PARAMETER ESTIMATION SCRIPT
(*Written by Kenneth Leonard*}
(* ::Package:: *)
CLEAR [ InFileName ] ;
InFileName = " ";
FileNameSetter [ Dynamic [ InFileName ] ]
Print [ "============================================================" ] ;
Print [ "----- Population data file ",InFileName ] ;
Clear [ DataMatrix ] ;
DataMatrix = Import [ InFileName ,"Data" ] ;
Print [ "----- Population data " ] ;
DataMatrix
Print [ "============================================================" ] ;
Flow=1/4.69;
SS = 1000 ;
Clear [ RK,C1C,C1N,CC,CN ] ;
FitOutput =
NonlinearModelFit [
DataMatrix,
{
((1-1/(1+E^(SS (C1C/C1N-CC/CN )/(C1C/C1N))))
*
(( RK CC)/(CC+C1C )-Flow)
+
(1-1/( 1+ E^( SS (C1N/C1C-CN/CC)/(C1N/C1C))))
*
(( RK CN)/(CN+C1N)-Flow)),
RK>0, C1C >0, C1N>0
},
{ RK, C1C , C1N } ,
{ CC , CN }
]
Print [ "----- BestFitParameters" ] ;
sRK = RK /. FitOutput [ "BestFitParameters" ] [ [ 1 ] ] ;
sC1C = C1C /. FitOutput [ "BestFitParameters" ] [ [ 2 ] ] ;
sC1N = C1N /. FitOutput [ "BestFitParameters" ] [ [ 3 ] ] ;
CNRatio = sC1C / sC1N ;
Print [ "---------- Maximum Capable Intrinsic Growth Rate" ]
sRK
Print [ "---------- Carbon Half-Max Concentration" ]
sC1C
Print [ "---------- Nitrogen Half-Max Concentration" ]
sC1N
Print [ "---------- Dual-Limiting C:N Ratio" ]
CNRatio
Print [ "----- RSquared" ] ; FitOutput [ "RSquared" ]
Print [ "----- AdjustedRSquared" ] ; FitOutput [ "AdjustedRSquared" ]
Print [ "----- AIC" ] ; FitOutput [ "AIC" ]
Print [ "----- ANOVATable" ] ; FitOutput [ "ANOVATable" ]
Print [ "----- ParameterConfidenceIntervalTable" ] ; FitOutput [ "ParameterConfidenceIntervalTable" ]
Print [ "----- ParameterTable" ] ; FitOutput [ "ParameterTable" ]
Print [ "============================================================" ] ;
GRAPHING SCRIPT
(*Written by Kenneth Leonard*}
PopNameY = PopName1 ;
RKY = ;
C1CY = ;
C1NY = ;
PopNameZ = PopName2 ;
RKZ = ;
C1CZ = ;
C1NZ = ;
Plots
(* Dual Surface Plot *)
plot1=Show [
Plot3D [
{ RKY Min [ C1C/(C1C+C1CY) , C1N/(C1N+C1NY) ] ,
RKZ Min [ C1C/(C1C+C1CZ) , C1N/(C1N+C1NZ) ] } ,
{ C1C , 0 , CChi } , { C1N , 0 , CNhi } ,
Exclusions -> None ,
LabelStyle -> { 30 , FontFamily -> "Helvetica" } ,
AxesEdge -> { { -1 , -1 } , { -1 , -1 } , { -1 , 1 } } ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
ViewPoint -> { -1.0` , -0.5 , 0.5` } ,
PlotStyle -> { RGBColor [ 1 , 1 , 0 ] , RGBColor [ 0 , 0 , 1 ] } ] ,
ParametricPlot3D [
{ C1C , C1NY / C1CY C1C , RKY C1C/(C1C+C1CY) } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> { Black , Thick } ] ,
ParametricPlot3D [
{ C1C , C1NZ / C1CZ C1C , RKZ C1C/(C1C+C1CZ) } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> { Black , Thick, Dashing[Large]} ] ]
(* Differential Surface *)
Clear [ ColorScale ] ;
ColorScale = Max [ Abs [ MaxValue [ { RKY Min [ C1C/(C1C +C1CY),C1N/(C1N+C1NY) ] - RKZ
Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi
} , { C1C , C1N } ] ] , Abs [ MinValue [ { RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] - RKZ
Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi } , { C1C , C1N
