finding-generalized-sexual-selection-equilibra.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load_ext autoreload"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%autoreload 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import integrate, linalg, optimize\n",
    "\n",
    "%aimport models\n",
    "import payoffs\n",
    "import selection_functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.style.use(\"ggplot\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding an equilibrium\n",
    "\n",
    "Finding an equilibrium is easy, finding a *stable* equilibrium is more difficult."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "optimize.least_squares?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# random initial guess\n",
    "prng = np.random.RandomState()\n",
    "x0, = prng.dirichlet(np.ones(4), 1)\n",
    "\n",
    "# embed relevant params into the function f whose root is an equilibrium\n",
    "UGA = lambda x_A: selection_functions.kirkpatrick_selection(x_A, 1.5)\n",
    "UgA = lambda x_A: selection_functions.kirkpatrick_selection(x_A, 1)\n",
    "payoff_kernel = payoffs.prisoners_dilemma_payoffs(prng)\n",
    "f = lambda x: models.generalized_sexual_selection(x.reshape(-1,1), UGA, UgA, payoff_kernel, mutation_rate=1e-3).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.700675087064 0.299324912936\n",
      "0.70066903161 0.299324912936\n",
      "0.700681142519 0.299324912936\n",
      "0.700675087064 0.299318857481\n",
      "0.700675087064 0.29933096839\n",
      "0.70066903161 0.299324912936\n",
      "0.700681142519 0.299324912936\n",
      "0.700675087064 0.299318857481\n",
      "0.700675087064 0.29933096839\n",
      "0.801283006433 0.248636285085\n"
     ]
    },
    {
     "ename": "AssertionError",
     "evalue": "1-x_A should equal x_a; actual difference is -0.04991929151804603",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-218-e18c73e621ab>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# use non-linear solver to find the equilibrium\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimize\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mleast_squares\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"3-point\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbounds\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgtol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-12\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_lsq/least_squares.py\u001b[0m in \u001b[0;36mleast_squares\u001b[0;34m(fun, x0, jac, bounds, method, ftol, xtol, gtol, x_scale, loss, f_scale, diff_step, tr_solver, tr_options, jac_sparsity, max_nfev, verbose, args, kwargs)\u001b[0m\n\u001b[1;32m    906\u001b[0m         result = trf(fun_wrapped, jac_wrapped, x0, f0, J0, lb, ub, ftol, xtol,\n\u001b[1;32m    907\u001b[0m                      \u001b[0mgtol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_nfev\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_scale\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss_function\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtr_solver\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 908\u001b[0;31m                      tr_options.copy(), verbose)\n\u001b[0m\u001b[1;32m    909\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    910\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmethod\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'dogbox'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_lsq/trf.py\u001b[0m in \u001b[0;36mtrf\u001b[0;34m(fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev, x_scale, loss_function, tr_solver, tr_options, verbose)\u001b[0m\n\u001b[1;32m    126\u001b[0m         return trf_bounds(\n\u001b[1;32m    127\u001b[0m             \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjac\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mJ0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mub\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mftol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxtol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgtol\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_nfev\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_scale\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 128\u001b[0;31m             loss_function, tr_solver, tr_options, verbose)\n\u001b[0m\u001b[1;32m    129\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_lsq/trf.py\u001b[0m in \u001b[0;36mtrf_bounds\u001b[0;34m(fun, jac, x0, f0, J0, lb, ub, ftol, xtol, gtol, max_nfev, x_scale, loss_function, tr_solver, tr_options, verbose)\u001b[0m\n\u001b[1;32m    339\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    340\u001b[0m             \u001b[0mx_new\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_strictly_feasible\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstep\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mub\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrstep\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 341\u001b[0;31m             \u001b[0mf_new\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_new\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    342\u001b[0m             \u001b[0mnfev\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    343\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/scipy/optimize/_lsq/least_squares.py\u001b[0m in \u001b[0;36mfun_wrapped\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m    792\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    793\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mfun_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 794\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0matleast_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    795\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    796\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mmethod\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'trf'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-217-2973baa53af5>\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mUgA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx_A\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mselection_functions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkirkpatrick_selection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_A\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mpayoff_kernel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpayoffs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mprisoners_dilemma_payoffs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprng\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 9\u001b[0;31m \u001b[0mf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mmodels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgeneralized_sexual_selection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mUGA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mUgA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpayoff_kernel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmutation_rate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/Research/evolution-of-cooperation/models.py\u001b[0m in \u001b[0;36mgeneralized_sexual_selection\u001b[0;34m(x, UGA, UgA, payoff_kernel, mutation_rate, number_of_potential_mates)\u001b[0m\n\u001b[1;32m     38\u001b[0m     \u001b[0mx_A\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_a\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     39\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_A\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_a\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 40\u001b[0;31m     \u001b[0;32massert\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mallclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_a\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mx_A\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0matol\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"1-x_A should equal x_a; actual difference is {}\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mx_A\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mx_a\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     42\u001b[0m     \u001b[0;31m# determine the payoffs\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAssertionError\u001b[0m: 1-x_A should equal x_a; actual difference is -0.04991929151804603"
     ]
    }
   ],
   "source": [
    "# use non-linear solver to find the equilibrium\n",
    "result = optimize.least_squares(f, x0, jac=\"3-point\", bounds=(0.0, 1.0), gtol=1e-12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " active_mask: array([0, 0, 0, 0])\n",
       "        cost: 4.3955587969635061e-14\n",
       "         fun: array([ -2.95410298e-07,  -1.92344596e-08,  -1.45823052e-08,\n",
       "         7.83094767e-09])\n",
       "        grad: array([  2.96801229e-07,  -8.36710669e-14,   1.59734395e-08,\n",
       "        -8.48627332e-14])\n",
       "         jac: array([[ -9.99998794e-01,  -1.81716371e-13,   4.92350261e-07,\n",
       "         -1.81716371e-13],\n",
       "       [ -5.14049948e-02,  -2.89331098e-01,  -5.14049350e-02,\n",
       "         -2.89331054e-01],\n",
       "       [  2.43038320e-08,  -7.46319093e-15,  -9.99999469e-01,\n",
       "         -7.46319093e-15],\n",
       "       [  5.14037643e-02,  -7.10668902e-01,   5.14039113e-02,\n",
       "         -7.10668946e-01]])\n",
       "     message: '`gtol` termination condition is satisfied.'\n",
       "        nfev: 20\n",
       "        njev: 20\n",
       "  optimality: 8.7678193354280249e-14\n",
       "      status: 1\n",
       "     success: True\n",
       "           x: array([  2.95410480e-07,   2.89331070e-01,   1.45823127e-08,\n",
       "         7.10668941e-01])"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check stability\n",
    "\n",
    "Asymptotic stability requires that the eigenvalues of the Jacobian matrix all have negative real parts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "f_jac = result[\"jac\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigvals = linalg.eigvals(f_jac)\n",
    "np.all(np.real(eigvals) < 0.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Interactive simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_generalized_sexual_selection(x0=0.25, x1=0.25, x2=0.25, selection_function=\"kirkpatrick\",\n",
    "                                      d0=1, d2=1, T=10, R=6, P=4, S=0, mutation_rate=0.0, max_time=10):\n",
    "\n",
    "    fig, ax = plt.subplots(1,1, figsize=(10,8))\n",
    "\n",
    "    # prepare the axes\n",
    "    ax.set_ylim((0, 1))\n",
    "    ax.set_xlabel(r\"Time, $t$\", fontsize=15)\n",
    "    ax.set_ylabel(r\"Female genotype shares, $x_i$\", fontsize=15)\n",
    "    \n",
    "    # create the initial condition\n",
    "    x3 = 1 - (x0 + x1 + x2)\n",
    "    y0=np.array([x0,x1,x2,x3])\n",
    "    assert np.allclose(y0.sum(), 1)\n",
    "    \n",
    "    # create the payoff kernel\n",
    "    assert T > R and R > P and R > S, \"Payoffs must satisfy either Prisoner's Dilemma or Stag Hunt constraints!\"\n",
    "    payoff_kernel = np.array([[R, S],\n",
    "                              [T, P]])\n",
    "    \n",
    "    # create the selection functions\n",
    "    if selection_function == \"kirkpatrick\":\n",
    "        UGA = lambda x_A: selection_functions.kirkpatrick_selection(x_A, d0)\n",
    "        UgA = lambda x_A: selection_functions.kirkpatrick_selection(x_A, d2)\n",
    "    elif selection_function == \"seger\":\n",
    "        UGA = lambda x_A: selection_functions.seger_selection(x_A, d0)\n",
    "        UgA = lambda x_A: selection_functions.seger_selection(x_A, d2)\n",
    "    else:\n",
    "      raise ValueError(\"selection_function must be one of \\\"kirkpatrick\\\" or \\\"seger\\\".\")\n",
    "    \n",
    "    # simulate the model starting from a random initial condition\n",
    "    f = lambda t, y: models.generalized_sexual_selection(y, UGA, UgA, payoff_kernel, mutation_rate)\n",
    "    result = integrate.solve_ivp(f, t_span=(0, max_time), y0=y0, rtol=1e-9, atol=1e-12,\n",
    "                                 dense_output=True, vectorized=True)\n",
    "    \n",
    "    ax.plot(result.t, result.y[0], label=\"GA\")\n",
    "    ax.plot(result.t, result.y[1], label=\"Ga\")\n",
    "    ax.plot(result.t, result.y[2], label=\"gA\")\n",
    "    ax.plot(result.t, result.y[3], label=\"ga\")\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/X0ePHm1Zvn37ds2aNUvz588PekAAAAAEWNrS09P10EMPqUuXLpo1a5bee+893XfffZo3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\nGQYU2kRERESGgf8HLhlifunp02AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ac6780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = plot_generalized_sexual_selection(selection_function=\"kirkpatrick\", T=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "175c4329766e46a98d4ce0bb31bf8dfc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "A Jupyter Widget"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sliders used to control the initial condition\n",
    "x0_slider = widgets.FloatSlider(value=0.45, min=0.0, max=1.0, step=0.01, description=r\"$x_0$\")\n",
    "x1_slider = widgets.FloatSlider(value=0.37, min=0.0, max=1.0, step=0.01, description=r\"$x_1$\")\n",
    "x2_slider = widgets.FloatSlider(value=0.13, min=0.0, max=1.0, step=0.01, description=r\"$x_2$\")\n",
    "\n",
    "# sliders used to control the Prisoner's Dilemma Payoffs\n",
    "T_slider = widgets.FloatSlider(value=4, min=0, max=100, step=0.1, description=r\"$T$\")\n",
    "R_slider = widgets.FloatSlider(value=3, min=0, max=100, step=0.1, description=r\"$R$\")\n",
    "P_slider = widgets.FloatSlider(value=2, min=0, max=100, step=0.1, description=r\"$P$\")\n",
    "S_slider = widgets.FloatSlider(value=1, min=0, max=100, step=0.1, description=r\"$S$\")\n",
    "\n",
    "# slider used to control which selection function is being used\n",
    "U_slider = widgets.Dropdown(options=[\"kirkpatrick\", \"seger\"], index=0, description=r\"$U$\")\n",
    "\n",
    "# slider that controls the parameters of the selection function\n",
    "d0_slider = widgets.FloatSlider(value=1.5, min=0.0, max=10, step=0.05, description=r\"$d_0$\")\n",
    "d2_slider = widgets.FloatSlider(value=1, min=0.0, max=10, step=0.05, description=r\"$d_2$\")\n",
    "\n",
    "# slider used to control the mutation rate\n",
    "e_slider = widgets.FloatSlider(value=0.01, min=0.0, max=1.0, step=1e-3, description=r\"$\\epsilon$\", readout_format=\".3f\")\n",
    "\n",
    "# slider that controls max simulation time\n",
    "max_time_slider = widgets.IntSlider(value=500, min=10, max=2000, description=r\"$\\max t$\")\n",
    "\n",
    "w = widgets.interactive(plot_generalized_sexual_selection, x0=x0_slider, x1=x1_slider, x2=x2_slider,\n",
    "                        selection_function=U_slider, d0=d0_slider, d2=d2_slider, \n",
    "                        T=T_slider, R=R_slider, P=P_slider, S=S_slider, \n",
    "                        mutation_rate=e_slider, max_time=max_time_slider)\n",
    "display(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 882,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,\n",
       "        1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])"
      ]
     },
     "execution_count": 882,
     "metadata": {},
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   "execution_count": null,
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    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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