;; Most of the global variables are to calculate/track/contain output stats
globals [artifact_count sample_size positives negatives percentage_found percentage_positive extrapolated_count dif num_patches
  tot_artifacts gridx gridy num_dense_patches mean_density mean_density_sd calculated_density calculated_density_sd density_dif ]
;; artifact_count = total number of artifacts recovered in all survey patches
;; sample_size = total number of survey patches
;; positives = number of survey patches with at least one artifact turtle
;; negatives = number of survey patches with no artifact turtles
;; percentage_found = percentage of the total number of artifacts found by survey
;; percentage_positive = positivity rate of the survey sample
;; extrapolated_count = extrapolated total number of artifacts based on the number recovered in survey and sample suze
;; dif = difference between true total number of artifacts and extrapolated count
;; num_patches = total number of patches in the world
;; tot_artifacts = true total number of artifact turtles
;; gridx = value of the x dimension of a systematic survey grid
;; gridy = value of the y dimension of a systematic survey grid
;; num_dense_patches = number of survey patches with artifact turtles above density threshold
;; mean_density = true average density of artifacts in the whole world
;; mean_density_sd = standard deviation of true artifact density
;; calculated_density = mean density of artifacts derived from the survey sample
;; calculated_density_sd = standard deviation of survey artifact density
;; density_dif = difference between true mean density and survey calculated density

breed [artifacts artifact] ;; artifacts are the only breed of turtle, represented as small black triangles
patches-own [ num_arts ] ;; patches are survey grids, which can contain a count of artifact turtles that fall within them

to reset_all
  ;; blank out everything and start fresh
  clear-all
  ask patches [ set pcolor brown ]
  set_header
  reset-ticks
end

to set_header
  ;; sets the header row of the output stats text window
  ;; header formatted for easy import to spreadsheet or R/Pandas
  output-type "% landscape sampled,# survey patches,# positive survey patches,# negative survey patches,# dense survey patches,% positive survey patches,# artifacts found,% artifacts found,extrapolated # artifacts,actual # artifacts,count difference,sampled density,sampled density sd,actual density,actual density sd,density difference,grid x,grid y,x offset,y offset"
  output-print ""
end

to setup_artifacts
  ;; places specified number of artifact turtles randomly or in random clusters
  ifelse artifact_clustering = 0 [
    crt num_artifacts [ setxy random-xcor random-ycor ]
  ] [
     ask n-of artifact_clustering patches
     [
     ;; total number of artifacts in clusters must be even
     sprout ( num_artifacts / artifact_clustering )
        [
        set xcor xcor + random-float cluster_x
        set ycor ycor + random-float cluster_y
        ]
     ]
  ]
  ask turtles [ set shape "default" set size 0.6 set color black] ;; black arrows sort of look like projectile points :)
end

to shuffle_artifacts
  ;; use a random walk to shuffle the initial position of artifacts
  ;; does not create new artifacts, but moves their position
  ;; helps alter the shape/density of initial artifact clusters
  ask turtles [ rt random 360 forward 1 ]
  tick
  if ticks >= 20 [ reset-ticks stop ]
end

to delete_artifacts
  ;; sometimes we just want the artifacts gone, but keep the survey patches
  clear-turtles
end

to countup
  ;; counts total artifacts and planned survey patches and calcualtes total density of artifacts in world
  set tot_artifacts count turtles ;; count total number of artifacts
  set num_patches count patches with [ pcolor = blue ] ;; count number of survey patches
  set sample_size ( num_patches / (count patches) ) * 100 ;; calculate the survey coverage proporation
  ask patches [ set num_arts count turtles-here ] ;; count artifacts in each patch
  set mean_density mean [ num_arts ] of patches ;; calculate true mean density of artifacts
end

to hide_some_artifacts
  ;; make some turtles invisible (e.g., to simulate a surface scatter above a subsurface assemblage)
  ask turtles [ set color black ]
  ask n-of (count turtles * proportion_hid) turtles [ set color brown ]
end

to show_artifacts
  ;; Make all turtles visible again
  ask turtles [ set color black ]
end

to random_patches
  ;; set up a random survey sampling frame
  ask n-of n patches [
   set pcolor blue
  ]
end

