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</div>
<div class="include-supplemental-container">
<input type="checkbox" aria-label="Include MeSH and other data" name="include-supplemental" id="email-include-supplemental" class="email-include-supplemental">
<label for="email-include-supplemental" class="email-include-supplemental-label">MeSH and other data</label>
</div>
<div class="form-field recaptcha ">
<div class="g-recaptcha" id="id-recaptcha" data-sitekey="6LfsWHMdAAAAAClKbtOpjQ2pMjgsGxvv7NdZW9uI"></div>
</div>
<div id="captcha-error-message" class="usa-input-error-message captcha-validation-message" role="alert"></div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Sending..."
data-ga-category="save_share"
data-ga-action="email"
data-ga-label="send">
Send email
</button>
<button class="action-panel-cancel"
aria-label="Close 'Email citations' panel"
ref="linksrc=close_email_panel"
aria-controls="email-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="email"
data-ga-label="cancel">
Cancel
</button>
</div>
<input type="hidden" name="email-search-details" value="" />
<input type="hidden" name="email-search-details-hash" value="0e42663a6c3bd85498fcb88798998fed7bfdc45d457db35281e41afe13cc0524" />
</form>
</div>
</div>
<div id="collections-action-panel"
class="collections-action-panel action-panel in-progress-dots-panel"
aria-hidden="true"
data-collections-open-panel-enabled="false"
data-collections-open-panel-url-hash="#open-collections-panel">
<div class="inner-wrap">
<h3 class="action-panel-heading">
Add to Collections
</h3>
<form id="collections-action-panel-form"
class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-existing-collections-url="/list-existing-collections/"
data-add-to-existing-collection-url="/add-to-existing-collection/"
data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/"
data-get-article-ids-by-search-url="/get-article-ids-by-search/"
data-myncbi-max-collection-name-length="100"
data-add-to-collection-max-amount="1000"
data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/">
<input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY">
<div class="choice-group" role="radiogroup">
<ul class="radio-group-items">
<li>
<input type="radio"
id="collections-action-panel-new"
class="collections-new"
name="collections"
value="new"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="collections_radio_new">
<label for="collections-action-panel-new">Create a new collection</label>
</li>
<li>
<input type="radio"
id="collections-action-panel-existing"
class="collections-existing"
name="collections"
value="existing"
checked="true"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="collections_radio_existing">
<label for="collections-action-panel-existing">Add to an existing collection</label>
</li>
</ul>
</div>
<div class="controls-wrapper">
<div class="action-panel-control-wrap new-collections-controls">
<label for="collections-action-panel-add-to-new" class="action-panel-label required-field-asterisk">
Name your collection:
</label>
<input
type="text"
name="add-to-new-collection"
id="collections-action-panel-add-to-new"
class="collections-action-add-to-new"
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/"
maxlength="100"
data-ga-category="save_share"
data-ga-action="create_collection"
data-ga-label="non_favorties_collection">
<div class="collections-new-name-too-long usa-input-error-message selection-validation-message">
Name must be less than 100 characters
</div>
</div>
<div class="action-panel-control-wrap existing-collections-controls">
<label for="collections-action-panel-add-to-existing" class="action-panel-label">
Choose a collection:
</label>
<select id="collections-action-panel-add-to-existing"
class="action-panel-selector collections-action-add-to-existing"
data-ga-category="save_share"
data-ga-action="select_collection"
data-ga-label="($('#collections-action-add-to-existing').val() === 'Favorites') ? 'Favorites' : 'non_favorites_collection'">
</select>
<div class="collections-retry-load-on-error usa-input-error-message selection-validation-message">
Unable to load your collection due to an error<br>
<a href="#">Please try again</a>
</div>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Adding..."
