2.From_simulation_to_inference_SOLUTION.ipynb

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    "# Practical 2. From simulation to inference\n",
    "\n",
    "At the end of this practical you should:\n",
    "\n",
    "- Understand why coalescent simulations are useful to gain intuition about population level processes.\n",
    "- Appreciate that the site frequency spectrum (SFS) is a fundamental summary of sequence variation and understand how it relates to genealogical branch lengths.\n",
    "- Understand that summary statistics are the currency for comparing real data to idealized models of population processes/history and that such comparisons can be done either via analytic results or simulations.\n",
    "- Know how coalescent simulations are used in approximate likelihood inference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "import msprime\n",
    "import tskit\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from IPython.display import SVG, set_matplotlib_formats\n",
    "from matplotlib import pyplot as plt\n",
    "#jupyter magic\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## 2.1 The expected site frequence spectrum"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "This practical is based on a python tutorial developed as part of a bookchapter which is available [here](https://link.springer.com/protocol/10.1007%2F978-1-0716-0199-0_9)."
   ]
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    "<div class=\"alert alert-block alert-info\">\n",
    "    <b>PopGen:</b>\n",
    "\n",
    "The site frequency spectrum (SFS) summarises variants by their frequency in a sample. The SFS is a fundamental summary of sequence variation in two ways:\n",
    "1. It is a lossless summary of unlinked variants, in other words any summary statistic that ignores linkage is just a further summary of the SFS (e.g. pairwise genetic diversity and divergence, $F_{st}$, Tajima's $D$ can all be computed from the SFS). \n",
    "2. The SFS forms the basis of many modern population genomic methods that infer demographyic history and/or selection from sequence variation: e.g. dadi, fastsimcoal, sweepfinder, DFE-alpha ... (we will encounter some in this course).\n",
    "\n",
    "The SFS is convenient analytically, because it only depends on the mean length and frequency of genealogical branches. For a single Wright-Fisher population of constant size, the coalescent can used to derive a simple analytic prediction for the expected SFS: $$ S_i = \\theta/i $$ for $i= 1,2,...,n-1$ (see lecture 2 and <a href=\"https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118087\"> Hudson's recent proof</a>). Analytic expressions are also possible for the SFS around the target of a hard selective sweep (see practical 5). However, most realistic models of demography and/or selection are too complex and analytic expectations for the SFS (or other summeries of genealogies) do not exist. In this practical, we will approximate the SFS using coalescence simulations.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by considering the SFS for a single tree. Since we want to not only simulate a genealogy, but also (in a second step) mutations, we need to specify a length of sequence. Let's use `sim_ancestry` to simulate a single genealogy for a sample of $n=9$ (haploid) individuals from a Wright-Fisher population of size $N_e =10^6$. We asumme a 1kb stretch of sequence and `sim_mutations` to simulate mutations occuring on this genealogy at a rate $\\mu = 10^{-9}$. These parameters correspond roughly to *Drosophila melanogaster*."
   ]
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   "cell_type": "code",
   "execution_count": 6,
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   "source": [
    "simple_ts = msprime.sim_ancestry(9, ploidy=1, sequence_length=1000, random_seed = 34, population_size=1_000_000);\n",
    "#note that e-9 is shorthand for *10^(-9)\n",
    "ts_with_muts = msprime.sim_mutations(simple_ts, rate=1e-9, random_seed = 34)\n",
    "display(SVG(ts_with_muts.draw_svg(size=(500, 500),y_axis=True)))"
   ]
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    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 1:</b> How many mutations are in this genealogy? Looking at the tree above, can you work out the SFS?\n",
    "    \n",
    "**Hint:** Typing in the name of the tree produces a useful report\n",
    "</div>"
   ]
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  {
   "cell_type": "code",
   "execution_count": 7,
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       "                          <a target=\"_blank\" href=\"https://tskit.readthedocs.io/en/latest/python-api.html#the-treesequence-class\"> Tree Sequence </a>\n",
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       "                      <tr><td>Trees</td><td>1</td></tr>\n",
       "                      <tr><td>Sequence Length</td><td>1000.0</td></tr>\n",
       "                      <tr><td>Sample Nodes</td><td>9</td></tr>\n",
       "                      <tr><td>Total Size</td><td>3.3 KiB</td></tr>\n",
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       "                    <td>Mutations</td>\n",
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       "                      <td>1</td>\n",
       "                      <td>216 Bytes</td>\n",
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       "                        ✅\n",
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   "source": [
    "#SOL\n",
    "# (3,0,1,0,0,0,0,2)\n",
    "ts_with_muts"
   ]
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   "cell_type": "markdown",
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   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Python recipe:</b> We can find the corresponding SFS using the <code>tskit</code> method <a href=\"https://tskit.dev/tskit/docs/stable/python-api.html?highlight=frequency#tskit.TreeSequence.allele_frequency_spectrum\"><code>.allele_frequency_spectrum()</code></a>. The output is a numpy array. Note that the number of singletons is at position 1 not 0, i.e. <code>simple_sfs_site[1]</code>. The first (0th) and last (nth) entry of the SFS includes the counts of mutation of frequency $0$ in $n$ in the focal population (but which may vary in some other population). Since we are only considering a single population, both $0$ and $n$ types have zero counts by definition.\n",
    "</div>"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <b>Exercise 2:</b> Read the documentation for <a href=\"https://tskit.dev/tskit/docs/stable/python-api.html?highlight=frequency#tskit.TreeSequence.allele_frequency_spectrum\"><code>.allele_frequency_spectrum()</code></a>, use this method to find the SFS of your tree and store the result as a new variable <code>simple_sfs_site</code>. How many entries does the SFS have? Is it folded or not? Does the output agree with your SFS?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.   , 0.005, 0.   , 0.001, 0.   , 0.   , 0.   , 0.   , 0.   ,\n",
