ts_workshop_part2.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Outline"
   ]
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  {
   "cell_type": "markdown",
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   "source": [
    "1. [<span style=\"color: gray\">The tree sequence format</span>](ts_workshop_part1.ipynb#ts)\n",
    "2. [Simulations (msprime & slim)](#msprime)\n",
    "3. [Calculating statistics with tree sequences](#stats)\n",
    "4. [<span style=\"color: gray\">Inferring tree sequences (tsinfer)</span>](ts_workshop_part3.ipynb#tsinfer)\n",
    "5. [<span style=\"color: gray\">Metadata in tree sequences</span>](ts_workshop_part3.ipynb#metadata)\n",
    "6. [<span style=\"color: gray\">References and Documentation</span>](ts_workshop_part3.ipynb#ref)"
   ]
  },
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   "source": [
    "from IPython.display import SVG, display, HTML\n",
    "import msprime\n",
    "import pyslim # to interface with SLiM files \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
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   "execution_count": 68,
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    "%%html\n",
    "<style>aside {color:grey;}</style>"
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   "source": [
    "<a id='msprime'></a>\n",
    "# 2. Simulation"
   ]
  },
  {
   "cell_type": "markdown",
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    "colab_type": "text",
    "id": "m_law_LbXPxl"
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   "source": [
    "## Reverse-time simulations with `msprime`\n",
    "The `msprime` program is an efficient reimplementation of Hudson's $\\texttt{ms}$ simulator which outputs coalescent trees using the tree sequence format. The easiest way to use it is through the Python API, which is well documented at https://msprime.readthedocs.io/en/stable/api.html. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2_pugFw0aejA"
   },
   "source": [
    "Running simulations is very straightforward, and produces trees with branch lengths as expected under the full coalescent."
   ]
  },
  {
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   "execution_count": 4,
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     "text": [
      "Number of Trees: 1\n"
     ]
    },
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   "source": [
    "# simulate the coalescent for 6 samples, with effective population size of 10,000\n",
    "# since the recombination rate defaults to zero, we should have only one tree\n",
    "singular_tree_seq = msprime.simulate(sample_size=6, Ne=10000, random_seed=10)\n",
    "\n",
    "# check there is only one tree in this ts\n",
    "print(\"Number of Trees:\",singular_tree_seq.num_trees)\n",
    "\n",
    "#take the first (only) tree and visualize\n",
    "first_tree=singular_tree_seq.first()\n",
    "SVG(first_tree.draw())"
   ]
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    "Here, we simulate the coalescent for a sample of size six with an effective population size of 10000 diploids, and then print out a depiction of the resulting tree. The `simulate()` function returns a standard `TreeSequence` object. Here there is only one tree because we have not provided a value for recombination_rate, which therefore defaults to zero. We can access the first (and only) tree in this sequence using `first()` method of a `TreeSequence` object.\n",
    "\n",
    "Note that although it is common for the lowest numbered nodes to correspond to the samples (i.e. tips of the trees, here with IDs 0 to 5) and the internal nodes to take higher values (e.g. the root node with ID 10), this may not always be the case e.g. in complex forward simulations or with ancient samples. Sometimes you may wish to check which node IDs correspond to samples, as follows:"
   ]
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    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5], dtype=int32)"
      ]
     },
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   "source": [
    "singular_tree_seq.samples()"
   ]
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    "\n",
    "Since the simulation was a basic one, the 6 samples take the first 6 node IDs. We can easily trace our path back to the root from a particular sample (e.g. the sample genome with ID 3) for any tree using the `parent()` method:"
   ]
  },
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     "text": [
      "node 3: time = 0.0\n",
      "node 7: time = 3332.0162387549144\n",
      "node 8: time = 7937.08724150321\n",
      "node 9: time = 13773.360032014867\n",
      "node 10: time = 18187.861182446646\n"
     ]
    }
   ],
   "source": [
    "node_id = 3\n",
    "while node_id != msprime.NULL_NODE:\n",
    "  print(\"node {}: time = {}\".format(node_id, first_tree.time(node_id)))\n",
    "  node_id = first_tree.parent(node_id)"
   ]
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    "Here we have iterated up the tree starting at node 3, stopping when we reached the root. We know that a node is a root if its parent is `msprime.NULL_NODE`, which is a special reserved node. (The value of the null node is -1, but we recommend using the symbolic constant to make code more readable.) We also use the `time()` method to get the time for each node, which corresponds to the time in generations at which the coalescence event happened during the simulation. \n",
    "\n",
    "We can also obtain the length of a branch joining a node to its parent using the `branch_length()` method; the total branch length in the tree is also stored in the `total_branch_length` attribute: "
   ]
  },
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   "cell_type": "code",
   "execution_count": 27,
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    "colab_type": "code",
    "id": "X04SaQQfa5Gg",
    "outputId": "ab99ce05-6a23-4cfb-951b-69001eb60923",
    "scrolled": true
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Branch length above node 7 is 4605.0710027482955\n",
      "Total branch length in tree is 63385.43180380048\n"
     ]
    }
   ],
   "source": [
    "node = 7\n",
    "print(\"Branch length above node\", node, \"is\", first_tree.branch_length(node))\n",
    "print(\"Total branch length in tree is\", first_tree.total_branch_length)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We can also do the standard tree traversals using the ``nodes`` iterator:"
   ]
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   "cell_type": "code",
   "execution_count": 111,
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   "outputs": [
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     "text": [
      "Default:\t [10, 2, 9, 6, 4, 5, 8, 0, 7, 1, 3]\n",
      "Preorder:\t [10, 2, 9, 6, 4, 5, 8, 0, 7, 1, 3]\n",
      "Inorder:\t [2, 10, 4, 6, 5, 9, 0, 8, 1, 7, 3]\n",
