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Unformatted text preview: ESPM 104/EEP 115 Fall 2010: Lecture 12 1. Beverton and Holt Yield per recruit (cohort) analysis. a. See Case 2000, p. 232-242 . b. See Part III Harvesting Theory Notes 2. Biomass of cohort at time t is x ( t )= n ( t ) w ( t ), x (0)= n w (0) where n ( t ) is number of individuals and w ( t ) is average weight of each individual. 3. Differentiating dx dt = w ( t ) dn dt + n ( t ) dw dt 4. Use the “prime” notation ′ x ( t *) = dx dt t = t * to obtain condition when x ( t ) is a maximum: if maximum is at t = t *>0, then ′ x ( t *) = which implies 1 n ( t *) ′ n ( t *) = − 1 w ( t *) ′ w ( t *) 5. If n ( t ) decreases exponentially at rate α : 1 n ( t ) ′ n ( t ) = − α ⇔ n ( t ) = n e − α t 6. Thus it follows that 1 w ( t *) ′ w ( t *) = − α and the assumptions that: a. w ( t ) is a positive increasing bounded function of t b. ′ w ( t ) / w ( t ) is a decreasing function of time (e.g. von Bertalanffy: w ( t ) = w max (1 − be − ct ) 3 then under “a total impulse harvest” at time...
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