{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Project 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For my analysis, I kept it simple, and decided to dive further into the given alignment data. \n",
    "Specifically, I analyzed four sets of aligned sequences, in decreasing order of distance to the \n",
    "concensus sequence.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: biopython in c:\\users\\samue\\anaconda3\\lib\\site-packages (1.76)\n",
      "Requirement already satisfied: numpy in c:\\users\\samue\\anaconda3\\lib\\site-packages (from biopython) (1.18.1)\n"
     ]
    }
   ],
   "source": [
    "!pip install biopython\n",
    "import numpy as np\n",
    "from Bio.Phylo.TreeConstruction import DistanceMatrix\n",
    "from Bio.Phylo.TreeConstruction import DistanceTreeConstructor\n",
    "from Bio import Phylo\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the given data from the position table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "position_table = pd.read_csv('../../data/position_table.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
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       "    </tr>\n",
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       "      <th>freq</th>\n",
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       "<p>4 rows × 3820 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             seqid S_1_1 S_1_2 S_1_3 S_2_1 S_2_2 S_2_3 S_3_1 S_3_2 S_3_3  ...  \\\n",
       "count          677   677   677   677   677   677   677   677   677   677  ...   \n",
       "unique         677     1     1     1     1     1     1     1     1     1  ...   \n",
       "top     MT019531.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "freq             1   677   677   677   677   677   677   677   677   677  ...   \n",
       "\n",
       "       S_1270_3 S_1271_1 S_1271_2 S_1271_3 S_1272_1 S_1272_2 S_1272_3  \\\n",
       "count       677      677      677      677      677      677      677   \n",
       "unique        1        1        1        1        1        1        1   \n",
       "top           A        C        A        T        T        A        C   \n",
       "freq        677      677      677      677      677      677      677   \n",
       "\n",
       "       S_1273_1 S_1273_2 S_1273_3  \n",
       "count       677      677      677  \n",
       "unique        1        1        1  \n",
       "top           A        C        A  \n",
       "freq        677      677      677  \n",
       "\n",
       "[4 rows x 3820 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = position_table.describe()\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
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       "      <td>C</td>\n",
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       "    <tr>\n",
       "      <th>676</th>\n",
       "      <td>MT334561.1</td>\n",
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       "      <td>T</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>677 rows × 3820 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          seqid S_1_1 S_1_2 S_1_3 S_2_1 S_2_2 S_2_3 S_3_1 S_3_2 S_3_3  ...  \\\n",
       "0    MT007544.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "1    MT019529.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "2    MT019530.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "3    MT019531.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "4    MT019532.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "..          ...   ...   ...   ...   ...   ...   ...   ...   ...   ...  ...   \n",
       "672  MT334544.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "673  MT334546.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "674  MT334547.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "675  MT334557.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "676  MT334561.1     A     T     G     T     T     T     G     T     T  ...   \n",
       "\n",
       "    S_1270_3 S_1271_1 S_1271_2 S_1271_3 S_1272_1 S_1272_2 S_1272_3 S_1273_1  \\\n",
       "0          A        C        A        T        T        A        C        A   \n",
       "1          A        C        A        T        T        A        C        A   \n",
       "2          A        C        A        T        T        A        C        A   \n",
       "3          A        C        A        T        T        A        C        A   \n",
       "4          A        C        A        T        T        A        C        A   \n",
