Algorithm 2.

ABC SMC for parameter inference and model selection.

(1)Given $N_{\hspace{0.17em}p}$ plant structures and $N_t(i)$ longitudinal observations for plant $i$, characterize the summary statistics $d_{ij}=\{B,\hspace{0.17em}L,\hspace{0.17em}\hat{l}\}$ from every plant $i$ and observation $j$ in the dataset. (2)Initialize tolerance vector $\mathbf{E}$ containing $T$ elements. Set population indicator $t=0$. (3)Set particle indicator $i=1$. (4)Sample model indicator $m^{\ast }$ from prior $\pi (m)$. (5)If $t=0$, sample ${\theta }^{\ast \ast }$ from $\pi (\theta (m^{\ast }))$. If $t>0$, sample ${\theta }^{\ast }$ from the previous population $\{\theta {(m^{\ast })}_{t-1}\}$ with weights $w{(m^{\ast })}_{t-1}$, and set ${\theta }^{\ast \ast }\sim K_t(\theta |{\theta }^{\ast })$. (6)If $\pi ({\theta }^{\ast \ast })=0$, go to 4. (7)Simulate $N_{\hspace{0.17em}p}$ instances of root growth using ${\theta }^{\ast \ast }$, recording the state of structure $i$ at each of the $N_t(i)$ time points corresponding to an experimental observation. (8)Compute $\rho$ using equation (2.2) above. (9)If $\rho \ge \mathbf{E}[t]$, go to 4. (10) Set $m_t^{(i)}=m^{\ast }$ and add ${\theta }^{\ast \ast }$ to the population $\{\theta {(m^{\ast })}_t\}$. If $t=0$, set weights $w_t^{(i)}=0$, otherwise $$w_t^{(i)}=\frac{\pi ({\theta }^{\ast \ast })}{\sum _{\hspace{0.17em}j=1}^N{w}_{t-1}^{(\hspace{0.17em}j)}{K}_t({\theta }_{t-1}^{(\hspace{0.17em}j)},{\theta }^{\ast \ast })}.$$ If $i<N$, set $i=i+1$, go to 4. (11)For every $m$, normalize the weights. If $t<T$, set $t=t+1$, go to 3.