Table 1 Different classes of PDE associated with the discrete model in appropriate parameter regimes.

	Nonlinear diffusivity	Degenerate diffusivity	Number of non-degenerate zeroes	Negative diffusivity	Source Term	Grouped agent death	Relevant previous analysis
Case 1	x	x	0	x	Fisher	x	18, 19, 20, 21,24,25,27,29
Case 2: Sub-case 1	✓	x	0	x	Fisher	x	58, 59, 60
Case 2: Sub-case 2	✓	✓	0	x	Fisher	x	40,57,69,70
Case 2: Sub-case 3	✓	x	2	✓	Fisher	x	36
Case 2: Sub-case 4	✓	✓	1	✓	Fisher	x	38
Case 3	x	x	0	x	Fisher	✓	18, 19, 20, 21,24,25,27
Case 4: Sub-case 1	✓	x	0	x	Fisher	✓	58, 59, 60
Case 4: Sub-case 2	✓	✓	0	x	Fisher	✓	40,57,69,70
Case 4: Sub-case 3	✓	x	2	✓	Fisher	✓	36
Case 4: Sub-case 4	✓	✓	1	✓	Fisher	✓	38
Case 4: Sub-case 5	✓	x	1	✓	Fisher	✓	38
Case 5	x	x	0	x	Allee	x	15,19,22,23,25,26,28,30
Case 6: Sub-case 1	✓	x	0	x	Allee	x	69,71
Case 6: Sub-case 2	✓	✓	0	x	Allee	x	41,72
Case 6: Sub-case 3	✓	x	2	✓	Allee	x	37
Case 6: Sub-case 4	✓	✓	1	✓	Allee	x	39
Case 7	x	x	0	x	Allee	✓	15,19,22,23,25,26,28,30
Case 8: Sub-case 1	✓	x	0	x	Allee	✓	69,71
Case 8: Sub-case 2	✓	✓	0	x	Allee	✓	41,72
Case 8: Sub-case 3	✓	x	2	✓	Allee	✓	37
Case 8: Sub-case 4	✓	✓	1	✓	Allee	✓	39
Case 8: Sub-case 5	✓	x	1	✓	Allee	✓	39

An Allee source term can correspond to either the weak, strong or reverse Allee effect. Degenerate diffusivity refers to the case where F(C*) = R(C*) = 0 for some value C*. A detailed analysis of all cases is presented in the Supplementary Material.

Quick links

Search