cos</mml:mi>
                          <mml:mo>⁡</mml:mo>
                          <mml:mi>θ</mml:mi>
                          <mml:mo>−</mml:mo>
                          <mml:msub>
                            <mml:mrow>
                              <mml:mover>
                                <mml:mi>y</mml:mi>
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                            <mml:mrow>
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                          <mml:mi>sin</mml:mi>
                          <mml:mo>⁡</mml:mo>
                          <mml:mi>θ</mml:mi>
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                        </mml:mrow>
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                          <mml:mn>2</mml:mn>
                        </mml:mrow>
                      </mml:msup>
                    </mml:mrow>
                    <mml:mi>n</mml:mi>
                  </mml:mfrac>
                </mml:msqrt>
              </mml:math>
            </disp-formula></p>
          </list-item>
        </list>
      </p>
      <p> Lastly, the density maps (Figures 4 and 5) aim to estimate the intensity of occurrence of
        a given specific phenomenon in a certain territory, giving the statistically significant hot
        and cold spots using the Getis-Ord Gi* statistic. Using this method, it is possible generate
        a grid with values that translate the phenomenon’s intensity in each area unit. </p>
      <p><disp-formula>
        
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                  </mml:munderover>
                  <mml:msubsup>
                    <mml:mi>w</mml:mi>
                    <mml:mrow>
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                      <mml:mo>,</mml:mo>
                      <mml:mi>j</mml:mi>
                    </mml:mrow>
                    <mml:mrow>
                      <mml:mn>2</mml:mn>
                    </mml:mrow>
                  </mml:msubsup>
                  <mml:mo>−</mml:mo>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:munderover>
                      <mml:mo>∑</mml:mo>
                      <mml:mrow>
                        <mml:mi>j</mml:mi>
                        <mml:mo>=</mml:mo>
                        <mml:mn>1</mml:mn>
                      </mml:mrow>
                      <mml:mrow>
                        <mml:mi>n</mml:mi>
                      </mml:mrow>
                    </mml:munderover>
                    <mml:msub>
                      <mml:mi>w</mml:mi>
                      <mml:mrow>
                        <mml:mi>i</mml:mi>
                        <mml:mo>,</mml:mo>
                        <mml:mi>j</mml:mi>
                      </mml:mrow>
                    </mml:msub>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>n</mml:mi>
                  <mml:mo>−</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
              </mml:mfrac>
            </mml:msqrt>
          </mml:mfrac>
        </mml:math>
      </disp-formula></p>
      <p>Getis-Ord Gi* (Spatial Statistics), where <italic>x<sub>i</sub></italic> is the attribute
        value for feature <italic>j</italic>, w<sub>i,j</sub>  is the spatial weight between feature
          <italic>i</italic> and <italic>j</italic>, and<italic>n</italic> is equal to the total
        number of features.</p>
      <p><bold>3.2. Short-term rentals in Portugal</bold></p>
      <p>In the summer of 2019, there were 84,835 short-term rental units in Portugal with a
        capacity to accommodate 489,659 visitors. <xref ref-type="table" rid="t1">Table 1</xref>,
        which shows these units by NUTS II, makes it possible to draw the following conclusions: a)
        Algarve (39.5%) and Lisbon Metropolitan Area (29.3%) stand out as the statistical regions
        with the largest percentages of short-term rentals; b) Alentejo has just 3.2% of the
        national total; c) North (16.8%) and Centre (11.3%) are in an intermediate position in terms
        of short-term rentals.</p>
      <p><table-wrap id="t1">
          <label>Table 1:</label>
          <caption>
            <title>Short-term rentals in Portugal in 2019, by NUTS II.</title>
          </caption>
          <table border="1"
            style="width:354.15pt;border-collapse:collapse;border:none;mso-border-alt:  solid #BFBFBF .5pt;mso-border-themecolor:background1;mso-border-themeshade:  191;mso-yfti-tbllook:1184;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-insideh:  .5pt solid #BFBFBF;mso-border-insideh-themecolor:background1;mso-border-insideh-themeshade:  191;mso-border-insidev:.5pt solid #BFBFBF;mso-border-insidev-themecolor:background1;  mso-border-insidev-themeshade:191"
            width="472">
            <thead>
              <tr>
                <td rowspan="1" colspan="1" valign="top"><bold>NUTS II</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>Short-term
                    rentals</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>Bed-places</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top">
                  <p><bold>Short-term rentals</bold></p>
                  <p><bold>(%)</bold></p>
                </td>
                <td rowspan="1" colspan="1" align="right" valign="top">
