{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Figure 2: Drawing a phase diagram of immune strategies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains the data analysis and visualization code needed to reproduce Figure 2. The figure explores optimal immune strategies as a function of the characteristic time and frequency of pathogens."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prerequisite: produce numerical data\n",
    "\n",
    "To generate the data needed for the following plot type\n",
    "\n",
    "    make run\n",
    "\n",
    "followed by\n",
    "\n",
    "    make agg\n",
    "    \n",
    "This will generate three data files `phases.npz`, `pienvcut.npz` and `tauenvcut.npz` which contain respectively numerical results about the position of various phase boundaries, optimal parameters along a cut for fixed $\\pi_{\\rm env}$, and optimal parameters along a cut for fixed $\\tau_{\\rm env}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import a number of packages that we will need in the following."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "use czrecursion, cztogrowthrate\n",
      "use cstepmarkov\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "sys.path.append('../lib/')\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "pd.options.mode.chained_assignment = None\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm, lines, transforms, gridspec, ticker\n",
    "%matplotlib inline\n",
    "import palettable\n",
    "import shapely.geometry\n",
    "import shapely.ops\n",
    "import plotting\n",
    "import evolimmune\n",
    "import analysis\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "plt.style.use(['paper'])\n",
    "eps = 1e-8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in data about the position of phase boundaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "df = analysis.loadnpz('data/phases.npz')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following gives a summary of the data we just have read in. The columns with a single unique entries correspond to parameters set to a fixed value throughout the different optimizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------------------------------------------\n",
      "values of columns with no more than 10 unique entries\n",
      "\n",
      "boundary: ac; ap; cm; io; mi; pc; pi; pm; po\n",
      "boundtol: 0.005\n",
      "cup: 0.1*pup+pup**2\n",
      "deltainit: 0.02\n",
      "deltatol: 0.0005\n",
      "lambda_: 3.0\n",
      "logfeps: -9.0\n",
      "mus: 1.0-2.0*epsilon/(1.0+epsilon), 1.0+0.8*epsilon\n",
      "nburnin: 10000.0\n",
      "niter: 1000000.0\n",
      "qboundtol: 0.0005\n",
      "xtol: 0.025\n",
      "xtolbound: 0.01\n",
      "-----------------------------------------------------\n",
      "summary statistics of other columns\n",
      "\n",
      "             aenv    pienvbnd\n",
      "count  126.000000  126.000000\n",
      "mean     0.499338    0.537614\n",
      "std      0.355532    0.291394\n",
      "min      0.000015   -0.025946\n",
      "25%      0.133078    0.354840\n",
      "50%      0.523847    0.582708\n",
      "75%      0.855588    0.759486\n",
      "max      0.951229    0.999274\n",
      "-----------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "analysis.intelligent_describe(df, nunique=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deduce phases from boundaries between strategies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "polygons = evolimmune.polygons_from_boundaries(df, yconv=evolimmune.to_tau)\n",