       "..       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "672        A        C        A        T        T        A        C        A   \n",
       "673        A        C        A        T        T        A        C        A   \n",
       "674        A        C        A        T        T        A        C        A   \n",
       "675        A        C        A        T        T        A        C        A   \n",
       "676        A        C        A        T        T        A        C        A   \n",
       "\n",
       "    S_1273_2 S_1273_3  \n",
       "0          C        A  \n",
       "1          C        A  \n",
       "2          C        A  \n",
       "3          C        A  \n",
       "4          C        A  \n",
       "..       ...      ...  \n",
       "672        C        A  \n",
       "673        C        A  \n",
       "674        C        A  \n",
       "675        C        A  \n",
       "676        C        A  \n",
       "\n",
       "[677 rows x 3820 columns]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position_table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pull out the concensus sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "S_1_1       A\n",
       "S_1_2       T\n",
       "S_1_3       G\n",
       "S_2_1       T\n",
       "S_2_2       T\n",
       "           ..\n",
       "S_1272_2    A\n",
       "S_1272_3    C\n",
       "S_1273_1    A\n",
       "S_1273_2    C\n",
       "S_1273_3    A\n",
       "Name: 0, Length: 3819, dtype: object"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "concensus_seq = position_table.drop('seqid',axis=1).mode(axis=0).T[0]\n",
    "concensus_seq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "position_table = position_table.set_index('seqid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Determine which samples are farthest from the concensus sequence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "seqid\n",
       "MT233522.1    82\n",
       "MT308696.1    71\n",
       "MT308694.1    53\n",
       "MT263453.1    48\n",
       "MT259284.1    33\n",
       "              ..\n",
       "MT326081.1     0\n",
       "MT263395.1     0\n",
       "MT263396.1     0\n",
       "MT263398.1     0\n",
       "MT262916.1     0\n",
       "Length: 677, dtype: int64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance_from_concensus_seq = position_table.apply(lambda row: sum(row != concensus_seq),axis=1)\n",
    "distance_from_concensus_seq_sorted = distance_from_concensus_seq.sort_values(ascending=False)\n",
    "distance_from_concensus_seq_sorted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select Sets of sequences"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I break from the outline, and I pull out four sets of distance data from the sorted list.\n",
    "All the following analysis will be in order of decreasing distance from the concensus sequence, since\n",
    "that is how the data is sorted.\n",
    "\n",
    "I also decided to look at the data in groups of eight instead of ten, since that will allow us to see the graphs better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Index(['MT233522.1', 'MT308696.1', 'MT308694.1', 'MT263453.1', 'MT259284.1',\n",
       "        'MT293180.1', 'MT263436.1', 'MT293224.1'],\n",
       "       dtype='object', name='seqid'),\n",
       " Index(['MT326129.1', 'MT259277.1', 'MT263431.1', 'MT293213.1', 'MT293196.1',\n",
       "        'MT326134.1', 'MT293200.1', 'MT293158.1'],\n",
       "       dtype='object', name='seqid'),\n",
       " Index(['MT246456.1', 'MT293198.1', 'MT326176.1', 'MT320538.1', 'MT322421.1',\n",
       "        'MT334557.1', 'MT322422.1', 'MT012098.1'],\n",
       "       dtype='object', name='seqid'),\n",
       " Index(['MT325596.1', 'MT322423.1', 'MT246482.1', 'MT326090.1', 'MT259249.1',\n",
       "        'MT263384.1', 'MT259281.1', 'MT326092.1'],\n",
       "       dtype='object', name='seqid')]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subset_seqs = []\n",
    "for i in range(0, 32, 8):\n",
    "    subset_seqs.append(distance_from_concensus_seq_sorted[i:i + 8].index)\n",
    "subset_seqs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate distances for each set of sequences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[            MT233522.1  MT259284.1  MT263436.1  MT263453.1  MT293180.1  \\\n",
       " MT233522.1           0         115          90         130         104   \n",
       " MT259284.1         115           0          43          81          47   \n",
       " MT263436.1          90          43           0          58          32   \n",
       " MT263453.1         130          81          58           0          68   \n",
       " MT293180.1         104          47          32          68           0   \n",
       " MT293224.1          90          43           0          58          32   \n",
       " MT308694.1         135          86          63         101          77   \n",
       " MT308696.1         151         104          79         119          93   \n",
       " \n",
       "             MT293224.1  MT308694.1  MT308696.1  \n",
       " MT233522.1          90         135         151  \n",
       " MT259284.1          43          86         104  \n",
       " MT263436.1           0          63          79  \n",
       " MT263453.1          58         101         119  \n",
       " MT293180.1          32          77          93  \n",
       " MT293224.1           0          63          79  \n",
       " MT308694.1          63           0          22  \n",
       " MT308696.1          79          22           0  ,\n",
       "             MT259277.1  MT263431.1  MT293158.1  MT293196.1  MT293200.1  \\\n",
       " MT259277.1           0           0          19           0           1   \n",
       " MT263431.1           0           0          19           0           1   \n",
       " MT293158.1          19          19           0          19          18   \n",
       " MT293196.1           0           0          19           0           1   \n",
       " MT293200.1           1           1          18           1           0   \n",
       " MT293213.1           0           0          19           0           1   \n",
       " MT326129.1           0           0          19           0           1   \n",
       " MT326134.1           1           1          18           1           0   \n",
       " \n",
       "             MT293213.1  MT326129.1  MT326134.1  \n",
       " MT259277.1           0           0           1  \n",
       " MT263431.1           0           0           1  \n",
       " MT293158.1          19          19          18  \n",
       " MT293196.1           0           0           1  \n",
       " MT293200.1           1           1           0  \n",
       " MT293213.1           0           0           1  \n",
       " MT326129.1           0           0           1  \n",
       " MT326134.1           1           1           0  ,\n",
       "             MT012098.1  MT246456.1  MT293198.1  MT320538.1  MT322421.1  \\\n",
       " MT012098.1           0          13          13           9           8   \n",
       " MT246456.1          13           0          18          14          13   \n",
       " MT293198.1          13          18           0          14          13   \n",
       " MT320538.1           9          14          14           0           7   \n",
       " MT322421.1           8          13          13           7           0   \n",
       " MT322422.1           8          13          13           7           0   \n",
       " MT326176.1          12          17          17          13          12   \n",
       " MT334557.1           8          13          13           7           6   \n",
       " \n",
       "             MT322422.1  MT326176.1  MT334557.1  \n",
       " MT012098.1           8          12           8  \n",
       " MT246456.1          13          17          13  \n",
       " MT293198.1          13          17          13  \n",
       " MT320538.1           7          13           7  \n",
       " MT322421.1           0          12           6  \n",
       " MT322422.1           0          12           6  \n",
       " MT326176.1          12           0          12  \n",
       " MT334557.1           6          12           0  ,\n",
       "             MT246482.1  MT259249.1  MT259281.1  MT263384.1  MT322423.1  \\\n",
       " MT246482.1           0           5           5           5           7   \n",
       " MT259249.1           5           0           2           4           4   \n",
       " MT259281.1           5           2           0           4           4   \n",
       " MT263384.1           5           4           4           0           6   \n",
       " MT322423.1           7           4           4           6           0   \n",
       " MT325596.1           7           4           4           6           6   \n",
