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

Wayne M. Getz; Richard Salter; Krti Tallam

The total number of cells in this set is K = 1 + 6(1 + 2 + ... + r) = 1 + 3r + 3r 2 (one 497 center cell plus each hexagonal ring centered on this center cell ring has 6 cells more 498 then the its immediate inscribed ring: i.e., 1+6+12+...+6(r-1)+6r cells). We use the 499 notation γ, δ i ≡ i, i = 1, ..., K to index a renumbering of cells in BLOCK α (r) . One 500 renumbering scheme, for example, is to label the center cell γ, δ, occupied by individual 501 α, as γ, δ = γ, δ 1 , the cell to its immediate west as γ, δ + 1 = γ, δ 2 , then going 502 counter-clockwise until the last of the cells in RING α (1) has been labeled 7 (i.e., 503 γ − 1, δ + 1 = γ, δ 7 and moving on to the west most cell in RING α (2) as 8 and so on 504 until all cells in RING α (r) have been labeled.