{ "metadata": { "name": "", "signature": "sha256:12efddc602bcf452e2b9768f313de2220b2307c92cc9e56189b6e3844752746a" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Logistic model estimation\n", "\n", "I will use the discrete logistic function, also called the logistic map.\n", "\n", "I will estimate the function parameters.\n", "\n", "- N(t) - num. individuals at time t\n", "- r - growth rate per hour\n", "- K - carrying capacity\n", "The equation is:\n", "$$\n", "N(t+1) = N(t) \\cdot e^{r (1 - N(t)/K)} \\Rightarrow \\\\\n", "N(t) = \\frac{K \\cdot N(0) e^{rt}}{K + N(0) (e^{rt} - 1)}\n", "$$\n", "and\n", "$$\n", "\\log{\\frac{N(t+1)}{N(t)}} = r(1 - N(t)/K)\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import linregress\n", "\n", "def trans(x):\n", " return log(x[1:]/x[:-1])\n", "\n", "def plot_gradient(x,y):\n", " x = array(x)\n", " y = array(y)\n", " \n", " fig,ax = subplots(2,2,figsize=(10,10))\n", " ax[0,0].plot(x, y, 'k-');\n", " ax[0,0].set_ylabel('cell density')\n", " \n", " ax[1,0].plot(x, gradient(y), 'k-');\n", " ax[1,0].set_xlabel('time (hours)')\n", " ax[1,0].set_ylabel('growth rate')\n", " \n", " ax[0,1].plot(y[:-1], trans(y), 'k-')\n", " ax[0,1].set_ylabel('growth rate / cell density')\n", " \n", " a, b, _, _, _ = linregress(y[:-1], trans(y))\n", " r = b\n", " K = -b/a\n", " label = 'log N(t+1)/N(t) = %.2g + %.2g N(t)\\nr=%.2g, K=%.2g' % (b,a,r,K)\n", " ax[1,1].plot(y, [b + a*z for z in y], 'k-')\n", " ax[1,1].set_xlabel('cell density')\n", " ax[1,1].set_ylabel('growth rate / cell density')\n", " ax[1,1].annotate(label, (0.65, 0.4), xycoords='figure fraction', bbox=dict(boxstyle=\"round\", fc=\"1\"))\n", " return r,K" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "def logistic(N0, r, K, tmax):\n", " N = array([N0]*tmax)\n", " for t in range(0,tmax-1):\n", " N[t+1] = N[t] * exp(r * (1 - N[t]/K))\n", " return N" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "r = 0.3\n", "K = 1000000.0\n", "N0 = 10.0\n", "x = arange(0,100)\n", "y = logistic(N0, r, K, len(x))\n", "print \"real: : r = %.3f, K=%.2g\" % (r,K)\n", "r_sol, K_sol = plot_gradient(x,y)\n", "print \"estimated: r = %.3f, K=%.2g\" % (r_sol,K_sol)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "real: : r = 0.300, K=1e+06\n", "estimated: r = 0.300, K=1e+06" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAApYAAAJlCAYAAABg9LK9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYRX/D3xzmWE+xQOBAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 57 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(x, y, 'k-', label='real');\n", "plot(x, logistic(y[0], r_sol,K_sol,len(x)), 'ko', label='estimated')\n", "xlabel('time')\n", "ylabel('population')\n", "legend(loc='lower right');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAEWCAYAAAA3h9P4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n", "text": [ "" ] } ], "prompt_number": 59 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }