  Populations of isogenic embryonic stem cells or clonal bacteria often exhibit
extensive phenotypic heterogeneity which arises from stochastic intrinsic
dynamics of cells. The internal state of the cell can be transmitted
epigenetically in cell division, leading to correlations in the phenotypic
states of cells related by descent. Therefore, a phenotypic snapshot of a
collection of cells with known genealogical structure, contains information on
phenotypic dynamics. Here we use a model of phenotypic dynamics on a
genealogical tree to define an inference method which allows to extract an
approximate probabilistic description of phenotypic dynamics based on measured
correlations as a function of the degree of kinship. The approach is tested and
validated on the example of Pyoverdine dynamics in P. aeruginosa colonies.
Interestingly, we find that correlations among pairs and triples of distant
relatives have a simple but non-trivial structure indicating that observed
phenotypic dynamics on the genealogical tree is approximately conformal - a
symmetry characteristic of critical behavior in physical systems. Proposed
inference method is sufficiently general to be applied in any system where
lineage information is available.
