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<title>Threshold-Modell</title>

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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Threshold-Modell</span></h1>

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<p>Das <b>Threshold-Modell</b> (<i>Schwellenwertmodell</i>) ist ein mathematisches Modell, bei dem sich ab einem <a href="Schwellenwert_(Chemie)" title="Schwellenwert (Chemie)">Schwellenwert</a> das Ergebnis der Modellberechnung stark ändert.

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<div class="mw-heading mw-heading2"><h2 id="Geschichte">Geschichte</h2></div>

<p>Das Konzept der Schwellenwerte in biologischen Systemen wurde erstmals in den 1930er Jahren untersucht, insbesondere von <a href="Sewall_Wright" title="Sewall Wright">Sewall Wright</a> zur Erklärung diskreter Merkmale wie der Anzahl von Zehen bei Meerschweinchen.

Ab den 1960er Jahren wurden die Modelle von Douglas Scott Falconer auf quantitative Merkmale und Erbkrankheiten ausgeweitet.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Moderne Anwendungen und Erweiterungen stammen u. a. von Axel Lange und Kollegen (2018).

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<div class="mw-heading mw-heading2"><h2 id="Eigenschaften">Eigenschaften</h2></div>

<p>In der <a href="Radiologie" title="Radiologie">Radiologie</a> und im <a href="Strahlenschutz" title="Strahlenschutz">Strahlenschutz</a> wird es, neben dem <a href="LNT-Modell" title="LNT-Modell">LNT-Modell</a> und der <a href="Hormesis" title="Hormesis">Hormesis</a>, zur Beschreibung der Auswirkungen von <a href="Ionisierende_Strahlung" title="Ionisierende Strahlung">ionisierender Strahlung</a> auf die Entstehung von <a href="Krebs_(Medizin)" title="Krebs (Medizin)">Krebs</a> verwendet.<sup id="cite_ref-Costantini_2-0" class="reference"><a href="#cite_note-Costantini-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In der <a href="Pharmakologie" title="Pharmakologie">Pharmakologie</a> und <a href="Toxikologie" title="Toxikologie">Toxikologie</a> wird es eingesetzt, um Schwellenwerte einer <a href="Wirkstoff" title="Wirkstoff">Wirkstoffgabe</a> in der <a href="Dosis-Wirkungs-Beziehung" class="mw-redirect" title="Dosis-Wirkungs-Beziehung">Dosis-Wirkungs-Beziehung</a> zu erklären,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> z. B. beim <a href="NOEL" title="NOEL">NOEL</a> und beim <a href="NOAEL" title="NOAEL">NOAEL</a>. In der <a href="Medizin" title="Medizin">Medizin</a> wird es bei der Entscheidung über Verfahren eingesetzt.<sup id="cite_ref-PMID10084191_4-0" class="reference"><a href="#cite_note-PMID10084191-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> In der <a href="Genetik" title="Genetik">Genetik</a> wurde 1934 die Bildung eines zusätzlichen Zehs an den hinteren Füßen von Meerschweinchen von <a href="Sewall_Wright" title="Sewall Wright">Sewall Wright</a> mit dem Modell erklärt, die nicht zu den bekannten Modellen eines <a href="Dominant-rezessiv" class="mw-redirect" title="Dominant-rezessiv">dominant-rezessiven</a> oder <a href="Intermedi%C3%A4rer_Erbgang" class="mw-redirect" title="Intermediärer Erbgang">intermediären Erbgangs</a> passten.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Erweiterungen des Modells wurden ab 1960 von Douglas Scott Falconer<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> und 2018 von Axel Lange und Kollegen beschrieben.<sup id="cite_ref-PMID29739620_11-0" class="reference"><a href="#cite_note-PMID29739620-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In der Mathematik gehört die Segmentierte Regression und einige nichtlineare autoregressive Modelle, die für <a href="Zeitreihenanalyse" title="Zeitreihenanalyse">Zeitreihenanalyse</a> formuliert wurden,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> zu den Schwellenwertmodellen.

