MaplePrimes - comments on Post, Genetic drift in Maple http://www.mapleprimes.com/posts/143661-Genetic-Drift-In-Maple en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 16:17:20 GMT Wed, 10 Jun 2026 16:17:20 GMT The latest comments added to the Post, Genetic drift in Maple http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Genetic drift in Maple http://www.mapleprimes.com/posts/143661-Genetic-Drift-In-Maple Founder effect http://www.mapleprimes.com/posts/143661-Genetic-Drift-In-Maple?ref=Feed:MaplePrimes:Genetic drift in Maple:Comments#comment143716 <p>An extreme case of genetic drift is known as the founder effect.</p> <p>I would like to point out that the proposterous idea of countries needing to protect themselves from zombie outbreaks might not be so rediculous.&nbsp; Far fetched yes but is it really?&nbsp; Should a few strange people be left stranded on an island, the idea of a zombie nation is possible.&nbsp; Unfortunately the very nature of a zombie is to consume others so really they would just basically wipe themselves out.&nbsp;</p> <p>Both genetic drift and the founder effect have interesting effects on the human population.&nbsp; I didn't really use much of maple here but the idea was interesting enough.&nbsp; With a little more thought and time, a better presentation could be made with Maple.&nbsp;</p> <p><br> </p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">An extreme case of genetic drift is known as the founder effect. &nbsp;If a small number of individuals migrate off to found a new population they may carry allels &nbsp;in different relative frequencies from the main population (Allels - two or more forms of a single gene). </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Again we can use Maple rather simply to simulate a demonstration of how it works. </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Imagine a jar of 5000 jellybeans, containing five equal colors. &nbsp;Pouring half of the jar out, you'll find roughly equal numbers of all five colors. &nbsp;But picking out only 3 jellybeans at random you'll be missing at least 2 of the colors present in the main population. &nbsp;You could concievably end up with 3 of one color as you can see in the following simulation. &nbsp;</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/6929e97183127a5c9b5b025275e02c35.gif" alt="restart; gc()" width="96" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/49d0dcfa2b5098007c3e1cbc4d00c41b.gif" alt="a := [seq(seq(j, j = 1 .. 5), i = 1 .. 5000)]:" width="261" height="23"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">#numbers representing 5 colors</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/5b44c85d21a488e631678d3c4c4b60ed.gif" alt="with(combinat):" width="112" height="23"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -126;" src="/view.aspx?sf=143716/454348/8624442e3138d7bfcd569dacf7c461bc.gif" alt="count := 0; do b := randcomb(a, 3); print(b); count := count+1; if numbperm(b) = 1 then break end if end do; print(&quot;It took&quot;, count, &quot; samplings to select all one value&quot;)" width="576" height="143" align="middle"><br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [2, 3, 2]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 3, 4]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [3, 3, 2]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 2, 4]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 4, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [4, 3, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [2, 5, 2]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 2, 4]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 2, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 2, 3]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [1, 4, 3]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [2, 1, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [4, 4, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [5, 4, 5]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [4, 1, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [4, 1, 1]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [5, 4, 2]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [4, 4, 4]<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; "It took", 18, " samplings to select all of one value"<br><br><br><br></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/3787d4d48fa611a294bb94a4d626a7e7.gif" alt="&quot;It took&quot;, 18, &quot; samplings to select all of one value&quot;" width="312" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right"><br>(1)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">The founder effect can be especially important in places such as Hawaii or the Galapagos islands where the populations of mainland species may be established by a handful of wanderers. &nbsp;Madagascar is one example of where lemurs have become completely different from lemurs elsewhere. &nbsp;Even within humans there are well-documented cases of the founder effect, where the mingling of their gene pool with the surrounding community is forbidden. &nbsp;An example is the Amish community in Pennsylvania, an orthodox religous group founded by a very small number of immigrants and allows no marriage to outsiders. &nbsp;Among the founders was a Mr. and Mrs. Samuel King. &nbsp;The Kings happen to carry a recessive allele that causes dwarfism, the growth of extra fingers, and heart defects. &nbsp;In the outside world the frequency of this allele is less than 1 in 1000 but in this Amish community it occurs at about 1 in 14.</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Just for fun we could put our little experiment into a procedure to observe sample sizes for different selection sizes </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/da8da6f853c5cacc7e1b74db857987c7.gif" alt="``" width="11" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/133cfb53c267bd5f152a18ddaf8f6685.gif" alt="``" width="11" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/d2aef225786a55b9c5db526eef2dfc88.gif" alt="NULL" width="11" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span> <br> <img style="vertical-align: -247;" src="/view.aspx?sf=143716/454348/10f3ac75cb062e25119991c207acd5af.gif" alt="foundereffect := proc (pop, diff, sel) local a, b, count; count := 0; a := [seq(seq(j, j = 1 .. diff), i = 1 .. pop/diff)]; do b := combinat:-randcomb(a, sel); print(b); count := count+1; if combinat:-numbperm(b) = 1 then break end if end do; print(&quot;It took&quot;, count, &quot; samplings to select all one value&quot;) end proc:" width="600" height="264" align="middle"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/655c42fd1f09b0e758509b5912fa01f7.gif" alt="foundereffect(9, 3, 3)" width="134" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left">&nbsp;</p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/2380ea1a3901d13ef252b0313cf73927.gif" alt="&quot;It took&quot;, 7, &quot; samplings to select all one value&quot;" width="288" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">For larger selection sizes, it would be wise to suppress the print outrput.</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=143716/454348/5c861fee07e0725fe1bf101b9e920b3c.gif" alt="NULL" width="11" height="23"></p> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p><br> </p> <p><a href="/view.aspx?sf=143716/454348/foundereffect2.mw">Download foundereffect2.mw</a></p> The latest comments added to the Post, Genetic drift in Maple 143716 Thu, 21 Feb 2013 01:14:37 Z Christopher2222 Christopher2222