{UTF-8}
Deforestation=
	MIN(Gap/MAX(Fertility of Lands,1),Forest/4)/Intensity
	~	km2/year
	~	Basically they deforest the amount of km2 that they need to close the Gap \
		(kg) considering the Land Fertility (kg/km2).      Function MAX is used to \
		prevent error if model need to divide by 0 .    Function MIN is used to \
		atemperate the response of model.  Intensity gives us a way to regulate \
		the speed of the model.  So, Intensity=1 means that every year they \
		deforest all the forest they need.
	|

Losses=
	Fertility of Lands*MIN(2,(Lands/Forest)^1.9)/Intensity
	~	kg/(km2*year)/year
	~	We can accept that Loses of Fertility are proportional to the Fertility \
		that exist, and of the difference from the Lands and Forests with a \
		quadratic relation (we like to avoid the use of a Table). We need to use \
		as exponent 1.9 to see the collapse in year 800, as text explains. If we \
		use 2 as exponent, the collapse occus in year 1000.
	|

Natural Increase=
	Population*Natural Increase Rate
	~	person/year
	~	The calculated value of 0.17% is the net value from birth and deceases. \
		With this rate population goes from 100,000 to 2,000,000 inhabitants in \
		1,800 years.
	|

Natural Increase Rate=
	0.0017
	~	1/year
	~	If the population doubles every 408 years, as in the text, the percentage \
		must be 0,170 % as we can see (1+0.0017)^408=2
	|

Emigration Ratio=
	0.05
	~	1/year
	~	Percentage of persons emigrating because of food shortage.
	|

Intensity=
	1
	~	year
	~	The same variable is used to regulate: 1.- The period of time that \
		population decide to close the gap, and deforest all that they need. 2.- \
		The speed in with teh Fertility of lands are taken place.
	|

Emigration=
	(Gap/Consumed Food per Person)*Emigration Ratio
	~	person/year
	~	We assume that if know the amount of Gap of food (kg/year) and the \
		comsumption per person and year (kg/person/year), we can obtain the \
		equivalent number of people without food (personas/aņo). We correct the \
		obtained value, aplying the Emigration Ratio (5%) asssuming that only a \
		small part of this people really emigrates (they redistribute the existing \
		food).
	|

Population= INTEG (
	Natural Increase-Emigration,
		100000)
	~	person
	~	If we assume 2,000,000 inhabitants in the moment of collapse (+800 A.D.), \
		we can obtain the initial value in year 1000 B.D., with a rate of 0.17%. \
		They  were 100.000 inhabitants aprox.
	|

Consumed Food per Person=
	400
	~	kg/(person*year)
	~	We assume a few more than 1 kilo per person and day.
	|

Demand of Food=
	Consumed Food per Person*Population
	~	kg/year
	~		|

Fertility of Lands= INTEG (
	-Losses,
		5e+006)
	~	kg/(km2*year)
	~	With the initial value of 5,000,000 kg/km2 we can obtain 40,000,000 kg if \
		we have  8 km2 of Land. This is equal to the inicial food demanded for \
		100,000 inhabitants with a Consumed food per person equal to 400 kg every \
		year.
	|

Gap=
	Demand of Food-Food Produced
	~	kg/year
	~		|

Food Produced=
	Fertility of Lands*Lands
	~	kg/year
	~		|

Lands= INTEG (
	Deforestation,
		8)
	~	km2
	~	Initial value is obtained from the total food consumed 40,000,000 kg every \
		year for the initial value of inhabitants: 100.000 persons, and an Initial \
		fertility of Land of 5.000.000 kg/km2 and year. (40,000,000/5,000,000=8)
	|

Forest= INTEG (
	-Deforestation,
		5000)
	~	km2
	~	Initial value is obtained from an assumed density of 400 person/km2, and \
		from the final inhabitants assumed: 2.000.000 persons (2 000 000/400=5,000)
	|