      "Postorder:\t [2, 4, 5, 6, 0, 1, 3, 7, 8, 9, 10]\n"
     ]
    }
   ],
   "source": [
    "display(SVG(first_tree.draw()))\n",
    "print(\"Default:\\t\", list(first_tree.nodes()))\n",
    "print(\"Preorder:\\t\", list(first_tree.nodes(order=\"preorder\")))\n",
    "print(\"Inorder:\\t\", list(first_tree.nodes(order=\"inorder\")))\n",
    "print(\"Postorder:\\t\", list(first_tree.nodes(order=\"postorder\")))"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "KUT_DbQpm_tB"
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   "source": [
    "### Recombination\n",
    "Simulating the history of a single locus is a very useful, but we are most often interesting in simulating the history of our sample across large genomic regions under the influence of recombination. The msprime API is specifically designed to make this common requirement both easy and efficient. To model genomic sequences under the influence of recombination we have two parameters to the `simulate()` function. The length parameter specifies the length of the simulated sequence, and is a floating point number, so recombination (and mutation) can occur at any location along the sequence (the units are arbitrary). If length is not supplied, it is assumed to be 1.0. The recombination_rate parameter specifies the rate of crossing over per unit of length per generation, and is zero by default. See the [API Documentation](https://msprime.readthedocs.io/en/stable/api.html#variable-recombination-rates) for a discussion of the precise recombination model used, and how to implement variable recombination rates.\n",
    "\n",
    "Here, we simulate the trees across over a 10kb region with a recombination rate of 2×10−8 per base per generation, with a diploid effective population size of 1000:"
   ]
  },
  {
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   "execution_count": 8,
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    "id": "N81SjbCbnM37",
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------------\n",
      "tree 0: interval = (0.0, 2070.5408305093974)\n"
     ]
    },
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     "text": [
      "--------------------\n",
      "tree 1: interval = (2070.5408305093974, 10000.0)\n"
     ]
    },
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   "source": [
    "simple_tree_seq = msprime.simulate(\n",
    "  sample_size=6, Ne=1000, length=1e4, recombination_rate=2e-8, random_seed=8)\n",
    "for tree in simple_tree_seq.trees():\n",
    "    print(\"-\" * 20)\n",
    "    print(\"tree {}: interval = {}\".format(tree.index, tree.interval))\n",
    "    display(SVG(tree.draw()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6W64MiMcnZrF"
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   "source": [
    "As before, we use the `trees()` method to iterate over the trees in the sequence. For each tree we print out its index (i.e. its position in the sequence) and the interval the tree covers (i.e. the genomic coordinates which all share precisely this tree) using the index and interval attributes. Thus, the first tree covers the first 2kb of sequence, the second tree covers the remaining 8kb.\n",
    "\n",
    "Note that this is a case where, although there has been a recombination event in the history of the samples, it has not changed the *topology* of the tree. Instead, it has changed the depth of one of the coalescent points: essentially, the subtree defined by node 10 has been pruned, and grafted back onto the same branch, a little lower down."
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zqm2YK_3nc2z"
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   "source": [
    "### Mutations\n",
    "Mutations are generated in msprime by throwing mutations down on the branches of trees at a particular rate. The mutations are generated under the infinite sites model, and so each mutation occurs at a unique (floating point) point position along the genomic interval occupied by a tree. The mutation rate for simulations is specified using the mutation_rate parameter of `simulate()`. For example, the following chunk simulates 50kb of nonrecombining sequence with a mutation rate of 1×10−8 per base per generation:"
   ]
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   "execution_count": 9,
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    "colab_type": "code",
    "id": "mKWFGnDqnfo3",
    "outputId": "0fddde7c-7725-4597-a859-cbf0ea5e2fd7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Num trees: 1\n",
      "Mutation 0 @ position 1556.54 over node 9\n",
      "Mutation 1 @ position 4485.17 over node 6\n",
      "Mutation 2 @ position 9788.56 over node 6\n",
      "Mutation 3 @ position 11759.03 over node 6\n",
      "Mutation 4 @ position 11949.32 over node 6\n",
      "Mutation 5 @ position 14321.77 over node 9\n",
      "Mutation 6 @ position 31454.99 over node 6\n",
      "Mutation 7 @ position 45125.69 over node 9\n",
      "Mutation 8 @ position 49709.68 over node 6\n"
     ]
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   ],
   "source": [
    "mut_tree_seq = msprime.simulate(\n",
    "  sample_size=6, Ne=1000, length=50e3, mutation_rate=1e-8, random_seed=30)\n",
    "print(\"Num trees:\", mut_tree_seq.num_trees)\n",
    "tree = mut_tree_seq.first()\n",
    "for site in tree.sites():\n",
    "    for mutation in site.mutations:\n",
    "        print(\"Mutation {} @ position {:.2f} over node {}\".format(\n",
    "        mutation.id, site.position, mutation.node))\n",
    "display(SVG(tree.draw()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vrwPN2TMoH2A"
   },
   "source": [
    "Mutations in the tree sequence lead to variable sites. By default, `msprime` creates mutations where the original (ancestral) state is `0` and the derived state is `1`. For example, in the above example, only samples 0 and 4 inherit the mutations *1* and *2* (which are at positions 4485.17 and 9788.56 along the sequence), meaning that they both have the variant `1` at those positions, whereas the other samples have the variant `0` at those positions.\n",
    "\n",
    "It should be clear that the mutations plus tree are enough to reconstruct the state of the variant sites for all samples. Thus the full tree sequence structure (which includes all mutations) encodes the full variant matrix. Often we do not need to actually deal with the variant matrix; nevertheless we will see later how to take a tree sequence and save the variant matrix as a VCF file, or extract the distribution of a specific variant into a numpy array for further analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lnEIoOjBQJGT"
   },
   "source": [
    "### Population structure in `msprime`\n",