to systematic_patches
  ;; set up systematic survey grid sampling frame. Constrain the grid to a square shape if asked.
  ifelse square_grid = True [
  set gridx grid_x
  set gridy grid_x
  ] [
  set gridx grid_x
  set gridy grid_y
  ]
  ask patches with [pxcor mod gridx = x_offset and pycor mod gridy = y_offset] [ set pcolor blue ]
end

to judgemental_patches
  ;; while this button is latched, user can click any patch to turn it blue
  ;; judgemental survey uses their existing knowledge to place survey patches
  if mouse-down?
    [ask patch mouse-xcor mouse-ycor
        [ set pcolor blue]
  ]
  display
end

to iterate
  ;; this is the iterative routine, so it will reset patches each time
  delete_patches
  ;; find out what type of sampling system to use
  if iterate_random = True [
    ifelse random_n = False
    [ random_patches ] [ ask n-of ( random n + 1 ) patches [ set pcolor blue ] ]
    ]
  ifelse iterate_grid_size = True [ ;; grid dimensions random within limits set by sliders
    set gridx random grid_x + 1
    set gridy random grid_y + 1
    ] [
    set gridx grid_x
    set gridy grid_y
    ]
  if iterate_grid_offset = True [ ;; grid offsets within limits set by sliders
    set x_offset random gridx
    set y_offset random gridy
    ]
  if square_grid = True [set gridy gridx] ;; Keep our grid square if asked
  if iterate_grid_size = True or iterate_grid_offset = True [
    ask patches with [pxcor mod gridx = x_offset and pycor mod gridy = y_offset] [ set pcolor blue ]
    ]
  countup
  get_results
  tick
  if ticks >= iterations [ stop ] ;; stopping rule
end

to step
  ;; this is the same as the "iterate" method, but works stepwise with each click
  delete_patches
  if iterate_random = True [
    ifelse random_n = False
    [ random_patches ] [ ask n-of ( random n + 1 ) patches [ set pcolor blue ] ]
    ]
  ifelse iterate_grid_size = True [ ;; grid dimensions random within limits set by sliders
    set gridx random grid_x + 1
    set gridy random grid_y + 1
    ] [
    set gridx grid_x
    set gridy grid_y
    ]
  if iterate_grid_offset = True [ ;; grid offsets within limits set by sliders
    set x_offset random gridx
    set y_offset random gridy
    ]
  if square_grid = True [set gridy gridx] ;; Keep our grid square if asked
  if iterate_grid_size = True or iterate_grid_offset = True [
    ask patches with [pxcor mod gridx = x_offset and pycor mod gridy = y_offset] [ set pcolor blue ]
    ]
  countup
  get_results
  tick-advance 1 ;; step forward one
end

to delete_patches
  ;; remove current set of survey patches so you can design a new survey but keep same artifact dist'n
  ask patches [ set pcolor brown ]
end

to reset_patches
  ;; clear the results of a past survey while retaining the same set of survey patches
  ;; you can then clear artifacts and use the same sampling frame with a new artifact dist'n
  ask patches [
    if pcolor = green
        [ set pcolor blue]
    if pcolor = cyan
        [ set pcolor blue]
    if pcolor = red
        [ set pcolor blue]
    ]
end