       "       0.   ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "simple_sfs_site = ts_with_muts.allele_frequency_spectrum()\n",
    "simple_sfs_site"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <div>\n",
       "              <style>\n",
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       "                    <thead>\n",
       "                      <tr>\n",
       "                        <th style=\"padding:0;line-height:21px;\">\n",
       "                          <img style=\"height: 32px;display: inline-block;padding: 3px 5px 3px 0;\" src=\"https://raw.githubusercontent.com/tskit-dev/administrative/main/tskit_logo.svg\"/>\n",
       "                          <a target=\"_blank\" href=\"https://tskit.readthedocs.io/en/latest/python-api.html#the-treesequence-class\"> Tree Sequence </a>\n",
       "                        </th>\n",
       "                      </tr>\n",
       "                    </thead>\n",
       "                    <tbody>\n",
       "                      <tr><td>Trees</td><td>1</td></tr>\n",
       "                      <tr><td>Sequence Length</td><td>1000.0</td></tr>\n",
       "                      <tr><td>Sample Nodes</td><td>9</td></tr>\n",
       "                      <tr><td>Total Size</td><td>3.3 KiB</td></tr>\n",
       "                      <tr>\n",
       "                        <td>Metadata</td><td style=\"text-align: left;\">No Metadata</td></tr>\n",
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       "                        <th style=\"line-height:21px;\">Table</th>\n",
       "                        <th>Rows</th>\n",
       "                        <th>Size</th>\n",
       "                        <th>Has Metadata</th>\n",
       "                      </tr>\n",
       "                    </thead>\n",
       "                    <tbody>\n",
       "                    \n",
       "                  <tr>\n",
       "                    <td>Edges</td>\n",
       "                      <td>16</td>\n",
       "                      <td>452 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Individuals</td>\n",
       "                      <td>9</td>\n",
       "                      <td>156 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Migrations</td>\n",
       "                      <td>0</td>\n",
       "                      <td>4 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Mutations</td>\n",
       "                      <td>6</td>\n",
       "                      <td>182 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Nodes</td>\n",
       "                      <td>17</td>\n",
       "                      <td>412 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Populations</td>\n",
       "                      <td>1</td>\n",
       "                      <td>216 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        ✅\n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Provenances</td>\n",
       "                      <td>2</td>\n",
       "                      <td>1.7 KiB</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
       "                    </tr>\n",
       "                \n",
       "                  <tr>\n",
       "                    <td>Sites</td>\n",
       "                      <td>6</td>\n",
       "                      <td>110 Bytes</td>\n",
       "                      <td style=\"text-align: center;\">\n",
       "                        \n",
       "                      </td>\n",
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       "                \n",
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       "            </div>\n",
       "            "
      ],
      "text/plain": [
       "<tskit.trees.TreeSequence at 0x7ff11aff8eb0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_with_muts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 3:</b> Run <code>allele_frequency_spectrum</code> again, setting the option <code>span_normalise = False</code>. What is the difference?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 3., 0., 1., 0., 0., 0., 0., 2., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "simple_sfs_count = ts_with_muts.allele_frequency_spectrum(span_normalise = False, polarised = True)\n",
    "simple_sfs_count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <b>PopGen:</b> The SFS is a set of counts which may or may not include the invariant category. We can normalize the SFS either by the total # of sites (<code>msprime</code> does this by default) or condition on variant sites only. In this case, invariant sites are removed and we divide by the total number of variant site counts. This choice of normalisations applies to many population genetic summary statistics! \n",
    "    \n",
    "The normalized SFS can be interpreted as a probability density function, i.e. it gives the probability that a randomly choosen site in the sequence is a singleton, doubleton etc.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Python recipe:</b> it is much more efficient to <b>NOT</b> simulate mutations in the first place. Instead, we can set <code>mode=branch</code> to record the relative length of the $i_{ton}$ branch types.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 4:</b> Run <code>allele_frequency_spectrum</code> on <code>ts_with_muts</code> again, setting the option <code>mode=\"branch\"</code>. What is the difference? What are the units of these SFS entries?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([      0.        , 2216377.30868057,  225496.61122083,\n",
       "        464025.1199517 ,       0.        ,  178614.56557942,\n",
       "             0.        ,       0.        , 1376729.37904293,\n",
       "             0.        ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "simple_sfs_branch = ts_with_muts.allele_frequency_spectrum(mode = \"branch\", polarised = True)\n",
    "simple_sfs_branch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 5:</b> Compare the site and branch based SFS of <code>simple_ts</code>. Why are some entries of the branch-based SFS non-zero, the corresponding entry of the mutation-based SFS is zero? What entries are zero in both versions of the SFS?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "#SOL\n",
    "#The branch based SFS has zero entries for mutation types that do NOT have corresponding branches in the genealogy.\n",
    "#For example, there are no i=6 branches.\n",
    "#For an entry to be non-zero in the mutation based SFS, both the correspondong branch types need to be present \n",
    "#AND carry mutations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, we have computed the SFS for individual trees under the coalescent. When using the SFS to summarize genome wide variation, we are computing an average SFS (i.e. the expectation) over many sites and genealogies. Let's use simulations to find the expectation for the average SFS.\n",
    "\n",
