Formula
Model information
θ estimate (ΔAIC)
Recursive biomass models Recursive biomass models
(M1)
\(B_{i,t+1}=\left(\alpha-\beta B_{i,t}+{\theta_{i}T}_{i,t}\right)B_{i,t}-C_{i,t}+\varepsilon_{i,t}\)
Changes in biomass B in ecoregion i over time t depend on biomass in the previous year, a growth term α, a carrying capacity term β and θ, which describes the influence of temperature T on the fish community. C is the observed demersal catch and is treated as an offset.
θ = 0.003 (2.0)
(M2)
\[B_{i,t+1}=\left(\alpha-\beta B_{i,t}-\frac{C_{i,t}}{B_{i,t}}\right)B_{i,t}\bullet\ e^{\text{θT}_{i,t}}\bullet\varepsilon_{i,t}\]
Same as M1, but now temperature affects the fish community with a multiplicative temperature term.
θ = 0.012 (1.9)
(M3)
\[B_{i,t+1}={(1-{\frac{C_{i,t}}{B_{i,t}})\bullet B}_{i,t}}^{(\alpha-\beta B_{i,t}+{\theta_{i}T}_{i,t})}\bullet\varepsilon_{i,t}\]
Ricker inspired equation with same terms as M1 and M2.
θ = 0.046 (-0.1)
Surplus production models Surplus production models
(M4)
\(P_{i,t}=r_{i}B_{i,\ t}\left(1-\frac{B_{i,\ t}}{K_{i}}\right)\bullet\ e^{\text{θT}_{i,t}}\ +\varepsilon_{i,t}\)
Surplus production model with a temperature term following Free et al. (2019). Surplus production Pi,t is calculated as the change in total biomass: Pi,t = Bi,t+1 - Bi,t + Ci,t. r is the intrinsic growth rate and K the carrying capacity. Temperature affects the fish community with a multiplicative temperature term.
θ = -0.253 (1.0)
(M5)
\(P_{i,t}=r_{i}B_{i,\ t}\left(1-\frac{B_{i,\ t}}{K_{i}\bullet e^{\text{θT}_{i,t}}}\right)\ +\varepsilon_{i,t}\)
Similar to M4, but now temperature only affects the carrying capacity K.
θ = -0.02 (1.9)