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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
  1. Notes: The initial cohort is age 0 at time 0. The 5-year stable growth rate is 0.9518. The proportional error in the Eq. (10) analytical projection in column (5) is calculated as [(2) − (4)]/(2), referring to columns (2) and (4)