Table 3. Perturbations, constraints, and resulting Lagrange Multipliers
used to generate Figures 5a-5h. The text describes how the constraints
are derived.
Figure Captions.
Figure 1. The architecture of DynaMETE. A. Selected mechanisms are
incorporated into transition functions. B. The time derivatives of state
variables update the state variables. C. The transition functions, which
depend upon the state variables are updated. D. Updated state variables
and transition functions are averaged over the prior (time t )
structure function to update the time derivatives of the state
variables. E. Under updated constraints and transition functions (dashed
box), MaxEnt updates the structure function. F. The macroecological
metrics are updated from the updated structure function. G. Steps B-F
are iterated.
Figure 2. Comparison of up- and down-scaled species richness using METE
and DynaMETE, starting with identical species richness and abundance at
the middle scale shown. The values of N , a proxy for area, span a
scale range of 27. Transition function parameters andS and N values for the middle scale are from Table 2; at
larger or smaller scales E c andm 0 are assumed to scale linearly with area and
the other parameters are held constant.
Figure 3. Responses of state variables to perturbations simulated from
Eqs. 38-40: a. reduction of immigration rate, m 0;
b. increase in death rate, d 0; c. reduction in
growth rate, \(\omega_{0};\ \)d. increase in the death rate and
reduction in the immigration and ontogenic growth rates. The inset in 3d
shows the state variable trajectories from 1985-2015 in the BCI 50 ha
tropical forest plot. The censuses include trees with dbh> 1 cm . Data from Condit (2019); Hubbell et al.,
(2005). The inset assumes that the metabolic rate of individuals scales
linearly with basal area.
Figure 4. Predicted recovery of state variables to their steady state
values in Table 1, as predicted from Eqs. 38-40, with steady state
parameters and each initial state variable equal to 80% of its steady
state value. The monotonic rise in S to steady state, along with the
sizeable overshoot and then damped oscillation in N , and the
smaller overshoot and then damped oscillation in E occur for a
wide range of initially depleted state variables, steady state state
variables, and parameter choices.
Figure 5. The effect of perturbations on the species abundance
distribution (SAD) and the distribution of metabolic rates over
individuals (MRDI). The relevant perturbation is in each plot’s title.
Insets in Figs. 5g and 5h show BCI data (see caption to Fig. 3).