progress_report_mash.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Progress Report of alignment-free distance measure\n",
    "## 04\\12\\2022 \n",
    "\n",
    "-load brca1 alignments from Cogent3 test suite and compute pairwise distance by ```distance_matrix()```\n",
    "\n",
    "-compute MASH distance via python\n",
    "\n",
    "-scatter plot: fraction difference vs MASH distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cogent3 import load_aligned_seqs, make_seq\n",
    "import mmh3\n",
    "import math\n",
    "import numpy \n",
    "import matplotlib.pyplot as plt\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_kmers(seq:str, kmer:int):\n",
    "    \"\"\"\n",
    "    Use a slide window to get k-mers in a string format sequence. \n",
    "    Return a list of k-mers.\n",
    "    \"\"\"\n",
    "    return [seq[poi:poi + kmer] for poi in range(len(seq) - kmer + 1)]\n",
    "\n",
    "\n",
    "def sketch_genome_32(genome1:str, genome2:str, kmer:int, sketch:int):\n",
    "    \"\"\"\n",
    "    This function takes two genomes. Then get the sketches of them. \n",
    "    Return two lists which stored the s smallest hash values of each genome. \n",
    "\n",
    "    Reference: https://github.com/sourmash-bio/sourmash/blob/master/utils/compute-dna-mh-another-way.py\n",
    "    \"\"\"\n",
    "    #get k-mers of each genomes.\n",
    "    kmers_seq1 = get_kmers(genome1,kmer)\n",
    "    kmers_seq2 = get_kmers(genome2,kmer)\n",
    "\n",
    "    #get canonical k-mers set for each seqs. Each element in the set is selected between \n",
    "    #k-mer and its reversed strand based on alphabetic order.\n",
    "    #\n",
    "    #simultaneously, get smallest hash sketch with size s for each set.\n",
    "    canonical_seq1 = []\n",
    "    canonical_seq2 = []\n",
    "\n",
    "    for mer in kmers_seq1:\n",
    "\n",
    "            seq = make_seq(mer, moltype=\"dna\")\n",
    "            reversed_str = str(seq.rc())\n",
    "\n",
    "            if mer < reversed_str: \n",
    "                canonical_seq1.append(mmh3.hash(mer, seed = 42, signed=False))\n",
    "            else:\n",
    "                canonical_seq1.append(mmh3.hash(reversed_str, seed = 42, signed=False))\n",
    "\n",
    "    for mer in kmers_seq2:\n",
    "            \n",
    "            seq = make_seq(mer, moltype=\"dna\")\n",
    "            reversed_str = str(seq.rc())\n",
    "\n",
    "            if mer < reversed_str: \n",
    "                canonical_seq2.append(mmh3.hash(mer, seed = 42, signed=False))\n",
    "            else:\n",
    "                canonical_seq2.append(mmh3.hash(reversed_str, seed = 42, signed=False))\n",
    "\n",
    "                \n",
    "    hash_value2 = sorted(set(canonical_seq2))[:sketch]\n",
    "\n",
    "    hash_value1 = sorted(set(canonical_seq1))[:sketch]\n",
    "\n",
    "    return hash_value1, hash_value2\n",
    "\n",
    "\n",
    "def sketch_genome_64(genome1:str, genome2:str, kmer:int, sketch:int):\n",
    "    \"\"\"\n",
    "    64 bit hashes to be used, based on the number of all possible kmers.\n",
    "    \"\"\"\n",
    "    \n",
    "    kmers_seq1 = get_kmers(genome1,kmer)\n",
    "    kmers_seq2 = get_kmers(genome2,kmer)\n",
    "\n",
    "    canonical_seq1 = []\n",
    "    canonical_seq2 = []\n",
    "\n",
    "    for mer in kmers_seq1:\n",
    "            \n",
    "        seq = make_seq(mer, moltype=\"dna\")\n",
    "        reversed_str = str(seq.rc())\n",
    "\n",
    "        if mer < reversed_str:  #select the canonical k-mer between its complement reverse k-mer and itself.\n",
    "            canonical_seq1.append(mmh3.hash64(mer, seed = 42, signed=False)[0])\n",
    "        else:\n",
    "            canonical_seq1.append(mmh3.hash64(reversed_str, seed = 42, signed=False)[0])\n",
    "\n",
    "    for mer in kmers_seq2:\n",
    "\n",
    "        seq = make_seq(mer, moltype=\"dna\")\n",
    "        reversed_str = str(seq.rc())\n",
    "\n",
    "        if mer < reversed_str: \n",
    "                canonical_seq2.append(mmh3.hash64(mer, seed = 42, signed=False)[0])\n",
    "        else:\n",
    "                canonical_seq2.append(mmh3.hash64(reversed_str, seed = 42, signed=False)[0])\n",
    "      \n",
    "                \n",
    "    hash_value2 = sorted(set(canonical_seq2))[:sketch]\n",
    "\n",
    "    hash_value1 = sorted(set(canonical_seq1))[:sketch]\n",
    "\n",
    "    return hash_value1, hash_value2\n",
    "\n",
    "\n",
    "def mash_d(hash_value1, hash_value2, kmer, sketch):\n",
    "    \"\"\"\n",
    "    Calculate mash distance based on estimate of jaccard index and k.\n",
    "    \"\"\"\n",
    "    hash_value_comb = hash_value1+hash_value2\n",
    "    sketch_comb = sorted(set(hash_value_comb))[:sketch]\n",
    "    numerator = set(sketch_comb).intersection(set(hash_value1),set(hash_value2))\n",
    "    Jaccard_index = len(numerator) / sketch if numerator else 1 / sketch     ## modify the jaccard_index estimate by adding 1 to avoid 0 in log function.\n",
    "    return -(1/kmer) * math.log((2*Jaccard_index)/(1+Jaccard_index))\n",
    "\n",
    "\n",
    "def pair_mash_distance(seq_coll:dict, kmer:int, sketch:int):\n",
    "    \"\"\"\n",
    "    Get pairwise mash distance. Use 64-bit hash. \n",
    "    \"\"\"\n",
    "    dim = len(seq_coll)\n",
    "    result = numpy.empty((dim,dim),dtype=object)\n",
    "    seq_names = sorted(list(seq_coll.keys()))\n",
    "\n",
    "    y = 0\n",
    "    for x, seq_name1 in enumerate(seq_names):\n",
    "        for seq_name2 in seq_names:\n",
    "            if result[x, y] is None:\n",
    "                if seq_name1 != seq_name2:\n",
    "\n",
    "                        seq1 = seq_coll[seq_name1]\n",
    "                        seq2 = seq_coll[seq_name2]\n",
    "                        hash1, hash2 = sketch_genome_64(seq1, seq2, kmer, sketch)\n",
    "\n",
    "                        distance = mash_d(hash1, hash2, kmer, sketch)\n",
    "                        result[x,y] = distance\n",
    "                        result[y,x] = distance\n",
    "                else:\n",
    "                    result[x,y] = 0\n",
    "            y+=1\n",
    "        y=0\n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute pairwise distance in fraction difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table>\n",
       "<tr class=\"num_row\"><td></td><td><b>0</b></td></tr>\n",
       "<tr><td class=\"label\">Rhino</td><td><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"C_dna\">C</span><span class=\"G_dna\">G</span><span class=\"A_dna\">A</span><span class=\"A_dna\">A</span><span class=\"T_dna\">T</span><span class=\"A_dna\">A</span><span class=\"C_dna\">C</span><span class=\"T_dna\">T</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"T_dna\">T</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"T_dna\">T</span><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"A_dna\">A</span><span class=\"A_dna\">A</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"T_dna\">T</span><span class=\"G_dna\">G</span><span class=\"T_dna\">T</span><span class=\"A_dna\">A</span><span class=\"T_dna\">T</span><span class=\"T_dna\">T</span><span class=\"A_dna\">A</span><span class=\"C_dna\">C</span><span class=\"T_dna\">T</span><span class=\"C_dna\">C</span><span class=\"A_dna\">A</span><span class=\"C_dna\">C</span><span class=\"T_dna\">T</span></td></tr>\n",
       "<tr><td class=\"label\">FlyingFox</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">G</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">T</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">DogFaced</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">T</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">FreeTaile</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">C</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">LittleBro</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"G_dna\">G</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">C</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">C</span></td></tr>\n",
       "<tr><td class=\"label\">TombBat</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"G_dna\">G</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">G</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">C</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">RoundEare</td><td><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">-</span><span class=\"ambig_dna\">N</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"ambig_dna\">N</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"ambig_dna\">N</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">C</span><span class=\"T_dna\">.</span><span class=\"G_dna\">G</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">FalseVamp</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">A</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">G</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">LeafNose</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">A</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">T</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">C</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "<tr><td class=\"label\">Horse</td><td><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">A</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"A_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"G_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">T</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"T_dna\">.</span><span class=\"T_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span><span class=\"C_dna\">.</span><span class=\"A_dna\">.</span><span class=\"C_dna\">.</span><span class=\"T_dna\">.</span></td></tr>\n",
       "</table>\n",
       "<p><i>55 x 3009 (truncated to 10 x 60) dna alignment</i></p>\n",
       "</div>"
      ],
      "text/plain": [
       "55 x 3009 alignment: FlyingFox[TGTGGCACAAA...], DogFaced[TGTGGCACAAA...], FreeTaile[TGTGGCACAGA...], ..."