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

FINAL TIME  = 1000
	~	year
	~	The final time for the simulation.
	|

INITIAL TIME  = -1000
	~	year
	~	The initial time for the simulation.
	|

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

TIME STEP  = 0.25
	~	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
$192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,100,0
10,1,Forest,238,132,40,29,3,3,0,0,0,0,0,0
10,2,Lands,598,133,42,28,3,3,0,0,0,0,0,0
10,3,Population,301,501,40,20,3,3,0,16,0,0,0,0,0-0-0,0-0-0,|12|B|0-0-0
10,4,Fertility of Lands,397,260,47,32,3,3,0,0,0,0,0,0
1,5,7,2,4,0,0,12,0,0,0,-1--1--1,,1|(495,140)|
1,6,7,1,100,0,0,12,0,0,0,-1--1--1,,1|(350,140)|
11,7,204,429,140,6,8,34,3,0,0,1,0,0,0
10,8,Deforestation,429,159,43,11,32,3,0,0,-1,0,0,0
12,9,48,586,259,10,8,0,3,0,0,-1,0,0,0
1,10,12,9,4,0,0,12,0,0,0,-1--1--1,,1|(548,260)|
1,11,12,4,100,0,0,12,0,0,0,-1--1--1,,1|(476,260)|
11,12,48,515,260,6,8,34,3,0,0,3,0,0,0
10,13,Losses,515,241,23,11,32,3,0,0,3,0,0,0
12,14,48,506,503,10,8,0,3,0,0,-1,0,0,0
1,15,17,14,4,0,0,12,0,0,0,-1--1--1,,1|(445,504)|
1,16,17,3,100,0,0,12,32,0,0,-1--1--1,Times New Roman|12||0-0-0,1|(362,504)|
11,17,48,389,504,6,8,34,3,0,0,3,0,0,0
10,18,Emigration,389,485,34,11,32,3,0,0,-1,0,0,0
1,19,1,13,1,0,0,12,0,64,0,-1--1--1,,1|(372,202)|
1,20,2,13,1,0,0,12,0,64,0,-1--1--1,,1|(608,179)|
1,21,4,8,1,0,0,12,0,64,0,-1--1--1,,1|(407,204)|
1,22,4,13,1,0,0,12,0,64,0,-1--1--1,,1|(457,252)|
10,23,Food Produced,569,379,40,20,3,3,0,1,0,0,0,0,255-255-255,0-0-0,|12||0-0-0
10,24,Demand of Food,203,352,40,20,3,3,0,1,0,0,0,0,255-255-255,0-0-0,|12||0-0-0
10,25,Consumed Food per Person,316,403,54,19,8,3,0,1,0,0,0,0,255-255-255,0-0-0,|12||0-0-0
10,26,Gap,340,323,15,11,0,3,0,0,0,0,0,0
1,27,1,8,1,0,0,12,0,64,0,-1--1--1,,1|(320,151)|
1,28,26,8,1,0,0,12,32,64,0,-1--1--1,Times New Roman|12||0-0-0,1|(314,239)|
1,29,4,23,1,0,0,12,0,64,0,-1--1--1,,1|(544,333)|
1,30,2,23,1,0,0,12,0,64,0,-1--1--1,,1|(645,222)|
1,31,23,26,1,0,0,12,0,64,0,-1--1--1,,1|(460,323)|
1,32,24,26,1,0,0,12,32,64,0,-1--1--1,Times New Roman|12||0-0-0,1|(286,315)|
1,33,25,24,1,0,0,12,0,64,0,-1--1--1,,1|(273,373)|
1,34,25,18,1,0,0,12,0,64,0,-1--1--1,,1|(365,441)|
1,35,26,18,1,0,0,12,32,64,0,-1--1--1,Times New Roman|12||0-0-0,1|(407,426)|
1,36,3,24,1,0,0,12,32,64,0,-1--1--1,Times New Roman|12||0-0-0,1|(245,424)|
12,37,48,110,493,10,8,0,3,0,0,-1,0,0,0
1,38,40,3,4,0,0,12,32,0,0,-1--1--1,Times New Roman|12||0-0-0,1|(208,496)|
1,39,40,37,100,0,0,12,0,0,0,-1--1--1,,1|(131,496)|
11,40,48,149,496,6,8,34,3,0,0,3,0,0,0
10,41,Natural Increase,149,477,52,11,32,3,0,0,3,0,0,0
1,42,3,41,1,0,0,12,0,0,0,-1--1--1,,1|(193,457)|
10,43,Emigration Ratio,493,441,52,11,0,3,0,0,0,0,0,0
1,44,43,18,1,0,0,12,0,0,0,-1--1--1,,1|(444,468)|
10,45,Natural Increase Rate,139,407,68,11,0,3,0,0,0,0,0,0
1,46,45,41,0,0,0,12,0,0,0,-1--1--1,,1|(142,433)|
10,47,Intensity,546,189,27,11,0,3,0,1,0,0,0,0,255-255-255,0-0-0,|12||0-0-0
1,48,47,8,1,0,0,12,0,0,0,-1--1--1,,1|(502,180)|
1,49,47,13,1,0,0,12,0,0,0,-1--1--1,,1|(524,202)|
///---\\\
:GRAPH GRAPH
:SCALE
:VAR Population
:SCALE
:VAR Forest
:SCALE
:VAR Lands
:SCALE
:VAR Fertility of Lands
:L<%^E!@
1:O:\00_E-BOOK-SD\1_Models\Case52CollapseMayaTBD\maya.vdf
9:maya
15:0,0,0,5,0,0
19:100,0
27:2,
34:0,
4:Time
5:Losses
24:-1000
25:1000
26:1000