    "phases = evolimmune.phases_from_polygons(polygons)\n",
    "complete = polygons['complete']\n",
    "c = phases['c']\n",
    "a = phases['a']\n",
    "pa = phases['p']\n",
    "one = phases['o']\n",
    "i = phases['i']\n",
    "mix = phases['m']\n",
    "qpos = shapely.ops.cascaded_union([c, mix, i])\n",
    "strategies = [a, pa, one, i, mix, c]\n",
    "strategies_s = ['a', 'p', 'o', 'i', 'm', 'c']\n",
    "strategies_s_long = [r'adaptive', 'proto-\\nadaptive', r'innate', 'innate\\nbet\\nhedging', r'mixed', r'CRISPR-like']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define some common plotting parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "commontextkwargs = dict(ha='center', va='center')\n",
    "phaselabelkwargs = dict(fontsize='large')\n",
    "phaselabelkwargs.update(commontextkwargs)\n",
    "ymargin = 0.05\n",
    "ymin, ymax = evolimmune.to_tau(df.aenv.min()), evolimmune.to_tau(df.aenv.max())\n",
    "pad = 0.25\n",
    "black = matplotlib.rcParams['text.color']\n",
    "grey = 'grey'\n",
    "colors = np.asarray(palettable.colorbrewer.qualitative.Set3_6.mpl_colors)[[4, 0, 2, 3, 5, 1]]\n",
    "linecolors = dict(zip(('pup', 'p', 'cconstitutive', 'q', 'tau', 'tau1'), palettable.colorbrewer.qualitative.Dark2_6.mpl_colors))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define helper functions for plotting and labelling phases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_phases(ax, ylimmax, patchkwargs=dict()):\n",
    "    for i, s in enumerate(strategies):\n",
    "        try:\n",
    "            ax.add_patch(analysis.shapely_to_mpl(s, ec='None', fc=colors[i], **patchkwargs))\n",
    "        except:\n",
    "            pass\n",
    "    ax.set_xlim(0, 1)\n",
    "    ax.set_ylim(ymin, ymax)\n",
    "    ax.set_yscale('log')\n",
    "    plotting.despine(ax, spines='all')\n",
    "\n",
    "sx = dict(a=0.18, p=0.54, o=0.87, i=0.87, m=0.65, c=0.35)\n",
    "sy = dict(a=0.5, p=0.3, o=0.3, i=3.5, m=4.2, c=8.0)\n",
    "def label_phases(ax, textkwargs):\n",
    "    for i, s in enumerate(strategies):\n",
    "        ax.text(sx[strategies_s[i]], sy[strategies_s[i]],\n",
    "                plotting.latexboldmultiline(strategies_s_long[i]), **textkwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce stand alone phase diagram (subfig A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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An35azp/+6X18//u/ZuvWw7z33n4OHDjDL3/512Rnpw/43Ovvcb1gck6dOv6G+5SXV/PK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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff03057e410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(ncols=1)\n",
    "plot_phases(ax, ymax)\n",
    "label_phases(ax, phaselabelkwargs)\n",
    "ax.yaxis.set_major_formatter(ticker.ScalarFormatter())\n",
    "l = ax.set_xlabel(r'frequency $\\pi_{\\rm env} = \\alpha / (\\alpha+\\beta)$', verticalalignment='top')\n",
    "l.set_position((l.get_position()[0]-0.02, l.get_position()[1]))\n",
    "ax.set_ylabel(r'characteristic time $\\tau_{\\rm env} = -1/\\ln(1-\\alpha-\\beta)$')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define function for plotting phase diagram of strategic choices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def boundaryplots(axes, ylimmax=1.0, ylimmin=0.0):\n",
    "    baseboundarykwargs = dict(lw=1.0)\n",
    "    boundarykwargs = dict(color=black)\n",
    "    boundarykwargs.update(baseboundarykwargs)\n",
    "    patchkwargs = dict(fill=None, linewidth=0.0, alpha=1.0)\n",