to get_results
  ;; calculate all statitistics for output windows
  set num_patches count patches with [ pcolor = blue ] ;; number of survey patches
  ask patches [ set num_arts count turtles-here ] ;; count artifacts in each patch
  set artifact_count sum [ num_arts ] of patches with [ pcolor = blue ] ;; count all artifacts found in survey patches
  carefully [ set calculated_density mean [ num_arts ] of patches with [ pcolor = blue ] ] [set calculated_density 0] ;; calcualte mean density of artifacts in survey patches
  carefully [ set calculated_density_sd standard-deviation [ num_arts ] of patches with [ pcolor = blue ] ] [ set calculated_density_sd 0 ] ;; calculate standard deviation of densisty in survey patches
  set tot_artifacts count turtles ;; calculate true total number of artifacts
  set mean_density mean [ num_arts ] of patches ;; calcualte true mean density of artifacts
  set mean_density_sd standard-deviation [ num_arts ] of patches ;; calculate true standard deviation of desnity of artifacts
    ask patches [
      if (pcolor = blue) and (any? turtles-here) ;; graphical show positive and negative survey patches
        [ set pcolor green]
      if pcolor = blue
        [ set pcolor red]
      ]
  set positives count patches with [ pcolor = green ] ;; count # positive survey patches
  set negatives count patches with [ pcolor = red ] ;;  count # negative survey patches
  ask patches with [ pcolor = green ] [
    if count turtles-here >= density_thresh ;; graphical show patches with dense artifacts
    [ set pcolor cyan ]
  ]
  set num_dense_patches count patches with [ pcolor = cyan ] ;; count # of dense patches
  set sample_size ( (positives + negatives) / (count patches) ) * 100 ;; calculate the survey coverage proporation
  carefully [ set percentage_found ( artifact_count / tot_artifacts ) * 100 ] [ set percentage_found 0 ] ;; calculate the proportion of recovered artifacts
  carefully [ set percentage_positive ( positives / ( positives + negatives ) ) * 100 ] [ set percentage_positive 0 ] ;; calculate the survey positivity rate
  carefully [ set extrapolated_count ( artifact_count / (sample_size / 100) ) ] [ set extrapolated_count 0 ] ;; calculate the extrapolated artifact count from the sampled population
  set dif extrapolated_count - tot_artifacts ;; difference of extrapolated to real total count
  set density_dif calculated_density - mean_density ;; difference of estimated to real mean density
  ;; write these stats to output variables
  output-type precision sample_size 3
  output-type ","
  output-type num_patches
  output-type ","
  output-type positives
  output-type ","
  output-type negatives
  output-type ","
  output-type num_dense_patches
  output-type ","
  output-type precision percentage_positive 3
  output-type ","
  output-type artifact_count
  output-type ","
  output-type precision percentage_found 3
  output-type ","
  output-type precision extrapolated_count 3
  output-type ","
  output-type tot_artifacts
  output-type ","
  output-type precision dif 3
  output-type ","
  output-type precision calculated_density 3
  output-type ","
  output-type precision calculated_density_sd 3
  output-type ","
  output-type precision mean_density 3
  output-type ","
  output-type precision mean_density_sd 3
  output-type ","
  output-type precision density_dif 3
  output-type ","
  output-type gridx
  output-type ","
  output-type gridy
  output-type ","
  output-type x_offset
  output-type ","
  output-type y_offset
  output-print ""
end
@#$#@#$#@
GRAPHICS-WINDOW
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1
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ticks
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BUTTON
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1) Setup Artifact Distribution
setup_artifacts
NIL
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T
OBSERVER
NIL
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NIL
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1

BUTTON
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280
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2a) Select n random survey patches
random_patches
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OBSERVER
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NIL
1

BUTTON
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355
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388
2b) Setup a systematic grid of survey patches
systematic_patches
NIL
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

BUTTON
35
430
293
463
2c) Interactively select survey patches
judgemental_patches
T
1
T
OBSERVER
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NIL
NIL
1

SLIDER
295
280
585
313
n
n
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2500
110.0
1
1
NIL
HORIZONTAL

TEXTBOX
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325
89
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or...
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15.0
1

TEXTBOX
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407
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425
or...
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BUTTON
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3) Display Results!
get_results
NIL
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T
OBSERVER
NIL
NIL
NIL
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1

SLIDER
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artifact_clustering
artifact_clustering
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15.0
1
1
NIL
HORIZONTAL

MONITOR
30
625
210
670
# of artifacts discovered
artifact_count
17
1
11

MONITOR
30
675
210
720
# of postive survey patches
positives
17
1
11

MONITOR
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725
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# of negative survey patches
negatives
17
1
11

TEXTBOX
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465
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Don't forget to \"unclick\" this button!
11
0.0
1

MONITOR
215
625
395
670
% of all artifacts discovered
percentage_found
2
1
11

MONITOR
215
675
440
720
Positivity rate (% of survey patches)
percentage_positive
2
1
11

MONITOR
215
725
440
770
Extrapolated number of artifacts
extrapolated_count
0
1
11

MONITOR
215
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395
620
Sample size (% of landscape)
sample_size
2
1
11

BUTTON
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585
183
Hide some artifacts
hide_some_artifacts
NIL
1
T
OBSERVER
NIL
NIL
NIL
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1

BUTTON
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Show artifacts
show_artifacts
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T
OBSERVER
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NIL
1

SLIDER
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proportion_hid
proportion_hid
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1.0
0.05
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NIL
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SLIDER
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grid_x
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10.0
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1
NIL
HORIZONTAL