       " MT326090.1           6           3           3           5           3   \n",
       " MT326092.1           5           2           2           4           4   \n",
       " \n",
       "             MT325596.1  MT326090.1  MT326092.1  \n",
       " MT246482.1           7           6           5  \n",
       " MT259249.1           4           3           2  \n",
       " MT259281.1           4           3           2  \n",
       " MT263384.1           6           5           4  \n",
       " MT322423.1           6           3           4  \n",
       " MT325596.1           0           5           4  \n",
       " MT326090.1           5           0           3  \n",
       " MT326092.1           4           3           0  ]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def calc_distances(subset_seqs):\n",
    "    distances = {}\n",
    "    for i,seqid1 in enumerate(subset_seqs):\n",
    "        distances[seqid1,seqid1]=0\n",
    "        for j in range(i+1,len(subset_seqs)):\n",
    "            seqid2 = subset_seqs[j]\n",
    "            distances[seqid1,seqid2] = sum(position_table.loc[seqid1] != position_table.loc[seqid2])\n",
    "            distances[seqid2,seqid1] = distances[seqid1,seqid2]\n",
    "    distances = pd.Series(distances).unstack()\n",
    "    return distances\n",
    "    \n",
    "distance_sets = [calc_distances(sequence) for sequence in subset_seqs]\n",
    "distance_sets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the distances from the concensus sequence drop off rapidly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[DistanceMatrix(names=['MT233522.1', 'MT259284.1', 'MT263436.1', 'MT263453.1', 'MT293180.1', 'MT293224.1', 'MT308694.1', 'MT308696.1'], matrix=[[0], [115, 0], [90, 43, 0], [130, 81, 58, 0], [104, 47, 32, 68, 0], [90, 43, 0, 58, 32, 0], [135, 86, 63, 101, 77, 63, 0], [151, 104, 79, 119, 93, 79, 22, 0]]),\n",
       " DistanceMatrix(names=['MT259277.1', 'MT263431.1', 'MT293158.1', 'MT293196.1', 'MT293200.1', 'MT293213.1', 'MT326129.1', 'MT326134.1'], matrix=[[0], [0, 0], [19, 19, 0], [0, 0, 19, 0], [1, 1, 18, 1, 0], [0, 0, 19, 0, 1, 0], [0, 0, 19, 0, 1, 0, 0], [1, 1, 18, 1, 0, 1, 1, 0]]),\n",
       " DistanceMatrix(names=['MT012098.1', 'MT246456.1', 'MT293198.1', 'MT320538.1', 'MT322421.1', 'MT322422.1', 'MT326176.1', 'MT334557.1'], matrix=[[0], [13, 0], [13, 18, 0], [9, 14, 14, 0], [8, 13, 13, 7, 0], [8, 13, 13, 7, 0, 0], [12, 17, 17, 13, 12, 12, 0], [8, 13, 13, 7, 6, 6, 12, 0]]),\n",
       " DistanceMatrix(names=['MT246482.1', 'MT259249.1', 'MT259281.1', 'MT263384.1', 'MT322423.1', 'MT325596.1', 'MT326090.1', 'MT326092.1'], matrix=[[0], [5, 0], [5, 2, 0], [5, 4, 4, 0], [7, 4, 4, 6, 0], [7, 4, 4, 6, 6, 0], [6, 3, 3, 5, 3, 5, 0], [5, 2, 2, 4, 4, 4, 3, 0]])]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def create_matrix(distances):\n",
    "    matrix = np.tril(distances.values).tolist()\n",
    "    for i in range(len(matrix)):\n",
    "        matrix[i] = matrix[i][:i+1]\n",
    "    dm = DistanceMatrix(list(distances.index), matrix)\n",
    "    return dm\n",
    "matrixs = [create_matrix(distances) for distances in distance_sets]\n",
    "matrixs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Construct a tree for each distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Tree(rooted=False),\n",
       " Tree(rooted=False),\n",
       " Tree(rooted=False),\n",
       " Tree(rooted=False)]"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_tree(dm):\n",
    "    constructor = DistanceTreeConstructor()\n",
    "    tree = constructor.nj(dm)\n",
    "    return tree\n",
    "\n",
    "trees = [make_tree(dm) for dm in matrixs]\n",
    "trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Draw a tree for each matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "%matplotlib inline\n",
    "\n",
    "def draw_tree(tree):\n",
    "    tree.ladderize()\n",
    "    Phylo.draw(tree)\n",
    "\n",
    "for tree in trees:\n",
    "    draw_tree(tree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows us visually that branch length drops off rapidly, with only the first few longest branches being \n",
    "over 50 in length. After that point, branch length stays well below 10, and only continues to decrease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "formats": "ipynb,md,py"
  },
  "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": "3.7.6"
  }
 },
 "nbformat": 4,
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