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aln = load_aligned_seqs(\"../repos/Cogent3/tests/data/brca1.fasta\", moltype=\"dna\")\n",
    "aln"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div class=\"c3table\">\n",
       "\n",
       "<style>\n",
       ".c3table table {margin: 10px 0;}\n",
       ".c3table tr:last-child {border-bottom: 1px solid #000;} \n",
       ".c3table tr > th {text-align: left; padding: 0 5px;}\n",
       ".c3table tr > td {text-align: left; padding: 5px;}\n",
       ".c3table tr:nth-child(even) {background: #f7f7f7 !important;}\n",
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       ".c3table .index {background: rgba(161, 195, 209, 0.25); margin: 10px; font-weight: 600;}\n",
       ".c3table .head_cell {background: rgba(161, 195, 209, 0.75); font-weight: bold; text-align: center;}\n",
       ".c3table caption {color: rgb(250, 250, 250); background: rgba(30, 140, 200, 1); padding: 3px; white-space: nowrap; caption-side: top;}\n",
       ".c3table .cell_title {font-weight: bold;}\n",
       ".c3col_left { text-align: left !important; display: block;}\n",
       ".c3col_right { text-align: right !important; display: block;}\n",
       ".c3col_center { text-align: center !important; display: block;}\n",
       "</style>\n",
       "\n",
       "<table>\n",
       "\n",
       "<thead class=\"head_cell\">\n",
       "<th>names</th><th>Aardvark</th><th>AfricanEl</th><th>Anteater</th><th>AsianElep</th><th>Bandicoot</th><th>Caenolest</th><th>Cat</th><th>Chimpanzee</th><th>Cow</th><th>Dog</th><th>DogFaced</th><th>Dugong</th><th>FalseVamp</th><th>FlyingFox</th><th>FlyingLem</th><th>FlyingSqu</th><th>FreeTaile</th><th>Galago</th><th>GiantElep</th><th>GoldenMol</th><th>Gorilla</th><th>HairyArma</th><th>Hedgehog</th><th>Hippo</th><th>Horse</th><th>HowlerMon</th><th>Human</th><th>HumpbackW</th><th>Jackrabbit</th><th>LeafNose</th><th>LesserEle</th><th>LittleBro</th><th>Llama</th><th>Madagascar</th><th>Manatee</th><th>Mole</th><th>Mouse</th><th>NineBande</th><th>OldWorld</th><th>Orangutan</th><th>Pangolin</th><th>Phascogale</th><th>Pig</th><th>Rat</th><th>Rhesus</th><th>Rhino</th><th>RockHyrax</th><th>RoundEare</th><th>Sloth</th><th>SpermWhale</th><th>Tenrec</th><th>TombBat</th><th>TreeHyrax</th><th>TreeShrew</th><th>Wombat</th>\n",
       "</thead>\n",
       "<tbody>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">Aardvark</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.1182</span></td><td><span class=\"c3col_right\">0.1665</span></td><td><span class=\"c3col_right\">0.1203</span></td><td><span class=\"c3col_right\">0.3989</span></td><td><span class=\"c3col_right\">0.4081</span></td><td><span class=\"c3col_right\">0.1775</span></td><td><span class=\"c3col_right\">0.1701</span></td><td><span class=\"c3col_right\">0.2060</span></td><td><span class=\"c3col_right\">0.1963</span></td><td><span class=\"c3col_right\">0.1842</span></td><td><span class=\"c3col_right\">0.1175</span></td><td><span class=\"c3col_right\">0.1860</span></td><td><span class=\"c3col_right\">0.1719</span></td><td><span class=\"c3col_right\">0.1620</span></td><td><span class=\"c3col_right\">0.1871</span></td><td><span class=\"c3col_right\">0.1706</span></td><td><span class=\"c3col_right\">0.2045</span></td><td><span class=\"c3col_right\">0.2051</span></td><td><span class=\"c3col_right\">0.1543</span></td><td><span class=\"c3col_right\">0.1697</span></td><td><span class=\"c3col_right\">0.1503</span></td><td><span class=\"c3col_right\">0.2335</span></td><td><span class=\"c3col_right\">0.1844</span></td><td><span class=\"c3col_right\">0.1633</span></td><td><span class=\"c3col_right\">0.1805</span></td><td><span class=\"c3col_right\">0.1712</span></td><td><span class=\"c3col_right\">0.1774</span></td><td><span class=\"c3col_right\">0.2082</span></td><td><span class=\"c3col_right\">0.1766</span></td><td><span class=\"c3col_right\">0.1872</span></td><td><span class=\"c3col_right\">0.1848</span></td><td><span class=\"c3col_right\">0.1724</span></td><td><span class=\"c3col_right\">0.2410</span></td><td><span class=\"c3col_right\">0.1144</span></td><td><span class=\"c3col_right\">0.2045</span></td><td><span class=\"c3col_right\">0.2955</span></td><td><span class=\"c3col_right\">0.1634</span></td><td><span class=\"c3col_right\">0.2960</span></td><td><span class=\"c3col_right\">0.1708</span></td><td><span class=\"c3col_right\">0.1788</span></td><td><span class=\"c3col_right\">0.3896</span></td><td><span class=\"c3col_right\">0.1914</span></td><td><span class=\"c3col_right\">0.2902</span></td><td><span class=\"c3col_right\">0.1775</span></td><td><span class=\"c3col_right\">0.1542</span></td><td><span class=\"c3col_right\">0.1726</span></td><td><span class=\"c3col_right\">0.2596</span></td><td><span class=\"c3col_right\">0.1529</span></td><td><span class=\"c3col_right\">0.1788</span></td><td><span class=\"c3col_right\">0.2696</span></td><td><span class=\"c3col_right\">0.1808</span></td><td><span class=\"c3col_right\">0.1741</span></td><td><span class=\"c3col_right\">0.1983</span></td><td><span class=\"c3col_right\">0.3888</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">AfricanEl</span></td><td><span class=\"c3col_right\">0.1182</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.1496</span></td><td><span class=\"c3col_right\">0.0043</span></td><td><span class=\"c3col_right\">0.3925</span></td><td><span class=\"c3col_right\">0.3973</span></td><td><span class=\"c3col_right\">0.1675</span></td><td><span class=\"c3col_right\">0.1552</span></td><td><span class=\"c3col_right\">0.1918</span></td><td><span class=\"c3col_right\">0.1841</span></td><td><span class=\"c3col_right\">0.1729</span></td><td><span class=\"c3col_right\">0.0755</span></td><td><span class=\"c3col_right\">0.1674</span></td><td><span class=\"c3col_right\">0.1624</span></td><td><span class=\"c3col_right\">0.1481</span></td><td><span class=\"c3col_right\">0.1763</span></td><td><span class=\"c3col_right\">0.1623</span></td><td><span class=\"c3col_right\">0.1937</span></td><td><span class=\"c3col_right\">0.1986</span></td><td><span class=\"c3col_right\">0.1457</span></td><td><span class=\"c3col_right\">0.1549</span></td><td><span class=\"c3col_right\">0.1316</span></td><td><span class=\"c3col_right\">0.2175</span></td><td><span class=\"c3col_right\">0.1681</span></td><td><span class=\"c3col_right\">0.1449</span></td><td><span class=\"c3col_right\">0.1646</span></td><td><span class=\"c3col_right\">0.1574</span></td><td><span class=\"c3col_right\">0.1596</span></td><td><span class=\"c3col_right\">0.1976</span></td><td><span class=\"c3col_right\">0.1648</span></td><td><span class=\"c3col_right\">0.1756</span></td><td><span class=\"c3col_right\">0.1686</span></td><td><span class=\"c3col_right\">0.1559</span></td><td><span class=\"c3col_right\">0.2388</span></td><td><span class=\"c3col_right\">0.0753</span></td><td><span class=\"c3col_right\">0.1898</span></td><td><span class=\"c3col_right\">0.2898</span></td><td><span class=\"c3col_right\">0.1486</span></td><td><span class=\"c3col_right\">0.2782</span></td><td><span class=\"c3col_right\">0.1552</span></td><td><span class=\"c3col_right\">0.1625</span></td><td><span class=\"c3col_right\">0.3798</span></td><td><span class=\"c3col_right\">0.1806</span></td><td><span class=\"c3col_right\">0.2800</span></td><td><span class=\"c3col_right\">0.1604</span></td><td><span class=\"c3col_right\">0.1406</span></td><td><span class=\"c3col_right\">0.1414</span></td><td><span class=\"c3col_right\">0.2434</span></td><td><span