{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem sheet 2 - Moran Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is similar to the Wright-Fisher model from problem sheet 1 (expect continuous time). Population of $L$ individuals. \n", "\n", "Let $N_t = \\sum_{i =1}^{L} \\delta_{X_{t(i),k}}$ be the number of individuals of a single type, $k \\in {1,...,L}$ at time $t$. Initially $N_0 =1 $ for all types. \n", "\n", "Recall, $ \\frac{d}{dt} \\mathbb{E}[f(N_t)] = \\mathbb{E}[\\mathcal{L}f(N_t)]$ - useful for part c" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We used am_done function for the wright fisher model" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def am_done(v):\n", " '''Return true if all elements of v the same. Else false.'''\n", " u=np.unique(v) # unique elements of v\n", " if u.shape[0]>1:\n", " return False\n", " else:\n", " return True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulation:\n", "- Run a process with rate $L$. \n", "- Waiting times are distributed exponentially with mean $\\beta = 1/L$. \n", "- When an event occurs pick an individual uniform at random to reproduce and pick an individual uniform at random to be killed." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "### Parameters ###\n", "\n", "L=50\n", "tmax=5000\n", "deltat=0.1\n", "\n", "#################\n", "\n", "X=np.arange(L) #initialize current state\n", "Y=np.zeros((1,L),dtype='int') # initialize output array\n", "Y[0,:]=X \n", "\n", "time=0.0\n", "nextout=deltat\n", "\n", "rate=L \n", "β=1.0/rate # mean wait time, uniformly picking 1/L individual at rate 1\n", "\n", "while (time" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (10,8))\n", "pcm = sns.heatmap(Y,cbar_kws={'label': 'types'.format(L)})\n", "pcm.figure.axes[-1].yaxis.label.set_size(16)\n", "plt.title('$X_t$ for fixed L={} individuals'.format(L), fontsize = 20)\n", "plt.xlabel('Individuals, L', fontsize = 20)\n", "plt.ylabel('Time/$\\Delta t$', fontsize = 20)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [], "source": [ "start_times=np.arange(np.shape(Y)[0])*deltat" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "def X_to_N(X):\n", " N=np.zeros_like(X)\n", " length=np.shape(N)[0]\n", " L=np.shape(N)[1]\n", " for row in range(length):\n", " row_list=list(X[row,:])\n", " for i in range(L):\n", " N[row,i]=row_list.count(i) \n", " return N" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "N=X_to_N(Y)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, '$N_t$ Number of individuals of each species \\n out of total population size L = 50')" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (15,8))\n", "for i in range(L):\n", " plt.plot(start_times,N[:,i],'o')\n", " \n", "plt.xlabel('Time, $t$', fontsize = 20)\n", "plt.ylabel('$N_t$', fontsize= 20)\n", "\n", "plt.title(\"$N_t$ Number of individuals of each species \\n out of total population size L = {}\".format(L), fontsize = 20)" ] } ], "metadata": { "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }