globals [sperm egg parent-generation color-locus] turtles-own [sex generation deathday age loc1 loc2] to setup ca ask patches [set pcolor black] set color-locus one-of ["loc1" "loc2"] create-turtles number-turtles [ setxy random-xcor random-ycor set age 0 set generation 0 ;; Poisson distribution with mean set by user set deathday precision (random-normal mean-lifespan (sqrt mean-lifespan)) 2 ] ask n-of (male-female-ratio * number-turtles) turtles [ set sex "male" ;set color blue ] ask turtles with [sex != "male"] [ set sex "female" set shape "dot" ;set color red ] assign-genotypes ask turtles [assign-color] report-freqs type "Turtles inititially colored according to genotype at locus " print color-locus end to assign-genotypes ask n-of (freqAA * number-turtles) turtles [ set loc1 ["A" "A"] ] ask n-of (freqGG * number-turtles) turtles with [loc1 != ["A" "A"]] [ set loc1 ["G" "G"] ] ask n-of (.5 * (1 - freqAA - freqGG) * number-turtles) turtles with [loc1 != ["A" "A"]] with [loc1 != ["G" "G"]] [ set loc1 ["A" "G"] ] ask turtles with [loc1 != ["A" "A"]] with [loc1 != ["G" "G"]] with [loc1 != ["A" "G"]] [ set loc1 ["G" "A"] ] ask n-of (freqCC * number-turtles) turtles [ set loc2 ["C" "C"] ] ask n-of (freqTT * number-turtles) turtles with [loc2 != ["C" "C"]] [ set loc2 ["T" "T"] ] ask n-of (.5 * (1 - freqCC - freqTT) * number-turtles) turtles with [loc2 != ["C" "C"]] with [loc2 != ["T" "T"]] [ set loc2 ["C" "T"] ] ask turtles with [loc2 != ["C" "C"]] with [loc2 != ["T" "T"]] with [loc2 != ["C" "T"]] [ set loc2 ["T" "C"] ] end to go tick ask turtles [ drop-dead set age precision (age + 1 / 50) 2 fd random-float 1 ;assign-color ] mate if ticks mod 50 = 0 [report-freqs] if not any? turtles [stop] update-plot if ((((count turtles with [loc1 = ["A" "A"]] + .5 * (count turtles with [loc1 = ["A" "G"]] + count turtles with [loc1 = ["G" "A"]]) / (count turtles)) = 0) or ((count turtles with [loc1 = ["G" "G"]] + .5 * (count turtles with [loc1 = ["A" "G"]] + count turtles with [loc1 = ["G" "A"]]) / (count turtles)) = 0)) and (((count turtles with [loc2 = ["C" "C"]] + .5 * (count turtles with [loc2 = ["C" "T"]] + count turtles with [loc2 = ["T" "C"]]) / (count turtles)) = 0) or ((count turtles with [loc2 = ["T" "T"]] + .5 * (count turtles with [loc2 = ["C" "T"]] + count turtles with [loc2 = ["T" "C"]]) / (count turtles))= 0))) [ report-freqs stop ] end to mate ask turtles with [sex = "male"] [ if count turtles < number-turtles [ set sperm sentence (one-of loc1) (one-of loc2) set parent-generation [generation] of self ;; enforce mating only within a generation if any? other turtles-here with [sex = "female"] with [generation = [generation] of self] [ ask one-of other turtles-here with [sex = "female"] with [generation = [generation] of self] [ set egg sentence (one-of loc1) (one-of loc2) reproduce ] ] ] ] end to reproduce hatch 1 [ assign-sex set age 0 set generation parent-generation + 1 set deathday precision (random-normal mean-lifespan (sqrt mean-lifespan)) 2 inherit-alleles assign-color set heading random-float 360 ] end to assign-sex ifelse random-float 1 < male-female-ratio [ set sex "male" set shape "default" ;set color blue ] [ set sex "female" set shape "dot" ;set color red ] end to inherit-alleles set loc1 sentence (item 0 sperm) (item 0 egg) set loc2 sentence (item 1 sperm) (item 1 egg) end to switch-color ifelse color-locus = "loc1" [set color-locus "loc2"] [set color-locus "loc1"] ask turtles [assign-color] type "Turtles now colored according to genotype at locus " print color-locus end to assign-color if color-locus = "loc1" [ if loc1 = ["A" "A"] [set color blue] if loc1 = ["A" "G"] or loc1 = ["G" "A"] [set color green] if loc1 = ["G" "G"] [set color yellow] ] if color-locus = "loc2" [ if loc2 = ["C" "C"] [set color red] if loc2 = ["C" "T"] or loc2 = ["T" "C"] [set color pink] if loc2 = ["T" "T"] [set color white] ] end to drop-dead if age >= deathday [die] end to report-freqs if not any? turtles [stop] clear-output let freq-AA precision ((count turtles with [loc1 = ["A" "A"]]) / count turtles) 3 let freq-GG precision ((count turtles with [loc1 = ["G" "G"]]) / count turtles) 3 let freq-AG precision (((count turtles with [loc1 = ["A" "G"]]) + (count turtles with [loc1 = ["G" "A"]])) / count turtles) 3 let freq-CC precision ((count turtles with [loc2 = ["C" "C"]]) / count turtles) 3 let freq-CT precision (((count turtles with [loc2 = ["C" "T"]]) + (count turtles with [loc2 = ["T" "C"]])) / count turtles) 3 let freq-TT precision ((count turtles with [loc2 = ["T" "T"]]) / count turtles) 3 let freq-A precision (((count turtles with [loc1 = ["A" "A"]]) + .5 * ((count turtles with [loc1 = ["A" "G"]]) + (count turtles with [loc1 = ["G" "A"]]))) / count turtles) 3 let freq-G precision (((count turtles with [loc1 = ["G" "G"]]) + .5 * ((count turtles with [loc1 = ["A" "G"]]) + (count turtles with [loc1 = ["G" "A"]]))) / count turtles) 3 let freq-C precision (((count turtles with [loc2 = ["C" "C"]]) + .5 * ((count turtles with [loc2 = ["C" "T"]]) + (count turtles with [loc2 = ["T" "C"]]))) / count turtles) 3 let freq-T precision (((count turtles with [loc2 = ["T" "T"]]) + .5 * ((count turtles with [loc2 = ["C" "T"]]) + (count turtles with [loc2 = ["T" "C"]]))) / count turtles) 3 output-type "Time (years): " output-print precision (ticks / 50) 2 output-type "freq of AA: " output-print freq-AA output-type "freq of AG: " output-print freq-AG output-type "freq of GG: " output-print freq-GG output-type "freq of CC: " output-print freq-CC output-type "freq of CT: " output-print freq-CT output-type "freq of TT: " output-print freq-TT output-type "A allele: " output-print freq-A output-type "G allele: " output-print freq-G output-type "C allele: " output-print freq-C output-type "T allele: " output-print freq-T end to update-plot set-current-plot "freq-alleles-plot" let freq-A precision (((count turtles with [loc1 = ["A" "A"]]) + .5 * ((count turtles with [loc1 = ["A" "G"]]) + (count turtles with [loc1 = ["G" "A"]]))) / count turtles) 3 let freq-G precision (((count turtles with [loc1 = ["G" "G"]]) + .5 * ((count turtles with [loc1 = ["A" "G"]]) + (count turtles with [loc1 = ["G" "A"]]))) / count turtles) 3 let freq-C precision (((count turtles with [loc2 = ["C" "C"]]) + .5 * ((count turtles with [loc2 = ["C" "T"]]) + (count turtles with [loc2 = ["T" "C"]]))) / count turtles) 3 let freq-T precision (((count turtles with [loc2 = ["T" "T"]]) + .5 * ((count turtles with [loc2 = ["C" "T"]]) + (count turtles with [loc2 = ["T" "C"]]))) / count turtles) 3 set-current-plot-pen "loc1-A" ifelse plot-allele-loc1 = "A" [plot-pen-down] [plot-pen-up] set-plot-pen-interval 1 / 50 plot freq-A set-current-plot-pen "loc1-G" ifelse plot-allele-loc1 = "G" [plot-pen-down] [plot-pen-up] set-plot-pen-interval 1 / 50 plot freq-G set-current-plot-pen "loc2-C" ifelse plot-allele-loc2 = "C" [plot-pen-down] [plot-pen-up] set-plot-pen-interval 1 / 50 plot freq-C set-current-plot-pen "loc2-T" ifelse plot-allele-loc2 = "T" [plot-pen-down] [plot-pen-up] set-plot-pen-interval 1 / 50 plot freq-T end ;;kenneth.chiou [at] wustl.edu @#$#@#$#@ GRAPHICS-WINDOW 182 10 702 551 25 25 10.0 1 10 1 1 1 0 1 1 1 -25 25 -25 25 0 0 1 ticks SLIDER 5 10 177 43 number-turtles number-turtles 0 2500 1000 50 1 NIL HORIZONTAL BUTTON 92 390 177 423 NIL go T 1 T OBSERVER NIL NIL NIL NIL BUTTON 5 390 90 423 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 5 43 177 76 male-female-ratio male-female-ratio 0 1 0.5 0.05 1 NIL HORIZONTAL BUTTON 710 518 985 551 report genotype/allele freqs report-freqs NIL 1 T OBSERVER NIL NIL NIL NIL OUTPUT 710 317 985 513 12 SLIDER 5 170 176 203 freqAA freqAA 0 1 0.25 0.01 1 NIL HORIZONTAL SLIDER 5 203 176 236 freqGG freqGG 0 1 - freqAA 0.25 0.01 1 NIL HORIZONTAL SLIDER 5 260 176 293 freqCC freqCC 0 1.0 0.4 0.01 1 NIL HORIZONTAL SLIDER 5 293 176 326 freqTT freqTT 0 1 - freqCC 0.4 0.01 1 NIL HORIZONTAL PLOT 710 10 984 160 freq-alleles-plot time (years) frequency 0.0 10.0 0.0 1.0 true true PENS "loc1-A" 1.0 0 -13345367 true "loc1-G" 1.0 0 -1184463 true "loc2-C" 1.0 0 -2674135 true "loc2-T" 1.0 0 -7500403 true