DISCUSSION
DynaMETE combines both mechanism and MaxEnt, links the micro-level of analysis to the macro-level with a novel iterative procedure (Fig. 1, Table 1), and predicts both static and dynamic behavior. DynaMETE is thus a hybrid MaxEnt-plus-mechanism extension to dynamic ecosystems of a static theory, METE, which was based solely on the MaxEnt inference procedure.
Static limit. In its static limit, DynaMETE recovers the static METE predictions for the distributions of abundances over species and metabolic rates over individuals, but also makes new predictions. First, it predicts a scaling relationship among productivity, biomass, species richness and abundance in steady state (Eq. 49); this relationship remains to be tested. Second, in the version of DynaMETE in which only immigration, not speciation, contributes to diversification, DynaMETE predicts a static-limit SAR increasing approximately as ln(A ), with a ln(ln(A )) correction, in very close agreement with the static SAR predicted by METE (Fig. 2).
If speciation but not immigration is assumed to drive diversification (Eqs. 33, 34), then there are problems with the current formulations of the speciation term in the transition functions. In particular, if the speciation rate is proportional to the birth rate (Eq. 34) or proportional to species richness (Eq. 33 with K>> S ), then the SAR is approximately linear at all scales, contrary to observation. On the other hand, ifS >> K then DynaMETE predicts a realistic SAR, but this contradicts the original motivation forS -dependent speciation from the fossil record, which is an increasing rate of diversification over time in the aftermath of extinction events. DynaMETE suggests a possible solution: a logarithmic dependence of speciation on species richness. Using the methods in SI-C, this results in:
\(\frac{S}{\ln^{\frac{3}{4}}(S)}\sim\ {(A)}^{\frac{1}{4}}\ln^{\frac{3}{4}}(\frac{1}{\beta)}\)(50)
and an increasing rate of diversification in the aftermath of extinction.
Dynamics. Assuming a static structure function (Eq. 3) in a lowest-order solution to the theory, Eqs. 38-40 predict signature time trajectories of the state variables for various types of perturbations in the transition function rate constants (Figs. 3). A combination of reduced immigration and growth rates and increased death rate generates trajectories that exhibit some of the features of those observed in the BCI tropical forest plot (see inset in Fig. 3d). Because these model simulations are based on extrapolating out in time only the first-order iteration of the full theory, they are only suggestive; empirical testing awaits further iteration of Eqs. 14-23.
DynaMETE also predicts trajectories of state variables during the recovery of an ecosystem from a depauperate state. The predicted overshoot and then decline to steady state of N (Fig. 4) suggests the “dog hair” stage of forest succession in which, post fire or other disturbance, the abundance of small trees increases rapidly,E /N decreases, and then self-thinning brings the system to a quasi steady state, until the next disturbance.
We also examined in a lowest order approximation the effect on the SAD and the MRDI that result from a variety of perturbations in the rate constants (Figs. 5). Importantly, different perturbations result in different patterns of deviation from static METE predictions for both the distribution of abundances over species and metabolic rates over individuals. These signature patterns can provide a way to identify the processes that are driving ecosystem change under natural or anthropogenic disturbance. Further analysis will determine whether the results from a single iteration to t = 25 differ significantly from the results we would obtain by carrying out 25 one-year iterations.
The SAD in the 50-ha BCI tropical forest plot, which deviates from the log-series distribution predicted by METE, resembles the DynaMETE prediction assuming a combined perturbation in death, growth and migration rates. That same perturbation also results in an MRDI that improves on the METE prediction for the high-metabolizing (large-size) individuals, but over-predicts the number of the lowest-metabolism individuals. Further study of different combinations of parameter perturbations coupled with analysis of higher order iterations of the dynamics are needed.