Jeff Montgomery added file figures/ex.predprey1/lokta volterra test.ipynb  over 9 years ago

Commit id: e8e4fed852fd92084cb01a7e328161d233e5abb4

deletions | additions      

         

{  "metadata": {  "name": "",  "signature": "sha256:47e791fb3c86f31d3f89862492a1814d1b54a55052e1030c127e87e0d2b7c3c1"  },  "nbformat": 3,  "nbformat_minor": 0,  "worksheets": [  {  "cells": [  {  "cell_type": "heading",  "level": 1,  "metadata": {},  "source": [  "Lokta-Volterra Ecology Modeling"  ]  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "The Lotka-Volterra Model demonstrates the relationship between two populations of organisms, one the predator and the other the prey. The entire system is modeled through two first-order ordinary differential equations (ODEs). These represent the overall growth rates of the two populations by incorporating various constants (we assume prey have unlimited food and reproduce at a constant rate, while the predator appetite is effectively unlimited given sufficient prey).\n",  "\n",  "This example will implement numpy, pylab, and scipy packages and is based off this wonderful tutorial: (http://wiki.scipy.org/Cookbook/LoktaVolterraTutorial)."  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "# du/dt = a*u - b*u*v this is the eqn for the prey population\n",  "# dv/dt = -c*v + d*b*u*v this is the eqn for the predator population"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 1  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "u is the prey population number \n",  "v is the predator population number \n",  "a is the constant growth rate of the prey (w/o predation) \n",  "b is the constant prey death rate due to predation \n",  "c is the constant predator death rate (w/o prey as the food source) \n",  "d is a constant that corresponds to how many prey a predator must consume to reproduce \n",  "\n",  "The array X will serve to represent the time-resolved growth rates resulting from the two ODEs above. "  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "from numpy import *\n",  "import pylab as p\n",  "\n",  "a = 1.\n",  "b = 0.1\n",  "c = 1.5\n",  "d = 0.75\n",  "\n",  "def dX_dt(X, t=0):\n",  " \"\"\" Return the growth rate of fox and rabbit populations. \"\"\"\n",  " return array([ a*X[0] - b*X[0]*X[1] ,\n",  " -c*X[1] + d*b*X[0]*X[1] ])"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 2  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "We need to define the equilibrium points where the growth rate for the system will be zero, as defined below. At these points, the system can be linearized by taking the Jacobian matrix (A) of it, defined as d2X_dt2:"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "X_f0 = array([ 0. , 0.])\n",  "X_f1 = array([ c/(d*b), a/b])\n",  "all(dX_dt(X_f0) == zeros(2) ) and all(dX_dt(X_f1) == zeros(2)) # => True\n",  "\n",  "def d2X_dt2(X, t=0):\n",  " \"\"\" Return the Jacobian matrix evaluated in X. \"\"\"\n",  " return array([[a -b*X[1], -b*X[0] ],\n",  " [b*d*X[1] , -c +b*d*X[0]] ])"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 3  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "X_f0 defines the point at which both species appear to be going to extinction (i.e. population growth goes to zero). As predator number drops sufficiently, the prey population can rebound.\n",  "X_f1, when evaluated by the Jacobian, gives imaginary eigenvalues, representative of the periodic nature of this model."  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "A_f0 = d2X_dt2(X_f0) \n",  "A_f1 = d2X_dt2(X_f1) \n",  " \n",  "lambda1, lambda2 = linalg.eigvals(A_f1) \n",  "\n",  "T_f1 = 2*pi/abs(lambda1) #this represents fluctuation period"  ],  "language": "python",  "metadata": {},  "outputs": [],  "prompt_number": 8  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "Now we are ready to integrate our system of equations through scipy:"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "from scipy import integrate\n",  "t = linspace(0, 15, 1000) # dimensionless time\n",  "X0 = array([10, 5]) # initials population numbers: 10 prey, 5 predator\n",  "X, infodict = integrate.odeint(dX_dt, X0, t, full_output=True)\n",  "infodict['message'] # >>> 'Integration successful.'"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "metadata": {},  "output_type": "pyout",  "prompt_number": 9,  "text": [  "'Integration successful.'"  ]  }  ],  "prompt_number": 9  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "Finally, we generate the plot that is incorporated in our original article:"  ]  },  {  "cell_type": "code",  "collapsed": false,  "input": [  "prey, predator = X.T\n",  "f1 = p.figure()\n",  "p.plot(t, prey, 'r-', label='Prey')\n",  "p.plot(t, predator , 'b-', label='Predator')\n",  "p.grid()\n",  "p.legend(loc='best')\n",  "p.xlabel('time')\n",  "p.ylabel('population')\n",  "p.title('Dynamics of Predator-Prey Populations')\n",  "f1.savefig('ex.predprey1.png')"  ],  "language": "python",  "metadata": {},  "outputs": [  {  "metadata": {},  "output_type": "display_data",  "png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEZCAYAAABxbJkKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",  "text": [  ""  ]  }  ],  "prompt_number": 10  },  {  "cell_type": "markdown",  "metadata": {},  "source": [  "There you have it. As is intuitive, increases in prey population lead to increases in predator population. \n",  "Increased predation has a negative feedback effect on system population, and the cycle restarts. \n",  "\n",  "If we calculate T_f1 from Line 8, we indeed see that the period matches to about 5.1 time units as seen in the plot.\n",  "\n",  "Ideally at this point, Authorea users would then change the parameters of the model, add additional parameters to model different/higher-complexity systems, and fork off the original article. "  ]  }  ],  "metadata": {}  }  ]  }