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<div class="mw-heading mw-heading2"><h2 id="Mathematische_Aspekte">Mathematische Aspekte</h2></div>

<ul><li>Schwellenwertmodelle lassen sich mit Segmentierte Regression oder nichtlinearen autoregressiven Modellen für <a href="Zeitreihenanalyse" title="Zeitreihenanalyse">Zeitreihenanalyse</a> mathematisch beschreiben.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li>

<li>Sie eignen sich zur Modellierung von Systemen mit diskreten Übergängen, z. B. beim Eintreten bestimmter biologischer oder medizinischer Ereignisse.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Anwendungen">Anwendungen</h2></div>

<ul><li><a href="Radiologie" title="Radiologie">Radiologie</a> und <a href="Strahlenschutz" title="Strahlenschutz">Strahlenschutz</a>: Abschätzung des Krebsrisikos bei Strahlenexposition.</li>

<li><a href="Pharmakologie" title="Pharmakologie">Pharmakologie</a>: Bestimmung von Minimal- oder Maximaldosen (NOEL/NOAEL).</li>

<li><a href="Medizin" title="Medizin">Medizin</a>: Entscheidungsunterstützung bei Therapieoptionen.</li>

<li><a href="Genetik" title="Genetik">Genetik</a>: Erklärung diskreter Merkmale in Populationen.</li>

<li><a href="%C3%96kologie" title="Ökologie">Ökologie</a>: Vorhersage von Populationsreaktionen auf Umweltstressoren.</li>

<li><a href="Agrarwissenschaft" class="mw-redirect" title="Agrarwissenschaft">Agrarwissenschaft</a>: Züchtungsprogramme für Merkmale mit Schwellencharakter.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Erweiterungen_und_Forschung">Erweiterungen und Forschung</h2></div>

<ul><li>Quantitative Schwellenwertmodelle für polygenetische Merkmale.</li>

<li>Kombination von genetischen und Umweltfaktoren, um das Auftreten bestimmter Merkmalsausprägungen vorherzusagen.</li>

<li>Anwendung in der Evolutionstheorie, z. B. zur Analyse der Selektion auf diskrete Merkmale.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<ul><li>Robertson, Lerner: <cite style="font-style:italic">The heritability of all-or-none traits: viability of poultry</cite>. In: <cite style="font-style:italic">Genetics</cite>. 34. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>4</span>, 1949, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>395–411</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1093/genetics%2F34.4.395">10.1093/genetics/34.4.395</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/17247323?dopt=Abstract">PMID 17247323</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1209454/">PMC 1209454</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=The+heritability+of+all-or-none+traits%3A+viability+of+poultry&rft.au=Robertson%2C%26%2332%3BLerner&rft.date=1949&rft.doi=10.1093%2Fgenetics%2F34.4.395&rft.genre=journal&rft.issue=4&rft.jtitle=Genetics&rft.pages=395-411&rft.pmc=1209454&rft.pmid=17247323&rft.volume=34.+Jahrgang" style="display:none"> </span></li>

<li>Dempster, Lerner: <cite style="font-style:italic">Heritability of threshold characters</cite>. In: <cite style="font-style:italic">Genetics</cite>. 35. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>2</span>, 1950, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>212–36</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1093/genetics%2F35.2.212">10.1093/genetics/35.2.212</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/17247344?dopt=Abstract">PMID 17247344</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1209482/">PMC 1209482</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=Heritability+of+threshold+characters&rft.au=Dempster%2C%26%2332%3BLerner&rft.date=1950&rft.doi=10.1093%2Fgenetics%2F35.2.212&rft.genre=journal&rft.issue=2&rft.jtitle=Genetics&rft.pages=212-36&rft.pmc=1209482&rft.pmid=17247344&rft.volume=35.+Jahrgang" style="display:none"> </span></li>

<li>Carter: <cite style="font-style:italic">Genetics of common disorders</cite>. In: <cite style="font-style:italic">British Medical Bulletin</cite>. 25. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>1</span>, 1969, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>52–7</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1093/oxfordjournals.bmb.a070671">10.1093/oxfordjournals.bmb.a070671</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/5782759?dopt=Abstract">PMID 5782759</a> (<a rel="nofollow" class="external text" href="https://www.dropbox.com/s/v8jk3wf133hp171/1969-carter.pdf">dropbox.com</a> [PDF]).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=Genetics+of+common+disorders&rft.au=Carter&rft.date=1969&rft.doi=10.1093%2Foxfordjournals.bmb.a070671&rft.genre=journal&rft.issue=1&rft.jtitle=British+Medical+Bulletin&rft.pages=52-7&rft.pmid=5782759&rft.volume=25.+Jahrgang" style="display:none"> </span></li>

<li>Crittenden: <cite style="font-style:italic">An interpretation of familial aggregation based on multiple genetic and environmental factors</cite>. In: <cite style="font-style:italic">Annals of the New York Academy of Sciences</cite>. 91. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>3</span>, 1961, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>769–780</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1111/j.1749-6632.1961.tb31106.x">10.1111/j.1749-6632.1961.tb31106.x</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/13696504?dopt=Abstract">PMID 13696504</a>, <a href="Bibcode" title="Bibcode">bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961NYASA..91..769C">1961NYASA..91..769C</a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=An+interpretation+of+familial+aggregation+based+on+multiple+genetic+and+environmental+factors&rft.au=Crittenden&rft.date=1961&rft.doi=10.1111%2Fj.1749-6632.1961.tb31106.x&rft.genre=journal&rft.issue=3&rft.jtitle=Annals+of+the+New+York+Academy+of+Sciences&rft.pages=769-780&rft.pmid=13696504&rft.volume=91.+Jahrgang" style="display:none"> </span></li>

<li>Smith: <cite style="font-style:italic">Concordance in twins - methods and interpretation</cite>. In: <cite style="font-style:italic">Journal</cite>. 26. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>4</span>, 1974, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>454–66</span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/4858380?dopt=Abstract">PMID 4858380</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1762601/">PMC 1762601</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=Concordance+in+twins+-+methods+and+interpretation&rft.au=Smith&rft.date=1974&rft.genre=journal&rft.issue=4&rft.jtitle=Journal&rft.pages=454-66&rft.pmc=1762601&rft.pmid=4858380&rft.volume=26.+Jahrgang" style="display:none"> </span></li>

<li>Gianola 1982, <a rel="nofollow" class="external text" href="https://www.researchgate.net/profile/Daniel_Gianola/publication/255634637_Theory_and_analysis_of_threshold_characters/links/5583241f08ae8bf4ba6f8a75.pdf">"Theory and analysis of threshold characters"</a></li>

<li>McGue: <cite style="font-style:italic">The transmission of schizophrenia under a multifactorial threshold-model</cite>. In: <cite style="font-style:italic">Am J Hum Genet</cite>. 35. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>6</span>, 1983, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>1161–78</span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/6650500?dopt=Abstract">PMID 6650500</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1685995/">PMC 1685995</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=The+transmission+of+schizophrenia+under+a+multifactorial+threshold-model&rft.au=McGue&rft.date=1983&rft.genre=journal&rft.issue=6&rft.jtitle=Am+J+Hum+Genet&rft.pages=1161-78&rft.pmc=1685995&rft.pmid=6650500&rft.volume=35.+Jahrgang" style="display:none"> </span></li>