    "The code chunk below sets up 10,000 replicates. As in practical 1, we use a `for` loop to populate an empty numpy array (which we have called `sfs_table`) with the SFS of each replicate. \n",
    "\n",
    "**Note:**\n",
    "\n",
    "- `sfs_table` is a 2D array (check its shape to convince yourself)\n",
    "- we are using the `branch` mode to compute the SFS; i.e. the simulations do not include mutations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_replicates = 10_000\n",
    "nsamp = 9\n",
    "sfs_table = np.zeros((num_replicates, nsamp+1))\n",
    "replicates = msprime.sim_ancestry(9, ploidy=1, num_replicates=num_replicates,  population_size=1_000_000, random_seed=42)\n",
    "for replicate_index, ts in enumerate(replicates):\n",
    "    sfs = ts.allele_frequency_spectrum(mode=\"branch\", polarised=True)\n",
    "    sfs_table[replicate_index] = sfs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use <code>.mean()</code> to calculate the mean SFS across all replicates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean SFS is: \n",
      " [2003169.40332324  994179.39193106  673246.0719543   503108.7012861\n",
      "  401099.64521601  331932.34051494  284554.30651258  254286.30056072]\n"
     ]
    }
   ],
   "source": [
    "sfs_mean = sfs_table.mean(0)[1:nsamp]\n",
    "print(\"The mean SFS is: \\n\", sfs_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Python recipe: pd dataframes</b>\n",
    "    \n",
    "    \n",
    "We have so far dealt with python lists and arrays. When analysing data, we often want to store many pieces of information together. A [pandas](https://pandas.pydata.org/docs/reference/index.html) dataframe lets us do just that (if you've used `R` before, you'll be familiar with dataframes)! Dataframes may seem fiddly at first but make further analysis and plotting with [seaborn](https://seaborn.pydata.org/api.html) much easier (we will use them extensively when dealing with real data later in the course). Here is a quick [introduction](https://pandas.pydata.org/docs/user_guide/10min.html) to pandas dataframes. \n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's store the (mean) simulated SFS as a pandas dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>itons</th>\n",
       "      <th>sfs</th>\n",
       "      <th>type</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2.003169e+06</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>9.941794e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>6.732461e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5.031087e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>4.010996e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>3.319323e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>2.845543e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>2.542863e+05</td>\n",
       "      <td>sim</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   itons           sfs type\n",
       "0      1  2.003169e+06  sim\n",
       "1      2  9.941794e+05  sim\n",
       "2      3  6.732461e+05  sim\n",
       "3      4  5.031087e+05  sim\n",
       "4      5  4.010996e+05  sim\n",
       "5      6  3.319323e+05  sim\n",
       "6      7  2.845543e+05  sim\n",
       "7      8  2.542863e+05  sim"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "itons = range(1,nsamp)\n",
    "type_sim = ['sim']*(nsamp-1)\n",
    "sfs_sim_df = pd.DataFrame({'itons':itons,'sfs':sfs_mean,'type':type_sim})\n",
    "sfs_sim_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Python recipe: barplot</b>\n",
    "    \n",
    "We can visualise the SFS using <a href=\"https://seaborn.pydata.org/generated/seaborn.barplot.html\"><code>barplot</code></a>\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZeAf4WtbXKmkupUCqAuojYvMB/VRmZnbIunsM4oBFxMwu+gO4oYO+BkoBYmZmBfHzIMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsKdeAkFQnaaukZknzE/3zJG3IXpskfSjphKzvJUkbs77GPOs0M7P95fbIUUlVwELgYqAFWC9pVUQ83zYmIhYAC7LxnwNuiojdZR9zYUT8Ia8azcysY3muICYCzRGxLSLeB5YD0zsZPxNYlmM9ZmZ2APIMiBHAK2XbLVnbfiQdDdQBD5Y1B/CopCZJczr6JpLmSGqU1Lhz584eKNvMzCDfgFCiLToY+zngiXa7lyZFxDnANOAGSRekJkbE4oiojYjaYcOGHVrFZma2V54B0QKcUrZdA2zvYOwM2u1eiojt2dcdwEpKu6zMzKyX5BkQ64ExkkZLGkgpBFa1HyTpOGAy8HBZ2zGSBre9B6YCm3Ks1czM2sntLKaIaJU0F3gEqALqI2KzpOuz/kXZ0L8EHo2It8umnwislNRW430RsTqvWs3MbH+5BQRARDQADe3aFrXbXgIsade2DRifZ21mZtY5X0ltZmZJDggzM0vKdReT9R/nzru36BIAaFpwTdElmB02vIIwM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZUq4BIalO0lZJzZLmJ/qnSHpD0obsdVt355qZWb5yex6EpCpgIXAx0AKsl7QqIp5vN/TxiLj8IOeamVlO8lxBTASaI2JbRLwPLAem98JcMzPrAXk+UW4E8ErZdgtwXmLcpyU9C2wHbo6IzQcwF0lzgDkAI0eO7IGyrS/zk+/Mek6eKwgl2qLd9jPAqRExHvgJ8NABzC01RiyOiNqIqB02bNjB1mpmZu3kGRAtwCll2zWUVgl7RcSbEfFW9r4BqJY0tDtzzcwsX3kGxHpgjKTRkgYCM4BV5QMknSRJ2fuJWT27ujPXzMzyldsxiIholTQXeASoAuojYrOk67P+RcCXgL+S1Aq8C8yIiACSc/Oq1czM9pfnQeq23UYN7doWlb2/A7iju3PNzKz3+EpqMzNLckCYmVmSA8LMzJIcEGZmlpTrQWozS/MV39YXeAVhZmZJDggzM0tyQJiZWZIDwszMkhwQZmaW5IAwM7Mkn+ZqZh2qhNNxfSpucbyCMDOzJAeEmZklOSDMzCzJAWFmZkk+SG1mfZ4Ppucj1xWEpDpJWyU1S5qf6L9K0nPZ60lJ48v6XpK0UdIGSY151mlmZvvLbQUhqQpYCFwMtADrJa2KiOfLhr0ITI6I1yRNAxYD55X1XxgRf8irRjMz61ieK4iJQHNEbIuI94HlwPTyARHxZES8lm0+BdTkWI+ZmR2API9BjABeKdtuYd/VQXvXAr8o2w7gUUkB/H1ELE5NkjQHmAMwcuTIQyrYzCxPfe1YSZ4BoURbJAdKF1IKiPPLmidFxHZJw4E1kl6IiLX7fWApOBYD1NbWJj/fzMwOXJ67mFqAU8q2a4Dt7QdJ+jhwNzA9Ina1tUfE9uzrDmAlpV1WZmbWS/IMiPXAGEmjJQ0EZgCrygdIGgmsAGZFxL+WtR8jaXDbe2AqsCnHWs3MrJ3cdjFFRKukucAjQBVQHxGbJV2f9S8CbgOGAHdKAmiNiFrgRGBl1jYAuC8iVudVq5mZ7S/XC+UiogFoaNe2qOz9dcB1iXnbgPHt283MrPf4VhtmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWZIDwszMkhwQZmaW5IAwM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmlpRrQEiqk7RVUrOk+Yl+Sfpx1v+cpHO6O9fMzPKVW0BIqgIWAtOAs4GZks5uN2waMCZ7zQHuOoC5ZmaWozxXEBOB5ojYFhHvA8uB6e3GTAfujZKngOMlndzNuWZmliNFRD4fLH0JqIuI67LtWcB5ETG3bMz/BG6PiHXZ9j8BtwCjuppb9hlzKK0+AM4AtvbwjzIU+EMPf2ZP6ws1guvsaa6zZ/WFOvOo8dSIGJbqGNDD36icEm3t06ijMd2ZW2qMWAwsPrDSuk9SY0TU5vX5PaEv1Aius6e5zp7VF+rs7RrzDIgW4JSy7RpgezfHDOzGXDMzy1GexyDWA2MkjZY0EJgBrGo3ZhVwTXY206eANyLi1W7ONTOzHOW2goiIVklzgUeAKqA+IjZLuj7rXwQ0AJcCzcA7wNc6m5tXrV3IbfdVD+oLNYLr7Gmus2f1hTp7tcbcDlKbmVnf5iupzcwsyQFhZmZJDogESfWSdkjaVHQtnZF0iqRfStoiabOkbxZdU4qkQZKelvRsVuf3i66pI5KqJP1Ldo1OxZL0kqSNkjZIaiy6nhRJx0v6uaQXsj+jny66pvYknZH9N2x7vSnpW0XXlSLppuzvzyZJyyQNyv17+hjE/iRdALxF6SrvsUXX05HsqvOTI+IZSYOBJuDzEfF8waXtQ5KAYyLiLUnVwDrgm9nV8xVF0reBWuDPIuLyouvpiKSXgNqIqNgLuyT9A/B4RNydnY14dES8XnBZHcpu8fN7Shfl/q7oespJGkHp783ZEfGupH8EGiJiSZ7f1yuIhIhYC+wuuo6uRMSrEfFM9n4PsAUYUWxV+8tupfJWtlmdvSruNxNJNcBlwN1F19LXSfoz4ALgpwAR8X4lh0Pms8BvKy0cygwAjpI0ADiaXrg2zAHRT0gaBXwC+OeCS0nKdt1sAHYAayKiEuv878DfAH8quI7uCOBRSU3Z7WYqzWnATuCebJfd3ZKOKbqoLswAlhVdREpE/B74b8DLwKuUrhl7NO/v64DoByQdCzwIfCsi3iy6npSI+DAiJlC6Kn6ipIradSfpcmBHRDQVXUs3TYqIcyjd8fiGbLdoJRkAnAPcFRGfAN4GKva2/dkusL8AHii6lhRJ/47SDUtHAx8BjpF0dd7f1wHRx2X79B8ElkbEiqLr6Uq2m+FXQF2xlexnEvAX2b795cCfS/pZsSV1LCK2Z193ACsp3QG5krQALWUrxZ9TCoxKNQ14JiL+b9GFdOAi4MWI2BkRHwArgM/k/U0dEH1YdvD3p8CWiPhR0fV0RNIwScdn74+i9If9hUKLaicibo2ImogYRWlXw/+OiNx/QzsYko7JTkog220zFaioM+4i4t+AVySdkTV9FqiokyfamUmF7l7KvAx8StLR2d/7z1I65pgrB0SCpGXAr4EzJLVIurbomjowCZhF6bfdttP0Li26qISTgV9Keo7SfbbWRERFn0Za4U4E1kl6Fnga+F8RsbrgmlJuBJZm/98nAP+l2HLSJB0NXEzpt/KKlK3Efg48A2yk9G937rfd8GmuZmaW5BWEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPC7CBJejL7OkrSlUXXY9bTHBBmByki2q5kHQU4IKzfcUCYHSRJbXeovR3499mFijdlz7+4J3tew79IujAbP1vSCkmrJf1G0n/N2qskLcnu879R0k1F/Uxm5QYUXYBZPzAfuLnt+RGS/hogIsZJOpPSXVdPz8ZOoHTX3T8CWyX9BBgOjGh79kjbbUnMiuYVhFnPOx/4HwAR8QLwO6AtIP4pIt6IiPco3ZvoVGAbcJqkn0iqAyryjrx2+HFAmPU8ddL3x7L3HwIDIuI1YDylu9zegB9YZBXCAWF26PYAg8u21wJXAWS7lkYCWzuaLGkocEREPAj8LZV9W2w7jPgYhNmhew5oze6uugS4E1gkaSPQCsyOiD+W7tKcNILSk9fafmG7Ned6zbrFd3M1M7Mk72IyM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJL+H1Px3A5mMU53AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = sns.barplot(data = sfs_sim_df, x='itons', y='sfs', hue= 'type')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 6:</b> What is the expected SFS for a neutrally evolving Wright-Fisher population (see mini lecture 2)? Define a list or array that gives this expectation for a sample of $n=9$ and store the result as a dataframe <code>sfs_exp_df</code> analogous to <code>sfs_sim_df</code>.