class=\"c3col_right\">0.1418</span></td><td><span class=\"c3col_right\">0.1619</span></td><td><span class=\"c3col_right\">0.2559</span></td><td><span class=\"c3col_right\">0.1677</span></td><td><span class=\"c3col_right\">0.1409</span></td><td><span class=\"c3col_right\">0.1848</span></td><td><span class=\"c3col_right\">0.3758</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">Anteater</span></td><td><span class=\"c3col_right\">0.1665</span></td><td><span class=\"c3col_right\">0.1496</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.1503</span></td><td><span class=\"c3col_right\">0.3998</span></td><td><span class=\"c3col_right\">0.4051</span></td><td><span class=\"c3col_right\">0.1590</span></td><td><span class=\"c3col_right\">0.1555</span></td><td><span class=\"c3col_right\">0.1892</span></td><td><span class=\"c3col_right\">0.1782</span></td><td><span class=\"c3col_right\">0.1674</span></td><td><span class=\"c3col_right\">0.1374</span></td><td><span class=\"c3col_right\">0.1694</span></td><td><span class=\"c3col_right\">0.1583</span></td><td><span class=\"c3col_right\">0.1405</span></td><td><span class=\"c3col_right\">0.1721</span></td><td><span class=\"c3col_right\">0.1582</span></td><td><span class=\"c3col_right\">0.1930</span></td><td><span class=\"c3col_right\">0.2333</span></td><td><span class=\"c3col_right\">0.1729</span></td><td><span class=\"c3col_right\">0.1555</span></td><td><span class=\"c3col_right\">0.1019</span></td><td><span class=\"c3col_right\">0.2167</span></td><td><span class=\"c3col_right\">0.1651</span></td><td><span class=\"c3col_right\">0.1466</span></td><td><span class=\"c3col_right\">0.1658</span></td><td><span class=\"c3col_right\">0.1591</span></td><td><span class=\"c3col_right\">0.1536</span></td><td><span class=\"c3col_right\">0.1965</span></td><td><span class=\"c3col_right\">0.1596</span></td><td><span class=\"c3col_right\">0.2168</span></td><td><span class=\"c3col_right\">0.1701</span></td><td><span class=\"c3col_right\">0.1600</span></td><td><span class=\"c3col_right\">0.2592</span></td><td><span class=\"c3col_right\">0.1363</span></td><td><span class=\"c3col_right\">0.1929</span></td><td><span class=\"c3col_right\">0.2851</span></td><td><span class=\"c3col_right\">0.1134</span></td><td><span class=\"c3col_right\">0.2774</span></td><td><span class=\"c3col_right\">0.1577</span></td><td><span class=\"c3col_right\">0.1608</span></td><td><span class=\"c3col_right\">0.3894</span></td><td><span class=\"c3col_right\">0.1767</span></td><td><span class=\"c3col_right\">0.2779</span></td><td><span class=\"c3col_right\">0.1614</span></td><td><span class=\"c3col_right\">0.1388</span></td><td><span class=\"c3col_right\">0.2020</span></td><td><span class=\"c3col_right\">0.2471</span></td><td><span class=\"c3col_right\">0.0934</span></td><td><span class=\"c3col_right\">0.1550</span></td><td><span class=\"c3col_right\">0.2816</span></td><td><span class=\"c3col_right\">0.1672</span></td><td><span class=\"c3col_right\">0.2006</span></td><td><span class=\"c3col_right\">0.1851</span></td><td><span class=\"c3col_right\">0.3806</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">AsianElep</span></td><td><span class=\"c3col_right\">0.1203</span></td><td><span class=\"c3col_right\">0.0043</span></td><td><span class=\"c3col_right\">0.1503</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.3933</span></td><td><span class=\"c3col_right\">0.3978</span></td><td><span class=\"c3col_right\">0.1679</span></td><td><span class=\"c3col_right\">0.1563</span></td><td><span class=\"c3col_right\">0.1937</span></td><td><span class=\"c3col_right\">0.1842</span></td><td><span class=\"c3col_right\">0.1748</span></td><td><span class=\"c3col_right\">0.0764</span></td><td><span class=\"c3col_right\">0.1685</span></td><td><span class=\"c3col_right\">0.1636</span></td><td><span class=\"c3col_right\">0.1488</span></td><td><span class=\"c3col_right\">0.1771</span></td><td><span class=\"c3col_right\">0.1627</span></td><td><span class=\"c3col_right\">0.1942</span></td><td><span class=\"c3col_right\">0.1986</span></td><td><span class=\"c3col_right\">0.1464</span></td><td><span class=\"c3col_right\">0.1556</span></td><td><span class=\"c3col_right\">0.1330</span></td><td><span class=\"c3col_right\">0.2195</span></td><td><span class=\"c3col_right\">0.1688</span></td><td><span class=\"c3col_right\">0.1449</span></td><td><span class=\"c3col_right\">0.1653</span></td><td><span class=\"c3col_right\">0.1585</span></td><td><span class=\"c3col_right\">0.1611</span></td><td><span class=\"c3col_right\">0.1992</span></td><td><span class=\"c3col_right\">0.1655</span></td><td><span class=\"c3col_right\">0.1749</span></td><td><span class=\"c3col_right\">0.1693</span></td><td><span class=\"c3col_right\">0.1578</span></td><td><span class=\"c3col_right\">0.2395</span></td><td><span class=\"c3col_right\">0.0762</span></td><td><span class=\"c3col_right\">0.1903</span></td><td><span class=\"c3col_right\">0.2891</span></td><td><span class=\"c3col_right\">0.1504</span></td><td><span class=\"c3col_right\">0.2801</span></td><td><span class=\"c3col_right\">0.1563</span></td><td><span class=\"c3col_right\">0.1622</span></td><td><span class=\"c3col_right\">0.3798</span></td><td><span class=\"c3col_right\">0.1818</span></td><td><span class=\"c3col_right\">0.2792</span></td><td><span class=\"c3col_right\">0.1612</span></td><td><span class=\"c3col_right\">0.1403</span></td><td><span class=\"c3col_right\">0.1418</span></td><td><span class=\"c3col_right\">0.2442</span></td><td><span class=\"c3col_right\">0.1425</span></td><td><span class=\"c3col_right\">0.1635</span></td><td><span class=\"c3col_right\">0.2558</span></td><td><span class=\"c3col_right\">0.1685</span></td><td><span class=\"c3col_right\">0.1412</span></td><td><span class=\"c3col_right\">0.1867</span></td><td><span class=\"c3col_right\">0.3758</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">Bandicoot</span></td><td><span class=\"c3col_right\">0.3989</span></td><td><span class=\"c3col_right\">0.3925</span></td><td><span class=\"c3col_right\">0.3998</span></td><td><span class=\"c3col_right\">0.3933</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.2077</span></td><td><span class=\"c3col_right\">0.4121</span></td><td><span class=\"c3col_right\">0.4007</span></td><td><span class=\"c3col_right\">0.4234</span></td><td><span class=\"c3col_right\">0.4141</span></td><td><span class=\"c3col_right\">0.4195</span></td><td><span class=\"c3col_right\">0.3878</span></td><td><span class=\"c3col_right\">0.4229</span></td><td><span class=\"c3col_right\">0.4121</span></td><td><span class=\"c3col_right\">0.3981</span></td><td><span class=\"c3col_right\">0.4067</span></td><td><span class=\"c3col_right\">0.4082</span></td><td><span class=\"c3col_right\">0.4128</span></td><td><span class=\"c3col_right\">0.4286</span></td><td><span class=\"c3col_right\">0.4076</span></td><td><span class=\"c3col_right\">0.4011</span></td><td><span class=\"c3col_right\">0.3913</span></td><td><span class=\"c3col_right\">0.4360</span></td><td><span class=\"c3col_right\">0.4192</span></td><td><span class=\"c3col_right\">0.3996</span></td><td><span class=\"c3col_right\">0.4105</span></td><td><span class=\"c3col_right\">0.4048</span></td><td><span class=\"c3col_right\">0.4140</span></td><td><span class=\"c3col_right\">0.4195</span></td><td><span class=\"c3col_right\">0.4113</span></td><td><span class=\"c3col_right\">0.4122</span></td><td><span class=\"c3col_right\">0.4076</span></td><td><span class=\"c3col_right\">0.4089</span></td><td><span class=\"c3col_right\">0.4458</span></td><td><span class=\"c3col_right\">0.3905</span></td><td><span class=\"c3col_right\">0.4175</span></td><td><span class=\"c3col_right\">0.4541</span></td><td><span class=\"c3col_right\">0.3916</span></td><td><span class=\"c3col_right\">0.4654</span></td><td><span class=\"c3col_right\">0.4028</span></td><td><span class=\"c3col_right\">0.4114</span></td><td><span class=\"c3col_right\">0.1828</span></td><td><span class=\"c3col_right\">0.4137</span></td><td><span class=\"c3col_right\">0.4515</span></td><td><span class=\"c3col_right\">0.4093</span></td><td><span class=\"c3col_right\">0.3997</span></td><td><span class=\"c3col_right\">0.4163</span></td><td><span class=\"c3col_right\">0.4497</span></td><td><span class=\"c3col_right\">0.3904</span></td><td><span class=\"c3col_right\">0.4171</span></td><td><span class=\"c3col_right\">0.4609</span></td><td><span class=\"c3col_right\">0.4062</span></td><td><span class=\"c3col_right\">0.4165</span></td><td><span class=\"c3col_right\">0.4024</span></td><td><span class=\"c3col_right\">0.1503</span></td></tr>\n",
       "<tr class=\"ellipsis\"><td><span class=\"c3col_left\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td><td><span class=\"c3col_right\">...</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">Tenrec</span></td><td><span class=\"c3col_right\">0.2696</span></td><td><span class=\"c3col_right\">0.2559</span></td><td><span class=\"c3col_right\">0.2816</span></td><td><span class=\"c3col_right\">0.2558</span></td><td><span class=\"c3col_right\">0.4609</span></td><td><span class=\"c3col_right\">0.4598</span></td><td><span class=\"c3col_right\">0.2894</span></td><td><span class=\"c3col_right\">0.2823</span></td><td><span class=\"c3col_right\">0.3031</span></td><td><span class=\"c3col_right\">0.3037</span></td><td><span class=\"c3col_right\">0.3061</span></td><td><span class=\"c3col_right\">0.2449</span></td><td><span class=\"c3col_right\">0.3034</span></td><td><span class=\"c3col_right\">0.2965</span></td><td><span class=\"c3col_right\">0.2737</span></td><td><span class=\"c3col_right\">0.3014</span></td><td><span class=\"c3col_right\">0.2960</span></td><td><span class=\"c3col_right\">0.3216</span></td><td><span class=\"c3col_right\">0.3198</span></td><td><span class=\"c3col_right\">0.2626</span></td><td><span class=\"c3col_right\">0.2812</span></td><td><span class=\"c3col_right\">0.2730</span></td><td><span class=\"c3col_right\">0.3335</span></td><td><span class=\"c3col_right\">0.2868</span></td><td><span class=\"c3col_right\">0.2770</span></td><td><span class=\"c3col_right\">0.2903</span></td><td><span class=\"c3col_right\">0.2845</span></td><td><span class=\"c3col_right\">0.2848</span></td><td><span class=\"c3col_right\">0.3101</span></td><td><span class=\"c3col_right\">0.2952</span></td><td><span class=\"c3col_right\">0.3009</span></td><td><span class=\"c3col_right\">0.2977</span></td><td><span class=\"c3col_right\">0.2896</span></td><td><span class=\"c3col_right\">0.1332</span></td><td><span class=\"c3col_right\">0.2466</span></td><td><span class=\"c3col_right\">0.3102</span></td><td><span class=\"c3col_right\">0.3633</span></td><td><span class=\"c3col_right\">0.2867</span></td><td><span class=\"c3col_right\">0.3694</span></td><td><span class=\"c3col_right\">0.2838</span></td><td><span class=\"c3col_right\">0.2970</span></td><td><span class=\"c3col_right\">0.4537</span></td><td><span class=\"c3col_right\">0.2941</span></td><td><span class=\"c3col_right\">0.3610</span></td><td><span class=\"c3col_right\">0.2896</span></td><td><span class=\"c3col_right\">0.2746</span></td><td><span class=\"c3col_right\">0.3009</span></td><td><span class=\"c3col_right\">0.3451</span></td><td><span class=\"c3col_right\">0.2775</span></td><td><span class=\"c3col_right\">0.2845</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.2993</span></td><td><span class=\"c3col_right\">0.3024</span></td><td><span class=\"c3col_right\">0.3042</span></td><td><span class=\"c3col_right\">0.4385</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">TombBat</span></td><td><span class=\"c3col_right\">0.1808</span></td><td><span class=\"c3col_right\">0.1677</span></td><td><span class=\"c3col_right\">0.1672</span></td><td><span class=\"c3col_right\">0.1685</span></td><td><span class=\"c3col_right\">0.4062</span></td><td><span class=\"c3col_right\">0.4232</span></td><td><span class=\"c3col_right\">0.1482</span></td><td><span class=\"c3col_right\">0.1622</span></td><td><span class=\"c3col_right\">0.1743</span></td><td><span class=\"c3col_right\">0.1659</span></td><td><span class=\"c3col_right\">0.1361</span></td><td><span class=\"c3col_right\">0.1586</span></td><td><span class=\"c3col_right\">0.1333</span></td><td><span class=\"c3col_right\">0.1245</span></td><td><span class=\"c3col_right\">0.1450</span></td><td><span class=\"c3col_right\">0.1738</span></td><td><span class=\"c3col_right\">0.0956</span></td><td><span class=\"c3col_right\">0.2009</span></td><td><span class=\"c3col_right\">0.2396</span></td><td><span class=\"c3col_right\">0.2034</span></td><td><span class=\"c3col_right\">0.1622</span></td><td><span class=\"c3col_right\">0.1571</span></td><td><span class=\"c3col_right\">0.2051</span></td><td><span class=\"c3col_right\">0.1520</span></td><td><span class=\"c3col_right\">0.1299</span></td><td><span class=\"c3col_right\">0.1677</span></td><td><span class=\"c3col_right\">0.1640</span></td><td><span class=\"c3col_right\">0.1392</span></td><td><span class=\"c3col_right\">0.1950</span></td><td><span class=\"c3col_right\">0.1272</span></td><td><span class=\"c3col_right\">0.2245</span></td><td><span class=\"c3col_right\">0.1108</span></td><td><span class=\"c3col_right\">0.1460</span></td><td><span class=\"c3col_right\">0.2783</span></td><td><span class=\"c3col_right\">0.1585</span></td><td><span class=\"c3col_right\">0.1785</span></td><td><span class=\"c3col_right\">0.2948</span></td><td><span class=\"c3col_right\">0.1658</span></td><td><span class=\"c3col_right\">0.2886</span></td><td><span class=\"c3col_right\">0.1651</span></td><td><span class=\"c3col_right\">0.1405</span></td><td><span class=\"c3col_right\">0.4005</span></td><td><span class=\"c3col_right\">0.1566</span></td><td><span class=\"c3col_right\">0.2915</span></td><td><span class=\"c3col_right\">0.1675</span></td><td><span class=\"c3col_right\">0.1200</span></td><td><span class=\"c3col_right\">0.2145</span></td><td><span class=\"c3col_right\">0.1964</span></td><td><span class=\"c3col_right\">0.1545</span></td><td><span class=\"c3col_right\">0.1404</span></td><td><span class=\"c3col_right\">0.2993</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.2114</span></td><td><span class=\"c3col_right\">0.1898</span></td><td><span class=\"c3col_right\">0.3926</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">TreeHyrax</span></td><td><span class=\"c3col_right\">0.1741</span></td><td><span class=\"c3col_right\">0.1409</span></td><td><span class=\"c3col_right\">0.2006</span></td><td><span class=\"c3col_right\">0.1412</span></td><td><span class=\"c3col_right\">0.4165</span></td><td><span class=\"c3col_right\">0.4211</span></td><td><span class=\"c3col_right\">0.2152</span></td><td><span class=\"c3col_right\">0.2041</span></td><td><span class=\"c3col_right\">0.2378</span></td><td><span class=\"c3col_right\">0.2245</span></td><td><span class=\"c3col_right\">0.2171</span></td><td><span class=\"c3col_right\">0.1302</span></td><td><span class=\"c3col_right\">0.2172</span></td><td><span class=\"c3col_right\">0.2059</span></td><td><span class=\"c3col_right\">0.1893</span></td><td><span