Figure 2. Bifurcating autoregressive inheritance models.

(A) Coupled inheritance of $d$ Gaussian latent variables $x_l$ and cell-intrinsic fluctuations generate cycle lengths. (B) Relative model evidences calculated for $d=1,2$, for the indicated inheritance matrices $\mathbf{𝐀}=[a_{lm}]$ and sister coupling $\gamma$. Although Model VII is the most parsimonious for replicates rep2 and rep3 (blue and gray bars), only Model V with unidirectionally coupled inheritance explains all data well, including rep1 (bordeaux bars). Error bars from Monte-Carlo integration. (C) Model fits for rep1. Single-variable inheritance (Model II) and pure cross-inheritance (VII) fails to generate strong intra-generational correlations; uncoupled inheritance (III) fails to generate low ancestral correlations; Model V fits the data best. Rank correlations of the data shown with bootstrap 95%-confidence bounds (black bars). Model prediction bands (colored bars) were generated from the range of the parameter sets with likelihood higher than 15% of the best fit, corresponding to a Gaussian 95% credible region. (D) Model V, best-fit ancestral autocorrelation functions, for cycle lengths $\tau$ and latent variables. Long-range memory in the latent variables is anticorrelated and masked in observed cycle times.

Figure 2—figure supplement 1. Gaussian model predictions of correlations for all three replicates.

Model VII generates intra-generational correlations only up to first cousins which is compatible with rep2 and rep3 but not rep1.