BUTTON
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Count survey patches/artifacts
countup
NIL
1
T
OBSERVER
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NIL
NIL
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1

MONITOR
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# of survey patches
num_patches
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BUTTON
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Reset survey patches
reset_patches
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T
OBSERVER
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NIL
NIL
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1

TEXTBOX
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610
58
READ THE \"MODEL INFO\" TAB FOR INSTRUCTIONS ON HOW TO USE THIS MODEL.
15
15.0
1

TEXTBOX
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577
Total number of landscape patches is 2500.
10
0.0
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BUTTON
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Clear artifact distribution
delete_artifacts
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1
T
OBSERVER
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1

BUTTON
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111
Start/Reset Experiment
reset_all
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OBSERVER
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MONITOR
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535
# of artifacts
tot_artifacts
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MONITOR
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605
770
Count difference
dif
0
1
11

OUTPUT
22
789
1338
863
12

TEXTBOX
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133
Click this first!
14
105.0
1

SLIDER
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cluster_x
cluster_x
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5.0
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1
NIL
HORIZONTAL

SLIDER
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cluster_y
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SLIDER
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grid_y
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SLIDER
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x_offset
x_offset
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SLIDER
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y_offset
y_offset
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SWITCH
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1565
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iterate_random
iterate_random
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1
-1000

SWITCH
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iterate_grid_size
iterate_grid_size
1
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-1000

INPUTBOX
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iterations
1000.0
1
0
Number

SWITCH
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iterate_grid_offset
iterate_grid_offset
1
1
-1000

BUTTON
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Iterate!
iterate
T
1
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OBSERVER
NIL
NIL
NIL
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TEXTBOX
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For iterative use, see the other side of the canvas --->
12
0.0
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TEXTBOX
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To save out your results to a file, right click on this output window, and select \"export.\"
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TEXTBOX
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Remember to click the \"Start/Reset Experiment\" button first!!
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TEXTBOX
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Offsets should be less than grid spacing.
10
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TEXTBOX
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Note that these switches are not mutually exclusive!
12
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1

BUTTON
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Reset iterations!
reset-ticks\ndelete_patches\nclear-output\nset_header
NIL
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OBSERVER
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BUTTON
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Clear output window
clear-output\nset_header
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OBSERVER
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BUTTON
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Step
step
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OBSERVER
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INPUTBOX
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density_thresh
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MONITOR
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# dense patches
num_dense_patches
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1
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BUTTON
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Clear survey patches
delete_patches
NIL
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OBSERVER
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NIL
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SWITCH
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1565
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random_n
random_n
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INPUTBOX
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num_artifacts
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1
0
Number

MONITOR
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Actual density
mean_density
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MONITOR
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Calculated density (#/patch)
calculated_density
2
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MONITOR
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Density difference
density_dif
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1
11

TEXTBOX
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The Archaeological Sampling Experimental Laboratory
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SWITCH
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square_grid
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-1000

TEXTBOX
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Only grid_x used when this is on
10
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BUTTON
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Shuffle Artifacts
shuffle_artifacts\n
T
1
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OBSERVER
NIL
NIL
NIL
NIL
1