class=\"c3col_right\">0.2168</span></td><td><span class=\"c3col_right\">0.2074</span></td><td><span class=\"c3col_right\">0.2394</span></td><td><span class=\"c3col_right\">0.2445</span></td><td><span class=\"c3col_right\">0.1949</span></td><td><span class=\"c3col_right\">0.2044</span></td><td><span class=\"c3col_right\">0.1834</span></td><td><span class=\"c3col_right\">0.2570</span></td><td><span class=\"c3col_right\">0.2213</span></td><td><span class=\"c3col_right\">0.1985</span></td><td><span class=\"c3col_right\">0.2103</span></td><td><span class=\"c3col_right\">0.2066</span></td><td><span class=\"c3col_right\">0.2106</span></td><td><span class=\"c3col_right\">0.2351</span></td><td><span class=\"c3col_right\">0.2095</span></td><td><span class=\"c3col_right\">0.2242</span></td><td><span class=\"c3col_right\">0.2172</span></td><td><span class=\"c3col_right\">0.2114</span></td><td><span class=\"c3col_right\">0.2764</span></td><td><span class=\"c3col_right\">0.1323</span></td><td><span class=\"c3col_right\">0.2347</span></td><td><span class=\"c3col_right\">0.3137</span></td><td><span class=\"c3col_right\">0.2007</span></td><td><span class=\"c3col_right\">0.3189</span></td><td><span class=\"c3col_right\">0.2037</span></td><td><span class=\"c3col_right\">0.2134</span></td><td><span class=\"c3col_right\">0.4023</span></td><td><span class=\"c3col_right\">0.2266</span></td><td><span class=\"c3col_right\">0.3079</span></td><td><span class=\"c3col_right\">0.2112</span></td><td><span class=\"c3col_right\">0.1917</span></td><td><span class=\"c3col_right\">0.0135</span></td><td><span class=\"c3col_right\">0.2875</span></td><td><span class=\"c3col_right\">0.1919</span></td><td><span class=\"c3col_right\">0.2147</span></td><td><span class=\"c3col_right\">0.3024</span></td><td><span class=\"c3col_right\">0.2114</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.2312</span></td><td><span class=\"c3col_right\">0.4052</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">TreeShrew</span></td><td><span class=\"c3col_right\">0.1983</span></td><td><span class=\"c3col_right\">0.1848</span></td><td><span class=\"c3col_right\">0.1851</span></td><td><span class=\"c3col_right\">0.1867</span></td><td><span class=\"c3col_right\">0.4024</span></td><td><span class=\"c3col_right\">0.4070</span></td><td><span class=\"c3col_right\">0.1816</span></td><td><span class=\"c3col_right\">0.1632</span></td><td><span class=\"c3col_right\">0.2010</span></td><td><span class=\"c3col_right\">0.2016</span></td><td><span class=\"c3col_right\">0.1942</span></td><td><span class=\"c3col_right\">0.1739</span></td><td><span class=\"c3col_right\">0.1966</span></td><td><span class=\"c3col_right\">0.1814</span></td><td><span class=\"c3col_right\">0.1573</span></td><td><span class=\"c3col_right\">0.1836</span></td><td><span class=\"c3col_right\">0.1824</span></td><td><span class=\"c3col_right\">0.1953</span></td><td><span class=\"c3col_right\">0.2513</span></td><td><span class=\"c3col_right\">0.2134</span></td><td><span class=\"c3col_right\">0.1646</span></td><td><span class=\"c3col_right\">0.1675</span></td><td><span class=\"c3col_right\">0.2351</span></td><td><span class=\"c3col_right\">0.1867</span></td><td><span class=\"c3col_right\">0.1697</span></td><td><span class=\"c3col_right\">0.1798</span></td><td><span class=\"c3col_right\">0.1680</span></td><td><span class=\"c3col_right\">0.1753</span></td><td><span class=\"c3col_right\">0.2042</span></td><td><span class=\"c3col_right\">0.1914</span></td><td><span class=\"c3col_right\">0.2328</span></td><td><span class=\"c3col_right\">0.1918</span></td><td><span class=\"c3col_right\">0.1778</span></td><td><span class=\"c3col_right\">0.2854</span></td><td><span class=\"c3col_right\">0.1759</span></td><td><span class=\"c3col_right\">0.1987</span></td><td><span class=\"c3col_right\">0.2874</span></td><td><span class=\"c3col_right\">0.1827</span></td><td><span class=\"c3col_right\">0.3104</span></td><td><span class=\"c3col_right\">0.1683</span></td><td><span class=\"c3col_right\">0.1790</span></td><td><span class=\"c3col_right\">0.3872</span></td><td><span class=\"c3col_right\">0.2004</span></td><td><span class=\"c3col_right\">0.2841</span></td><td><span class=\"c3col_right\">0.1700</span></td><td><span class=\"c3col_right\">0.1604</span></td><td><span class=\"c3col_right\">0.2325</span></td><td><span class=\"c3col_right\">0.2651</span></td><td><span class=\"c3col_right\">0.1780</span></td><td><span class=\"c3col_right\">0.1772</span></td><td><span class=\"c3col_right\">0.3042</span></td><td><span class=\"c3col_right\">0.1898</span></td><td><span class=\"c3col_right\">0.2312</span></td><td><span class=\"c3col_right\">0.0000</span></td><td><span class=\"c3col_right\">0.3834</span></td></tr>\n",
       "<tr><td class=\"index\"><span class=\"c3col_left\">Wombat</span></td><td><span class=\"c3col_right\">0.3888</span></td><td><span class=\"c3col_right\">0.3758</span></td><td><span class=\"c3col_right\">0.3806</span></td><td><span class=\"c3col_right\">0.3758</span></td><td><span class=\"c3col_right\">0.1503</span></td><td><span class=\"c3col_right\">0.1740</span></td><td><span class=\"c3col_right\">0.3914</span></td><td><span class=\"c3col_right\">0.3831</span></td><td><span class=\"c3col_right\">0.4039</span></td><td><span class=\"c3col_right\">0.3962</span></td><td><span class=\"c3col_right\">0.4018</span></td><td><span class=\"c3col_right\">0.3684</span></td><td><span class=\"c3col_right\">0.4035</span></td><td><span class=\"c3col_right\">0.3916</span></td><td><span class=\"c3col_right\">0.3786</span></td><td><span class=\"c3col_right\">0.3956</span></td><td><span class=\"c3col_right\">0.3899</span></td><td><span class=\"c3col_right\">0.3976</span></td><td><span class=\"c3col_right\">0.4157</span></td><td><span class=\"c3col_right\">0.3943</span></td><td><span class=\"c3col_right\">0.3831</span></td><td><span class=\"c3col_right\">0.3720</span></td><td><span class=\"c3col_right\">0.4192</span></td><td><span class=\"c3col_right\">0.3976</span></td><td><span class=\"c3col_right\">0.3771</span></td><td><span class=\"c3col_right\">0.3934</span></td><td><span class=\"c3col_right\">0.3882</span></td><td><span class=\"c3col_right\">0.3928</span></td><td><span class=\"c3col_right\">0.4053</span></td><td><span class=\"c3col_right\">0.3911</span></td><td><span class=\"c3col_right\">0.3950</span></td><td><span class=\"c3col_right\">0.3940</span></td><td><span class=\"c3col_right\">0.3899</span></td><td><span class=\"c3col_right\">0.4245</span></td><td><span class=\"c3col_right\">0.3715</span></td><td><span class=\"c3col_right\">0.4008</span></td><td><span class=\"c3col_right\">0.4407</span></td><td><span class=\"c3col_right\">0.3741</span></td><td><span class=\"c3col_right\">0.4498</span></td><td><span class=\"c3col_right\">0.3855</span></td><td><span class=\"c3col_right\">0.3875</span></td><td><span class=\"c3col_right\">0.1358</span></td><td><span class=\"c3col_right\">0.3938</span></td><td><span class=\"c3col_right\">0.4382</span></td><td><span class=\"c3col_right\">0.3899</span></td><td><span class=\"c3col_right\">0.3790</span></td><td><span class=\"c3col_right\">0.4037</span></td><td><span class=\"c3col_right\">0.4361</span></td><td><span class=\"c3col_right\">0.3746</span></td><td><span class=\"c3col_right\">0.3961</span></td><td><span class=\"c3col_right\">0.4385</span></td><td><span class=\"c3col_right\">0.3926</span></td><td><span class=\"c3col_right\">0.4052</span></td><td><span class=\"c3col_right\">0.3834</span></td><td><span class=\"c3col_right\">0.0000</span></td></tr>\n",
