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.