{ "metadata": { "name": "Evolutionary_cycles_of_defection_and_cooperation" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Using pyevodyn to study a simple matrix game*" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "* Work in progress" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%reset\n", "import numpy as np\n", "import pyevodyn.numerical as num\n", "import matplotlib.pyplot as plt" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook analyzes the game in **\"Evolutionary cycles of defection and cooperation\"** by Imhof, Fudenberg and Nowak (*PNAS*, 2005). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first create a function to get the game as a numpy matrix. Strategies are *ALLC*, *ALLD* and *TFT*. Here *r*, *s*, *t*, *p* are the parameters of the one-shot PD game (reward, sucker, temptation and punishment); *c* is the cost of the conditional strategy and *m* is the expected number of rounds. Default values are those reported in Figure 1 of the paper." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def get_me_the_game(r=3.0, s=0.1, t=5.0, p=1.0, m=10.0, c=0.8):\n", " ans = np.empty(shape=(3,3))\n", " ans[0,0] = r*m\n", " ans[0,1] = s*m\n", " ans[0,2] = r*m\n", " ans[1,0] = t*m\n", " ans[1,1] = p*m\n", " ans[1,2] = t+p*(m-1.0)\n", " ans[2,0] = r*m-c\n", " ans[2,1] = s+p*(m-1.0)-c\n", " ans[2,2] = r*m-c\n", " return ans" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Deterministic dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot deterministic dynamics using the function **replicator_trajectory**, in the *numerical* module. Here we do it for a couple of starting points." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#firt, we get the game\n", "game_matrix = get_me_the_game()\n", "#we define a starting point\n", "x_0 = np.array([0.5, 0.2, 0.3])\n", "# we use the function replicator_trajectory from the numerical module\n", "orbits = num.replicator_trajectory(game_matrix, x_0, maximum_iterations= 80000)\n", "#Plotting stuff\n", "plt.rc('lines', linewidth=2.0)\n", "plt.figure(figsize=(20,4))\n", "plt.plot(orbits[0], 'b-', label='ALLC')\n", "plt.plot(orbits[1], 'r-', label = 'ALLD')\n", "plt.plot(orbits[2], 'g-', label='TFT')\n", "plt.rc('lines', linewidth=2.0)\n", "plt.legend()\n", "plt.title('(ALLC,ALLD,TFT) starting at $x_0$ = ' + str(x_0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 21, "text": [ "" ] }, { "output_type": "display_data", "png": 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Qkelg3SPrYGei3uF/1Dno6uiiu3V3dLfurtInqVZei7TiNFy5eQWXbl4S241L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IiIyAoTRkREREREREREZIUJIyIiIiIiIiIissKEERERERERERERWWHCiIiIiIiIiIiI\nrDBhREREREREREREVv4PxtSxGNlbekIAAAAASUVORK5CYII=\n" } ], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "#firt, we get the game\n", "game_matrix = get_me_the_game()\n", "#we define a starting point\n", "x_0 = np.array([0.4, 0.4, 0.2])\n", "# we use the function replicator_trajectory from the numerical module\n", "orbits = num.replicator_trajectory(game_matrix, x_0, maximum_iterations= 95000)\n", "#Plotting stuff\n", "plt.rc('lines', linewidth=2.0)\n", "plt.figure(figsize=(20,4))\n", "plt.plot(orbits[0], 'b-', label='ALLC')\n", "plt.plot(orbits[1], 'r-', label = 'ALLD')\n", "plt.plot(orbits[2], 'g-', label='TFT')\n", "plt.rc('lines', linewidth=2.0)\n", "plt.legend()\n", "plt.xlabel('Time')\n", "plt.ylabel('Frequency')\n", "plt.title('(ALLC,ALLD,TFT) starting at $x_0$ = ' + str(x_0))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 26, "text": [ "" ] }, { "output_type": "display_data", "png": 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cOULNmjWtXf49U3gkZcaRK0c4FX8KPzc/OtfubOtyREREKixvF2+6B3Wne1B3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} ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Stochastic dynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will inspect the stationary distribution of a Moran Process with small mutations (i.e., monomorphic populations). Payoff-to-fitness mapping uses an exponential function." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us first look at strategy abundance as a function of the intensity of selection. We use the function **monomorphous_transition_matrix**." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#we set the fixed parameters, mutation probability, population size and the game\n", "u = 0.001\n", "N=30\n", "game_matrix= get_me_the_game()\n", "#build the result for a range of intensity of selections\n", "intensity_vector = np.arange(start=0.0, stop=1.0, step= 0.01)\n", "allc_list= []\n", "alld_list= []\n", "tft_list= []\n", "for intensity_of_selection in intensity_vector:\n", " markov_chain = num.monomorphous_transition_matrix(intensity_of_selection, mutation_probability=u, population_size=N, game_matrix=game_matrix, mapping ='LIN')\n", " (allc, alld,tft) = num.stationary_distribution(markov_chain)\n", " allc_list.append(allc)\n", " alld_list.append(alld)\n", " tft_list.append(tft)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "#Plotting stuff\n", "plt.rc('lines', linewidth=2.0)\n", "plt.figure(figsize=(6,5))\n", "plt.plot(intensity_vector, allc_list, 'b-', label='ALLC')\n", "plt.plot(intensity_vector, alld_list, 'r-', label = 'ALLD')\n", "plt.plot(intensity_vector, tft_list, 'g-', label='TFT')\n", "plt.rc('lines', linewidth=2.0)\n", "plt.legend(loc='center right')\n", "#plt.title('Frequency in stationarity')\n", "plt.xlabel('Intensity of selection')\n", "plt.ylabel('Abundance')\n", "plt.xlim((0.0, 0.2))\n", "#plt.ylim((-0.01, 1.01))\n", "#plt.xscale('log')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 17, "text": [ "(0.0, 0.2)" ] }, { "output_type": "display_data", "png": 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xiIuLU5Xx8/NTBcLVq1fRtGlTrFixAvfff79m5W6Hh7q8ojzc9f5dcHNyw7W51+Di6KJd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\nvvpnarO+NuV1zefmMhyIiKg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} ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that cooperation only flourishes for weak intensity of selection! Now let's see how things depend on the expected number of rounds." ] }, { "cell_type": "code", "collapsed": false, "input": [ "#we set the fixed parameters, mutation probability, population size and intensity of selection\n", "u = 0.001\n", "N=30\n", "intensity_of_selection = 0.05\n", "\n", "#build the result for a range of m\n", "m_vector = np.arange(start=0.1, stop=20.0, step= 0.1)\n", "allc_list= []\n", "alld_list= []\n", "tft_list= []\n", "for m in m_vector:\n", " game_matrix= get_me_the_game(m=m)\n", " markov_chain = num.monomorphous_transition_matrix(intensity_of_selection, mutation_probability=u, population_size=N, game_matrix=game_matrix, mapping ='EXP')\n", " (allc, alld,tft) = num.stationary_distribution(markov_chain)\n", " allc_list.append(allc)\n", " alld_list.append(alld)\n", " tft_list.append(tft)\n", "#Plotting stuff\n", "plt.rc('lines', linewidth=2.0)\n", "plt.figure(figsize=(10,4))\n", "plt.plot(m_vector, allc_list, 'b-', label='ALLC')\n", "plt.plot(m_vector, alld_list, 'r-', label = 'ALLD')\n", "plt.plot(m_vector, tft_list, 'g-', label='TFT')\n", "plt.rc('lines', linewidth=2.0)\n", "plt.legend(loc='best')\n", "plt.title('Frequency in stationarity')\n", "plt.xlabel('Expected number of rounds')\n", "plt.ylabel('Abundance')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "pyout", "prompt_number": 43, "text": [ "" ] }, { "output_type": "display_data", "png": 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hWm/yH/+Af/4TjhyBH38ENze9qxNCCGECGZkZxKbEEp0UTUxyDDHJMUQn597P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\nQgg7kCRMCCGEEMIOJAkTQgghhLCD/wNniBJ1LVoqLgAAAABJRU5ErkJggg==\n" } ], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Cooperation does better with many rounds! Duh." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }