<% Digits = 6 ' Repeat = "Yes" %>

Zachriel's Nest of Letters

Zachriel’s Nest of Letters
“A nested-hierarchy is not just a mere similarity, but a family resemblance.”

(graphic version)
 

Sometimes, when looking at a baby, we will say she has her father's nose, or her mother's eyes. But we normally look at a combination of features to decide resemblance. That's because though one feature or another may vary, a large number of features will be shared by many or most of the members of a family. 

Zachriel's Nest of Letters is a software simulation of random aspects of population dynamics. Selection is completely random, with each mutation a simple random point-change. The model compares Nestless and Nested descent, and shows how birth, death, genetic fixation, extinction, and common ancestry can somewhat surprisingly impose order. You can download Zachriel's Nest of Letters here

These are two screenshots from Nest of Letters. The first is Nestless Descent, the second is Nested Descent. 
 

Nestless Descent

Nested Descent
 

Nestless  Nested
NKZE..
CZ.R.G
Q.QSHM
..WP.K
TQSNXG
K.CT..
BUB.H.
R...E.
V...E.
SHCA..
SHCAK.
.HX...
.HXM..
.KX...
TKX...
.MXV..
.HXV..
"......"
7th Generation
Nest Size = 7
Clone = 0%
Mutation = 100%
"......"
7th Generation
Nest Size = 7
Clone = 33%
Mutation = 33%

A Parent's Surprise

Take a look at these two surprisingly different results after just seven generations (G). Each family tree began exactly the same way—from "......". In Nestless Descent, each parent has one and exactly one mutant child. In Nested Descent, each parent can either birth a clone or a mutant, both or neither. In other words, each parent can have zero, one or two children. If there is plenty of room in the Nest, then both children will survive. But when the Nest is full, survivors are selected randomly. 

Note the wide differences in results. While the Nestless Descent shows no sign of a pattern, the Nested Descent shows many interlocking patterns; for instance, the prevalence of X in the third letter position, and that SH is always followed by C

 

Using Zachriel's Nest of Letters

After downloading Zachriel's Nest of Letters, press ctrl-n to create a new family tree. You can then trace the genealogy of any family member, or any range of family members, by highlighting the range and pressing ctrl-g. Clear the genealogy by pressing ctrl-z or by selecting a trace from the earliest generations. 

ctrl-n New Nested Family Tree
ctrl-g Genealogy
ctrl-f Fossils
ctrl-h Clear Genealogy
ctrl-r Resemblance
ctrl-t New Nestless Family Tree
ctrl-w Winners
 
ctrl-z Remove all traces no color
ctrl-x Trace from 1st generation 1 color
ctrl-c Trace from 2nd generation 2 colors
ctrl-v Trace from 3rd generation 4 colors
ctrl-b Trace from 4th generation 8 colors
 
Esc Interrupt Program

 

 
User Options on Variables screen

There are a number of options available on the "Variables" worksheet.  Valid options are highlighted in yellow. You can set the Patriarch, that is, the founding parent. You can set the number of generations and the size of the nest. You can also set the chance of cloning or mutation in the children. (Cloning + Mutation should be set to no more than 100% to prevent runaway population growth.)

 

Fixation on Nesting

Genetic Fixation
 

Over a number of generations, random chance means some lines-of-descent will be winners, and some will be losers. In this image, we have traced the descent of the eight parents from the fourth generation (ctrl-b). After a few dozen generations, most of the lines have disappeared. Only two remain, the Purple and the Orange, and even the Orange is close to extinction. The process of change in proportions between these populations is called "genetic drift", and when one population takes over, the result is called "fixation". 

This process of drift and fixation can be explained in part as an exception to the Hardy-Weinberg Equilibrium. Hardy-Weinberg posits that a population will remain in equilibrium under the following conditions:

  • Random mating
  • Infinite population size
  • No mutation
  • No Genetic Migration
  • No natural selection

Though the Nest of Letters uses only random mutation, the population is not infinite, so drift and fixation are the inevitable results.

MNWB...GBT..
MNWB...GBT..
MNWB...XBTO.
MNWF...XBTO.
.NWB.X.GBT..
.NWB.X.GBTI.
.NWB.X.GBTK.
.NGB.X.GBTK.
.NAB.X.GBTK.
.NAB.X.GBTK.
.NWB.X.UBT..
.NWB.X.UBTC.
.NWB.X.UMT..
.NWP.X.UMT..
"............"
32nd Generation
Nest Size = 24
Clone = 33%
Mutation = 33%

Common Ancestor or Country Cousin

This is a portion of a population after thirty-two generations (AF). Clearly, nested-descent is implied by the structure of the population. We therefore hypothesize the existence of a common ancestor and search for fossils of the (most recent) common ancestor—or a close relative of this ancestor.

In the following image, the Nest of Letters has been set to fossil- mode (ctrl-f). Looking at the fossils we have available, the closest match appears to be ".NWB.A..BT.." (X2 in Blue) which shares features with all of the current population including the second-letter "N" and the tenth-letter "T". There is no way to determine from examining the fossil itself if it is a direct descendent of any of our population, however, we can see that it is a probably close relative of the (most recent) common ancestor. 

Zachriel's Nest of Letters gives us the capability of actually tracing the lines-of-descent. We trace (ctrl-g) the ancestry of the fossil (X2 in Blue), the genealogy of the current population (AF) which starts with "MN" in Purple, and the population which starts with ".N" in Orange. We can see that the actual common ancestor we were looking for is a missing fossil (Y1 in Orange), and that our fossil (X2 in Blue) shares a common ancestor too (W1 in Orange), but split off and dies out later on (AB in Blue).  

 

Most recent common ancestor
 
 

What hatched!

So, we can see that the process of discovery is finding and verifying the existence of (most recent) common ancestors and their close relatives. Hopefully, the Nest of Letters shows a bit how a nested-hierarchy implies common descent, and how each fossil found or genome decoded adds confirmation to the biological Theory of Common Descent. 

 

Zachriel's Nest of Letters
Zachriel's Nest of Letters

~200KB
(Right-click & select Save Target as....
Requires VBA6 which is included in Office 2000 and Excel 2000. )
Certified Virus-Free

©2005 Zachriel

    

Also try out: 
Word Mutagenation
Word Mutagenation

NEW!
Zachriel's New Word Mutation and Evolution Experiment

 


Zachriel's Nest of Letters brought to you by 
Moods in Music - MIDI Music by Lee Croteau
Moods in Music
All music written, performed and copyrighted by Lee Croteau.
All rights reserved. ©1995-2004  

 

Great Place to Shop


Web Presence Provider

Hosted By Crown Mall and Designed by Web King.

<%=HitCount%>