Ex. 6

In Example 11.9, assume that we start with a hybrid bred to a hybrid. Find u(1), u(2), and u(3). What would u(n) be?

hybrid<-matrix(c(.5,.25,0,.5,.5,.5,0,.25,.5), nrow=3,ncol=3)
hybrid

##      [,1] [,2] [,3]
## [1,] 0.50  0.5 0.00
## [2,] 0.25  0.5 0.25
## [3,] 0.00  0.5 0.50

u<-c(0,1,0)
u

## [1] 0 1 0

P1<-hybrid
u1<-u%*%P1
u1

##      [,1] [,2] [,3]
## [1,] 0.25  0.5 0.25

P2<-hybrid%*%hybrid
P2

##       [,1] [,2]  [,3]
## [1,] 0.375  0.5 0.125
## [2,] 0.250  0.5 0.250
## [3,] 0.125  0.5 0.375

u2<-u%*%P2
u2

##      [,1] [,2] [,3]
## [1,] 0.25  0.5 0.25

P3<-hybrid%*%P2
P3

##        [,1] [,2]   [,3]
## [1,] 0.3125  0.5 0.1875
## [2,] 0.2500  0.5 0.2500
## [3,] 0.1875  0.5 0.3125

u3 = u%*%P3
u3

##      [,1] [,2] [,3]
## [1,] 0.25  0.5 0.25

u^(n)=(.25,.5,.25)

Data605_Discussion10