data-pinger-ignore
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="add">
Add
</button>
<button class="action-panel-cancel"
aria-label="Close 'Add to Collections' panel"
ref="linksrc=close_collections_panel"
aria-controls="collections-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="collections"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="bibliography-action-panel"
class="bibliography-action-panel action-panel in-progress-dots-panel"
aria-hidden="true"
data-bibliography-open-panel-enabled="false"
data-bibliography-open-panel-url-hash="#open-bibliography-panel">
<div class="inner-wrap">
<h3 class="action-panel-heading">
Add to My Bibliography
</h3>
<form id="bibliography-action-panel-form"
class="bibliography-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-add-to-bibliography-max-amount="100"
data-add-to-bibliography-batch-size="10"
data-bibliography-delegates-url="/list-bibliography-delegates/"
data-add-to-bibliography-url="/add-to-bibliography/"
data-get-article-ids-by-search-url="/get-article-ids-by-search/"
data-mybib-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/mybibliography/">
<input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY">
<div class="action-panel-control-wrap bibliographies-controls">
<div class="choice-group">
<ul class="bibliographies-action-add radio-group-items">
<li>
<input name="bibliography" id="my-bibliography" class="my-bibliography" type="radio" checked/>
<label for="my-bibliography">My Bibliography</label>
</li>
</ul>
</div>
</div>
<div class="bibliographies-retry-load-on-error usa-input-error-message selection-validation-message">
Unable to load your delegates due to an error<br>
<a href="#">Please try again</a>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Adding..."
data-pinger-ignore>
Add
</button>
<button class="action-panel-cancel"
aria-label="Close 'Add to bibliography' panel"
ref="linksrc=close_bibliography_panel"
aria-controls="bibliography-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="mybib"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="saved-search-action-panel" class="saved-search-action-panel action-panel " aria-hidden="true"
data-saved-search-open-panel-enabled="false"
data-saved-search-open-panel-url-hash="#open-saved-search-panel">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Your saved search
</h2>
<form id="saved-search-action-panel-form"
class="saved-search-action-panel-form action-panel-content action-form"
data-create-saved-search-url="/create-saved-search/"
data-try-search-terms-url="/try-search-term/"
data-saved-search-root-url="https://www.ncbi.nlm.nih.gov/myncbi/searches/">
<input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY">
<div class="action-panel-control-wrap">
<label for="saved-search-name" class="action-panel-label saved-search-name-label required-field-asterisk">
Name of saved search:
</label>
<input maxlength="200"
type="text"
name="saved-search-name"
id="saved-search-name"
class="saved-search-name"
value=""
required
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/">
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-term" class="action-panel-label required-field-asterisk">
Search terms:
</label>
<textarea name="saved-search-term" id="saved-search-term" class="saved-search-term" required></textarea>
</div>
<div class="test-search-term-wrap">
<a href="#" class="try-search-term">Test search terms</a>
</div>
<div class="choice-group action-panel-extra-margin-top">
<span class="action-panel-label" id="fieldset-label">
Would you like email updates of new search results?
</span>
<fieldset id="saved-search-alert" aria-describedby="fieldset-label">
<legend class="usa-sr-only">Saved Search Alert Radio Buttons</legend>
<ul class="radio-group-items">
<li>
<input type="radio" id="saved-search-alert-yes" class="saved-search-alert-yes" name="saved-search-alert" value="yes" checked>
<label for="saved-search-alert-yes" class="action-panel-label">Yes</label>
</li>
<li>
<input aria-label="No radio input" type="radio" id="saved-search-alert-no" class="saved-search-alert-no" name="saved-search-alert" value="no">
<label for="saved-search-alert-no" class="action-panel-label">No</label>
</li>
</ul>
</fieldset>
</div>
<div class="alert-schedule-wrap">
<div class="action-panel-control-wrap">
<label class="action-panel-label">
Email:
</label>
<span aria-label="Email address" id="saved-search-email" class="action-panel-label"><span class="action-panel-label-bold"></span> (<a class="myncbi-account-settings" href="https://www.ncbi.nlm.nih.gov/account/settings/">change</a>)</span>
</div>
<div class="action-panel-control-wrap action-panel-extra-margin-top">
<label for="saved-search-frequency" class="action-panel-label">
Frequency:
</label>
<select id="saved-search-frequency" class="no-border-panel-selector saved-search-frequency">
<option value="monthly">Monthly</option>
<option value="weekly">Weekly</option>
<option value="daily">Daily</option>
</select>
</div>
<div class="action-panel-control-wrap saved-search-monthly-additional">
<label for="saved-search-monthly-on-day" class="action-panel-label">
Which day?
