Table 1 

The most parsimonious SETAR models of the population dynamics of wolves on Isle Royale, Michigan, 1959–99. Covariates included winter snow accumulation (SW_{t}), Northern Hemisphere temperature anomalies (T_{t}), number of packs in the previous year (PA_{t1}), and mean pack size in the previous year (PS_{t1}). X_{t }is log_{e}transformed density, and a_{i,j }are statistical parameters (i = 1 and 2 corresponds to lower and upper regimes, respectively, j = 0, 1, 2, 3 correspond to the constant, lag1 density coefficients, number of packs coefficients, and climatic coefficients, respectively). n indicates the number of data points in each regime. Parameter estimates were obtained by the method of conditional least squares. X* is the equilibrium point on the logscale. 

Full Model 
θ 
Coefficients 
SE 
p 
n 
AIC 
R^{2} 
Equilibrium 



X_{t }= a_{1,0 }+ a_{1,1}X_{t1 }+ a_{1,2}PA_{t1 }+ a_{1,3}T_{t }+ a_{1,4}SW_{t} 
X_{t1 }< 3.40 
a_{1,0 }= 1.89 
0.43 
0.0002 
32 
14.18 
0.58 
X* = 2.40 

NonLinear Model 
a_{1,1 }= 0.50 
0.14 
0.001 
Stable 

a_{1,2 }= 0.06 
0.04 
0.17 

a_{1,3 }= 0.47 
0.16 
0.009 

a_{1,4 }= .0008 
0.0005 
0.15 

X_{t }= a_{2,0 }+ a_{2,1}X_{t1 }+ a_{2,2}PS_{t1 }+ a_{2,3}PA_{t1 }+ a_{2,4}SW_{t} 
X_{t1 }≥ 3.40 
a_{2,0 }= 5.82 
1.43 
0.03 
8 
0.96 
X* = 3.58 

a_{2,1 }= 2.63 
0.46 
0.01 
Unstable 

a_{2,2 }= 0.06 
0.03 
0.11 

a_{2,3 }= 0.24 
0.05 
0.02 

a_{2,4 }= 0.002 
0.0009 
0.12 

Linear Model 
X_{t }= a_{0}+ a_{1}X_{t1 }+ a_{2}PA_{t1 }+ a_{3}T_{t} 
a_{0 }= 0.86 
0.33 
0.01 
40 
27.98 
0.69 
X* = 2.97 

a_{1 }= 0.81 
0.12 
0.00 
Stable 

a_{2 }= 0.07 
0.03 
0.06 

a_{3 }= 0.39 
0.18 
0.04 



Ellis and Post BMC Ecology 2004 4:2 doi:10.1186/1472678542 