Lec20.Nonlin2 - Further Examination of Nonlinear Regression...

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Further Examination of Nonlinear Regression Logistic Growth Model Variance Estimation Other Approaches
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  Arrowtooth Flounder Atheresthes stomias Most abundant groundfish (GOA) 15 to 30 cm fish feed predominantly on  shrimp, euphausids, capelin and herring 40 cm eat mostly pollock Caught as bycatch in other fisheries Used for meal and surimi, but no directed  harvest at this time
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Year Biomass (Thousands of mt) 1982 1984 1986 1988 1990 1992 1994 0 100 200 300 400 500 Arrowtooth Flounder Biomass
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arrowtooth = read.table( ‘arrowtooth.txt’,header=T) arrowtooth      Bobs    Cobs   1  104.02  14.357  2  124.90  18.364  3  124.80  17.113  4  132.50  11.518  5  219.10  13.969  6  252.70   9.452  7  279.40   7.375  8  351.60   6.903  9  410.10   4.539 10  382.20   5.883 11  486.40   3.222 12  534.90   4.232 13  461.60   4.069 14  470.00   8.516
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t t t B B B k B - = 1 Logistic Model
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B 2 / B 0 200 400 600 800 1000 . P -200 -100 100 0 2000 4000 6000 8000 Biomass . dP/dB
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t t t t C B B B k B - - = 1 Change in Biomass
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Future Biomass Related to Current Biomass Levels ) ( 1 t t t B B B B + = +
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Observation Stochasticity t t t t t t B Bobs B B B B ε + = + = + ) ( 1
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biomass.obs = function(param,data=arrowtooth) { Binf = param[1] k    = param[2] Bobs = data$Bobs Cobs = data$Cobs B = Bobs[1] n = length(Bobs) Time = seq(n) dP = rep(0,n) for(i in Time[-n])    {    dP[i] = k*(1-B[i]/Binf)*B[i]    B[i+1] = B[i]+dP[i]-Cobs[i]    } B.pred <<- B RSS = sum((B-Bobs)^2) return(RSS)
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Nonlinear Model Fitting Using nlminb biomass.obs.fit =  nlminb(biomass.obs,c(500,0.5)) biomass.obs.fit$parameters   525.0800158 0.4215014 k B
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Lec20.Nonlin2 - Further Examination of Nonlinear Regression...

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