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extensions [array]

globals [
  num-new-papers
  num-papers-to-date
  num-new-authors
  num-authors-to-date
  
  papers-by-year
  papers-to-date-by-year
  authors-by-year
  authors-to-date-by-year
  papers-per-author
  
]

breed [papers paper] ; The coloured balls
breed [authors author] ; The balls' colours

directed-link-breed [alinks alink] ; paper x has the author y
directed-link-breed [wlinks wlink] ; author y wrote paper x

papers-own [
  year
]

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to setup
  clear-all
  
  set num-papers-to-date 0
  set num-authors-to-date 0
  set num-new-papers 0
  set num-new-authors 0
  set papers-by-year []
  set papers-to-date-by-year []
  set authors-by-year []
  set authors-to-date-by-year []
  set papers-per-author []
  
  ; Create initial papers
  repeat Foundational-Papers [
    generate-founding-paper
  ]
  
  update-stats
  update-plots
  
end

to generate-founding-paper
  let new-paper nobody
  
  create-papers 1 [
    set hidden? hide-papers?
    set color blue
    set shape "square"
    setxy 0 random-ycor
    set new-paper self
    set year 0
  ]
  set num-papers-to-date num-papers-to-date + 1 ; Option: Omit foundational papers from field size?
  set num-new-papers num-new-papers + 1
  
  generate-new-author new-paper
  
end

to update-stats
  set papers-by-year fput num-papers-to-date papers-by-year
  set papers-to-date-by-year fput num-new-papers papers-to-date-by-year
  set authors-by-year fput num-authors-to-date authors-by-year
  set authors-to-date-by-year fput num-new-authors authors-to-date-by-year
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to go
  if ticks >= Number-Of-Years [
    stop
  ]  
  
  tick
  
  set num-new-papers 0
  set num-new-authors 0
  
  repeat (First-Year-Papers * (field-growth ^ (ticks - 1))) [
    generate-paper
  ]  
  
  update-stats
  update-plots
  
  if ticks = Number-Of-Years [
    final-plots
    stop
  ]
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to generate-new-author [given-paper]
  create-authors 1 [
    set hidden? hide-authors?
    set color red
    set shape "person"
    setxy ([xcor] of given-paper) ([ycor] of given-paper)
    create-alink-from given-paper [ set hidden? true ]
    create-wlink-to given-paper [ set hidden? hide-links? ]
  ]
  set num-authors-to-date num-authors-to-date + 1
  set num-new-authors num-new-authors + 1
end

to-report recent-paper
  report one-of papers with [(year < ticks) and (ticks - year <= recency-param1)]  
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to generate-paper
  let new-paper nobody
  let cur-author nobody
  
  create-papers 1 [
    set hidden? hide-papers?
    set color green
    set shape "square"
    setxy (max-pxcor * ticks / Number-Of-Years) random-ycor
    set new-paper self
    set year ticks
  ]
  
  set num-papers-to-date num-papers-to-date + 1
  set num-new-papers num-new-papers + 1

  ifelse (random-float 1) < Chance-Author-New [
    ; Author is new
    generate-new-author new-paper
  ]
  [
    set cur-author one-of [out-alink-neighbors] of recent-paper
    ask cur-author [
      create-alink-from new-paper [ set hidden? true ]
      create-wlink-to new-paper [ set hidden? hide-links? ]
      setxy ([xcor] of new-paper) ([ycor] of new-paper)
    ]
  ]
  
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to update-plots
  set-current-plot "# Papers To Date"
  plotxy ticks num-papers-to-date
  set-current-plot "# Papers Added"
  plotxy ticks num-new-papers
  
  set-current-plot "# Authors To Date"
  plotxy ticks num-authors-to-date
  set-current-plot "# Authors Added"
  plotxy ticks num-new-authors
  
end

to final-plots
  let histolist []
  
  ; NB: This includes foundational papers. Might prefer to leave them out.
  set histolist sort ([count out-wlink-neighbors] of authors)
  set-current-plot "Papers Per Author"
  set-plot-x-range 0 (1 + max histolist)
  histogram histolist
  
  ; log-log plot
  set papers-per-author []
  let curval first histolist
  set histolist but-first histolist
  let curfreq 1
  set-current-plot "log-log"
  while [0 < length histolist] [
    ifelse curval = first histolist [
      set curfreq curfreq + 1
    ]
    [
      set papers-per-author fput (list curval curfreq) papers-per-author
      plotxy (log curval 10) (log curfreq 10)
      set curval first histolist
      set curfreq 1
    ]
    set histolist but-first histolist
  ]
  set papers-per-author fput (list curval curfreq) papers-per-author
  plotxy (log curval 10) (log curfreq 10)
    
end

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
to print-evolution
  print "# Papers Added:"
  foreach reverse papers-by-year [ print ? ]
  print ""
  
  print "# Papers To Date:"
  foreach reverse papers-to-date-by-year [ print ? ]
  print ""

  print "# Authors Added:"
  foreach reverse authors-by-year [ print ? ]
  print ""

  print "# Authors To Date:"
  foreach reverse authors-to-date-by-year [ print ? ]
  print ""

end

to print-distributions
  print "# Papers Per Author [Papers Frequency]:"
  foreach reverse papers-per-author [ print ? ]
  print ""
end
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@#$#@#$#@
PAPERS PER AUTHOR
-----------------
A simple simulation model of the growth in numbers of papers and authors of a scientific field. 


HOW IT WORKS
------------
The simulation is initialised by the creation of a number of foundational papers.

Thereafter, each time step (representing a year) a number of new papers is added. The number of new papers to be added can grow geometrically each year.

For simplicity, we assume each paper has just one author. There is a fixed chance that this author is new to the field. Otherwise, an author is sampled from a recent paper. "Recent" here means within a given number of time ticks (years).

The x coordinate is used to represent time. Papers appear at the time they are created, and at arbitrary y coordinates. Authors appear at the position of their most recent paper. Links connect authors to all their papers. Papers are represented by squares (blue for foundational papers, green for later papers). Authors are represented by the "person" shape.

The numbers of papers and authors are plotted over time.

At the end, the frequency distribution of papers per author is plotted, which for some parameter settings may tend towards a scale-free distribution.


RELATED MODELS
--------------
Herbert Simon (1955) described a method for generating data similar to that observed by Lotka of the number of papers per author.

Gilbert (1997) developed this method into a simulation model of Academic Science Structure (the GASS model). 

Bentley et al (2009) describe an algorithm with new items (in our case, papers) being added in batches, and categories (in our case, authors) being chosen with restriction to those that recent items have belonged to.

This model is intended as a introduction to the more sophisticated CitationAgents model described in Watts & Gilbert (forthcoming).

CREDITS AND REFERENCES
----------------------
Watts, CJ & GN Gilbert (forthcoming) "Does cumulative advantage affect collective learning in science? An agent-based simulation", Scientometrics.

Bentley, R. A., Ormerod, P., Batty, M. (2009) "An evolutionary model of long tailed distributions in the social sciences". arXiv:0903.2533v1 [physics.soc-ph] 14 Mar 2009 http://arxiv.org/PS_cache/arxiv/pdf/0903/0903.2533v1.pdf . Accessed 1 May 2010.

Gilbert, N. (1997) "A Simulation of the Structure of Academic Science". Sociological Research Online, 2(2)3, http://www.socresonline.org.uk/socresonline/2/2/3.html .

Simon, H. A. (1955) "On a Class of Skew Distribution Functions". Biometrika, 42(3/4), 425-440.
 
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