    "`Msprime` provides a flexible and simple way to model past demographic events in arbitrary combinations. Here is an example, taken from the [`msprime` documentation](https://msprime.readthedocs.io/en/stable/tutorial.html#demography), describing the Gutenkunst et al. out-of-Africa model (2009). Figure 2B is a schematic of this model, reproduced below. See [Table 1](https://journals.plos.org/plosgenetics/article/figure?id=10.1371/journal.pgen.1000695.t001)  for the values used. Coalescent simulation moves from the present back into the past, so times are in units of generations ago, and we build the model with most recent events first.\n",
    "\n",
    "The following is figure 2b from the paper:\n",
    "\n",
    "<img style=\"width: 400px;\" src=\"images/gutenkunst_cropped_fig2b.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Qy99bUpPQal5"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "def out_of_africa():\n",
    "    # First we set out the maximum likelihood values of the various parameters\n",
    "    # given in Table 1.\n",
    "    N_A = 7300\n",
    "    N_B = 2100\n",
    " \n",
    "    N_AF = 12300\n",
    "    N_EU0 = 1000\n",
    "    N_AS0 = 510\n",
    "    \n",
    "    # Times are provided in years, so we convert into generations.\n",
    "    generation_time = 25\n",
    "    T_AF = 220e3 / generation_time\n",
    "    T_B = 140e3 / generation_time\n",
    "    T_EU_AS = 21.2e3 / generation_time\n",
    "    # We need to work out the starting (diploid) population sizes based on\n",
    "    # the growth rates provided for these two populations\n",
    "    r_EU = 0.004\n",
    "    r_AS = 0.0055\n",
    "    N_EU = N_EU0 / math.exp(-r_EU * T_EU_AS)\n",
    "    N_AS = N_AS0 / math.exp(-r_AS * T_EU_AS)\n",
    "    # Migration rates during the various epochs.\n",
    "    m_AF_B = 25e-5\n",
    "    m_AF_EU = 3e-5\n",
    "    m_AF_AS = 1.9e-5\n",
    "    m_EU_AS = 9.6e-5\n",
    "    # Population IDs correspond to their indexes in the population\n",
    "    # configuration array. Therefore, we have 0=YRI, 1=CEU and 2=CHB\n",
    "    # initially.\n",
    "    model = dict(\n",
    "        #we simulate two chromosomes from each population\n",
    "        population_configurations = [\n",
    "            msprime.PopulationConfiguration(\n",
    "                sample_size=2, initial_size=N_AF),\n",
    "            msprime.PopulationConfiguration(\n",
    "                sample_size=2, initial_size=N_EU, growth_rate=r_EU),\n",
    "            msprime.PopulationConfiguration(\n",
    "                sample_size=2, initial_size=N_AS, growth_rate=r_AS)\n",
    "        ],\n",
    "        migration_matrix = [\n",
    "            [      0, m_AF_EU, m_AF_AS],\n",
    "            [m_AF_EU,       0, m_EU_AS],\n",
    "            [m_AF_AS, m_EU_AS,       0],\n",
    "        ],\n",
    "        demographic_events = [\n",
    "            # CEU and CHB merge into B with rate changes at T_EU_AS\n",
    "            msprime.MassMigration(\n",
    "                time=T_EU_AS, source=2, destination=1, proportion=1.0),\n",
    "            msprime.MigrationRateChange(time=T_EU_AS, rate=0),\n",
    "            msprime.MigrationRateChange(\n",
    "                time=T_EU_AS, rate=m_AF_B, matrix_index=(0, 1)),\n",
    "            msprime.MigrationRateChange(\n",
    "                time=T_EU_AS, rate=m_AF_B, matrix_index=(1, 0)),\n",
    "            msprime.PopulationParametersChange(\n",
    "                time=T_EU_AS, initial_size=N_B, growth_rate=0, population_id=1),\n",
    "            # Population B merges into YRI at T_B\n",
    "            msprime.MassMigration(\n",
    "                time=T_B, source=1, destination=0, proportion=1.0),\n",
    "            # Size changes to N_A at T_AF\n",
    "            msprime.PopulationParametersChange(\n",
    "                time=T_AF, initial_size=N_A, population_id=0)\n",
    "        ]\n",
    "    )\n",
    "    # Use the demography debugger to print out the demographic history\n",
    "    # that we have just described.\n",
    "    dd = msprime.DemographyDebugger(\n",
    "        population_configurations=model[\"population_configurations\"],\n",
    "        migration_matrix=model[\"migration_matrix\"],\n",
    "        demographic_events=model[\"demographic_events\"])\n",
    "    dd.print_history()\n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HjAXzo3sUzcW"
   },
   "source": [
    "The DemographyDebugger provides a method to debug the history that you have described so that you can be sure that the migration rates, population sizes and growth rates are all as you intend during each epoch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 799
    },
    "colab_type": "code",
    "id": "76381zueUSCS",
    "outputId": "caa6d14a-7919-4e0b-8ea5-f28c7a88a6c4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=============================\n",
      "Epoch: 0 -- 848.0 generations\n",
      "=============================\n",
      "     start     end      growth_rate |     0        1        2    \n",
      "   -------- --------       -------- | -------- -------- -------- \n",
      "0 |1.23e+04 1.23e+04              0 |     0      3e-05   1.9e-05 \n",
      "1 |2.97e+04   1e+03           0.004 |   3e-05      0     9.6e-05 \n",
      "2 |5.41e+04    510           0.0055 |  1.9e-05  9.6e-05     0    \n",
      "\n",
      "Events @ generation 848.0\n",
      "   - Mass migration: lineages move from 2 to 1 with probability 1.0\n",
      "   - Migration rate change to 0 everywhere\n",
      "   - Migration rate change for (0, 1) to 0.00025\n",
      "   - Migration rate change for (1, 0) to 0.00025\n",
      "   - Population parameter change for 1: initial_size -> 2100 growth_rate -> 0 \n",
      "==================================\n",
      "Epoch: 848.0 -- 5600.0 generations\n",
      "==================================\n",
      "     start     end      growth_rate |     0        1        2    \n",
      "   -------- --------       -------- | -------- -------- -------- \n",
      "0 |1.23e+04 1.23e+04              0 |     0     0.00025     0    \n",
      "1 | 2.1e+03  2.1e+03              0 |  0.00025     0        0    \n",
      "2 |   510   2.27e-09         0.0055 |     0        0        0    \n",
      "\n",
      "Events @ generation 5600.0\n",
      "   - Mass migration: lineages move from 1 to 0 with probability 1.0\n",
      "===================================\n",
      "Epoch: 5600.0 -- 8800.0 generations\n",
      "===================================\n",
      "     start     end      growth_rate |     0        1        2    \n",
      "   -------- --------       -------- | -------- -------- -------- \n",
      "0 |1.23e+04 1.23e+04              0 |     0     0.00025     0    \n",
      "1 | 2.1e+03  2.1e+03              0 |  0.00025     0        0    \n",
      "2 |2.27e-09 5.17e-17         0.0055 |     0        0        0    \n",
      "\n",
      "Events @ generation 8800.0\n",
      "   - Population parameter change for 0: initial_size -> 7300 \n",
      "================================\n",
