Chesapeake-Bay-Crab-Fishing.nlogo

;; -----------------------------------------------------------------------
;;
;; agent-based model to demonstrate population dynamics of crabs and
;; and economics of commercial crab fishing in the Chesapeake Bay area
;;
;; -----------------------------------------------------------------------


;; =============================================================
;;
;; Global declarations
;;
;; =============================================================
;;
;; Note: the following are the definitions of
;; NetLogo variables mapped into the Schafer model
;;
;; Schaefer variable      Definition          NetLogo Model variable
;; -----------------      ----------          ----------------------
;; x                      population-size     (crab variable)
;; r                      growth-rate         (GUI slider)
;; K                      carrying-capacity   (GUI slider)
;; q                      catchability-rate   (GUI slider)
;; E                      num-vessels         (GUI slider)
;;

breed [crabs crab]
breed [fishermen fishman]
;; --------------------------------------------------------------
;;
;; global variables
;;
;; --------------------------------------------------------------
globals [

  ;; totals
  total-population-size   ; cumulative total population size of crabs for all time periods
  total-catch-size        ; total catch size of all fishermen this time period
  previous-catch-size     ; catch size previous time period
  annual-catch-size       ; total catch size this year (prev-catch + total-catch-size)

  ;; crab globals
  num-active-pods         ; number of locations with active crab populations
  mean-pod-size           ; average number of crabs at the location

  ;; fishermen globals
  num-active-fishermen    ; number of active fishermen (i.e. number of vessels)
  mean-fisherman-wealth   ; mean wealth of all fishermen

  ;; time globals
  initial-year            ; first year of simulation
  final-year              ; final year of simulation
  current-year            ; current year of the simulation

]

;; --------------------------------------------------------------
;; crab breed definitions
;;
;; define crab breed attributes
;;
;; --------------------------------------------------------------

crabs-own [
  population-size      ; total number of crabs in this pod

  ;;
  ;; currently not used, could be used if model extended
  ;; for a more realistic age cohort model
  ;;
  ;popsize-yr0          ; number of crabs aged 0 to 1 yr
  ;popsize-yr1          ; number of crabs aged 1 to 2 yr
  ;popsize-yr2          ; number of crabs aged 2 to 3 yr
  ;popsize-yr3          ; number of crabs aged 3 yrs
]

;; --------------------------------------------------------------
;; fisherman breed attributes
;;
;; define fisherman breed attributes
;;
;; --------------------------------------------------------------

fishermen-own [
  catch-size           ; current catch size in crabs
  wealth               ; current wealth in arbitrary economic units
  operating-expense    ; cost of operating the business
]

;; --------------------------------------------------------------
;; patches definitions
;;
;; setup spatial feature for geo-based fishing restrictions
;;
;; --------------------------------------------------------------
patches-own [
  fishing-allowed
]


;; --------------------------------------------------------------
;; setup-globals
;;
;; establish initial values for global variables
;;
;; --------------------------------------------------------------
to setup-globals
  ;; catchability-rate
  set total-population-size sum [population-size] of crabs
  set total-catch-size 0
  set previous-catch-size 0
  set annual-catch-size 0

  ifelse ((count fishermen) > 0)
  [set mean-fisherman-wealth mean [wealth] of fishermen]
  [set mean-fisherman-wealth 0]

  set mean-pod-size mean [population-size] of crabs

  set num-active-pods count crabs
  set num-active-fishermen count fishermen

  set initial-year 1982
  set final-year 1999
  set current-year initial-year

end



;; =============================================================
;;
;; Setup functions
;;
;; =============================================================


;; --------------------------------------------------------------
;; setup-chesapeake
;;
;; setup the chesapeake abstract spatial model and geography
;;
;; --------------------------------------------------------------
to setup-chesapeake
  define-bay
end

;; --------------------------------------------------------------
;; define-bay
;;
;; make the bay all blue (for the water)
;; and configure the fishing availability
;;
;; --------------------------------------------------------------
to define-bay
  ;;
  ;; set basic configuration
  ;;
  ask patches
  [
    set pcolor blue
    set fishing-allowed true
  ]

  ;;
  ;; reconfigure if spatial restrictions are active
  ;;
  if (spatial-restriction = true) [
    ask patches [
      ;;
      ;; note:
      ;; this can be used to implement a small checkerboard model
      ;; if ((pxcor mod 2) = 0) and ((pycor mod 2) = 0)