@#$#@#$#@
## WHAT IS IT?
The Archaeological Sampling Experimental Laboratory (tASEL) is an interactive tool for setting up and conducting experiments about sampling strategies for archaeological excavation, survey, and prospection. Banning’s (2021) American Antiquity article, “Sampled to Death? The Rise and Fall of Probability Sampling in Archaeology,” points out that archaeologists typically do not consider probability theory at all when determining a sampling frame. Sampling is considered necessary, but almost always is done as a matter of routine and convenience (i.e., we do what we know, and what is easy). This means that most of the time either, a) we have spent a lot of valuable time and resources to cover larger areas than we needed to cover, or, b) our samples are skewed, biased, and almost certainly statistically insignificant. In short, when a less than “full coverage” sampling frame has been used, much of what we think we have learned about the spatial patterning of archaeological artifacts or sites is likely to be wrong. This has contributed greatly to the prevailing feeling that the only “proper” sampling strategy is “full coverage,” and that any probability-informed sampling strategy is too time-consuming to undertake. 
The tASEL model is designed to combat these issues by meeting archaeologists where they are at. Rather than trying to convince people to run through a series of seemingly arcane probability equations, tASEL gives them an interactive graphical interface with both visual and statistical output. It can be used in a simple manual way, or automated for robust experimentation. Because of this flexible interface, tASEL can be used a teaching tool and as a research and planning tool. The overall goal is to increase “sampling literacy” in the world of archaeology, so that we can be producing the most robust datasets possible within the limited set of resources that are typically available to most archaeologists.
tASEL is meant to be intuitive and flexible. There are two ways to use this model: “Manual” mode or “Iterative” mode. Manual mode is useful for simple experiential experimentation, teaching and learning, or when setting up a more complex set of experiments. You can get a quick initial sense of the comparative utility of different potential sampling frames for different types of artifact distributions. Iterative mode, on the other hand, allows the deployment of an iterative sampling experiment that can provide robust statistical quantification of the performance of different sampling frames with different artifact distributions. It can also help you to understand and quantify the expected error of any specific style of sampling with different types of artifact distributions.
tASEL produces both graphical and numeric output. Simple color codes are used to display the spatial patterning of experiment results in the world display. This means that the spatial aspects of sampling choices can be assessed visually at the end of any sampling experiment. Numerical results are displayed individually in specific, well-labeled output areas, as well as amalgamated into a CSV-formatted text area at the bottom of the interface. For single, informal “manual runs,” the graphical patterns and basic numerical data are easy to assess at a quick glance. When more complex experiments are designed, including in “iterative” mode, the formatted numerical results capture enough information to be displayed in a variety of informative plots via third-party statistical software (e.g., a basic spreadsheet program, R or Pandas).

## HOW IT WORKS

You first seed a simple "landscape" with a random, clustered, or a mixed distribution of "artifacts" (but these could be sites or anything else in practice). You then create a sampling frame with set of sampling patches either by randomly distributing them, uniformly laying out on a grid or transect, or by judgmentally placing them by clicking on the map. You can combine techniques for a "stratified" or "mixed" approach as well. Finally, the program will then count up the number of "artifacts" that were detected, calculate the sample positivity rate, sample density, and the statistically extrapolated estimate of the total number of "artifacts" that would be predicted from the sample (among other measures). A "good" sampling strategy for a given distribution of artifacts would predict an extrapolated count that closely matches the actual total number of artifacts that were seeded across the landscape.

The landscape consists of a 50 x 50 grid of survey patches (2500 total landscape patches). The simulated survey landscape is scale-free, so there is no specific spatial scale to the patches. It may, however, be useful to imagine the landscape at a familiar scale, such as a series of 1x1 meter grid squares, to help you visualize these results in a "real world" context.

## HOW TO USE IT

There are two ways to use this model: 1) "Manual" mode, or 2) "Iterative" mode. Manual mode is useful for simple experiental experimentation, teaching and learning, or when setting up a more complex set of experiments. You can get a quick inital sense of the comparative utility of different potential sampling frames for different types of artifact distributions. Iterative mode, on the other hand, allows the deployment of an iterative sampling experiment that can provide robust statistical quantification of the performance of different sampling frames with different artifact distributions. It can also help you to understand and quantify the expected error of any specific style of sampling with different types of artifact distributions. Workflows for both modes are explained here.

For either Manual or Iterative operation of the model, you must first click the *Start/Reset Experiment* button to set up a blank landscape before conducting any experimentation. Note that this button can also be used to clear all existing distributions, sampling frames, and results once you've started using the model.

### Manual Mode

All of the tools for Manual Mode appear to the left side of landscape window (i.e., the "world" display in NetLogo terminology).

For manual experimentation, you must first set up the artifact distribution using the *Setup artifact distribution* button in conjunction with a series of parameters related to the type of distribution you desire. The *num_artifacts* sets the total number of artifacts, and the *artifact_clustering* slider sets up the way they are distributed across the landscape. If *artifact_clustering* is set to 0, then a true Gaussian random distribution of artifacts is used. If set to 1 or higher, then artifacts are randomly distributed within neighborhoods around a set of cluster centers. The number of cluster centers is the same as the value set by *artifact_clustering* (i.e., *artifact_cluster* of 5 will make 5 clusters, etc.). The size and shape of the cluster neighborhoods are determined with the "cluster_x" and "cluster_y" sliders in number of cells per dimension. Use the *Setup Artifact Distribution* button to place the artifacts. Clusters are initially created within square areas. You can create more natural shapes to the clusters using the *Shuffle artifacts* button. This button activates a 20-tick "random walk" for all artifacts, which effectively "jitters" their location within a 20-cell radius. This button could be used more than once if necessary.

