Tuesday, October 17, 2006,
3:00 PM
The tall gene in plants are dominant while the short ones are recessive... Mendel's experiment proved that... He then came up with Mendel's 1st Law and Mendel's 2nd Law...
Long after his death, he was considered the Father of Modern Genetics...
However, it came as a surprise to me to learn that the short gene in the
homo sapien are dominant while the tall gene is recessive... Therefore, for this prediction, I shall use S, standing for the dominant short gene, while s is the recessive tall gene...
The 1st 2 people on Earth that were created were Adam and Eve...
We can only assume that both of them had one dominant and one recessive gene, Ss and Ss respectively... Therefore, both Adam and Eve were short...
Now we know that Adam and Eve had 2 sons: Cain and Abel... however, Cain killed Abel, so we are left with only 1 son...
Also, Cain had a wife and they had more children and their children had more children...
Therefore, we concluded that Adam and Eve had Cain, Abel and another daughter...
So then...
Ss x Ss
SS (.25 chance) Ss (.5 chance) ss (.25 chance)
Short (.75 chance), Tall (.25 chance)
Hmmm... now with the assumption that every couple after Cain and wife bore 2 sons and 2 daughters...
Time started around 6000 BC
1 generation lasts 30 years
Therefore, 6000 + 2006 = 8006 years has passed now...
n(generations) = 8006/30 = 266.866666667 = 266 generations
Now we know that the number of children produced bu each couple differ from different generations with every generation decreasing production as time goes by...
We can assume that the number of children produced is modelled by a linear model...
If an average of 2 children is produced in this generation, and there were 8 produced 2 generations before, and about 5 produced the previous generation, it would only mean WE NEED MORE DATA!!! Lol...
Jacob had 12 sons... and if every couple in Jacob's generation produced 12 children, then number of children = 12 x N(children produced in the previous generation)/2
Erm, assume that Jacob was the 6th generation (Adam, Cain, Noah, Abraham, Issac, Jacob!)
Ok, so... t=6, N=12; t=(1960+6000)/30 = 265.33, N=8, t=(1990+6000)/30 = 266.33, N=5, t=(2000+ 6000)/30 = 266.67, N=2
So we have our least squares regression line, N(t) = -0.02699t + 12.1773, with our coefficient correlation, r(tN) = -0.8217, which indicates a strong negative linear relationship... So, we can say our linear model is pretty much appropriate...
That is the model to predict the number of children every couple will produce, so the total number of children produced in a particular generation is...
There are 266 generations
So, we have to calculate 266 times (zzzz...)
1 couple in the 2nd generation, so number of children produced, N'(t)...
N'(1) = 1 x 12.1503 = 12.1503
N'(2) = 12.1503/2 x N(2) = 6.0752 x 12.1233 = 73.6509
Hence, we have N'(t) = [N'(t-1)]/2 . N(t)
Sigh... it's times like this I'm glad I have a programmable graphic calculator...
So, we have
N'(266)
= N'(265)/2 . N(266)
= N'(264)/2^2 . N(265) . N(266)
= N'(263)/2^3 . N(264) . N(265) . N(266)
and so on, and so forth, and so we have...
N'(266)
= N'(3)/2^263 . N(4) . N(5) . N(6) .... . N(266)
= N'(2)/2^264 . N(3) . N(4) . N(5) .... . N(266)
= N'(1)/2^265 . N(2) . N(3) . N(4) .... . N(266)
This is not taken into consideration number of deaths... which means more complicated calculations... and more googling... sigh...
Hmmm, at the moment, anyone care calculating N'(266) for me pls??? I appreciate answers correct to 8 significant figures... anyone who helps me will get free lunch!!!
