diff --git a/content/Population dynamics I (2024).ipynb b/content/Population dynamics I (2024).ipynb new file mode 100644 index 0000000..fecc4f9 --- /dev/null +++ b/content/Population dynamics I (2024).ipynb @@ -0,0 +1,1732 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "29e1ab71", + "metadata": {}, + "source": [ + "# Population Dynamics\n", + "\n", + "This is part of Nathaniel Virgo's lectures on population dynamics, as part of the ELSI course.\n", + "\n", + "These notes roughly follow the first few chapters of Hofbauer and Sigmund's book *Evolutionary Games and Population Dynamics*.\n", + "\n", + "---\n", + "\n", + "You can download this notebook and run it locally if you have Python installed, but you can also access it online at https://nathanielvirgo.github.io/shared-notebooks/lab?path=Population+dynamics.ipynb.\n", + "\n", + "If you're viewing this online you can edit the document and run Python code. Your edits will only exist in your browser's cache - other people can't see them.\n", + "\n", + "It's better to use a recent version of Chrome or Firefox when viewing this notebook. If you have problems, try using Chrome.\n", + "\n", + "To run Python code, hold shift and press enter. If you run each cell in sequence, it should re-create all the graphs. If you get an error it probably means you have to run one of the other cells first.\n", + "\n", + "---" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e4bc066c", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.integrate import solve_ivp\n", + "plt.rcParams['figure.figsize'] = [12, 6]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f8063302", + "metadata": {}, + "outputs": [], + "source": [ + "# a convenient function for plotting - put the axes at x=0, y=0.\n", + "def center_axes():\n", + " ax = plt.gca()\n", + " ax.spines['top'].set_color('none')\n", + " ax.spines['left'].set_position('zero')\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['bottom'].set_position('zero')" + ] + }, + { + "cell_type": "markdown", + "id": "6b52f57a", + "metadata": {}, + "source": [ + "# Exponential growth\n", + "\n", + "The simplest model of an ecological population: each member has $r$ offspring per unit time and a probability $s$ of dying per unit time. \n", + "\n", + "This gives the equation\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = (r-s)x.\n", + "$$\n", + "\n", + "The parameter $r$ is called the **growth rate** and $s$ is the **death rate**.\n", + "\n", + "This equation has solutions given by\n", + "$$\n", + "x(t) = x_0 e^{(r-s)t}.\n", + "$$\n", + "\n", + "Let's plot this." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "7f927c6a", + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 0.1 # initial x value\n", + "r = 1 # growth rate\n", + "s = 0.1 # death rate\n", + "\n", + "max_T = 5 # integrate from 0 to max_T\n", + "tsteps = 1000 # number of time steps for plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "481108f8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t = np.linspace(0, max_T, tsteps)\n", + "x = x0*np.exp(r*t)\n", + "\n", + "plt.title(\"exponential growth\")\n", + "plt.ylabel(\"population x\")\n", + "plt.xlabel(\"time\")\n", + "plt.plot(t,x, label=\"$x(t) = x_0e^{rt}$\")\n", + "plt.xlim(0,max_T)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2d4dea32", + "metadata": {}, + "source": [ + "---\n", + "**Try increasing `max_T` from 5 to 15.** Note the scale on the x axis.\n", + "\n", + "**What happens if $s>r$, so that $r-s$ is negative?** The result is called **exponential decay.** Can you give a biological interpretation?\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "32e6f517", + "metadata": {}, + "source": [ + "# logistic growth\n", + "\n", + "In nature, exponential growth never continues forever.\n", + "\n", + "An alternative model is **logistic growth**, given by\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = rx\\left(1 - \\frac{x}{K}\\right)\n", + "$$\n", + "\n", + "In addition to the growth rate $r$ we have a new parameter $K$ called the **carrying capacity**." + ] + }, + { + "cell_type": "markdown", + "id": "b7021e4f", + "metadata": {}, + "source": [ + "It's solution is given by\n", + "\n", + "$$\n", + "x(t) = \\frac{Kx_0e^{rt}}{K+x_0(e^{rt}-1)}\n", + "$$\n", + "\n", + "(eq. 1.5 in the book)\n", + "\n", + "let's plot it:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "2b531b0b", + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 0.1 # initial x value\n", + "r = 1 # growth rate\n", + "K = 10 # carrying capacity\n", + "\n", + "max_T = 15 # integrate from 0 to max_T\n", + "tsteps = 1000 # number of time steps for plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "a08048dd", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "t = np.linspace(0, max_T, tsteps)\n", + "x = K*x0*np.exp(r*t)/(K + x0*(np.exp(r*t)-1))\n", + "\n", + "k = K*np.ones_like(t) # just for plotting\n", + "\n", + "plt.title(\"logistic growth\")\n", + "plt.ylabel(\"population x\")\n", + "plt.xlabel(\"time\")\n", + "plt.plot(t,x, label=\"x(t)\")\n", + "plt.plot(t,k,\"k:\", label=\"K\")\n", + "plt.xlim(0,max_T)\n", + "plt.ylim(0,max(K,x0)+1)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "efabc0f2", + "metadata": {}, + "source": [ + "---\n", + "\n", + "**Try changing $x_0$ to something greater than 10.**\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "1f37615c", + "metadata": {}, + "source": [ + "What does logistic growth look like compared to exponential growth?" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "b31ce324", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "max_T = 15 # integrate from 0 to max_T\n", + "\n", + "g = x0*np.exp(r*t)\n", + "\n", + "plt.title(\"logistic growth compared to exponential growth\")\n", + "plt.ylabel(\"population x\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(t,x, label=\"x(t)\")\n", + "plt.plot(t,g, label=\"$x_0\\,e^{rt}$\")\n", + "plt.plot(t,k,\"k:\", label=\"K\")\n", + "plt.xlim(0,max_T)\n", + "plt.ylim(0,K+1)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "80909f53", + "metadata": {}, + "source": [ + "At first they look the same, but logistic growth *saturates* as it gets closer to the carrying capacity." + ] + }, + { + "cell_type": "markdown", + "id": "7edeff7f", + "metadata": {}, + "source": [ + "---\n", + "\n", + "**Try changing the parameters**, e.g.\n", + "\n", + "* $x_0 = 0.001$ instead of $0.1$\n", + "* $K=5$ instead of $10$\n", + "* $r=10$ instead of $1$\n", + "\n", + "what will happen if $x_0 = 0$?\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "id": "723b2ce7", + "metadata": {}, + "source": [ + "# Lotka-Volterra equations\n", + "\n", + "Let's start with the Lotka-Volterra *predator-prey* equations. (There are more general versions of the Lotka-Volterra equations.) These are\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by)\n", + "$$\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx)\n", + "$$\n", + "\n", + "(equation 2.1 in the book.) That's two simultaneous ordinary differential equations. The parameters are all positive, $a>0, b>0, c>0, d>0$.\n", + "\n", + "To understand this equation note the following:\n", + "\n", + " * if $y=0$ then it becomes $\\mathrm{d}x/\\mathrm{d}t = ax$, so $x$ will increase exponentially without $y$\n", + " \n", + " * if $x=0$ then it becomes $\\mathrm{d}y/\\mathrm{d}t = -cy$, so $y$ will *decrease* exponentially without $x$\n", + "\n", + " * but because $b>0$, increasing $y$ causes $x$'s growth rate to decrease\n", + " \n", + " * and because $d>0$, increasing $x$ causes $y$'s growth rate to increase\n", + "\n", + "There is no analytical solution for this either, so we have to solve numerically." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "d0ec12ec", + "metadata": {}, + "outputs": [], + "source": [ + "def lotka_volterra(t, state, a, b, c, d):\n", + " x, y = state\n", + " dx = x*(a-b*y)\n", + " dy = y*(-c+d*x)\n", + " return [dx,dy]\n", + "\n", + "a = 1\n", + "b = 1\n", + "c = 0.2\n", + "d = 0.2\n", + "\n", + "t_span = (0.0,30.0)\n", + "t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + "initial_state = [0.4, 0.4]\n", + "\n", + "result = solve_ivp(lotka_volterra, t_span, initial_state, t_eval=t_points, args=(a,b,c,d), method='RK45', rtol=1e-10, atol=1e-10)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "805a2bc5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator-prey equation\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result.t, result.y[0,:], label=\"prey\")\n", + "plt.plot(result.t, result.y[1,:], label=\"predators\")\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e749b78f", + "metadata": {}, + "source": [ + "Interpretation of this plot:\n", + "\n", + " * at first there are not very many predators, so the prey start to multiply\n", + " * but then at around t=3 there are lots of prey, so the predators start to multiply quickly\n", + " * by about t=4.5 the predator population is so high the prey population starts to decrease\n", + " * by about t=7 the prey population has fallen so far that the predators start to die off\n", + " * at about t=12 there are so few predators that the prey starts to increase again\n", + " * then the whole cycle can repeat" + ] + }, + { + "cell_type": "markdown", + "id": "d2b6a121", + "metadata": {}, + "source": [ + "Now let's try plotting predators on the y axis and prey on the x axis:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "09fdc11c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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T6NEmLcBUIgfG3fkqaxsTp63mla/XVXtuzzZN+cFR3fj28M4aOCkiIuVUXMshef7L1dz0ytzy7S6tGvPKz44hIy0lwFQi0ePuzFi1jeenreblmdUX3Ef1aMVlx3TnlH7tSNR4AhGRBknFtRyUqcu2cNETX5Zvd2ieylvXH68+qtIguDszV2/jX5+v4tUqFj0qc+nRmVxydCbdNRe3iEiDoOJaDsi23YUMvWPKXvs+v/FbdGjeOKBEInVDUUkp78zfxFNTVzK9mqXfD2ubxmXHZHLe0M40bqT53EVE6hsV1xKxG16czQvT15Zvv3bNMRzeuUVwgUTquM0783n2y9U8NXUlufnFVZ533rBO/OS4HvTr0KwW04mISCyouJYaLdmUy2n3f1y+/YtTenPdKb0CTCQSn8oGTD41dWW1M5QM6dKCn57Yk1P7tdNc8CIicUbFtVTJ3bnm+a+ZNHcDAOkpSXx18ylamlwkinbmF/GfaWt4/JMVZOcWVHpORloKPz2xJxeO7EKTRlrsRkSkLgukuDazLsA/gXaAA4+7+4P7nGPAg8BYIA+41N1nho9dAtwcPvVOd3+mptdUcX1g1m/fw9ET3i/ffuT7wxh3eIcAE4k0DKWlzvuLNvPXj5Yzo5q+25cdk8lPjutBxxYa7yAiUpcEVVx3ADq4+0wzSwdmAOe4+4IK54wFfk6ouD4SeNDdjzSzVsB0YAShwnwGMNzdq/4phIrrA/HvaasZ/3Joer1GiQnMue00tVaLBGjB+p387ePl/K+amUnOHNyRq0/qSd/26rctIhKkOtEtxMz+Bzzs7lMq7Psb8KG7TwxvLwZOLHu4+5WVnVcVFdc1c3dGP/AxSzaFloceP6YvV53QM+BUIrKv7NwCnv5sJX/9cDmlVfwzPXpAO64/pbcGSYqI1LLqiuta6dhnZpnAUODLfQ51AtZU2F4b3lfVfjkEuwqKGXjr2+Xb7/3qBHpqdUWROqlNegq/Gd2X34zuC8CewhImTlvNwx8sY+vuQgDenr+Jt+dvKr9m7KD2XHdyb/q0Tw8ks4iI1EJxbWZpwEvA9e6+Mwb3vwK4AqBr167Rvn29sXhjLqMf+GY2kGV3jSEpMSHARCJyIBo3SuRHx3bnR8d2ByC/qIT/Tl/D/e8uLS+235y7kTfnfjNDybjDO3D9yb3o1U7FtohIbYlptxAzSwbeAN529z9XclzdQmrBW/M2ctWzMwAYM7A9f/3B8IATiUi05ReV8O9pq7n/3aXs2FNU6TlnDe7IL07trZUkRUQOUVADGg14Btjq7tdXcc444Bq+GdD4F3cfGR7QOAMYFj51JqEBjVure00V1/t78tOV3P5GaAzpnecM5AdHdQs4kYjUhvyiEp7/cjX3v7ukysVtLj06k6tPOow26Sm1nE5EJL4FVVwfC3wCzAVKw7tvAroCuPtj4QL8YeB0QlPxXebu08PX/yh8PsBd7v5UTa+p4npvd76xgCc+XQnAs5cfybG9MgJOJCJB2VNYwr++yOJP7yyhsLh0v+ONkhIYf3pfLjqqKylJmjlIRKQ6dWK2kNqg4vobN748h4nTQmNCJ193nGYTEJG9bM8r5LGPVvDYR8srPd67XRrjx/TlpD5tCbWDiIhIGRXXDcxNr8zl+S9XA/DJDSfRpVWTgBOJSF23bPMu/vT2Yt6aX/mS7af2b8cNo/tocKSICCquG5TbXpvP059lAfDpb0+ic0sV1iJyYNydD5dk83+TF7FoY26l51x1Qk9+dlJPmqUm13I6EZHgqbhuIB7/eDl3v7kIUIu1iERPQXEJE79czYS3FpFftH9/7U4tGnPLGf0ZPaCdupCISIOg4roBmDRnA1c/PxOAKb84Xr+6FZGYyc4t4C/vLeVfX6yq9Pj3RnThV6N70zY9tZaTiYjUDhXX9dzctTs48+FPAXj+J0dydE/NCiIiteeLFTnc8cYC5q/ff52wjLQUbjurP+MGdVCrtojUGyqu67HteYUMuX0KAH/8zuGcP6JLwIlEpCHbXVDMYx8t56H3l1V6/LxhnbhhdF/aN1ertojELxXX9VRpqdPjpjcB+O6Iztz7ncEBJxIR2duMVdu4/Y0FzF6zfb9jLZokc9uZAzhrcEcSEtSqLSLxQ8V1PXXk3e+yaWcB6SlJzP3D6KDjiIhUa09hCY9/vIL7311S6fELjujCr0f3ISNNK0aKSN2m4roe+senK7kjvKz5irvHqtVHROLO7DXbuf2NBcxYtW2/Y73bpXH3uYMYkdkqgGQiItVTcV3PrM7J4/g/fgBoLmsRqR92FxTzyAfLePTDyleM/MNZA/jBUd1IVEOCiNQBKq7rkYr9rO84ewAXj8oMNpCISJS5O+8s2MTvXpnLll2F+x3/7ojO/Pb0vrRW9xERCYiK63pk9P0fs3hTLh2bp/LZjScHHUdEJOZWbtnNra/N5+Ml2fsd69+hGXedO5ChXVsGkExEGioV1/XEZ8u28P0nvgTUz1pEGqa8wmIefr/q7iP3nDeI743oon8fRSSmVFzXAxW7g7z001EM76ZBPiLSsLk7k+dt5MaX57JjT9F+x688oQfXndyLJo2SAkgnIvWZiut64KyHP2XO2h0M7NSMN35+XNBxRETqnGWbc/ndK/P4cuXW/Y6dPaQjt5zRX9P8iUhUqLiOc7PWbOecR6YC6g4iIhKJbbsL+b+3FvHvr9bsd+zonq25+9xBZGY0DSCZiNQHKq7jXOb4SQD86/KRHNerTcBpRETiS35RCY9+sIy/VLIke6+2afzp/MEM7tKi9oOJSNxScR3HHnpvKfdNCa1mljVhXMBpRETiW2mp89y01dzy6rz9jrVsksyfvzeEk/q0DSCZiMQTFddxqrC4lN43Twbg61tOpWXTRgEnEhGpX96at4Ff/Gc2e4pK9jt277cP5/wRnTFTVzwR2ZuK6zg19sFPWLBhJ2MHtefRi4YHHUdEpF6btnIrv/rvLNZs3bPfsT+cNYCLj+qmMS8iAqi4jkubd+Yz8u73AFh5z1i1nIiI1KKlm3L5zYtzmLVm+37HbjmjP5cdnalCW6QBU3Edh/reMpn8olJuPbM/lx3TPeg4IiIN1uqcPMa/PIfPlufsd0wt2iINk4rrOLM6J4/j//gBoEGMIiJ1ydpteYx/aS6fLtuy37E7zxnIRUd21W8aRRoAFddxpmzqvfu/N5hzh3YOOI2IiFRmzdY8bnhxDp+v2L9F+57zBnHBEV1UaIvUUyqu48jy7F2cfN9HgFqtRUTixaqc3fzmv3OYlrX/6pD3fudwzh+uWUdE6hMV13GkrNX6rxcNY8ygDgGnERGRA7Vyy25+/d/ZzFi1bb9jf7lwKGce3kGFtkicU3EdJ7JzCzjirncBtVqLiNQHy7N38csXZjN7n1lHUpISePyHIziht1bdFYlH1RXXSbUdRqp27qNTAbh5XL+Ak4iISDT0bJPG/64+BoDFG3P5+cSZLNm0i4LiUi55choAXVs14bEfDKd/x2ZBRhWRKFFxXUfkF5Wwdlto4YIfH9cj4DQiIhJtfdqn884vTgBgxqptXPXsDLJzC1i9NY+xf/kEgKN7tubP3x1C++apQUYVkUOg4rqO+OULswC4cGSXYIOIiEjMDe/Wkq9+dwoQWoL9qmdnAvDZ8hyOuie0gNj5wztz61kDSEvRj2qReKI+13VE2UDGpXeNITkxIeA0IiJS20pLnSenruTOSQv3O/bLU3vzsxN7kqSfDyJ1gvpc13H/m7UOgIy0RiqsRUQaqIQE48fH9eDHx/Ugv6iECZMX8fRnWQD8ecoS/jxlCQD3nT+Y84Z10owjInWUWq7rgLJW6w9+fSLdM5oGnEZEROqSLbsKGP/SHN5duHmv/empSTx92REM79YqoGQiDVcgLddm9iRwBrDZ3QdWcvw3wEUVcvQD2rj7VjPLAnKBEqC4qvD1QXZuQflzFdYiIrKvjLQUnrjkCACWbd7FNc/PZNHGXHLzi/n2Xz8HYGRmKx68cAgdmjcOMqqIEMOWazM7HtgF/LOy4nqfc88EfuHu3wpvZwEj3H3LgbxmPLZcX/TEF0xdlsMNp/fhZyceFnQcERGJE58szebSp76ipHTvn+NXndCTX53WW90MRWIokJZrd//YzDIjPP1CYGKsstRlU5flAHDV8T0DTiIiIvHkuF5tWH732P0GQj720XIe+2g5AE9eOoJv9W0XZEyRBifwAY1m1gQ4Hbimwm4H3jEzB/7m7o8HEi7Gpq3cCkBSgpGQoIEpIiJy4CoOhNyxp4jfvjiHt+ZvBOBHT4d+m3t45+b89QfD6dRC3UZEYi3w4ho4E5jq7lsr7DvW3deZWVtgipktcvePK7vYzK4ArgDo2rVr7NNG0Q+f/BKAf11+ZMBJRESkPmjeOJnHLh4OwNy1O7jkqWls3V3InLU7OGbC+wD85Lju/GZ0XxolqduISCzUhb9ZF7BPlxB3Xxf+uhl4BRhZ1cXu/ri7j3D3EW3atIlp0Ghyd/KLSgEY1bN1wGlERKS+GdS5OTNvOZWV94zljrMHlO//+ycr6X3zZDLHT+KdcAu3iERPoC3XZtYcOAH4QYV9TYEEd88NPz8NuD2giDHz/LTVAAzr2iLYICIiUq+ZGRePyuTiUZnk5hdx48tzeWPOBgCu+NcMAPp3aMbfLxmhbiMiURDL2UImAicCGcAm4FYgGcDdHwufcylwurtfUOG6HoRaqyFU/D/v7ndF8prxNFtI2dzWH/76RDI1BZ+IiNSyeet2cNnTX+01JSzAdSf34tqTe5GosUAiVaputhAtIhMAd6f7jW8CkDVhXMBpRESkIXN3nv1yNbe8Om+v/U0aJfLClaMY2Kl5QMlE6i4tf17HvBpe7nxgp2YBJxERkYbOzLj4qG5cfFQ3tu0u5Pr/zOKjJdnkFZZwxkOfAvDDUd24eVx/DYIUiYBargNQ1iXk7euPp0/79IDTiIiI7O/9RZvKp/IrYwYvXjVKS65Lg6eW6zpKhbWIiNRV3+rbjqwJ48grLOa3L83l9dnrcad8yfXvDO/MnecMJDU5MeCkInWLfr9Ty6YuC63orhHZIiISD5o0SuKhC4eSNWEcz//km3UZXpyxlr63vEXm+EnlP9tERC3Xte7W1+YDcMc5A2o4U0REpG45umcGWRPGkV9Uwq3/m89/pq8B4KInQouijRvUgXu/czhNU1ReSMOlPte1rKy/9cp7xmKmaY5ERCS+zVi1je/+7XNKSveuJ569/EiO7ZURUCqR2FKf6zpix56i8ucqrEVEpD4Y3q0ly+8eS1FJKXdNWsjTn2UB8IN/hFqz1TdbGhr1ua5FD723FIBLRnULOImIiEh0JScmcNtZA8iaMI5XfnY0ZW1IZX2z+//+LRZvzA02pEgtULeQWlTWJeTrW06lZdNGAacRERGJrfyiEm56ZS4vz1y31/5bzujPj47J1G9xJW5V1y1ELdcBUGEtIiINQWpyIn/+7hCyJozjbxcPL99/xxsL6H7jm5z/2GdszysMMKFI9Km4riUrsncBkJqsj1xERBqe0QPakzVhHNNuOpm+4XUevsraxpDbp2g6P6lXNKCxljz8wTIArju5d8BJREREgtO2WSpvXX887s6D7y3lgXdD45HKpvO79OhMbh7Xj6RENUZJfFKf61pS1t96/h9Ga/5PERGRCmat2c45j0zda1/7Zqm8cOUourZuElAqkaqpz3UdosJaRERkb0O6tCBrwjjm/2E0p/RrB8DGnfkc/8cPyBw/iddnrw84oUjkVFzXgpVbdgPQKEkft4iISFWapiTxxCUjyJowjj+dP7h8/88nfk3m+Enc8OJsikpKA0woUjNVe7XgkfL+1r0CTiIiIhIfvjO8M1kTxvHer06gWWrot74vTF9Lr99N5oQ/fsCmnfkBJxSpnIrrWvDijLUAXKzFY0RERA5IzzZpzLltNIvuOJ1xgzoAsConjyPvfo/M8ZP4fHlOwAlF9qbiuhY1S00OOoKIiEhcSk1O5JGLhpE1YRx/OGtA+f4L//4FmeMn8Y9PVwaYTuQbKq5jrKC4JOgIIiIi9colR2eSNWEcL//s6PJ9d7yxgMzxk/j5xK8pLFa/bAmOiusYmzRnAwAn9WkTcBIREZH6ZVjXlqGFaX53Mj3aNAXg9dnr6X3zZE6+70NydhUEnFAaIhXXMfb0Z1kAXHZM92CDiIiI1FNt01N5/1cnsuTOMZwzpCMAy7N3M/zOd8kcP4kF63cGnFAaEhXXMTZn7Q4Ajj0sI+AkIiIi9VujpAQeuGAoWRPGcdPYvuX7x/7lEzLHT+L9RZsCTCcNhYrrWpKQYEFHEBERaTCuOL4nWRPG8dSlR5Tv+9HT08kcP4mnpmrwo8SOiusY2p5XGHQEERGRBu2kvm3JmjCOt64/rnzfH14PDX68440FuHuA6aQ+UnEdQ6+HBzOeO7RTwElEREQatr7tm5UPfuzUojEA//h0Jd1vfJMr/zVdM4xI1Ki4jqFXZoYWjzlvmIprERGRuqBteipTx3+L+X8YzcjMVgC8PX8TvW+ezDmPTGVXQXHACSXeqbiOoZmrtwNwdE8NZhQREalLmqYk8cJVo1h215jy3zDPWrOdgbe+zTET3tc0fnLQVFzXgkQNZhQREamTkhITuP97Q1h5z1iuPL4HAOu272H4ne8y6Na32bBjT8AJJd6ouI6R0lINkBAREYkXZsaNY/vtNY1fbkExo+55n8zxk1iVszvghBIvVFzHyFdZWwHo36FZwElERETkQJRN43f3uYPK953wxw/JHD+JZZt3BZhM4oGK6xh5eeY6QIMZRURE4tX3j+xK1oRxPHjBkPJ9p/z5IzLHT2LxxtzggkmdVmNxbWbnmdlSM9thZjvNLNfMtI5oDV6bvR6As8LLsIqIiEh8OntIJ7ImjOOvFw0r3zf6gY/JHD+JpZtUZMveImm5vhc4y92bu3szd093d/V1qMGeohIgNOWPiIiIxL8xgzqQNWEcf//hiPJ9p97/sbqLyF4iKa43ufvCA72xmT1pZpvNbF4Vx08Mt4bPCj9+X+HY6Wa22MyWmdn4A31tERERkVg5tX87siaM428XDy/fV9ZdRAMfJSmCc6ab2X+AV4HySR/d/eUarnsaeBj4ZzXnfOLuZ1TcYWaJwCPAqcBa4Csze83dF0SQtU7QUqoiIiL13+gB7UNLq8/bwFXPzgRCAx/NYOpvv0XH8EqQ0rBE0nLdDMgDTgPODD/OqPYKwN0/BrYeRKaRwDJ3X+HuhcC/gbMP4j6BmbtuBwC92qYFnERERERi7fSBHfYa+OgOR094n6G3v8PW3YXBhpNaV2PLtbtfFsPXH2Vms4H1wK/dfT7QCVhT4Zy1wJFV3cDMrgCuAOjatWsMo0bunfmbgNCvjURERKRhOHtIJ84e0omJ01Zz48tz2ZZXxLA7ptCrbRqvXn0MTVMi6TAg8S6S2UI6m9kr4f7Tm83sJTPrHIXXngl0c/fBwEOEup0cMHd/3N1HuPuINm3aRCHWoZuyQMW1iIhIQ3XhyNAUfr8Z3QeApZt3MeDWt/nBE19SVFIacDqJtUi6hTwFvAZ0DD9eD+87JO6+0913hZ+/CSSbWQawDuhS4dTO4X1xY3F4Wp7BnVsEG0REREQCc/VJh7HynrH86JjuAHy6bAu9fjeZG1+eo/FZ9VgkxXUbd3/K3YvDj6eBQ24iNrP2Zmbh5yPDWXKAr4BeZtbdzBoBFxAq7uNOQoIFHUFEREQCZGb8/sz+LL97LKcPaA/AxGlr6H7jmzzxyYqA00ksRFJc55jZD8wsMfz4AaEiuFpmNhH4HOhjZmvN7HIzu8rMrgqf8h1gXrjP9V+ACzykGLgGeBtYCLwQ7ostIiIiEpcSE4zHLh7OojtOp3+H0HIhd05aSOb4SeXdSaV+sJp+LWFm3Qj1iR4FOPAZcK27r459vAMzYsQInz59eqAZiktKOex3kwHImjAu0CwiIiJSN2XnFnD0hPcoKvmmDnvr+uPo217r9MUDM5vh7iMqOxbJbCGrgLOinqqemhOehm9AR/3lEBERkcq1SU9h6V1jWbwxl9EPfAzA6Q98QmpyAp+PP5mWTRsFnFAOVpXFtZnd4O73mtlDhFqs9+Lu18Y0WZz6bNkWAI7u2TrgJCIiIlLX9WmfTtaEcby3cBOXPzOd/KJSht4xheN6ZfD0ZSNJ1PituFNdn+uyJc+nAzMqeUglPlse6o5+9GEZAScRERGReHFyv3Z7Td/3ydIt9LzpTf764fKAk8mBqrK4dvfXw0/z3P2Zig9CKzZKJcqK65GZrQJOIiIiIvHm6pMOY/ndYzmuV6iR7v/eWkTm+El8saLGuSSkjohktpAbI9wnFWgVJhERETkYiQnGvy4/khk3n0JZr5ALHv+CzPGTyNlVEGw4qVF1fa7HAGOBTmb2lwqHmgHFsQ4mIiIi0pC1TkthxT3jmLFqG9/+62cADL/zXU7t347HLx5OeLkQqWOqa7leT6i/dT5797V+DRgd+2giIiIiMrxbS7ImjGP8mL4ATFmwie43vsn/ZsXVAtYNRiTzXCe7e1Et5TkkQc9znV9UQt9b3gI0x7WIiIhEX1FJKec+OpV563aW7/v0tyfRuWWTAFM1PNXNcx1Jn+tMM3vRzBaY2YqyR5Qz1gsLNoS+0TXHtYiIiMRCcmICb/z8OD789Ynl+479vw/44ZPTKC2tvsFUakckxfVTwF8J9bM+Cfgn8GwsQ8Wr2Wu2AzCkS4tAc4iIiEj9lpnRlKwJ45hw3iAAPl6STY+b3mTy3A0BJ5NIiuvG7v4eoS4kq9z9NkB9HipRVlwPVnEtIiIiteCCkV1ZdteY8trjp8/NJHP8JLbnFQYbrAGLpLguMLMEYKmZXWNm5wJpMc4Vl2ap5VpERERqWVJiAv+7+him/OL48n1Dbp/CnW8sCDBVwxVJcX0d0AS4FhgOXAxcEstQ8SorJ7S2Ts82+r+HiIiI1K5e7UJLqV97ci8Anvh0JZnjJ7F0U27AyRqWGotrd//K3Xe5+1p3v8zdz3P3L2ojXLxKTNC8kyIiIhKMX57am7m3nVa+fer9H/P9v39BTTPESXRUt4jM60CVfwruflZMEomIiIjIIUlPTSZrwjgmz93AT5+byWfLc+h+45u8cOUoRnZvFXS8eq26Nbr/VGspRERERCTqxgzqwLK7xjD6gY9Znr2b7/7tc3q3S2PydcfrN+0xUmVx7e4f1WaQeKdftYiIiEhdlJSYwHu/OpHPl+dw4d+/YMmmXfS86U2e+/GRHHNYRtDx6p0a+1yb2cqKi8doEZnKbdpZAEDrpo0CTiIiIiKyv1E9W7Pi7rEM69oCgIue+JLTH/hYi89EWSSzhYwAjgg/jgP+ghaR2c+S8EjcPu3TA04iIiIiUrmEBOPlnx3Di1eNAmDRxlx63PRm+XTCcugimS0kp8Jjnbs/gBaR2U9Zcd27nYprERERqdtGZLZixd1j6dehGQDnPDKVHz/zlbq5RkEk3UKGVXiMMLOrqH4gZINUVlz3aqc5rkVERKTuS0gwJl93HE9fdgQA7y7cTPcb32TN1ryAk8W3SLqF3FfhcQ+hhWS+G8tQ8WjJpl2AWq5FREQkvpzYpy2L7zydxsmJABx37wc89N7SgFPFr0i6hZxU4XGqu//E3RfXRrh4Urb6Ue+2Kq5FREQkvqQkJbLwjtO5/ewBANw3ZQmZ4ydRUFwScLL4E0m3kNZm9hczm2lmM8zsQTNrXRvh4snuwtA3X/MmyQEnERERETk4PxyVyVe/O6V8u8/NbzE9a2uAieJPJN1C/g1kA98GvhN+/p9YhhIRERGRYLRJTyFrwjhO6tMGgO889jm/fXFOwKniRyTFdQd3v8PdV4YfdwLtYh1MRERERILz1GUjeeZHIwH4z/Q1ZI6fxJ5CdROpSSTF9TtmdoGZJYQf3wXejnUwEREREQnWCb3bMPe208q3+/3+Leas3R5coDgQSXH9E+B5oDD8+DdwpZnlmtnOWIYTERERkWClpyaTNWEcoweEOi6c9fBUHnh3ScCp6q5IZgtJd/cEd08KPxLC+9LdvVlthKzrNOG6iIiI1Hd/u3gEj140DIAH3l3KqHveUw1UiUharjGzs8zsT+HHGbEOFW+25xUBkJ6qtXVERESk/ho7qANf3HgyABt25NP9xjfZnlcYcKq6JZKp+CYA1wELwo/rzOyeWAeLJ2u2hVYy6tKyScBJRERERGKrffNUlt89lpSkUBk55PYpzF6zPdhQdUgkLddjgVPd/Ul3fxI4HRgX21jxZc3WPQB0adU44CQiIiIisZeYYCy+cwwXjuwCwNmPTOW5L1cFnKpuiKhbCNCiwvPmkVxgZk+a2WYzm1fF8YvMbI6ZzTWzz8xscIVjWeH9s8xseoQZA1PWct21lVquRUREpOG457zDefCCIQD87pV5XDvx62AD1QGRFNf3AF+b2dNm9gwwA7grguueJtTKXZWVwAnuPgi4A3h8n+MnufsQdx8RwWsFas3WcLcQFdciIiLSwJw9pBPv/OJ4AF6bvZ4Rd77boAc6RjJbyETgKOBl4EVglLvXuEKju38MVLleprt/5u7bwptfAJ0jSlwHrdkW6hbSuaW6hYiIiEjD07tdOrN/H5oPe8uuArrf+CZFJaUBpwpGpN1CRgEnhh+jYpDjcmByhW0ntHjNDDO7IgavF1Vrt2pAo4iIiDRszZsks/zuseXbvX43mZ35RQEmCkYks4U8ClwFzAXmEVpA5pFoBTCzkwgV17+tsPtYdx8GjAGuNrPjq7n+CjObbmbTs7OzoxXrgJT1ue6s4lpEREQasMQEI2vCODo2TwXg8NveYcOOPQGnql2RtFx/Cxjt7k+5+1OEZg/5VjRe3MwOB54Aznb3nLL97r4u/HUz8Aowsqp7uPvj7j7C3Ue0adMmGrEOWFFJqF9R40aJgby+iIiISF3y2Y0nc0q/tgCMuud9lm3eFXCi2hNJcb0M6Fphu0t43yExs66E+nFf7O5LKuxvambpZc+B0wi1mIuIiIhInHjikiO4+KhuAJzy54+Yt25HwIlqRyTFdTqw0Mw+NLMPCC0k08zMXjOz16q6yMwmAp8DfcxsrZldbmZXmdlV4VN+D7QGHt1nyr12wKdmNhuYBkxy97cO8v2JiIiISEDuOGcgvzilNwBnPPQpsxrAYjORrNf9+4O5sbtfWMPxHwM/rmT/CmDw/leIiIiISLy57pRepCYncM/kRZzzyFRe/tnRDOvaMuhYMVNjce3uH9VGEBERERGpn648oSeNkhL4w+sLOO/Rz3jj58cysFNE6xLGnUin4hMREREROWiXHdOd343tB4S6iCzPrp+DHFVci4iIiEit+MnxPfjlqaE+2Cff9xGbduYHnCj6qi2uzSzRzJ6rrTAiIiIiUr9de3Ivvn9kaCK6I+9+j10FxQEniq5qi2t3LwG6mVmjWsojIiIiIvXc3ecO4oTeofVJBt76NiWlHnCi6ImkW8gKYKqZ3WJmvyx7xDpYvCgsLgXALOAgIiIiInHkmR+NpFlqaG6Nnje9GXCa6ImkuF4OvBE+N73CQ4Cc3QUAtElLCTiJiIiISHyZfetp5c8v/seXASaJnkim4vsDgJmlhbfr59DOg7QltxCANukqrkVEREQOhJmx8PbT6ff7t/hk6Rae/HQlPzq2e9CxDkmNLddmNtDMvgbmA/PNbIaZDYh9tPiwZVeo5TpDLdciIiIiB6xxo0Q+/PWJANz+xgIWbtgZbKBDFEm3kMeBX7p7N3fvBvwK+HtsY8WP7FwV1yIiIiKHIjOjKX/+bmiB7jEPflI+pi0eRVJcN3X3D8o23P1DoGnMEsWZ7LKW63RNqCIiIiJysM4b1pmR3VsB0PeWyQGnOXgRzRYSnikkM/y4mdAMIgJs2x3qc926qYprERERkUPxnyuOAqDU4dEPlwWc5uBEUlz/CGgDvAy8BGQAl8UyVDzJzQ9NfJ6emhxwEhEREZH4ZmZMu+lkAO59a3FcruAYSXF9irtf6+7D3H24u18PnBrjXHGjbFWhtJQaJ14RERERkRq0bZbKTWP7AqEVHONNJMX1jRHua5ByC8parlVci4iIiETDFcf3LH/+8PtLA0xy4Kosrs1sjJk9BHQys79UeDwN1K9F4A/BrvwiQMW1iIiISDRNv/kUAP70zhL2FJYEnCZy1bVcrwemA/nAjAqP14DRsY8WH8r6XKelqM+1iIiISLRkpKVw4ciuAJzwxw9qOLvuqLK51d1nA7PN7Hl3L6rFTHGlvM+1Wq5FREREourucwcycdpqNucWsHLLbrpn1P3ZoCPpc51pZi+a2QIzW1H2iHmyOLErX32uRURERGLBzHj4+0MBOOlPHwYbJkKRFNdPAX8l1M/6JOCfwLOxDBVPygY0Nm2k4lpEREQk2s44vGP58zlrtwcXJEKRFNeN3f09wNx9lbvfBoyLbaz4k5hgQUcQERERqZee+/GRAJz18NSAk9QskuK6wMwSgKVmdo2ZnQukxTiXiIiIiAgAxxyWUf58zda8AJPULJLi+jqgCXAtMBy4GLgklqFERERERCr643cOB+C8v34WcJLq1Vhcu/tX7r7L3de6+2Xufp67f1Eb4UREREREAM4f0QWA7NwCSko94DRVq3IUnpm9DlSZ3N3PikkiEREREZFKHN2zNZ8tz+GJT1Zw5Qk9a74gANW1XP8JuA9YCewB/h5+7AKWxz6aiIiIiMg37v/eEADumbwo2CDVqG4RmY8AzOw+dx9R4dDrZjY95slERERERCpo1yy1/HlpqZNQB2dri2RAY1Mz61G2YWbdgbq/PI6IiIiI1DujerQG4MWZawNOUrlIiutfAB+a2Ydm9hHwAXB9TFOJiIiIiFTiprH9ALh/ypKAk1SuxmUF3f0tM+sF9A3vWuTuBbGNJSIiIiKyv0GdmwOwYUd+wEkqV2PLtZk1AX4DXOPus4GuZnZGzJOJiIiIiMSZSLqFPAUUAqPC2+uAO2OWSERERESkGi2bJAOwdlvdW60xkuK6p7vfCxQBuHseUPeGZoqIiIhIg3BC7zYATF22JeAk+4ukuC40s8aEF5Qxs55ARH2uzexJM9tsZvOqOG5m9hczW2Zmc8xsWIVjl5jZ0vBDy62LiIiICABHhmcMmbZyW8BJ9hdJcX0r8BbQxcyeA94Dbojw/k8Dp1dzfAzQK/y4AvgrgJm1Cr/ukcBI4FYzaxnha4qIiIhIPda7XRoAy7J3BZxkf9XOFmJmCUBL4DzgKELdQa5z94ja4N39YzPLrOaUs4F/ursDX5hZCzPrAJwITHH3reEcUwgV6RMjeV0RERERqb/apIUWk8nZVfcmsKu2uHb3UjO7wd1fACbF4PU7AWsqbK8N76tqv4iIiIg0cI0bJQKQV1gScJL9RdIt5F0z+7WZdTGzVmWPmCeLkJldYWbTzWx6dnZ20HFEREREJMYKikNFdWpSJKVs7apxERnge+GvV1fY50CPSs49UOuALhW2O4f3rSPUNaTi/g8ru4G7Pw48DjBixAiPQiYRERERqcM27Qx1B8lITwk4yf5qLPfdvXslj2gU1gCvAT8MzxpyFLDD3TcAbwOnmVnL8EDG08L7RERERKSBW7wxF4De7dIDTrK/GluuzSwV+BlwLKEW60+Ax9y9xjUnzWwioRboDDNbS2gGkGQAd38MeBMYCywD8oDLwse2mtkdwFfhW91eNrhRRERERBq26VmhsnBIlxbBBqlEJN1C/gnkAg+Ft78P/As4v6YL3f3CGo47e3c3qXjsSeDJCPKJiIiISAMyZcEmAE7q2zbgJPuLpLge6O79K2x/YGYLYhVIRERERKQ6uQXFAHRq0TjgJPuLZIjlzHB/aADM7EhgeuwiiYiIiIhULtTxoe6KpOV6OPCZma0Ob3cFFpvZXEI9Ow6PWToRERERkQrKuoQM6Ngs4CSVi6S4rm75chERERGRWnPDS3MAuO2sAQEnqVyNxbW7r6qNICIiIiIiNdmeVwTAEZl1Zk3DvdS9ZW1ERERERCrxv1nrAOjSqu4NZCyj4lpERERE4sJ1/54FwNOXjQw2SDVUXIuIiIhInbdo487y5z3bpAWYpHoqrkVERESkzjv9gU8A+MclIwJOUj0V1yIiIiJSp325Iqf8+cn92gWYpGYqrg+RWehrcUlpsEFERERE6qnvPf4FAC/99OiAk9RMxfUhapaaDMCu8DKcIiIiIhI9f3h9PgBJCcbwbi0DTlMzFdeHKD01NFX4zj0qrkVERESiac3WPJ6amgXA178/NdgwEVJxfYjKWq535hcFnERERESk/nB3jrv3AwDuOGcg6eGaq65TcX2ImjUOt1yruBYRERGJmnMemQpAo6QELj6qW8BpIqfi+hCVt1yrW4iIiIhIVPzj05XMXrsDgPl/GB1wmgOj4voQNW8cKq635RUGnEREREQk/n25Ioc73lgAwIe/PpHkxPgqV+MrbR3UvnkqAJt25gecRERERCS+rdyyu3zavUcvGkZmRtOAEx04FdeHqKy43rhDxbWIiIjIwdq8M5+T/vQhANef0ouxgzoEG+ggqbg+RO2bhYtrtVyLiIiIHJTNufmMvPs9AC44ogvXn9I74EQHT8X1IVLLtYiIiMjBW7stj5F3hQrrsYPaM+Hbhwec6NCouD5EHZo3BmCDimsRERGRA7Jo406O/b/QXNZnDe7IoxcNDzjRoUsKOkC8a9kkNFvIjj2a51pEREQkUu8t3MTlz0wH4PJju3PLGf0DThQdKq4PkZkFHUFEREQkrtz3zmIeen8ZALefPYAfjsoMNlAUqbgWERERkVrh7px6/8cs27wLgOd+fCTHHJYRcKroUnEtIiIiIjGXs6uA4Xe+W779+Y3fKh+7Vp+ouBYRERGRmJo8dwM/fW4mAGaw9M4xJMXZyouRUnEtIiIiIjHh7pzx0KfMX78TgCtP6MGNY/oFnCq2VFyLiIiISNTNX7+DcX/5tHz7jZ8fy8BOzQNMVDtUXEdRQXEJKUmJQccQERERCYy785N/TufdhZsB6NyyMR/95iQSExrGDGsqrqOgZ5umLM/ezcotu+nbvlnQcUREREQCMWPVVr7918/Ltx+/eDinDWgfYKLap+I6Cnq1TWd59m6Wbtql4lpEREQanILiEk7644esD69Y3aF5Kh/95iQaJdXPQYvVUXEdBb3apfHWfFi6KTfoKCIiIiK16pEPlvHHtxeXb0/8yVGM6tk6wETBimlxbWanAw8CicAT7j5hn+P3AyeFN5sAbd29RfhYCTA3fGy1u58Vy6yHole7dACWbNoVcBIRERGR2vFV1lbOf+ybLiDnDu3En787uMGvXh2z4trMEoFHgFOBtcBXZvaauy8oO8fdf1Hh/J8DQyvcYo+7D4lVvmga2DHUFWTuuh0BJxERERGJrY078jnqnvf22jfzllNp1bRRQInqlli2XI8Elrn7CgAz+zdwNrCgivMvBG6NYZ6Y6Z7RFIB12/cEnEREREQkNnYVFHPmQ5+ycsvu8n0vXjWKEZmtAkxV98SyuO4ErKmwvRY4srITzawb0B14v8LuVDObDhQDE9z91SquvQK4AqBr166HnvogNPRff4iIiEj9VVBcwiVPTuOLFVvL99117kAuOrJbgKnqrroyoPEC4EV3L6mwr5u7rzOzHsD7ZjbX3Zfve6G7Pw48DjBixAivnbgiIiIi9VthcSlXPTuD9xdtLt93xfE9uHFMXzUsViOWxfU6oEuF7c7hfZW5ALi64g53Xxf+usLMPiTUH3u/4lpEREREoie/qIQfPzOdT5dtKd933rBO/Ok7g0loIAvBHIpYFtdfAb3MrDuhovoC4Pv7nmRmfYGWwOcV9rUE8ty9wMwygGOAe2OYNWryCotp0qiu/EJAREREJDI78or43uOfs2jjN1MLnz2kI/edP5ikxIY3X/XBilkV6O7FZnYN8DahqfiedPf5ZnY7MN3dXwufegHwb3ev2KWjH/A3MysFEgj1ua5qIGSdMLxbS2as2sas1ds5+rCMoOOIiIiIRGTllt2MfuBjCotLy/ddcEQX7j53kFqqD0JMm1jd/U3gzX32/X6f7dsque4zYFAss0Xbt4d1ZsaqbeTsLgw6ioiIiEiN3l+0iR89PX2vfded3IvrT+mlPtWHQP0XouSUfm256RXYquJaRERE6qiSUueeNxfyxKcr99r/0IVDOXNwx4BS1S8qrqOkTXoKaSlJrMjWKo0iIiJSt6zdlsdFT3zJqpy8vfZPvu44+nVoFlCq+knFdZSYGT3aNGVFhYnVRURERILi7jz35WpufnXeXvtP7NOGh78/jLQUlYGxoE81inpkNOWrrG1BxxAREZEGbM3WPH7yz+l7zfoBMOG8QVwwMpgF9xoSFddR1KNNGq/OWs+ewhIaN0oMOo6IiIg0EIXFpfzx7UX8/ZO9+1L3aZfOU5cdQccWjQNK1vCouI6iPu3TAVi0cSdDu7YMOI2IiIjUd2/P38iV/5qx3/4J5w3ie0d00awfAVBxHUUDOoYGBMxfr+JaREREYmPJplyu+teM/cZ5nXF4B+4+bxDNUpMDSiag4jqqOrVoTIsmycxfvyPoKCIiIlKPrNu+h9/8dzafLc/Za3/7Zqk8eekR9O+oGT/qChXXUWRmDOjYjHnrdgYdRUREROLcpp35/PalOXy4OHu/Y5qXuu5ScR1lAzs256mpWRQWl9IoKSHoOCIiIhJHsnMLuPnVubw9f9N+x249sz+XjMrUkuR1nIrrKBvatSV/+3gFc9dtZ3i3VkHHERERkTpu7bY8fvfKPD5asn8L9Y1j+vLj43qQqII6bqi4jrIjMkMDGaet3KbiWkRERCr15Yocbnx5bqWLz/3q1N5cdWJPkhP1G/B4pOI6ylqnpXBY2zSmrczhpyf2DDqOiIiI1AElpc7z01Zzyz6rJZa55Yz+XHp0plqo6wEV1zFwRGYr3piznpJS118SERGRBmrr7kLue2cxz325er9jbdNTmPDtQZzUp63moq5nVFzHwFE9WjFx2mrmrdvB4C4tgo4jIiIitcDd+WDxZu54YyErK+nucVyvDP5w1gB6tEkLIJ3UFhXXMXDsYRmYwQeLN6u4FhERqcfWbd/Dn95ezCtfr6v0+JUn9OCakw4jXQu7NBgqrmOgdVoKQ7q04P1Fm7n+lN5BxxEREZEoKSop5fkvV3PnpAUUlfh+x/u2T+emsf04rleGuns0UCquY+Rbfdpy35QlbM7Np216atBxRERE5CCUdfW4963FLNqYW+k5vz6tN5cf24PGjRJrOZ3URSquY+Tkfu24b8oS3pm/iR8c1S3oOCIiIhIBd+fTZVu4f8oSZq7eXuk5p/Rry/gxfTmsbXrthpO4oOI6Rvp1SOewtmn8b9Y6FdciIiJ1lLvz5cqt3D9lCV+u3FrpOf06NOOG0X04sU8bdfWQGqm4jhEz45whHfnTO0tYuy2Pzi2bBB1JRESkwXN3PlqSzcPvL2P6qm2VntOrbRq/OLU3pw9or6XG5YCpuI6hs4d04k/vLOF/s9Zz9UmHBR1HRESkwckvKuG/09fw2EcrWLd9T6XndM9oyvWn9OKMwztqfQo5ZCquY6hLqyYc2T005/VVJ/TUX1gREZEYW799D098spInp66s8pz+HZpx7cmHcVp/tUxL9Km4jrFLj87kp8/N5L2FmzhtQPug44iIiNQbpaWhmTye+GQln6/IqfK8sYPac+XxPbX2hNQKFdcxdmr/dnRsnsrTn2WpuBYRETkEy7N38cxnWfzz81VVnpNgcNUJPbn0mExNhSuBUHEdY0mJCVw8KpP/e2sR89btYGCn5kFHEhERqfN25hfx4vS1PPN5Fqty8qo8b2jXFvz42B6MHtCOpMSEWkwoUjkV17XgoqO68thHy/nzlCU8eekRQccRERGpU/YUlvDGnPVMnLa6yrmlAVo2SebSo7tz4ZFd1CotdZaK61rQLDWZK47vwR/fXszXq7cxtGvLoCOJiIgEYndBMW/MWc/z09Ywe832as89Z0hHLj2mO4M7N9f80hI3VFzXkkuPzuTJT1dy95sLeeHKUfpHQkRE6r3teYX8b9Z6/vPVGhZs2Fntuaf1b8eFI7tyfO82ml1L4pqK61rSNCWJG07vw29fmssrX6/jvGGdg44kIiISNQs37OSlGWt5aeZatuUVVXvumIHtuXBkV449LENT4Um9o+K6Fp0/vAsTp63h7jcXcXK/djRvnBx0JBERkQOSX1TCews38/LMtby3aHON5583tBPnj+jCkd1bqZCWBkHFdS1KSDDuPGcgZz8yld//bx4PXjA06EgiIiKVKi11vl6zjddnb+CNOevZsquw2vM7t2zMt4d15tyhncjMaFpLKUXqnpgW12Z2OvAgkAg84e4T9jl+KfBHYF1418Pu/kT42CXAzeH9d7r7M7HMWlsGdmrOdSf34s9TlnBSn7acM7RT0JFERKQBc3eWbNrF67PX8/qc9dVOe1fmuF4ZfGd4Z07r357GjRJrIaVI/IhZcW1micAjwKnAWuArM3vN3Rfsc+p/3P2afa5tBdwKjAAcmBG+dlus8tamn53Yk4+XZHPLq/M4vHNzerRJCzqSiIg0AKtz8nhzXqglet666gcYAvRtn86ZgzsyblAHtUaLRCiWLdcjgWXuvgLAzP4NnA3sW1xXZjQwxd23hq+dApwOTIxR1lqVlJjAAxcM4ayHp/Ljf07nlZ8do/7XIiISFWXdOd6Zv4l3Fmxi5ZbdNV7TqUVjzhzckTMO78CAjs00o5XIIYhlcd0JWFNhey1wZCXnfdvMjgeWAL9w9zVVXFuv+k90btmEv140jIue+JJrnp/JE5eMICVJv1oTEZHI7Mwv4oNFm5myYBPvzN9EYUlpjddkpKUwdlB7xg7qwBGZrTTlnUgMBD2g8XVgorsXmNmVwDPAtw7kBmZ2BXAFQNeuXaOfMIaO7NGau88bxA0vzuG6ibN4+PtDtXSriIiUc3eWbt7Fews3886CjXxdzeqFFfXr0IzRA9pxWv/29OuQrpZokVoUy+J6HdClwnZnvhm4CIC751TYfAK4t8K1J+5z7YeVvYi7Pw48DjBixAg/lMBB+O6ILuTmF3PHGwv45Quzue+7g0lWgS0i0qBkbdnNh4s38+GSbD5cnB3xdaf0a8dpA9pxct+2tE5LiWFCEYlULIvrr4BeZtadULF8AfD9iieYWQd33xDePAtYGH7+NnC3mZWtE34acGMMswbq8mO7U1hcyv+9tYjc/CIevWi4Rl+LiNQzWVt288HizXx0gAV0l1aNOblvO07r344jurdSA4xIHRez4trdi83sGkKFciLwpLvPN7Pbgenu/hpwrZmdBRQDW4FLw9duNbM7CBXoALeXDW6sr356Yk+aN07m5lfncuHfv+BvFw+nXbPUoGOJiEiESkudxZty+XTpFj5ems0nS7dEfG37Zqmc2KcNJ/ZpyzGHtSY9VYPcReKVucddT4oqjRgxwqdPnx50jEPy1ryN/PKFWTRNSeLRi4ZxRGaroCOJiEhYdm4Bn6/I4bNlW/h02RbWbtsT8bXfFNBtOPqwDJqpgBaJW2Y2w91HVHYs6AGNso/TB7ane8YxXPmv6Vz4+Bdcf0ovrjqhpwY6iojUgvyiEmau3sZny3KYunxLxAMIy3TPaMpxvTI4rlcbjurRSi3QIg2Qius6qE/7dP53zbHc9Mpc/vTOEqYs3Mx95w/msLZabEZE5FDszC9ixqptfLVyK9NWbmX6qgNbmywtJYljDmvNMYdlcHTP1vRsk6aZOERkL+oWUse9Pns9t/xvHnkFJfz4uO5cfdJhNE3R/4lERPbl7qzdtoevskKF87SsrazIrnkBlX0N69oiXDxnMLRrC1KTNcBcRPambiFx7MzBHTmyRysmTF7Eox8u56WZa7lhdF/OGdpJk/+LSIOyZVcBs1Zv5+s12/h69Xa+Xr2dPUUlB3SP5ETjiMxWHJHZipHdWzG0awuaNNKPQhGJHrVcx5EZq7Zx22vzmbtuBz0ymnLdKb044/COKrJFJK65O+t35PP16rKieRtfr9nOwfx4apOewsjurRgZLp77tEsnQf9GikiUVddyreI6zpSWOu8s2MgD7y5l0cZcemQ05dJjMvn2sM7qLiIidU5JqbMiexez1+4oL54XbNh5UPdKT01iSJcWDO3akqFdWzCkcwtaNm0U5cQiIjVTcV0PlZY6k+dt5PGPlzN77Q7SU5P47oguXDiyqwY+ikjMFRaXsnRzLvPX7WTuuh3MW7+D+et2UlhSelD3a5OewtAuLRjStQVDu7Tk8M7N1WAgInWWiut6zN35es12npqaxeS5GygudQZ3acG3h3XizMM7qlVHRA7I7oJiFm7Yybx1O5i7bifz1+9g0cbcQ7pnZusmHN65RbjVuQX9OzYjJUmDBEUkfqm4biA25+bz2qz1vDhjLYs25pKcaIzqmcFp/dtxav92WvFRpIHakVfE4k25LN64k0Ubc1kcfuQWFB/SfXu3S2Ngx+YM6NScgR2b0b9jM83rLCINgorrBmjB+p28Omsd78zfSFZOHgCDu7TgW+GldQd3aUGyFqYRiUulpc667XvChfI3BfPSzbsO+d4JBoM6NWdg2aNjc3q3T1NLs4hIBSquGzB3Z9nmXbyzYBPvLNjEnLWhEfhNGyUysnsrOrZoTP+OzThvaGcaN9IPT5Eg7MwvYkX2bpZt3sXy7F0sL/t6EHM0V6Zpo0T6tE+nT/tm9GmXRt8OzejTLl3dxkREDpKKaym3bXchX6wILes7dVkOK7fs/8N73KAO/HBUN0Z2b6WVx0QOgLuTs7uQVTm7WZWTR1ZOHiu37Gblll2syN5NXuGBzclcnQ7NU+kbLphDX9Pp0aapWphFRGqBimup0szV2/j7xyuYPG9jtecd3rk55wzpxBmHd6Ct+m5LPVdYXMqabXmszsljVc5usnLyWL01j6yc3azOyaO4NLr/bjZplEjPNmn0bNOUw9qmhZ63TaNb6yYqlkVE6iAV1xKx3QXFvPz1Op77YlVEMwRkpDXipD5tOalvW0b1aK1fM0udkF9UwoYd+azfvod12/awbvse1m/fw/odoe312/MPesq4mrRskkzX1k3JbN2Ebq2a0L1NU7pnpNE9oynNG2uwn4hIfaDiWg5JSanz5YocXvl6HZPnbWTXAcww0L5ZKiMyWzKkS2j6rf4dmtGiiQpwqdyewhI27cxnc24Bm3Pz2byzoPz5pp355QVzflFsCuOKMls3oWvrpnRr1YRurZvQLVwwd2nVhNRktSaLiDRkKq4lZtZszePDxZv5YHE2X67IYfdB9ilNSjAyM8oKmaZ0z2hS3vrXqUVjkjSzSZ3h7uwuLGHb7kK27i5ka15h+fNteeF9uwvJ2VVI9q4CNu8sYE9R9PoaRyIpwejYojEdW6TSqUUTOrVIDW83plPLxnRs3lgDeEVE5KCpuJZAuDtrtu7hq6ytzFm7nYUbclm4Yechz61blRZNkmmTlkLLpo1o3jiZ9NQkmqUm06xxMs0bJ9MsNanC82SaNU6ieeNkmjZKIiGhbg/cdHeKS538ohLyi0opKN7na1EJe4pK2FVQTG5+cfhrEbn5xRUe4e2Cb/aXRLnv8KFKSUqgbbMU2qWn0rZZCm3SUmjbLJW26Sm0b55K+2apdGjRmDSt3CciIgGqrrjWTyiJGTOja+smdG3dhG8P71ztuflFJaEBY1t2kxUeQLYqZzdZW/JYt31PRK+3Pa+I7XlF0YguNWjSKJFWTRvRqmkjWjap+DWZVk1TaNkkmYz0FDLSUmibnqJlrEVEpMHQTzypE1KTE+ndLp3e7dIP6vrSUmdbXiGbcwvYlldIbn4xO/YUsXNPETvzi8Nfi9i5pzj89ZtjB9KHPEhJCUZKUgIpyYmkJiWQmpxISnJiaF9SAk0aJdIkJYlmqUmkpyaTnpJEevh5WmpSeUt+emoSaSlJpKUmaSYKERGRKFNxLfVCQoLROi2F1mkpQUcRERGRBkyjxEREREREokTFtYiIiIhIlKi4FhERERGJEhXXIiIiIiJRouJaRERERCRKVFyLiIiIiESJimsRERERkShRcS0iIiIiEiUqrkVEREREokTFtYiIiIhIlKi4FhERERGJEhXXIiIiIiJRouJaRERERCRKzN2DzhA1ZpYNrIrBrTOALTG4r9Rf+p6RA6XvGTlQ+p6RA6Xvmejp5u5tKjtQr4rrWDGz6e4+IugcEj/0PSMHSt8zcqD0PSMHSt8ztUPdQkREREREokTFtYiIiIhIlKi4jszjQQeQuKPvGTlQ+p6RA6XvGTlQ+p6pBepzLSIiIiISJWq5FhERERGJEhXX1TCz081ssZktM7PxQeeRus/MnjSzzWY2L+gsUveZWRcz+8DMFpjZfDO7LuhMUveZWaqZTTOz2eHvmz8EnUnqPjNLNLOvzeyNoLPUdyquq2BmicAjwBigP3ChmfUPNpXEgaeB04MOIXGjGPiVu/cHjgKu1r8zEoEC4FvuPhgYApxuZkcFG0niwHXAwqBDNAQqrqs2Eljm7ivcvRD4N3B2wJmkjnP3j4GtQeeQ+ODuG9x9Zvh5LqEffJ2CTSV1nYfsCm8mhx8aQCVVMrPOwDjgiaCzNAQqrqvWCVhTYXst+qEnIjFiZpnAUODLgKNIHAj/in8WsBmY4u76vpHqPADcAJQGnKNBUHEtIhIwM0sDXgKud/edQeeRus/dS9x9CNAZGGlmAwOOJHWUmZ0BbHb3GUFnaShUXFdtHdClwnbn8D4Rkagxs2RChfVz7v5y0Hkkvrj7duADNNZDqnYMcJaZZRHq4votM3s22Ej1m4rrqn0F9DKz7mbWCLgAeC3gTCJSj5iZAf8AFrr7n4POI/HBzNqYWYvw88bAqcCiQENJneXuN7p7Z3fPJFTLvO/uPwg4Vr2m4roK7l4MXAO8TWiQ0QvuPj/YVFLXmdlE4HOgj5mtNbPLg84kddoxwMWEWpJmhR9jgw4ldV4H4AMzm0OoIWiKu2t6NZE6Qis0ioiIiIhEiVquRURERESiRMW1iIiIiEiUqLgWEREREYkSFdciIiIiIlGi4lpEREREJEpUXIuISMTMLMvMMmo456Z9tj+LbSoRkbpDU/GJiNQRZpbo7iVB56hOeJW3Ee6+pZpzdrl7Wu2lEhGpO9RyLSISY2aWaWaLzOw5M1toZi+aWZPwsSwz+z8zmwmcb2anmdnnZjbTzP5rZmlm9i0ze7XC/U41s1cqeZ0sM7vXzOaa2TQzO6zC679vZnPM7D0z6xre/7SZPWZm081siZmdEd5/qZk9XOG+b5jZiZW83qtmNsPM5pvZFeF9E4DG4QVxngvv2xX+amb2RzObF874vfD+E83sw/DnUvY5WVQ+fBGRWqbiWkSkdvQBHnX3fsBO4GcVjuW4+zDgXeBm4JTw9nTgl8AHQF8zaxM+/zLgySpeZ4e7DwIeBh4I73sIeMbdDweeA/5S4fxMYCQwDnjMzFIP4D39yN2HAyOAa82stbuPB/a4+xB3v2if888DhgCDgVOAP5pZh/CxocD1QH+gB6HVK0VE4o6KaxGR2rHG3aeGnz8LHFvh2H/CX48iVFxONbNZwCVANw/13/sX8AMzawGMAiZX8ToTK3wdFX4+Cng+/Pxf+7z2C+5e6u5LgRVA3wN4T9ea2WzgC6AL0KuG848FJrp7ibtvAj4Cjggfm+bua929FJhFqOgXEYk7SUEHEBFpIPYd4FJxe3f4qwFT3P3CSq5/CngdyAf+6+7FEbxOJINqKstVzN6NL/u1Zoe7iZwCjHL3PDP7sLLzDkBBhecl6OeTiMQptVyLiNSOrmZW1pL8feDTSs75AjimQl/ppmbWG8Dd1wPrCXUbeaqa1/leha+fh59/BlwQfn4R8EmF8883swQz60moO8ZiIAsYEt7fhVC3kX01B7aFC+u+hFrdyxSZWXIl13wCfM/MEsNdXI4HplXzXkRE4o5aBkREasdi4GozexJYAPx13xPcPdvMLgUmmllKePfNwJLw8+eANu6+sJrXaWlmcwi1BJe1gP8ceMrMfgNkE+qzXWY1oQK3GXCVu+eb2VRgZTjnQmBmJa/zFnCVmS0Mv7cvKhx7HJhjZjP36Xf9CqEuKrMJtZDf4O4bw8W5iEi9oKn4RERizMwygTfcfeAh3udh4Gt3/0cVx7OoYZq8fc5/OpzrxUPJJSIi31DLtYhIHDCzGYT6Zv8q6CwiIlI1tVyLiIiIiESJBjSKiIiIiESJimsRERERkShRcS0iIiIiEiUqrkVEREREokTFtYiIiIhIlKi4FhERERGJkv8HifK/AK9TLykAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator versus prey\")\n", + "plt.ylabel(\"predator population\")\n", + "plt.xlabel(\"prey population\")\n", + "\n", + "plt.plot(result.y[0,:], result.y[1,:])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6ed5465d", + "metadata": {}, + "source": [ + "Over time, the system moves around this curve. See the book (fig. 2.1) for how this looks when we change the initial populations." + ] + }, + { + "cell_type": "markdown", + "id": "45b065b5", + "metadata": {}, + "source": [ + "Now let's improve this plot by adding the **isoclines**. These are the lines $\\frac{\\mathrm{d}x}{\\mathrm{d}t} = 0$ and $\\frac{\\mathrm{d}y}{\\mathrm{d}t} = 0$. We can calculate them like this:\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by) = 0 \n", + "\\,\\,\\Longrightarrow\\,\\, a - by = 0 \n", + "\\,\\,\\Longrightarrow\\,\\, y = \\frac{a}{b} \n", + "\\qquad\\text{(assuming $x>0$)}\n", + "$$\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx) = 0 \n", + "\\,\\,\\Longrightarrow\\,\\, -c + dx = 0\n", + "\\,\\,\\Longrightarrow\\,\\, x = c/d\n", + "\\qquad\\text{(assuming $y>0$)}\n", + "$$\n", + "\n", + "The resulting plot is called a **phase portrait**." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "79342914", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator versus prey\")\n", + "plt.ylabel(\"predator population\")\n", + "plt.xlabel(\"prey population\")\n", + "\n", + "plt.plot(result.y[0,:], result.y[1,:],label=\"populations\")\n", + "plt.axvline(x=c/d, ls=\":\", color='k', label=\"$dy/dt=0$\")\n", + "plt.axhline(y=a/b, ls=\"--\", color='k', label=\"$dx/dt=0$\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5152da2a", + "metadata": {}, + "source": [ + "Notice that the curve passes vertically through the dashed line and horizontally through the dotted line. This will always be the case for isoclines." + ] + }, + { + "cell_type": "markdown", + "id": "21ca9fcf", + "metadata": {}, + "source": [ + "**Disclaimer**: this version of the Lotka-Volterra predator-prey equations are kind of an unrealistic model. In nature we *do* see oscillations like this, but you have to add more terms into the equations to really model them properly. The reasons are explained in chapter 4 of the book, but they are a bit beyond the scope of this lecture." + ] + }, + { + "cell_type": "markdown", + "id": "b811c255", + "metadata": {}, + "source": [ + "# Adding intraspecific competition terms\n", + "\n", + "In the Lotka-Volterra predator-prey equations above, if we set $y=0$ then the equations become\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = ax\n", + "$$\n", + "\n", + "So if there are no predators then the prey will grow exponentially, without saturating.\n", + "\n", + "This is unrealistic, so to fix it we can add a new term. Instead of \n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by)\n", + "$$\n", + "$$\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx)\n", + "$$\n", + "\n", + "we now have\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by - ex) \\\\[1em]\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx).\n", + "$$\n", + "\n", + "Now when $y=0$ it becomes\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a - ex).\n", + "$$\n", + "\n", + "This is logistic growth, with $r=a$ and $K = a/e$.\n", + "\n", + " * Check: $\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = rx\\left(1 - \\frac{x}{K}\\right) = \\frac{\\mathrm{d}x}{\\mathrm{d}t} = ax\\left(1 - \\frac{x}{a/e}\\right) = ax\\left(1 - \\frac{ex}{a}\\right) = x(a - ex).\n", + "$\n", + "\n", + "So without predators the prey population will saturate instead of growing forever.\n", + "\n", + "This extra term is called an **intraspecific competition** term. (\"Intraspecific\" means \"within a species\".)\n", + "\n", + "We can also add an intraspecific term to the predators, so that the equations become\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by - ex) \\\\[1em]\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx - fy).\n", + "$$\n", + "\n", + "Let's solve them numerically." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "id": "9dcf5330", + "metadata": {}, + "outputs": [], + "source": [ + "def lotka_volterra_2(t, state, a, b, c, d, e, f):\n", + " x, y = state\n", + " dx = x*( a - b*y - e*x)\n", + " dy = y*(-c + d*x - f*y)\n", + " return [dx,dy]\n", + "\n", + "a = 1\n", + "b = 1\n", + "c = 0.2\n", + "d = 0.2\n", + "e = 0.05\n", + "f = 0.05\n", + "\n", + "t_span = (0.0,80.0)\n", + "t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + "initial_state = [1, 1]\n", + "\n", + "result_2 = solve_ivp(lotka_volterra_2, t_span, initial_state, t_eval=t_points, args=(a,b,c,d,e,f), method='RK45', rtol=1e-10, atol=1e-10)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "id": "9ebf38c8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator-prey with intraspecific competition\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_2.t, result_2.y[0,:], label=\"prey\")\n", + "plt.plot(result_2.t, result_2.y[1,:], label=\"predators\")\n", + "plt.xlim(*t_span)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "5524e9ee", + "metadata": {}, + "source": [ + "The oscillations die out. This phenomenon is called **damping**." + ] + }, + { + "cell_type": "markdown", + "id": "705774c6", + "metadata": {}, + "source": [ + "Now let's make the phase portrait. First we calculate the isoclines.