globals [biomass-unit days dollars grazecountdown mcal]
breeds [cow]
patches-own [biomass]
turtles-own [energy] ; as Mcal

to setup
    ca
    set biomass-unit 2.5 ; each increment of biomass (0-10) is valued at this many lbs. dry weight 
    ifelse start-patches-even?
        [ask patches [set biomass 4]]
        [ask patches [set biomass (random 4.0) * 2]]
    if update-patches?
    [ask patches [update-patches]]
    setup-plot
    setup-histogram
end

to go
   ask patches [grow-grass-and-weeds
               cycle-plants]
   if update-patches?
   [ask patches [update-patches]]
   plot-biomass
   histo-patches
   set days days + 1
   set grazecountdown grazecountdown - 1
   wait 0.5
   if any turtles 
       [ ask cow [graze] ]
end

to cycle-plants ;; patch procedure representing mortality and new establishment
      if biomass <= .3 [
      if ( random 100 ) < 5
        [ set biomass 0 ]
                       ]
        
      if biomass = 0 [  
      if ( random 100 ) < 3
        [ set biomass 1 ]
                     ]
end

to update-patches ;; patch procedure

    if biomass <= 2 [set pcolor 68] 
    if biomass > 2 [set pcolor 66]
    if biomass > 6 [set pcolor 64]
    if biomass > 8 [set pcolor 44]
    if biomass <= 0 [set pcolor brown] 
end

to cattle-in
    set-default-shape cow "cow"
    create-custom-cow num-cows  ;; create the cows, then initialize their variables
          [ 
    set color black
    set energy 0
    setxy (random screen-size-x) (random screen-size-y) ; spreads them around
    rt random 360
          ] 
    set grazecountdown grazeperiod   
end

to cattle-out
    ask turtles [die]
    set grazecountdown 0
end

;;;;; GRAZING PROCEDURES

to graze  ;; daily cow procedure
   if grazecountdown <= 0 [die]
   repeat (.4 / bitesize) [move bite]
   check-fill
   gain
end     
                       
to move                                
    rt random 50 - random 50 fd 1
    repeat selectivity
        [
    if biomass < 1 or biomass > 8 [fd 3]
        ]
end

to bite
       ifelse biomass < 1 or biomass > 8 
       [  set energy energy + (biomass * biomass-unit * bitesize * .4)] ; less energy: .4 Mcal per lb.
       [  set energy energy + (biomass * biomass-unit * bitesize * .7)] ; more energy: .7 Mcal per lb.
       set biomass (biomass * (1 - bitesize)) ; patch loses biomass in proportion to bitesize   
end

to check-fill
    repeat (1.6 / bitesize) [if energy < 20 [move bite]] ; attempt to harvest 20 Mcal
end

to gain
    set dollars dollars + (((energy - 5) / 7) * .4) 
    ;assumes 5 Mcal for maintenance
    ;assumes 7 Mcal needed for pound of $.40 gain
    set mcal energy; records the energy harvest of last cow
    set energy 0
end

;;;;; PLANT GROWTH

to grow-grass-and-weeds ;; patch procedure
    if biomass < 7.5 ;; stage at which growth slows
    [set biomass biomass + (((precision (biomass ^ .667) 2) / 40) * grassrate)] 
    ; gives about 2.5% daily growth with grassrate 1.0
    if biomass >= 7.5 
    [set biomass biomass + (((10 - biomass) / 40) * grassrate)]
end

;;;; PLOTTING PROCEDURES

to setup-plot
    set-current-plot "ecology and economy"
    set-current-plot-pen "avg-biomass"
    set-plot-y-range 0 10
    set-current-plot-pen "dollars per week"
    set-plot-y-range 0 10
end

to setup-histogram
    set-current-plot "patch biomass histogram"
    ;set-plot-x-range 0 10
    set-plot-y-range 0 100
    set-histogram-num-bars 11
end

to plot-biomass 
    set-current-plot "ecology and economy"
    set-current-plot-pen "avg-biomass"
    plot mean values-from patches [biomass]
    set-current-plot-pen "dollars per week"
    plot dollars / (days + .001) * 7
end

to histo-patches
    set-current-plot "patch biomass histogram"
    histogram patches [ biomass ]  ; using the default plot pen
end

; ***NetLogo Model Copyright Notice***

; Copyright 2003 by Peter Donovan. All rights reserved.

; Permission to use, modify, or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from Peter Donovan.
; Contact Peter Donovan (peter@managingwholes.com) for appropriate licenses
; for redistribution for profit.

; To refer to this model in academic publications, please use: 
; Donovan, Peter. (2003).  NetLogo Grazing Model # 1. 
; http://managingwholes.com/models/graze1.htm.
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@#$#@#$#@
WHAT IS IT?
-----------

This is a simple pasture management or grazing model. There is NO predictive value to this model. Its purpose is to help you experiment and see what happens when relatively simple behaviors interact in complex ways over time. Suggestions for improvements would be appreciated; peter@managingwholes.com. In the future ManagingWholes.com hopes to have grazing models that mimic both grass and weeds, the herding behavior of livestock, the effects of cross-fencing, and multiple species of grazing animals (e.g. cows and goats).


HOW TO USE IT
-------------

Click the SETUP button to start. This gives you a small pasture to manage, with plants in a variety of vegetative growth stages. The only livestock available are cattle, and a generalized grass plant grows on the patches. In this simplified ecosystem, water and sunlight are evenly available from day to day. To simulate drought, rainfall, or seasonal variations, you may adjust the GRASSRATE slider at any time. Click RUN to start the simulation. The RUN button turns black when the simulation is running; click again to pause the simulation. To start over, stop RUN and click SETUP. 