</label>
<select id="saved-search-monthly-on-day" class="no-border-panel-selector">
<option value="Sunday">The first Sunday</option>
<option value="Monday">The first Monday</option>
<option value="Tuesday">The first Tuesday</option>
<option value="Wednesday">The first Wednesday</option>
<option value="Thursday">The first Thursday</option>
<option value="Friday">The first Friday</option>
<option value="Saturday">The first Saturday</option>
<option value="day">The first day</option>
<option value="weekday">The first weekday</option>
</select>
</div>
<div class="action-panel-control-wrap saved-search-weekly-additional">
<label for="saved-search-weekly-on-day" class="action-panel-label">
Which day?
</label>
<select id="saved-search-weekly-on-day" class="no-border-panel-selector saved-search-weekly-on-day">
<option value="Sunday">Sunday</option>
<option value="Monday">Monday</option>
<option value="Tuesday">Tuesday</option>
<option value="Wednesday">Wednesday</option>
<option value="Thursday">Thursday</option>
<option value="Friday">Friday</option>
<option value="Saturday">Saturday</option>
</select>
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-report" class="action-panel-label">
Report format:
</label>
<select id="saved-search-report" class="no-border-panel-selector saved-search-report">
<option value="DocSum">Summary</option>
<option value="DocSumText">Summary (text)</option>
<option value="Abstract">Abstract</option>
<option value="AbstractText">Abstract (text)</option>
<option value="MEDLINE">PubMed</option>
</select>
</div>
<div class="action-panel-control-wrap">
<label for="saved-search-amount" class="action-panel-label">
Send at most:
</label>
<select id="saved-search-amount" class="no-border-panel-selector saved-search-amount">
<option value="1">1 item</option>
<option value="5" selected>5 items</option>
<option value="10">10 items</option>
<option value="20">20 items</option>
<option value="50">50 items</option>
<option value="100">100 items</option>
<option value="200">200 items</option>
</select>
</div>
<div>
<input type="checkbox" id="saved-search-send-if-no-result" class="saved-search-send-if-no-result" name="saved-search-send-if-no-result">
<label for="saved-search-send-if-no-result" class="action-panel-label smaller-checkbox">
Send even when there aren't any new results
</label>
</div>
<div class="action-panel-control-wrap option-text-in-email-wrap">
<label for="saved-search-email-text" class="action-panel-label">
Optional text in email:
</label>
<textarea name="saved-search-email-text"
id="saved-search-email-text"
class="saved-search-email-text"></textarea>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Saving..."
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="save">
Save
</button>
<button class="action-panel-cancel"
aria-label="Close 'Your saved search' panel"
ref="linksrc=close_saved_search_panel"
aria-controls="saved-search-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="citation-manager-action-panel" class="citation-manager-action-panel action-panel" aria-hidden="true">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Create a file for external citation management software
</h2>
<form id="citation-manager-action-panel-form"
class="action-panel-content action-form"
action="/results-export-ids/"
data-by-search-action="/results-export-search-data/"
data-by-ids-action="/results-export-ids/"
method="post"
data-by-search-method="post"
data-by-ids-method="post">
<input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY">
<input name="results-format" type="hidden" value="pubmed"/>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Sending..."
data-ga-category="save_share"
data-ga-action="citation_manager"
data-ga-label="save">
Create file
</button>
<button class="action-panel-cancel"
aria-label="Close 'Send citations to citation manager' panel"
ref="linksrc=close_citation_manager_panel"
aria-controls="citation-manager-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="citation_manager"
data-ga-label="cancel">
Cancel
</button>
</div>
</form>
</div>
</div>
<div id="rss-action-panel" class="rss-action-panel action-panel " aria-hidden="true">
<div class="inner-wrap">
<h2 class="action-panel-heading">
Your RSS Feed
</h2>
<form id="rss-action-panel-form"
class="rss-action-panel-form action-panel-content action-form"
data-create-rss-feed-url="/create-rss-feed-url/"
data-search-form-term-value="">
<input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY">
<div class="action-panel-control-wrap">
<label for="rss-name" class="action-panel-label required-field-asterisk">
Name of RSS Feed:
</label>
<input maxlength="200"
placeholder="Name"
type="text"
name="rss-name"
id="rss-name"
class="rss-name"
value=''
required
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/">
</div>
<div class="rss-limit-wrap">
<div class="action-panel-control-wrap action-panel-extra-margin-top">
<label for="rss-limit" class="action-panel-label">
Number of items displayed:
</label>
<select id="rss-limit" class="no-border-panel-selector rss-limit">
<option value="5">5</option>
<option value="10">10</option>
<option value="15" selected="selected">15</option>
<option value="20">20</option>
<option value="50">50</option>
<option value="100">100</option>
</select>
</div>
</div>
<div class="action-panel-actions">
<button class="action-panel-submit"
type="submit"
data-loading-label="Creating..."