      "Epoch: 8800.0 -- inf generations\n",
      "================================\n",
      "     start     end      growth_rate |     0        1        2    \n",
      "   -------- --------       -------- | -------- -------- -------- \n",
      "0 | 7.3e+03  7.3e+03              0 |     0     0.00025     0    \n",
      "1 | 2.1e+03  2.1e+03              0 |  0.00025     0        0    \n",
      "2 |5.17e-17     0            0.0055 |     0        0        0    \n",
      "\n"
     ]
    }
   ],
   "source": [
    "model = out_of_africa()\n",
    "OOA_tree_seq = msprime.simulate(**model,\n",
    "                              length=5e3, \n",
    "                              recombination_rate=1e-8, \n",
    "                              random_seed=11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qxk2Z7rQYQ6P"
   },
   "source": [
    "Let's look at the output from running the simulation with the following parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1241
    },
    "colab_type": "code",
    "id": "Oek_DGeDVhh_",
    "outputId": "670455c1-9840-4161-856c-74972e1463ef"
   },
   "outputs": [
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   "source": [
    "for tree in OOA_tree_seq.trees():\n",
    "    display(SVG(tree.draw(mutation_labels={},\n",
    "        node_labels={0:\"AFR1\",1:\"AFR2\", 2:\"EUR1\",3:\"EUR2\",4:\"ASN1\",5:\"ASN2\"},\n",
    "        width=500)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "95z7C7h1odgn"
   },
   "source": [
    "### Saving files\n",
    "Let's throw some mutations onto this genealogy, then save the resulting tree sequence file. We can also save the variation data into a VCF file, which we will use when demonstrating `tsinfer` in section 4. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3zNTYcCgodC7"
   },
   "outputs": [],
   "source": [
    "# Add mutations to an existing tree sequence\n",
    "OOA_with_mutations = msprime.mutate(OOA_tree_seq, rate=1e-6, random_seed=1, keep=True)\n",
    "\n",
    "# Save the tree sequence file (recommended suffix is .trees)\n",
    "OOA_with_mutations.dump(\"data/OOA.trees\")\n",
    "\n",
    "# Save as vcf\n",
    "with open(\"data/3pop_simulation.vcf\", \"w\") as vcf_file:\n",
    "    OOA_with_mutations.write_vcf(vcf_file, ploidy=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward Simulations with `SLiM`\n",
    "Although msprime is very effective for producing simulations under the coalescent, there are many evolutionary processes that are hard to simulate using coalescent methodology (e.g. models with natural selection, complex demography, or complex life histories). Recently a fast forwards simulator called [SLiM](https://messerlab.org/slim/) (Selection on Linked Mutations) has been developed that can save tree sequences as output.\n",
    "\n",
    "\n",
    "---\n",
    "\n",
    "SLiM is fast yet extremely flexible. Simulations are specified using a simple R-like language called `Eidos`: there is a GUI (Mac OS X only) which can help considerably in debugging and visualising simulations. However, for portability, here we simply save the Eidos commands into a temporary file and give that file to the `slim` executable in Python. Using python to do this allows us to manipulate the tree sequence output after the simulation is done. \n",
    "\n",
    "<aside>By default, SLiM does not save tree sequences: this functionality is activated by calling `initializeTreeSeq();` when initializing the simulation</aside>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A simple model\n",
    "\n",
    "The Eidos script embedded into Python below is taken from recipe 16.3 of the  [extensive SLiM manual](http://benhaller.com/slim/SLiM_Manual.pdf), with a few additional comments (`//double slashes distinguish comments in Eidos`). We will not go into many details of the Eidos language: it is well covered in the manual. Nevertheless, for anyone familiar with genetic simulations in R or Python, it should be reasonably obvious what is going on in the eidos_script defined below. By default, SLiM runs a standard Wright-Fisher with panmixis and discrete generations. Top-level blocks delimited by `{}` are each run at a different generation (or range of generations). As in C, code needs to be semicolon-terminated.\n",
    "\n",
    "The script simulates genomes with a background level of mildly deleterious mutations, and introduces a single advantageous mutation after a certain number of burn in generations, tracking it until it is lost (in which case we restart the simulation from when it was introduced) or is fixed (in which case we save the output to a tree sequence). Although it is fast as forward simulations go, it is still much slower than coalescent simulators, especially for large population sizes (e.g. here we only simulate a population of 500 diploids)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output from SLiM follows:\n",
      "SLiM> // Initial random seed:\n",
      "SLiM> 123\n",
      "SLiM> \n",
      "SLiM> // RunInitializeCallbacks():\n",
      "SLiM> initializeTreeSeq();\n",
      "SLiM> initializeMutationRate(1e-08);\n",
      "SLiM> initializeMutationType(2, 0.5, \"g\", -0.01, 1);\n",
      "SLiM> initializeMutationType(3, 1, \"f\", 0.05);\n",
      "SLiM> initializeGenomicElementType(1, m2, 1);\n",
      "SLiM> initializeGenomicElement(g1, 0, 99999);\n",
      "SLiM> initializeRecombinationRate(1e-07);\n",
      "SLiM> \n",
      "SLiM> // Starting run at generation <start>:\n",
      "SLiM> 1 \n",
      "SLiM> \n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: lost - restarting\n",
      "SLiM> 123: fixed and saved to 'data/slim_fixed.trees'\n"
     ]
    }
   ],
   "source": [
    "import subprocess\n",
    "import string\n",
    "import tempfile\n",
    "\n",
    "# NB: use string.Template to pass parameters from Python into the Eidos script\n",
    "# These python-substituted parameters are written in CAPS\n",
    "eidos_script = string.Template(r\"\"\"\n",
    "initialize() {\n",
    "    initializeTreeSeq();\n",
    "    initializeMutationRate($MU_DEL);\n",
    "    initializeMutationType(\"m2\", $H_DEL, \"g\", $S_DEL, 1.0);  // deleterious\n",
    "    initializeMutationType(\"m3\", $H_ADV, \"f\", $S_ADV);       // advantageous\n",
    "    // only deleterious mutations (type m2) should be introduced automatically\n",
    "    initializeGenomicElementType(\"g1\", m2, 1.0);\n",
    "    initializeGenomicElement(g1, 0, $LENGTH);\n",
    "    initializeRecombinationRate($RHO);\n",
    "}\n",
    "\n",
    "1 { // in the first generation, add a standard population of $POPSIZE diploids\n",
    "    defineConstant(\"simID\", getSeed());\n",
    "    sim.addSubpop(\"p1\", $POPSIZE);\n",
    "}\n",
    "\n",
    "$BURN_IN_GENS late() { // after $BURN_IN_GENS introduce an advantageous mutation\n",
    "    target = sample(p1.genomes, 1);\n",
