{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supporting material for\n",
    "# The probability of improvement in Fisher's geometric model: a probabilistic approach\n",
    "## by [Yoav Ram](http://www.yoavram.com) and [Lilach Hadany](https://sites.google.com/site/hadanylab/people/lilach-hadany)\n",
    "\n",
    "an article published in [_Theoretical Population Biology_](http://www.journals.elsevier.com/theoretical-population-biology/).\n",
    "\n",
    "This [IPython notebook](http://ipython.org/) is provided for reproduction of Figure 2 of the article. It can be viewed by copying its URL to [nbviewer](http://nbviewer.ipython.org) and it can be run by opening it in [binder](http://mybinder.org/repo/yoavram/FGMProb). The notebook also contains functions for deterministic and stochastic calculation of different quantities in FGM."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up\n",
    "\n",
    "We start by loading required modules and extensions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['draw_if_interactive', 'new_figure_manager']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "# This will probably produce a warning. That's OK.\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import scipy.stats as st\n",
    "import scipy.special as sp\n",
    "from scipy.integrate import quad as integrate\n",
    "rcParams['figure.figsize'] = 8,6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied (use --upgrade to upgrade): ipycache in d:\\workspace\\fgmprob\\venv\\lib\\site-packages\n"
     ]
    }
   ],
   "source": [
    "# http://nbviewer.ipython.org/github/rossant/ipycache/blob/master/examples/example.ipynb\n",
    "!pip install ipycache"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The ipycache extension is already loaded. To reload it, use:\n",
      "  %reload_ext ipycache\n"
     ]
    }
   ],
   "source": [
    "%load_ext ipycache"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "d = 1.0\n",
    "r = 0.1\n",
    "n = 10\n",
    "A = zeros(n)\n",
    "A[0] = d/2\n",
    "assert allclose(norm(A), d/2)\n",
    "reps = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`draw` is used to draw a random mutation in Fisher's geometric model, i.e., a random vector of magnitude `r`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def draw(d,r,n):\n",
    "    Z = normal(0,1,n)\n",
    "    X = r * Z / norm(Z)\n",
    "    assert allclose(r, norm(X))\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "X = draw(d,r,n)\n",
    "print X[0]/r < -r/d\n",
    "print norm(X + A) < norm(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Xs = array([draw(d,r,n) for _ in range(reps)])\n",
    "assert [X[0]/r < -r/d for X in Xs] == [norm(X + A) < norm(A) for X in Xs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of improvement\n",
    "\n",
    "We with the basic result, first presented by Fisher, of the probability of improvement in FGM.\n",
    "\n",
    "We estimate this probability by drawing many mutations and calculating the fraction of mutations that are beneficial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.38600000000000001, 0.015402637476784374)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate_pben(d,r,n):\n",
    "    A = zeros(n)\n",
    "    A[0] = d/2\n",
    "    assert allclose(norm(A), d/2)\n",
    "    Xs = array([draw(d,r,n) for _ in range(reps)])\n",
    "    ps = [(norm(X + A) < norm(A)) for X in Xs]\n",
    "    mean_p = mean(ps)\n",
    "    std_p = std(ps, ddof=1)/sqrt(float(reps))\n",
    "    return mean_p, std_p\n",
    "simulate_pben(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is $p_n^*$ from our article, first shown in (Kimura 1983) (see main text for references):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3849374999460683"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def kimura_pben(d,r,n): # Kimura\n",
    "    return 0.5 * sp.betainc((n-1)/2., 0.5, 1-r**2/d**2)\n",
    "kimura_pben(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is Fisher's original result from (Fisher 1930):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.37591481702292462"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def fisher_pben(d,r,n):\n",
    "    return 1-st.norm.cdf(sqrt(n)*r/d)\n",
    "fisher_pben(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is $p^{\\#}_{n}$, from (Hartl & Taubes 1996; Rice 1990):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38493749994606824"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def hartl_pben(d,r,n): # Hartl & Taubes 1996, eq. 1\n",
    "    numer = integrate(lambda x: sin(x)**(n-2), 0, arccos(r/d))[0]\n",
    "    denom = integrate(lambda x: sin(x)**(n-2), 0, pi)[0]\n",
    "    return numer/denom\n",
    "hartl_pben(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now do the calculations and plot a figure, which is not used in the main text:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Skipped the cell's code and loaded variables nrange, pben_emp from file 'D:\\workspace\\FGMProb\\pben_emp.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache pben_emp.pkl nrange pben_emp\n",
    "nrange = range(2,102,5)\n",
    "pben_emp = array([simulate_pben(d,r,n) for n in nrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pben_kimura = [kimura_pben(d,r,n) for n in nrange]\n",
    "pben_fisher = [fisher_pben(d,r,n) for n in nrange]\n",
    "pben_hartl = [hartl_pben(d,r,n) for n in nrange]\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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8KpWKadOmvVEbhb0PDUH6UH/Sh/qTRECIQmj8+PE8e/aMQ4cOaT1PL4QQOUkSASGEEKIQ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\nAiIiIg5MjYCIiIgDUyMgIiLiwP4/bGbkiFmGM14AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe409ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorbar(nrange, pben_emp[:,0], yerr=pben_emp[:,1], fmt='.k', capsize=10, label='Empricial')\n",
    "plot(nrange, pben_kimura, '-k', lw=2, label='Theoretical')\n",
    "plot(nrange, pben_fisher, '--r', label='Fisher')\n",
    "plot(nrange, pben_hartl, '-b', label='Hartl')\n",
    "xlim(-5,105)\n",
    "xticks([1]+range(20,101,20))\n",
    "yticks(arange(0.15,0.5,0.1))\n",
    "xlabel(\"$n$\", fontsize=16)\n",
    "ylabel(r\"$P(|A+X|<|A|)$\", fontsize=16)\n",
    "title(\"Probability of a beneficial mutation\")\n",
    "legend(fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expected improvement towards optimum\n",
    "\n",
    "Next, we evaluate the expected improvement towards the optimum in FGM. Functions denoted by `TPB` refer to equations derived in the main text."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.033368079181765507, 0.00050703916553601364)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate_X1(d,r,n):\n",
    "    A = zeros(n)\n",
    "    A[0] = d/2\n",
    "    assert allclose(norm(A), d/2)\n",
    "    p = kimura_pben(d,r,n)\n",
    "    Xs = array([draw(d,r,n) for _ in range(int(reps/p))])\n",
    "    X1 = [abs(X[0]) for X in Xs if (norm(A + X) < norm(A))]\n",
    "    mean_X1 = mean(X1)\n",
    "    std_X1 = std(X1, ddof=1)/sqrt(len(X1))\n",
    "    return mean_X1, std_X1\n",
    "simulate_X1(d,r,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.032115722558925502"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def TPB_X1(d,r,n):\n",
    "    r2d2 = (r**2) / (d**2)\n",
    "    n_min_1_by_2 = 0.5 * (n-1)\n",
    "    numer = 2 * r * (1 - r2d2)**n_min_1_by_2\n",
    "    denom = (n - 1) * sp.betainc(n_min_1_by_2, 0.5, 1 - r2d2) * sp.beta(n_min_1_by_2, 0.5)\n",
    "    return numer/denom\n",
    "TPB_X1(d,r,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Skipped the cell's code and loaded variables X1_emp from file 'D:\\workspace\\FGMProb\\X1_emp.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache X1_emp.pkl X1_emp\n",