Select the stocking rate and duration with the NUM-COWS and GRAZEPERIOD sliders. Slider handles can be dragged, or click to right or left of the handle to fine-tune. CATTLE IN will start grazing. Should you wish to cease grazing before your grazeperiod runs out, hit CATTLE OUT. (Sometimes CATTLE IN doesn't "catch" so keep an eye on the monitors in case you need to hit it again.)

The UPDATE-PATCHES? switch allows you to turn off the flickering color updates of the patches in the pasture. The START-PATCHES-EVEN? switch allows you to experiment with patches at an even starting biomass of 4. When this switch is off, starting biomass is a random distribution between 0 and 7.9.


THINGS TO TRY
-------------

1. See if you can make more than $1.00 a day over a year or more from this pasture using a GRASSRATE of 1.0.

2. Can you reproduce the pattern often seen in continuously grazed pastures of a mosaic of wolfy, dormant, or overrested plants plus short regrowth? In the histogram this would be a U-shape, representing poor energy flow. How do you turn this around into a hump or normal curve? Try changing BITESIZE and SELECTIVITY as well as NUM-COWS and GRAZEPERIOD.


HOW IT WORKS
------------

PLANT GROWTH. Plant growth is divided into four color-coded stages: early, vegetative, going to seed (progressively darker shades of green), and dormant (tan). Each day, plants grow and increase their biomass, which is recorded on a scale of 0 to 10. (In this simplified model, each increment represents 2.5 pounds of dry matter, so that a patch can grow up to 25 dry-weight pounds of biomass, roots included). 

Biomass is a measure of volume. Plants in early and vegetative states increase daily roughly in proportion to their area (biomass to the two-thirds power). In the later stages of growth (beyond biomass 7.5 in this model), they increase daily according to (10 - biomass)^.667. Thus growth slows markedly from biomass 7.5 to 10, to represent the combined effects of plant maturity, competition, and shading. At random, some patches with low biomass die out and turn dark brown, indicating bare ground, simulating the effect of overgrazing plants. At random, seedlings establish in some of the bare patches, returning them to productivity.

CATTLE GRAZING. In building this model, it was assumed that each animal needs 5.0 megacalories (Mcal) daily for maintenance, and that 7.0 Mcal above the maintenance requirement was sufficient to put on a pound of gain (worth $0.40 in this model). The forage harvested by the cow has energy values of .4 or .7 Mcal per pound of dry matter. Patches with biomass between 2 and 8 yield the higher energy value. Each time a patch is grazed, its biomass is reduced by 10 to 40 percent, depending on the BITESIZE slider. If gain turns negative, it will cost you. The Mcal/day monitor shows how much energy the last animal harvested from the pasture. If this falls below 7.0 you are in the losing zone.

MOVING AND SELECTIVITY. With BITESIZE set at .4 (40% removal of biomass with grazing) and SELECTIVITY set to 1, cows move a minimum of 1 times and a maximum of 4 times each day to a different patch on the model, which is a lattice of 289 patches. Each move starts out with the cow moving randomly forward 1 square. If SELECTIVITY is 1, she evaluates the patch she lands on. If the biomass is between 1 and 8.5 (vegetative plants), she grazes. Otherwise she moves forward again, and grazes the patch she lands on regardless. If after 1 such moves she has not harvested 20 Mcal worth of forage, she makes up to 3 additional moves in an attempt to do so. The SELECTIVITY slider controls how many moves she will make in an attempt to find a vegetative patch to graze. Lowering BITESIZE or increasing SELECTIVITY will increase the daily movement.

PLOTS. The red pen plots dollars per week; the violet pen plots average biomass. Should you make a lot of money in a hurry, or lose lots of money, the vertical scale may increase to the point where average biomass becomes difficult to gauge. The histogram shows the distribution of patches with a given biomass or stage of growth.


WHAT THIS MODEL DOES NOT REPRESENT
----------------------------------

1. The ability of pastures to improve, grow more forage with good management, the effects of animal impact on pasture productivity, or any of the myriad factors relating to soil health.

2. Seasonal variations in the patterns of plant growth (some of these could be simulated with the GRASSRATE slider, but not photoperiod effects). In effect, patches on the lattice grow biomass independently of any season or photoperiod, nutrient availability, or energy storage.

3. Subleties of grazing behavior, for example varying "bites" on plants of different growth stages, or the variation of bite depending on numbers of animals.

4. Varying maintenance requirements of cattle owing to reproductive cycles, cold temperatures, stress, travel needed to fill rumen, or weight gain or loss.

5. Natural biodiversity within species and among species. This is a monoculture of generic cattle and generic plants, both of which "convert energy" in linear fashion. The irregularities that emerge result from the accumulation of random, probabilistic interactions between linear automata.


CREDITS AND REFERENCES
----------------------
Diven, Dick. (2001). Low Cost Cow-Calf Livestock Nutrition manual.

Savory, Allan, with Jody Butterfield. (1999). Holistic Management: A New Framework for Decision Making. Washington, DC: Island Press.

The NetLogo manual. See http://ccl.northwestern.edu/netlogo/

To refer to this model, please use: Donovan, Peter. (2003).  NetLogo Grazing Model # 1. http://managingwholes.com/models/graze1.htm.
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NetLogo 1.1 (Rev F)
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