Maps of variability in cell lineage trees

New approaches to lineage tracking have allowed the study of differentiation in multicellular organisms over many generations of cells. Understanding the phenotypic variability observed in these lineage trees requires new statistical methods. Whereas an invariant cell lineage, such as that for the nematode Caenorhabditis elegans, can be described by a lineage map, defined as the pattern of phenotypes overlaid onto the binary tree, a traditional lineage map is static and does not describe the variability inherent in the cell lineages of higher organisms. Here, we introduce lineage variability maps which describe the pattern of second-order variation in lineage trees. These maps can be undirected graphs of the partial correlations between every lineal position, or directed graphs showing the dynamics of bifurcated patterns in each subtree. We show how to infer these graphical models for lineages of any depth from sample sizes of only a few pedigrees. This required developing the generalized spectral analysis for a binary tree, the natural framework for describing tree-structured variation. When tested on pedigrees from C. elegans expressing a marker for pharyngeal differentiation potential, the variability maps recover essential features of the known lineage map. When applied to highly-variable pedigrees monitoring cell size in T lymphocytes, the maps show that most of the phenotype is set by the founder naive T cell. Lineage variability maps thus elevate the concept of the lineage map to the population level, addressing questions about the potency and dynamics of cell lineages and providing a way to quantify the progressive restriction of cell fate with increasing depth in the tree.Author summary: Multicellular organisms develop from a single fertilized egg by sequential cell divisions. The progeny from these divisions adopt different traits that are transmitted and modified through many generations. By tracking how cell traits change with each successive cell division throughout the family, or lineage, tree, it has been possible to understand where and how these modifications are controlled at the single-cell level. This helps address questions about, for example, the developmental origin of tissues, the sources of differentiation in immune cells, or the relationship between primary tumors and metastases. Such lineages often show large variability, with apparently similar founder cells giving rise to different patterns of descendants. In addition, questions about the range of accessible cell types at different stages of the lineage tree are actually questions about lineage variability. To characterize this variation, and thus understand the lineage at the population level, we introduce lineage variability maps. Using data from worm and mammalian cell lineages we show how these maps provide quantifiable answers to questions about any developing lineage, such as the potency of progenitor cells and the restriction of cell fate at different stages of the tree.