      ;;
      ;; implement large spatial restriction model
      ;;
      if ((pxcor <= 0) and (pycor < 0)) or ((pxcor >= 0) and (pycor > 0))  ;; large safe havens model
      [
        set fishing-allowed false
        set pcolor (blue - 3) ;; make off-limits patches a dark blue color
      ]
    ]
  ]
end

;; --------------------------------------------------------------
;; setup-crabs
;;
;; setup and locate the crab populations
;;
;; --------------------------------------------------------------
to setup-crabs[ num ]
  create-crabs num [
    set shape "blue crab"
    set color (blue + 3)
    set population-size pod-size

    ;;set size 1.0
    set size (population-size / carrying-capacity)
    if (size < 0.25) [
      set size 0.25
    ]

    setxy random-xcor random-ycor
    set heading 0
  ]
end

;; --------------------------------------------------------------
;; setup-fishermen
;;
;; setup and locate the fishermen
;;
;; --------------------------------------------------------------
to setup-fishermen[ num ]
  let MAX-WEALTH 100
  let MAX-EXPENSES 10

    create-fishermen num [
    set shape "crab boat"
    set size 2.0
    set color (gray + 2)
    set catch-size 0
    set wealth (random MAX-WEALTH) + 1
    set operating-expense (random MAX-EXPENSES) + 1
    setxy random-xcor random-ycor
    set heading 0
  ]
end

;; --------------------------------------------------------------
;; setup
;;
;; setup the model
;;
;; --------------------------------------------------------------
to setup
  ;; (for this model to work with NetLogo's new plotting features,
  ;; __clear-all-and-reset-ticks should be replaced with clear-all at
  ;; the beginning of your setup procedure and reset-ticks at the end
  ;; of the procedure.)
  __clear-all-and-reset-ticks
  setup-chesapeake

  setup-crabs num-pods
  setup-fishermen num-vessels

  setup-globals

  setup-plot
  setup-histogram

  do-plot
  do-histogram
end


;; ===============================================================
;; ===============================================================
;; go
;;
;; main "go" procedure for simulation
;;
;; ===============================================================
;; ===============================================================
to go
  step
end


;; --------------------------------------------------------------
;; step
;;
;;
;; step function executes one time tick of action
;; (also useful for slow motion)
;;
;; --------------------------------------------------------------
to step

  ;;
  ;; check for end of simulation time, stop if occurred
  ;;
  if (current-year >= final-year) [ stop ]

  ;;
  ;; check for crab extinction, stop simulation if crabs extinct
  ;;
  if not any? crabs [ stop ]
  if sum [population-size] of crabs <= 0 [ stop ]

  ;; ------------
  ;; crab actions
  ;; ------------
  ask crabs [
    crab-move
    crab-breed
  ]

  ;; -----------------
  ;; fishermen actions
  ;; -----------------
  fishermen-add-new-vessels
  ask fishermen [
    set catch-size 0
    fishermen-move
    ;; fishermen-harvest
    fishermen-harvest-spatial
    fishermen-sell
    fishermen-pay-excess-catch-tax
  ]

  ;; ---------------------------------------
  ;; check for overfished pods, die if empty
  ;; ---------------------------------------
  ask crabs [
    if (population-size <= 1) [
      die
    ]
  ]

  ;; ------------------------------------------
  ;; check for bankrupt fishermen, die if broke
  ;; ------------------------------------------
  ask fishermen [
    if (wealth <= 1) [
      die
    ]
  ]

  ;; -----------------------------------
  ;; update globals and refresh displays
  ;; -----------------------------------
  tick
  update-globals
  do-plot
  do-histogram
end

;; --------------------------------------------------------------
;; update globals
;;
;; keep track of some key variables for display purposes
;;
;; --------------------------------------------------------------
to update-globals

  set total-population-size sum [population-size] of crabs
  set previous-catch-size total-catch-size
  set total-catch-size sum [catch-size] of fishermen
  set annual-catch-size (previous-catch-size + total-catch-size)

  ifelse (count fishermen) > 0
  [set mean-fisherman-wealth mean [wealth] of fishermen]
  [set mean-fisherman-wealth 0]

  ifelse (count crabs) > 0
  [set mean-pod-size mean [population-size] of crabs]
  [set mean-pod-size 0]

  set num-active-pods count crabs
  set num-active-fishermen count fishermen

  if ((ticks > 0) and ((ticks mod 2) = 0)) [
    set current-year (current-year + 1)
  ]
end


