The Fundamental Theorem of Natural Selection.

Area of Science:

• Evolutionary biology
• Mathematical biology
• Population genetics

Background:

• The rate of population change is influenced by individual fitness.
• Understanding evolutionary dynamics requires modeling population changes.
• Fisher's fundamental theorem of natural selection provides a foundational concept.

Purpose of the Study:

• To establish a relationship between the speed of evolutionary change and fitness variance.
• To present a modified version of Fisher's fundamental theorem.
• To analyze the dynamics of self-replicating entities in a population.

Main Methods:

• Mathematical modeling of population dynamics.
• Utilizing the Fisher information metric to quantify evolutionary speed.
• Analyzing continuous functions of population fitness.

Main Results:

• The speed of population distribution change, measured by the Fisher information metric, is equivalent to the variance in fitness.
• This finding offers a new perspective on the rate of information processing in natural selection.
• The study provides a quantitative link between fitness variation and evolutionary rate.

Conclusions:

• The variance in fitness directly correlates with the speed of evolutionary adaptation.
• This work extends and modifies Fisher's fundamental theorem of natural selection.
• The findings have implications for understanding the dynamics of self-replicating systems and evolutionary processes.