TEXTBOX 21 133 171 151 Set initial genotype freqs 12 0.0 1 TEXTBOX 63 244 110 262 Locus 2 12 0.0 1 SLIDER 5 76 177 109 mean-lifespan mean-lifespan 0 20 4 1 1 years HORIZONTAL CHOOSER 710 166 843 211 plot-allele-loc1 plot-allele-loc1 "A" "G" 0 CHOOSER 851 166 984 211 plot-allele-loc2 plot-allele-loc2 "C" "T" 0 BUTTON 710 217 985 250 color turtles at other locus switch-color NIL 1 T OBSERVER NIL NIL NIL NIL TEXTBOX 63 154 108 172 Locus 1 12 0.0 1 TEXTBOX 711 254 980 294 Locus 1: AA (blue) AG (green) GG (yellow)\nLocus 2: CC (red) CT (pink) TT (white) 12 0.0 1 @#$#@#$#@ WHAT IS IT? ----------- This agent-based model seeks to simulate Hardy-Weinberg equilibrium in a random-mating population. All Hardy-Weinberg assumptions are followed here except for an infinite population size. Therefore, this model also simulates genetic drift. HOW IT WORKS ------------ The organisms ("turtles") in this model navigate through space with a fixed orientation but at random speeds. Turtles are divided into males (arrowheads) and females (circles) and are further distinguished by their genotypes at two loci. The first locus (loc1) is A/G polymorphic and the second locus (loc2) is C/T polymorphic. Provided the population limit is not reached, hatchlings are created whenever two turtles in the same generation and of opposite sex come across one another. Hatchlings then randomly inherit one allele per locus from each parent. Lifespans are randomly distributed according to an approximate Poisson distribution with a mean set by the user. In this model, one year is equivalent to 50 ticks (each tick equals approximately one week). HOW TO USE IT ------------- The initial population size is set as "number-turtles." This is also the population limit. New hatchlings will not be born while the population size equals number-turtles. The ratio of males to females can be set in the "male-female-ratio" slider. New hatchlings will also be assigned their sexes according to this ratio. Initial genotype frequencies are set by four sliders. Only homozygote frequencies are set (with the homozygote and heterozygote frequencies summing to 1). Actual observed genotype numbers will be rounded if necessary. "Setup" and "Go" to begin! For clarity, only the frequency of one allele at each locus is plotted (with the frequencies of both alleles at a single locus summing to 1). The allele that is plotted can be toggled in the choosers below the plot. Turtles are initially colored according to genotype at one of the two loci. To toggle which locus is colored, press the "color turtles at other locus" button. The output screen, displaying genotype and allele frequencies, is updated every "year" (50 ticks). The output can be manually updated using the button below. THINGS TO TRY ------------- Set the population size to around 100 to more easily witness the stochastic effects of genetic drift. The population should reach fixation at both loci relatively rapidly. Then set the population size higher (to around 1000). The population should approximate Hardy-Weinberg equilibrium and take much longer to reach fixation. Set both genotype frequencies to 0.25 at one locus. See if the genotype frequences stay in 1:2:1 equilibrium. Set the genotype frequencies at the other locus to 0.4 and 0.4. See if the the genotype frequencies gravitate towards a 1:2:1 ratio. EXTENDING THE MODEL ------------------- I am currently working to incorporate recombination and to track linkage disequilribium in the model. Retaining these simple rules, I also hope to incorporate gene flow, mutation, and natural selection in this model. CREDITS AND REFERENCES ---------------------- Original Model Copyright Notice: Copyright 2010 Kenneth Chiou. All rights reserved. Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed: a) this copyright notice is included. b) this model will not be redistributed for profit without permission from Kenneth Chiou. Contact Kenneth Chiou for appropriate licenses for redistribution for profit. 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