    "    target.addNewDrawnMutation(m3, $SELECTED_VARIANT_POS);\n",
    "    sim.treeSeqOutput(\"data/slim_init.trees\"); // save in case restart needed\n",
    "}\n",
    "\n",
    "$BURN_IN_GENS:$MAX_GENS late() { // check every subsequent generation for fixation or loss\n",
    "    if (sim.countOfMutationsOfType(m3) == 0) {\n",
    "        if (sum(sim.substitutions.mutationType == m3) == 1) {\n",
    "            fn = \"data/slim_fixed.trees\";\n",
    "            sim.treeSeqOutput(fn);\n",
    "            catn(simID + \": fixed and saved to '\" + fn + \"'\");\n",
    "            sim.simulationFinished();\n",
    "        } else {\n",
    "            catn(simID + \": lost - restarting\");\n",
    "            sim.readFromPopulationFile(\"data/slim_init.trees\");\n",
    "            setSeed(getSeed() + 1); // try again with a different seed\n",
    "        }\n",
    "    }\n",
    "}\"\"\")\n",
    "random_seed = 123\n",
    "sim_script = eidos_script.substitute(\n",
    "    H_DEL = 0.5,   # deleterious dominance coeffficient,\n",
    "    H_ADV = 1.0,   # advantageous dominance_coef\n",
    "    S_DEL = -0.01, # deleterious selection_coefficient,\n",
    "    S_ADV = 0.05,  # advantageous selection_coefficient,\n",
    "    MU_DEL = 1e-8, # per base per generation mutation rate for deleterious muts\n",
    "    RHO= 1e-7,     # recombination rate,\n",
    "    POPSIZE = 500,\n",
    "    LENGTH = 99999, # chromosome length\n",
    "    SELECTED_VARIANT_POS = 50000, # chromosome length\n",
    "    BURN_IN_GENS = 1000,\n",
    "    MAX_GENS = 100000\n",
    "    )\n",
    "with tempfile.NamedTemporaryFile(mode='w+t') as script:\n",
    "    script.write(sim_script)\n",
    "    script.flush()\n",
    "    process = subprocess.Popen(['slim','-seed',str(random_seed), script.name],\n",
    "        stdout=subprocess.PIPE, stderr=subprocess.STDOUT, \n",
    "        universal_newlines=True)\n",
    "    print(\"Output from SLiM follows:\")\n",
    "    for line in iter(process.stdout.readline, ''):\n",
    "        print(\"SLiM> \" + line, end=\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding neutral mutations\n",
    "The SLiM simulation should have resulted in population with a fixed advantageous mutation, and generated a tree sequence file for further use. The main reason that the simulation is relatively fast is that we have not had to track neutral mutations during the run. Since (by definition), neutral mutations do not affect the simulation, we can add any number of them after the simulation has finished, as we did with the out of Africa simulation in msprime, then dump the tree sequence out to a `.trees` file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "ename": "FileFormatError",
     "evalue": "No such file or directory",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mFileFormatError\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/msprime/trees.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(path)\u001b[0m\n\u001b[1;32m   1194\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1195\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mTreeSequence\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1196\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0m_msprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mVersionTooNewError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/msprime/trees.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(cls, path)\u001b[0m\n\u001b[1;32m   1740\u001b[0m         \u001b[0mts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_msprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTreeSequence\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1741\u001b[0;31m         \u001b[0mts\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1742\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mTreeSequence\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileFormatError\u001b[0m: No such file or directory",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mOSError\u001b[0m                                   Traceback (most recent call last)",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/msprime/formats.py\u001b[0m in \u001b[0;36mraise_hdf5_format_error\u001b[0;34m(filename, original_exception)\u001b[0m\n\u001b[1;32m    250\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 251\u001b[0;31m         \u001b[0;32mwith\u001b[0m \u001b[0mh5py\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfilename\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"r\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mroot\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    252\u001b[0m             \u001b[0mversion\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mroot\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattrs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"format_version\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/h5py/_hl/files.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, name, mode, driver, libver, userblock_size, swmr, **kwds)\u001b[0m\n\u001b[1;32m    311\u001b[0m                 \u001b[0mfapl\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_fapl\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdriver\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlibver\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 312\u001b[0;31m                 \u001b[0mfid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmake_fid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0muserblock_size\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfapl\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mswmr\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mswmr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    313\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/h5py/_hl/files.py\u001b[0m in \u001b[0;36mmake_fid\u001b[0;34m(name, mode, userblock_size, fapl, fcpl, swmr)\u001b[0m\n\u001b[1;32m    141\u001b[0m             \u001b[0mflags\u001b[0m \u001b[0;34m|=\u001b[0m \u001b[0mh5f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mACC_SWMR_READ\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 142\u001b[0;31m         \u001b[0mfid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mh5f\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfapl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfapl\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    143\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mmode\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'r+'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mh5py/_objects.pyx\u001b[0m in \u001b[0;36mh5py._objects.with_phil.wrapper\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mh5py/_objects.pyx\u001b[0m in \u001b[0;36mh5py._objects.with_phil.wrapper\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mh5py/h5f.pyx\u001b[0m in \u001b[0;36mh5py.h5f.open\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mOSError\u001b[0m: Unable to open file (unable to open file: name = 'data/slim_fixed.trees', errno = 2, error message = 'No such file or directory', flags = 0, o_flags = 0)",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mFileFormatError\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-52-000716cbd1e5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;31m# NB for efficiency, we could .simplify() this tree seq, as in the SLiM manual\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mts_fwd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpyslim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"data/slim_fixed.trees\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Number of (selected) mutations at end of forward simulation:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mts_fwd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnum_mutations\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mts_fwd_mut\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmsprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmutate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mts_fwd\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrate\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1e-7\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrandom_seed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkeep\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/pyslim/slim_tree_sequence.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(path)\u001b[0m\n\u001b[1;32m     19\u001b[0m     \u001b[0;34m:\u001b[0m\u001b[0mparam\u001b[0m \u001b[0mstring\u001b[0m \u001b[0mpath\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mThe\u001b[0m \u001b[0mpath\u001b[0m \u001b[0mto\u001b[0m \u001b[0ma\u001b[0m \u001b[0;34m.\u001b[0m\u001b[0mtrees\u001b[0m \u001b[0mfile\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m     '''\n\u001b[0;32m---> 21\u001b[0;31m     \u001b[0mts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSlimTreeSequence\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     22\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mts\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/pyslim/slim_tree_sequence.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(cls, path)\u001b[0m\n\u001b[1;32m    124\u001b[0m         '''\n\u001b[1;32m    125\u001b[0m         \u001b[0;31m# roundabout way to load just the tables\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 126\u001b[0;31m         \u001b[0mts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmsprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mload\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    127\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    128\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/msprime/trees.py\u001b[0m in \u001b[0;36mload\u001b[0;34m(path)\u001b[0m\n\u001b[1;32m   1199\u001b[0m         \u001b[0;32mraise\u001b[0m \u001b[0mexceptions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mVersionTooOldError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1200\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0m_msprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileFormatError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1201\u001b[0;31m         \u001b[0mformats\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mraise_hdf5_format_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpath\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1202\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1203\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/site-packages/msprime/formats.py\u001b[0m in \u001b[0;36mraise_hdf5_format_error\u001b[0;34m(filename, original_exception)\u001b[0m\n\u001b[1;32m    255\u001b[0m                 \"to upgrade this file to the latest version\".format(version))\n\u001b[1;32m    256\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mIOError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mOSError\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 257\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mexceptions\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFileFormatError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moriginal_exception\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    258\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    259\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mFileFormatError\u001b[0m: No such file or directory"
     ]
    }
   ],
   "source": [
    "import pyslim # To load ts files from SLiM use pyslim, not `msprime` or `tskit`\n",
    "\n",
    "# NB for efficiency, we could .simplify() this tree seq, as in the SLiM manual\n",
    "ts_fwd = pyslim.load(\"data/slim_fixed.trees\")\n",
    "print(\"Number of (selected) mutations at end of forward simulation:\", ts_fwd.num_mutations)\n",
    "ts_fwd_mut = msprime.mutate(ts_fwd, rate=1e-7, random_seed=1, keep=True)\n",
    "print(\"Number of mutations after adding neutral variation:\", ts_fwd_mut.num_mutations)\n",
    "ts_fwd_mut.dump(\"data/slim_fixed_with_neutral.trees\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that an important property of forwards time trees is that not all lineages are guaranteed to have coalesced, so they may contain **multiple roots**. Thus more than one tree-like structure may exist for each \"tree\" in the tree sequence, as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
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   "source": [
    "ts_sub = ts_fwd.simplify(ts_fwd.samples()[:10])\n",
    "for tree in ts_sub.trees():\n",
    "    display(SVG(tree.draw()))\n",
    "    if tree.index == 1:\n",
    "        break # only draw the first 2 \"trees\""
   ]
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   "source": [
    "<a id='stats'></a>\n",
    "# 3. Calculations on Tree Sequences\n",
    "The tree sequence format can be seen as an \"evolutionary encoding\" of DNA sequence data: although it is often not needed, the raw sequence (or variant) data can be easily extracted from a tree sequence. The tree sequence also allows efficient calculation of statistics of interest such as pairwise diversity statistics and recombination maps. "
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   "source": [
    "### Extracting sequence data or variants\n",
    "We might be interested in accessing the sequence data that results from simulations directly. The most efficient way to do this is by using the `TreeSequence.variants()` method, which returns an iterator over all the Variant objects arising from the trees and mutations. Each variant contains a reference to the site object, as well as the alleles and the observed sequences for each sample in the genotypes field. As a demonstration, we do this for the simple mutated tree sequence we calculated previously, that only contains one tree."