;; =============================================================
;;
;; Crab functions
;;
;; =============================================================


;; --------------------------------------------------------------
;; crab-move
;;
;; basic crab movement
;;
;; --------------------------------------------------------------
to crab-move
  ;;
  ;; move in the summer/fall, sleep during the winter
  ;;
  let CRAB_MOVE_FREQUENCY 2
  let move-flag 0
  if ((ticks mod CRAB_MOVE_FREQUENCY) = 0) [
    set move-flag 1
  ]

  ;;
  ;; if it's summer/fall, move
  ;; if it's winter/spring, don't move
  ;;
  ;; min and max movement distances are in km
  ;; km_per_cell allows conversion from actual movement in km
  ;; to NetLogo cell distances.
  ;;
  ;; scale is set by analyzing total Chesapeake Bay area divided
  ;; by number of cells in model.  Default is 33x33 cells.
  ;;
  ;;
  let MIN_MOVE_DISTANCE 14
  let MAX_MOVE_DISTANCE 70
  let KM_PER_CELL 2.7

  let move-distance (random (MAX_MOVE_DISTANCE - MIN_MOVE_DISTANCE) / KM_PER_CELL )
  if (move-flag = 1) [
    rt random 50
    lt random 50
    fd move-distance
  ]
  set heading 0
end

;; --------------------------------------------------------------
;; crab-breed
;;
;; define crab reproduction
;;
;; --------------------------------------------------------------
to crab-breed

  ;;
  ;; only breed in summer/fall, sleep during the winter
  ;;
  ;; to implement this, let 2 ticks == 1 year, so
  ;; breeding occurs every other tick
  ;;
  let CRAB_BREED_FREQUENCY 2
  let breed-flag 0
  if ((ticks mod CRAB_BREED_FREQUENCY) = 0) [
    set breed-flag 1
  ]

  ;;
  ;; dxdt is from the equation for a Schaefer model
  ;;
  if (breed-flag = 1) [
    let dxdt 0
    set dxdt (growth-rate * population-size) * (1 - (population-size / carrying-capacity))
    set population-size (population-size + dxdt)

    ;;
    ;; pod dies out if too small
    ;;
    if (population-size <= 1) [
      die
    ]

    ;;
    ;; change crab icon display size based on population-size
    ;;
    ;; provides quick visual of how big the pod is compared to
    ;; how big it could be.  Override size if less than 0.25 since
    ;; it's too hard to see on the screen if below 0.25
    ;;
    set size (population-size / carrying-capacity)
    if (size < 0.25) [
      set size 0.25
    ]
  ]
end


;; =============================================================
;;
;; Fishermen functions
;;
;; =============================================================


;; --------------------------------------------------------------
;; fishermen-add-new-vessels
;;
;; define adding new fishermen.  Since fishermen occasionally
;; go broke, this method simulates new fishermen joining the
;; fleet (or displaced fishermen returning from other lines
;; of work).
;;
;; --------------------------------------------------------------
to fishermen-add-new-vessels
  let current-fleet-size (count fishermen)
  if ((current-fleet-size < num-vessels) and (num-vessels > 0)) [
    let i 0
    let num (num-vessels - current-fleet-size)
    while [i < num] [
      let prob (1.0 - (current-fleet-size / num-vessels))
      if ((random-float 1.0) > prob) [
        setup-fishermen 1
      ]
      set i (i + 1)
    ]
  ]
end

;; --------------------------------------------------------------
;; fishermen-move
;;
;; define fishermen movement.  This simulates fishermen sailing
;; about in the bay area.
;;
;; Note: this is a *gross* oversimplification.  In real life,
;; fishermen sail fairly wide distances and drop crab pots in
;; the summer, or do dredging in the winter.  The model only
;; allows very limited sailing distances.  Since each cell
;; is approx 2.7 km by 2.7 km, a 10 cell voyage is only 27 km
;; distance.  However, due to the temporal resolution of the
;; model, this means the fisherman is only harvesting in a 27 km
;; region every 6 months.
;;
;; --------------------------------------------------------------
to fishermen-move
  let sailing-distance random 10
  let new-heading random 360
  ifelse ((random-float 1.0) > 0.5)
  [rt new-heading]
  [lt new-heading]
  fd sailing-distance
  set heading 0
end

