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).