Note that you can change the artifact distribution settings and click the *Setup artifact distribution* button again to superimpose different distributions. This is useful, for example, to create mixed random background scatter with clusters of artifacts. You can click the *Clear artifact distribution* to erase any previous distributions. Note that for some values of *artifact_clustering*, the actual number of artifacts may be automatically adjusted to evenly divide artifacts across clusters. To display the actual count of seeded artifacts, you can at any time click the *Count Survey Patches/Artifacts* button. 

At this stage, you can choose to save out your artifact distribution so that you can load it in at another stage (e.g., in order to repeat your experiments again). To do so, go to the File menu in NetLogo, and choose *Export > Export World...*. Give a descriptive name for the output .csv file so that you will know what kind of distribution is in it. Note that this also exports the current state of any sliders or switches, so ensure that all of those are set to a neutral or otherwise desired position to avoid future mistakes. To reimport the distribution, go to the File menu and choose *Import > Import World...*, and choose the file you exported previously. 

Once the artifacts are distributed, you can optionally use the *hide some artifacts* button in conjunction with the *proportion_hid* slider to hid a portion of the artifacts from view. This would allow you to, for example,use the distribution of a small proportion of "surface" artifacts when planning a "shovel test" grid, which will then be used to prospect for buried artifacts as well. You could even choose to hide all artifacts, and then layout a grid with no a priori knowledge of artifact locations at all. It is, therefore, a useful tool for limiting the impact of bias when setting up your survey patches.

Next you will need to set up your survey patches. There are three tools that you can use for this, and they can be used separately or in any combination. As you add survey patches, they will turn blue on the map.

The *Select n random survey patches* tool works in conjunction with the *n* slider to randomly distribute some number of survey patches around the landscape. 

The *Setup a systematic grid of survey patches* button is used in conjunction with four other sliders to create an evenly distributed sampling grid with survey patches at the grid intersections. The value of *grid_x* is the number of patches between each survey patch in the x direction, and the value of "grid_y" is the number of patches between each survey patch in the y direction. The *x_offset* and *y_offset* sliders set the distance (in # of patches) of the lower left survey patch from the lower left corner of the landscape. It is important the values for x and y offsets be lower than the values for the grid x and y dimensions, respectively. These four sliders can be used together to position your survey grid very precisely.

The *Interactively select survey patches* button is used to interactively click on patches on the map to select them as survey patches. This can be used to create a "judgemental" sampling strategy, where you use your prior knowledge to choose the location of each sampling patch. This button is a "latching" button, so you must "unclick" it once you've finished your selection of judemental survey patches.

Once you have selected your patches, you can optionally click the *Count survey patches/artifact* button to quickly count the number of survey patches you've created. This is useful if you need to constrain the number of patches for your experiment (e.g., you are limited by time or budget to a set maximum number of survey patches). You can also use the *Reset survey patches* button to return all survey patches to a blank (blue) state. This is useful if you want to use the same survey sampling frame with a new artifact distribution. Alternatively, you can use the *Clear survey patches* to delete your current set of surve patches so that you can design a new one. This is useful if you've made a mistake, gone over your survey patch limit, or if you want to keep the same artifact distribution, but test different survey patch arrangements.

Once your artifact distribution and survey patches are set up, you can use the *Display Results!* button to quickly calculate a series of summary statistics and to change the color of the positive survey patches to green, and negative patches to red. There is one variable that you can set in this area, which is the *density_thresh* variable. The value you enter here will determine which survey patches are thought to be in a dense area of artifacts. If the count within a positive survey patch is greater than or equal to *density_thresh*, then the color of that patch will turn to cyan, and the total number of positive patches in "dense" areas will be counted.

### Iterative Mode

The additional tools for Iterative Mode are on the right side of landscape window. There are three buttons, one text entry box, and five switches. You must first create or load in an existing artifact distribution. You can create a new distribution as described in Manual Mode above, and you can save and reload an existing distribution with the Export World and Import World options in the File menu as described above. 