    "X1_emp = array([simulate_X1(d,r,n) for n in nrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X1_TPB = array([TPB_X1(d,r,n) for n in nrange])\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qIzw8PEpdXtY8JZUtX90ePHiATz75RPOrunPnzjhw4AC2bt2qSQQWLVoEmUyG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\nSMSYCBAREYkYEwEiIiIR+z8l03DIDQKWogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe6c0828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorbar(nrange, X1_emp[:,0], yerr=X1_emp[:,1], fmt='.k', capsize=10, label='empricial')\n",
    "plot(nrange, X1_TPB, '--k', lw=2, label='Theoretical')\n",
    "xlim(-5,105)\n",
    "xticks([1]+range(20,101,20))\n",
    "xlabel(\"$n$\", fontsize=16)\n",
    "ylabel(r\"$E[|X_1| | |A+X|<|A|]$\", fontsize=16)\n",
    "title(\"Expected effect towards optimum in beneficial mutations\")\n",
    "legend(fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expected $\\Delta d$\n",
    "\n",
    "The following quantity does not appear at all in the meain text, but rather in (Hartl and Taubes 1996). Here $\\Delta$ is the change in phenotypic distance to the optimal phenotype."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.022234901179445685, 0.00052840418560986993)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d,r,n = 1., 0.1, 10\n",
    "def simulate_deltad(d,r,n):\n",
    "    A = zeros(n)\n",
    "    A[0] = d/2\n",
    "    assert allclose(norm(A), d/2)\n",
    "    p = kimura_pben(d,r,n)\n",
    "    Xs = array([draw(d,r,n) for _ in range(int(reps/p))])\n",
    "    deltad = [abs(norm(A+X) - norm(A)) for X in Xs if (norm(A + X) < norm(A))]\n",
    "    mean_deltad = mean(deltad)\n",
    "    std_deltad = std(deltad, ddof=1)/sqrt(len(deltad))\n",
    "    return mean_deltad, std_deltad\n",
    "simulate_deltad(d,r,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0229329880606476"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def hartl_deltad(d,r,n): # Hartl & Taubes 1996, eq. 3\n",
    "    delta = lambda theta: d/2 - sqrt(0.25 * d**2 + r**2 - r * d * cos(theta))\n",
    "    numer = integrate(lambda x: delta(x) * sin(x)**(n-2), 0, arccos(r/d))[0]\n",
    "    denom = integrate(lambda x: sin(x)**(n-2), 0, arccos(r/d))[0]\n",
    "    return numer/denom\n",
    "hartl_deltad(d,r,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Skipped the cell's code and loaded variables deltad_emp from file 'D:\\workspace\\FGMProb\\deltad_emp.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache deltad_emp.pkl deltad_emp\n",
    "deltad_emp = array([simulate_deltad(d,r,n) for n in nrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "deltad_hartl = array([hartl_deltad(d,r,n) for n in nrange])\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aNWs0zvPjjz9CoVDgvffeQ2lpKZYtW4ZnnnkGe/fuhUwmU5c7c+YM5s2bh1df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\nxP4/pCv0rdNonDoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe567208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorbar(nrange, deltad_emp[:,0], yerr=deltad_emp[:,1], fmt='.k', capsize=10, label='empricial')\n",
    "plot(nrange, deltad_hartl, '-b', label='Hartl')\n",
    "xlim(-5,105)\n",
    "#ylim(0.1, 0.5)\n",
    "xticks([1]+range(20,101,20))\n",
    "#yticks(arange(0.15,0.5,0.1))\n",
    "xlabel(\"$n$\", fontsize=16)\n",
    "ylabel(r\"$E[|A+X|-|A| | |A+X|<|A|]$\", fontsize=16)\n",
    "title(\"Expected change in distance in beneficial mutations\")\n",
    "legend(fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expected _s_\n",
    "\n",
    "Here we analyze the expected change in fitness in beneficial mutations. Fitness is defined by:\n",
    "$$\\omega(A) = 1 - ||A||^2$$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fitness(A):\n",
    "    return 1 - norm(A)**2\n",
    "assert fitness([d/2,0,0]) == 1 - d**2/4\n",
    "assert fitness(zeros(n)) == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.030619426578933063, 0.00070996698649594962)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d,r,n = 1., 0.1, 10\n",
    "def simulate_s(d,r,n):\n",
    "    A = zeros(n)\n",
    "    A[0] = d/2\n",
    "    assert allclose(norm(A), d/2)\n",
    "    fitness_A = fitness(A)\n",
    "    p = kimura_pben(d,r,n)\n",
    "    Xs = array([draw(d,r,n) for _ in range(int(reps/p))])\n",
    "    s = array([fitness(X + A)/fitness_A - 1 for X in Xs])\n",
    "    s = s[s > 0]\n",
    "    mean_s = mean(s)\n",
    "    std_s = std(s, ddof=1)/sqrt(len(s))\n",
    "    return mean_s, std_s\n",
    "simulate_s(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is equation (10) from the main text:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.029487630078567334"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def TPB_s(d,r,n):\n",
    "    r2d2 = (r**2) / (d**2)    \n",
    "    n1by2 = 0.5 * (n-1)\n",
    "    s = 2 * d * r * (1 - r2d2)**n1by2\n",
    "    s /= (n - 1) * (1 - 0.25 * d**2) * sp.betainc(n1by2, 0.5, 1 - r2d2) * sp.beta(n1by2, 0.5)\n",
    "    s -= r**2 / (1 - 0.25 * d**2)    \n",
    "    return s\n",
    "TPB_s(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same value, calculated from $\\Delta$ (Hartl & Taubes 1996):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.029876088159010328"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def hartl_s(d,r,n):\n",
    "    deltad = hartl_deltad(d,r,n)\n",
    "    s = fitness(d/2 - deltad)/fitness(d/2) - 1\n",
    "    return s\n",
    "hartl_s(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the results, once for $n$, number of traits, and once for $r$, the mutation size ($d$ is fixed at 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Skipped the cell's code and loaded variables reps, s_emp from file 'D:\\workspace\\FGMProb\\s_emp.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache s_emp.pkl reps s_emp\n",
    "reps = 500\n",
    "s_emp = array([simulate_s(d,r,n) for n in nrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s_TPB= array([TPB_s(d,r,n) for n in nrange])\n",
    "s_hartl = array([hartl_s(d,r,n) for n in nrange])\n",
    "n = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cuLq6olWrVnj++ef15aKiorBu3TrEx8dj3LhxUCgUiIiIwLvvvluuW7+i/Rq7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\nfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe5c87b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorbar(nrange, s_emp[:,0], yerr=s_emp[:,1], fmt='ok', capsize=10, label='Empricial')\n",
    "plot(nrange, s_TPB, '--k', lw=2, label='Theoretical')\n",
    "plot(nrange, s_hartl, '-b', label='Hartl')\n",
    "xlim(-5,105)\n",
    "ylim(0, 0.09)\n",
    "xticks([1]+range(20,101,20))\n",
    "yticks(arange(0.02,0.1,0.02))\n",
    "xlabel(\"$n$\", fontsize=16)\n",
    "ylabel(r\"$E[s | s>0]$\", fontsize=16)\n",
    "title(\"Expected selection coefficient in beneficial mutations\")\n",
    "legend(fontsize=16);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "rrange = linspace(0.001,0.5,25)\n",
    "s_TPB_r = array([TPB_s(d,r,n) for r in rrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Skipped the cell's code and loaded variables reps, s_emp_r from file 'D:\\workspace\\FGMProb\\s_emp_r.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache s_emp_r.pkl reps s_emp_r\n",
    "reps = 500\n",
    "s_emp_r = array([simulate_s(d,r,n) for r in rrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YO1X171DeOazvOSqTycp9b1U51w3l7bffxq5du/Dxxx/D398ftra2mD17NvLz8ytdlrYh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\nCAAAYGEUAQAALOx/jemt4noDh1kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe567780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "errorbar(rrange, s_emp_r[:,0], yerr=s_emp_r[:,1], fmt='ok', capsize=10, label='Empricial')\n",
    "plot(rrange, s_TPB_r, '--k', lw=2, label='Theoretical')\n",
    "xlim(-0.01,0.51)\n",
    "ylim(0, 0.09)\n",
    "#xticks([1]+range(20,101,20))\n",
    "yticks(arange(0.02,0.1,0.02))\n",
    "xlabel(\"$r$\", fontsize=16)\n",
    "ylabel(r\"$E[s | s>0]$\", fontsize=16)\n",
    "title(\"Expected selection coefficient in beneficial mutations\")\n",
    "legend(loc=2,fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fixation probability\n",
    "\n",
    "The main result of this notebook, the probability that a mutation (a) is beneficial, and (b) avoids extinction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "d = 1.\n",