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="save">
Create RSS
</button>
<button class="action-panel-cancel"
aria-label="Close 'Your RSS' panel"
ref="linksrc=close_rss_panel"
aria-controls="rss-action-panel"
aria-expanded="false"
data-ga-category="save_share"
data-ga-action="alert"
data-ga-label="cancel">
Cancel
</button>
</div>
<div class="action-panel-control-wrap rss-link-copy-wrap">
<label for="rss-link" class="usa-sr-only">RSS Link</label>
<input placeholder="Your RSS Feed Link" type="text" name="rss-link" id="rss-link" class="rss-link" title="RSS Link">
<button
type="button"
disabled
class="rss-link-copy-button disabled"
data-ga-category="save_share"
data-ga-action="rss"
data-ga-label="copy">
Copy
</button>
</div>
</form>
</div>
</div>
</div>
</div>
<div class="article-page" id="article-page" data-article-pmid="12097644">
<aside class="page-sidebar">
<div class="inner-wrap">
<div class="full-text-links">
<div class="full-view">
<h3 class="title">
Full text links
</h3>
<div class="full-text-links-list">
<a class="link-item
dialog-focus"
href="https://www.pnas.org/doi/10.1073/pnas.142680199?url_ver=Z39.88-2003&amp;rfr_id=ori:rid:crossref.org&amp;rfr_dat=cr_pub 0pubmed"
target="_blank"
rel="noopener"
ref="linksrc=fulltextorjournal_fulltext&amp;is_pmc=False&amp;PrId=4487&amp;itool=Abstract-def&amp;log$=linkouticon&amp;uid=12097644&amp;db=pubmed&amp;nlmid=7505876"
title="See full text options at Atypon"
data-ga-category="full_text"
data-ga-action="Atypon"
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><img src="https://cdn.ncbi.nlm.nih.gov/corehtml/query/egifs/https:--pnas.org-pb-assets-images-pubmed-pnas-pubmed-fulltext.png" alt="Atypon full text link"><span class="text">
Atypon
</span></a><a class="link-item
pmc
"
href="https://pmc.ncbi.nlm.nih.gov/articles/pmid/12097644/"
target="_blank"
rel="noopener"
ref="linksrc=fulltextorjournal_fulltext&amp;is_pmc=True&amp;PrId=3494&amp;itool=Abstract-def&amp;log$=linkouticon&amp;uid=12097644&amp;db=pubmed&amp;nlmid=7505876"
title="Free full text at PubMed Central"
data-ga-category="full_text"
data-ga-action="PMC"
data-ga-label="12097644"
><span class="text">
Free PMC article
</span></a>
</div>
</div>
<div class="short-view">
<a href="#" class="full-text-links-button full-text-links-dialog-trigger">
Full text links
</a>
</div>
</div>
<div class="actions-buttons sidebar"><h3 class="title">Actions</h3><div class="inner-wrap"><button class="citation-button citation-dialog-trigger"
aria-label="Open dialog with citation text in different styles"
data-ga-category="save_share"
data-ga-action="cite"
data-ga-label="open"
data-all-citations-url="/12097644/citations/"
data-citation-style="nlm"
data-pubmed-format-link="/12097644/export/"><span class="button-label">Cite</span></button><link type="text/css" href="ncbi-overlay-block/src/overlay-block.css"><div class="collections-button-container" data-article-id="12097644" data-article-db="pubmed"><button class="collections-button collections-dialog-trigger"
aria-label="Save article in MyNCBI collections."
