Weight g Weight of Lake Trout Cubic von Bertalanffy Nonlinear Fit Data Joseph M

Weight g weight of lake trout cubic von bertalanffy

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Weight (g) Weight of Lake Trout Cubic von Bertalanffy Nonlinear Fit Data Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (61/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury Accumulation in Lake Trout 8 Concentration of Hg in Lake Trout: c ( t ) = H ( t ) W ( t ) The solution for Hg accumulation is H ( t ) = κW * 6 b ( 6 bt + 18 e - bt - 9 e - 2 bt + 2 e - 3 bt - 11 ) The weight model satisfies W ( t ) = W * ( 1 - e - bt ) 3 MatLab is used to fit the c ( t ) of Hg vs time data (See MatLab Programming file) The 2 parameters sets W * , b , and κ are fit to Hg vs time data From the von Bertalanffy fit, b = 0 . 14553, W * = 6295 . 4, and κ = 0 . 071406 From the time/weight data fit, b = 0 . 16960, W * = 5677 . 67, and κ = 0 . 066953 Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (62/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Modeling Mercury in Fish 9 Concentration of Mercury in Lake Trout The concentration of Hg is measured in ppm (of mercury) c ( t ) = H ( t ) w ( t ) 0 2 4 6 8 10 12 14 16 18 20 0 0.1 0.2 0.3 0.4 0.5 0.6 Age (Years) Hg (ppm) Mercury in Lake Trout Cubic von Bertalan ff y Nonlinear Fit Data Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (63/64) Introduction Falling Cat 1 st Order Linear DEs Examples Pollution in a Lake Example 2 Mercury in Fish Modeling Mercury in Fish Mercury Accumulation in Lake Trout 10 Discussion of Model for Mercury in Lake Trout: Observe data and model show accelerating accumulation of Hg Data are more scattered for Hg concentration, showing variability in environment It is clear why the Michigan Department of Health advises against eating larger fish Model weaknesses Kleiber’s Law suggests food intake W 3 / 4 , which decreases accumulation Larger (older) Lake Trout eat larger prey containing higher concentrations of Hg, which increases accumulation Spatial variation of Hg concentration occurs in Lake Superior (PDE?) Joseph M. Mahaffy, h [email protected] i Lecture Notes – Linear Differential Equations — (64/64)
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