Table 2. Median (and 95% credible intervals) of simulation-derived probability distributions for theoretical maximum values of r_max derived using the Demographic Invariant Method, population-specific values of r_max derived using a projection matrix, allowable total harvest (or harvest rate for eider) derived from population-specific r_max values at θ = 1 and θ = 2 to bracket the functional form of density dependence, observed total harvest (harvest rate for eider) including sport and subsistence harvest adjusted for crippling loss, and percent of simulations where observed harvest was ≤ allowable harvest when θ = 1 and θ = 2 for seven populations of North American sea ducks.

Population	Demographic Invariant Method rmax (95% CI)	Matrix Model rmax (95% CI)	Allowable harvest θ = 1 (95% CI)	Allowable harvest θ = 2 (95% CI)	Observed harvest (95% CI)	Percent Observed < Allowable θ = 1	Percent Observed < Allowable θ = 2
Common Eider	0.155 (0.109;0.218)	0.003 (-0.157; 0.144)	0.001 (-0.085; 0.067)	0.002 (-0.117; 0.087)	0.026 (0.021; 0.033)	19%	26%
Eastern Black Scoter	0.176 (0.120; 0.249)	0.143 (0.005; 0.420)	29,946 (988; 90,952)	39,062 (1,316; 115,850)	28,528 (19,567; 42,281)	53%	68%
Western Black Scoter	0.176 (0.120; 0.249)	0.136 (-0.057; 0.450)	13,844 (-6,351; 40,843)	18,077 (-8,549; 51,319)	16,724 (10,324; 27,019)	41%	52%
Eastern Surf Scoter	0.178 (0.123; 0.247)	0.133 (-0.023; 0.333)	23,359 (-4,225; 76,355)	30,497 (-5,656; 98,627)	37,522 (27,666; 52,108)	22%	37%
Western Surf Scoter	0.178 (0.123; 0.247)	0.079 (-0.131; 0.313)	14,721 (-32,348; 82,245)	19,348 (-44,093;105,207)	9,560 (5,399; 16,939)	60%	66%
White-winged Scoter	0.172 (0.119; 0.245)	0.038 (-0.109; 0.268)	9,864 (-32,019; 65,987)	13,068 (-43,540; 84,905)	23,733 (14,140; 39,899)	29%	37%
Long-tailed Duck	0.184 (0.126; 0.258)	-0.063 (-0.283; 0.121)	-23,940 (-118,692; 61,722)	-32,329 (-167,742;80,713)	42,853 (32,657; 57,977)	5%	7%