;; --------------------------------------------------------------
;; fishermen-harvest [harvest-radius]
;;
;; driver function to manage fishermen harvesting of crabs
;;
;; harvest-radius is the radius in which the fisherman can "see"
;; to look for crab pods to harvest.
;;
;; harvesting is subject to "excess-tax" policy, which is a
;; policy alternative that puts an increasing graduated tax
;; on harvests that are in excess of the fleet's mean harvest
;; size.  Fishermen are taxed highly if they take a catch that
;; is in excess of the mean catch size of the fleet, which
;; incentivizes them to limit their catch sizes for economic
;; purposes.
;;
;; if the excess-tax is set to 0, then this policy is not enforced.
;; if the excess-tax is set to > 0, then the excess catch is taxed
;; at the excess-tax rate for the quantity of catch above the
;; fleet average catch size.
;;
;; --------------------------------------------------------------
to fishermen-harvest[ harvest-radius ]
  let CATCH-RADIUS harvest-radius

  let crabs-this-catch 0
  let total-catch 0
  let targetList crabs in-radius CATCH-RADIUS


  ifelse (extra-tax = 0) [
    ;;
    ;; no excess catch taxation policy in place
    ;;

    ;; conduct the harvest
    ;;
    ask targetList [
      if population-size > 0 [
        set crabs-this-catch ((random-float catchability-rate) * population-size)
        set population-size (population-size - crabs-this-catch)
        set total-catch (total-catch + crabs-this-catch)
      ]
    ]
    set catch-size (catch-size + total-catch)
  ]
  [
    ;;
    ;; excess catch will be heavily taxed
    ;;

    ;; determine average and sd of fleet catch size
    let average-catch-size mean [catch-size] of fishermen
    let sd-catch-size sqrt (variance [catch-size] of fishermen)
    if (sd-catch-size = 0)
    [set sd-catch-size 1]

    ;; conduct the harvest
    ;;
    ask targetList [
      if population-size > 0 [
        set crabs-this-catch ((random-float catchability-rate) * population-size)

        ;;
        ;; before actually taking the harvest,
        ;; check to see if this puts us over quota...
        ;;
        ifelse ((total-catch + crabs-this-catch) < average-catch-size) [
          ;;
          ;; go ahead and harvest, since we're still under quota
          ;;
          set population-size (population-size - crabs-this-catch)
          set total-catch (total-catch + crabs-this-catch)
        ]
        [
          ;;
          ;; harvest with reduced probability, since we're already over catch
          ;;
          let prob-harvest (1 / (( (total-catch + crabs-this-catch) / sd-catch-size) ^ 1))
          if (prob-harvest > (random-float 1.0)) [
            set population-size (population-size - crabs-this-catch)
            set total-catch (total-catch + crabs-this-catch)
          ]
        ]
      ]
    ]
    set catch-size (catch-size + total-catch)
  ]
end

;; --------------------------------------------------------------
;; fishermen-harvest-spatial
;;
;; define fishermen harvesting of crabs, subject to spatial
;; harvesting constraints.  If fishing is allowed, then
;; harvesting is conducted within a specified radius.  If fishing
;; is not allowed, it means that the vessel has sailed into a
;; restricted area and can not harvest in this area.
;;
;; --------------------------------------------------------------
to fishermen-harvest-spatial

  ;;
  ;; check to see if fishing is allowed here
  ;;
  let fishing-allowed-here true
  let location patch-here
  ask location [
    set fishing-allowed-here fishing-allowed
  ]

  ;;
  ;; proceed to fish if allowed at this location
  ;;
  if (fishing-allowed-here = true) [
    ;let CATCH-RADIUS random 4 + 1
    let CATCH-RADIUS 1
    fishermen-harvest CATCH-RADIUS
  ]
end

;; --------------------------------------------------------------
;; fishermen-sell
;;
;; define economics of selling crabs.  Fishermen compute their
;; gross profit, gross expenses, and determine their net return.
;; the net return is subject to basic taxation.  The final
;; after tax return is added (subtracted) to the fisherman's
;; cumulative wealth.
;;
;; --------------------------------------------------------------
to fishermen-sell
  let SALES_INTERVAL 1

  if ((ticks > 0) and ((ticks mod SALES_INTERVAL) = 0)) [

    ;;
    ;; optional future work:
    ;; do this if you are using a dynamic market price
    ;; based on current and previous catch sizes.  market price
    ;; can fluctuate based on ratio of current fleet catch
    ;; with previous fleet catch, simulating changes in the
    ;; supply side of the market
    ;;
    ;; let market-price ((sum [catch-size] of fishermen) / total-catch-size)
    ;;

