Appendix 1—figure 6. Models of circadian-clock-driven correlation patterns (a–d) Kicked cell cycle model.

(a) Model schematic. The mother to daughter IDT inheritance is given by $\beta =\frac{(a-2)}{4}$ where $a$ is the size control parameter. The ‘kick’ to the cell cycle us produced by a two-dimensional complex eigenvalued inheritance matrix model system with oscillator behaviour. (b) Region plot for $\beta =-0.25$ (blue) and $\beta =0.25$ (grey), demonstrating the region for this model where the cousin inequality is satisfied. Here we fix the variances of the noise terms ${\xi }_1,{\xi }_2$ and ${\xi }_{\tau }$ all equal to 0.1. (c–d) Plot of the generalised tree correlation function for (c) $(D,P)=(0.85,2.5)$ and (d) $(D,P)=(0.85,5)$. In both these plots we take $\beta =-0.25$, meaning the model has a mixture of alternator and oscillator behaviours. The cousin inequality is satisfied for both these parameter choices. (e–h) Circadian cell size control model (e) Model schematic. The parameter $a$ gives how the daughter’s birth size depends on the mother’s birth size; and $b$ gives the coupling of the circadian oscillator to the size control. (f) Region plot demonstrating where the cousin inequality is satisfied. We fix $a=1,b=1$. Correlations between noise terms are fixed equal to 0 and we set ${\eta }_i=0.1$ for $i\in \{1,2,A\}$. (g–h) Plots of the generalised tree correlation function for the same fixed parameters specified in panel (f), with (g) $(D,P)=(0.85,2.5)$, and (h) $(D,P)=(0.85,5)$. As we fix $a=1$, these plots show a combination of aperiodic and oscillator behaviour. We note that for $(D,P)=(0.85,2.5)$, the cousin inequality is not satisfied. This demonstrate that oscillatory behaviour is not a necessary condition for the cousin inequality to be satisfied.