To run an experiment, use the Manual Mode sliders to parameterize a random or a systematic sampling frames as described in Manual Mode, and then use the switches to turn on various aspects of the iterative sampling procedure. The *iterate_random* switch will create a series of random sampling surveys with *n* survey patches. The *iterate_grid_size* switch will create a series of systematic grid-based sampling surveys where the x and y spacing of the sampling grid will vary randomly between 0 and the values set by *grid_x* and *grid_y*. The *iterate_grid_offset* switch will create a series of systematic grid-based sampling surveys where the offset from the lower left corner will randomly be chosen between 0 and the values set by *grid_x* and *grid_y*. Note that these three switches are *not* mutually exclusive! You can have all three enabled, and this will potentially produce very complex combinations of random and systemic grid-based sampling frames. This may produce undesired behavior, so it is important ot carefully check both the status of these three switches *and* the state of the sliders on the left side of the landscape window before proceeding.

A fourth switch, *random_n* allows for a random number of patches (randomly chosen between 1 and the value of "n" set by the *n* slider) to be selected at each tick during iterative use of the model. When unchecked, the number "n" is fixed at the value set by the slider *n* so that a fixed number "n" of random patches is selected at each tick during iterative use of the model. This is useful, for example, for determining the smallest number of random survey patches that can still provide a robust sampling result. Note that *random_n* only has an effect when the *iterate_random* switch is also set to "on." 

The fifth and final switch, *square_grid*, will instruct the model to only use the *grid_x* variable for both the x and y dimensions when setting the grid size if *iterate_grid_size* is also checked. This will ensure that all the sampling grids created in the iterative grid size changing routine will only be square in shape.

At this point you can start to run your experiment. To manually step through a series of iterations, you can click the "Step" button as many or as few times as you would like. Each click of the *Step* button will advance the tick counter by one. The latest sampling frame and results will be shown in the landscape window and output areas, respectively. If you would like to quickly run through a set number of iterations, you can enter the total number of iterations desired into the *iterations* text entry box, and then click the *Iterate!* button. You will see the tick counter automatically advance, and the landscape window and output area will rapidly change with the various scenarios and results.

The output area at the bottom of the window will create a new line of statistics for each iteration of your experiment. When the experiment is complete, you can save this out either by right clicking on the output area and slecting *Export...* or by going to the File menu, and selecting *Export > Export output...*. 

To quickly proceed with a new sampling experiment while keeping the current artifact distribution loaded in, you can click the *Reset Iterations!* button. Note that this will clear the output area, so be sure that you have saved out that data if you wish to keep a record of your previous experimental results. If you would like to start completely fresh, you can use the *Start/Reset Experiment* button on the left side of the window, which will also blank out the artifact distribution.

### Summary statistics

Summary statistics are shown on the bottom left side in labeled output boxes, and formatted as comma-delimited text in the bottom text output window. They include (note that some of these are only inlcluded in the formatted text output window):

- The sample size (% of the total landscape that was surveyed)
- The total number of survey patches
- The number of survey patches that contained some artifacts (positive patches)
- The number of survey patches that had no artifacts (negative patches)
- The number of survey patches with a number of artifacts above the density threshold
- The positivity rate (% of survey patches with artifacts in them)
- The raw count of discovered artifacts (artifacts that fell inside a survey patch)
- The percentage of the total number of artifacts that were discovered 
- The extrapolated estimate of the total number of artifacts based on the sampling proportion and the number of artifacts discovered in the survey patches.
- The differnce between the extrapolated count and the actual count of artifacts
- The calculated density of artifacts in the sampled patches (mean number of artifacts per patch)
- The calculated standard deciation of the density of artifacts in the sampled patches
- The actual mean density of artifacts in the landscape (mean number of artifacts per patch)
- The actual standard deviation of artifact density in the landscape
- The difference between the calculated density in the sampled patches and the real density of artifacts in the total landscape
- The grid x interval (# of patches)
- The grid y interval (# of patches)
- The grid x offset (# of patches)
- The grid y offset (# of patches)

The count of survey patches and total number of artifacts are also updated if you have not yet used the "Count survey patches/artfiacts" button.

The extrapolated count is calculated as the number of artifacts discovered in the current sampling frame divided by the sample size (percent of landscape covered). If this number is close to the actual number of seeded artifacts (*num_artifacts*), then it can be concluded that the sampling strategy is effective. The "Count difference" output window shows you this comparison, and similarly, the "Density difference" output window shows you the difference between the calcualted artifact density in the sampling frame versus the true density of artifacts in the total landscape.

