A quantitative narrative on movement, disease and patch exploitation in nesting agent groups

Wayne M. Getz; Richard Salter; Krti Tallam

The mathematical equations are provided in Section 6, which are placed at the end of 184 the manuscript because it is not necessary to go through these details before the 185 presentation and discussion of our simulation results (those wishing to see the equations 186 before the results should read Section 6 before starting Section 3). These equations were 187 used to code the model using the Numerus Model Builder (NMB) platform that greatly 188 facilitated rapid, accurate construction of the model through NMB's hierarchical 189 architecture and chip design. More specifically, cell equations and agent equations were 190 first constructed as individual modules, which were then used to populate a "world" 191 with an open-ended number of agents moving over an 18×18 hexagonal cellular array 192 that contained 9 regularly spaced nest cells (Fig. 1) . A toroidal topology was used to 3.1 Base-line scenario: no disease, no colony switching 218 We ran two instances of the baseline scenario and obtained similar results with some 219 stochastic variation across runs. A plot of the number of agents N t over time (all are in 220 the susceptible disease state) for the the two runs is provided in Fig. 3 and can are seen 221 to be close in both period and amplitude. We note that our baseline scenario places us 222 at a particular point in the consumer-resource growth-rate, extraction, and interaction 223 parameter value space of our model. Table 3 ). The top left graphic panel depicts the 18 × 18 hexagonal landscape: colony nest cells are indicated using fully saturated colors and their territory cells using corresponding partially saturated colors (note "boundary spillover" effects due to the toroidal landscape topology). The number of individuals in each colony at time t = 1959 are plotted in the central bar graph, using matching colony nest-cell colors. decrease the mutual interference level (parameter q in Eq. 6) from 1 (resource extraction 228 inefficiencies due to self and others are proportional to the total biomass of all agents in 229 cells) to 0 (inefficiencies arise only from self) or increase it to 10 (inefficiencies increase 230 ten fold for each competitor in the cell, presumably due to territorial conflicts) then we 231 see a small decrease in the oscillation frequency in the former case (compare plots Fig. 3 232 with orange plot in Fig. 4A ), but a very different type of trajectory in the strong mutual 233 interference case (compare plots in Fig. 3 with orange plot in Fig. 4B ).