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "#SOL\n",
    "sfs_exp = [1/i for i in range(1,nsamp)]\n",
    "type_exp = ['exp']*(nsamp-1)\n",
    "sfs_exp_df = pd.DataFrame({'itons':itons,'sfs':sfs_exp,'type':type_exp})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = sns.barplot(x='itons', y='sfs', hue= 'type', data = sfs_exp_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can concatenate the simulated and expected SFS into a single dataframe and plot both using the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sfs_concat_df = pd.concat([sfs_sim_df, sfs_exp_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_concat_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 8:</b> What explains the difference between expected and observed SFS? Normalize both SFS by the total length of genealogical branches and replot! \n",
    "    \n",
    "**Hint:** <code>sfs_mean/=np.sum(sfs_mean)</code> can be used to assign a normalized (by the total) sfs to the same variable name. Once you have normalized both SFSs, you need to define the dataframe <code>sfs_concat_df</code> again.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEGCAYAAAB/+QKOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAZkElEQVR4nO3dfZBV1Z3u8e9D04QRSbzBJpPQKugQDYIQbXEiXMWrImhKNCaDCCgzsZCKZMbkqmCVQyXRuppxMpU4QbmUg44jBhIDCZUwKpqxDJoI3RkUFJkgvnXQC0J8Q1BefvePs5s5dK+mT9Nn92k6z6eq6+y99lr7/I4CT++1X44iAjMzs+Z6VLoAMzPrmhwQZmaW5IAwM7MkB4SZmSU5IMzMLKlnpQsop6OPPjoGDhxY6TLMzA4bDQ0Nb0VETWpbtwqIgQMHUl9fX+kyzMwOG5JebW2bp5jMzCzJAWFmZkkOCDMzS+pW5yDMzMph9+7dNDY2smvXrkqXUja9e/emtraW6urqksc4IMzMmmlsbKRv374MHDgQSZUup8Migm3bttHY2MigQYNKHucpJjOzZnbt2kW/fv26RTgASKJfv37tPiJyQJiZJXSXcGhyKJ/HAWFmZkkOCDOzMnv77be56667Kl1Gh3Xrk9Sn3XB/h/extO8dHRp/7Jy1Ha7BzA4vTQHxta99rdKldIiPIMzMymz27Nm89NJLjBgxgq985Sv8/Oc/379t8uTJLFu2jPvuu48JEyYwbtw4TjzxRL797W/v7/PAAw8wcuRIRowYwTXXXMPevXsr8TEcEGZm5Xb77bdzwgknsGbNGmbOnMm9994LwDvvvMPTTz/NhRdeCMCqVatYuHAha9as4Sc/+Qn19fWsX7+exYsX89RTT7FmzRqqqqpYuHBhRT5Ht55iMjOrtLPPPptrr72WLVu2sGTJEi677DJ69iz803v++efTr18/AL70pS+xcuVKevbsSUNDA6effjoAO3fupH///hWp3QFhZpazqVOnsnDhQhYtWsSCBQv2tze/9FQSEcFVV13Fbbfd1tlltuApJjOzMuvbty/vvffe/vVp06bx/e9/H4CTTz55f/uKFSvYvn07O3fu5Gc/+xmjRo3i3HPP5aGHHmLLli0AbN++nVdfbfWJ3LnyEYSZWZn169ePUaNGMXToUMaPH88dd9zB5z73OS655JID+o0ePZqpU6eyceNGrrjiCurq6gC49dZbGTt2LPv27aO6upq5c+dy3HHHdfrnyDUgJI0DfgBUAfdExO3Ntk8AbgH2AXuA6yJiZbbtFeA9YC+wJyLq8qzVzKycHnzwwf3LH3zwAb///e+ZNGnSAX369+/PD3/4wxZjJ06cyMSJE3OvsS25TTFJqgLmAuOBIcAkSUOadXscGB4RI4C/Ae5ptv2ciBjhcDCzw9Vjjz3GSSedxNe//nU+8YlPVLqcdsnzCGIksDEiNgFIWgRMAF5o6hAR7xf17wNEjvWYmXW68847j9dee61F+7Rp05g2bVrnF9QOeZ6kHgC8XrTemLUdQNKlkl4EfknhKKJJAI9KapA0vbU3kTRdUr2k+q1bt5apdDMzyzMgUo8ObHGEEBFLI+Ik4BIK5yOajIqIUylMUV0r6azUm0TE/Iioi4i6mpqaMpRtZmaQb0A0AscUrdcCm1vrHBFPAidIOjpb35y9bgGWUpiyMjOzTpJnQKwGBksaJKkXcDmwrLiDpL9QdqeIpFOBXsA2SX0k9c3a+wBjgXU51mpmZs3kdpI6IvZImgk8QuEy1wUR8bykGdn2ecBlwJWSdgM7gYkREZI+BSzNsqMn8GBEPJxXrWZmB1OOJ0MXa7jjykMad/XVV/PNb36TIUOaXxCaj1zvg4iI5cDyZm3zipa/C3w3MW4TMDzP2szMDjf33NP8ToB8+VEbZmZd0I4dO7jooosYPnw4Q4cOZfHixYwZM4b6+noAjjzySGbNmsVpp53Geeedx6pVqxgzZgzHH388y5Yta2PvpXFAmJl1QQ8//DCf+cxnePbZZ1m3bh3jxo07YPuOHTsYM2YMDQ0N9O3bl5tvvpkVK1awdOlS5syZU5YaHBBmZl3QsGHDeOyxx5g1axa//vWvW9yF3atXr/2hMWzYMM4++2yqq6sZNmwYr7zySllq8MP6zMy6oM9+9rM0NDSwfPlybrrpJsaOHXvA9urq6v2PC+/Rowcf+9jH9i/v2bOnLDU4IMzMuqDNmzfzyU9+kilTpnDkkUdy3333dXoNDggzszYc6mWpHbF27VpuuOEGevToQXV1NXfffTfXX399p9bggDAz64IuuOACLrjgggPannjiif3L77//3886/da3vnVAv+JtHeGT1GZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS/JlrmZmbXjtO8PKur9j56wt6/7y4iMIMzNLckCYmXVRDzzwACNHjmTEiBFcc801PPPMM5xyyins2rWLHTt2cPLJJ7Nu3TqeeOIJzjrrLC699FKGDBnCjBkz2LdvX4ff3wFhZtYFrV+/nsWLF/PUU0+xZs0aqqqq2LBhAxdffDE333wzN954I1OmTGHo0KEArFq1iu9973usXbuWl156iSVLlnS4Bp+DMDPrgh5//HEaGho4/fTTAdi5cyf9+/dnzpw5nH766fTu3Zs777xzf/+RI0dy/PHHAzBp0iRWrlzJl7/85Q7V4IAwM+uCIoKrrrqK22677YD2N998k/fff5/du3eza9cu+vTpA7D/0d9Nmq8filynmCSNk7RB0kZJsxPbJ0h6TtIaSfWSRpc61sysOzv33HN56KGH2LJlCwDbt2/n1VdfZfr06dxyyy1MnjyZWbNm7e+/atUqXn75Zfbt28fixYsZPXp0a7suWW5HEJKqgLnA+UAjsFrSsoh4oajb48CyiAhJpwA/Bk4qcayZWaeoxGWpQ4YM4dZbb2Xs2LHs27eP6upqJkyYQM+ePbniiivYu3cvZ555Jr/61a/o0aMHX/jCF5g9ezZr167df8K6o/KcYhoJbIyITQCSFgETgP3/yEdE8TNp+wBR6lgzs+5u4sSJTJw4MbmtqqqKZ555Big8BvyII45g8eLFZX3/PKeYBgCvF603Zm0HkHSppBeBXwJ/056x2fjp2fRU/datW8tSuJmZ5RsQqTMk0aIhYmlEnARcAtzSnrHZ+PkRURcRdTU1NYdaq5nZYWvMmDH84he/KPt+8wyIRuCYovVaYHNrnSPiSeAESUe3d6yZWblFJH8nPWwdyufJMyBWA4MlDZLUC7gcWFbcQdJfKLsWS9KpQC9gWyljzczy0rt3b7Zt29ZtQiIi2LZtG717927XuNxOUkfEHkkzgUeAKmBBRDwvaUa2fR5wGXClpN3ATmBiFP6PJMfmVauZWbHa2loaGxvpTuc1e/fuTW1tbbvG5HqjXEQsB5Y3a5tXtPxd4LuljjUz6wzV1dUMGjSo0mVUnJ/FZGZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWVKuASFpnKQNkjZKmp3YPlnSc9nP05KGF217RdJaSWsk1edZp5mZtdQzrx1LqgLmAucDjcBqScsi4oWibi8DZ0fEHyWNB+YDZxRtPyci3sqrRjMza12eRxAjgY0RsSkiPgIWAROKO0TE0xHxx2z1t0BtjvWYmVk75BkQA4DXi9Ybs7bWfBX496L1AB6V1CBpemuDJE2XVC+pfuvWrR0q2MzM/ltuU0yAEm2R7CidQyEgRhc1j4qIzZL6AyskvRgRT7bYYcR8ClNT1NXVJfdvZmbtl+cRRCNwTNF6LbC5eSdJpwD3ABMiYltTe0Rszl63AEspTFmZmVknyTMgVgODJQ2S1Au4HFhW3EHSscASYGpE/FdRex9JfZuWgbHAuhxrNTOzZnKbYoqIPZJmAo8AVcCCiHhe0oxs+zxgDtAPuEsSwJ6IqAM+BSzN2noCD0bEw3nVamZmLeV5DoKIWA4sb9Y2r2j5auDqxLhNwPDm7WZm1nl8J7WZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJuQaEpHGSNkjaKGl2YvtkSc9lP09LGl7qWDMzy1duASGpCpgLjAeGAJMkDWnW7WXg7Ig4BbgFmN+OsWZmlqM8jyBGAhsjYlNEfAQsAiYUd4iIpyPij9nqb4HaUseamVm+SgoISaMk9cmWp0j6J0nHtTFsAPB60Xpj1taarwL/3t6xkqZLqpdUv3Xr1jZKMjOzUpV6BHE38EF2juBG4FXg/jbGKNEWyY7SORQCYlZ7x0bE/Iioi4i6mpqaNkoyM7NSlRoQeyIiKEzz/CAifgD0bWNMI3BM0XotsLl5J0mnAPcAEyJiW3vGmplZfkoNiPck3QRMAX6ZnUSubmPMamCwpEGSegGXA8uKO0g6FlgCTI2I/2rPWDMzy9dBA0LSx7LFicCHwFcj4k0K5wPuONjYiNgDzAQeAdYDP46I5yXNkDQj6zYH6AfcJWmNpPqDjT2UD2hmZoemZxvbfwOcCtwREVObGiPiNdo+B0FELAeWN2ubV7R8NXB1qWPNzKzztBUQvSRdBZwp6UvNN0bEknzKMjOzSmsrIGYAk4GjgC9SuLqo+GoiB4SZWTd10ICIiJXASkkvA/Mi4l1Jfw98Hri1Mwo0M7PKaOsIosmUiPgHSaOB84HvUbg34ozcKrOSvfadYR3ex7Fz1pahEjPrTkoNiL3Z60UUjiR+Lulb+ZT0p+e0G9o8339QS9u6I8XM7BCUeh/EHyT9X+CvgOXZ5a9+VLiZWTdW6j/yf0XhnoRxEfE28EnghryKMjOzyitpiikiPqDoiqWIeAN4I6+izMys8jxNZGZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZUq4BIWmcpA2SNkqandh+kqTfSPpQ0vXNtr0iaa2kNZLq86zTzMxaKvX7INpNUhUwl8IXDDUCqyUti4gXirptB/4WuKSV3ZwTEW/lVaOZmbUuzyOIkcDGiNgUER8Bi4AJxR0iYktErAZ251iHmZkdgjwDYgDwetF6Y9ZWqgAeldQgaXprnSRNl1QvqX7r1q2HWKqZmTWXZ0Ao0RbtGD8qIk4FxgPXSjor1Ski5kdEXUTU1dTUHEqdZmaWkGdANALHFK3XAptLHRwRm7PXLcBSClNWZmbWSfIMiNXAYEmDJPUCLgeWlTJQUh9JfZuWgbHAutwqNTOzFnK7iiki9kiaSeG7rKuABRHxvKQZ2fZ5kv4cqAc+DuyTdB0wBDgaWCqpqcYHI+LhvGo1M7OWcgsIgIhYDixv1javaPlNClNPzb0LDM+zNjMzOzjfSW1mZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJud5Jbd3HaTfc3+F9NNxxZRkqMbPO4oCwTvPad4Z1eB/HzllbhkrMrBSeYjIzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWZIDwszMkhwQZmaWlGtASBonaYOkjZJmJ7afJOk3kj6UdH17xpqZWb5yCwhJVcBcYDwwBJgkaUizbtuBvwX+8RDGmplZjvI8ghgJbIyITRHxEbAImFDcISK2RMRqYHd7x5qZWb7yDIgBwOtF641ZW95jzcysDPIMCCXaotxjJU2XVC+pfuvWrSUXZ2ZmB5dnQDQCxxSt1wKbyz02IuZHRF1E1NXU1BxSoWZm1lKeAbEaGCxpkKRewOXAsk4Ya2ZmZZDb90FExB5JM4FHgCpgQUQ8L2lGtn2epD8H6oGPA/skXQcMiYh3U2PzqtXMzFrK9QuDImI5sLxZ27yi5TcpTB+VNNasLeX45rulfe/o8D78xUbWHfhOajMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0vK9U5qM0vzHd92OPARhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWZIDwszMknyZq5m1qitcjutLcSvHRxBmZpbkgDAzs6RcA0LSOEkbJG2UNDuxXZLuzLY/J+nUom2vSForaY2k+jzrNDOzlnI7ByGpCpgLnA80AqslLYuIF4q6jQcGZz9nAHdnr03OiYi38qrRzMxal+dJ6pHAxojYBCBpETABKA6ICcD9ERHAbyUdJenTEfFGjnWZWTfjk+n5yHOKaQDwetF6Y9ZWap8AHpXUIGl6blWamVlSnkcQSrRFO/qMiojNkvoDKyS9GBFPtniTQnhMBzj22GM7Uq+ZmRXJ8wiiETimaL0W2Fxqn4hoet0CLKUwZdVCRMyPiLqIqKupqSlT6WZmlucRxGpgsKRBwB+Ay4ErmvVZBszMzk+cAbwTEW9I6gP0iIj3suWxwHdyrNXMLHcdPVfS2d8BkltARMQeSTOBR4AqYEFEPC9pRrZ9HrAcuBDYCHwA/HU2/FPAUklNNT4YEQ/nVauZmbWU66M2ImI5hRAobptXtBzAtYlxm4DhedZmZmYH5zupzcwsyQFhZmZJDggzM0tyQJiZWZIDwszMkhwQZmaW5IAwM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZUq4BIWmcpA2SNkqandguSXdm25+TdGqpY83MLF+5BYSkKmAuMB4YAkySNKRZt/HA4OxnOnB3O8aamVmO8jyCGAlsjIhNEfERsAiY0KzPBOD+KPgtcJSkT5c41szMcqSIyGfH0peBcRFxdbY+FTgjImYW9fkFcHtErMzWHwdmAQPbGlu0j+kUjj4ATgQ2lPmjHA28VeZ9ltvhUCO4znJzneV1ONSZR43HRURNakPPMr9RMSXamqdRa31KGVtojJgPzG9faaWTVB8RdXntvxwOhxrBdZab6yyvw6HOzq4xz4BoBI4pWq8FNpfYp1cJY83MLEd5noNYDQyWNEhSL+ByYFmzPsuAK7Ormf4SeCci3ihxrJmZ5Si3I4iI2CNpJvAIUAUsiIjnJc3Its8DlgMXAhuBD4C/PtjYvGptQ27TV2V0ONQIrrPcXGd5HQ51dmqNuZ2kNjOzw5vvpDYzsyQHhJmZJTkgEiQtkLRF0rpK13Iwko6R9B+S1kt6XtLfVbqmFEm9Ja2S9GxW57crXVNrJFVJ+s/sHp0uS9IrktZKWiOpvtL1pEg6StJDkl7M/ox+odI1NSfpxOy/YdPPu5Kuq3RdKZK+kf39WSfpR5J65/6ePgfRkqSzgPcp3OU9tNL1tCa76/zTEfE7SX2BBuCSiHihwqUdQJKAPhHxvqRqYCXwd9nd812KpG8CdcDHI+KLla6nNZJeAeoiosve2CXpX4FfR8Q92dWIR0TE2xUuq1XZI37+QOGm3FcrXU8xSQMo/L0ZEhE7Jf0YWB4R9+X5vj6CSIiIJ4Htla6jLRHxRkT8Llt+D1gPDKhsVS1lj1J5P1utzn663G8mkmqBi4B7Kl3L4U7Sx4GzgH8BiIiPunI4ZM4FXupq4VCkJ/BnknoCR9AJ94Y5ILoJSQOBzwPPVLiUpGzqZg2wBVgREV2xzu8DNwL7KlxHKQJ4VFJD9riZruZ4YCtwbzZld4+kPpUuqg2XAz+qdBEpEfEH4B+B14A3KNwz9mje7+uA6AYkHQn8FLguIt6tdD0pEbE3IkZQuCt+pKQuNXUn6YvAlohoqHQtJRoVEadSeOLxtdm0aFfSEzgVuDsiPg/sALrsY/uzKbCLgZ9UupYUSf+DwgNLBwGfAfpImpL3+zogDnPZnP5PgYURsaTS9bQlm2Z4AhhX2UpaGAVcnM3tLwL+l6QHKltS6yJic/a6BVhK4QnIXUkj0Fh0pPgQhcDoqsYDv4uI/1fpQlpxHvByRGyNiN3AEuDMvN/UAXEYy07+/guwPiL+qdL1tEZSjaSjsuU/o/CH/cWKFtVMRNwUEbURMZDCVMOvIiL339AOhaQ+2UUJZNM2Y4EudcVdRLwJvC7pxKzpXKBLXTzRzCS66PRS5jXgLyUdkf29P5fCOcdcOSASJP0I+A1woqRGSV+tdE2tGAVMpfDbbtNlehdWuqiETwP/Iek5Cs/ZWhERXfoy0i7uU8BKSc8Cq4BfRsTDFa4p5evAwuz/+wjg/1S2nDRJRwDnU/itvEvKjsQeAn4HrKXwb3fuj93wZa5mZpbkIwgzM0tyQJiZWZIDwszMkhwQZmaW5IAwM7MkB4TZIZL0dPY6UNIVla7HrNwcEGaHKCKa7mQdCDggrNtxQJgdIklNT6i9Hfif2Y2K38i+/+Le7Psa/lPSOVn/aZKWSHpY0u8l/UPWXiXpvuw5/2slfaNSn8msWM9KF2DWDcwGrm/6/ghJ/xsgIoZJOonCU1c/m/UdQeGpux8CGyT9M9AfGND03SNNjyUxqzQfQZiV32jg3wAi4kXgVaApIB6PiHciYheFZxMdB2wCjpf0z5LGAV3yibz2p8cBYVZ+Osi2D4uW9wI9I+KPwHAKT7m9Fn9hkXURDgizjnsP6Fu0/iQwGSCbWjoW2NDaYElHAz0i4qfA39O1H4ttf0J8DsKs454D9mRPV70PuAuYJ2ktsAeYFhEfFp7SnDSAwjevNf3CdlPO9ZqVxE9zNTOzJE8xmZlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJ/x9vifPl48kckAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#SOL\n",
    "sfs_mean/=np.sum(sfs_mean)\n",
    "sfs_exp/=np.sum(sfs_exp)\n",
    "sfs_sim_df = pd.DataFrame({'itons':itons,'sfs':sfs_mean,'type':type_sim})\n",
    "sfs_exp_df = pd.DataFrame({'itons':itons,'sfs':sfs_exp,'type':type_exp})\n",
    "sfs_concat_df = pd.concat([sfs_sim_df, sfs_exp_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_concat_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Note:</b> You could measure how well your simulated SFS fits the expectation by cimputing the sum of squared differences. You can use the functions <code>np.sum()</code> and <code>np.square()</code>. Both are vectorized operations for numpy arrays, i.e. fact that <code>np.square()</code> applies  <code>**2 </code> to each element of the array.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.839388257037742e-06"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "np.sum(np.square(sfs_mean-sfs_exp))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 9:</b> \n",
    "The code chunk below generates an expectation for the SFS based on mutation counts in 1,000 replicates (each 1kb of sequence) and a mutation rate of $\\mu = 0.001$ as above. Store the new simulated SFS based on sites as a dataframe and add it to your existing SFS dataframe (using concatenate). Plot all three site frequency spectra. Which simulated SFS gives a closer fit to the analytic expectation? \n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "sfs_sites_table = np.zeros((num_replicates, nsamp+1))\n",
    "replicates = msprime.sim_ancestry(9, ploidy=1, num_replicates=num_replicates, sequence_length=1_000, random_seed=42)\n",
    "for replicate_index, ts in enumerate(replicates):\n",
    "    ts_with_muts = msprime.sim_mutations(ts, rate=0.001, random_seed = 34)\n",
    "    sfs = ts_with_muts.allele_frequency_spectrum(polarised=True)\n",
    "    sfs_sites_table[replicate_index] = sfs\n",
    "\n",
    "sfs_sites_mean = sfs_sites_table.mean(0)[1:nsamp]\n",
    "sfs_sites_mean /=np.sum(sfs_sites_mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "#SOL\n",
    "itons = range(1,nsamp)\n",
    "type_sites = ['sites']*(nsamp-1)\n",
    "sfs_sites_df = pd.DataFrame({'itons':itons,'sfs':sfs_sites_mean,'type':type_sites})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sfs_concatB_df = pd.concat([sfs_sim_df, sfs_exp_df, sfs_sites_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_concatB_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0019066780918453926"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "diff_sfs=(sfs_sites_mean-sfs_exp);\n",
    "np.sum(np.square(diff_sfs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 The SFS of Sub-Saharan *Drosophila melanogaster*"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import an SFS from a real population (we will learn more about summarizing real sequence variation in practical 4)! For now, we will use an example from the king of all (lab) organisms: *D. melanogaster*.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "This [dataset](https://www.genetics.org/content/203/2/975) was generated from whole genome sequence (WGS) data from 17 haploid (**!!!**) *D. melanogaster* sequences sampled from Rwanda as part the Drosophila Population Genomics Project."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Python recipe: data download using wget</b>\n",