       "</tbody>\n",
       "</table>\n",
       "\n",
       "</div>"
      ],
      "text/plain": [
       "=======================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================\n",
       "names         Aardvark    AfricanEl    Anteater    AsianElep    Bandicoot    Caenolest       Cat    Chimpanzee       Cow       Dog    DogFaced    Dugong    FalseVamp    FlyingFox    FlyingLem    FlyingSqu    FreeTaile    Galago    GiantElep    GoldenMol    Gorilla    HairyArma    Hedgehog     Hippo     Horse    HowlerMon     Human    HumpbackW    Jackrabbit    LeafNose    LesserEle    LittleBro     Llama    Madagascar    Manatee      Mole     Mouse    NineBande    OldWorld    Orangutan    Pangolin    Phascogale       Pig       Rat    Rhesus     Rhino    RockHyrax    RoundEare     Sloth    SpermWhale    Tenrec    TombBat    TreeHyrax    TreeShrew    Wombat\n",
       "---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
       "Aardvark        0.0000       0.1182      0.1665       0.1203       0.3989       0.4081    0.1775        0.1701    0.2060    0.1963      0.1842    0.1175       0.1860       0.1719       0.1620       0.1871       0.1706    0.2045       0.2051       0.1543     0.1697       0.1503      0.2335    0.1844    0.1633       0.1805    0.1712       0.1774        0.2082      0.1766       0.1872       0.1848    0.1724        0.2410     0.1144    0.2045    0.2955       0.1634      0.2960       0.1708      0.1788        0.3896    0.1914    0.2902    0.1775    0.1542       0.1726       0.2596    0.1529        0.1788    0.2696     0.1808       0.1741       0.1983    0.3888\n",
       "AfricanEl       0.1182       0.0000      0.1496       0.0043       0.3925       0.3973    0.1675        0.1552    0.1918    0.1841      0.1729    0.0755       0.1674       0.1624       0.1481       0.1763       0.1623    0.1937       0.1986       0.1457     0.1549       0.1316      0.2175    0.1681    0.1449       0.1646    0.1574       0.1596        0.1976      0.1648       0.1756       0.1686    0.1559        0.2388     0.0753    0.1898    0.2898       0.1486      0.2782       0.1552      0.1625        0.3798    0.1806    0.2800    0.1604    0.1406       0.1414       0.2434    0.1418        0.1619    0.2559     0.1677       0.1409       0.1848    0.3758\n",
       "Anteater        0.1665       0.1496      0.0000       0.1503       0.3998       0.4051    0.1590        0.1555    0.1892    0.1782      0.1674    0.1374       0.1694       0.1583       0.1405       0.1721       0.1582    0.1930       0.2333       0.1729     0.1555       0.1019      0.2167    0.1651    0.1466       0.1658    0.1591       0.1536        0.1965      0.1596       0.2168       0.1701    0.1600        0.2592     0.1363    0.1929    0.2851       0.1134      0.2774       0.1577      0.1608        0.3894    0.1767    0.2779    0.1614    0.1388       0.2020       0.2471    0.0934        0.1550    0.2816     0.1672       0.2006       0.1851    0.3806\n",
       "AsianElep       0.1203       0.0043      0.1503       0.0000       0.3933       0.3978    0.1679        0.1563    0.1937    0.1842      0.1748    0.0764       0.1685       0.1636       0.1488       0.1771       0.1627    0.1942       0.1986       0.1464     0.1556       0.1330      0.2195    0.1688    0.1449       0.1653    0.1585       0.1611        0.1992      0.1655       0.1749       0.1693    0.1578        0.2395     0.0762    0.1903    0.2891       0.1504      0.2801       0.1563      0.1622        0.3798    0.1818    0.2792    0.1612    0.1403       0.1418       0.2442    0.1425        0.1635    0.2558     0.1685       0.1412       0.1867    0.3758\n",
       "Bandicoot       0.3989       0.3925      0.3998       0.3933       0.0000       0.2077    0.4121        0.4007    0.4234    0.4141      0.4195    0.3878       0.4229       0.4121       0.3981       0.4067       0.4082    0.4128       0.4286       0.4076     0.4011       0.3913      0.4360    0.4192    0.3996       0.4105    0.4048       0.4140        0.4195      0.4113       0.4122       0.4076    0.4089        0.4458     0.3905    0.4175    0.4541       0.3916      0.4654       0.4028      0.4114        0.1828    0.4137    0.4515    0.4093    0.3997       0.4163       0.4497    0.3904        0.4171    0.4609     0.4062       0.4165       0.4024    0.1503\n",
       "Caenolest       0.4081       0.3973      0.4051       0.3978       0.2077       0.0000    0.4163        0.4068    0.4319    0.4228      0.4202    0.3915       0.4272       0.4125       0.4044       0.4177       0.4164    0.4230       0.4444       0.4138     0.4068       0.3965      0.4345    0.4222    0.4052       0.4133    0.4111       0.4196        0.4315      0.4164       0.4241       0.4174    0.4160        0.4407     0.3931    0.4223    0.4560       0.3963      0.4796       0.4076      0.4178        0.2004    0.4232    0.4502    0.4120    0.4049       0.4196       0.4592    0.3991        0.4234    0.4598     0.4232       0.4211       0.4070    0.1740\n",
       "Cat             0.1775       0.1675      0.1590       0.1679       0.4121       0.4163    0.0000        0.1595    0.1746    0.1229      0.1566    0.1565       0.1490       0.1453       0.1473       0.1770       0.1409    0.1982       0.2449       0.1984     0.1595       0.1520      0.2021    0.1495    0.1304       0.1726    0.1623       0.1351        0.1946      0.1420       0.2217       0.1555    0.1400        0.2709     0.1563    0.1793    0.2901       0.1669      0.2817       0.1605      0.1354        0.3951    0.1620    0.2797    0.1667    0.1216       0.2167       0.2400    0.1582        0.1391    0.2894     0.1482       0.2152       0.1816    0.3914\n",
       "Chimpanzee      0.1701       0.1552      0.1555       0.1563       0.4007       0.4068    0.1595        0.0000    0.1797    0.1741      0.1680    0.1468       0.1594       0.1532       0.1235       0.1523       0.1505    0.1663       0.2419       0.1878     0.0053       0.1430      0.2145    0.1587    0.1396       0.0665    0.0092       0.1501        0.1848      0.1563       0.2131       0.1581    0.1502        0.2599     0.1464    0.1750    0.2556       0.1550      0.2678       0.0137      0.1531        0.3881    0.1688    0.2532    0.0381    0.1320       0.2055       0.2419    0.1499        0.1484    0.2823     0.1622       0.2041       0.1632    0.3831\n",
       "Cow             0.2060       0.1918      0.1892       0.1937       0.4234       0.4319    0.1746        0.1797    0.0000    0.1996      0.1801    0.1849       0.1758       0.1680       0.1735       0.1961       0.1629    0.2224       0.2547       0.2221     0.1797       0.1775      0.2309    0.1245    0.1512       0.1862    0.1805       0.1084        0.2206      0.1629       0.2448       0.1733    0.1388        0.2857     0.1823    0.1955    0.2868       0.1878      0.2967       0.1801      0.1651        0.4114    0.1499    0.2877    0.1896    0.1480       0.2375       0.2555    0.1784        0.1124    0.3031     0.1743       0.2378       0.2010    0.4039\n",
       "Dog             0.1963       0.1841      0.1782       0.1842       0.4141       0.4228    0.1229        0.1741    0.1996    0.0000      0.1821    0.1739       0.1692       0.1696       0.1602       0.1909       0.1602    0.2180       0.2549       0.2165     0.1730       0.1676      0.2309    0.1734    0.1451       0.1864    0.1765       0.1555        0.2058      0.1624       0.2440       0.1744    0.1614        0.2829     0.1733    0.1917    0.2989       0.1800      0.2935       0.1737      0.1599        0.4025    0.1804    0.2878    0.1813    0.1360       0.2257       0.2560    0.1736        0.1636    0.3037     0.1659       0.2245       0.2016    0.3962\n",
