ESPM-EEP%202010%20Lecture%2025

# ESPM-EEP%202010%20Lecture%2025 - p i s i i =2,3 P 4 = s 4 3...

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ESPM 104/EEP 115 Fall 2010: Lecture 25 1. Life Cycle Graphs (A special case of state transition diagrams). These are from Caswell 2001 2. Lefkovitch stage-structured model (life cycle drawn on the board): 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 ): proportion 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

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Model: x ( t + 1) = L x ( t ) where x = x 1 ,..., x n ( ) T and L = (1 p 1 ) s 0 b 1 s 0 b 2 s 0 b n 1 s 0 b n p 1 s 1 (1 p 2 ) s 2 0 0 0 p 2 s 2 0 0 0 0 p n 1 s n 1 s n This matrix represents life cycle 4.1 (b) for the case F i = s 0 b i , i =2,3,4. G i = p i s i , i =1,2,3 P 1 = (1– p 1 ) s 0 b 1 ; P i = (1–
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Unformatted text preview: p i ) s i , i =2,3; P 4 = s 4 3. Harvesting (See Getz 1989). Let h i be the proportion of individuals harvested in stage class i . Define H = diag h 1 ,..., h n ( ) = h 1 … h n ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ Harvest before transition L : x ( t + 1) = L I − H ( ) x ( t ), Yield= H x ( t ) Harvest after transition L : x ( t + 1) = I − H ( ) L x ( t ), Yield= HL x ( t ) Use model for finding optimal uneven-aged stand management. In some forestry models the first term is not linear (as in the Leslie model) but is a none linear “ingrowth function” model....
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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 Berkeley.

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ESPM-EEP%202010%20Lecture%2025 - p i s i i =2,3 P 4 = s 4 3...

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