Recursive biomass models |
Recursive
biomass models |
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(M1)
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\(B_{i,t+1}=\left(\alpha-\beta B_{i,t}+{\theta_{i}T}_{i,t}\right)B_{i,t}-C_{i,t}+\varepsilon_{i,t}\)
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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.
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θ = 0.003
(2.0)
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(M2)
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\[B_{i,t+1}=\left(\alpha-\beta B_{i,t}-\frac{C_{i,t}}{B_{i,t}}\right)B_{i,t}\bullet\ e^{\text{θT}_{i,t}}\bullet\varepsilon_{i,t}\]
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Same as M1, but now temperature affects the fish community with a
multiplicative temperature term.
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θ = 0.012
(1.9)
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(M3)
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\[B_{i,t+1}={(1-{\frac{C_{i,t}}{B_{i,t}})\bullet B}_{i,t}}^{(\alpha-\beta B_{i,t}+{\theta_{i}T}_{i,t})}\bullet\varepsilon_{i,t}\]
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Ricker inspired equation with same terms as M1 and M2.
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θ = 0.046
(-0.1)
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Surplus production models |
Surplus
production models |
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(M4)
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\(P_{i,t}=r_{i}B_{i,\ t}\left(1-\frac{B_{i,\ t}}{K_{i}}\right)\bullet\ e^{\text{θT}_{i,t}}\ +\varepsilon_{i,t}\)
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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.
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θ = -0.253
(1.0)
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(M5)
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\(P_{i,t}=r_{i}B_{i,\ t}\left(1-\frac{B_{i,\ t}}{K_{i}\bullet e^{\text{θT}_{i,t}}}\right)\ +\varepsilon_{i,t}\)
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Similar to M4, but now temperature only affects the carrying capacity
K.
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θ = -0.02
(1.9)
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