Backgrounder:

Along the diagonal of the matrix are the transition elements that tell you what fraction of the individuals in each group are still in that group at the end of one year.For example, element P[2,2] is 0.8 indicating that 80% of the individuals age 5-9 are still in the 5-9 age group at the end of the one year.Note that this makes sense because roughly 20% of the individuals age 5-9 are likely to be 9 years old and after one year, they will be in the 10-14 age group.

The elements on the subdiagonal (just below the diagonal) are the rates for transitioning to the next age group.For example, element P[3,2] is 0.2, indicating that 20% of the individuals in group 2 (5-9) transition to group 3 (10-14) in one year.

The elements across the top row indicate the fecundities?the average number of babies (which are in the 0-4 age group) born each year to the individual age groups?recall that each column of the P matrix indicates a different age group, so a value in position P[1,3] would be the fecundity of the third age group (10-14), which makes sense as described above.