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_button"
data-collections-open-dialog-enabled="false"
data-collections-open-dialog-url="https://account.ncbi.nlm.nih.gov/?back_url=https%3A%2F%2Fpubmed.ncbi.nlm.nih.gov%2F12097644%2F%23open-collections-dialog"
data-in-collections="false"><span class="button-label">Collections</span></button><div class="overlay" role="dialog"><div id="collections-action-dialog"
class="dialog collections-dialog"
aria-hidden="true"><div class="title">Add to Collections</div><div class="collections-action-panel action-panel"><form id="collections-action-dialog-form"
class="collections-action-panel-form action-panel-content action-form action-panel-smaller-selectors"
data-existing-collections-url="/list-existing-collections/"
data-add-to-existing-collection-url="/add-to-existing-collection/"
data-create-and-add-to-new-collection-url="/create-and-add-to-new-collection/"
data-myncbi-max-collection-name-length="100"
data-collections-root-url="https://www.ncbi.nlm.nih.gov/myncbi/collections/"><input type="hidden" name="csrfmiddlewaretoken" value="lTICdanqFPUw2EoP08J06bQ86b20Fo3ECGsHQ0QMfqH0W5uFDrm2AjmMEfKcyZBY"><div class="choice-group" role="radiogroup"><ul class="radio-group-items"><li><input type="radio"
id="collections-action-dialog-new"
class="collections-new"
name="collections"
value="new"
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_radio_new"><label for="collections-action-dialog-new">Create a new collection</label></li><li><input type="radio"
id="collections-action-dialog-existing"
class="collections-existing"
name="collections"
value="existing"
checked="true"
data-ga-category="collections_button"
data-ga-action="click"
data-ga-label="collections_radio_existing"><label for="collections-action-dialog-existing">Add to an existing collection</label></li></ul></div><div class="controls-wrapper"><div class="action-panel-control-wrap new-collections-controls"><label for="collections-action-dialog-add-to-new" class="action-panel-label required-field-asterisk">
Name your collection:
</label><input
type="text"
name="add-to-new-collection"
id="collections-action-dialog-add-to-new"
class="collections-action-add-to-new"
pattern="[^&quot;&amp;=&lt;&gt;\/]*" title="The following characters are not allowed in the Name field: &quot;&amp;=&lt;&gt;/"
maxlength="100"
data-ga-category="collections_button"
data-ga-action="create_collection"
data-ga-label="non_favorties_collection"><div class="collections-new-name-too-long usa-input-error-message selection-validation-message">
Name must be less than 100 characters
</div></div><div class="action-panel-control-wrap existing-collections-controls"><label for="collections-action-dialog-add-to-existing" class="action-panel-label">
Choose a collection:
</label><select id="collections-action-dialog-add-to-existing"
class="action-panel-selector collections-action-add-to-existing"
data-ga-category="collections_button"
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The absolute diversity of prokaryotes is widely held to be unknown and unknowable at any scale in any environment. However, it is not necessary to count every species in a community to estimate the number of different taxa therein. It is sufficient to estimate the area under the species abundance curve for that environment. Log-normal species abundance curves are thought to characterize communities, such as bacteria, which exhibit highly dynamic and random growth. Thus, we are able to show that the diversity of prokaryotic communities may be related to the ratio of two measurable variables: the total number of individuals in the community and the abundance of the most abundant members of that community. We assume that either the least abundant species has an abundance of 1 or Preston's canonical hypothesis is valid. Consequently, we can estimate the bacterial diversity on a small scale (oceans 160 per ml; soil 6,400-38,000 per g; sewage works 70 per ml). We are also able to speculate about diversity at a larger scale, thus the entire bacterial diversity of the sea may be unlikely to exceed 2 x 10(6), while a ton of soil could contain 4 x 10(6) different taxa. These are preliminary estimates that may change as we gain a greater understanding of the nature of prokaryotic species abundance curves. Nevertheless, it is evident that local and global prokaryotic diversity can be understood through species abundance curves and purely experimental approaches to solving this conundrum will be fruitless.
