Comparison of forest size structure with and without considering
of growth variance
To compare the difference between forest size structure with and without
considering the stochasticity, I first assume V , G , andM as constants (Eq. 3 and Eq. 4), since analytic solution cannot
be directly given for the original form of Kolmogorov forward equation.
(3)
(4)
Equilibrium solutions of Eq. 3 and Eq. 4 can be easily obtained using
the methods of variable separation and characteristic equation (see
Supporting information), which
are:
Solution of Eq. 3 can be transformed as
Obviously, the exponent of N (D )Eq. 4 is
less negative than that of N (D )Eq. 3,
which means in prediction of forest size structure, the decreasing rate
of tree numbers with size increase will be slower in considering of a
constant growth rate variance, which also implicates that the −2
power-law distribution in MSTF might be reduced from the −7/3 power due
to the effect of growth rate variance.