    "    \n",
    "We can run any <code>bash</code> command from within a jupyter notebook by including `!` at the beginning of a code cell. To download a csv file containing the <i>D. melanogaster</i> sfs we will use <a href=\"https://g.co/kgs/VqTPwJ\"><code>wget</code></a> (we will use <code>wget</code> to download data throughout the course): \n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "dmel_sfs.csv          0%[                    ]       0  --.-KB/s               \r",
      "dmel_sfs.csv        100%[===================>]     274  --.-KB/s    in 0s      \r\n"
     ]
    }
   ],
   "source": [
    "! wget https://www.dropbox.com/s/xr56safng7hzs75/dmel_sfs.csv -q --show-progress -O dmel_sfs.csv\n",
    "#--show-progress https://www.dropbox.com/s/xr56safng7hzs75/dmel_sfs.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that the file is in our working directory:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "! ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>itons</th>\n",
       "      <th>sfs</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>900040.004336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>17923.612355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>7805.649778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>5063.585760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3667.575585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>3044.973523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>2539.840965</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>2257.735257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>2066.146167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>1781.853833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10</td>\n",
       "      <td>1693.264743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>11</td>\n",
       "      <td>1582.159035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>12</td>\n",
       "      <td>1432.026477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>13</td>\n",
       "      <td>1358.424415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>1305.414240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15</td>\n",
       "      <td>1386.350222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>16</td>\n",
       "      <td>1568.387645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>17</td>\n",
       "      <td>81764.995664</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    itons            sfs\n",
       "0       0  900040.004336\n",
       "1       1   17923.612355\n",
       "2       2    7805.649778\n",
       "3       3    5063.585760\n",
       "4       4    3667.575585\n",
       "5       5    3044.973523\n",
       "6       6    2539.840965\n",
       "7       7    2257.735257\n",
       "8       8    2066.146167\n",
       "9       9    1781.853833\n",
       "10     10    1693.264743\n",
       "11     11    1582.159035\n",
       "12     12    1432.026477\n",
       "13     13    1358.424415\n",
       "14     14    1305.414240\n",
       "15     15    1386.350222\n",
       "16     16    1568.387645\n",
       "17     17   81764.995664"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dmel_sfs = pd.read_csv('dmel_sfs.csv')\n",
    "dmel_sfs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 10:</b> Check whether the <i>D. melanogaster</i> SFS is normalized. What is the total number of sites? Assign this to a new variable <code>n_dmel_total</code>. Are $0$ and $n$ entries for monomorphic and fixed sites included?\n",
    "   </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Dmel SFS contains 1038282.0000000001 sites\n"
     ]
    }
   ],
   "source": [
    "#SOL\n",
    "n_dmel_total = np.sum(dmel_sfs['sfs']);\n",
    "print(\"The Dmel SFS contains\", n_dmel_total, \"sites\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Dmel SFS contains 18 entries. i=0 is inlcuded, i=n is NOT included.\n"
     ]
    }
   ],
   "source": [
    "#SOL\n",
    "print(\"The Dmel SFS contains\", len(dmel_sfs), \"entries. i=0 is inlcuded, i=n is NOT included.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is helpful to give the variant only, normalized SFS a new variable name and store it as a dataframe. The code chunk below uses python indices and assign the SFS without the first and last entry to a new variable, defines an SFS that is normalized (by the total number of variable of sites) and stores this as a dataframe:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <b>PopGen:</b> As in section 1 above, we will normalize the SFS by the total number of variable sites. In contrast, <code>msprime</code> normalizes by the total number of sites (i.e. the sequence length) by default.\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsamp_dmel = 17\n",
    "dmel_sfs_var = dmel_sfs['sfs'][1:nsamp_dmel]\n",
    "dmel_sfs_var_norm = dmel_sfs_var/np.sum(dmel_sfs_var)\n",
    "itons = range(1,nsamp_dmel)\n",
    "type_dmel = ['dmel']*(nsamp_dmel-1)\n",
    "sfs_dmel_df = pd.DataFrame({'itons':itons,'sfs':dmel_sfs_var_norm,'type':type_dmel})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 11:</b> Compare the <i>D. melanogaster</i> SFS to the neutral expectation for a sample from a Wright-Fisher population of constant size. Which entries show the greatest deviation from neutrality? What might be the cause?\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#SOL\n",
    "#This sets up the expected SFS as a dataframe\n",
    "exp_branches =[1/i for i in range(1,nsamp_dmel)]\n",
    "exp_sfs = exp_branches/np.sum(exp_branches)\n",
    "type_exp = ['exp']*(nsamp_dmel-1)\n",
    "sfs_exp_df = pd.DataFrame({'itons':itons,'sfs':exp_sfs,'type':type_exp})\n",
    "\n",
    "#Combines it with the dmel_SFS dataframe\n",
    "sfs_dmel_concat_df = pd.concat([sfs_dmel_df, sfs_exp_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_dmel_concat_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 12:</b>\n",
    "Compute Watterson's $\\theta$ (per base) for the <i>D. melanogaster</i> SFS (see lecture 2)\n",
    "\n",
    "<b>Hint:</b> Use <code>exp_branches</code> defined above and  <code>n_dmel_total</code> (exercise 12).\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3807289932289937"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wattersons_correction17 = np.sum(exp_branches)\n",
    "wattersons_correction17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Watterson's theta is 0.01608962552193177\n"
     ]
    }
   ],
   "source": [
    "#SOL\n",
    "wattersons_theta = np.sum(dmel_sfs_var)/(n_dmel_total *  wattersons_correction17);\n",
    "print(\"Watterson's theta is\", wattersons_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 13:</b> Assume a mutation rate of $\\mu= 3.5 \\times 10^{-9}$ <a href=\"https://genome.cshlp.org/content/19/7/1195\">(Keightley et al 2009)</a>. Translate your estimate of $\\theta_W$ into the effective population size ($N_e$) for this species.\n",
