The analysis of all groups of Archaea performed in two-dimensions have demonstrated a specific
distribution of Archaean species as a function of pH/temperature, temperature/salinity and pH/salinity. Work
presented here is an extension of this analysis with a three dimensional (3D) modeling in logarithmic scale. As it
was shown in 2D representation, the “Rules of the Diagonal” have been expressed even more clearly in 3D
modeling. In this article, we used a 3D Mesh modeling to show the range of distribution of each separate group of
Archaea as a function of pH, temperature, and salinity. Visible overlap and links between different groups indicate a
direction of evolution in Archaea. The major direction in ancestral life (vector of evolution) has been indicated: from
high temperature, acidic, and low-salinity system towards low temperature, alkaline and high salinity systems.
Specifics of the geometrical coordinates and distribution of separate groups of Archaea in 3 D scale were analyzed
with a mathematical description of the functions.
Based on the obtained data, a new model for the origin and evolution of life on Earth is proposed. The
geometry of this model is described by a hyperboloid of one sheet. Conclusions of this research are consistent with
previous results derived from the two-dimensional diagrams. This approach is suggested as a new method for
analyzing any biological group in accordance to its environmental parameters.