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.