{ "cells": [ { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Volterra’s (1926) simple model\n", "\n", "#1. The prey population finds ample food at all times.\n", "#2. The food supply of the predator population depends entirely on the size of the prey population.\n", "#3. The rate of change of population is proportional to its size.\n", "#4. During the process, the environment does not change in favor of one species, and genetic adaptation is inconsequential.\n", "#5. Predators have limitless appetite\n", "\n", "b = .8 #rate of prey increase\n", "d = .1 #predator mortality rate\n", "k1 = .02 #predation rate\n", "k2 = .002 #consumption rate\n", "\n", "n1 = 6 #number of prey\n", "n2 = 2 #number of predators\n", "\n", "m = 10000 #prey carrying capacity\n", "\n", "#keep track of iterations\n", "predator_cumulative = []\n", "prey_cumulative = []" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MmJk/nlJaVcJxaRJo7eimrqaKmbXFN7Gpra6yj7ckSdIwiulq8l/AV4Ee4C+A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\noyN6arI1iU59c4cE3qJ/xCR0Te/dnb/dDKyr2W5yHKsLzO2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(0,100):\n", " d1 = b*n1*((m-n1)/m) - k1*n1*n2 #dampered by carrying capacity\n", " d2 = k2*n1*n2 - d*n2\n", " \n", " #d1 = b*n1 - k1*n1*n2 #unbounded\n", "\n", " n1 = n1 + d1\n", " n2 = n2 + d2\n", "\n", " if(n1<3):\n", " n1=3\n", " \n", " if(n2<1):\n", " n2=1\n", "\n", " prey_cumulative.append(n1)\n", " predator_cumulative.append(n2)\n", "\n", " #print(n1, n2)\n", " \n", "times = []\n", "for t in range(0, len(predator_cumulative)):\n", " times.append(t)\n", "\n", "plt.subplots(figsize=(12, 7))\n", "plt.plot(times, prey_cumulative, label='prey')\n", "plt.plot(times, predator_cumulative, label='predator')\n", "plt.ylabel('Number of Animals')\n", "plt.xlabel('Timestep')\n", "plt.title('Counts of Animals')\n", "plt.legend(loc='upper left')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "95.7 98.6 1.03\n" ] } ], "source": [ "#numerical analysis\n", "sum_predator = 0\n", "sum_prey = 0\n", "\n", "for n in range(0, len(times)):\n", " sum_predator = sum_predator + predator_cumulative[n]\n", " sum_prey = sum_prey + prey_cumulative[n]\n", " \n", "avg_predator = sum_predator/len(times)\n", "avg_prey = sum_prey/len(times)\n", "\n", "prey_predator_ratio = avg_prey/avg_predator\n", "\n", "print('{0:.3g}'.format(avg_predator), '{0:.3g}'.format(avg_prey), '{0:.3g}'.format(prey_predator_ratio))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "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": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 2 }