turtles-own [ variant ] ; a stylistic variant such as the first name of a baby globals [ ; three different lists root-set ; = first (setup-) set of variants chosen-set ; = chosen variants of the individuals per tick innovation-set ; = set of innovations store-set ; = stores all variants which have been chosen per tick counter ; used for reporter procedure 'set-index' ] to setup ca set root-set n-values N [ [?1] -> ?1 ] ; each turtle starts with its own specific variant set chosen-set [] ; empty list set innovation-set n-values I [ [?1] -> ?1 + N ] ; I values, starting from N + 1 set store-set [] set counter n-values (N + I) [ [?1] -> ?1 ] create-turtles N [ ; N individuals setxy random-xcor random-ycor set variant choose-variant ] ask turtles [ check-variant set chosen-set fput variant chosen-set set store-set fput variant store-set ] reset-ticks end to-report choose-variant report item (random N) root-set ; to choose a random item from the list; one-of root-set does the same end to check-variant ; removes duplicates in the first round while [ any? other turtles with [ variant = [variant] of myself] ] [ set variant choose-variant ] end to go if (length innovation-set) = 0 [ stop ] ; stop condition let old-list chosen-set ; stores variants from the previous set set chosen-set [] ; empty the list to report new list later ask turtles [ ifelse random-float 1 > m [ set variant one-of old-list set chosen-set fput variant chosen-set set store-set fput variant store-set ] [ if (length innovation-set) = 0 [ stop ] let new-item first innovation-set set variant new-item set chosen-set fput new-item chosen-set set store-set fput new-item store-set set innovation-set remove new-item innovation-set ] ; removes the new item from the innovation set such that only new innovations will be used later ] ; show chosen-set tick end ;=============================== Reporters to-report frequency [ element lst ] report length filter [ [number] -> number = element ] lst end ;; reports the frequency of the occurrences of the respective list to-report frequency-of-variants report map [ [elements] -> frequency elements store-set ] n-values (N + I) [ [?1] -> ?1 ] end ;; see monitor to-report sorting report sort-by [ [freq coun] -> first freq > first coun ] set-index end to-report set-index report (map [ [lst1 lst2] -> (list lst1 lst2) ] frequency-of-variants counter) end ;=============================== Plotting to plot-f clear-plot let x (sort-by > frequency-of-variants) let y n-values (N + I) [ [?1] -> ?1 ] (foreach x y [ [?1 ?2] -> plotxy ?2 ?1 ]) end @#$#@#$#@ GRAPHICS-WINDOW 374 103 415 145 -1 -1 1.0 1 10 1 1 1 0 1 1 1 -16 16 -16 16 0 0 1 ticks 30.0 SLIDER 51 162 223 195 N N 0 25 9.0 1 1 NIL HORIZONTAL BUTTON 40 109 103 142 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 105 109 169 142 go once go NIL 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 51 232 223 265 m m 0 1 0.102 0.001 1 NIL HORIZONTAL SLIDER 51 196 223 229 I I 50 500 100.0 50 1 NIL HORIZONTAL BUTTON 171 109 234 142 NIL go T 1 T OBSERVER NIL NIL NIL NIL 0 PLOT 261 46 620 293 Frequency distribution of variants variants frequency 0.0 100.0 0.0 100.0 true false "" "" PENS "default" 1.0 1 -16777216 true "" "plot-f" MONITOR 262 297 632 342 first number = occurrence of variant; second number = respective variant sorting 17 1 11 @#$#@#$#@ ## WHAT IS IT? In evolution frequencies of variants in a population change over time. This holds both for biological and cultural phenomena (e.g. names). Similar to genetic variants the number of cultural variants may change in frequency over time, resulting from evolutionary mechanisms like natural selection or genetic drift. This model simulates the classic phenomenon 'random genetic drift', "which describes how the diversity of variants evolve when the dominant process is one of random copying" (Bentley et al. 2004, p. 1443). Such a model is also known as the 'neutral model' due to the fact that variants are neutral regarding the success of the individual (see Kimura 1968). ## HOW IT WORKS N individuals (N = number of individuals) setup with a unique cultural variant v. Per tick each individual randomly copies an individual's variant v from the previous tick. However, there is a certain chance that the individual chooses an alternative variant I (= innovation), which is given by the mutation rate m. Consequently, new unique variants appear and old disappear. Under certain conditions this can lead to a power law distribution of the frequencies of the variants (m < 0.1). ## HOW TO USE IT Change the parameters I, N and the mutation rate m. Click on 'Setup' to initialize the model. Click on 'go' or 'go once' and check the monitors to see the frequency of the chosen variables per tick and how they change over time. The first monitor reports all variants and their occurrences, the second monitor reports a pair of two values. The first value indicates the occurrence of the second value, which is the respective variant, starting with the variant with the highest occurrence. The plot represents the frequency distribution of the variants. Further statistical processing of the data is necessary to show how well the data fits a power law distribution. ## THINGS TO NOTICE Change the mutation rate m and the number of individuals N and see how this affects the frequency distribution of the variants. Under which conditions is it more likely that the model produces a power law distribution of the frequency of the variants? ## THINGS TO TRY See 'How to use it'. ## EXTENDING THE MODEL ## NETLOGO FEATURES Note that elements are added to the respective list with lput. It doesn't make a difference (also with regarding the performance) whether one uses fput or lput, since the frequency reporter will report the number of occurrences starting from 0 and ending with N + I, irrespectively of the order of the elements in the given list. ## RELATED MODELS See 'Genetic Drift' in the models library. ## CREDITS AND REFERENCES Bentley, R., Hahn, M., & Shennan, S. (2004): Random drift and culture change. Proceedings. Biological sciences / The Royal Society, 271(1547), 1443–1450. doi:10.1098/rspb.2004.2746 KIMURA, MOTOO (1983): The neutral theory of molecular evolution. 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