Coral_Reef.ipynb

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  "name": "",
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pyurdme\n",
      "from IPython.display import display, clear_output\n",
      "import time"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class CoralReef(pyurdme.URDMEModel):\n",
      "    \"\"\" Model developed by Briggs and Drawert 3/31/2014, based on a \n",
      "        non-spatial model by Briggs and Adam.\n",
      "    \"\"\"\n",
      "\n",
      "    def __init__(self, name=\"coral_reef\", D_c=1.0, D_m=1.0, version=1):\n",
      "        pyurdme.URDMEModel.__init__(self, name)\n",
      "\n",
      "        # Species\n",
      "        Coral = pyurdme.Species(name=\"Coral\",diffusion_constant=0.0)\n",
      "        Coral_m = pyurdme.Species(name=\"Coral_m\",diffusion_constant=D_c)\n",
      "        MA = pyurdme.Species(name=\"MA\", diffusion_constant=0.0)\n",
      "        MA_m = pyurdme.Species(name=\"MA_m\", diffusion_constant=D_m)\n",
      "        Turf = pyurdme.Species(name=\"Turf\", diffusion_constant=0.0)\n",
      "        self.add_species([Coral, MA, Coral_m, MA_m, Turf])\n",
      "\n",
      "        # Parameters\n",
      "        phi_c = pyurdme.Parameter(name=\"phi_c\", expression=0.0011) #1/year\n",
      "        phi_m = pyurdme.Parameter(name=\"phi_m\", expression=0.001) #1/year\n",
      "        g_tc = pyurdme.Parameter(name=\"g_tc\", expression=0.1) #1/year\n",
      "        g_tm = pyurdme.Parameter(name=\"g_tm\", expression=0.2) #1/year\n",
      "        Gamma = pyurdme.Parameter(name=\"Gamma\", expression=0.05)\n",
      "        dc = pyurdme.Parameter(name=\"dc\", expression=0.05) #1/year\n",
      "        dm = pyurdme.Parameter(name=\"dm\", expression=1.0) #1/year\n",
      "        #dm = pyurdme.Parameter(name=\"dm\", expression=0.2) #1/year\n",
      "        phi_g = pyurdme.Parameter(name=\"psi_g\", expression=0.0)\n",
      "        # Death rate of mobile propgules.  Combine with diffusion to determine spread.\n",
      "        mu_c = pyurdme.Parameter(name=\"mu_c\", expression=1.0) #1/year\n",
      "        mu_m = pyurdme.Parameter(name=\"mu_m\", expression=1.0) #1/year\n",
      "        # mobile propogules destroyed by estabilished \n",
      "        alpha_c = pyurdme.Parameter(name=\"alpha_c\", expression=0.1) #1/year\n",
      "        alpha_m = pyurdme.Parameter(name=\"alpha_m\", expression=0.5) #1/year\n",
      "        # Production of mobile propogules\n",
      "        R_c = pyurdme.Parameter(name=\"R_c\", expression=1.0) #1/year\n",
      "        R_m = pyurdme.Parameter(name=\"R_m\", expression=1.0) #1/year\n",
      "\n",
      "        self.add_parameter([phi_c, phi_m, g_tc, g_tm, Gamma, dc, dm, phi_g, mu_c, mu_m, alpha_c, alpha_m, R_c, R_m])\n",
      "                \n",
      "\n",
      "        # Reactions:\n",
      "        # C -> T : dc\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R3\", reactants={Coral:1}, products={Turf:1}, rate=dc))\n",
      "        # MA -> T : dm\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R4\", reactants={MA:1}, products={Turf:1}, rate=dm))\n",
      "        # T + C_m -> C : phi_c\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R5\", reactants={Turf:1, Coral_m:1}, products={Coral:1}, rate=phi_c))\n",
      "        # T + MA_m -> MA : phi_m\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R6\", reactants={Turf:1, MA_m:1}, products={MA:1}, rate=phi_m))\n",
      "        # C + T -> 2C : g_tc * exp(-1.0 * psi_g * MA / 100)\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R7\", reactants={Turf:1, Coral:1}, products={Coral:2}, propensity_function=\"g_tc*Turf*Coral*exp(-1.0 * psi_g * MA / Space_per_voxel)/vol\"))\n",
