Individuality and the Living Tree of Life: An Information-Geometric Theory of Biological Form.

We develop an information-theoretic criterion for identifying biological individuals across organizational scales in branching evolutionary systems. The living tree of life is modeled as a branching-process Random Iterated Function System (bRIFS), in which realized reproductive histories form sequences of static structures and living entities arise as resolution-dependent limits over these histories. Here, we study this construction under neutral, asexual reproduction, providing a minimal evolutionary setting in which individuality can be examined in the absence of selection and sexual reproduction. On this probabilistic substrate, we define geometric and information-theoretic quantities that measure joint and mutual certainty between lineages. Their relative magnitudes determine whether two lineages are informationally divergent or instead remain coherent. These quantities are combined in a dilation equation that expresses relative lifespans as dimensionless pairwise ratios, thereby endowing the living tree with the structure of a nearness space. Coherent solutions induce recursively nested equivalence classes, yielding a hierarchy of higher-order individuals across ancestral scales. In the simulated realization, these higher-order individuals emerge under pure drift and asexual fission, without requiring selection or sexual reproduction. Biological individuality therefore emerges as a measurable relational property of the information geometry of descent rather than as a presupposed biological primitive.