                  <p><bold>Area (NUTS) </bold></p>
                  <p><bold>(km2)</bold></p>
                </td>
              </tr>
            </thead>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1" valign="top">North</td>
                <td rowspan="1" colspan="1" align="right" valign="top">14,262</td>
                <td rowspan="1" colspan="1" align="right" valign="top">82,847</td>
                <td rowspan="1" colspan="1" align="right" valign="top">16.8</td>
                <td rowspan="1" colspan="1" align="right" valign="top">21,278</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1" valign="top">Centre</td>
                <td rowspan="1" colspan="1" align="right" valign="top">9,557</td>
                <td rowspan="1" colspan="1" align="right" valign="top">70,021</td>
                <td rowspan="1" colspan="1" align="right" valign="top">11.3</td>
                <td rowspan="1" colspan="1" align="right" valign="top">28,405</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1" valign="top">Lisbon Metropolitan Area</td>
                <td rowspan="1" colspan="1" align="right" valign="top">24,847</td>
                <td rowspan="1" colspan="1" align="right" valign="top">144,900</td>
                <td rowspan="1" colspan="1" align="right" valign="top">29.3</td>
                <td rowspan="1" colspan="1" align="right" valign="top">3,015</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1" valign="top">Alentejo</td>
                <td rowspan="1" colspan="1" align="right" valign="top">2,695</td>
                <td rowspan="1" colspan="1" align="right" valign="top">20,486</td>
                <td rowspan="1" colspan="1" align="right" valign="top">3.2</td>
                <td rowspan="1" colspan="1" align="right" valign="top">31,711</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1" valign="top">Algarve</td>
                <td rowspan="1" colspan="1" align="right" valign="top">33,474</td>
                <td rowspan="1" colspan="1" align="right" valign="top">171,405</td>
                <td rowspan="1" colspan="1" align="right" valign="top">39.5</td>
                <td rowspan="1" colspan="1" align="right" valign="top">5,412</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>Total</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>84,835</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>489,659</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>100</bold></td>
                <td rowspan="1" colspan="1" align="right" valign="top"><bold>-</bold></td>
              </tr>
            </tbody>
          </table>
        </table-wrap>Source: RNT and SIGTUR.</p>
      <p>This territorial analysis can be deepened. For example, the Lisbon Metropolitan Area is the
        second statistical region in terms of short-term rental units, but is the smallest region
        geographically, that is, its short-term rental units are closer together. By contrast,
        Alentejo has the lowest percentage of short-term rental units and is the largest region,
        that is, the spatial distribution of short-term rentals in this region is very dispersed
        when compared to other regions (<xref ref-type="table" rid="t1">Table 1</xref> and <xref
          ref-type="fig" rid="f1">Figure 1</xref>).</p>
      <p>
        <fig id="f1">
          <label>Figure 1:</label>
          <caption>
            <p>Short-term rentals in Portugal and NUTS II.</p>
          </caption>
          <p><graphic xlink:href="THM-27-581-f1.jpg"/></p>
          <p>Source: RNT and SIGTUR.</p>
        </fig>
      </p>
      <p><xref ref-type="fig" rid="f1">Figure 1</xref> presents the spatial distribution of
        short-term rentals units in Portugal. The following points summarise the most important
        trends: </p>
      <p>
        <list>
          <list-item>
            <p>The distribution of short-term rental units is not uniform, with higher
              concentrations near the coast and lower numbers on the eastern border with Spain. This
              spatial distribution of short-term rentals can be empirically correlated with
              population density. In fact, there are more short-term rental units in the main
              Portuguese urban areas on the coastline, particularly around Lisbon, Porto, and in
              Algarve, and the interior of the country presents low numbers, with minor exceptions
              in places with more tourism activity and in medium and small urban conglomerations;
            </p>
          </list-item>
          <list-item>
            <p>There is a significant and fairly even distribution in the Algarve region. This
              spatial distribution can be empirically related to a longstanding demand from tourists
              for second homes, with Portuguese and foreign visitors arriving in this region in the
              warmer months;   </p>
          </list-item>
          <list-item>
            <p>The short-term rental units that exist in Lisbon and Porto (and surrounding areas)
              are recent and result from the growth in urban tourism; </p>
          </list-item>
        </list>
      </p>
      <p> The above trends have not been inferred from mere observation of <xref ref-type="fig"