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<strong class="figure-label">
<p> Fig 1. </p>
</strong>
<div class="figure-caption-contents"><p> Species abundance and individual abundance.… </p></div>
</div>
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<div class="figure-caption-medium figure-caption-text" aria-hidden="true">
<strong class="figure-label">
<p> Fig 1. </p>
</strong>
<div class="figure-caption-contents"><p> Species abundance and individual abundance. ( <i> A </i> ) The lognormal species abundance curve.… </p></div>
</div>
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<strong class="figure-label">
Fig 1.
</strong>
<div class="figure-caption-contents">Species abundance and individual abundance. (<i>A</i>) The lognormal species abundance curve. The <i>x</i> axis shows log<sub>2</sub>(<i>N</i>), where <i>N</i> is bacterial abundance; the number of individuals within a species. The <i>y</i> axis shows the number of species, <i>S</i>, occurring at any abundance (<i>N</i>). <i>N</i><sub><i>max</i></sub> (<i>x</i> axis) is the number of individuals in most abundant species, <i>N</i><sub><i>min</i></sub> (<i>x</i> axis) is the number of individuals in the least abundant species, and <i>N</i><sub>0</sub> (<i>x</i> axis) is the modal species abundance. The total diversity, <i>S</i><sub><i>T</i></sub>, is the area under the species abundance curve. The width of the species curve is inversely proportional to the spread parameter <i>a</i>. Here, one species with 2<sup>24</sup> ( = 1.6 × 10<sup>7</sup>) individuals occurs at <i>N</i><sub><i>max</i></sub> and one species with 2<sup>0</sup> (=1) individuals occurs at <i>N</i><sub><i>min</i></sub>. (<i>B</i>) The individuals curve (solid) is found by multiplying abundance, <i>N</i>, by <i>S</i>, the number of species at that abundance (dots and dashes as in <i>A</i> not to scale). The total number of individuals in the sample is <i>N</i><sub><i>T</i></sub>, which corresponds the area under the individuals curve. <i>N</i><sub><i>max</i></sub> is the number of individuals in the most abundant species. Both <i>N</i><sub><i>max</i></sub> and <i>N</i><sub><i>T</i></sub> can be easily measured. This example obeys Preston's canonical hypothesis which states that the peak of the individuals curve coincides with <i>N</i><sub><i>max</i></sub>. This fixes the value of <i>a</i>. <i>A</i> and <i>B</i> show that most species occur with very low abundance, so direct empirical measurement of diversity is impractical.</div>
</figcaption>
</figure>
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itemprop="contentUrl"
aria-describedby="figure-caption-1"
role="button"
data-image-width="679"
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data-pmc-id="PMC124953"
data-figure-id="f2">
<img class="figure-thumb" itemprop="thumbnail"
id="article-image-1"
src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/2080/124953/7503c893f2d7/pq1426801002.gif"
alt="Fig 2." />
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<div class="figure-caption figure-caption-text" itemtype="http://schema.org/ImageObject" itemprop="caption" aria-hidden="true">
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<strong class="figure-label">
<p> Fig 2. </p>
</strong>
<div class="figure-caption-contents"><p> Relating species diversity to things… </p></div>
</div>
</div>
<div class="figure-caption-medium figure-caption-text" aria-hidden="true">
<strong class="figure-label">
<p> Fig 2. </p>
</strong>
<div class="figure-caption-contents"><p> Relating species diversity to things we can measure. The figure shows how the… </p></div>
</div>
<figcaption id="figure-caption-1" class="figure-caption-full figure-caption-text" itemtype="http://schema.org/ImageObject" itemprop="description">
<strong class="figure-label">
Fig 2.
