Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment

Table 2

Net reproduction rates and the permanence of model (39) under different dispersal rates.

Dispersal rates	𝑅^𝑥1	𝑅^𝑦1	𝑅^𝑥2	𝑅^𝑦2	Permanence of model (39)
𝑑12=0,𝑑21=0	−0.0847	−0.0411	0.1737	0.0154	No, predator in patch 1 is extinct
𝑑12=0.18,𝑑21=0	−0.0793	−0.0346	0.1737	0.0154	No, predator in patch 1 is extinct
𝑑12=0.36,𝑑21=0	−0.0762	−0.0312	0.1737	0.0154	No, predator in patch 1 is extinct
𝑑12=0.55,𝑑21=0	−0.0742	−0.0289	0.1737	0.0154	No, predator in patch 1 is extinct
𝑑12=1,𝑑21=0	−0.0715	−0.0260	0.1737	0.0154	No, predator in patch 1 is extinct
𝑑12=0.55,𝑑21=0.02	−0.0742	−0.0289	0.1835	0.0163	No, predator in patch 1 is extinct
𝑑12=0.55,𝑑21=0.07	−0.0742	−0.0289	0.2030	0.0157	Yes
𝑑12=0.55,𝑑21=0.14	−0.0742	−0.0289	0.2224	0.0116	Yes
𝑑12=0.55,𝑑21=0.21	−0.0742	−0.0289	0.2362	0.0063	Yes
𝑑12=0.55,𝑑21=0.28	−0.0742	−0.0289	0.2464	0.00086	Yes