Fig. 3.
Lineage graphs of real organisms. a Lineage graphs from real organisms: Volvox: R = reproductive cell, S = somatic cell [25]; human hematopoietic system: P = progenitor cells, Me = megakaryocytes, E = erythrocytes, B = basophils, L = lymphocytes, D = dendritic cells, Mo = monocytes, N = neutrophils [26]; hydra: Ec = ectoderm, En = endoderm, IS = interstitial cell, H = hypostome, T = tentacle, F = foot, E = egg, S = sperm, GN = ganglion neuron, SN = sensory neuron, B = battery cell, N = nematocyst, Z = zymogen granule cell, GM = granular mucous granule cell, SM = spumous mucous granule cell [27]; and the mouse entero-endocrine system: G = goblet cell, E = EC cell, K = K cell, D = δ cell, X = X cell, L = L cell, I = I cell, N = N cell [28]. b Scatter plot of the number of branches versus the number of links for acyclic lineage graphs with nl and nb<= 20. The inset shows the nl versus nb scatter plot for all acyclic graphs. Noise has been added to points to make density of points more apparent. 1,217,108 graphs were used to generate this plot. c Relaxed definition of treeness: the x-axis represents nl/nb, our measure of a threshold for “treeness.” nl/nb=0, represents the traditional, strict definition of trees, whereas at nl/nb=1, all branched acyclic graphs are considered trees. At intermediate values, the fraction of graphs labeled as trees increases slowly. A total of 521,136 graphs were used to generate this plot