    ;;
    ;; compute individual fisherman results
    ;;
    let market-price market-price-per-unit
    ask fishermen [
      let gross-profit (catch-size * market-price)
      let gross-expenses (catch-size * production-cost-per-unit)
      let net-return (gross-profit - gross-expenses)
      let after-tax-return (net-return * (1.0 - base-tax))

      set wealth (wealth + after-tax-return - (random operating-expense))
    ]
  ]
end

;; --------------------------------------------------------------
;; fishermen-pay-excess-catch-tax
;;
;;
;; fishermen have to pay a high tax for any catch
;; over the average catch size for the period.  This is only
;; the case if the excess-tax value is set to > 0.0
;;
;; --------------------------------------------------------------
to fishermen-pay-excess-catch-tax

  ;; determine how frequently fishermen sell their catch
  ;; default is every tick (~ 6 months in simulated time).
  let SALES_INTERVAL 1

  ;;
  ;; is excess-tax policy being used?
  ;;
  if (extra-tax > 0) [
    if ((ticks > 0) and ((ticks mod SALES_INTERVAL) = 0)) [

      let mean-catch-size mean [catch-size] of fishermen
      let sd-catch-size sqrt (variance [catch-size] of fishermen)

      ;;
      ;; compute individual fisherman taxation on excess catch
      ;;
      ask fishermen [
        let excess-catch-size (catch-size - mean-catch-size)
        if (excess-catch-size > 0) [
          let excess-tax-factor (excess-catch-size / sd-catch-size )
          let excess-catch-tax (excess-catch-size * excess-tax-factor)
          set wealth (wealth - excess-catch-tax)
        ]
      ]
    ]
  ]
end


;; =============================================================
;;
;; Plot functions
;;
;; =============================================================


;; --------------------------------------------------------------
;; setup plot
;;
;; setup the plot. This currently doesn't do anything, but
;; is put here in case special plot setup is needed later,
;; such as setting ranges or other configurations.
;;
;; --------------------------------------------------------------
to setup-plot
  ;;set-current-plot "crab-population"
  ;;set-plot-y-range 0 number
end

;; --------------------------------------------------------------
;; setup-histogram
;;
;; set up the histogram of fisherman wealth categories
;;
;; --------------------------------------------------------------
to setup-histogram
  set-current-plot "fisherman-wealth"
  set-plot-x-range 0 10
  set-plot-y-range 0 100
  set-histogram-num-bars 10
end

;; --------------------------------------------------------------
;; do-plot
;;
;; update the plots.
;; crab-population:  plot of current crab population
;; total-catch:      plot of total crab harvest
;; fisherman-wealth: plot of fisherman accumulated wealth
;;
;; --------------------------------------------------------------
to do-plot
  set-current-plot "crab-population"

  set-current-plot-pen "crabs"
  plot sum [population-size] of crabs

  set-current-plot "annual-catch"
  set-current-plot-pen "catch"
  ;plot total-catch-size
  plot annual-catch-size

  set-current-plot "fisherman-wealth"
  set-current-plot-pen "wealth"
  ;;plot mean [log wealth 10] of fishermen
  ifelse ((count fishermen) > 0)
  [plot mean [wealth] of fishermen]
  [plot 0]
end

;; --------------------------------------------------------------
;; do-histogram
;;
;; update the histogram
;;
;; --------------------------------------------------------------
to do-histogram
  set-current-plot "wealth-groups"
  set-current-plot-pen "wealth"
  histogram [log wealth 10] of fishermen
end
@#$#@#$#@
GRAPHICS-WINDOW
210
10
647
448
-1
-1
13.0
1
10
1
1
1
0
1
1
1
-16
16
-16
16
0
0
1
ticks
30.0

BUTTON
8
15
71
48
NIL
setup
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

BUTTON
77
16
140
49
NIL
go
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

PLOT
654
12
814
132
crab-population
time
size
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"crabs" 1.0 0 -11221820 true "" ""

SLIDER
8
136
189
169
growth-rate
growth-rate
0.0
1.0
0.07
0.01
1
NIL
HORIZONTAL

BUTTON
144
16
207
49
step
step
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