<li>Roff: <cite style="font-style:italic">The Evolution of Threshold Traits in Animals</cite>. In: <cite style="font-style:italic">The Quarterly Review of Biology</cite>. 71. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>1</span>, 1996, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>3–35</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1086/419266">10.1086/419266</a></span>, <a href="JSTOR" title="JSTOR">JSTOR</a>:<a rel="nofollow" class="external text" href="http://www.jstor.org/stable/3037828">3037828</a>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=The+Evolution+of+Threshold+Traits+in+Animals&rft.au=Roff&rft.date=1996&rft.doi=10.1086%2F419266&rft.genre=journal&rft.issue=1&rft.jtitle=The+Quarterly+Review+of+Biology&rft.pages=3-35&rft.volume=71.+Jahrgang" style="display:none"> </span></li>

<li>Rijsdijk & Sham 2002, <a rel="nofollow" class="external text" href="https://academic.oup.com/bib/article-pdf/3/2/119/439480/119.pdf">"Analytic approaches to twin data using structural equation models"</a></li>

<li>Chevin, Lande: <cite style="font-style:italic">Evolution of discrete phenotypes from continuous norms of reaction</cite>. In: <cite style="font-style:italic">Am Nat</cite>. 182. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>1</span>, 2013, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>13–27</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1086/670613">10.1086/670613</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/23778223?dopt=Abstract">PMID 23778223</a>, <a href="Bibcode" title="Bibcode">bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2013ANat..182...13C">2013ANat..182...13C</a> (<a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/239947184">researchgate.net</a> [PDF]).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=Evolution+of+discrete+phenotypes+from+continuous+norms+of+reaction&rft.au=Chevin%2C%26%2332%3BLande&rft.date=2013&rft.doi=10.1086%2F670613&rft.genre=journal&rft.issue=1&rft.jtitle=Am+Nat&rft.pages=13-27&rft.pmid=23778223&rft.volume=182.+Jahrgang" style="display:none"> </span></li>

<li>Visscher & Wray 2015, <a rel="nofollow" class="external text" href="http://www.gwern.net/docs/genetics/2015-visscher.pdf">"Concepts and Misconceptions about the Polygenic Additive Model Applied to Disease"</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Falconer 1960, 1965, 1967</span>

</li>

<li id="cite_note-Costantini-2"><span class="mw-cite-backlink"><a href="#cite_ref-Costantini_2-0">↑</a></span> <span class="reference-text">D. Costantini, B. Borremans: <i>The linear no-threshold model is less realistic than threshold or hormesis-based models: An evolutionary perspective.</i> In: <i>Chemico-biological interactions.</i> Band 301, März 2019, S. 26–33, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1016/j.cbi.2018.10.007">10.1016/j.cbi.2018.10.007</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/30342016?dopt=Abstract">PMID 30342016</a> (Review).</span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Calabrese, E.J.; Baldwin, L.A. (2003). "The Hormetic Dose-Response Model Is More Common than the Threshold Model in Toxicology". Toxicological Sciences. 71 (2): 246–250. <a href="https://doi.org/10.1093/toxsci/71.2.246" class="extiw external" title="doi:10.1093/toxsci/71.2.246">doi:10.1093/toxsci/71.2.246</a>. <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/12563110?dopt=Abstract">PMID 12563110</a>.</span>

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<li id="cite_note-PMID10084191-4"><span class="mw-cite-backlink"><a href="#cite_ref-PMID10084191_4-0">↑</a></span> <span class="reference-text">J. D. Lurie, H. C. Sox: <i>Principles of medical decision making.</i> In: <i>Spine.</i> Band 24, Nummer 5, März 1999, S. 493–498, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1097/00007632-199903010-00021">10.1097/00007632-199903010-00021</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/10084191?dopt=Abstract">PMID 10084191</a> (Review).</span>