Finally, note that there is an output text window at the very bottom of the screen that will keep a running tally of all the results that are calculated each time you click the "Display Results!" button, the "Step" button, or the "Iterate" button. If you are using the model for statistical analysis or comparison, this formatted text area will help you export all of the salient information you will need. The text in this window is formatted as comma-delimited columns with a header row of column labels. This means that it can be directly imported (or copied and pasted) into a standard spreadsheet or other statistical analysis software. You can quickly save out the entire contents of the output window either by right clicking on the output area and slecting *Export...* or by going to the File menu, and selecting *Export > Export output...*. By default, the text export will be saved with a ".txt" file suffix, but you can change this to ".csv" for simpler import into your favorite spreadsheet program. At any point, you can clear and reset the output window by clicking the *Clear output window* button that appears just to the left of the output window.

## THINGS TO TRY

Set up a single artifact distribution, and then create a series of different sampling frames using the "Clear survey patches" button each time to blank out the previous sampling frame. This tests the effectiveness of different sampling frames for one type of artifact distribution

Set up a single sampling frame, and then create a series of different artifact distributions using the "Clear artifact distribution" and "Reset survey patches" buttons. This can test the effectiveness of a single sampling frame on multiple types of artifact distributions.

Try iteratively increasing the number of survey patches, and note how the extrapolated prediction changes. Is it possible to "under sample" and get a prediction that is too small? Is it possible to "oversample" and get a prediction that is too large? Are you ever able to predict the exact number of artifacts? How big is the window of sample sizes where predicted results are reasonably accurate? 

Try combining survey sampling strategies. You can, for example, create a "stratified random" sampling strategy by combining an overall random distribution with some interactive (but randomly chosen) "clicked" sampling patches in a specific part of th map.

Try increasing the artifact cluster size. As it gets larger and larger, the distribution of seed artifacts approaches a uniform distribution.

Experiment with the artifact cluster number and dimensions set by "cluster_x" and "cluster_y". By carefully superimposing different types and sizes of artifact clusters, you can create very realistic "palimpsests" of activity areas, occupational phases, or regional site histories. You can also superimpose a sparse "background scatter' of artifacts by setting "num_artifacts" to a small number, and choosing 0 clusters for a random distribution.

You can create continuous linear survey "transects" in the x or y direction by setting one of "grid_x" or "grid_y" to 1. You would want to set the cooresponding "offset" slider to 0 (e.g., if you set "grid_x" to 1, then also set "x_offset" to 0) if you wanted your transects to cross the entire length or breadth of the landscape. The transect spacing and locations would then be controled by the value you set in the other grid dimension and offset.

Use the iterate controls on the right side of the landscape window to automatically step through various types of sampling frames. This can give you a statistical sense of the effectiveness of your potential sampling system.

## EXTENDING THE MODEL

The gridded sampling frame is only available as a rectangular grid oriented orthogonally to the landscape grid. It would be useful to add the functionality for the sampling grid to be rotated obliquely to the landscape grid, and for the ability to design triangular or hexagonal grids. In the same way, artifact clusters can only be oriented in the x and y directions. It would be useful to allow them to be rotated as well, although this can be approximated using the grid spacing variables (but the actual orentation of the square patches remains orthagonal to the world frame). It would require a more complex setup routine. Finally, the iterative version of the model only alters the sampling frame, but not the artifact distribution. Therefore, the model tests the efficacy of different samplng frames for a single artifact distribution. It might be interesting to be able to automatically iterate through a series of possible artifact distributions using the same sampling frame, and so test the efficacy of a single sampling frame on different types of artifact distributions.


## RELATED MODELS

The DIDI and DICI models (www.DigItTools.net) are also NetLogo models developed for survey experiments. This model is much simpler, and is aimed more at education than true statistical analysis of real survey strategies.

## CREDITS AND REFERENCES

This model was created by Isaac I.T. Ullah, PhD, 2022, at San Diego State University. It is intended for educational purposes only, and comes with no warantee or guarantee of accuracy. The model derives from an analog sampling experiment lab created as part of ANTH 302 "Principles of Archaeology," and is used in a presention I have given at the 2022 Society for American Archaeology meetings in Chicago. It is available under the GNU public license, and is published on the web at http://isaacullah.github.io/models/Sampling_Experiment.html. Please cite the author if you use this model in any publication.
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