          rid="f1">Figure 1</xref> (the scale may be misleading and hide thousands of overlapping
        points) but also from spatial statistics, namely the ‘standard distance’, ‘standard
        deviational ellipse’ and ‘central feature’ measures<fn>
          <p>These measures take into consideration the exact geographical location of the 84,835
            short-term rental units. </p>
        </fn>: <list>
          <list-item>
            <p>The ‘standard distance’ measure makes it possible to perceive that the tendency for
              concentration of short-term rental units in Portugal is especially in the Centre and
              Algarve statistical regions;</p>
          </list-item>
          <list-item>
            <p>The ‘standard deviational ellipse’ reinforces the idea of a tendency for centrality
              between the Centre and South of the country. Most importantly, the ellipse makes it
              possible to highlight the tendency for short-term rental units to be near the
              coast;</p>
          </list-item>
          <list-item>
            <p>The ‘central feature’ point is located southeast of the municipality of Lisbon. This
              is the case because the municipality of Lisbon accounts for 22% of the national total
              of short-term rental units and the Lisbon Metropolitan Area 29%. It should be
              highlighted that the analysis of the 84,835 short-term rental units across Portugal
              indicates centrality precisely for the country’s capital.</p>
          </list-item>
        </list></p>
      <p><bold>3.3. Short-term rentals in the municipality of Lisbon</bold></p>
      <p> In July 2019, Lisbon had 18,661 short-term rental units with 106,721 bed-places <fn>
          <p>These 106,721 bed-places are equivalent to 21% of Lisbon’s resident population (about
            507,000). </p>
        </fn>.</p>
      <p>
        <fig id="f2">
          <label>Figure 2:</label>
          <caption>
            <p>Distribution of short-term rental units in the municipality of Lisbon.</p>
          </caption>
          <p><graphic xlink:href="THM-27-581-f2.jpg"/></p>
          <p>Source: RNT and SIGTUR.</p>
        </fig>
      </p>
      <p>According to <xref ref-type="fig" rid="f2">Figure 2</xref>, in the municipality of Lisbon
        short-term rentals are very concentrated in the city’s historic centre. By contrast, more
        peripheral areas, although they tend to have a higher population density, have fewer
        short-term rental units. For example, the parish of Santa Maria Maior (Lisbon’s most
        central, covering the downtown area) in 2019 had more than 4,500 short-term rental units,
        while the parish of Santa Clara (on the northern edge of the city) had fewer than 10.</p>
      <p>
        <fig id="f3">
          <label>Figure 3:</label>
          <caption>
            <p>Short-term rental units per square km (left) and short-term rental bed-places per 100
              inhabitants (right). The smooth white traces display general buildings.</p>
          </caption>
          <p><graphic xlink:href="THM-27-581-f3.jpg"/></p>
          <p>Source: RNT and SIGTUR.</p>
        </fig>
      </p>
      <p>Observing <xref ref-type="fig" rid="f3">Figure 3</xref>, specifically the city centre, in
        the parishes of Santa Maria Maior and Misericórdia there are more than 1,000 short-term
        rental units per square kilometre, and more than 100 bed-places per 100 inhabitants (in
        fact, almost 200 bed-places per 100 inhabitants). In some peripheral parishes, as in the
        case of Santa Clara, the corresponding figures are near zero. This shows that short-term
        rental units are very much concentrated in the oldest parishes of Lisbon, not only based on
        their geographical position and on absolute numbers (<xref ref-type="fig" rid="f2">Figure
          2</xref>) but also on relative ones (<xref ref-type="fig" rid="f3">Figure 3</xref>).</p>
      <p>
        <fig id="f4">
          <label>Figure 4:</label>
          <caption>
            <p>Clustering of short-term rentals in the municipality of Lisbon.</p>
          </caption>
          <p><graphic xlink:href="THM-27-581-f4.jpg"/></p>
          <p>Source: RNT and SIGTUR.</p>
        </fig>
      </p>
      <p>Following the spatial analysis, <xref ref-type="fig" rid="f4">Figure 4</xref> makes it
        possible to observe the tendency for clustering and the spatial patterns of short-term
        rental units in Lisbon. The majority of short-term rentals are downtown, in a tightly
        circumscribed geographical space. As shown in <xref ref-type="fig" rid="f4">Figure 4</xref>,
        most short-term rental units are concentrated in the red area (hotspot area). Regarding this
        very circumscribed area, some results should be highlighted: a) the red zone contains more
        than 12,000 short-term rental units, which is 65% of the city’s total and 14% of the
        national total; b) the red area is 4 square kilometres and so has more than 3,000 short-term
        rental units per square kilometre; c) in these 4 square kilometres are located 14% of all
        short-term rental units in Portugal.</p>