    "   </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1149258.9658522692"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "mu = 3.5e-9\n",
    "neDmel = wattersons_theta/ (4 * mu)\n",
    "neDmel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <b>PopGen:</b> Remember that for a population of constant $N_e$, the frequency of singletons is also an estimator of the scaled mutation rate $\\theta$ (see lecture 2).\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 14:</b> How does the estimate of $N_e$ based on singletons differ from the estimate based on $\\theta_W$ above?\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1233054.2428330095"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SOL\n",
    "dmel_sfs_var[1]/ (n_dmel_total * 4 * mu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Class discussion:</b>\n",
    "\n",
    "- What biological processes could explain the difference between the estimates of $N_e$ based on $\\theta_w$ and the number of singleton mutations?\n",
    "- What bioinformatic artefacts could generate an artefactual excess of singletons?\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Fitting models of population growth and decline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is an infinite number of possible models of population size change. A simple possibility (1 parameter) is to assume that the population size has been growing or shrinking deterministically: e.g. we could assume exponential growth. A more complex (2 parameter) model is a population change at some time $T$ in the past. The code chunk below defines a function that simulates a single genealogy from a population that has undegone exponential growth."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_growth_sims(num_samp, rate, num_rep=None, seed=123):    \n",
    "    demography = msprime.Demography()\n",
    "    demography.add_population(initial_size=1/2)\n",
    "    demography.add_population_parameters_change(time=0, growth_rate= rate, population=0)\n",
    "    return msprime.sim_ancestry(\n",
    "        samples=[msprime.SampleSet(num_samp, ploidy=1)],\n",
    "        num_replicates=num_rep,\n",
    "        demography=demography,\n",
    "        random_seed=seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 15:</b> Use the function <code>run_growth_sims</code> to simulate a single genealogy for a sample of the same size as the <i>D. melanogaster</i> dataset. Assume a growth rate of 5 and use the <code>draw_svg</code> method to plot the resulting tree. How does this genealogy differ from the a genealogy sampled for a population of fixed size?\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that a growth rate of 5 is extreme population growth! Going back in time, the population size at time $T=0.5 \\times 2N_e$ generations ago (1 million <i>D. melanogaster</i> generations) would be roughly an order of magnitude smaller than at present (time = 0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.arange(0., 5., 0.2)\n",
    "ty = np.exp(t*-5)\n",
    "plt.ylabel('N_e')\n",
    "plt.xlabel('time')\n",
    "p = sns.lineplot(x =t, y =ty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "#SOL\n",
    "ts_grow = run_growth_sims(17, rate=5, num_rep=None, seed=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:ev=\"http://www.w3.org/2001/xml-events\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" baseProfile=\"full\" height=\"500\" version=\"1.1\" width=\"500\"><defs><style type=\"text/css\"><![CDATA[.background path {fill: #808080; fill-opacity: 0}.background path:nth-child(odd) {fill-opacity: .1}.axes {font-size: 14px}.x-axis .tick .lab {font-weight: bold; dominant-baseline: hanging}.axes, .tree {font-size: 14px; text-anchor: middle}.axes line, .edge {stroke: black; fill: none}.y-axis .grid {stroke: #FAFAFA}.node > .sym {fill: black; stroke: none}.site > .sym {stroke: black}.mut text {fill: red; font-style: italic}.mut.extra text {fill: hotpink}.mut line {fill: none; stroke: none}.mut .sym {fill: none; stroke: red}.mut.extra .sym {stroke: hotpink}.node .mut .sym {stroke-width: 1.5px}.tree text, .tree-sequence text {dominant-baseline: central}.plotbox .lab.lft {text-anchor: end}.plotbox .lab.rgt {text-anchor: start}]]></style></defs><g 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      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#SOL\n",
    "display(SVG(ts_grow.draw_svg(size=(500, 500),y_axis=True)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#SOL: It is much shallower ($T_{MRCA}= 0.52!$) and has an excess of singleton branches than a typical genealogy from a pop of constant size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "        <b>Exercise 16:</b> Use <code>run_growth_sims</code> to simulate the mean SFS for a population that has undergone exponential growth at rate 5. Does this history give a better fit to the Dmel history than a population of constant size?\n",
    "    \n",
    "<b>Hint:</b> Set <code>nsamp_dmel</code>\n",
    "<code>growth_rate</code> and <code>num_replicates</code> in the code chunk below and run it to compute the mean across replicates as in section 2.1. Combine the dataframe with the Dmel SFS daraframe and plot.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "nsamp_dmel = 17\n",
    "growth_rate = 5\n",
    "num_replicates = 10_000\n",
    "sfs_table = np.zeros((num_replicates, nsamp_dmel+1))\n",
    "replicates = run_growth_sims(nsamp_dmel, rate=growth_rate, num_rep=num_replicates)\n",
    "for replicate_index, ts in enumerate(replicates):\n",
    "    sfs = ts.allele_frequency_spectrum(mode=\"branch\", polarised=True)\n",
    "    sfs_table[replicate_index] = sfs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "sfs_mean_g5 = sfs_table.mean(0)[1:nsamp_dmel]\n",
    "sfs_mean_g5/=np.sum(sfs_mean_g5)\n",
    "\n",
    "type_sim_g5 = ['sim_g5']*(nsamp_dmel-1)\n",
    "sfs_sim_g5_df = pd.DataFrame({'itons':itons,'sfs':sfs_mean_g5,'type':type_sim_g5})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sfs_mean_g5 = sfs_table.mean(0)[1:nsamp_dmel]\n",
    "sfs_mean_g5/=np.sum(sfs_mean_g5)\n",
    "\n",
    "type_sim_g5 = ['sim_g5']*(nsamp_dmel-1)\n",
    "sfs_sim_g5_df = pd.DataFrame({'itons':itons,'sfs':sfs_mean_g5,'type':type_sim_g5})\n",
    "\n",
    "#Combines this with the dmel_SFS dataframe\n",
    "sfs_dmel_concat3_df = pd.concat([sfs_dmel_concat_df, sfs_sim_g5_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_dmel_concat3_df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Finding plausible demographic histories with Approximate Likelihood inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fitting real data to a model can be challenging. For very simple models, such a neutrally evolving Wright-Fisher population of constant size analytic expectations exist for summaries of sequence variation and one can use likelihood approaches maximise the fit between data and model. \n",
    "\n",
