{ "cells": [ { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import sys\n", "import os\n", "import math\n", "import importlib\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import random\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "def simulate(initialRatio):\n", " rand = random.Random(1337)\n", " nprand = np.random.RandomState(1337)\n", " populationSize = 5000 # small town \n", " # model # of children as Poisson:\n", " # 2.5 avg children, and for Poisson, mean=variance\n", " # note that the 2.5 number is for present day - that's a conservative choice for it\n", " # since in past it's much higher:\n", " # https://ourworldindata.org/fertility-rate#the-number-of-children-per-woman-over-the-very-long-run\n", " numChildrenMeanVariance = 2.5\n", " # initialize the initial generation\n", " initialSeeds = rand.sample(range(populationSize), int(populationSize * initialRatio))\n", " population = [False]*populationSize \n", " for i in initialSeeds:\n", " population[i] = True\n", " \n", " result = [(populationSize, len(initialSeeds))]\n", " \n", " # start simulating\n", " generations = 10\n", " for generation in range(generations):\n", " # shuffle the array\n", " newpopulation = []\n", " rand.shuffle(population)\n", " popWithTrait = 0\n", " # for each (randomly shuffled) pair:\n", " endval = len(population) & ~1\n", " for i in range(0, endval, 2):\n", " # generate number of children\n", " # if any parent has it, child has it\n", " hasIt = population[i] or population[i+1]\n", " numChildren = int(nprand.poisson(numChildrenMeanVariance))\n", " newpopulation = newpopulation + [hasIt]*numChildren\n", " if hasIt:\n", " popWithTrait += numChildren\n", " print(len(newpopulation), popWithTrait)\n", " result.append((len(newpopulation), popWithTrait))\n", " population = newpopulation\n", " return result" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "starting 0.01\n", "6274 122\n", "7931 309\n", "9802 762\n", "12308 1893\n", "15391 4408\n", "19233 9394\n", "24130 17844\n", "30183 28139\n", "37865 37670\n", "47289 47289\n", "starting 0.05\n", "6274 641\n", "7931 1511\n", "9802 3410\n", "12308 7127\n", "15391 12619\n", "19233 18552\n", "24130 24091\n", "30183 30183\n", "37865 37865\n", "47289 47289\n", "starting 0.1\n", "6274 1193\n", "7931 2673\n", "9802 5470\n", "12308 9924\n", "15391 14831\n", "19233 19214\n", "24130 24130\n", "30183 30183\n", "37865 37865\n", "47289 47289\n", "starting 0.15\n", "6274 1768\n", "7931 3907\n", "9802 7301\n", "12308 11511\n", "15391 15294\n", "19233 19233\n", "24130 24130\n", "30183 30183\n", "37865 37865\n", "47289 47289\n", "starting 0.2\n", "6274 2247\n", "7931 4629\n", "9802 8152\n", "12308 11904\n", "15391 15380\n", "19233 19233\n", "24130 24130\n", "30183 30183\n", "37865 37865\n", "47289 47289\n" ] } ], "source": [ "ratios = [0.01, 0.05, 0.10, 0.15, 0.20]\n", "simresults = []\n", "for ratio in ratios:\n", " print(\"starting\", ratio)\n", " simresults.append(simulate(ratio))" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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