</strong>
<div class="figure-caption-contents">Relating species diversity to things we can measure. The figure shows how the number of species (color) varies with spread parameter, <i>a</i>, and the ratio of the total number of individuals (<i>N</i><sub><i>T</i></sub>) to the number of individuals in the most abundant single species (<i>N</i><sub><i>max</i></sub>).</div>
</figcaption>
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itemprop="contentUrl"
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id="article-image-2"
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<strong class="figure-label">
<p> Fig 3. </p>
</strong>
<div class="figure-caption-contents"><p> Estimating the spread parameter, <i> a… </i> </p></div>
</div>
</div>
<div class="figure-caption-medium figure-caption-text" aria-hidden="true">
<strong class="figure-label">
<p> Fig 3. </p>
</strong>
<div class="figure-caption-contents"><p> Estimating the spread parameter, <i> a </i> , by using Preston's canonical hypothesis. The color… </p></div>
</div>
<figcaption id="figure-caption-2" class="figure-caption-full figure-caption-text" itemtype="http://schema.org/ImageObject" itemprop="description">
<strong class="figure-label">
Fig 3.
</strong>
<div class="figure-caption-contents">Estimating the spread parameter, <i>a</i>, by using Preston's canonical hypothesis. The color shows the number of species as spread parameter <i>a</i> and <i>N</i><sub><i>T</i></sub>/<i>N</i><sub><i>max</i></sub> vary. Preston's hypothesis states that the peak of the individuals curve coincides with <i>N</i><sub><i>max</i></sub>, the number of individuals in the most abundant species. This fixes the spread parameter, <i>a</i>, at a value that is shown by the solid line. Thus, where Preston's hypothesis is true, the total number of species for any value of <i>N</i><sub><i>T</i></sub>/<i>N</i><sub><i>max</i></sub> should lie along the solid black line.</div>
</figcaption>
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data-image-alt="Fig 4."
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data-figure-id="f4">
<img class="figure-thumb" itemprop="thumbnail"
id="article-image-3"
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<strong class="figure-label">
<p> Fig 4. </p>
</strong>
<div class="figure-caption-contents"><i> S </i> <sub> <i> T </i> </sub> estimated by assuming…</div>
</div>
</div>
<div class="figure-caption-medium figure-caption-text" aria-hidden="true">
<strong class="figure-label">
<p> Fig 4. </p>
</strong>
<div class="figure-caption-contents"><i> S </i> <sub> <i> T </i> </sub> estimated by assuming the value of <i> N </i> <sub> <i> min </i> </sub> , the abundance…</div>
</div>
<figcaption id="figure-caption-3" class="figure-caption-full figure-caption-text" itemtype="http://schema.org/ImageObject" itemprop="description">
<strong class="figure-label">
Fig 4.
</strong>
<div class="figure-caption-contents"><i>S</i><sub><i>T</i></sub> estimated by assuming the value of <i>N</i><sub><i>min</i></sub>, the abundance of the least abundant species is 1.</div>
</figcaption>
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itemprop="contentUrl"
aria-describedby="figure-caption-4"
role="button"
data-image-width="676"
data-image-height="486"
data-image-alt="Fig 5."
data-pmc-id="PMC124953"
data-figure-id="f5">
<img class="figure-thumb" itemprop="thumbnail"
id="article-image-4"
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<strong class="figure-label">
<p> Fig 5. </p>
</strong>
<div class="figure-caption-contents"><p> The maximum possible diversity for… </p></div>
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<div class="figure-caption-medium figure-caption-text" aria-hidden="true">
<strong class="figure-label">
<p> Fig 5. </p>
</strong>
<div class="figure-caption-contents"><p> The maximum possible diversity for differing numbers of individuals and different <i> N <sub> T… </sub> </i> </p></div>
</div>
<figcaption id="figure-caption-4" class="figure-caption-full figure-caption-text" itemtype="http://schema.org/ImageObject" itemprop="description">
<strong class="figure-label">
Fig 5.
</strong>
<div class="figure-caption-contents">The maximum possible diversity for differing numbers of individuals and different <i>N<sub>T</sub></i>/<i>N<sub>max</sub></i> ratios (under the assumption that <i>N<sub>min</sub></i> = 1). A ratio of 1,000100 might apply to soils and sediments, whereas a ratio of 4 might apply to the sea or a lake. To crudely estimate the diversity of communities where <i>N<sub>min</sub></i> = &gt;1 subtract the proposed <i>N<sub>min</sub></i> value from the known <i>N<sub>T</sub></i> value.</div>
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