    "However, for most biologically interesting/realistic models analytic predictions do NOT exits. This has led to the development of likelihood-free inference methods, that use simulations to fit data to models of demographic history including Approximate Bayesian Computation (ABC) ([Beaumont 2002](https://www.genetics.org/content/162/4/2025)) and machine learning. \n",
    "\n",
    "We will demonstrate how `msprime` can be used for a simple approximate inference. Given the poor fit an exponential growth model when choosing an arbitrary growth rate (above), our aim is to infer the growth rate parameter that gives the best fit to the *D. melanogaster* SFS."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code chunk below defines a function `approx_1DS_SFS` that sets up a number of replicate msprime simulations under an arbitrary demography and returns the mean SFS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "def approx_1D_SFS(num_samp, demography, num_rep=None, seed=123):\n",
    "    sfs_table = np.zeros((num_rep, num_samp+1))\n",
    "    replicates = msprime.sim_ancestry(\n",
    "        samples=[msprime.SampleSet(num_samp, ploidy=1)],\n",
    "        num_replicates=num_rep,\n",
    "        demography=demography,\n",
    "        random_seed=seed)\n",
    "    for replicate_index, ts in enumerate(replicates):\n",
    "        sfs = ts.allele_frequency_spectrum(mode=\"branch\", polarised=True)\n",
    "        sfs_table[replicate_index] = sfs\n",
    "    sfs_mean = sfs_table.mean(0)[1:num_samp]\n",
    "    return sfs_mean / np.sum(sfs_mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to find the best fitting history, we need to compare the real data to simulations under a range of growth models. Let's define a numpy array of growth rates from 0 to 0.5: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "growth_rate_grid = np.arange(-0.02,0.5,0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can  use <code>approx_1D_SFS</code> to find the approximate SFS (based on 1,000 replicate simulations) for each value in <code>growth_rate_grid</code>:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_rep = 1_000\n",
    "sfs_exp_grid = np.zeros((len(growth_rate_grid), nsamp_dmel-1))\n",
    "for rate_index, rate in enumerate(growth_rate_grid):\n",
    "    demography = msprime.Demography()\n",
    "    demography.add_population(initial_size=1/2)\n",
    "    demography.add_population_parameters_change(time = 0, growth_rate = rate, population=0)\n",
    "    sfs_exp_grid[rate_index] = approx_1D_SFS(num_samp = nsamp_dmel, demography = demography, num_rep = num_rep, seed=123)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    <b>PopGen:</b>\n",
    "\n",
    "How do we compare the real and simulated SFS? There are two obvious options:\n",
    " - We could compute sum of squared differences, aka the Euclidean distance between the observed and simulated (mean) SFS. ABC inference is based on this measure of goodness of fit.\n",
    " - Alternatively, we can could compute a likelihood. Remember that the normalised SFS can be interpreted as a probability distribution; i.e. each entry gives the probability of the correspoding $n_{ton}$ type. The overal log likelihood (support) of the model ($\\Theta$) given a set of SFS counts $\\bar{j} = \\{j_1, j_2 \\ldots j_{n-1}\\}$ is:\n",
    "\n",
    "\\begin{equation}\n",
    "ln(L[\\Theta |\\bar{j}]) = \\sum_{i=1}^{n-1} j_i \\times ln(p_i)\n",
    "\\end{equation}\n",
    " </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "support = np.zeros(len(growth_rate_grid))\n",
    "for idx, sfs in enumerate(sfs_exp_grid):\n",
    "    support[idx] = sum(np.log(sfs) * dmel_sfs_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('growth_rate')\n",
    "plt.ylabel('support (lnL)')\n",
    "p = sns.lineplot(x = growth_rate_grid, y = support)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 17:</b> How do you interpret the support curve above? \n",
    "    </div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code chunk below sets up an instantaneous bottleneck at time $t=0.2$ (on the coalescence scale of 2 $N_e$ generations) will be useful. To keep things simple, we will keep the bottleneck time fixed (at 0.2) and explore strengths between 0 and 11."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "demography = msprime.Demography()\n",
    "demography.add_population(initial_size=1/2)\n",
    "demography.add_instantaneous_bottleneck(time=0.2, strength=0.2, population=0)\n",
    "bottle_ts = msprime.sim_ancestry(\n",
    "        samples=[msprime.SampleSet(nsamp_dmel, ploidy=1)],\n",
    "        demography=demography,\n",
    "        random_seed=123)\n",
    "bottle_tree = bottle_ts.first()\n",
    "display(SVG(bottle_tree.draw_svg(size=(500, 500),y_axis=True)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This sets up an empty 2D array and <code>sfs_bott_grid</code> and stores the simulated SFS for each bottleneck strength: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_rep = 5_000\n",
    "num_samp = 17\n",
    "bott_grid = np.arange(0,1,0.05)\n",
    "sfs_bott_grid = np.zeros((len(bott_grid), num_samp-1))\n",
    "for strength_index, strength in enumerate(bott_grid):\n",
    "    demography = msprime.Demography()\n",
    "    demography.add_population(initial_size=1/2)\n",
    "    demography.add_instantaneous_bottleneck(time=0.2, strength=strength , population=0)   \n",
    "    sfs_bott_grid[strength_index] = approx_1D_SFS(num_samp = num_samp, demography = demography, num_rep = num_rep)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 18:</b> The code below computes the approximate likelihood for each bottleneck strength parameter and plots it! Which history best fits the data (and which entry in <code>sfs_bott_grid</code> corresponds to it)?\n",
    "        </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "support_bott = np.zeros(len(bott_grid))\n",
    "for idx, sfs in enumerate(sfs_bott_grid):\n",
    "    support_bott[idx] = sum(np.log(sfs) * dmel_sfs_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel('bottleneck strength')\n",
    "plt.ylabel('support (lnL)')\n",
    "p = sns.lineplot(x = bott_grid, y = support_bott)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\">    \n",
    "    <b>Exercise 19:</b> Compare the SFS under the best fitting bottleneck history to both the observed and the neutral SFS. Check whether low or high frequency mutations (or both) is better predicted under this model. Do you think this model is biologically plausible for Sub-Saharan African populations of <i>D. melanogaster</i>?\n",
    "    </div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#SOL\n",
    "type_sim_bott = ['sim_bott']*(nsamp_dmel-1)\n",
    "sfs_sim_best_bottle_df = pd.DataFrame({'itons':itons,'sfs':sfs_bott_grid[7],'type':type_sim_bott})\n",
    "\n",
    "#Combines it with the dmel_SFS dataframe\n",
    "sfs_dmel_concat4_df = pd.concat([sfs_dmel_concat3_df,sfs_sim_best_bottle_df])\n",
    "p = sns.barplot(x='itons', y='sfs', hue='type', data=sfs_dmel_concat4_df)"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}