      "        # MA + T -> 2MA : g_tm\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R8\", reactants={Turf:1, MA:1}, products={MA:2}, rate=g_tm))\n",
      "        # C + MA -> 2MA : Gamma * g_tm\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R9\", reactants={Coral:1, MA:1}, products={MA:2}, propensity_function=\"g_tm*Gamma*Coral*MA/vol\"))\n",
      "        # C -> C + C_m : R_c\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R10\", reactants={Coral:1}, products={Coral:1, Coral_m:1}, rate=R_c))\n",
      "        # MA -> MA + MA_m : R_m\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R11\", reactants={MA:1}, products={MA:1, MA_m:1}, rate=R_m))\n",
      "        # C_m -> 0 : mu_c\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R12\", reactants={Coral_m:1}, products={}, rate=mu_c))\n",
      "        # MA_m -> 0 : mu_m\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R13\", reactants={MA_m:1},  products={}, rate=mu_m))\n",
      "        # MA + C_m -> MA : alpha_c\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R14\", reactants={MA:1, Coral_m:1},  products={MA:1}, rate=alpha_c))\n",
      "        # C + MA_m -> C : alpha_m\n",
      "        self.add_reaction(pyurdme.Reaction(name=\"R15\", reactants={Coral:1, MA_m:1},  products={Coral:1}, rate=alpha_m))\n",
      " \n",
      "        \n",
      "\n",
      "        # A unit square\n",
      "        # each grid point is 10cm x 10cm, domain is 5m x 5m\n",
      "        self.mesh = pyurdme.URDMEMesh.generate_square_mesh(L=5, nx=50, ny=50, periodic=True)\n",
      "\n",
      "        # Place the A molecules in the voxel nearest the center of the square\n",
      "        #self.placeNear({Coral:100}, point=[10,10])\n",
      "        \n",
      "        Space_per_voxel = 10\n",
      "        self.add_parameter(pyurdme.Parameter(name=\"Space_per_voxel\", expression=Space_per_voxel)) #1/year\n",
      "        \n",
      "                          \n",
      "        if True:\n",
      "            # Start with two colonys\n",
      "            self.set_initial_condition_distribute_uniformly({Turf:Space_per_voxel})\n",
      "            self.set_initial_condition_place_near({Coral:Space_per_voxel}, point=[1,1])\n",
      "            self.set_initial_condition_place_near({Turf:0}, point=[1,1])\n",
      "            self.set_initial_condition_place_near({MA:Space_per_voxel}, point=[4,4])\n",
      "            self.set_initial_condition_place_near({Turf:0}, point=[4,4])\n",
      "        else:\n",
      "            # Every voxel is the same\n",
      "            self.set_initial_condition_distribute_uniformly({Turf:0})\n",
      "            self.set_initial_condition_distribute_uniformly({Coral:Space_per_voxel-1})\n",
      "            self.set_initial_condition_distribute_uniformly({MA:1})\n",
      "\n",
      "\n",
      "        for vndx in range(self.u0.shape[1]):\n",
      "            tot = 0\n",
      "            for sndx, sname in enumerate(self.listOfSpecies):\n",
      "                tot += self.u0[sndx][vndx]\n",
      "            if tot > 100:\n",
      "                for sndx, sname in enumerate(self.listOfSpecies):\n",
      "                    print \"u0[{0}][{1}] = {2}\".format(sname, vndx, self.u0[sndx][vndx])\n",
      "\n",
      "        #self.timespan(numpy.linspace(0,500,501)) #500 years\n",
      "        #self.timespan(numpy.linspace(0,5,72)) #5 years, by months\n",
      "        self.timespan(numpy.linspace(0,11,66)) #10 years, by 2 months"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = CoralReef()\n",
      "%time result = model.run()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CPU times: user 3.14 s, sys: 240 ms, total: 3.38 s\n",
        "Wall time: 19.3 s\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_vals = model.mesh.coordinates()[:, 0]\n",