</li>

<li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">S Wright: <cite style="font-style:italic">An Analysis of Variability in Number of Digits in an Inbred Strain of Guinea Pigs</cite>. In: <cite style="font-style:italic">Genetics</cite>. 19. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>6</span>, 1934, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>506–36</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1093/genetics%2F19.6.506">10.1093/genetics/19.6.506</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/17246735?dopt=Abstract">PMID 17246735</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1208511/">PMC 1208511</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=An+Analysis+of+Variability+in+Number+of+Digits+in+an+Inbred+Strain+of+Guinea+Pigs&rft.au=S%26%2332%3BWright&rft.date=1934&rft.doi=10.1093%2Fgenetics%2F19.6.506&rft.genre=journal&rft.issue=6&rft.jtitle=Genetics&rft.pages=506-36&rft.pmc=1208511&rft.pmid=17246735&rft.volume=19.+Jahrgang" style="display:none"> </span></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">S Wright: <cite style="font-style:italic">The Results of Crosses between Inbred Strains of Guinea Pigs, Differing in Number of Digits</cite>. In: <cite style="font-style:italic">Genetics</cite>. 19. Jahrgang, <span style="white-space:nowrap">Nr.<span style="display:inline-block;width:.2em"> </span>6</span>, 1934, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>537–51</span>, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1093/genetics%2F19.6.537">10.1093/genetics/19.6.537</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/17246736?dopt=Abstract">PMID 17246736</a>, <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1208512/">PMC 1208512</a> (freier Volltext).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rfr_id=info:sid/de.wikipedia.org:Threshold-Modell&rft.atitle=The+Results+of+Crosses+between+Inbred+Strains+of+Guinea+Pigs%2C+Differing+in+Number+of+Digits&rft.au=S%26%2332%3BWright&rft.date=1934&rft.doi=10.1093%2Fgenetics%2F19.6.537&rft.genre=journal&rft.issue=6&rft.jtitle=Genetics&rft.pages=537-51&rft.pmc=1208512&rft.pmid=17246736&rft.volume=19.+Jahrgang" style="display:none"> </span></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">ch18, "Threshold characters", <a rel="nofollow" class="external text" href="https://archive.org/details/introductiontoq00falc"><i>Introduction to Quantitative Genetics</i></a>, Falconer 1960</span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160815214451/https://dl.dropboxusercontent.com/u/182368464/1965-falconer.pdf">"The inheritance of liability to certain diseases, estimated from the incidence among relatives"</a>, Falconer 1965</span>

</li>

<li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160815203446/https://dl.dropboxusercontent.com/u/182368464/1967-falconer.pdf">"The inheritance of liability to diseases with variable age of onset, with particular reference to diabetes mellitus"</a>, Falconer 1967</span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.genetics.org/content/167/4/1529">"D. S. Falconer and <i>Introduction to Quantitative Genetics</i>"</a>, Hill & Mackay 2004</span>

</li>

<li id="cite_note-PMID29739620-11"><span class="mw-cite-backlink"><a href="#cite_ref-PMID29739620_11-0">↑</a></span> <span class="reference-text">A. Lange, H. L. Nemeschkal, G. B. Müller: <i>A threshold model for polydactyly.</i> In: <i>Progress in biophysics and molecular biology.</i> Band 137, September 2018, S. 1–11, <a href="Digital_Object_Identifier" title="Digital Object Identifier">doi</a>:<span class="uri-handle" style="white-space:nowrap"><a rel="nofollow" class="external text" href="https://doi.org/10.1016/j.pbiomolbio.2018.04.007">10.1016/j.pbiomolbio.2018.04.007</a></span>, <a class="external mw-magiclink-pmid" rel="nofollow" href="https://www.ncbi.nlm.nih.gov/pubmed/29739620?dopt=Abstract">PMID 29739620</a> (Review).</span>

</li>

<li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">H. Tong: <i>Non-linear Time Series: A Dynamical System Approach</i>, 1990, OUP. ISBN 0-19-852224-X.</span>

</li>

</li>

<li id="cite_note-14"><span class="mw-cite-backlink"><a href="#cite_ref-14">↑</a></span> <span class="reference-text">Chevin & Lande 2013</span>

</li>

</ol>

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