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    "outputId": "af8446a4-d858-4a38-a655-ca5d9168a2c7"
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   "outputs": [
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     "text": [
      "Variant\t0\t1556.5376146696508\t('0', '1')\t[0 1 1 1 0 1]\n",
      "Variant\t1\t4485.169367399067\t('0', '1')\t[1 0 0 0 1 0]\n",
      "Variant\t2\t9788.562881294638\t('0', '1')\t[1 0 0 0 1 0]\n",
      "Variant\t3\t11759.025033097714\t('0', '1')\t[1 0 0 0 1 0]\n",
      "Variant\t4\t11949.318321421742\t('0', '1')\t[1 0 0 0 1 0]\n",
      "Variant\t5\t14321.766176726669\t('0', '1')\t[0 1 1 1 0 1]\n",
      "Variant\t6\t31454.991386272013\t('0', '1')\t[1 0 0 0 1 0]\n",
      "Variant\t7\t45125.69225626066\t('0', '1')\t[0 1 1 1 0 1]\n",
      "Variant\t8\t49709.6843784675\t('0', '1')\t[1 0 0 0 1 0]\n"
     ]
    }
   ],
   "source": [
    "display(SVG(mut_tree_seq.first().draw()))\n",
    "for variant in mut_tree_seq.variants():\n",
    "    print(\n",
    "        \"Variant\", variant.site.id, variant.site.position,\n",
    "        variant.alleles, variant.genotypes, sep=\"\\t\")"
   ]
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   "source": [
    "Here we have looped through each variant, printing out the observed state of each sample as an array of zeros and ones, along with the index and position of the corresponding mutation. In this example, the alleles are always '0' (the ancestral state) and '1' (the derived state), because we are simulating with the infinite sites mutation model, in which each mutation occurs at a unique position in the genome. More complex models are possible, however.\n",
    "\n",
    "This way of working with the sequence data is quite efficient because we do not need to keep the entire genotype matrix in memory at once. However, if we do want the full genotype matrix it is simple to obtain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mxjlAsjfZr3s"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 0, 1],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [0, 1, 1, 1, 0, 1],\n",
       "       [1, 0, 0, 0, 1, 0],\n",
       "       [0, 1, 1, 1, 0, 1],\n",
       "       [1, 0, 0, 0, 1, 0]], dtype=uint8)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = mut_tree_seq.genotype_matrix()\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UczpeoDMq_jU"
   },
   "source": [
    "## Integration with `scikit-allel`\n",
    "\n",
    "Because tskit integrates tightly with numpy, we can export data into a number of upstream toolkits very efficiently. In particular, we can export data into [scikit allel](scikit-allel.readthedocs.io/en/latest/) very easily:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6jprOcpvp63c"
   },
   "outputs": [],
   "source": [
    "# Run a simple simulation\n",
    "ts = msprime.simulate(\n",
    "    sample_size=1000, Ne=10000, length=1e6, mutation_rate=1e-8,\n",
    "    recombination_rate=1e-8,random_seed=10)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3076, 1000)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.num_sites, ts.num_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "TFTFHW5v5Bxl",
    "outputId": "01ebc8cd-e428-4ef7-c0db-b29ec8b008a7",
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3076 1000\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div class=\"allel allel-DisplayAs2D\"><span>&lt;HaplotypeArray shape=(3076, 1000) dtype=uint8&gt;</span><table><thead><tr><th></th><th style=\"text-align: center\">0</th><th style=\"text-align: center\">1</th><th style=\"text-align: center\">2</th><th style=\"text-align: center\">3</th><th style=\"text-align: center\">4</th><th style=\"text-align: center\">...</th><th style=\"text-align: center\">995</th><th style=\"text-align: center\">996</th><th style=\"text-align: center\">997</th><th style=\"text-align: center\">998</th><th style=\"text-align: center\">999</th></tr></thead><tbody><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">0</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">1</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">1</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">2</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">...</th><td style=\"text-align: center\" colspan=\"12\">...</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">3073</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">3074</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr><tr><th style=\"text-align: center; background-color: white; border-right: 1px solid black; \">3075</th><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">...</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td><td style=\"text-align: center\">0</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "<HaplotypeArray shape=(3076, 1000) dtype=uint8>\n",
       "0 0 0 0 0 ... 0 0 0 0 0\n",
       "0 0 0 0 0 ... 1 0 0 0 0\n",
       "0 0 0 0 0 ... 0 0 0 0 0\n",
       "...\n",
       "0 0 0 0 0 ... 0 0 0 0 0\n",
       "0 0 0 0 0 ... 0 0 0 0 0\n",
       "0 0 0 0 0 ... 0 0 0 0 0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import allel\n",
    "\n",
    "# Export the genotype data to allel. Unfortunately there's a slight mismatch in the \n",
    "# terminology here where genotypes and haplotypes mean different things in the two\n",
    "# libraries.\n",
    "h = allel.HaplotypeArray(ts.genotype_matrix())\n",
    "print(h.n_variants, h.n_haplotypes)\n",
    "h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sckit.allel has a wide-ranging and efficient suite of tools for working with genotype data, so should provide anything that's needed. For example, we can compute pairwise diversity, $\\pi$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "W9Do3oeHqska",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02177978, 0.34577778, 0.002     , ..., 0.003996  , 0.003996  ,\n",
       "       0.002     ])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ac = h.count_alleles()\n",
    "v = allel.stats.mean_pairwise_difference(ac)\n",
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tskit also supports computing statistics directly from the trees, and can be much faster than alternatives for large tree sequences, especially if (as we shall soon see) the statistic can be calculated incrementally. Only a handful of statistics are currently supported, but many will be implemented soon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(404.21165765765767, 404.2116576576576)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.pairwise_diversity(), np.sum(v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cx631TSWkvQR"
   },
   "source": [
    "## LD Plot\n",
    "The msprime API provides methods to efficiently calculate population genetics statistics. For example, the LdCalculator class allows us to compute pairwise linkage disequilibrium coefficients. Here we use the get_r2_matrix() method to easily make an LD plot using matplotlib. (Thanks to the excellent scikit-allel for the basic plotting code used here.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iUj2SKlakshk"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "ts = msprime.simulate(100, recombination_rate=10, mutation_rate=20, random_seed=1)\n",
    "ld_calc = msprime.LdCalculator(ts)\n",
    "A = ld_calc.r2_matrix()\n",
    "# Now plot this matrix.\n",
    "x = A.shape[0] / plt.rcParams['figure.dpi']\n",
    "x = max(x, plt.rcParams['figure.figsize'][0])\n",
    "fig, ax = plt.subplots(figsize=(x, x))\n",
    "fig.tight_layout(pad=0)\n",
    "im = ax.imshow(A, interpolation=\"none\", vmin=0, vmax=1, cmap=\"Blues\")\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "for s in 'top', 'bottom', 'left', 'right':\n",
    "    ax.spines[s].set_visible(False)\n",
    "plt.gcf().colorbar(im, shrink=.5, pad=0);     \n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uAYu1lw1UwQM"
   },
   "source": [
    "## Very large datasets\n",
    "\n",
