Living systems allometric scaling laws

The spatial and temporal structuring and functioning of living systems are associated with scaling independent qualitative characteristics (gauge invariance) and quantitative laws (power laws). This is allowed by the emergence of new blueprints through the systems merging into ‘Associations for the Reciprocal and Mutual Sharing of Advantages and Dis-Advantages’ (ARMSADA). The local actors become more and more mutually integrated into their new global Whole. Then they are more and more independent from their previous local situations of emergence. Reversely (systemic constructal law), the global Whole is more and more integrating local parceners. The relationship between actors within a living system was described using allometric laws, e.g. the metabolic rate of a lot of species was supposed to be proportional to its mass according to a 3/4 exponent power-law (Kleiber’s law). But, according to the gauge invariance paradigm, an other explanation of the invariant scaling of living systems is proposed with a 2/3 power-law. Whatever its level of organization, a living system, ‘system of systems’ emerging by embedments and juxtapositions of previous ones, effectively functions in 4 dimensions (VA: the Adult system Volume, and tg: the time of generation, the duration that is necessary to acquire the capacity of reproduction). Looking at the gauge invariance paradigm as a ‘factual’ system, from the quantum of Planck to the Universe as a Whole, a meta-analysis of a database of the systems internal (endophysiotope) and external (ecoexotope) interactions can allow to quantify 45×18 allometric relationships. This allows to evidence a ‘grammar’: 1. Invariant independent processes (power-laws with exponent € = 0); 2. Simultaneous limiting interactions regulation processes (€ = +1); 3:F eedback (€ = -1); 4. Competition between actors (€ = 1/2); 5. Optimal exchanges flow (€ = 2/3) processes. Brownian motion is the basic fundamental process that governs all functions. From the Monera to the ecosystem levels the increasing of regulation processes allows more and more autonomy of the endophysiotope from the ecoexotope dependence. From the point of view of matter and energy flows, living systems optimize the input and output exchanges at their interface. The greater diversity of regulation processes occurs for the endophysiotope throughput flows. Whatever the organization level, living systems optimize their survival by adjusting ‘the capacity to be hosted’ of their endophysiotope (HOSTED) to the changes of ‘the hosting capacity’ of their ecoexotope (HOSTING).