    "    analysis.plot_interior_boundary(axes[0], pa, ylimmax=ylimmax, ylimmin=ylimmin, **boundarykwargs)\n",
    "    analysis.plot_interior_boundary(axes[0], a, ylimmax=ylimmax, ylimmin=ylimmin, **boundarykwargs)\n",
    "    textkwargs = dict(color=linecolors['cconstitutive'], transform=axes[0].transAxes, **commontextkwargs)\n",
    "    axes[0].text(0.53, 0.2, r'{\\setlength{\\jot}{-2pt}\\begin{gather*}\\bm{c_{\\rm con.}}\\\\\\bm{<}\\\\\\bm{c_{\\rm def.}}\\end{gather*}}', **textkwargs)\n",
    "    axes[0].text(0.2, 0.35, r'{\\setlength{\\jot}{-2pt}\\begin{gather*}\\bm{c_{\\rm con.}}\\\\\\bm{=}\\\\\\bf{min}\\end{gather*}}', **textkwargs)\n",
    "    axes[0].text(0.67, 0.72, r'{\\setlength{\\jot}{-2pt}\\begin{gather*}\\bm{c_{\\rm constitutive}}\\\\\\bm{=}\\\\\\bm{c_{\\rm defense}}\\end{gather*}}', **textkwargs)\n",
    "\n",
    "    analysis.plot_interior_boundary(axes[1], qpos, ylimmax=ylimmax, ylimmin=ylimmin, **boundarykwargs)\n",
    "    textkwargs = dict(fontsize='medium', color=linecolors['q'], transform=axes[1].transAxes, **commontextkwargs)\n",
    "    axes[1].text(0.67, 0.82, r'$\\bm{q > 0}$', **textkwargs)\n",
    "    axes[1].text(0.37, 0.23, r'$\\bm{q = 0}$', **textkwargs)\n",
    "    \n",
    "    analysis.plot_interior_boundary(axes[2], c, ylimmax=ylimmax, ylimmin=ylimmin, color=black, **baseboundarykwargs)\n",
    "    analysis.plot_interior_boundary(axes[2], shapely.ops.cascaded_union((c, mix)), ylimmax=ylimmax, ylimmin=ylimmin, color=black, **baseboundarykwargs)\n",
    "    text = axes[2].text(0.5, 0.2, r'$\\bm{p > 0}$', fontsize='large', color=linecolors['p'], transform=axes[2].transAxes, **commontextkwargs)\n",
    "    textbox = plotting.box_from_text(text)\n",
    "    axes[2].add_patch(analysis.shapely_to_mpl(complete-c-shapely.geometry.box(*textbox.flatten()),\n",
    "                                              hatch=r'////', ec=linecolors['p'], **patchkwargs))\n",
    "    text = axes[2].text(0.34, 0.89, r'$\\bm{p_{\\rm uptake} > 0}$', color=linecolors['pup'], transform=axes[2].transAxes, **commontextkwargs)\n",
    "    textbox = plotting.box_from_text(text)\n",
    "    axes[2].add_patch(analysis.shapely_to_mpl(shapely.ops.cascaded_union((c, mix))-shapely.geometry.box(*textbox.flatten()),\n",
    "                                              hatch=r'\\\\\\\\', ec=linecolors['pup'], **patchkwargs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Produce stand alone phase diagram of strategic choices (subfig B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oKGDq29MpVBWQOLQNLT08jOZiKranRO7n1w0HeW/4MJq166f7sRkju0nWuBsF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\nAAAc/QJ7i0fIcNVcLwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff02cddf290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(ncols=3, figsize=(4.0, 1.5))\n",
    "for ax in axes:\n",
    "    plot_phases(ax, ymax, patchkwargs=dict(alpha=0.3))\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "boundaryplots(axes, ylimmax=ymax, ylimmin=ymin)\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define functions to plot optimal parameter values along cuts of constant $\\pi_{\\rm env}$ or $\\tau_{\\rm env}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def cutaxes(ax, label, color=black, labelkwargs=dict(), ymax=1.0, twin=False, yticklabels=None):\n",
    "    plotting.despine(ax, spines='all')\n",
    "    #yticks = [0.0, ymax/2, ymax]\n",
    "    yticks = [0.0, ymax]\n",
    "    ax.set_yticks(yticks)\n",
    "    if yticklabels is None:\n",
