Table 1 The statistical models of the dynamics at three trophic levels on Isle Royale, USA, 1958–88. The first model given at each trophic level is the full model, showing the autoregressive structure of the time series and co-variates expected to be significant if the relationships depicted in the process-oriented ecological model in Figure 1 are all important. AIC _c is the corrected Akaike Information Criterion score; bold type indicates the most parsimonious model.

a) wolves

b) moose

Y _t = β₀ + (3 + β₁)Y_t-1 + (2 + β₂)Y_t-2 + (1 + β₃)Y_t-3 + ω₁U _Dt + ω₂U_Dt-1 + ω₃U_Dt-2 + + ω₄U _Pt-1 +ω₅U_Pt-1

Y _t =β₀ + (3 + β₁)Y_t-1 + (2 + β₂)Y_t-2 + (1 + β₃)Y_t-3 + ω₁U _Dt + ω₂U_Dt-1 + ω₄U _Pt + ω₅U_Pt-1

Y _t =β₀ + (3 + β₁)Y_t-1 + (2 + β₂)Y_t-2 + (1 + β₃)Y_t-3 + ω₁U _Dt + ω₄U _Pt + ω₅U_Pt-1

Y _t =β₀ + (3 + β₁)Y_t-1 + (2 + β₂)Y_t-2 + (1 + β₃)Y_t-3 + ω₁U _Dt + ω₅U_Pt-1

c) fir

Z _t = γ₀ + (2 + γ₁)Z_t-1 + (1 + γ₂)Z_t-2 + ω₁U _Dt + ω₂U_Dt-1 + ω₃U _Pt

Z _t = γ₀ + (2 + γ₁)Z_t-1 + (1 + γ₂)Z_t-2 + ω₁U _t + ω₂U_t-1

Z _t = γ₀ + (2 + γ₁)Z_t-1 + (1 + γ₂)Z_t-2 + ω₁U _t

Z _t = γ₀ + (2 + γ₁)Z_t-1 + ω₁U _t