      <p>In the blue areas (cold spots) one can find various intermediate areas, in which there is
        still a significant concentration of short-term rentals; these areas correspond to more
        recent urban areas built in the first half of the 20th century. In the rest of the city,
        spatial statistics make it possible to identify areas of little significance, that is, where
        short-term rental units are very scattered, and areas in which this activity is absent.</p>
      <p>
        <fig id="f5">
          <label>Figure 5:</label>
          <caption>
            <p>Clustering of numbers of bed-places in short-term rental units in the municipality of
              Lisbon.</p>
          </caption>
          <p><graphic xlink:href="THM-27-581-f5.jpg"/></p>
          <p>Source: RNT and SIGTUR.</p>
        </fig>
      </p>
      <p>As can be seen in <xref ref-type="fig" rid="f5">Figure 5</xref>, the concentration of
        establishments with a high number of bed-places is not exactly in the centre of the city,
        but rather in areas that are immediately adjacent to it. This relates to the average size of
        housing units, which are generally smaller in the historic centre. In this way, the higher
        numbers of bed-places are still in a central area, but in neighbourhoods built in the first
        half of the 20th century and not in the historic centre, where the housing stock is
        older.</p>
    </sec>
    <sec sec-type="discussion">
      <label>4. THE SHORT-TERM RENTALS DEBATE</label>
      <p>As pointed out in section 2, in the last decade the tourism in Portugal has grown extremely
        fast. It is to be noted that short-term rentals were a minor activity at the start of the
        2010s, based on informal and seasonal models (<xref ref-type="bibr" rid="Rio2019a">Rio Fernandes et al. 2019a</xref>). This
        tourist activity was almost exclusively in the Algarve region, with the practice of second
        homes being rented out to tourists during the summer. In the decade that followed,
        short-term rentals spread across the whole country (<xref ref-type="bibr" rid="Rio2019a">Rio Fernandes et al.
        2019a</xref>). Looking more closely at the municipality of Lisbon, in 2010 the number of
        short-term rental units there was around 3,000, with explosive growth to 18,661 units in
        mid-2019 (that is, growth of more than 500%).</p>
      <p><bold>4.1. Short-term rentals in the municipality of Lisbon</bold></p>
      <p>As analysed in section 3.2., the distribution of short-term rental units in Portugal is
        uneven. The spatial concentration of short-term rental units is predominantly near the
        coast, especially in the Algarve region. However, the most significant growth has been seen
        on the west coast, mainly in the Lisbon and Porto Metropolitan Areas, with the municipality
        of Lisbon alone having 22% of the national total.</p>
      <p><xref ref-type="bibr" rid="Adamiak2018">Adamiak (2018)</xref> identifies the European cities with the highest number of
        Airbnb listings in 2017, showing Paris (56,800), London (55,400) and Rome (25,300) as the
        top 3. The city of Lisbon, which has 12,400 Airbnb listings, was very close of Amsterdam
        (12,500), Istanbul (12,900), Madrid (14,900) and Berlin (16,600). However, based on the
        number of Airbnb listings per 1,000 inhabitants, the Portuguese capital was in sixth
        position, behind Batumi, Split, Marbella, Venice, and Florence (<xref ref-type="bibr" rid="Adamiak2018">Adamiak 2018</xref>).
        It is thus evident that the city of Lisbon stands out in the European context for the great
        significance of its short-term rentals, in both the absolute and relative approaches.</p>
      <p>The boom in short-term rentals in Lisbon is thus one more case of a major European city
        that is having to cope with the excessive concentration of this activity (<xref ref-type="bibr" rid="Adamiak2018">Adamiak
          2018</xref>).It should be noted that the city of Lisbon until recently had no tradition of
        tourist accommodation aside from hotels (<xref ref-type="bibr" rid="Rio2019b">Rio Fernandes et al. 2019b</xref>). The
        figure of 18,661 short-term rental units in the municipality of Lisbon thus testifies to a
        violent social, economic, cultural and urban transformation that has occurred in a short
        space of time (mainly in the period 2014-2019).</p>
      <p>This spatial-quantitative scenario analysed in section 3.2 demonstrates a functional
        imbalance that creates an unavoidable tension between residential and tourist functions
        (<xref ref-type="bibr" rid="Mendes2020">Mendes 2020</xref>). This tension is all the greater if one considers that the
        transformation has taken place in a very short period. It should be noted that a wider
        analysis of tourism in Lisbon would be necessary to take account also of the number of beds
        available in hotels, which are also concentrated in the city centre. These functional
        imbalances necessarily take our analysis to other concepts, such as the tourism carrying
        capacity (<xref ref-type="bibr" rid="Barata2017">Barata-Salgueiro et al. 2017</xref>).</p>
      <p>The rising profile of tourism in the Portuguese capital has not gone unnoticed by
        international players. According to the “<italic>Global Destination Cities Index
          2019</italic>”, the city of Lisbon is among those that stand out in global terms where the
        growth of tourism is concerning (<xref ref-type="bibr" rid="Mastercard">Mastercard 2019</xref>). The references to Lisbon in
        these international studies are relatively recent, in a trend that has become established
        only in the last decade, due to the rapid growth in urban tourism in the capital. The
        countless tourism awards attributed to Lisbon are another factor, to the extent that they
        reflect tourists’ preferences. It can be said that urban marketing policies and efforts to
        raise the profile of Lisbon as a city with a history and which is safe and has a good
        quality of life, have been successful. This economic model has been widely advocated by
        policymakers during and after economic crises (<xref ref-type="bibr" rid="Seixas2019">Seixas and Antunes 2019</xref>).</p>
      <p>In parallel with the growth in the short-term rental business, interest in the city’s
        property stock has also increased on the part of international investors (<xref ref-type="bibr" rid="Antunes2020">Antunes and
          Seixas 2020</xref>; <xref ref-type="bibr" rid="Gonçalves">Gonçalves et al. 2020</xref>; <xref ref-type="bibr" rid="Franco">Franco and Santos
          2021</xref>). This phenomenon is cited in the annual study <italic>Emerging Trends in Real
          Estate: Europe 2020®</italic>, which places the Portuguese capital 10th among European
        cities in terms of its attractiveness for property investment, in part due to the projected
        returns on investment in the tourism business (<xref ref-type="bibr" rid="ULI">ULI and PwC 2019</xref>). For its part,
        the Organisation for Economic Co-operation and Development goes so far as to link the growth
        in tourism and the rise in housing prices, in stating that “<italic>the boom in the tourism
          sector and demand by non-residents (responding to government incentives tying visas to
          dwelling purchases) have been significant factors behind the strong growth in house prices
          in some locations</italic>” (<xref ref-type="bibr" rid="OECD">OECD 2019, 21</xref>).</p>
      <p>Inevitably, tourism creates externalities in destinations and is a catalyst of change, due
        to pressures generated from tourist flows and activities. As studies on tourism carrying
        capacity have shown, it is difficult (or even impossible) to define <italic>a specific
          number for how much is too much</italic> (<xref ref-type="bibr" rid="OReilly">O’Reilly 1986</xref>; <xref ref-type="bibr" rid="Coccossis">Coccossis and
            Mexa 2004</xref>; <xref ref-type="bibr" rid="McCool">McCool and Lime 2001</xref>; <xref ref-type="bibr" rid="Zelenka">Zelenka and Kacetl 2014</xref>;
        <xref ref-type="bibr" rid="Kennell">Kennell 2014</xref>). Although tourism carrying capacity has been studied for
        several decades, a theoretical or practical consensus is still a long way off. The tourism
        carrying capacity concept is based on the idea that tourism development must be related to
        sustainability principles; otherwise, local systems can be affected and even the
        destination’s quality, competitiveness and attractiveness undermined. Tourism carrying
        capacity has presented various difficulties in terms of the quantitative measuring of
        overcapacity, although there are cases of practical use, especially in nature reserves, and
        some studies have also tried to apply the carrying capacity concept in urban areas, using a
        combination of quantitative and qualitative approaches (<xref ref-type="bibr" rid="Coccossis">Coccossis and Mexa
          2004</xref>; <xref ref-type="bibr" rid="McKinsey">McKinsey and WTTC 2017</xref>).</p>
      <p>The measurement of carrying capacity is not only complex but must be adapted to each
        context (<xref ref-type="bibr" rid="McCool">McCool and Lime 2001</xref>; <xref ref-type="bibr" rid="Kennell">Kennell 2014</xref>). <xref ref-type="bibr" rid="Getz">Getz
          (1983)</xref> identifies six categories that must be especially taken into account, namely
        the ‘physical’, ‘economic’, ‘perceptual’, ‘social’, ‘ecological’, and ‘political’
        dimensions. In the same way, <xref ref-type="bibr" rid="McKinsey">McKinsey and WTTC (2017)</xref> identify some topics that
        are especially important to identify excessive tourist concentration, namely ‘alienated
        local residents’, ‘degraded tourist experience’, ‘overloaded infrastructure’, ‘damage to
        nature’ and ‘threats to culture and heritage’.</p>
      <p>Looking at the case of Lisbon, it is possible to observe that most of these domains are
        undergoing transformation, if not saturation. For this reason, it is not surprising that a
        broad range of scientific studies has underscored the multidimensional negative impacts of
        short-term rentals in Portuguese urban areas, especially in the municipality of Lisbon.