    "        yticklabels = ['%g' % yticks[0], '', '%g' % yticks[-1]]\n",
    "    yticklabels = [yticklabels[0], yticklabels[-1]]\n",
    "    ax.set_yticklabels(yticklabels)\n",
    "    # add an invisible point to fool margin calculation\n",
    "    ax.plot([0.0], [ymax], alpha=0.0)\n",
    "    if twin:\n",
    "        x = 1.05\n",
    "    else:\n",
    "        x = -.08\n",
    "    ax.text(x, 0.5, label, color=color, transform=ax.transAxes, **ylabelkwargs)\n",
    "    ax.margins(y=ymargin)\n",
    "    for tl in ax.get_yticklabels():\n",
    "        tl.set_color(color)\n",
    "    return ax\n",
    "\n",
    "def shade_according_to_phase(ax, phases, colors, x=None, y=None, transform=None, vspankwargs=dict()):\n",
    "    if transform is None:\n",
    "        transform = lambda val: val\n",
    "    if x is not None:\n",
    "        line = shapely.geometry.LineString(((x, 0), (x, 100)))\n",
    "    if y is not None:\n",
    "        line = shapely.geometry.LineString(((0, y), (1, y)))\n",
    "    for i, phase in enumerate(phases):\n",
    "        intersections = phase.boundary.intersection(line)\n",
    "        if isinstance(intersections, shapely.geometry.MultiPoint):\n",
    "            x0, y0 = intersections[0].xy\n",
    "            x0, y0 = x0[0], y0[0]\n",
    "            x1, y1 = intersections[1].xy\n",
    "            x1, y1 = x1[0], y1[0]\n",
    "            if x is not None:\n",
    "                from_, to = y0, y1\n",
    "            if y is not None:\n",
    "                from_, to = x0, x1\n",
    "            ax.axvspan(transform(from_), transform(to), color=colors[i], **vspankwargs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in data for cuts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dftauenvcut = analysis.loadnpz('data/tauenvcut.npz')\n",
    "dftauenvcut.p = pd.to_numeric(dftauenvcut.p, errors='coerce')\n",
    "evolimmune.derived_quantities(dftauenvcut)\n",
    "dftauenvcut_dict = dict((aenv, dfg) for aenv, dfg in dftauenvcut.groupby('aenv'))\n",
    "aenvcuts = [key for key in dftauenvcut_dict][::-1]\n",
    "dfpienvcut = analysis.loadnpz('data/pienvcut.npz')\n",
    "dfpienvcut.p = pd.to_numeric(dfpienvcut.p, errors='coerce')\n",
    "evolimmune.derived_quantities(dfpienvcut)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7ff02c962d50>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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33kl6ejozZ84MjulZsGABEyZMaNVxLCIiEjofbX2J3E//QJPfTfeE/kwb8zcibJFmx2pR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\nERERsQ0VExEREbENFRMRERGxjf8HrZvfqPhpI68AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff02c79f110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dfpienvcut = dfpienvcut[dfpienvcut.pi<0.9999]\n",
    "axtau = plt.gca()\n",
    "axtau.plot(dfpienvcut.tauenv, dfpienvcut.tau1, '-', c=linecolors['tau1'], label='present')\n",
    "axtau.plot(dfpienvcut.tauenv, dfpienvcut.tau, '-', c=linecolors['tau'], label='absent')\n",
    "axtau.legend(loc='best', title='pathogen')\n",
    "plotting.despine(axtau)\n",
    "axtau.set_xlabel(r'$\\tau_{\\rm env}$')\n",
    "axtau.set_ylabel(r'$\\tau$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Put it all together and produce the final figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/andreas/miniconda2/envs/evolimmune/lib/python2.7/site-packages/matplotlib/gridspec.py:302: UserWarning: This figure includes Axes that are not compatible with tight_layout, so its results might be incorrect.\n",
