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.