        These studies highlight some major concerns about the intensification of tourism, such as
        gentrification, the financialisation of housing and touristification (<xref ref-type="bibr" rid="Tulumello2016">Tulumello
          2016</xref>; <xref ref-type="bibr" rid="Antunes2018">Antunes 2018</xref>, <xref ref-type="bibr" rid="Antunes2019">2019</xref>, <xref ref-type="bibr" rid="Antunes2021">2021</xref>;
        <xref ref-type="bibr" rid="Cocola">Cocola-Gant 2018</xref>; <xref ref-type="bibr" rid="Ferreira">Ferreira and Antunes 2020</xref>; <xref ref-type="bibr" rid="Mendes2020">Mendes
          2016</xref>, <xref ref-type="bibr" rid="Mendes2018">2018</xref>, <xref ref-type="bibr" rid="Mendes2019">2019</xref>; <xref ref-type="bibr" rid="Lestegás">Lestegás 2019</xref>,
        <xref ref-type="bibr" rid="Lestegás">Lestegás et al. 2019</xref>; <xref ref-type="bibr" rid="Santos">Santos 2019</xref>; <xref ref-type="bibr" rid="Sequera">Sequera and Nofre
          2020</xref>; <xref ref-type="bibr" rid="Tulumello2021">Tulumello and Allegretti 2021</xref>; <xref ref-type="bibr" rid="Van">Van Heerden et al.
            2020</xref>), the rapid rise in house prices and rents (<xref ref-type="bibr" rid="OECD">OECD 2019</xref>;
        <xref ref-type="bibr" rid="Antunes2020">Antunes and Seixas 2020</xref>; <xref ref-type="bibr" rid="Gonçalves">Gonçalves et al. 2020</xref>; <xref ref-type="bibr" rid="Franco">Franco and
          Santos 2021</xref>), the displacement of local shops (<xref ref-type="bibr" rid="Barata2020">Barata-Salgueiro 2020</xref>),
        and urban tensions that are visible, for example, in the growth of social movements and
        activists (<xref ref-type="bibr" rid="Seixas2020">Seixas and Guterres 2020</xref>; <xref ref-type="bibr" rid="Mendes2020">Mendes 2020</xref>). These big
        topics – already widely studied by academics – overshadow other important concerns, such as
        the economy’s dependency on tourism sector (in terms of GDP and employment) or issues more
        familiar to the perception of locals, such as the tension between residential and tourist
        functions, the saturation and overloading of local infrastructure (e.g. public transport,
        public spaces) and negative feelings towards tourism. </p>
      <p>All these negative externalities are more intense in the city centre, where, as shown in
        the analysis above, there are around 12,000 short-term rental units (14% of all short-term
        rentals in Portugal), circumscribed in 4 square kilometres in Lisbon’s older neighbourhoods.
        In this small and fragile area, the intensification of short-term rental is a new urban
        challenge with multidimensional impacts. </p>
      <p>In the absence of an exact measure that could indicate how much is too much, it seems that
        there are overall, complex and multidimensional factors that could qualitatively point to
        this in urban areas. For example, a rapid increase in prices per square metre to buy and
        rent houses, growing difficulties in accessing affordable housing, signs of changes in the
        social fabric and the forced departure of local people, the saturation of local
        infrastructure, neighbourhoods becoming deserted at night, or the substitution of retail
        establishments serving the needs of local people by souvenir shops with global esthetical
        symbology.</p>
      <p> To deal with these multiple negative externalities, Lisbon and Porto municipalities
        decided to create a tourist tax (to cover the annual investment on the requalification of
        the public space, to assure artistic and cultural dynamism and adequate urban services)
        (<xref ref-type="bibr" rid="Borges">Borges et al. 2020</xref>), and more recently decided to suspend the licensing of
        new short-term rental units in the so-called ‘areas of contention’ (<xref ref-type="bibr" rid="Antunes2020">Antunes
          2020</xref>; <xref ref-type="bibr" rid="Pereira2020">Pereira 2020</xref>). </p>
      <p>To a degree, it can be said that the negative impacts cited here are not a consequence of
        the existence of short-term rental units, but of their excessive concentration in certain
        areas, coming close to monopolising the land use. However, this concentration is not in
        itself a clear indicator. For example, the Algarve is the region in Portugal with the most
        short-term rental units, but there is no debate about negative impacts from that activity
        (<xref ref-type="bibr" rid="Rio2019a">Rio Fernandes et al. 2019a</xref>). This means that the definition of the excessive
        concentration of short-term rental varies depending on the area and on the pre-existing
        multidimensional dynamics in the territory.</p>