\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by - ex) = 0\n", + "$$\n", + "$$\n", + "\\,\\,\\Longrightarrow\\,\\, a-by-ex = 0\n", + "$$\n", + "$$\n", + "\\,\\,\\Longrightarrow\\,\\, y = \\frac{a-ex}{b}\n", + "$$\n", + "(assuming $x>0$)\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx - fy) = 0\n", + "$$\n", + "$$\n", + "\\,\\,\\Longrightarrow\\,\\, -c + dx - fy = 0\n", + "$$\n", + "$$\n", + "\\,\\,\\Longrightarrow\\,\\, y = \\frac{-c+dx}{f}\n", + "$$\n", + "(assuming $y>0$)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "53b836f8", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator versus prey with intraspecific competition\")\n", + "plt.ylabel(\"predator population\")\n", + "plt.xlabel(\"prey population\")\n", + "\n", + "# first the trajectory\n", + "plt.plot(result_2.y[0,:], result_2.y[1,:], label=\"prey\")\n", + "xlim = plt.gca().get_xlim()\n", + "ylim = plt.gca().get_ylim()\n", + "\n", + "# x isocline\n", + "x = np.array([0.1,20])\n", + "y = (a-e*x)/b \n", + "plt.plot(x,y,'k:',label=\"$dx/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "# y isocline\n", + "x = np.array([0.1,20])\n", + "y = (-c+d*x)/f \n", + "plt.plot(x,y,'k--',label=\"$dy/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "#center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "419472e0", + "metadata": {}, + "source": [ + "let's try a different initial condition" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "id": "9fd9ee46", + "metadata": {}, + "outputs": [], + "source": [ + "initial_state = [20, 0.0001]\n", + "\n", + "result_2 = solve_ivp(lotka_volterra_2, t_span, initial_state, t_eval=t_points, args=(a,b,c,d,e,f), method='RK45', rtol=1e-10, atol=1e-10)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "id": "cab803e4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator-prey with intraspecific competition\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_2.t, result_2.y[0,:], label=\"prey\")\n", + "plt.plot(result_2.t, result_2.y[1,:], label=\"predators\")\n", + "plt.xlim(*t_span)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cd6d6ac6", + "metadata": {}, + "source": [ + "a zoomed-in version of that last plot:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "157541c3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator-prey with intraspecific competition\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_2.t, result_2.y[0,:], label=\"prey\")\n", + "plt.plot(result_2.t, result_2.y[1,:], label=\"predators\")\n", + "plt.xlim(0,10)\n", + "plt.ylim(0,5)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "cccdbfce", + "metadata": {}, + "source": [ + "The phase portrait:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "8ef6ded4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra predator versus prey with intrspecific competition\")\n", + "plt.ylabel(\"predator population\")\n", + "plt.xlabel(\"prey population\")\n", + "\n", + "plt.plot(result_2.y[0,:], result_2.y[1,:], label=\"prey\")\n", + "\n", + "xlim = plt.gca().get_xlim()\n", + "ylim = plt.gca().get_ylim()\n", + "\n", + "# x isocline\n", + "x = np.array([0.1,20])\n", + "y = (a-e*x)/b \n", + "plt.plot(x,y,'k:',label=\"$dx/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "# y isocline\n", + "x = np.array([0.1,20])\n", + "y = (-c+d*x)/f \n", + "plt.plot(x,y,'k--',label=\"$dy/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ed8980a2", + "metadata": {}, + "source": [ + "# Assignment\n", + "\n", + "The code in the following cell will solve the Lotka-Volterra equations with intraspecific competition terms and create both plots. (The trajectories and the phase portrait.)\n", + "\n", + "### Task 1.\n", + "\n", + "Explore the effects of the initial conditions, i.e. the variables `initial_x` and `initial_y` below. How do the initial conditions affect the dynamics? Can you find initial conditions where the prey and/or predator populations crash almost to zero after the predators are introduced? Explain your answer (1-2 paragraphs). Feel free to include copies of the plots in your writeup.\n", + "\n", + "### Task 2.\n", + "\n", + "What about the parameters a, b, c, d, e, f? Briefly explore the effect they have on the dynamics. (You don't have be systematic, just try to get a feel for it.) Can you find parameter settings where the oscillations die out very quickly, or where they last a long time before dying out? Explain your answer and feel free to include plots. (1-2 paragraphs.)\n", + "\n", + "\n", + "as a reminder, the equations are:\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a-by - ex) \\\\[1em]\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(-c + dx - fy).\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "id": "af06f8e1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# parameters of the Lotka-Volterra equations (for predator-prey with intraspecific competition)\n", + "\n", + "a = 1 # growth rate of prey\n", + "b = 1 # rate at which predators decrease the prey population\n", + "\n", + "c = 0.2 # death rate of predators\n", + "d = 0.2 # rate at which prey increase the predator population\n", + "\n", + "e = 0.05 # intraspecific competition for prey\n", + "f = 0.05 # intraspecific competition for predators\n", + "\n", + "max_time = 80.0 # simulate until this time\n", + "\n", + "initial_x = 1 # initial population of prey\n", + "initial_y = 1 # initial population of predators\n", + "\n", + "\n", + "# you don't need to change anything below this line.\n", + "# --------------------------------------------------------------------------------------------------------\n", + "\n", + "def lotka_volterra_2(t, state, a, b, c, d, e, f):\n", + " x, y = state\n", + " dx = x*( a - b*y - e*x)\n", + " dy = y*(-c + d*x - f*y)\n", + " return [dx,dy]\n", + "\n", + "\n", + "t_span = (0.0,max_time)\n", + "t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + "initial_state = [1, 1]\n", + "\n", + "result_2 = solve_ivp(lotka_volterra_2, t_span, initial_state, t_eval=t_points, args=(a,b,c,d,e,f), method='RK45', rtol=1e-10, atol=1e-10)\n", + "\n", + "\n", + "# first plot: populations over time\n", + "\n", + "plt.title(\"Lotka-Volterra predator-prey with intraspecific competition\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_2.t, result_2.y[0,:], label=\"prey\")\n", + "plt.plot(result_2.t, result_2.y[1,:], label=\"predators\")\n", + "plt.xlim(*t_span)\n", + "#center_axes()\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# second plot: phase diagram\n", + "\n", + "plt.title(\"Lotka-Volterra predator versus prey with intrspecific competition\")\n", + "plt.ylabel(\"predator population\")\n", + "plt.xlabel(\"prey population\")\n", + "\n", + "plt.plot(result_2.y[0,:], result_2.y[1,:], label=\"prey\")\n", + "\n", + "xlim = plt.gca().get_xlim()\n", + "ylim = plt.gca().get_ylim()\n", + "\n", + "# x isocline\n", + "x = np.array([0.1,20])\n", + "y = (a-e*x)/b \n", + "plt.plot(x,y,'k:',label=\"$dx/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "# y isocline\n", + "x = np.array([0.1,20])\n", + "y = (-c+d*x)/f \n", + "plt.plot(x,y,'k--',label=\"$dy/dt=0$\",scalex=False, scaley=False)\n", + "\n", + "#center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "949d4ac7", + "metadata": {}, + "source": [ + "# Lotka-Volterra competition equations\n", + "\n", + "In the predator-prey system we had the following relationships:\n", + "\n", + " * Prey can reproduce on their own without predators\n", + " * Predators cannot reproduce without prey\n", + " * Prey have a *positive* effect on predators\n", + " * Predators have a *negative* effect on prey\n", + " \n", + "Often we want a more symmetric relationship that looks like this:\n", + " \n", + " * Species $X$ can reproduce on their own without species $Y$\n", + " * and also species $Y$ can reproduce on their own without species $X$\n", + " * Species $Y$ has a *negative* effect on species $X$\n", + " * and also species $X$ has a *negative* effect on species $Y$\n", + " \n", + "Think of two plants growing in the same place. Both of them can grow by themselves, but they compete for space (and light, water, nutrients etc.)\n", + "\n", + "We can model this with the same equations as above, except that we change the signs of some of the parameters. We keep the intraspecific competition terms, because otherwise our popoulations could grow exponentially forever.