}]]];
plot2=Plot3D [
{ RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] RKZ Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] } ,
{ C1C,0,CChi } , { C1N,0,CNhi } ,
Exclusions -> None ,
LabelStyle -> { 30 , FontFamily -> "Helvetica" } ,
AxesEdge-> { { -1,-1 } , { -1,-1 } , { -1,1 } } ,
PlotPoints->Ppoints,
ImageSize-> { Pwidth,Pwidth } ,
ViewPoint-> { -1.0`,-0.4,.7` } ,
ColorFunction-> Function [ { x, y, z } ,
RGBColor [ Max [ 0, (z/ColorScale) ] , 1 - Max [ 0, -(z/ColorScale) ] ,
Max [ 0, -z/ColorScale ] ] ] ,
ColorFunctionScaling->False ]
(* Differential Density *)
Clear [ ColorScale ] ;
ColorScale = Max [ Abs [ MaxValue [ { RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] - RKZ Min
[ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi
} , { C1C , C1N } ] ] , Abs [ MinValue [ { RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] - RKZ
Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi } , { C1C , C1N
}]]];
plot3=Show [
DensityPlot [
RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] RKZ Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] ,
{ C1C,0,CChi } , { C1N,0,CNhi } ,
Exclusions -> None ,
LabelStyle -> { 30 , FontFamily -> "Helvetica" } ,
PlotPoints->Ppoints,
ImageSize-> { Pwidth,Pwidth } ,
ColorFunction-> Function [ { z } ,
RGBColor [ Max [ 0, (z/ColorScale) ] , 1 - Max [ 0, -(z/ColorScale) ] ,
Max [ 0, -z/ColorScale ] ] ] ,
ColorFunctionScaling->False ] ,
Plot [
{ C1NY / C1CY C1C } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> {Black , Thick} ] ,
Plot [
{ C1NZ / C1CZ C1C } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> { Black , Thick, Dashing[Large]} ] ]
(* Differential Contour *)
Clear [ ColorScale ] ;
ColorScale = Max [ Abs [ MaxValue [ { RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] - RKZ Min
[ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi
} , { C1C , C1N } ] ] , Abs [ MinValue [ { RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] - RKZ
Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] , 0 <= C1C <= CChi , 0 <= C1N <= CNhi } , { C1C , C1N
}]]];
plot4=Show [
ContourPlot [
RKY Min [ C1C/(C1C+C1CY),C1N/(C1N+C1NY) ] RKZ Min [ C1C/(C1C+C1CZ),C1N/(C1N+C1NZ) ] ,
{ C1C,0,CChi } , { C1N,0,CNhi } ,
Exclusions -> None ,
Contours -> { -0.1 , -0.05 , -0.04 ,-0.03 , -0.02 , -0.01 , 0 , 0.01 , 0.02 , 0.03 , 0.04 , 0.05 , 0.1 } ,
ContourLabels -> (Text[Style[#3, 30], {#1, #2}] &),
LabelStyle -> { 30 , FontFamily -> "Helvetica" } ,
Frame -> False ,
Axes -> True ,
PlotPoints->Ppoints,
ImageSize-> { Pwidth,Pwidth } ,
Contours-> 30,
ColorFunction-> Function [ { z } ,
RGBColor [ Max [ 0, (z/ColorScale) ] , 1 - Max [ 0, -(z/ColorScale) ] ,
Max [ 0, -z/ColorScale ] ] ] ,
ColorFunctionScaling->False ] ,
Plot [
{ C1NY / C1CY C1C } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> { Black , Thick } ] ,
Plot [
{ C1NZ / C1CZ C1C } ,
{ C1C , 0 , CChi } ,
Exclusions -> None ,
PlotPoints -> Ppoints ,
ImageSize -> { Pwidth , Pwidth } ,
PlotStyle -> { Black , Dashing[Large]} ] ]