      <p><bold>4.2. COVID-19: an opportunity for local people?</bold></p>
      <p> In a way that no one had foreseen, the boom in urban tourism was stopped in its tracks not
        by the pressure of social movements or political decisions, but by Nature, in the form of a
        global pandemic. Around the world, tourism has undergone a major contraction
        (<xref ref-type="bibr" rid="Bhrammanachote">Bhrammanachote and Sawangdee 2021</xref>). The short-term rental business, which
        had until very recently been a low-risk investment with rapid returns, is facing serious
        difficulties. In the case of Portugal, the country is among the European countries that are
        most vulnerable to the economic impacts of COVID-19, mainly due to the importance of the
        tourism sector for GDP and exports (<xref ref-type="bibr" rid="UNWTO">UNWTO 2020</xref>). </p>
      <p>Just what transformations will result from the pandemic has yet to be seen and calculated
        (<xref ref-type="bibr" rid="Ferreira">Ferreira and Antunes 2020</xref>). However, from a political point of view, some
        answers are already forthcoming. The mayor of Lisbon, in an interview with The Guardian,
        said that:</p>
      <p> “<italic>In a certain sense Covid has created an opportunity.… The virus didn’t ask us for
          permission to come in, but we have the ability to use this time to think and to see how we
          can move in a direction to correct things and put them on the right track.… There is that
          tension: too much of a thing [short-term rentals] is not good, but too little of it is a
          problem.… It’s a question of balance.” (The Guardian, 1 December 2020, Fernando Medina,
          mayor of Lisbon). Accessed on 5 December 2020</italic>
        <fn>
          <p>‘'Covid created an opportunity': Lisbon to turn tourist flats into homes’, The
            Guardian,
            https://www.theguardian.com/world/2020/dec/01/covid-created-an-opportunity-lisbon-turns-20000-tourist-flats-into-homes.</p>
        </fn>. </p>
      <p> These statements from Fernando Medina are very pertinent, since they represent a
        recognition that the short-term rental business has created imbalances in the functioning of
        the city and that the pandemic is an opportunity to get it back “on the right track”<fn>
          <p>These comments also represent an evolution (or at least a different perspective), in
            relation to those made by the mayor of Porto (Portugal’s second city), who in 2018
            declared that the “drama about tourism” was “very boring talk” and that gentrification
            was a “boring idea of a reactionary Left speaking about something that does not exist.”
              (<xref ref-type="bibr" rid="Carvalho">Carvalho et al. 2019</xref>). </p>
        </fn>. In the same interview, the mayor also declared that: </p>
      <p><italic>“We need to make a shift. It should change the way the housing market works here in
          the city.… Having a house cannot be such a burden that you have to have two or three jobs
          – that’s not a dignified life for anyone.” (idem). </italic></p>
      <p> This series of statements by the mayor of Lisbon were made in the context of a new
        programme set up by the municipality named ‘Renda Segura’ (Secure Rent) that was launched in
        the early weeks of the epidemic. The programme’s objective is to transfer apartments used
        for short-term rentals over to long-term rentals, with landlords receiving rent at market
        rates, thanks to a monthly payment assured by the city council on top of the affordable rent
        paid by tenants<fn>
          <p>The owners rent out their properties to the council, which pays the market price and
            then sublets at affordable rents, for at least five years. </p>
        </fn> Despite the municipality’s efforts, by December 2020 just 177 owners had agreed to
        take part in the programme, with only 47 of these being former short-term rental units. This
        lack of participation is due to the expectation that the economic situation will soon return
        to normal and that the slump in revenue will be reversed in the short term (<xref
          ref-type="bibr" rid="Pereira2021">Pereira et al. 2021</xref>). To a certain degree, this
        measure is only of interest to short-term rental owners who were already thinking of
        withdrawing from this activity, due to the saturation that was being felt in the market. It
        should also be noted that owners’ expectation of a “return to normality” is not very
        different from the expectations of the population in general, who given the opportunity are
        also eager to see tourism rebound (<xref ref-type="bibr" rid="Pereira2021">Pereira et al.
