Question 1. What is the effective size of a heard of 10 dairy cows and one bull? What is it for 40 cows and 1 bull? For 10 cows and 2 bulls? What about X-Linked genes in these three cases?
![[Graphics:Images/bio434ss1.pdf_gr_1.gif]](Images/bio434ss1.pdf_gr_1.gif)
![[Graphics:Images/bio434ss1.pdf_gr_2.gif]](Images/bio434ss1.pdf_gr_2.gif)
autosomal 10 cows, 1 bull;
![[Graphics:Images/bio434ss1.pdf_gr_3.gif]](Images/bio434ss1.pdf_gr_3.gif)
![[Graphics:Images/bio434ss1.pdf_gr_4.gif]](Images/bio434ss1.pdf_gr_4.gif)
autosomal 40 cows, 1 bull;
![[Graphics:Images/bio434ss1.pdf_gr_5.gif]](Images/bio434ss1.pdf_gr_5.gif)
![[Graphics:Images/bio434ss1.pdf_gr_6.gif]](Images/bio434ss1.pdf_gr_6.gif)
autosomal 10 cows, 2 bulls;
![[Graphics:Images/bio434ss1.pdf_gr_7.gif]](Images/bio434ss1.pdf_gr_7.gif)
![[Graphics:Images/bio434ss1.pdf_gr_8.gif]](Images/bio434ss1.pdf_gr_8.gif)
x-linked 10 cows, 1 bull
![[Graphics:Images/index_gr_2.gif]](Images/index_gr_2.gif)
![[Graphics:Images/index_gr_3.gif]](Images/index_gr_3.gif)
x-linked 40 cows, 1 bull
![[Graphics:Images/index_gr_4.gif]](Images/index_gr_4.gif)
![[Graphics:Images/index_gr_5.gif]](Images/index_gr_5.gif)
x-linked 10 cows, 2 bulls
![[Graphics:Images/index_gr_6.gif]](Images/index_gr_6.gif)
![[Graphics:Images/index_gr_7.gif]](Images/index_gr_7.gif)
2. Construct the transition probability matrix when
![[Graphics:Images/bio434ss1.pdf_gr_15.gif]](Images/q2-function.gif)
![[Graphics:Images/pre-q2.gif]](Images/pre-q2.gif)
a) N=2
The number of dimensions of a transition probability matrix = 2N+1. Therefore we will have a matrix with the dimensions 5x5. For the matrix displayed below, remember that Indeterminate means 1!
![[Graphics:Images/bio434ss1.pdf_gr_16.gif]](Images/q2a-a.gif)
![[Graphics:Images/bio434ss1.pdf_gr_17.gif]](Images/q2a-b.gif)
b) N=3
The number of dimensions of a transition probability matrix = 2N+1. Therefore we will have a matrix with the dimensions 7x7! For the matrix displayed below, remember that Indeterminate means 1!
![[Graphics:Images/bio434ss1.pdf_gr_18.gif]](Images/q3a-a.gif)
![[Graphics:Images/bio434ss1.pdf_gr_19.gif]](Images/q3a-b.gif)
![[Graphics:Images/bio434ss1.pdf_gr_20.gif]](Images/bio434ss1.pdf_gr_20.gif)
![[Graphics:Images/bio434ss1.pdf_gr_21.gif]](Images/bio434ss1.pdf_gr_21.gif)
![[Graphics:Images/bio434ss1.pdf_gr_22.gif]](Images/bio434ss1.pdf_gr_22.gif)
![[Graphics:Images/bio434ss1.pdf_gr_23.gif]](Images/bio434ss1.pdf_gr_23.gif)
![[Graphics:Images/bio434ss1.pdf_gr_24.gif]](Images/bio434ss1.pdf_gr_24.gif)
![[Graphics:Images/bio434ss1.pdf_gr_25.gif]](Images/bio434ss1.pdf_gr_25.gif)
![[Graphics:Images/bio434ss1.pdf_gr_26.gif]](Images/bio434ss1.pdf_gr_26.gif)
![[Graphics:Images/bio434ss1.pdf_gr_27.gif]](Images/bio434ss1.pdf_gr_27.gif)
![[Graphics:Images/bio434ss1.pdf_gr_28.gif]](Images/bio434ss1.pdf_gr_28.gif)
Converted by Mathematica
February 3, 2004