Matriz_examen_II.R

A <- matrix(c(0, 30, 60, 10, 0.25, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0.35, 0), nr = 4, byrow = TRUE)
A

##      [,1] [,2]  [,3] [,4]
## [1,] 0.00 30.0 60.00   10
## [2,] 0.25  0.0  0.00    0
## [3,] 0.00  0.5  0.00    0
## [4,] 0.00  0.0  0.35    0

nt <- matrix(c(500, 100, 300, 50), ncol = 1)
nt

##      [,1]
## [1,]  500
## [2,]  100
## [3,]  300
## [4,]   50

nt1= A %*% nt
nt1

##       [,1]
## [1,] 21500
## [2,]   125
## [3,]    50
## [4,]   105

years=8
n.projections <- matrix(0, nrow = nrow(A), ncol = years + 1)
n.projections

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,]    0    0    0    0    0    0    0    0    0
## [2,]    0    0    0    0    0    0    0    0    0
## [3,]    0    0    0    0    0    0    0    0    0
## [4,]    0    0    0    0    0    0    0    0    0

n.projections[, 1] <- nt
n.projections

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## [1,]  500    0    0    0    0    0    0    0    0
## [2,]  100    0    0    0    0    0    0    0    0
## [3,]  300    0    0    0    0    0    0    0    0
## [4,]   50    0    0    0    0    0    0    0    0

for (i in 1:years) n.projections[, i + 1] <- A %*% n.projections[,i]
n.projections

##      [,1]  [,2]   [,3]       [,4]       [,5]       [,6]        [,7]
## [1,]  500 21500 7800.0 165175.000 219968.750 1306718.75 2891990.625
## [2,]  100   125 5375.0   1950.000  41293.750   54992.19  326679.688
## [3,]  300    50   62.5   2687.500    975.000   20646.88   27496.094
## [4,]   50   105   17.5     21.875    940.625     341.25    7226.406
##              [,8]        [,9]
## [1,] 11522420.312 31586556.64
## [2,]   722997.656  2880605.08
## [3,]   163339.844   361498.83
## [4,]     9623.633    57168.95

matplot(0:years, t(n.projections), type = "l", lty = 1:3,col = 1, ylab = "Stage Abundance", xlab = "Year")
legend("topleft", legend = c("Semilla", "Adulto pequeño", "Adulto mediano", "Adulto grande"),lty = 1:4, col = 1, bty = "n")