{ "metadata": { "name": "", "signature": "sha256:f646e26c5334eff5abd9743b66077e85e5b068c2a46ecc92ec173a944c3cb2d5" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "def selection(p,s):\n", " return p * (1+s) / (p * (1+s) + (1-p))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "s = 0.01\n", "p0 = 0.01\n", "pt = [p0]\n", "\n", "while pt[-1] < 1 - p0:\n", " pt.append(selection(pt[-1], s))\n", "pt = array(pt)\n", "plot(pt)\n", "xlabel('t')\n", "ylabel('p(t)');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": true, "input": [ "plot(log(pt/(1-pt)))\n", "xlabel('t')\n", "ylabel(r'$\\log{(\\frac{p}{1-p})}$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "gradient(log(pt/(1-pt)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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TCmSGAYt2sJHPsn/ispuNYn9kN8UT7pYXrvNby3+OSbjWx5YCq5WAcIQZW1EU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\nJvHaSPjmdzfV1tYiPz8/7jm//vWvMXv2bBQWmoGiy5cvo6amBn6/H5I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x8OBBrF+/3tN1\nEmlqasJ7772H9evX47XXXsPnn38+LOuUE0qCIAiC8IasdzcRBEEQ3kFKgiAIgnCFlARBEAThCikJ\ngiAIwhVSEgRBEIQrpCQIgiAIV0hJEARBEK6QkiAIgiBc+X/qsPgL6XeE6QAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "'%.3f' % (log(2)/2.)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "'0.347'" ] } ], "prompt_number": 26 }, { "cell_type": "code", "collapsed": false, "input": [ "'%.3f' % (-0.1 * log(2))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 28, "text": [ "'-0.069'" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## SI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- $M$ - # of mutant cells\n", "- $N$ - # of wildtype cells\n", "- $r_x$ - intrinsic rate of density-dependent increase of strain $x$\n", "- $f$ - function relating dependence of growth on total population size or density ($f(X) = X$ leads to logsitic population growth)\n", "- $K_x$ - carrying capacity of strain $x$\n", "- $i_x$ - interaction term: competition ($i_m,i_w<0$), mutualism ($i_m,i_w>0$), explotation ($i_m i_w < 0$).\n", "$$\n", "\\frac{d \\log{M}}{dt} = \n", "r_m (1- \\frac{f(M+N)}{f(K_m)}) + i_m \\frac{N}{M+N} \\\\\n", "\\frac{d \\log{N}}{dt} =\n", "r_w(1-\\frac{f(M+N)}{f(K_w)}) + i_w \\frac{M}{M+N}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Density and frequency independent selection: $i_m=i_w=0$\n", "\n", "$$\n", "\\frac{d \\log{M}}{dt} = \n", "r_m (1- (M+N)/K) \\\\\n", "\\frac{d \\log{N}}{dt} =\n", "r_w(1-(M+N)/K) \n", "$$\n", "\n", "\n", "$\\Rightarrow s=r_m-r_w$ is constant in time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete generations\n", "\n", "$$\n", "M' = \\lambda_m ^{1-\\frac{f(M+N)}{f(K_m)}} i_m^{\\frac{N}{N+M}} M\\\\\n", "N' = \\lambda_w ^{1-\\frac{f(M+N)}{f(K_w)}} i_w^{\\frac{M}{N+M}} N\\\\\n", "$$\n", "\n", "- $\\lambda$ is multiplicative fitness in absence of density dependence\n", "- $K$ is carrying capacity\n", "- $i$ is interaction term\n", "\n", "Selection is _frequency and density independent_ if $i_w=i_m=1$ and $\\lambda_w ^{1/f(K_w)}=\\lambda_m^{1/f(K_m)}$:\n", "\n", "$$\n", "M' = M \\cdot \\lambda_m ^{1-\\frac{M+N}{K_m}} \\\\\n", "N' = N \\cdot \\lambda_w ^{1-\\frac{M+N}{K_w}} \\\\\n", "$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "logistic_competition = lambda m,n: (lam_m**(1-(m+n)/K_m) * i_m**(n/(n+m)) * m, lam_w**(1-(m+n)/K_w) * i_m**(m/(n+m)) * n)\n", "logistic_isolation = lambda m,n: (lam_m**(1-(m)/K_m) * m, lam_w**(1-(n)/K_w) * n)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 56 }, { "cell_type": "code", "collapsed": false, "input": [ "M,N=[],[]\n", "m,n = 1e6,1e6\n", "lam_m,lam_w = exp(1.5*0.327),exp(1.5*0.311)\n", "K_w = 128*1e6\n", "K_m = K_w #* log(lam_m) / log(lam_w)\n", "i_m,i_w = 1,1\n", "\n", "for _ in range(24):\n", " m,n = logistic_isolation(m,n)\n", " M.append(m)\n", " N.append(n)\n", "M = array(M)\n", "N = array(N)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 330 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(N, color='b', label=\"mut\")\n", "plot(M, color='g', label=\"wt\")\n", "#plot(M+N, label=\"tot\")\n", "xticks(range(0,24,2))\n", "xlim(0,16)\n", "legend(loc=2)\n", "ylabel('# cells')\n", "xlabel('time (hours)');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 331, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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1i2effRYHBwdWr16NXq9n+fLldOvWjR49elR0PiGqtKjUKN46+RYb/r0BdSnr\nTcTF3b/xbuHCZPz95cY7Ub6MahY2Njb06NFDmoMQJpSrz2XUwVFMaDGBR6s/WmJtXt79G+8GDcqk\nSxe58U6UP6NGQ23dupXIyMgC34uMjGT79u0VEkoIAe//+j41XGvwUuBLpdZ+8IE7zs4Kr78uN96J\nimFUs9i9ezd+fn4Fvle7dm2+//77CgklRFW3P2o/u2/tZuGTC0u9TrFrlxO7dzuxeHGS3HgnKkyZ\n1uAusKOdHXl5Mn5biPJ2J/0OU49NJbRrKF5OJY84vHbNjhkzPNi4MRGNRmaSFRXHqCOLevXqsXfv\n3gLfO3DgAPXr16+QUEJUVTqDjrGHxvJy05dpVbNVibXp6SpeftmLN99Mo1kz+cNNVCyjjiyGDRvG\ne++9x7Fjx6hRowaxsbEkJyfz9ttvV3Q+IaqUBWcW4GTnxJhHx5RYpygwebInrVvnMmiQ3HgnKp5R\nzeKhhx4iJCSEM2fOoNVqadOmDY899hhOTk4VnU+IKuPonaNsurrJqPUpPv/clT/+sGXr1iQTpRNV\nnVHNAsDZ2Zknnih92UYhRNnFZcYx8chEQjqGUN2leom1P//swGefubFzZwLy95owFVnmTggzMygG\nxh8Zz6CHB9GhdocSa2NibBg92otFi5J56CG58U6YjjQLIcxs6bml5Opzeb3l6yXW5eXBa695MXRo\nBh07yo13wrSMPg0lhCh/v8b8ypqINezusxs7m5L/Oc6a5YG7u8KECekmSifEX4xuFvHx8VSvXvK5\n1JKcO3eOsLAwDAYDnTt3pk+fPoVqIiIi+OKLL9Dr9ajVambPnv3AryeEpUvMTmTMoTF88uQn+Lr5\nlli7YYMLx487sGtXAjZyPkCYgdHNYtq0aaxdu5bdu3eXeY4og8HA6tWreeedd9BoNMyYMYOgoKAC\nd4VnZGSwevVq3nrrLby9vWWtDFGpKYrC6z++Tu/6velap+TZm3/91YH589Vs3ZqAu7vceCfMo8Rm\n8cYbb1C/fn3q1auHwXB/WcZvv/22zM0iMjKSmjVr5q/r3b59e06fPl2gWRw/fpw2bdrg7e0N3F9c\nSYjKKvRiKNosLau6riqx7s6d+zPJhoQkExAgF7SF+ZTYLCZNmsSNGze4fv06ubm5TJs2jby8PC5e\nvEj9+vVxcXEx6kUSExPzmwCARqMpNDHhvXv30Ov1zJkzh6ysLHr06MGTTz75AG9JCMt2Pv48S84t\nYddzu3C+0bGMAAAgAElEQVSwdSi2LitLxUsvaXjllXQ6dZIL2sK8SmwWiqLQrl072rVrx8GDB5k2\nbRoTJ05k79693Lx5E1tbWxYvXlwuQfR6PTdv3mTmzJnk5OTw9ttv07BhQ2rVqlWgLiIigoiIiPzH\nwcHBqNUlz/NvCRwcHCRnObKGnEVlTMlJYfTh0Xza9VMCawcWu6+iwIQJTjRpAlOn2qBSVdx7tYbP\nEiRnRdi0aVP+14GBgQQGFv8zWWKzCAkJISEhAT8/P/Ly8khPT8fe3p4pU6YAkJZm3HTIGo0GrVab\n/1ir1RZYohXA29sbtVqNg4MDDg4ONGnShKioqELNoqg3ZGwOc1Kr1ZKzHFlDzv/NqCgKow+N5knf\nJ+lSq0uJ+Zcvd+PqVYUtWxJIr+DBT9bwWYLkLG9qtZrg4GCj60scV/HBBx/w2Wef8cILL6BSqVi7\ndi1ZWVmsWrWKH374gfj4eKNeJCAggJiYGOLi4tDpdJw8eZKgoKACNa1ateL333/HYDCQk5PDtWvX\nCk2LLoQ123BlA5HJkcxqO6vEuoMHHQkNdWX16kRZGlVYjFJHQ9nZ2VGvXj3s7OyYM2cOw4YNIzAw\nkOvXr3Py5ElmzpxZ6ovY2toyYsQI5s2blz901s/PjwMHDgDQrVs3ateuzaOPPsqUKVNQqVR06dJF\nmoWoNC5pLzH/9Hy29t6Kk13xc3RERtry+uuerF6dhK+vwYQJhSiZ0UNnX3zxxfyvH3/8cR5//PEy\nvVCLFi1o0aJFge9169atwONnn32WZ599tkzPK4Sly8zLZNShUcxqO4sGng2KrUtJUTF8uDfTp6fR\nqlWuCRMKUTqjb+/p2LEjAEuXLq2oLEJUSm+dfIuWPi3p37B/sTV6PYwd68VTT2UzeLBMOS4sT5mn\n+3Bzc6uIHEJUSt9d+46zcWfZ02dPiXXz56vJylIxa5bcjCosk8wNJUQFuZZ4jTk/z+GbHt/gYl/8\nPUnbtjmzfbszu3cnYG9vwoBClIE0CyEqQJYui2HfD2Na0DQe8X6k2LrffrPnnXfc+fprLRqNXNAW\nlkumJBOinCmKwuSjk2ns3ZghjYcUWxcfb8PLL3vx4YcpBAbqTJhQiLKTIwshyllIeAhRqVHsG7gP\nXXbRTSA3F1591YsBA7Lo2TPbxAmFKDs5shCiHH1/83s2XtnImu5rcLYv+o46RYG33/bA09PA5MmW\nf6evECBHFkKUm4sJF5l+fDpfPvMlNVxqFFu3bp0Lp045sGOHrE0hrIc0CyHKQWxmLMP3D+eD9h/w\nr2r/Krbup58cWLhQzfbtCajVsjaFsB7yd40Q/1C2LpuXDrzE4MaD6VW/V7F10dG2jB7txZIlydSt\nK2tTCOsizUKIf0BRFKYcncJDbg8xscXEYusyM1UMH65h1Kh0nnxS1qYQ1kdOQwnxDyw5t4QbKTfY\n3HszKpWqyBpFgddf9+SRR/J45ZUMEycUonxIsxDiAe25uYd1l9ex67ldONsVP5f4kiVu3Lljy3ff\nJVBMPxHC4kmzEOIBXNReZNrxaWz49wZqutYstm7/fke++MKV77+Px6n4mcmFsHjSLIQoo7jMOEbs\nH8G8x+fxaPVHi627csWGKVM8Wbs2kZo1ZSoPYd3kArcQZfDnyKfnGz3PswHFr72SmKhi4EBn3nor\nlcceyzNhQiEqhjQLIYykKApTj03F19WX11u+XmxdSoqKwYO96dMnj+efzzJhQiEqjpyGEsJIy84v\nIzI5ki29t2CjKvrvrIwMFUOHetOqVS6zZimkp5s4pBAVRJqFEEbYd2sfay+tLXHkU1YWDBumoWHD\nPObMSUWlUps4pRAVR5qFEKWI0EYw5dgU1v97PbVcaxVZc38WWQ0+Pnrmz0+ROZ9EpSM/0kKUID4z\nnhH7RzD38bk0r968yBqdDsaM8cLeXmHRomRsbU0cUggTkCMLIYqRo8/h5R9epn/D/jwX8FyRNQbD\n/buzMzNVrFmTKMuiikpLmoUQRVAUhWnHpuHj4sPkxyYXUwPTp3tw754t69cn4uho4pBCmJDJTkOd\nO3eOiRMnMn78eLZt21ZsXWRkJAMHDuSXX34xVTQhCvnst8+4kniFkKdCihz5pCgwe7Y7ly/bExaW\niLOzTDcuKjeTNAuDwcDq1at58803WbhwISdOnCA6OrrIuo0bN9K8eXMURf7xCfPYH7Wf1RdXs7b7\nWlzsXYqsmT9fzU8/ObJhgxY3N/lZFZWfSZpFZGQkNWvWxMfHBzs7O9q3b8/p06cL1e3Zs4e2bdvi\n7u5uilhCFHI58TJTjk5hVbdV+Lr5FlmzZIkbe/c68dVXWjw8pFGIqsEkzSIxMRFvb+/8xxqNhsTE\nxEI1p0+fpnv37gDFTvcsREVJyEpg+L7hzGk3h5Y+LYusCQ115euvXfj6ay3e3jLfk6g6LOYCd1hY\nGIMHD0alUqEoSrGnoSIiIoiIiMh/HBwcjFpt+Tc