Generate and total Leslie population states
A dune-restoration model records grasses in equal-width growth stages. The same rates apply in every model period
Use the group order new sprouts, juvenile plants, and established plants. One application represents one growing season. The groups have equal widths, so a survivor advances one group in one application
This model counts all individuals. A fertility entry is the expected number of new first-group entrants per current individual in one period. A survival entry is the proportion advancing from one group to the next
\[L=\begin{bmatrix} 1.2 & 1.4 & 1 \\ 0.8 & 0 & 0 \\ 0 & 0.6 & 0 \end{bmatrix}\]
\[S_0=\begin{bmatrix} 15 \\ 40 \\ 30 \end{bmatrix}\]
\[S_{n+1}=L S_n\]
Give exact values
The entries of each state column are expected counts of plants