globals [ min-fertility max-fertility-range degree-of-mutation mutation-change ] turtles-own [ mutation-rate ; mutation rates can evolve fertility ; the whole number part of fertility fertility-remainder ; the fractional part (after the decimal point) ] to setup clear-output set min-fertility 1 ;set max-fertility min-fertility + starting-variance set max-fertility-range 3 ; The limit on the starting variance set degree-of-mutation 0.2 set mutation-change 0.1 setup-experiment end to setup-experiment clear-patches clear-turtles clear-all-plots clear-ticks create-turtles carrying-capacity [ let temp-fertility min-fertility setxy random-xcor random-ycor ; randomize turtle locations set mutation-rate 0.1 set fertility 3 set fertility-remainder 0 set color red + (10 * floor (((temp-fertility - min-fertility) / max-fertility-range) * 10)) set size 2 ; easier to see ] reset-ticks end to go reproduce grim-reaper tick end ;; to enable many repetitions with same settings to go-experiment go if ticks > 5000 [ output-print (word "At 5,000 generations, ave. mutation rate " mean [mutation-rate] of turtles " and fertility " mean [fertility + fertility-remainder] of turtles) setup-experiment ] end to wander ;; turtle procedure rt random-float 30 - random-float 30 fd 0.1 end to reproduce ask turtles [ ifelse (random-float 100) < (100 * fertility-remainder) [ hatch fertility + 1 [ give-birth ]] [ hatch fertility [ give-birth ]] ] end to give-birth set mutation-rate mutation-rate * (1 - mutation-change + (random-float (2 * mutation-change))) if (random-float 1.0) < mutation-rate [ let temp-fertility (fertility + fertility-remainder) ;set temp-fertility (temp-fertility - (degree-of-mutation / 2)) set temp-fertility (temp-fertility - random-float degree-of-mutation) set fertility floor temp-fertility set fertility-remainder (temp-fertility - (floor temp-fertility)) ; This color setting isn't quite right, because fertility can increase over the max set color red + (10 * floor (((temp-fertility - min-fertility) / max-fertility-range) * 10)) ] wander end ;; kill turtles in excess of carrying capacity ;; note that reds and blues have equal probability of dying to grim-reaper let num-turtles count turtles if num-turtles <= carrying-capacity [ stop ] let chance-to-die (num-turtles - carrying-capacity) / num-turtles ask turtles [ if random-float 1.0 < chance-to-die [ die ] ] end ; Copyright 1997 Uri Wilensky. ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 290 10 702 423 -1 -1 4.0 1 10 1 1 1 0 1 1 1 -50 50 -50 50 1 1 1 ticks 30.0 BUTTON 145 25 265 58 run-experiment go-experiment T 1 T OBSERVER NIL NIL NIL NIL 0 SLIDER 15 65 265 98 carrying-capacity carrying-capacity 10 1000 1000.0 10 1 turtles HORIZONTAL BUTTON 15 25 75 58 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 80 25 140 58 go go T 1 T OBSERVER NIL NIL NIL NIL 0 OUTPUT 10 495 700 620 12 PLOT 5 105 285 255 Fertility NIL NIL 0.0 6.0 0.0 1000.0 true false "" "" PENS "default" 0.1 1 -16777216 true "" "histogram [ fertility + fertility-remainder ] of turtles" PLOT 5 260 280 410 Mutation Rates NIL NIL 0.0 10.0 0.0 0.15 true false "" "" PENS "default" 0.01 0 -16777216 true "" "plot mean [mutation-rate] of turtles" MONITOR 10 435 230 480 Average Mutation Rate mean [mutation-rate] of turtles 17 1 11 MONITOR 270 435 377 480 Average fertility mean [fertility + fertility-remainder] of turtles 4 1 11 @#$#@#$#@ ## WHAT IS IT? This is a simple model of the evolution of mutation rate and population size. Every time step (tick) is a generation, where each organism reproduces asexually, and its offspring inherit its fertility and its mutation rate. If the population rises above the terrain's carrying capacity, organisms randomly die (starve) until the population is reduced below the terrain's carrying capacity. Each time an organism is born, there is a probability, set the by its mutation rate, that the offspring's fertility will differ from the parent's. If the fertility of the offspring does mutate, the model chooses a random number between 0 and 0.2 (with uniform distribution), and subtracts that from the parent's fertility rate. So all mutations are deleterious. In addition, a random number is chosen between 0.5 and 1.5 (with uniform probability) and that number is multiplied against the parent's mutation rate to determine the offspring's mutation rate. So the offspring's mutation rate may be up to 50% lower or 50% higher than the parent's. ## HOW TO USE IT Always use the SETUP button at the start of these models to initialize the population of organisms. The CARRYING-CAPACITY slider sets the carrying capacity of the terrain. The model is initialized to have a total population of CARRYING-CAPACITY. The GO button runs the model. Clicking it again stops the model. The FERTILITY plot shows a histogram of the fertilities in the population. The MUTATION RATE plot shows the average mutation rate in the population over time. The RUN-EXPERIMENT button lets you experiment with many trials at the same settings, stopping at 5,000 ticks and reporting the average mutation rate. ## THINGS TO DO Set the starting carrying capacity to 100. Run the model for a while to see what happens to the average mutation rate in the population. Does it increase or decrease? Why? Run an experiment and for at least 5 runs with a carrying capacity of 100, record the exponent on the average mutation rate and the aveage fertility to 4 decimal places. Now increase the carrying capacity to 1,000 and run another experiment for at least 5 runs. Calculate the average order of magnitude (exponent) of the mutation rates. Does the larger population evolve a lower or higher mutation rate? Why? Calculate the average fertility across your runs. Does the larger population evolve a lower or higher fertility? Why? ## EXTENDING THE MODEL If you want to download the model and change the code, try changing the range by which the fertility changes and the mutation rate change. What happens if 1% of the mutations are beneficial, increasing the mutation rate? What happens if half of them are? ## HOW TO CITE This model is based on Wilensky's Simple Birth Rates modelm, and was extended by Carlo C. Maley in 2018. To cite 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/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. ## COPYRIGHT AND LICENSE Copyright 1997 Uri Wilensky. ![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png) This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu. This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612. This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2001. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon 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240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle 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0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 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