\n", + "\n", + "This gives the equations (eq. 3.8 in the book)\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x}{\\mathrm{d}t} = x(a - bx - cy) \\\\[1em]\n", + "\\frac{\\mathrm{d}y}{\\mathrm{d}t} = y(d - ex - fy)\n", + "$$\n", + "\n", + "where now we interpret the parameters as follows:\n", + "\n", + " * $a$ - intrinsic growth rate of species $X$\n", + " * $b$ - intraspecific competition term for species $X$\n", + " * $c$ - the negative effect of species $Y$ on species $X$\n", + "\n", + " * $d$ - intrinsic growth rate of species $Y$\n", + " * $e$ - the negative effect of species $X$ on species $Y$\n", + " * $f$ - intraspecific competition term for species $Y$\n", + "\n", + "The parameters $c$ and $e$ are called **interspecific competition** terms. (\"inter\" means \"between\" while \"intra\" means \"within\".)\n", + "\n", + "Now the isoclines are given by\n", + "\n", + "$$\n", + "a- bx - cy = 0 \\qquad\\text{or}\\qquad y = \\frac{a-bx}{c}%x = \\frac{cy-a}{b}\n", + "$$\n", + "\n", + "and\n", + "\n", + "$$\n", + "d - ex - fy \\qquad\\text{or}\\qquad y = \\frac{d-ex}{f}%x = \\frac{fy-d}{e}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "3a400976", + "metadata": {}, + "source": [ + "Now let's plot it. The behaviour depends on the parameters - I'll write a function so we can play with the parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "dca93b23", + "metadata": {}, + "outputs": [], + "source": [ + "# helper function\n", + "def rand_range(low, hi):\n", + " return np.random.random()*(hi-low) + low\n", + "\n", + "# a version that's biased toward the low end, which makes better plots\n", + "def rand_range_biased(low, hi):\n", + " return np.random.random()*(np.random.random()*0.5+0.5)*(hi-low) + low\n", + "\n", + "\n", + "def plot_competition(a, b, c, d, e, f, x_range, y_range):\n", + " # a, b, c, d, e, f are the parameters\n", + " # x_range and y_range should be of the form [min_x, max_x] and [min_y, max_y].\n", + " \n", + " for i in range(15):\n", + " # solve and plot the equations from a few random starting points\n", + " \n", + " def lotka_volterra_competition(t, state):\n", + " x, y = state\n", + " dx = x*(a - b*x - c*y)\n", + " dy = y*(d - e*x - f*y)\n", + " return [dx,dy]\n", + "\n", + " t_span = (0.0,80.0)\n", + " t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + " initial_state = [rand_range_biased(*x_range), rand_range_biased(*y_range)]\n", + "\n", + " result = solve_ivp(lotka_volterra_competition, t_span, initial_state, t_eval=t_points, method='RK45', rtol=1e-10, atol=1e-10)\n", + " \n", + " plt.plot(result.y[0,:], result.y[1,:])\n", + " \n", + "\n", + " # x isocline\n", + " x = np.array([0.1,20])\n", + " y = (a-b*x)/c \n", + " plt.plot(x,y,'k:',label=\"$dx/dt=0$\",scalex=False, scaley=False)\n", + "\n", + " # y isocline\n", + " x = np.array([0.1,20])\n", + " y = (d-e*x)/f\n", + " plt.plot(x,y,'k--',label=\"$dy/dt=0$\",scalex=False, scaley=False)\n", + "\n", + " plt.xlabel(\"Species $X$\")\n", + " plt.ylabel(\"Species $Y$\")\n", + " \n", + " plt.xlim(x_range)\n", + " plt.ylim(y_range)\n", + "\n", + " center_axes()\n", + " plt.legend()\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "30bdc5ee", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# intrinsic growth rates\n", + "a = 1\n", + "d = 1 \n", + "\n", + "# intraspecific competition\n", + "b = 0.2\n", + "f = 0.2\n", + "\n", + "# interspecific competition - try changing these to more or less than 0.2\n", + "c = 0.3\n", + "e = 0.3\n", + "\n", + "plot_competition(a, b, c, d, e, f, [0,8], [0,8])" + ] + }, + { + "cell_type": "markdown", + "id": "9df77664", + "metadata": {}, + "source": [ + "# What about cooperation?\n", + "\n", + "We've looked at two different relationship between two species:\n", + "\n", + " * **predator-prey** had a *postitive* effect of $X$ on $Y$ but a *negative* effect of $Y$ on $X$\n", + " * **competition** had a *negative* effect of $X$ on $Y$ and a *negative* effect of $Y$ on $X$\n", + " \n", + "Is there a case where both species have a *positive* effect on each other.\n", + "\n", + "Yes! This relationship is called *mutualism*. It is very important in nature! E.g. think of insects polenating flowers.\n", + "\n", + "Unfortunately though, the Lotka-Volterra equations are not very good for modeling mutualism. If you try to put positive interactions in both directions, the populations can keep growing forever. To model it properly you need different equations with more nonlinear terms, so we skip it." + ] + }, + { + "cell_type": "markdown", + "id": "e475aaf2", + "metadata": {}, + "source": [ + "# More than two species\n", + "\n", + "You might have noticed that when we write the Lotka-Volterra equations, the part inside the brackets is a linear function.\n", + "\n", + "This lets us generalise the Lotka-Volterra equations to more than two species. We can write them as\n", + "\n", + "$$\n", + "\\frac{\\mathrm{d}x_i}{\\mathrm{d}t} = x_i f_i,\n", + "$$\n", + "\n", + "where \n", + "\n", + "$$\n", + "\\mathbf{f} = \\mathbf{b} + A\\mathbf{x}.\n", + "$$\n", + "\n", + "Here I'm using bold for vectors, and $A$ is a matrix. The elements of $\\mathbf{b}$ are the intrinsic growth or death rates, depending on whether they're positive or negative. The only restriction on elements of $A$ is that if $A_{ij}>0$ then we should have $A_{ji}\\le 0$. (You can't have positive terms in both directions, as mentioned above.)\n", + "\n", + "I won't explain this in detail, but the book has a lot more information if you're interested.\n", + "\n", + "All I want to do here is to demonstrate modeling a **food web**. \n", + "\n", + "In this case we have a situation where\n", + "\n", + " * species $X$ can grow by itself (e.g. it's a plant)\n", + " * species $Y$ eats species $X$ (so $X$ and $Y$ are a predator-prey system)\n", + " * species $Z$ eats both species $Y$ and species $X$\n", + " \n", + "E.g. species $X$ could be a plant, species $Y$ a herbivore (animal that eats plants) and species $Z$ could be an omnivore (animal that eats both plants and other animals). We call species $X$ a **producer** (because it produces energy) and we call $Y$ and $Z$ **consumers**.\n", + "\n", + " \n", + "We can do that by choosing\n", + "\n", + "$$\\mathbf{b} = \\begin{pmatrix}+\\\\-\\\\-\\end{pmatrix},\n", + "\\qquad\n", + "A = \\begin{pmatrix}- & - & -\\\\+ & 0 & -\\\\+ & + & 0\\end{pmatrix},\n", + "$$\n", + "where \"$-$\" means any negative number and \"$+$\" means any positive one. ($a_{22}$ and $a_{33}$ are zero because we don't include intraspecific terms for the consumers.)\n", + "\n", + "The main reason I want to do this is to show something that can't happen with only two species." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "ecc7d68b", + "metadata": {}, + "outputs": [], + "source": [ + "# parameters taken from \n", + "\n", + "# Omnivory Creates Chaos in Simple Food Web Models\n", + "# Kumi Tanabe and Toshiyuki Namba\n", + "# Ecology Vol. 86, No. 12 (Dec., 2005), pp. 3411-3414 (4 pages)\n", + "# https://www.jstor.org/stable/3450749\n", + "\n", + "\n", + "# growth rate of primary producer\n", + "b1 = 5\n", + "\n", + "# death rate of consumers\n", + "b2 = -1\n", + "b3 = -1.2\n", + "\n", + "# intraspecific competition on producers only\n", + "a11 = -0.4\n", + "\n", + "# interactions between species 1 and 2\n", + "a12 = -1\n", + "a21 = 1\n", + "\n", + "# interactions between species 2 and 3\n", + "a13 = -15\n", + "a31 = 0.1\n", + "\n", + "# interactions between species 2 and 3\n", + "a23 = -1\n", + "a32 = 1\n", + "\n", + "\n", + "def lotka_volterra_three_species(t, state):\n", + " x1, x2, x3 = state\n", + "\n", + " dx1 = x1*(b1 + a11*x1 + a12*x2 + a13*x3 )\n", + " dx2 = x2*(b2 + a21*x1 + a23*x3 )\n", + " dx3 = x3*(b3 + a31*x1 + a32*x2 )\n", + " \n", + " return [dx1,dx2,dx3]\n", + "\n", + "t_span = (0.0,100)\n", + "t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + "initial_state = [5,5,5]\n", + "\n", + "result_3 = solve_ivp(lotka_volterra_three_species, t_span, initial_state, t_eval=t_points, method='RK45', rtol=1e-10, atol=1e-10)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "22ed0b2e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title(\"Lotka-Volterra three-species food web\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_3.t, result_3.y[0,:], label=\"species 1\")\n", + "plt.plot(result_3.t, result_3.y[1,:], label=\"species 2\")\n", + "plt.plot(result_3.t, result_3.y[2,:], label=\"species 3\")\n", + "plt.xlim(*t_span)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "bed76847", + "metadata": {}, + "source": [ + "Try increasing the time span from 100 to 500 or so.