/OTg4SM5yVN45c3Q5jPx+JM8HPs8LLV4osiYs\nzJ7Vqx3YvTuTOnVcTZ6xokjO8mUtOQE2bdqU/3VgYCCBgYHF1pqkWWg0GrRabf5jrVaLRqMpUHPj\nxg0WLVoEQFpaGufOncPOzo6goKACdUW9obS0tApKXn7UarXkLEflmVNRFCYdnYSXgxcT/jWhyOfd\nvNmZ99934bvv4vHy0mPMS1fFz7IiSc7ypVarCQ4ONrreJM0iICCAmJgY4uLi0Gg0nDx5kgkTJhSo\nWbp0af7Xy5cv57HHHivUKIQobwbFwNsn3+Zq0lW+7fltkSOfdu92Yu5cd77+Wku9erJ2tqiaTNIs\nbG1tGTFiBPPmzcNgMNC5c2f8/Pw4cOAAAN26dTNFDCEK0Bl0TDk6hajUKL7u8XWRI58OHnRkxgwP\nNm7U8vDDOjOkFMIyqJRKMEb17t275o5QKms6NK0KOXP1uYw9PJa03DRWd1tdZKM4ccKBUaO8WLs2\n8YHWpKgqn6WpSM7y5etb9Gi/4sjcUKLKydJl8dKBl9Ab9IQ9HVZkozh1yp5Ro7xYuTJJFi8SAmkW\noopJz01n6N6heDh4sKLrChxtC8/RceGCPS+9pCEkJJl27XLNkFIIyyPNQlQZyTnJDNwzkPoe9Qnp\nGIK9TeFZ/65csWPoUA3z56fQqVOOGVIKYZmkWYgqISErgQG7BhDkE8RHT3yErU3hecRv3LDlP//x\nZvbsVP7972wzpBTCclnMTXlCVJS76XcZuHsgzwY8y+SWk4ucHSA62paBA72ZMiWNPn1k3Wwh/pcc\nWYhKLSo1in67+jHo4UFMeWxKkY3ixg1bnn/em9dey2DQoEwzpBTC8kmzEJXWtaRr9NvVj9eavcao\nR0cVWXP4sCN9+lRj1Kh0RozIMHFCIayHnIYSldLFhIsM3TuUN1u/yYBGAwptVxRYvtyN1atdCQ1N\nonVrGfUkREmkWYhK53TsaV468BLvt3+fnvV6FtqelaVi8mQPbt2yY9eueHx9ZfZYIUojp6FEpXL8\nznGG7x/Op099WmSjuH3blueeq4adHWzenCCNQggjSbMQlcYPf/zA6EOjWdllJZ0f6lxo+4kTDjz7\nbDUGDMgkJCQZZ2czhBTCSsl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"text": [ "" ] } ], "prompt_number": 331 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(gradient(N), label=\"wt\")\n", "plot(gradient(M), label=\"mut\")\n", "plot(gradient(M+N), label=\"tot\")\n", "#yscale('log')\n", "grid(False, 'minor')\n", "legend(loc=2)\n", "ylabel('growth rate')\n", "xlabel('time')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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FpKQkqqqqAhiV1Bm3W7Bnh5W8iaHog3yBwL4UGqaSMdpI4S4bU88PD3Q4UoDIZqgA+Go7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\n1PQYZueM/mxMUFGDWF44WMNeP82O4bGi0Njr4rr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"text": [ "" ] } ], "prompt_number": 302 }, { "cell_type": "code", "collapsed": false, "input": [ "p = M/(M+N)\n", "p = p[1:]\n", "q = log(p/(1-p))\n", "fig,ax = subplots(1,2)\n", "ax[0].plot(q)\n", "ax[0].set_title('log(p/(1-p))')\n", "ax[1].plot(gradient(q))\n", "ax[1].set_title('d log(p/(1-p))/dt')\n", "fig.tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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OpGeeeYZOnz5NRES//vorvfTSSzR79mx6+umnaePGjfr2NTU19PLLL9OTTz5Jr7zyCtXW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\ndHCP3Gkw1iGiX2yXug5FB3ZDWvoPKKY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"text": [ "" ] } ], "prompt_number": 303 }, { "cell_type": "code", "collapsed": false, "input": [ "s_T1 = log(lam_m/lam_w)\n", "s_T2 = log(2) * log(lam_m/lam_w) / log(lam_w)\n", "print s_T1, s_T2" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.016 0.0356603051092\n" ] } ], "prompt_number": 304 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evolutionary simulation\n", "\n", "We let them grow like the above, then sample, then let them grow again, until one wins." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M,N=[],[]\n", "m,n = 1e6,1e6\n", "lam_m,lam_w = exp(0.327),exp(0.311)\n", "K_w = 128*1e6\n", "K_m = K_w #* log(lam_m) / log(lam_w)\n", "i_m,i_w = 1,1\n", "\n", "for _ in range(30):\n", " for _ in range(24):\n", " m,n = logistic(m,n)\n", " M.append(m)\n", " N.append(n)\n", " m,n = 1e6*m/float(m+n), 1e6*n/float(m+n)\n", " #m,n = multinomial(200, [m/(m+n), n/(m+n)])\n", "M = array(M)\n", "N = array(N)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 305 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(N, label=\"wt\")\n", "plot(M, label=\"mut\")\n", "#plot(M+N, label=\"tot\")\n", "#yscale('log')\n", "grid(False, 'minor')\n", "legend(loc=2)\n", "ylabel('# cells')\n", "xlabel('time');" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 306, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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g2uh2NTAmvi/tno3AraLT6SjlmFtGu22CBeLnvt2zEbRKME0TgUzOsmGUw98X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\nh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TfcgM7OTgDAgQMH8Mgjj2DXrl1oamrCZZddhnPOOeddnmWMGHyII44YMTiwevVqdHR0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\nAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 306 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import linregress\n", "\n", "p = M/(M+N)\n", "p = p[1:]\n", "q = log(p/(1-p))\n", "slope, intercept, r_value, p_value, std_err = linregress(range(len(q)), q)\n", "abline = [intercept + slope*i for i in range(len(q))]\n", "print 's =', slope\n", "\n", "fig,ax = subplots(1,3, figsize=(10,5), sharex=True)\n", "ax[0].plot(p)\n", "ax[0].set_title('p')\n", "ax[0].set_xticks(range(0, len(p)+5*24, 5*24))\n", "ax[0].set_xticklabels(range(0, 2+len(p)/24, 5))\n", "ax[1].plot(q)\n", "ax[1].plot(abline, ls='--')\n", "ax[1].set_title('log(p/(1-p))')\n", "ax[2].plot(gradient(q))\n", "ax[2].set_title('d log(p/(1-p))/dt')\n", "ax[2].axhline(y=slope, ls='--',color='k')\n", "fig.tight_layout();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "s = 0.00986516222219\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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fL6B1GLI9Qk8od2WMZMbtAaJRRg2wQW20oihAbdhez0sFNgAQquLW81pt9MZe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R6MFv9A7aUauVBKQY5t28hkMli6dCk6Ojpw00034dZbb/Uco/r9zaRSiCeTsBob0R+LocV1P7Op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\nHcOECRNQVlYGn8+HBQsWoK6uLuFxpmlmL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