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Growth, Reproduction Rate


Growth kinetics in arithmetic and logarithmic representation



A population of Nt individuals is at the time t very large. During a finite period of time (t), the number of individuals changes due to new (b) and leaving individuals (d). This means that

delta Nt = (b - d) Nt t ,

with the difference between b and d being the rate of growth. The growth rate again depends on

More simplified, the equation runs:

delta Nt = rNt t ,

If delta t > 0, then

delta Nt / dt = rNt

The same equation written in its integrated state runs

rt = ln Nt - ln N0 ,

with N0 being the original number of individuals and Nt being the number of individuals at the end of the time period dt.

Remodelled, the equation runs

nt= N0 e rt or

ln Nt = ln N0 + rt,

This latter equation is the formula of the general growth function though it is valid only under idealized conditions, i.e. during the logarithmic growth phase of a bacteria culture or a culture of single-celled algae.

er is the same as w that symbolizes the fitness (Wright’s fitness) of the individuals. If, for example, the fitness of an individual is 1 and that of another is 2, then the second individual produces twice the amount of progeny of individual 1. Resolved to r, the above formula runs

r = ln w

The growth rate is accordingly the same as the log naturalis of the value of the fitness, which again depends on the selection coefficient (s):

w = 1 - s


© Peter v. Sengbusch - b-online@botanik.uni-hamburg.de