\n", + "\n", + "This \"bursty\" pattern continues forever, but it can be proved that it never quite repeats.\n", + "\n", + "This is another example of **chaos**.\n", + "\n", + "In continuous systems, chaos can't happen if you only have species, so this is the simplest kind of chaotic food web model." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "eb85c39c", + "metadata": {}, + "outputs": [ + { + "ename": "SyntaxError", + "evalue": "invalid character '§' (U+00A7) (1036121371.py, line 1)", + "output_type": "error", + "traceback": [ + "\u001b[0;36m Input \u001b[0;32mIn [31]\u001b[0;36m\u001b[0m\n\u001b[0;31m §\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid character '§' (U+00A7)\n" + ] + } + ], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "078d2f46", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0a499a85", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d47dc3a6", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c0d51caf", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "02a87e43", + "metadata": {}, + "outputs": [], + "source": [ + "# parameters taken from \n", + "\n", + "# Omnivory Creates Chaos in Simple Food Web Models\n", + "# Kumi Tanabe and Toshiyuki Namba\n", + "# Ecology Vol. 86, No. 12 (Dec., 2005), pp. 3411-3414 (4 pages)\n", + "# https://www.jstor.org/stable/3450749\n", + "\n", + "\n", + "# growth rate of primary producer\n", + "b1 = 3\n", + "\n", + "# death rate of consumers\n", + "b2 = -1\n", + "b3 = -1.2\n", + "\n", + "# intraspecific competition on producers only\n", + "a11 = -1\n", + "\n", + "# interactions between species 1 and 2\n", + "a12 = -4\n", + "a21 = 1\n", + "\n", + "# interactions between species 2 and 3\n", + "a13 = -15\n", + "a31 = 0.1\n", + "\n", + "# interactions between species 2 and 3\n", + "a23 = -0.5\n", + "a32 = 1\n", + "\n", + "\n", + "def lotka_volterra_three_species(t, state):\n", + " x1, x2, x3 = state\n", + "\n", + " dx1 = x1*(b1 + a11*x1 + a12*x2 + a13*x3 )\n", + " dx2 = x2*(b2 + a21*x1 + a23*x3 )\n", + " dx3 = x3*(b3 + a31*x1 + a32*x2 )\n", + " \n", + " return [dx1,dx2,dx3]\n", + "\n", + "t_span = (0.0,200)\n", + "t_points = np.linspace(t_span[0], t_span[1], 1000)\n", + "\n", + "initial_state = [5,5,5]\n", + "\n", + "result_3 = solve_ivp(lotka_volterra_three_species, t_span, initial_state, t_eval=t_points, method='RK45', rtol=1e-10, atol=1e-10)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "83623d72", + "metadata": {}, + "outputs": [], + "source": [ + "plt.title(\"Lotka-Volterra three-species food web\")\n", + "plt.ylabel(\"population\")\n", + "plt.xlabel(\"time\")\n", + "\n", + "plt.plot(result_3.t, result_3.y[0,:], label=\"species 1\")\n", + "plt.plot(result_3.t, result_3.y[1,:], label=\"species 2\")\n", + "plt.plot(result_3.t, result_3.y[2,:], label=\"species 3\")\n", + "plt.xlim(*t_span)\n", + "center_axes()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e239148", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "b3e79ea8", + "metadata": {}, + "source": [ + "# Bonus material: what happens in discrete time?\n", + "\n", + "We won't cover this in class, but if you're interested in chaos you can take a look.\n", + "\n", + "In continuous time, you need at least three species for chaos to occur. But if time is discrete then one species is enough.\n", + "\n", + "Let's imagine that instead of continuous time, we have discrete generations. E.g. think of a species that reproduces once per year. Then a somewhat analogous equation is\n", + "\n", + "$$\n", + "x_{t+1} = R x_t \\left( 1 - \\frac{x_t}{K} \\right)\n", + "$$\n", + "\n", + "but let's set $K=1$, so it becomes\n", + "\n", + "$$\n", + "x_{t+1} = R x_t \\left( 1 - x_t \\right)\n", + "$$\n", + "\n", + "This equation is called the **Logistic map**.\n", + "\n", + "There isn't an analyical solution to this one, so let's iterate it and plot it.\n", + "\n", + "I'll define a function that does the iteration and plots it, so I can show you different parameter values." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "013e9985", + "metadata": {}, + "outputs": [], + "source": [ + "def plot_logistic_map(x0, R, tsteps):\n", + " \n", + " x = np.zeros(tsteps)\n", + " x[0] = x0\n", + " for t in range(1,tsteps):\n", + " x[t] = R*x[t-1]*(1-x[t-1])\n", + " t = np.arange(0,tsteps)\n", + " \n", + " plt.title(\"iteration of logistic map\")\n", + " plt.ylabel(\"population x\")\n", + " plt.xlabel(\"time\")\n", + "\n", + " plt.plot(t,x, \"-bo\", label=\"x(t)\")\n", + " plt.xlim(0,tsteps)\n", + " plt.ylim(0,1)\n", + " center_axes()\n", + " plt.legend()\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "57ebcf94", + "metadata": {}, + "source": [ + "for $R$ between 1 and 2 it behaves like the continuous time case" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "8c4fea61", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x0 = 0.01\n", + "R = 1.7\n", + "tsteps = 20\n", + "\n", + "plot_logistic_map(x0, R, tsteps)" + ] + }, + { + "cell_type": "markdown", + "id": "dd9e99ff", + "metadata": {}, + "source": [ + "for $R$ between 2 and 3 something different starts to happen" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "aae73712", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x0 = 0.01\n", + "R = 2.8\n", + "tsteps = 20\n", + "\n", + "plot_logistic_map(x0, R, tsteps)" + ] + }, + { + "cell_type": "markdown", + "id": "8fdef549", + "metadata": {}, + "source": [ + "above 3 we get permanent oscillations" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "a8771d61", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x0 = 0.01\n", + "R = 3.4\n", + "tsteps = 20\n", + "\n", + "plot_logistic_map(x0, R, tsteps)" + ] + }, + { + "cell_type": "markdown", + "id": "4830b783", + "metadata": {}, + "source": [ + "At higher values they become more complex" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "17378289", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x0 = 0.01\n", + "R = 3.55\n", + "tsteps = 30\n", + "\n", + "plot_logistic_map(x0, R, tsteps)" + ] + }, + { + "cell_type": "markdown", + "id": "4d19581f", + "metadata": {}, + "source": [ + "Above the value of $3.56995\\dots$ we get **chaos** - the sequence never repeats" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "bfad7908", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x0 = 0.01\n", + "R = 3.6\n", + "tsteps = 70 # try changing this to 170\n", + "\n", + "plot_logistic_map(x0, R, tsteps)" + ] + }, + { + "cell_type": "markdown", + "id": "8ac6475d", + "metadata": {}, + "source": [ + "The logistic map is a classic example in chaos theory and there is a *lot* more that can be said about it!\n", + "\n", + "[Wikipedia](https://en.wikipedia.org/wiki/Logistic_map) is not a bad place to start for an overview. The book has some explanations of why this happens.\n", + "\n", + "But for now we are really interested in the continuous time case. You can also have chaos in continuous time, but not in a one-variable case like this. (You actually need at least *three* variables for chaos in a continuous system!) So now we'll leave the logistic map and turn to another set of equations.\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}