    "One of the big advantages of msprime/tskit is that we can simulate and process genetic data on a very large scale. For example, here is a simulation of 100K human-like 10Mb chromosomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 6.59 s, sys: 172 ms, total: 6.76 s\n",
      "Wall time: 6.88 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "ts = msprime.simulate(\n",
    "    sample_size=10**5, length=1e7, recombination_rate=1e-8, Ne=10**4, random_seed=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45287"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.num_trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lJiA1DtyUt8X"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size = 16.711803436279297MiB\n"
     ]
    }
   ],
   "source": [
    "# Write the tree sequence to file.\n",
    "ts.dump(\"data/large-ts-no-mutations.trees\")\n",
    "\n",
    "# Get the size\n",
    "import os\n",
    "print(\"File size = {}MiB\".format(os.path.getsize(\"data/large-ts-no-mutations.trees\") / 2**20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ce0NEqUPaejX"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 31 ms, sys: 24 ms, total: 54.9 ms\n",
      "Wall time: 54.4 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Loading is fast\n",
    "ts = msprime.load(\"data/large-ts-no-mutations.trees\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000000.0 10000000.0\n",
      "CPU times: user 197 ms, sys: 6.75 ms, total: 204 ms\n",
      "Wall time: 209 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# So is iterating over all trees\n",
    "total = 0  \n",
    "for tree in ts.trees():\n",
    "    total += tree.interval[1] - tree.interval[0] # Just to do *something* in the loop\n",
    "\n",
    "print(total, ts.sequence_length)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 16.2 s, sys: 2.56 s, total: 18.8 s\n",
      "Wall time: 20.7 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# Insert a ridiculous number of mutations\n",
    "mutated_ts = msprime.mutate(ts, rate=1e-6, random_seed=42) # deliberately high mutation rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We just created 4,844,253 variant sites!\n"
     ]
    }
   ],
   "source": [
    "print(\"We just created {:,} variant sites!\".format(mutated_ts.num_sites))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tree sequence size = 192.27MiB\n"
     ]
    }
   ],
   "source": [
    "mutated_ts.dump(\"data/large-ts-mutations.trees\")\n",
    "\n",
    "print(\"Tree sequence size = {:.2f}MiB\".format(os.path.getsize(\"data/large-ts-mutations.trees\") / 2**20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Genotype matrix size: 451.16GiB\n"
     ]
    }
   ],
   "source": [
    "print(\"Genotype matrix size: {:.2f}GiB\".format(\n",
    "    mutated_ts.num_sites * mutated_ts.num_samples / 2**30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 98.1 ms, sys: 4.04 ms, total: 102 ms\n",
      "Wall time: 102 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "400360.76293350634"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "mutated_ts.pairwise_diversity()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incremental calculations\n",
    "\n",
    "The tree sequence data structure is efficient because it captures the shared structure between adjacent trees. Understanding how trees change as we move across the sequence is also critical for defining efficient algorithms.\n",
    "\n",
    "Consider the problem of computing the total branch length. In a single tree, all we can do is to iterate over all the nodes and sum the length of each branch. If we repeat this for every tree in the sequence, this ends up being a slow operation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[571111.36722641 570906.04178704 570929.28798328 570929.26852078\n",
      " 570842.83922985]\n",
      "CPU times: user 1min 10s, sys: 910 ms, total: 1min 11s\n",
      "Wall time: 1min 13s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "total_branch_length = np.zeros(ts.num_trees)\n",
    "for tree in ts.trees():\n",
    "    total_branch_length[tree.index] = tree.total_branch_length\n",
    "    if tree.index == 50:\n",
    "        break\n",
    "\n",
    "print(total_branch_length[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here it takes tens of seconds to compute the total branch length for the first 50 trees --- these are large trees with 200K nodes! Since there are about 1000 times more trees than this, it will take a long time to compute the total branch length for all trees.\n",
    "\n",
    "However, we can do much better than this. As we noted in the introductory section, the [`edge_diffs()`](https://msprime.readthedocs.io/en/stable/api.html#msprime.TreeSequence.edge_diffs) method returns an iterator over the edges that are inserted and removed for each tree in turn. Trees don't change very much as we move across the tree sequence; in fact, for coalescent trees, we know that there are at most **four** edges that are removed and inserted at each tree transition. By taking this information into account, we can compute the total branch length for all trees in a tiny fraction of the time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[571111.36722641 570906.04178704 570929.28798328 570929.26852078\n",
      " 570842.83922985]\n",
      "CPU times: user 487 ms, sys: 23.9 ms, total: 511 ms\n",
      "Wall time: 510 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "current = 0\n",
    "total_branch_length = np.zeros(ts.num_trees)\n",
    "node_time = ts.tables.nodes.time\n",
    "for j, (_, edges_out, edges_in) in enumerate(ts.edge_diffs()):\n",
    "    for e in edges_out:\n",
    "        current -= node_time[e.parent] - node_time[e.child]\n",
    "    for e in edges_in:\n",
    "        current += node_time[e.parent] - node_time[e.child]\n",
    "    total_branch_length[j] = current\n",
    "\n",
    "print(total_branch_length[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "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.plot(total_branch_length);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tables API\n",
    "\n",
    "The tables API provides a very efficient way of getting at the underlying numerical data representing the tree sequence. Suppose we wished to plot the distribution of the length of the edges in the simulation (an edge is a (left, right, parent, child) tuple describing a branch in the trees spanning the interval from left to right).\n",
    "\n",
    "See the [documentation](https://msprime.readthedocs.io/en/stable/api.html#tables-api) on this API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 38.6 ms, sys: 3.84 ms, total: 42.4 ms\n",
      "Wall time: 41.2 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "tables = mutated_ts.tables\n",
    "edge_length = tables.edges.right - tables.edges.left"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "scrolled": true
   },
   "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.hist(edge_length);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use this to access information about the sites and mutations (which are in their own respective tables --- see the [data model](https://msprime.readthedocs.io/en/stable/interchange.html#sec-data-model) for details). Here, for example, we get an array of the time of each mutation (or, more accurately, the time of the node over which each mutation occured), find how many of these are old and plot their age distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of mutations older than 10% of the oldest time =  83443\n"
     ]
    }
   ],
   "source": [
    "oldest_time = np.max(tables.nodes.time)\n",
    "mutation_time = tables.nodes.time[tables.mutations.node]\n",
    "index = mutation_time > (oldest_time / 10)\n",
    "print(\"number of mutations older than 10% of the oldest time = \", np.sum(index))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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.hist(mutation_time[index]);"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "ts_workshop.ipynb",
   "provenance": [],
   "toc_visible": true,
   "version": "0.3.2"
  },
  "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}