:MACRO: P EXP(input)
P EXP = EXP(MAX(-50,MIN(50,input)))
	~	input
	~	Exponentiation protected against over/underflow
	|

:END OF MACRO:
:MACRO: SSHAPE(input)
SSHAPE = EXP(MAX(-50,MIN(50,input)))/(1+EXP(MAX(-50,MIN(50,input))))
	~	dmnl
	~	Exponential s-shaped curve; -infinity -> 0, 0 -> .5, infinity -> 1
	|

:END OF MACRO:
Effective Natural Capital=
	MIN(Natural Capital Upper Bound,MAX(Natural Capital Lower Bound,Natural Capital))
	~	NKU
	~		|

Natural Capital Lower Bound=
	1e-005
	~	NKU
	~		|

Natural Capital Upper Bound=
	0.9999
	~	NKU
	~		|

********************************************************
	.Output
********************************************************~
	|

Contraction Rate=
	 0.1
	~	1/year
	~	eta
		Contraction rate when natural capital = 0
	|

Output Growth Rate=
	 Growth Rate-(Growth Rate+Contraction Rate)*(1-Effective Natural Capital)^Contraction Nonlin
	~	1/year
	~		|

Contraction Nonlin = 2
	~	dmnl
	~	lambda
	|

Growth Rate = 0.04
	~	1/year
	~	gamma
		Growth rate when natural capital = 1
	|

Net per Capita Output = Output per Capita-Pollution Control
	~	$/person/year
	~	ybar
	|

Output Net Change Rate = Output per Capita*Output Growth Rate
	~	$/person/year/year
	~		|

Output per Capita = INTEG(Output Net Change Rate,1)
	~	$/person/year
	~	y(t)
	|

********************************************************
	.NaturalCapital
********************************************************~
	|

Natural Capital Net Change Rate=
	 Regeneration Rate*Effective Natural Capital*(1-Effective Natural Capital)
	~	NKU/year
	~		|

Cleansing Flow=
	 Cleansing Rate/Regen Coeff*Effective Natural Capital^Cleansing Coeff
	~	PU/year
	~		|

Cleansing Coeff = 2
	~	dmnl
	~	rho
	|

Cleansing Rate = 1
	~	dmnl
	~	delta
	|

Natural Capital = INTEG(Natural Capital Net Change Rate,0.98)
	~	NKU
	~	z(t)
	|

Normal Regen Rate = 1
	~	1/NKU/year
	~	nu
	|

Regen Coeff = 0.1
	~	1/PU*year
	~	omega
	|

Regeneration Rate = Normal Regen Rate*(P EXP(Regen Coeff*(Cleansing Flow-Net Pollution Flow\
		))-1)
	~	1/NKU/year
	~		|

********************************************************
	.Population
********************************************************~
	|

Envir Effect Death=
	 1+Envir Death Scale*MAX(0.01,1-Effective Natural Capital)^Envir Death Nonlin
	~	dmnl
	~	MIN added to prevent floating point error.
	|

Birth Coeff 1 = 0.04
	~	1/year
	~	beta1
	|

Birth Coeff 2 = 1.375
	~	dmnl
	~	beta2
	|

Birth Income Effect = 0.16
	~	1/$*person*year
	~	beta
	|

Birth Rate = Birth Coeff 1*(Birth Coeff 2-SSHAPE(Birth Income Effect*Net per Capita Output\
		))
	~	1/year
	~		|

Births = Birth Rate*Population
	~	people/year
	~		|

Death Coeff 1 = 0.01
	~	1/year
	~	delta1
	|

Death Coeff 2 = 2.5
	~	dmnl
	~	delta2
	|

Death Income Effect = 0.18
	~	1/$*person*year
	~	alpha
	|

Death Rate = Normal Death Rate*Envir Effect Death
	~	1/year
	~		|

Deaths = Population*Death Rate
	~	people/year
	~		|

Envir Death Nonlin = 15
	~	dmnl
	~	upsilon
	|

Envir Death Scale = 4
	~	dmnl
	~	delta3
	|

Normal Death Rate = Death Coeff 1*(Death Coeff 2-SSHAPE(Death Income Effect*Net per Capita Output\
		))
	~	1/year
	~		|