       "DogFaced        0.1842       0.1729      0.1674       0.1748       0.4195       0.4202    0.1566        0.1680    0.1801    0.1821      0.0000    0.1638       0.1408       0.0517       0.1547       0.1839       0.1278    0.2041       0.2501       0.2075     0.1672       0.1599      0.2213    0.1574    0.1406       0.1766    0.1698       0.1455        0.2011      0.1361       0.2365       0.1374    0.1556        0.2758     0.1632    0.1831    0.2991       0.1718      0.2937       0.1695      0.1498        0.4088    0.1687    0.2899    0.1749    0.1279       0.2190       0.2203    0.1604        0.1474    0.3061     0.1361       0.2171       0.1942    0.4018\n",
       "Dugong          0.1175       0.0755      0.1374       0.0764       0.3878       0.3915    0.1565        0.1468    0.1849    0.1739      0.1638    0.0000       0.1562       0.1536       0.1340       0.1615       0.1537    0.1872       0.1878       0.1269     0.1464       0.1201      0.2057    0.1604    0.1369       0.1580    0.1497       0.1475        0.1846      0.1543       0.1631       0.1631    0.1504        0.2216     0.0152    0.1794    0.2686       0.1374      0.2684       0.1468      0.1508        0.3722    0.1656    0.2644    0.1513    0.1298       0.1310       0.2360    0.1299        0.1492    0.2449     0.1586       0.1302       0.1739    0.3684\n",
       "FalseVamp       0.1860       0.1674      0.1694       0.1685       0.4229       0.4272    0.1490        0.1594    0.1758    0.1692      0.1408    0.1562       0.0000       0.1265       0.1540       0.1853       0.1229    0.2113       0.2489       0.2076     0.1587       0.1607      0.2085    0.1514    0.1288       0.1719    0.1617       0.1367        0.1943      0.1156       0.2324       0.1301    0.1447        0.2761     0.1534    0.1794    0.2929       0.1681      0.2858       0.1598      0.1411        0.4121    0.1613    0.2833    0.1664    0.1210       0.2177       0.2234    0.1664        0.1398    0.3034     0.1333       0.2172       0.1966    0.4035\n",
       "FlyingFox       0.1719       0.1624      0.1583       0.1636       0.4121       0.4125    0.1453        0.1532    0.1680    0.1696      0.0517    0.1536       0.1265       0.0000       0.1394       0.1690       0.1125    0.1936       0.2407       0.1975     0.1532       0.1442      0.2126    0.1476    0.1252       0.1599    0.1551       0.1320        0.1880      0.1197       0.2237       0.1208    0.1409        0.2706     0.1528    0.1681    0.2884       0.1571      0.2843       0.1551      0.1377        0.4010    0.1540    0.2805    0.1584    0.1134       0.2054       0.2112    0.1486        0.1351    0.2965     0.1245       0.2059       0.1814    0.3916\n",
       "FlyingLem       0.1620       0.1481      0.1405       0.1488       0.3981       0.4044    0.1473        0.1235    0.1735    0.1602      0.1547    0.1340       0.1540       0.1394       0.0000       0.1430       0.1436    0.1688       0.2274       0.1733     0.1231       0.1284      0.2045    0.1463    0.1254       0.1322    0.1266       0.1365        0.1654      0.1455       0.2122       0.1542    0.1421        0.2587     0.1344    0.1718    0.2597       0.1381      0.2594       0.1259      0.1377        0.3819    0.1538    0.2549    0.1275    0.1164       0.1914       0.2362    0.1318        0.1374    0.2737     0.1450       0.1893       0.1573    0.3786\n",
       "FlyingSqu       0.1871       0.1763      0.1721       0.1771       0.4067       0.4177    0.1770        0.1523    0.1961    0.1909      0.1839    0.1615       0.1853       0.1690       0.1430       0.0000       0.1702    0.1935       0.2528       0.2019     0.1520       0.1608      0.2303    0.1802    0.1628       0.1647    0.1562       0.1696        0.1971      0.1736       0.2291       0.1816    0.1734        0.2795     0.1641    0.1976    0.2616       0.1753      0.2627       0.1552      0.1671        0.4014    0.1885    0.2563    0.1582    0.1544       0.2165       0.2530    0.1686        0.1740    0.3014     0.1738       0.2168       0.1836    0.3956\n",
       "FreeTaile       0.1706       0.1623      0.1582       0.1627       0.4082       0.4164    0.1409        0.1505    0.1629    0.1602      0.1278    0.1537       0.1229       0.1125       0.1436       0.1702       0.0000    0.1923       0.2351       0.1958     0.1497       0.1505      0.2020    0.1423    0.1159       0.1603    0.1512       0.1293        0.1919      0.1136       0.2228       0.0856    0.1348        0.2757     0.1543    0.1693    0.2762       0.1617      0.2769       0.1523      0.1365        0.4001    0.1517    0.2719    0.1600    0.1119       0.2085       0.1975    0.1483        0.1315    0.2960     0.0956       0.2074       0.1824    0.3899\n",
       "Galago          0.2045       0.1937      0.1930       0.1942       0.4128       0.4230    0.1982        0.1663    0.2224    0.2180      0.2041    0.1872       0.2113       0.1936       0.1688       0.1935       0.1923    0.0000       0.2712       0.2219     0.1663       0.1854      0.2454    0.2000    0.1852       0.1831    0.1695       0.1927        0.2197      0.1963       0.2466       0.2027    0.1903        0.2961     0.1879    0.2190    0.3021       0.1996      0.3043       0.1681      0.1967        0.4048    0.2154    0.2928    0.1697    0.1750       0.2395       0.2840    0.1909        0.1917    0.3216     0.2009       0.2394       0.1953    0.3976\n",
       "GiantElep       0.2051       0.1986      0.2333       0.1986       0.4286       0.4444    0.2449        0.2419    0.2547    0.2549      0.2501    0.1878       0.2489       0.2407       0.2274       0.2528       0.2351    0.2712       0.0000       0.2128     0.2408       0.2181      0.2873    0.2328    0.2278       0.2514    0.2440       0.2303        0.2704      0.2406       0.2018       0.2445    0.2334        0.2991     0.1881    0.2605    0.3433       0.2267      0.3485       0.2444      0.2434        0.4164    0.2513    0.3368    0.2490    0.2170       0.2435       0.3184    0.2206        0.2308    0.3198     0.2396       0.2445       0.2513    0.4157\n",
       "GoldenMol       0.1543       0.1457      0.1729       0.1464       0.4076       0.4138    0.1984        0.1878    0.2221    0.2165      0.2075    0.1269       0.2076       0.1975       0.1733       0.2019       0.1958    0.2219       0.2128       0.0000     0.1864       0.1638      0.2471    0.2050    0.1827       0.1955    0.1904       0.1944        0.2312      0.1993       0.2008       0.2039    0.1908        0.2420     0.1262    0.2165    0.3069       0.1771      0.3046       0.1896      0.1910        0.3983    0.2080    0.2955    0.1946    0.1754       0.1945       0.2832    0.1712        0.1933    0.2626     0.2034       0.1949       0.2134    0.3943\n",
       "Gorilla         0.1697       0.1549      0.1555       0.1556       0.4011       0.4068    0.1595        0.0053    0.1797    0.1730      0.1672    0.1464       0.1587       0.1532       0.1231       0.1520       0.1497    0.1663       0.2408       0.1864     0.0000       0.1434      0.2141    0.1594    0.1392       0.0661    0.0088       0.1501        0.1852      0.1567       0.2153       0.1574    0.1495        0.2588     0.1460    0.1757    0.2563       0.1553      0.2667       0.0134      0.1534        0.3894    0.1681    0.2532    0.0378    0.1316       0.2059       0.2408    0.1506        0.1484    0.2812     0.1622       0.2044       0.1646    0.3831\n",
