globals [ ; These are set in the plotting object in the interface A-count B-count AB-count O-count A-freq O-freq B-freq AA-freq AB-freq BB-freq Ao-freq Bo-freq oo-freq ;; Math stuff D ] ;; We assume turtles are hermaphroditic and don't worry about keeping track of sexes ;; A = AA, Ao ;; B = BB, Bo ;; AB = AB ;; O = oo turtles-own [ allele1 ; A or B or o allele2 ; A or B or o ] to setup clear-output if (starting-freq-of-phenotype-A + starting-freq-of-phenotype-B + starting-freq-of-phenotype-AB + starting-freq-of-phenotype-O) > 1 [ print "Error: The frequencies of P genotypes is greater than 1" set starting-freq-of-phenotype-A (0.25) set starting-freq-of-phenotype-B (0.25) set starting-freq-of-phenotype-AB (0.25) set starting-freq-of-phenotype-O (0.25) ] ;; estimate allele frequencies from phenotype frequencies using the Bernstein method set O-freq (sqrt starting-freq-of-phenotype-O) set A-freq (1 - sqrt (starting-freq-of-phenotype-B + starting-freq-of-phenotype-O)) set B-freq (1 - sqrt (starting-freq-of-phenotype-A + starting-freq-of-phenotype-O)) set D (1 - (A-freq + B-freq + O-freq)) set A-freq (A-freq * (1 + (D / 2))) set B-freq (B-freq * (1 + (D / 2))) set O-freq (1 - (A-freq + B-freq)) ;; Calculate genotype frequencies from allele frequencies using Hardy-Weinberg equation set AA-freq (A-freq ^ 2) set AB-freq (2 * A-freq * B-freq) set BB-freq (B-freq ^ 2) set Ao-freq (2 * A-freq * O-freq) set Bo-freq (2 * B-freq * O-freq) set oo-freq (O-freq ^ 2) setup-experiment end to setup-experiment clear-patches clear-turtles clear-all-plots clear-ticks create-turtles initial-population-size [ setxy random-xcor random-ycor ; randomize turtle locations ;; ///A turtles/// ;; AA ifelse who < initial-population-size * AA-freq ; start out user specified [ set allele1 "A" set allele2 "A" set color red ] ;; Ao [ ifelse who < initial-population-size * (Ao-freq + AA-freq) [ set allele1 "A" set allele2 "O" set color red ] ;; ///AB turtles/// [ ifelse who < initial-population-size * (Ao-freq + AA-freq + AB-freq) [ set allele1 "A" set allele2 "B" set color orange ] ;; ///B turtles/// ;; BB [ ifelse who < initial-population-size * (Ao-freq + AA-freq + AB-freq + BB-freq) [ set allele1 "B" set allele2 "B" set color blue ] ;; Bo [ ifelse who < initial-population-size * (Ao-freq + AA-freq + AB-freq + BB-freq + Bo-freq) [ set allele1 "B" set allele2 "O" set color blue ] ;;///O turtles [ set allele1 "O" set allele2 "O" set color green ] ] ] ] ] set size 1 ; easier to see ] reset-ticks end to go reproduce-and-die ;death ;print(count turtles) tick end to wander ;; turtle procedure rt random-float 30 - random-float 30 fd 1 end to reproduce-and-die ask turtles [ ; Choose a random mate and one of its alleles, randomly let mate-allele one-of [list allele1 allele2] of one-of turtles ; Choose one of my alleles randomly let my-allele one-of (list allele1 allele2) ; Identify genotype and set color (default to heterozygous blue = Aa) let offspring-color red ifelse (mate-allele = my-allele) [ ; homozygous ifelse (mate-allele = "A") [set offspring-color red] [ ifelse (mate-allele = "B") [set offspring-color blue] [ set offspring-color green ] ] ] ; heterozygous [ ifelse (((my-allele = "A") and (mate-allele = "B")) or ((my-allele = "B") and (mate-allele = "A"))) [set offspring-color orange] [ ifelse (((my-allele = "A") and (mate-allele = "O")) or ((my-allele = "O") and (mate-allele = "A"))) [set offspring-color red] [set offspring-color blue] ] ] hatch 1 [ set color offspring-color set allele1 my-allele set allele2 mate-allele wander ] ifelse (Natural-Selection) [ ifelse (my-allele = Resistant-Blood-Group) [if (random-float 1 > Resistance-%) [die]] [die] ] [ die ] ; parent dies after reproducing ] end ;; if the overall population is greater than the original number, ;; randomly kill turtles to keep population roughly constant to death let total-turtles count turtles if total-turtles >= initial-population-size [ ask turtles [ let my-allele one-of (list allele1 allele2) if random total-turtles > initial-population-size [ ifelse (Natural-Selection) [ ifelse (my-allele = Resistant-Blood-Group) [if (random-float 1 > Resistance-%) [die]] [die] ] [ die ] ; parent dies after reproducing ] ] ] end ; Copyright 1997 Uri Wilensky. ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 490 35 1018 564 -1 -1 5.15 1 10 1 1 1 0 1 1 1 -50 50 -50 50 1 1 1 ticks 30.0 BUTTON 80 25 207 58 one-generation go\n NIL 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 20 100 270 133 initial-population-size initial-population-size 10 15000 14546.0 10 1 NIL HORIZONTAL BUTTON 15 25 75 58 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 210 25 270 58 go go T 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 20 205 470 238 starting-freq-of-phenotype-B starting-freq-of-phenotype-B 0.0 1.0 0.224 0.001 1 NIL HORIZONTAL SLIDER 20 170 470 203 starting-freq-of-phenotype-A starting-freq-of-phenotype-A 0.0 1.0 0.234 0.001 1 NIL HORIZONTAL PLOT 5 330 330 549 ABO blood group system populations Generations Population 0.0 5.0 0.0 1200.0 true true "set-plot-y-range 0 floor (initial-population-size * 1.2)" "set O-freq (sqrt (O-count / count turtles))\nset A-freq (1 - sqrt ((B-count / count turtles) + (O-count / count turtles)))\nset B-freq (1 - sqrt ((A-count / count turtles) + (O-count / count turtles)))\n\nset D (1 - (A-freq + B-freq + O-freq))\n\nset A-freq (A-freq * (1 + (D / 2)))\nset B-freq (B-freq * (1 + (D / 2)))\nset O-freq (1 - (A-freq + B-freq))\n \n;; Calculate genotype frequencies from allele frequencies using Hardy-Weinberg equation\nset AA-freq (count turtles with [ allele1 = \"A\" and allele2 = \"A\" ]) / count turtles\nset AB-freq (count turtles with [ (allele1 = \"A\" and allele2 = \"B\") or (allele1 = \"B\" and allele2 = \"A\") ]) / count turtles\nset BB-freq (count turtles with [ allele1 = \"B\" and allele2 = \"B\" ]) / count turtles\nset Ao-freq (count turtles with [ (allele1 = \"A\" and allele2 = \"O\") or (allele1 = \"O\" and allele2 = \"A\") ]) / count turtles\nset Bo-freq (count turtles with [ (allele1 = \"O\" and allele2 = \"B\") or (allele1 = \"B\" and allele2 = \"O\") ]) / count turtles\nset oo-freq (count turtles with [ allele1 = \"O\" and allele2 = \"O\" ]) / count turtles" PENS "Type A" 1.0 0 -2674135 true "" "set A-count count turtles with [ color = red ]\nplot A-count" "Type B" 1.0 0 -13345367 true "" "set B-count count turtles with [ color = blue ]\nplot B-count" "Type O" 1.0 0 -10899396 true "" "set O-count count turtles with [ color = green ]\nplot O-count" "Type AB" 1.0 0 -955883 true "" "set AB-count count turtles with [ color = orange ]\nplot AB-count" MONITOR 30 615 165 660 Freq AA AA-freq 17 1 11 MONITOR 175 615 310 660 Freq Ao Ao-freq 17 1 11 MONITOR 320 615 455 660 Freq oo oo-freq 17 1 11 SLIDER 20 240 470 273 starting-freq-of-phenotype-AB starting-freq-of-phenotype-AB 0.0 1.0 0.046 0.001 1 NIL HORIZONTAL SLIDER 20 275 470 308 starting-freq-of-phenotype-O starting-freq-of-phenotype-O 0.0 1.0 0.485 0.001 1 NIL HORIZONTAL MONITOR 30 665 165 710 Freq AB AB-freq 17 1 11 MONITOR 175 665 310 710 Freq Bo Bo-freq 17 1 11 MONITOR 320 665 455 710 Freq BB BB-freq 17 1 11 MONITOR 30 755 165 800 Freq A A-freq 17 1 11 MONITOR 175 755 310 800 Freq B B-freq 17 1 11 MONITOR 320 755 455 800 Freq o O-freq 17 1 11 TEXTBOX 30 590 180 608 