      "  warnings.warn(\"This figure includes Axes that are not \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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6mtrtdoqLi/sdxEA7aAGXK5V7bqhEUZxqhzPozJ49iWnTrmPlyk958MHXURSl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\n+ij+/v6du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P7+/p267+yTbZv0Z0Jex8barqgvYXXRo5ySYbRPEPeHr8FH0bEBs6SI6g5t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\nBAKBQCAQCGrx/y7cUmJK3ZVLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff02c679a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7.0, 4.5))\n",
    "gsleft = gridspec.GridSpec(2, 3, height_ratios=[2.9, 1]) \n",
    "\n",
    "axphase = fig.add_subplot(gsleft[0, :])\n",
    "plot_phases(axphase, ymax)\n",
    "label_phases(axphase, phaselabelkwargs)\n",
    "axphase.yaxis.set_major_formatter(ticker.ScalarFormatter())\n",
    "l = axphase.set_xlabel(r'frequency $\\pi_{\\rm env} = \\alpha / (\\alpha+\\beta)$', verticalalignment='top')\n",
    "l.set_position((l.get_position()[0]-0.02, l.get_position()[1]))\n",
    "axphase.set_ylabel(r'characteristic time $\\tau_{\\rm env} = -1/\\ln(1-\\alpha-\\beta)$')\n",
    "\n",
    "smallaxes = []\n",
    "for counter in range(3):\n",
    "    ax = fig.add_subplot(gsleft[1, counter])\n",
    "    smallaxes.append(ax)\n",
    "for ax in smallaxes:\n",
    "    plot_phases(ax, ymax, patchkwargs=dict(alpha=0.5))\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])\n",
    "smallaxes[0].set_title('adaptability')\n",
    "smallaxes[1].set_title('heritability')\n",
    "smallaxes[2].set_title('acquisition mode')\n",
    "# layout needs to be done before boundaryplots are drawn in order for cutouts to work\n",
    "gsleft.tight_layout(fig, rect=(0, 0, 0.62, 1), h_pad=1.0, pad=pad, w_pad=0.5)\n",
    "boundaryplots(smallaxes, ylimmax=ymax, ylimmin=ymin)\n",
    "\n",
    "plotkwargs = dict()\n",
    "vspankwargs = dict(alpha=0.5, ec='none')\n",
    "ylabelkwargs = dict(rotation=90, ha='center', va='center', fontsize='medium')\n",
    "switchingmax = 0.1\n",
    "\n",
    "gsright = gridspec.GridSpec(2, 1) \n",
    "\n",
    "#### upper constant characteristic time cut panel ####\n",
    "pienvcut = 0.7\n",
    "dftauenvcut_sub = dftauenvcut_dict[aenvcuts[0]]\n",
    "dftauenvcut_sub.sort_values(by='pienv', inplace=True)\n",
    "axuppercut = fig.add_subplot(gsright[0])\n",
    "shade_according_to_phase(axuppercut, strategies, colors, y=evolimmune.to_tau(aenvcuts[0]), vspankwargs=vspankwargs)\n",
    "cutaxes(axuppercut, r'$p_{\\rm uptake}$', color=linecolors['pup'], labelkwargs=ylabelkwargs,\n",
    "        ymax=switchingmax, twin=False)\n",
    "axuppercut.plot(dftauenvcut_sub.pienv, dftauenvcut_sub.pup, '-', c=linecolors['pup'], **plotkwargs)\n",
    "axuppercut.set_xlabel('')\n",
    "axuppercut.grid(axis='y')\n",
    "plt.setp(axuppercut.get_xticklabels(), visible=False)\n",
    "axuppercuttwin = cutaxes(axuppercut.twinx(), r'$p$', color=linecolors['p'], labelkwargs=ylabelkwargs, ymax=switchingmax, twin=True)\n",
    "axuppercuttwin.plot(dftauenvcut_sub.pienv, dftauenvcut_sub.p, '-', c=linecolors['p'], **plotkwargs)\n",
    "\n",
    "#### lower constant characteristic time cut panel ####\n",
    "dftauenvcut_sub2 = dftauenvcut_dict[aenvcuts[1]]\n",
    "dftauenvcut_sub2.sort_values(by='pienv', inplace=True)\n",
    "axlowercut = fig.add_subplot(gsright[1], sharex=axuppercut)\n",
    "cutaxes(axlowercut, r'$c_{\\rm constitutive}$', color=linecolors['cconstitutive'], labelkwargs=ylabelkwargs,\n",
    "        ymax=1.0, twin=False, yticklabels=['min', '', 'max'])\n",
    "x, y = plotting.jumpify(dftauenvcut_sub2.pienv, dftauenvcut_sub2.cconstitutive, threshold=0.2)\n",
    "axlowercut.plot(x, y, '-', c=linecolors['cconstitutive'], **plotkwargs)\n",
    "axlowercut.set_xlabel(r'$\\pi_{\\rm env}$')\n",
    "axlowercut.margins(y=ymargin)\n",
    "axlowercuttwin = cutaxes(axlowercut.twinx(), r'$q$', color=linecolors['q'], labelkwargs=ylabelkwargs, ymax=switchingmax, twin=True)\n",
    "shade_according_to_phase(axlowercuttwin, strategies, colors, y=evolimmune.to_tau(aenvcuts[1]), vspankwargs=vspankwargs)\n",
    "axlowercuttwin.grid(axis='y')\n",
    "x, y = plotting.jumpify(dftauenvcut_sub2.pienv, dftauenvcut_sub2.q, threshold=0.02)\n",
    "axlowercuttwin.plot(x, y, '-', c=linecolors['q'], **plotkwargs)\n",
    "# cconstitutive line on top of q line\n",
    "axlowercut.set_zorder(axlowercuttwin.get_zorder()+1)\n",
    "axlowercut.patch.set_visible(False)\n",
    "\n",
    "#### frequency cut panel ####\n",
    "dfpienvcut.sort_values(by='tauenv', inplace=True)\n",
    "dfpienvcut = dfpienvcut[dfpienvcut.pi<0.9999]\n",
    "gstau = gridspec.GridSpec(1, 1) \n",
    "axtau = fig.add_subplot(gstau[0])\n",
    "axtau.plot(dfpienvcut.tauenv, dfpienvcut.tau1, '-', c=linecolors['tau1'], label='present')\n",
    "axtau.plot(dfpienvcut.tauenv, dfpienvcut.tau, '-', c=linecolors['tau'], label='absent')\n",
    "lims = [0, 8]\n",
    "axtau.set_xlim(*lims)\n",
    "w = (lims[1]-lims[0])*0.5\n",
    "axtau.set_ylim(lims[0]-ymargin*w, lims[1]+ymargin*w)\n",
    "axtau.set_xlabel(r'$\\tau_{\\rm env}$')\n",
    "axtau.set_ylabel(r'$\\tau$')\n",
    "axtau.legend(loc='best', title='pathogen')\n",
    "axtau.locator_params(nbins=6)\n",
    "shade_according_to_phase(axtau, strategies, colors, x=pienvcut, vspankwargs=vspankwargs)\n",
    "plotting.despine(axtau, spines='all')\n",
    "\n",
    "#### make link to cuts ####\n",
    "# plot lines corresponding to plots on the right\n",
    "vlinekwargs=dict(color=grey, alpha=0.4, lw=0.8)\n",
    "axphase.vlines([pienvcut], [0], [lims[1]], **vlinekwargs)\n",
    "for aenv in aenvcuts:\n",
    "    axphase.axhline(evolimmune.to_tau(aenv), **vlinekwargs)\n",
    "offset = -.15\n",
    "arrowprops = dict(edgecolor=grey, facecolor='w', arrowstyle='-|>',\n",
    "         mutation_scale=8, shrinkA=0, clip_on=False)\n",
    "transformB = transforms.blended_transform_factory(axlowercut.transAxes, axphase.transData)\n",
    "axphase.annotate(\"\", xy=(1.0, evolimmune.to_tau(aenvcuts[0])), xycoords=('axes fraction', 'data'),\n",
    "     xytext=(offset, evolimmune.to_tau(aenvcuts[0])), textcoords=transformB,\n",
    "     arrowprops=arrowprops)\n",
    "transformB = transforms.blended_transform_factory(axuppercut.transAxes, axphase.transData)\n",
    "axphase.annotate(\"\", xy=(1.0, evolimmune.to_tau(aenvcuts[1])), xycoords=('axes fraction', 'data'),\n",
    "     xytext=(-0.15, evolimmune.to_tau(aenvcuts[1])), textcoords=transformB,\n",
    "     arrowprops=arrowprops)\n",
    "transformB = transforms.blended_transform_factory(axtau.transAxes, axphase.transAxes)\n",
    "axphase.annotate(\"\", xy=(pienvcut, 0.0), xycoords=('data', 'axes fraction'),\n",
    "     xytext=(-0.15, -0.08), textcoords=transformB,\n",
    "     arrowprops=dict(connectionstyle='angle,angleA=180,angleB=-90,rad=0', **arrowprops))\n",
    "for ax in [axlowercut, axuppercut, axtau]:\n",
    "    line = lines.Line2D([offset, offset], [0.0, 1.0], color=grey, transform=ax.transAxes,\n",
