Table 1

The most parsimonious SETAR models of the population dynamics of wolves on Isle Royale, Michigan, 1959–99. Covariates included winter snow accumulation (SWt), Northern Hemisphere temperature anomalies (Tt), number of packs in the previous year (PAt-1), and mean pack size in the previous year (PSt-1). Xt is loge-transformed density, and ai,j are statistical parameters (i = 1 and 2 corresponds to lower and upper regimes, respectively, j = 0, 1, 2, 3 correspond to the constant, lag-1 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 log-scale.

Full Model

θ

Coefficients

SE

p

n

AIC

R2

Equilibrium


Xt = a1,0 + a1,1Xt-1 + a1,2PAt-1 + a1,3Tt + a1,4SWt

Xt-1 < 3.40

a1,0 = 1.89

0.43

0.0002

32

14.18

0.58

X* = 2.40

Non-Linear Model

a1,1 = 0.50

0.14

0.001

Stable

a1,2 = -0.06

0.04

0.17

a1,3 = -0.47

0.16

0.009

a1,4 = -.0008

0.0005

0.15

Xt = a2,0 + a2,1Xt-1 + a2,2PSt-1 + a2,3PAt-1 + a2,4SWt

Xt-1 ≥ 3.40

a2,0 = -5.82

1.43

0.03

8

0.96

X* = 3.58

a2,1 = 2.63

0.46

0.01

Unstable

a2,2 = 0.06

0.03

0.11

a2,3 = -0.24

0.05

0.02

a2,4 = 0.002

0.0009

0.12

Linear Model

Xt = a0+ a1Xt-1 + a2PAt-1 + a3Tt

a0 = 0.86

0.33

0.01

40

27.98

0.69

X* = 2.97

a1 = 0.81

0.12

0.00

Stable

a2 = -0.07

0.03

0.06

a3 = -0.39

0.18

0.04


Ellis and Post BMC Ecology 2004 4:2   doi:10.1186/1472-6785-4-2

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