Population = INTEG(Births-Deaths,1)
	~	people
	~	x(t)
	|

********************************************************
	.Pollution
********************************************************~
	|

Pollution Control=
	 Control Scale*(1-Effective Natural Capital)^Control Nonlin*Output per Capita
	~	$/person/year
	~	c(y,z)
	|

Abatement Coeff = 2
	~	PU/year
	~	kappa
	|

Control Effect = 0.02
	~	1/$*year
	~	epsilon
	|

Control Nonlin = 2
	~	dmnl
	~	mu
	|

Control Scale = 0.5
	~	dmnl
	~	j
	|

Net Pollution Flow = Pollution Output-Pollution Abatement
	~	PU/year
	~	f(x,y,z,p)
	|

Pollution Abatement = Abatement Coeff*(SSHAPE(Control Effect*Pollution Control*Population\
		)-0.5)
	~	PU/year
	~		|

Pollution Change Rate = -0.03
	~	1/year
	~	chi
	|

Pollution Intensity Change Rate = Pollution per Unit Output*Pollution Change Rate
	~	PU/$/year
	~	chi
	|

Pollution Output = Population*Output per Capita*Pollution per Unit Output
	~	PU/year
	~		|

Pollution per Unit Output = INTEG(Pollution Intensity Change Rate,1)
	~	PU/$
	~	p(t)
	|

********************************************************
	.Control
********************************************************~
		Simulation Control Paramaters
	|

FINAL TIME  = 300
	~	year
	~	The final time for the simulation.
	|

INITIAL TIME  = 0
	~	year
	~	The initial time for the simulation.
	|

SAVEPER  = 
        TIME STEP
	~	year
	~	The frequency with which output is stored.
	|

TIME STEP  = 0.5
	~	year
	~	The time step for the simulation.
	|

\\\---/// Sketch information - do not modify anything except names
V300  Do not put anything below this section - it will be ignored
*View 1
$0,0,Times New Roman|12||0-0-0|0-0-0|0-0-0|-1--1--1|-1--1--1|96,96
10,1,Population,366,121,40,20,3,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||128-0-255
12,2,48,518,120,8,8,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
11,3,48,473,121,5,8,34,3,0,0,1,0,0,0
10,4,Births,473,137,20,11,32,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||128-0-255
12,5,48,191,122,8,8,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
11,6,48,253,120,5,8,34,3,0,0,1,0,0,0
10,7,Deaths,253,136,23,11,32,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,8,Output per Capita,378,322,40,20,3,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||255-0-0
12,9,48,162,320,8,8,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
11,10,48,261,319,5,8,34,3,0,0,1,0,0,0
10,11,Output Net Change Rate,261,335,78,11,32,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,12,Natural Capital,275,469,40,20,3,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||0-128-0
12,13,48,512,470,8,8,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
11,14,48,423,469,5,8,34,3,0,0,1,0,0,0
10,15,Natural Capital Net Change Rate,423,488,103,11,32,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,16,Pollution per Unit Output,796,280,40,20,3,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||128-64-0
12,17,48,1000,297,8,8,0,3,0,0,-1,0,0,0
11,18,48,938,279,5,8,34,3,0,0,1,0,0,0
10,19,Pollution Intensity Change Rate,938,295,96,11,32,3,0,2,0,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,20,Pollution Control,505,322,53,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,21,Net per Capita Output,434,256,71,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,22,Net Pollution Flow,694,379,59,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,23,Death Rate,171,184,36,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,24,Birth Rate,503,196,33,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,25,Cleansing Flow,490,542,49,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,26,Regeneration Rate,641,435,58,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,27,Normal Regen Rate,782,438,62,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,28,Regen Coeff,674,524,40,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,29,Cleansing Coeff,571,572,50,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,30,Cleansing Rate,420,575,47,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||0-128-0
10,31,Pollution Output,701,228,51,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,32,Pollution Abatement,639,318,63,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,33,Abatement Coeff,565,286,54,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-64-0
10,34,Control Effect,585,362,45,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-64-0
10,35,Control Nonlin,535,402,47,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,36,Control Scale,489,383,44,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-64-0
10,37,Output Growth Rate,269,368,64,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,38,Growth Rate,309,398,41,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,39,Contraction Rate,169,398,54,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,40,Contraction Nonlin,239,418,60,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||255-0-0
10,41,Envir Effect Death,118,277,57,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,42,Normal Death Rate,270,220,61,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,43,Death Coeff 1,192,250,45,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,44,Death Coeff 2,235,264,45,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,45,Death Income Effect,286,282,64,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,46,Envir Death Nonlin,-1,318,60,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,47,Envir Death Scale,39,358,56,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-0-255