    "                        linewidth=matplotlib.rcParams['patch.linewidth'], clip_on=False)\n",
    "    ax.add_line(line)\n",
    "\n",
    "#### overall layout ####\n",
    "gsright.tight_layout(fig, rect=(0.66, 0.45, 1.0, 1), h_pad=0.5, pad=pad)\n",
    "gstau.tight_layout(fig, rect=(0.66, 0.0, 0.975, 0.43), pad=pad)\n",
    "subfiglabelkwargs = dict(fontsize='large', verticalalignment='top', horizontalalignment='left')\n",
    "axphase.text(0.005, 1.0, r'\\textbf{A}',\n",
    "         transform=transforms.blended_transform_factory(fig.transFigure, axphase.transAxes),\n",
    "         **subfiglabelkwargs)\n",
    "smallaxes[0].text(0.005, 1.15, r'\\textbf{B}',\n",
    "         transform=transforms.blended_transform_factory(fig.transFigure, smallaxes[0].transAxes),\n",
    "         **subfiglabelkwargs)#\n",
    "axuppercut.text(0.63, 1.0, r'\\textbf{C}',\n",
    "         transform=transforms.blended_transform_factory(fig.transFigure, axuppercut.transAxes),\n",
    "         **subfiglabelkwargs)\n",
    "axuppercut.text(0.63, 1.0, r'\\textbf{D}',\n",
    "         transform=transforms.blended_transform_factory(fig.transFigure, axlowercut.transAxes),\n",
    "         **subfiglabelkwargs)\n",
    "axtau.text(0.63, 1.0, r'\\textbf{E}',\n",
    "         transform=transforms.blended_transform_factory(fig.transFigure, axtau.transAxes),\n",
    "         **subfiglabelkwargs)\n",
    "\n",
    "fig.savefig('figure2.pdf')\n",
    "fig.savefig('figure2.svg')"
   ]
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    "**Optimal immune strategies as a function of the  frequency and characteristic time of pathogens.**\n",
    "**(A)** Distinct optimal immune strategies emerge for different statistics of appearance of the pathogens. Each phase is characterized by the value of parameters indicated in panel B and named after a known immune system that has similar characteristics (the name 'adaptive' is after the vertebrate immune system).\n",
    "**(B)** The different phases of immunity are defined by the values of parameters along three main axes: adaptability (constitutive cost $c_{\\rm constitutive}$), heritability ($1-q$) and mode of acquisition ($p$ and $p_{\\rm uptake}$). \n",
    "**(C)** and **(D)** Optimal parameters as a function of $\\pi_{\\rm env}$ for $\\tau_{\\rm env} = 12$ (C) and  $\\tau_{\\rm env} = 0.8$ (D). For slowly varying environments (C), rare pathogens are best targeted by CRISPR-like uptake of protection, while frequent pathogens are best dealt with by spontaneous acquisition of protection, with a crossover in-between where both co-exist. For faster varying environments (D), the constitutive cost invested in the protection goes from negligible to maximal as the pathogen frequency increases. When it is maximal, the best strategy transitions from bet-hedging ($q>0$) to a full protection of the population ($q=0$).\n",
    "**(E)** The correlation times of protection in absence of the pathogen, $\\tau = -1/\\ln(1 - p - q)$, and in its presence, $\\tau = -1/\\ln(1 - p - p_{\\rm uptake} - q)$, are shown for $\\pi_{\\rm env} = 0.7$ as a function of $\\tau_{\\rm env}$. Both increase with the correlation time of the pathogen. In this figure, an infinite population size is assumed and the following parameters are used: $c_{\\rm infection} = 3; \\; c_{\\rm constitutive} = \\left(1.8 - c_{\\rm defense}\\right) / \\left(c_{\\rm defense} - 0.2\\right); \\; c_{\\rm uptake}(p_{\\rm uptake}) = 0.1\\times p_{\\rm uptake} + p_{\\rm uptake}^2$ (see Fig. S2 for other choices)."
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