    "r = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a Wright-Fisher simulation. A single mutation appears in the population, and if it is beneficial, the evolutionary process proceeds until the mutation either reaches majority (`f > 0.5`) or goes to extinction (`f < 1/N`). $N$ is the variance effective population size. The simulation includes both selection:\n",
    "$$\n",
    "f' = f / \\bar{\\omega} \\\\\\\\\n",
    "\\bar{\\omega} = f + (1-f)(1-s),\n",
    "$$\n",
    "and drift:\n",
    "$$\n",
    "n \\sim Bin(N,f) \\\\\\\\\n",
    "f'' = n/N.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulation(d,r,n,N = 1e6):\n",
    "    N = float(N)\n",
    "    A = zeros(n)\n",
    "    A[0] = d/2\n",
    "    X = draw(d,r,n)\n",
    "    s = fitness(A + X)/fitness(A) - 1\n",
    "    if s < 0:\n",
    "        return False    \n",
    "    f = 1/N\n",
    "    while True:\n",
    "        assert 0 <= f <= 1\n",
    "        if f < 1/N: return False\n",
    "        elif f > 0.5: return True        \n",
    "        f = f \n",
    "        f /= 1 - s * (1 - f)\n",
    "        f = binomial(N,f)/N\n",
    "simulation(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function estimates the fixation probability by running many simulations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.031, 0.0054807846153630381)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate_pfix(d,r,n,reps=1000):\n",
    "    fixes = array([simulation(d,r,n) for _ in range(reps)])\n",
    "    return mean(fixes), std(fixes) / sqrt(reps)\n",
    "simulate_pfix(d,r,n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is equation (6) from the main text:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02270178920355639"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def TPB_pfix(d,r,n):\n",
    "    s = TPB_s(d,r,n)\n",
    "    p = kimura_pben(d,r,n)\n",
    "    return 2*s*p\n",
    "TPB_pfix(d,r,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rrange = linspace(0.001,0.5,25)\n",
    "pfix_TPB = array([TPB_pfix(d,r,n) for r in rrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[Saved variables pfix_emp, reps to file 'D:\\workspace\\FGMProb\\pfix_emp.pkl'.]\n"
     ]
    }
   ],
   "source": [
    "%%cache pfix_emp.pkl pfix_emp reps\n",
    "reps = 100000\n",
    "pfix_emp = array([simulate_pfix(d,r,n,reps=reps) for r in rrange])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 10\n",
    "r = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we plot Figure 2, the fixation probability as a function of $r/d$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JicH48eOLfE5xYgKAp0+fYuTIkYiLi8PevXsxc+ZMDBs2DCYmJrCyskLlypURERGB+Ph4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\ngQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe8813c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = subplots(1, 1, figsize=(10,8))\n",
    "ax.errorbar(rrange, pfix_emp[:,0], yerr=pfix_emp[:,1], fmt='.k', capsize=5, label='Empricial')\n",
    "ax.plot(rrange, pfix_TPB, '-k', lw=2, label='Theoretical')\n",
    "ax.set_xlabel(\"Relative mutation size - $r/d$\", fontsize=24)\n",
    "ax.set_ylabel(r\"Fixation probability - $p_{fix}$\", fontsize=24)\n",
    "ax.set_xlim(-0.01, 0.51)\n",
    "ax.set_xticks(arange(0, 0.51, 0.1))\n",
    "ax.set_ylim(-0.001, 0.0311)\n",
    "ax.set_yticks(arange(0, 0.031, 0.01))\n",
    "ax.set_title(\"Fixation probability of beneficial mutations\")\n",
    "\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ax.set_title('')\n",
    "ax.legend().set_visible(False)\n",
    "fig.savefig(\"fig2.png\")\n",
    "fig.savefig(\"fig2.pdf\", dpi=300, papertype='a4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fin\n",
    "\n",
    "This IPython notebook was written by [Yoav Ram](http://www.yoavram.com) as supplementry material for a TPB article. \n",
    "\n",
    "The content is licensed under a CC-BY-SA 3.0 lincese."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}