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Inferring fitness landscapes and selection on phenotypic states from single-cell genealogical data

Fig 2

Chronological and retrospective probabilities of single-cell lineages.

A. Chronological and retrospective probabilities on a fixed tree. Here we consider a representative fixed lineage tree spanning from time t₀ to t₁ = t₀ + τ. The number of cells in this tree at t₁ is cells, and each of these cells distinguishes a unique lineage (e.g. the cyan and orange lines in the tree). is the probability that a cell lineage i () is chosen by descending the tree from t₀ to t₁ (green arrow). At every division point, we randomly select one daughter cell’s lineage with the probability of 1/2 (light green arrows). The probability that we choose lineage i in this manner is , where D_i is the number of cell divisions on lineage i. is the probability of choosing cell lineage i among lineages with equal weight (pink arrow). Thus, . We call and the chronological probability and retrospective probability, respectively, based on the time directions of the green and pink arrows. The chronological and retrospective probabilities for the cell lineages 3 and 9 are shown in cyan and orange texts, respectively. B. A tree on which all the cell lineages have the same number of cell divisions. In this case, the chronological and the retrospective probabilities are equal for all the lineages. C. General case with a large collection of lineage trees. denotes a tree each descended from a different ancestor cell at time t₀. The definitions of the chronological and retrospective joint probabilities of division count D and lineage phenotype x are shown in green and pink, respectively. n(D, x) denotes the total number of cell lineages with D and x, i.e. .

doi: https://doi.org/10.1371/journal.pgen.1006653.g002