      "y_vals = model.mesh.coordinates()[:, 1]\n",
      "C_vals = result.get_species(\"Coral\")\n",
      "MA_vals = result.get_species(\"MA\")\n",
      "Turf_vals = result.get_species(\"Turf\")\n",
      "num_vox = len(x_vals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#heatmap\n",
      "plt.figure(figsize=(12,6), dpi=100)\n",
      "plt.figure(1)\n",
      "for tndx, tval in enumerate(model.tspan):\n",
      "    plt.figure(figsize=(12,4), dpi=100)\n",
      "    plt.subplot(1,3,1)\n",
      "    heatmap, xedges, yedges = np.histogram2d(x=x_vals, y=y_vals, weights=C_vals[tndx,:], bins=int(sqrt(num_vox)))\n",
      "    plt.imshow(heatmap)\n",
      "    cb = plt.colorbar()\n",
      "    plt.title('Coral population')\n",
      "    plt.subplot(1,3,2)\n",
      "    heatmap, xedges, yedges = np.histogram2d(x=x_vals, y=y_vals, weights=MA_vals[tndx,:], bins=int(sqrt(num_vox)))\n",
      "    plt.imshow(heatmap)\n",
      "    cb = plt.colorbar()\n",
      "    plt.title('MA population')\n",
      "    plt.xlabel('t={0}'.format(tval))\n",
      "    plt.subplot(1,3,3)\n",
      "    heatmap, xedges, yedges = np.histogram2d(x=x_vals, y=y_vals, weights=Turf_vals[tndx,:], bins=int(sqrt(num_vox)))\n",
      "    plt.imshow(heatmap)\n",
      "    cb = plt.colorbar()\n",
      "    plt.title('Free Turf')\n",
      "    plt.xlabel('t={0}'.format(tval))\n",
      "    clear_output()\n",
      "    plt.show()\n",
      "    time.sleep(.05)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Q4YBVavhaDNxt1/K4+8aJXtvwmEnV62TTAM6BBj4azPE6q7zGLLtGk7dn4LqwPBBOwMwa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nWpXhXMu7KlfJhXKS+TO4uCNOaq7sqWNF7Mq5SXtJm1gauC2SMk5cO8SnmxB1dK5L/UByCpNvMq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\n83lkWeQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f5f57be8290>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "For comparison, we also present an ODE simulation of well-mixed version of this model."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.integrate import ode"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def par(name):\n",
      "    return model.listOfParameters[name].value\n",
      "def coral_ode(t, rp):\n",
      "    C = rp[0]\n",
      "    M = rp[1]\n",
      "    C_m = rp[2]\n",
      "    M_m = rp[3]\n",
      "    T = rp[4]\n",
      "    return [\n",
      "        par('phi_c')*C_m*T  + par('g_tc')*T*C - par('Gamma')*par('g_tm')*M*C - par('dc')*C ,\n",
      "        par('phi_m')*M_m*T  + par('g_tm')*T*M + par('Gamma')*par('g_tm')*M*C - par('dm')*M ,\n",
      "        par('R_c')*C - par('mu_c')*C_m  - par('alpha_c')*M*C_m,\n",
      "        par('R_m')*M - par('mu_m')*M_m  - par('alpha_m')*C*M_m,\n",
      "        par('dc')*C + par('dm')*M - par('phi_c')*C_m*T - par('phi_m')*M_m*T - par('g_tc')*T*C - par('g_tm')*T*M\n",
      "        ]\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "solver = ode(coral_ode).set_integrator('vode', method='bdf', order=15, atol=1e-6)\n",
      "rp0 = ([99.0, 1.0, 0.0, 0.0, 0.0]) # starting function\n",
      "solver.set_initial_value(rp0, 0)\n",
      "T = 60\n",
      "dt = T/5000.\n",
      "rp = []; t = []\n",
      "while solver.successful() and solver.t <= T:\n",
      "    solver.integrate(solver.t + dt)\n",
      "    rp.append(solver.y); t.append(solver.t)\n",
      "    \n",
      "# Plotting    \n",
      "rp = np.array(rp)\n",
      "plt.figure()\n",
      "plt.plot(t, rp[:,  0], t, rp[:, 1], t, rp[:,4])\n",
      "plt.title(\"Coral & MA\")\n",
      "plt.legend(['Coral','MA','Turf'])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.legend.Legend at 0x7f5f5586ec50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f5f57a08850>"
       ]
      }
     ],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}