Journal of Population Sciences
Table 2 The total size of a cohort and its descendants, as calculated by projection and by Eq. (10), for NRR = 0.75 and μ = 29 years
From: The time to decline: tracing a cohort’s descendants in below replacement populations
(1) | (2) | (3) | (4) | (5) |
|---|---|---|---|---|
Time (t) [years] | Projected total size [PT(t)] | Growth rate [PT(t)/PT(t − 5)] | Total size from Eq. (10) | Proportional error |
0 | 1.0 | |||
5 | 1.0 | 1.0 | ||
10 | 1.0 | 1.0 | ||
15 | 1.0 | 1.0 | ||
20 | 1.1642 | 1.1642 | ||
25 | 1.4064 | 1.2081 | ||
30 | 1.5625 | 1.1110 | ||
35 | 1.6475 | 1.0544 | ||
40 | 1.7418 | 1.0572 | ||
45 | 1.8534 | 1.0641 | ||
50 | 1.9695 | 1.0626 | ||
55 | 2. 0730 | 1.0526 | ||
60 | 2.1651 | 1.0444 | ||
65 | 2.2544 | 1.0412 | ||
70 | 2.3417 | 1.0387 | ||
75 | 2.4244 | 1.0353 | ||
80 | 2.5023 | 1.0321 | ||
85 | 1.5763 | 0.6300 | 1.9352 | − 0.2277 |
90 | 1.6474 | 1.0451 | 1.8420 | − 0.1181 |
95 | 1.7153 | 1.0412 | 1.7533 | − 0.0221 |
100 | 1.7796 | 1.0375 | 1.6689 | 0.0622 |
105 | 1.6764 | 0.9420 | 1.5885 | 0.0524 |
110 | 1.4923 | 0.8902 | 1.5120 | − 0.0132 |
115 | 1.3916 | 0.9325 | 1.4392 | − 0.0342 |
120 | 1.3594 | 0.9769 | 1.3699 | − 0.0077 |
125 | 1.3153 | 0.9675 | 1.3039 | 0.0087 |
130 | 1.2515 | 0.9515 | 1.2411 | 0.0083 |
135 | 1.1809 | 0.9436 | 1.1813 | − 0.0004 |
140 | 1.1206 | 0.9490 | 1.1244 | − 0.0034 |
145 | 1.0698 | 0.9546 | 1.0703 | − 0.0005 |
150 | 1.0197 | 0.9532 | 1.0187 | 0.0009 |
155 | 0.9697 | 0.9510 | 0.9697 | 0.000 03 |
160 | 0.9225 | 0.9513 | 0.9230 | − 0.000 54 |
165 | 0.8785 | 0.9523 | 0.8785 | − 0.000 06 |
170 | 0.8366 | 0.9524 | 0.8362 | 0.000 48 |
175 | 0.7962 | 0.9516 | 0.7960 | 0.000 26 |
180 | 0.7574 | 0.9514 | 0.7576 | − 0.000 23 |
185 | 0.7209 | 0.9518 | 0.7211 | − 0.000 28 |
190 | 0.6864 | 0.9521 | 0.6864 | 0.000003 |
195 | 0.6535 | 0.9520 | 0.6534 | 0.000 17 |
200 | 0.6219 | 0.9518 | 0.6219 | 0.000 08 |