RESULTS
We first derive predicted state variable trajectories in time, at and
near steady state, from a set of coupled time-differential equations for
the state variables that result from a truncation, at step 2 in Table 1,
of the full iteration procedure. In this approximation, the form of the
structure function in Eq. 3 is retained
(\(\lambda_{3},\ \lambda_{4},\ \lambda_{5}=0)\) and we derive a set of
non-linear time-differential equations of motion (Eqs. 38-40) for the
state variables that will depend upon both the state variables
themselves and the values of the parameters in the transition functions.
We explore here both the steady state properties of these equations and
the dynamics they predict near steady state. These results should only
be good approximations to the actual DynaMETE predictions for small
deviations from steady state because they derive from the static
structure function.
Then, in a first iteration of the full theory, we use Eqs. 14-23 to
calculate lowest-order effects of various perturbations in the
transition function rate constants on the structure function. From the
perturbed structure function we then derive altered shapes of the
abundance and metabolic rate distributions. We emphasize that these
results may differ considerably from a fully-iterated solution to
DynaMETE.