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Alphabet Option (1024) - New Malthusian Scale - constant rate
Alphabet Option (512) - New Malthusian Scale - constant rate
Alphabet Option (1024) - New Malthusian Scale - variable rate
Alphabet Option (512) - New Malthusian Scale - variable rate 

The Mechanism Of Population Doubling

Alphabet Option For The New Malthusian Scale (variable rate) 

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population." Malthus (1830) - A Summary View on The Principle Of Population

Time                      
A-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
B-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
C-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
D-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
E-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
F-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
G-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
H-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
I-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
J-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
K-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
L-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
M-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
N-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
O-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
P-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
Q-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
R-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
S-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
T-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
U-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
V-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
W-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
X-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
Y-pops 1 2 4 8 16 32 64 128 256 512 1024
Time                      
Z-pops 1 2 4 8 16 32 64 128 256 512 1024

Table 1: Alphabet pops at variable growth rate, based on the New Malthusian Scale

Note:  1A-pop = 1024 pops, 1B-pop = 1024 A-pops, 1 C-pop = 1024 B-pops etc.

This scale for exponential growth assumes a variable rate of growth. Hence the population is subject to the Couttsian Growth Model. The advantage of this scale is that it makes it easy to document the variable population doubling times which result from a variable rate of growth. This scale is more realistic than the Alphabet Option For The New Malthusian Scale (constant rate).

To use this scale, print it and then write your variable population doubling times across each row. This could be in minutes, hours, days, months or years (depending upon the nature of the replicator population being measured). 

Typically, for any real-life population of replicators experiencing a period of growth, you should find that population doubling times increase as you move up the scale (as the rate of growth decreases). This can be due to the increasing scarcity of resources as the limits to growth are approached, a corresponding increase in a population of predators upon a growing prey species, or the increased likelihood of disease in a vastly expanded population pool. I'm sure you can think of other examples. Humanity, of course, does its best to avoid each of these natural types of checks.

Eventually, a population will reach a state of dynamic equilibrium in which it oscillates between positive and negative growth rates.

If you prefer, you can use a version of this table with the 1024 column removed

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Copyright © 2001 David A. Coutts
Last modified: 08 November, 2009