SLIDER
8
210
191
243
num-vessels
num-vessels
0
500
120.0
10
1
NIL
HORIZONTAL

SLIDER
8
174
189
207
carrying-capacity
carrying-capacity
0
1000000
790000.0
10000
1
NIL
HORIZONTAL

SLIDER
9
247
190
280
catchability-rate
catchability-rate
0
1.0
0.15
0.01
1
NIL
HORIZONTAL

SLIDER
7
59
135
92
num-pods
num-pods
0
10000
400.0
100
1
NIL
HORIZONTAL

SLIDER
7
97
134
130
pod-size
pod-size
0
250000
20000.0
10000
1
crabs
HORIZONTAL

MONITOR
652
137
814
182
total crab population
total-population-size
0
1
11

MONITOR
655
299
786
344
total catch size
total-catch-size
0
1
11

SLIDER
10
349
192
382
market-price-per-unit
market-price-per-unit
0
10
3.3
0.10
1
NIL
HORIZONTAL

SLIDER
10
386
193
419
production-cost-per-unit
production-cost-per-unit
0
10
2.4
0.10
1
NIL
HORIZONTAL

SLIDER
9
427
101
460
base-tax
base-tax
0
4.0
0.2
0.05
1
NIL
HORIZONTAL

MONITOR
740
186
828
231
mean pod size
mean-pod-size
2
1
11

MONITOR
657
411
778
456
mean fisherman wealth
mean-fisherman-wealth
2
1
11

MONITOR
653
186
740
231
num active pods
num-active-pods
0
1
11

MONITOR
655
250
788
295
num active fishermen
num-active-fishermen
0
1
11

PLOT
839
139
999
259
wealth-groups
income category
log(wealth)
0.0
10.0
0.0
100.0
true
false
"" ""
PENS
"wealth" 1.0 1 -10899396 true "" ""

SWITCH
10
299
191
332
spatial-restriction
spatial-restriction
1
1
-1000

MONITOR
932
413
989
458
Year
current-year
0
1
11

PLOT
838
12
998
132
annual-catch
time
size
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"catch" 1.0 0 -2674135 true "" ""

PLOT
838
269
998
389
fisherman-wealth
NIL
NIL
0.0
10.0
0.0
10.0
true
false
"" ""
PENS
"wealth" 1.0 0 -10899396 true "" ""

MONITOR
790
412
863
457
percent catch
(sum [catch-size] of fishermen) / (total-population-size + 1)
2
1
11

MONITOR
136
75
208
120
total-pop
num-pods * pod-size
0
1
11

MONITOR
870
413
927
458
F
(total-catch-size) / ((1.0 + growth-rate) * total-population-size)
2
1
11

SLIDER
103
427
195
460
extra-tax
extra-tax
0
1.0
0.15
0.05
1
NIL
HORIZONTAL

MONITOR
656
347
784
392
annual catch size
annual-catch-size
0
1
11

@#$#@#$#@
## WHAT IS IT?

This model is used to explore population dynamics and harvest economics of the Blue Crab in the Chesapeake Bay

## HOW IT WORKS

The model uses two main classes of agents: crabs and fishermen.  Crab agents represent a group of crabs (called a "pod").  Fishermen agents represent a single fisherman on a vessel.

The model simulates 1982 to 1999 in order to compare with published crab harvest data.  Each tick represents 6 months of real time.  Crabs move and reproduce during the summer/fall seasons, and do not move or reproduce during the winter/spring seasons.

The model includes three types of scenarios.  The first scenario is the "default" scenario, in which fisherman may sail anywhere in the waterscape and harvest without any restrictions.  The second scenario implements a spatial restriction, such that fishermen are not allowed to harvest in certain geographic areas.  The third scenario implements a tax-based harvest limiting policy, in which fishermen are heavily taxed for harvesting more than the average catch taken by the fishing fleet each period.

The model begins by defining constants and the initial waterscape, establishing the crab populations, and placing the fishermen.  The main "go" method for the model alternates between actions for the crab and fishermen populations. The crabs move (in the summer/fall season only), then breed once per year (again in the summer/fall season). The fishermen move, harvest, sell their catch, pay taxes, accumulate wealth, and potentially pay additional taxes if they overfish.

## HOW TO USE IT

There are a number of parameter settings on the model.

num-pods:
controls the number of pods of crabs in the simulation.

pod-size:
controls the number of crabs in each pod in the simulation.
The total initial crab population is defined by the product of num-pods * pod-size.  Typical estimated values for the Chesapeake Bay crab population vary, however, figures of from 230 to 870 million are plausible.

growth-rate:
controls the reproductive efficiency of the crab populations.  Typical values range from 3% to 15% or more.

carrying-capacity:
controls the maximum number of crabs in a pod. In population biology,
the carrying capacity K is a function of the geographic region in which the population resides, and reflects the influcences of habitat suitability.  In this model, K is stylized to represent the maximum size a crab pod can obtain, even though crab pods move from place to place.  The relationship  between carrying-capacity and pod-size is important: as pod-size approaches carrying-capacity, the rate of growth for the pod declines.  If pod-size is greater than carrying capacity, the the rate of growth becomes negative and the population declines until it reaches the carrying capacity value.  In the simulation, changing the carrying-capacity value then indirectly governs the regeneration rate of the crab population.

num-vessels:
controls the size of the fishing fleet.  Each vessel is assumed to be independent and represents one fisherman.

catchability-rate:
controls the efficiency of the fishing operation.  This value is used to represent the ability of the fleet to harvest the target species.  It includes the effectiveness of the fishing equipment as well as the ability of the species to avoid being captured.  Typical values for crab fishing are about 17%.

spatial-restriction:
This toggle is used to enable and disable the use of spatial restrictions on crab fishing.  If disabled, vessels may sail anywhere in the waterscape and fish at will.  If enabled, large sections of the waterscape are "off limits" for fishing, and vessels sailing in these regions are not allowed to fish.  The effect of this is to limit the fishing pressure on the crabs.

market-price-per-unit:
arbitrary value used to express the market price for crabs.  This is not intended to be aligned with any particular currency, but rather is used as a stylized measurement of the economic value of a harvested crab.

production-cost-per-unit:
arbitrary value used to represent production costs associated with harvesting crabs.  This is not intended to be aligned with any particular currency, but rather is used as a stylized measurement of the economic cost associated with harvesting a crab.

base-tax:
arbitrary amount by which the entire catch is taxed.  This is roughly equivalent to a "sales tax" except that it is paid by the fisherman rather than the buyer.  The intent is to represent state-sponsored taxation of crab fishing as an economic tool to regulate harvesting.

extra-tax:
arbitrary amount by which harvests in excess of the mean harvest are taxed. Under this method, if the extra-tax is 0, then excess harvesting is not taxed.  However, if the extra-tax is > 0, then each fisherman's harvest is compared to the average catch size for the fleet, and any amount in excess of the average is taxed using a graduated scale of (base-tax * sd), where sd is the number of standard deviations above the mean for the excessive catch size. Thus, fishermen are incentivized to limit catches that would put them over the mean catch size, as this would result in negative utility even though they are harvesting more crabs.



## THINGS TO NOTICE

The base scenario is sensitive to the relationship between pod-size and carrying-capacity.

Note the differences in population dynamics when the spatial restrictions are used and not used, even with all other things being equal.

## THINGS TO TRY

1. Try changing the pod-size and num-pods to alter the population size.
2. Try changing the number of vessels in the fleet or the catchability-rate
3. Try altering the base-tax and extra-tax rates to see the effect on harvesting

## EXTENDING THE MODEL

The crab population model is very simple now, and does not account for variations in age in the population. This is important for crab biology, as only mature 3 year old females can reproduce.  In addition, most harvesting is limited to 2 or 3 year old crabs (the actual restrictions are usually based on carapice size).

The crab movement model is very simple, and does not reflect geographically realistic migration patterns. These could be incorporated to more accurately show the spatial location of crabs at different times of the year.

The model uses a stylized landscape. A more explict model could use a better representation of the Chesapeake Bay geography.

The economic model is very simple. More advanced models could be implemented, such as using subsidies for under-harvesting, for example.

## NETLOGO FEATURES

No particularly unusual NetLogo features were used.

## RELATED MODELS

Some related models in the Biology library may be of interest.  The Wolf Sheep predation and the Rabbits Grass Weeds models are good demonstrations of population dynamics involving harvest and competition.

## CREDITS AND REFERENCES

An excellent reference on the mathematics of sustainable fisheries harvesting is:

Clark, Colin.  Mathematical Bioeconomics: The Optimal Management of Renewable Resources. John Wiley and Sons,  New York, NY.  1990.
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