\begin{equation}
FPC = \frac{CN \cdot IND}{FRAC} \cdot \left[ 1 - \exp \left( -1 \cdot 
    LM_{\rm max} \cdot SLA \cdot coff \right) \right]
\end{equation}
where $FPC$ is foliage projective cover (``fpc\_nat'' in source code),
$CN$ crown area (cn\_ind; m$^{2}$), $IND$ number of individuals (ind;
m$^{-2}$), $FRAC$ total fraction occupied by natual vegetation
(fracnat), $LM_{\rm max}$ maximum leaf mass in last year
(lm\_lastyearmax; g C m$^{-2}$), $SLA$ specific leaf area (sla;
m$^{2}$ (g C)$^{-1}$), and $coff$ coefficient (ext\_coeff).

\begin{equation}
  EST_{\rm tree} = EST_{clm} \left[1 - \exp \left( -5 \cdot (1 - FPC_{\rm woody}) 
    \right) \right] \cdot (1 - FPC_{\rm woody})
\end{equation}
where $EST_{\rm tree}$ is maximum tree establishment rate
(estab\_rate\_max\_tree), $EST_{clm}$ maximum tree establishment rate
controled by climate (estab\_rate\_\\max\_climate\_tree), $FPC_{\rm
  woody}$ total woody FPC (sumfpc\_wood).

\begin{equation}
  EST_{\rm grass} = \max \left[  \min \left[ EST_{clm}, 0.98 - FPC_{\rm sum} \right], 
    0 \right]
\end{equation}
where $EST_{\rm grass}$ is maximum grass establishment rate
(estab\_rate\_max\_grass) and $FPC_{\rm sum}$ total natural fpc
(sumfpc).

\begin{equation}
FPC = \min \left[ 1, CN \right] \cdot IND \cdot \max \left[ 1 - \exp 
  \left( -coff \cdot LAI \right), MIN_{\rm cover} \right]
\end{equation}
where $MIN_{\rm cover}$ is fraction of crown area invaded by other
trees (min\_cover = 0.05)



