7.4. Estimation of stable age distributionEquation [5] can be
re-written as:
Substituting this equation into [3] we get the relationship between the
number of organisms in age x and in age 0 in a stable age distribution:
Now we can estimate the proportion of organisms, c , in age x:
![](Estimation of stable age distribution_files/eq18.gif) |
[7] |
Age, x |
lx |
exp(-rx) |
lxexp(-rx) |
cx |
Simulated cx |
0 |
1.000 |
1.0000 |
1.0000 |
0.2413 |
0.2413 |
1 |
0.845 |
0.8507 |
0.7188 |
0.1734 |
0.1734 |
2 |
0.824 |
0.7237 |
0.5963 |
0.1439 |
0.1439 |
3 |
0.795 |
0.6156 |
0.4894 |
0.1181 |
0.1181 |
4 |
0.755 |
0.5237 |
0.3954 |
0.0954 |
0.0954 |
5 |
0.699 |
0.4455 |
0.3114 |
0.0751 |
0.0751 |
6 |
0.626 |
0.3790 |
0.2373 |
0.0572 |
0.0572 |
7 |
0.532 |
0.3224 |
0.1715 |
0.0414 |
0.0414 |
8 |
0.418 |
0.2743 |
0.1147 |
0.0277 |
0.0277 |
9 |
0.289 |
0.2333 |
0.0674 |
0.0163 |
0.0163 |
10 |
0.162 |
0.1985 |
0.0322 |
0.0078 |
0.0078 |
11 |
0.060 |
0.1689 |
0.0101 |
0.0024 |
0.0024 |
Total |
|
|
4.1445 |
1.0000 |
1.0000 |
Age distribution estimated using equation [7] (column 5) coincided with
simulated age distribution after 50 iterations of the model.
|