10,48,Birth Coeff 1,381,196,42,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,49,Birth Coeff 2,401,179,42,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,50,Birth Income Effect,397,214,61,11,0,3,0,2,-1,0,0,0,-1--1--1,0-0-0,|12||128-0-255
10,51,Pollution Change Rate,953,349,69,11,0,3,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-64-0
1,52,3,1,4,0,0,22,0,0,0,-1--1--1,,1|(437,121)|
1,53,3,2,100,0,0,22,0,0,0,-1--1--1,,1|(494,121)|
1,54,6,5,4,0,0,22,0,0,0,-1--1--1,,1|(223,120)|
1,55,6,1,100,0,0,22,0,0,0,-1--1--1,,1|(292,120)|
1,56,10,8,4,0,0,22,0,0,0,-1--1--1,,1|(302,319)|
1,57,10,9,68,0,0,22,0,0,0,-1--1--1,,1|(213,319)|
1,58,14,12,4,0,0,22,0,0,0,-1--1--1,,1|(366,469)|
1,59,14,13,68,0,0,22,0,0,0,-1--1--1,,1|(466,469)|
1,60,18,16,4,0,0,22,0,0,0,-1--1--1,,1|(884,279)|
1,61,18,17,68,0,0,22,0,0,0,-1--1--1,,1|(1000,279)|
1,62,8,20,0,0,0,0,0,0,0,-1--1--1,,1|(428,322)|
1,63,8,21,1,0,0,0,0,0,0,-1--1--1,,1|(397,279)|
1,64,20,21,1,0,0,0,0,0,0,-1--1--1,,1|(485,286)|
1,65,1,4,1,0,0,0,0,0,0,-1--1--1,,1|(425,140)|
1,66,1,7,1,0,0,0,0,0,0,-1--1--1,,1|(303,142)|
1,67,21,24,1,0,0,0,0,0,0,-1--1--1,,1|(474,229)|
1,68,24,4,1,0,0,0,0,0,0,-1--1--1,,1|(499,165)|
1,69,23,7,1,0,0,0,0,0,0,-1--1--1,,1|(210,149)|
1,70,22,26,1,0,0,0,0,0,0,-1--1--1,,1|(677,407)|
1,71,25,26,1,0,0,0,0,0,0,-1--1--1,,1|(574,504)|
1,72,26,15,1,0,0,0,0,0,0,-1--1--1,,1|(556,475)|
1,73,27,26,0,0,0,0,0,0,0,-1--1--1,,1|(716,436)|
1,74,28,26,0,0,0,0,0,0,0,-1--1--1,,1|(659,486)|
1,75,28,25,0,0,0,0,0,0,0,-1--1--1,,1|(593,531)|
1,76,29,25,0,0,0,0,0,0,0,-1--1--1,,1|(537,559)|
1,77,30,25,0,0,0,0,0,0,0,-1--1--1,,1|(448,561)|
1,78,1,31,1,0,0,0,0,0,0,-1--1--1,,1|(549,96)|
1,79,8,31,1,0,0,0,0,0,0,-1--1--1,,1|(536,260)|
1,80,16,31,1,0,0,0,0,0,0,-1--1--1,,1|(776,245)|
1,81,31,22,1,0,0,0,0,0,0,-1--1--1,,1|(717,294)|
1,82,20,32,0,0,0,0,0,0,0,-1--1--1,,1|(560,320)|
1,83,32,22,1,0,0,0,0,0,0,-1--1--1,,1|(673,342)|
1,84,33,32,0,0,0,0,0,0,0,-1--1--1,,1|(595,299)|
1,85,34,32,0,0,0,0,0,0,0,-1--1--1,,1|(606,344)|
1,86,1,32,1,0,0,0,0,0,0,-1--1--1,,1|(609,173)|
1,87,35,20,0,0,0,0,0,0,0,-1--1--1,,1|(522,368)|
1,88,36,20,0,0,0,0,0,0,0,-1--1--1,,1|(494,359)|
1,89,37,11,0,0,0,0,0,0,0,-1--1--1,,1|(267,358)|
1,90,8,11,1,0,0,0,0,0,0,-1--1--1,,1|(340,350)|
1,91,39,37,0,0,0,0,0,0,0,-1--1--1,,1|(211,384)|
1,92,38,37,0,0,0,0,0,0,0,-1--1--1,,1|(294,386)|
1,93,40,37,0,0,0,0,0,0,0,-1--1--1,,1|(249,398)|
1,94,41,23,1,0,0,0,0,0,0,-1--1--1,,1|(132,233)|
1,95,42,23,0,0,0,0,0,0,0,-1--1--1,,1|(227,204)|
1,96,43,42,0,0,0,0,0,0,0,-1--1--1,,1|(223,237)|
1,97,44,42,0,0,0,0,0,0,0,-1--1--1,,1|(247,247)|
1,98,45,42,0,0,0,0,0,0,0,-1--1--1,,1|(280,257)|
1,99,21,42,0,0,0,0,0,0,0,-1--1--1,,1|(358,239)|
1,100,46,41,0,0,0,0,0,0,0,-1--1--1,,1|(51,299)|
1,101,47,41,0,0,0,0,0,0,0,-1--1--1,,1|(73,322)|
1,102,48,24,0,0,0,0,0,0,0,-1--1--1,,1|(439,196)|
1,103,49,24,0,0,0,0,0,0,0,-1--1--1,,1|(449,186)|
1,104,50,24,0,0,0,0,0,0,0,-1--1--1,,1|(457,204)|
1,105,16,19,1,0,0,0,0,0,0,-1--1--1,,1|(842,313)|
1,106,51,19,0,0,0,0,0,0,0,-1--1--1,,1|(947,328)|
10,107,Effective Natural Capital,139,468,76,11,0,3,0,0,0,0,0,0
10,108,Natural Capital Upper Bound,79,548,92,11,0,3,0,0,0,0,0,0
10,109,Natural Capital Lower Bound,189,578,92,11,0,3,0,0,0,0,0,0
1,110,108,107,0,0,0,0,0,64,0,-1--1--1,,1|(104,513)|
1,111,109,107,0,0,0,0,0,64,0,-1--1--1,,1|(166,529)|
1,112,12,107,1,0,0,0,0,64,0,-1--1--1,,1|(231,468)|
1,113,107,15,1,0,0,0,0,64,0,-1--1--1,,1|(329,518)|
1,114,107,25,1,0,0,0,0,64,0,-1--1--1,,1|(287,545)|
1,115,107,41,1,0,0,0,0,64,0,-1--1--1,,1|(103,355)|
1,116,107,20,1,0,0,0,0,64,0,-1--1--1,,1|(361,405)|
1,117,107,37,0,0,0,0,0,64,0,-1--1--1,,1|(197,422)|
12,118,0,326,14,156,11,0,4,0,0,-1,0,0,0
Wonderland Model by Warren C. Sanderson et al.
12,119,0,330,70,240,11,0,4,0,0,-1,0,0,0
Replicated in Vensim by Tom Fiddaman, Ventana Systems, tom@Vensim.com
12,120,0,350,40,375,11,0,4,0,0,-1,0,0,0
From Alexandra Milik et al., "Slow-fast Dynamics in Wonderland," Environmental Modeling and Assessment 1 (1996) 3-17
///---\\\
:GRAPH NATURAL_CAPITAL
:TITLE Natural Capital
:SCALE
:VAR Effective Natural Capital
:SCALE
:VAR Cleansing Flow
:VAR Net Pollution Flow
:SCALE
:VAR Regeneration Rate
:L<%^E!@
1:nm.vdf
1:Nightmare2.vdf
9:nm
22:$,Dollar,Dollars,$s
22:Day,Days
22:dmnl,NKU
22:Hour,Hours
22:Month,Months
22:Person,People,Persons
22:Unit,Units
22:Week,Weeks
22:Year,Years
15:0,0,0,1
19:100,0
4:Time
5:Effective Natural Capital