Genotype frequencies 15 0.0 1 TEXTBOX 30 730 180 748 Allele frequencies 15 0.0 1 MONITOR 490 615 620 660 Freq A A-count / (count turtles) 17 1 11 MONITOR 490 665 620 710 Freq B B-count / (count turtles) 17 1 11 MONITOR 630 615 760 660 Freq AB AB-count / (count turtles) 17 1 11 MONITOR 630 665 760 710 Freq O O-count / (count turtles) 17 1 11 TEXTBOX 490 590 640 608 Phenotype frequencies 15 0.0 1 SWITCH 300 25 470 58 Natural-Selection Natural-Selection 0 1 -1000 CHOOSER 300 65 470 110 Resistant-Blood-Group Resistant-Blood-Group "A" "B" "AB" "O" 3 SLIDER 300 120 472 153 Resistance-% Resistance-% 0.0 1.0 0.66 0.01 1 NIL HORIZONTAL @#$#@#$#@ ## WHAT IS IT? This is a simple model of Hardy-Weinberg equilibrium and genetic drift in an ABO blood type group system. Here the organisms mate randomly and a certain phenotype can have a resistance to death after reproduction to simulate an infected population with a disease. Allele frequencies evolve purely by genetic drift. ## HOW TO USE IT The initial-population-size slider sets the carrying capacity of the terrain. The model is initialized to have a total population of initial-population-size with the respective phenotype frequencies in each color presented on the plot. The starting-freq-ofphenotype-A slider sets what proportion of the intial population has the A phenotype. The starting-freq-ofphenotype-B slider sets what proportion of the intial population has the B phenotype. The starting-freq-ofphenotype-AB slider sets what proportion of the intial population has the AB phenotype. The starting-freq-ofphenotype-O slider sets what proportion of the intial population has the O phenotype. The GO button runs the model. The ONE GENERATION button simulates a single generation (single tick). The POPULATIONS plot displays the number of individuals with the four different phenotypes: A (reds), B (blues), O (green) and AB (orange). The monitor windows show the frequencies of the 6 different genotypes, the 3 different alleles and the 4 different phenotypes. ## THINGS TO DO Set the carrying capacity to 14,546. Set the initial frequency of the A phenotype to 0.3, the initial frequency of the B phenotype to 0.3, the initial frequency of the AB phenotype to 0.2 and the initial frequency of the O phenotype to 0.2. Now simulate one generation. What are the resulting frequencies of the 6 genotypes? Now run the model forward by pressing the GO button. What happens to the 6 genotypes? Now set the initial frequency of the A phenotype to 0.1 and the initial frequency of the O phenotype to 0.4, and reset the model by pressing the SETUP button. Simulate one generation. What are the resulting frequencies of the 6 genotypes? Now run the model forward by pressing the GO button. What happens to the 6 genotypes? Now set the carrying capacity to 4000 and repeat the experiments above. What happens after 1 generation? What happens if you let those models run? ## EXTENDING THE MODEL ## HOW TO CITE This model was based on the Random Mating Diploid Drift model by Carlo C. Maley and then extended by João C. Carvalho in 2023 The orinal model was based on the Simple Birth Rates model by U. Wilensky, and then extended by Carlo C. Maley in 2018. If you mention this model or the NetLogo software in a publication, we ask that you include the citations below. For the original model itself: * Wilensky, U. (1997). NetLogo Simple Birth Rates model. http://ccl.northwestern.edu/netlogo/models/SimpleBirthRates. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. Please cite the NetLogo software as: * Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. 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