          2021</xref>). </p>
      <p>The current moment is one of uncertainty. The short-term rental market will in future face
        two big challenges. On the one hand, recovering from the COVID-19 crisis and awaiting the
        return of normality, on the other, dealing with new policies to constrain and regulate the
        segment, as has already happened in many major cities in Europe and North America.</p>
    </sec>
    <sec>
      <label> 5. Concluding remarks: Lisbon and the international context of short-term
        rental</label>
      <p> In many major cities, the discussion today is no longer about how much is too much, but
        rather about how to restore the balance of urban life (tourism and living, landscapes and
        urban real scenarios, national prices or inflated real estate profit margins). Similar
        developments have been seen in many cities in Europe and North America. The short-term
        rental market has driven the rapid transformation of leading urban destinations, prompting
        several major cities (e.g. Barcelona, Amsterdam and New York) to move to limit the spread of
        short-term rentals. The policymakers are making use of various models to constrain the
        activity, such as the suspension of new registrations and limits on the number of days that
        they may operate as such (<xref ref-type="bibr" rid="Gurran">Gurran and Phibbs 2017</xref>). It can be seen that even
        cities and regions that have historically received foreign tourists, such as the Balearic
        Islands (Spain), have moved to contain the short-term rental business, in large part because
        this activity affects the supply of housing and the property market in general, and so the
        lives of local people (<xref ref-type="bibr" rid="Yrigoy">Yrigoy 2019</xref>). </p>
      <p>As happens in Lisbon, international studies that have analysed the social impacts of the
        short-term rental phenomenon have tended to link the excessive concentration of this
        activity with issues such as gentrification, housing financialization and touristification
        of places. As summarised by <xref ref-type="bibr" rid="Becker">Becker (2013)</xref>, short-term rentals make for happy
        consumers (who save money) and for happy homeowners (who make money), but for very unhappy
        neighborhoods.</p>
      <p>This paper has analysed the spatial scenario of short-term rental units in the summer of
        2019, that is, during its functional peak. It was in that scenario that several studies
        warned for disruptive effects of the excessive concentration of short-term rentals. These
        are complex and non-linear, such as the appropriation of cities for tourism, driving a
        substitution of the social fabric and a loss of identity in historic urban centres,
        gradually turning them into a huge monofunctional tourist resort, with few residents and a
        total void of cultural interest and authenticity. As several studies point out, it is not
        possible to define a magic number that indicates how much is too much. However, the spatial
        concentration identified in this study in the case of Lisbon, as well as the various
        scientific studies carried out over the last few years on the multidimensional repercussions
        of the intensification of short-term rental, all seem to converge in one direction.</p>
      <p>Based on official numbers and using a geographical information system to specialize the
        phenomena, this paper highlights the spatial distribution of short-term rental units in
        Portugal and Lisbon, by showing their location and different gradients of concentration.
        This geographical approach is crucial to understand how to deal with these (sometimes)
        excessive numbers. Only by analyzing its spreading throughout space, it is possible to apply
        different levels of legislation that vary according to city parishes, areas, neighborhoods
        or even streets. This paper also highlights a different approach to the problem because
        seeing numbers on a map is much more real than looking them on a spreadsheet. This
        methodology also allows different scales of analysis. When focused on a particular street,
        results are sometimes even more alarming in terms of concentration. Of course, official
        databases could be outdated, and short-term rentals may even have closed (temporarily or
        permanently), continuing to be referenced on the database, but that´s a problem of all
        databases.</p>
      <p>It seems unquestionable that the only way to achieve a balance between the positive and
        negative externalities without affecting the quality of urban life for those who live, work
        and use the city, is by having a clear scenario of what happened in the past to achieve
        better results for the future. In this sense, the work presented here, before the global
        pandemic crisis also shows the way to a needed practical framework adapted to different
        economic scenarios, some of them, no one could expect, but vital for future planning
        policies. At this moment, future works are already in progress showing a more a detailed
        analysis for some of Lisbon’ parishes and streets and taking into account population from
        2021 Portuguese Census data.</p>
      <p>During a global pandemic that has halted international tourism flows, it is now the right
        moment to reflect on what has been done in recent years and what kind of city we want for
        our future. Today, it is more unanimous that the local and regional economy needs the
        tourism industry, and that major European cities should have tourism, but that they should
        not be converted into mere tourist destinations. In the near future, it will be fundamental
        to ensure the sustainability of tourism and achieve a balance between its positive and
        negative externalities, so as not to undermine the quality of urban life for those who live,
        work and use their city for everyday activities.</p>
    </sec>
  </body>
  <back>
    <ack>
      <p>This work is financed by national funds through FCT - Foundation for Science and
        Technology, I.P., within the scope of the project «UIDB / 04647/2020» of CICS.NOVA - Centro
        Interdisciplinar de Ciências Sociais da Universidade Nova de Lisboa.</p>
    </ack>
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