Appendix 1—figure 5. Mapping mechanistic models to the inheritance matrix model framework.

(a–f) Simple cell size control model. (a) Model schematic. (b) The cousin-mother inequality cannot be satisfied for any choice of parameter $a$. (c–d) Generalised tree correlation function plots (c) for $a=1$ and (d)$a=-1.5$ resulting in aperiodic and an alternator pattern respectively. (e–f) Same vs alternate factor mother-daughter correlation plots for (e)$a=1$ and (f)$a=-1.5$. In panels (b–f) we fix $\mathrm{IE}[\xi ]=1,\mathrm{Var}(\xi )=0.1,\kappa =1$. (g–l) Cell size control model with correlated growth rate. (g) Model schematic. (h) Region plot with fixed parameter $a=1$ showing the parameter space $b,c\text{in}(-1,1)$ that satisfies the cousin-mother inequality (blue). Example parameter choices are also plotted for an aperiodic (yellow) and an alternator (red) pattern. (i–j) Generalised tree correlation function plots for (i)$(b,c)=(0.2,0.7)$ and (j)$(b,c)=(-0.81,0.88)$ resulting in aperiodic and an alternator pattern respectively. (k,l) Same vs alternate factor mother-daughter correlation plots for (k)$(b,c)=(0.2,0.7)$ and (l)$(b,c)=(-0.81,0.88)$. In panels (h–l) we fix $\mathrm{IE}[\xi ]=\mathrm{IE}[\varphi ]=1,\mathrm{Var}(\xi )=\mathrm{Var}(\varphi )=1,\kappa =1$. (m–r) Two cell cycle phase model (m) Model schematic. (n) Region plot with fixed parameter $b=-0.75$ showing the parameter space $a,c\text{in}(-1,1)$ that satisfies the cousin-mother inequality (blue). Example parameter choices are also plotted for an aperiodic (yellow) and an alternator (red) pattern. (o–p) Generalised tree correlation function plots (o) for $(a,c)=(0.3,0.4)$ and (p)$(a,c)=(-0.25,0.9)$ resulting in aperiodic and an alternator pattern respectively. (q–r) Same vs alternate factor mother-daughter correlation plots for (q)$(a,c)=(0.3,0.4)$ and (r)$(a,c)=(-0.25,0.9)$. In panels (n–r) we fix $\mathrm{Var}(\xi )=\mathrm{Var}(\varphi )=1$.