A Mathematical Theory of Evolutionary Behavior

“A Mathematical Theory of Evolutionary Behavior, Inclusive of Contextual and Environmental Factors”

The purpose of this model is to provide a framework enabling quantification of the health of bodies, as well as guide safe and effective rule-based innovation and efficient resource allocation within a system of systems environment.

As utilized below, the framework describes the biological system of a human incorporating current understanding of the body and environmental factors; it may be additionally utilized for other biological entities, corporate bodies, cyber-physical systems, intelligent systems including AI/ML reasoning systems, and more complex systems of systems such as The Supply Chain Interoperability Specification platform of platforms.

The model may further be employed for the evaluation and assurance of technology products existing within the platform environment to provide a mathematical assurance mechanism (a lemma) capable of being translated into computer code and visualization technologies.

Let: E! ≥ B(E(Un, Ec, Bi, So, Cu, En, Gv))^2/ logT


E! = a quantity of behaviors, defined as equal to or greater than 1, is expressed as an evolutionary sum;


B = a body (entity class); a set of factors S(S1, …, Sn); in particle physics, these are measured as mass, charge, spin, decays, and scattering.

In humans, we may identify the composition of a body as a set of measurable factors: particles, atoms, molecules, cells, organs, the complex body, and consciousness (logic and emotion), itself a seventh property emerging from measurable complexity.

Environmental factors E are organized into sets composed as follows:

Un = universal factors, S(S1, ..., Sn)

Ec = ecological factors, S(S1, …, Sn)

Bi = biological factors, S(S1, …, Sn)

So = social factors, S(S1, …, Sn)

Cu = cultural factors, S(S1, …, Sn)

En = economic factors, S(S1, …, Sn)

Gv = governmental factors, S(S1, …, Sn)

logT = Time

I further define D! as a devolutionary negative sum of expressed behaviors should the equation resolve as < 1.

Additional body compositions may be measurably defined for additional biological systems, products or services, small/medium size businesses, enterprises, governments, and other systems, to establish measurable frameworks for determining their health and evolutionary or devolutionary potential.

As a body is also an environment, categories contained within the environmental set may also be used for the organization and communication of information of a body within the entity class.