### Table 2 Generic processes relevant to the predator-prey model.

"... In PAGE 7: ...gous representation. Table2 shows ve generic processes relevant to modeling predator-prey interaction. Each generic process consists of ve components: a name, a set of variables, a set of parameters, a set of conditions, and a set of equation forms.... ..."

### Table IV. A generic model from the predator{prey domain wherein variables are mapped but parameters remain constrained by their bounds.

### Table 1: True parameters used to simulate the classical predator{prey model and parameter estimates from model fltting. Standard errors are included in parentheses. Parameters True values (A) UKF estimates with (B) UKF estimates with

"... In PAGE 17: ...odel (i.e., there is no process noise; see Equations 44{ 45). For illustration purposes, we set to be a diagonal matrix with very small process noise variances. We simulated data using true parameters in Table1 with (1) a single time{series with N = 1 and T = 200 and (2) multiple{subject data with N = 200 and T = 50. Results from model fltting are summarized in Table 1.... ..."

### Table 4: A set of generic processes for predator-prey models. generic process logistic growth; variables Sfpreyg; parameters psi [0, 3], kappa [0, 1]; equations d[S,t,1] = psi* S * (1 kappa * S); generic process exponential growth; variables Sfpreyg;

2006

"... In PAGE 9: ... As noted earlier, before RPM can improve an incomplete model of this sort, the user must provide a set of generic processes it can use to this end. Table4 shows some processes that we extracted from our reading of the Jost and Adiriti article. Again, each generic process speci es one or more generic variables with type constraints (in braces), a set of parameters with ranges for their values (in brackets), and a set of algebraic or di erential equations that encode causal relations among the variables.... In PAGE 10: ... All four processes are generic in the sense that they do not commit to speci c variables. We ran RPM on the Veilleux time series, telling it to retain the aurelia decay process from Table 3 but to consider removing the other two processes and to consider adding processes from Table4 . We also told it to improve the parameters in any processes that were retained.... ..."

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### Table 1: Discretization of predator-prey range and bearing. Range is mea- sured in Manhattan distance.

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### Table 2. Results of application of Scheme 4 to the predator-prey problem. average fitness average number average length of average number of co-

### Table V. An alternative set of generic processes that capture the interaction between predators and prey.

### Table V. Additional generic processes for the predator{prey domain. Variable type constraints are denoted in braces following the local name, while parameter bounds are speci ed within brackets. The notation d[S; t; 1] indicates the rst derivative of S with respect to time.

### Table 1: Invariant simulation probabilities. For each individual simulation there were two more important parameters, which were varied between simulations as part of the study. The rst of these parame- ters was the carrying capacity of a location ( eld) with respect to the prey species. The Lotka-Volterra oscillations are produced without this factor, and cannot be stochastically modelled without an exponential explosion in the populations. How- ever when carrying capacity was introduced by Volterra [Volterra, 1931] the result- ing Volterra Oscillations do lend themselves to stochastic modelling. The carrying capacity was the maximum prey population that a location could support in the absence of predators. This was therefore a limiting factor to prevent prey popu- lations rising exponentially. The prey birth routine reduces the the probability of 5

"... In PAGE 5: ... Additionally there are probabilities to determine whether members of either species will migrate to another cell. Table1 lists all the prob- abilities relating to a single time-step; these remain invariant throughout all the simulations. These parameter values were those used by Wol in his work, and have been chosen since they produce the desired Predator-Prey oscillations for a... ..."

### Table 4 A quantitative process model of the Ross Sea ecosystem.

"... In PAGE 12: ... Suspected in uences include the availability of nutrients and light, as well as grazing behavior by zooplankton. Table4 shows an initial process model for this ecosystem. As in the protist model, variables appear rst.... In PAGE 14: ... As in the predator{prey example, we provided types for the variables and a list of generic processes. Table4 shows the types in the original model, whereas the generic processes that we let Prometheus instan- tiate and add to this model appear in Table 5. In addition, we let the environ- ment alter the parameters of all current processes except for light availability, light production, and set constants.... ..."