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ESPM-EEP 2010 Le - b i t life table natality parameter for stage i at time t s i t proportion of individuals surviving period t to t 1 p i t

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ESPM 104/EEP 115 Fall 2010: Lecture 20 1. Fisheries dynamics model x i ( t ): number of individuals aged i at time t α i ( t ): natural mortality rate of individuals aged i at time t q i ( t ): catchability coefficient for individuals aged i at time t v : effort level (harvesting intensity at time t therefore : q i ( t ) v : fishing mortality rate of individuals aged i at time t dx i dt = i x i q i vx i = i + q i v ( ) x i for t [ k , k + 1) 2. Integrate model to obtain: x i ( t ) = x i ( k ) e i + q i v ( ) ( t k ) for k t < k + 1 If we take ageing into account at t = k +1: x i + 1 ( k + 1) = x i ( k ) e i + q i v ( ) This is Leslie model ageing equations with s i = e i + q i v ( ) 3. Replace linear Leslie recruitment x 1 ( t + 1) = s 0 b i x i ( t ) i = 1 n ( ) = s 0 x 0 ( t ), where x 0 = b i x i i = 1 n with a nonlinear stock recruitment function x 1 ( t + 1) = f x 0 ( t ) ( ) , e.g. B&H: f ( x 0 ) = ax 0 K + x 0 4. Yield: Y i , k + 1 ( v ) = w i q i vx i ( t ) k k + 1 = w i q i vx i ( k ) e i + q i v ( ) ( t k ) dt k k + 1 = w i q i vx i ( k ) 1 e i + q i v ( ) i + q i v Y k + 1 ( v ) = Y i , k + 1 ( v ) i = 1 n = v w i q i x i ( k ) 1 e i + q i v ( ) ( ) i + q i v i = 1 n

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5. Lefkovitch stage-structured model:
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Unformatted text preview: b i ( t ): life table natality parameter for stage i at time t s i ( t ): proportion of individuals surviving period t to t +1 p i ( t ): proportiopn of individuals transitioning from stage i to i +1 over period t to t +1 1-p i ( t ): proportion of individuals staying in stage i over period t to t +1 Model: x ( t + 1) = L x ( t ) where x = x 1 ,..., x n ( ) T and L = (1 − p 1 ) s b 1 s b 2 s b n − 1 s b n p 1 s 1 (1 − p 2 ) s p 2 s 2 p n − 1 s n − 1 s n ⎛ ⎝ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟...
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This note was uploaded on 02/09/2011 for the course EEP 115 taught by Professor Waynem.getz during the Fall '10 term at University of California, Berkeley.

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ESPM-EEP 2010 Le - b i t life table natality parameter for stage i at time t s i t proportion of individuals surviving period t to t 1 p i t

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