       "HairyArma       0.1503       0.1316      0.1019       0.1330       0.3913       0.3965    0.1520        0.1430    0.1775    0.1676      0.1599    0.1201       0.1607       0.1442       0.1284       0.1608       0.1505    0.1854       0.2181       0.1638     0.1434       0.0000      0.2102    0.1586    0.1341       0.1523    0.1448       0.1440        0.1767      0.1553       0.2039       0.1593    0.1532        0.2517     0.1208    0.1826    0.2740       0.0614      0.2667       0.1444      0.1491        0.3799    0.1653    0.2639    0.1482    0.1281       0.1844       0.2461    0.0853        0.1463    0.2730     0.1571       0.1834       0.1675    0.3720\n",
       "Hedgehog        0.2335       0.2175      0.2167       0.2195       0.4360       0.4345    0.2021        0.2145    0.2309    0.2309      0.2213    0.2057       0.2085       0.2126       0.2045       0.2303       0.2020    0.2454       0.2873       0.2471     0.2141       0.2102      0.0000    0.2078    0.1948       0.2172    0.2171       0.1984        0.2433      0.2116       0.2756       0.2133    0.1952        0.3169     0.2037    0.2113    0.3399       0.2230      0.3357       0.2160      0.2032        0.4186    0.2199    0.3307    0.2151    0.1829       0.2575       0.2852    0.2148        0.1985    0.3335     0.2051       0.2570       0.2351    0.4192\n",
       "Hippo           0.1844       0.1681      0.1651       0.1688       0.4192       0.4222    0.1495        0.1587    0.1245    0.1734      0.1574    0.1604       0.1514       0.1476       0.1463       0.1802       0.1423    0.2000       0.2328       0.2050     0.1594       0.1586      0.2078    0.0000    0.1257       0.1706    0.1598       0.0793        0.2005      0.1395       0.2207       0.1470    0.1141        0.2696     0.1580    0.1782    0.2718       0.1668      0.2786       0.1598      0.1440        0.4037    0.1224    0.2709    0.1682    0.1197       0.2210       0.2341    0.1608        0.0817    0.2868     0.1520       0.2213       0.1867    0.3976\n",
       "Horse           0.1633       0.1449      0.1466       0.1449       0.3996       0.4052    0.1304        0.1396    0.1512    0.1451      0.1406    0.1369       0.1288       0.1252       0.1254       0.1628       0.1159    0.1852       0.2278       0.1827     0.1392       0.1341      0.1948    0.1257    0.0000       0.1530    0.1424       0.1143        0.1762      0.1206       0.2128       0.1298    0.1197        0.2605     0.1351    0.1553    0.2674       0.1482      0.2660       0.1399      0.1195        0.3820    0.1411    0.2606    0.1479    0.0729       0.2007       0.2124    0.1418        0.1183    0.2770     0.1299       0.1985       0.1697    0.3771\n",
       "HowlerMon       0.1805       0.1646      0.1658       0.1653       0.4105       0.4133    0.1726        0.0665    0.1862    0.1864      0.1766    0.1580       0.1719       0.1599       0.1322       0.1647       0.1603    0.1831       0.2514       0.1955     0.0661       0.1523      0.2172    0.1706    0.1530       0.0000    0.0696       0.1580        0.1939      0.1652       0.2263       0.1658    0.1583        0.2613     0.1571    0.1864    0.2666       0.1629      0.2803       0.0679      0.1627        0.3990    0.1812    0.2631    0.0690    0.1454       0.2126       0.2459    0.1609        0.1587    0.2903     0.1677       0.2103       0.1798    0.3934\n",
       "Human           0.1712       0.1574      0.1591       0.1585       0.4048       0.4111    0.1623        0.0092    0.1805    0.1765      0.1698    0.1497       0.1617       0.1551       0.1266       0.1562       0.1512    0.1695       0.2440       0.1904     0.0088       0.1448      0.2171    0.1598    0.1424       0.0696    0.0000       0.1498        0.1882      0.1588       0.2175       0.1581    0.1498        0.2603     0.1492    0.1778    0.2582       0.1575      0.2686       0.0173      0.1538        0.3903    0.1699    0.2550    0.0410    0.1338       0.2085       0.2434    0.1524        0.1477    0.2845     0.1640       0.2066       0.1680    0.3882\n",
       "HumpbackW       0.1774       0.1596      0.1536       0.1611       0.4140       0.4196    0.1351        0.1501    0.1084    0.1555      0.1455    0.1475       0.1367       0.1320       0.1365       0.1696       0.1293    0.1927       0.2303       0.1944     0.1501       0.1440      0.1984    0.0793    0.1143       0.1580    0.1498       0.0000        0.1867      0.1289       0.2185       0.1427    0.0979        0.2635     0.1481    0.1642    0.2783       0.1539      0.2776       0.1498      0.1267        0.3966    0.1065    0.2752    0.1564    0.1084       0.2118       0.2301    0.1452        0.0254    0.2848     0.1392       0.2106       0.1753    0.3928\n",
       "Jackrabbit      0.2082       0.1976      0.1965       0.1992       0.4195       0.4315    0.1946        0.1848    0.2206    0.2058      0.2011    0.1846       0.1943       0.1880       0.1654       0.1971       0.1919    0.2197       0.2704       0.2312     0.1852       0.1767      0.2433    0.2005    0.1762       0.1939    0.1882       0.1867        0.0000      0.1905       0.2538       0.2011    0.1969        0.2911     0.1865    0.2181    0.2955       0.1921      0.2935       0.1841      0.1933        0.4050    0.2082    0.2852    0.1871    0.1745       0.2355       0.2652    0.1879        0.1917    0.3101     0.1950       0.2351       0.2042    0.4053\n",
       "LeafNose        0.1766       0.1648      0.1596       0.1655       0.4113       0.4164    0.1420        0.1563    0.1629    0.1624      0.1361    0.1543       0.1156       0.1197       0.1455       0.1736       0.1136    0.1963       0.2406       0.1993     0.1567       0.1553      0.2116    0.1395    0.1206       0.1652    0.1588       0.1289        0.1905      0.0000       0.2226       0.1253    0.1371        0.2740     0.1527    0.1759    0.2793       0.1641      0.2760       0.1563      0.1397        0.4028    0.1528    0.2747    0.1636    0.1155       0.2114       0.2121    0.1557        0.1326    0.2952     0.1272       0.2095       0.1914    0.3911\n",
       "LesserEle       0.1872       0.1756      0.2168       0.1749       0.4122       0.4241    0.2217        0.2131    0.2448    0.2440      0.2365    0.1631       0.2324       0.2237       0.2122       0.2291       0.2228    0.2466       0.2018       0.2008     0.2153       0.2039      0.2756    0.2207    0.2128       0.2263    0.2175       0.2185        0.2538      0.2226       0.0000       0.2293    0.2180        0.2826     0.1632    0.2461    0.3236       0.2151      0.3394       0.2157      0.2226        0.4025    0.2305    0.3180    0.2238    0.2021       0.2224       0.3012    0.2073        0.2179    0.3009     0.2245       0.2242       0.2328    0.3950\n",
       "LittleBro       0.1848       0.1686      0.1701       0.1693       0.4076       0.4174    0.1555        0.1581    0.1733    0.1744      0.1374    0.1631       0.1301       0.1208       0.1542       0.1816       0.0856    0.2027       0.2445       0.2039     0.1574       0.1593      0.2133    0.1470    0.1298       0.1658    0.1581       0.1427        0.2011      0.1253       0.2293       0.0000    0.1434        0.2798     0.1625    0.1803    0.2836       0.1660      0.2822       0.1570      0.1483        0.3983    0.1644    0.2797    0.1631    0.1233       0.2176       0.2014    0.1578        0.1433    0.2977     0.1108       0.2172       0.1918    0.3940\n",
       "Llama           0.1724       0.1559      0.1600       0.1578       0.4089       0.4160    0.1400        0.1502    0.1388    0.1614      0.1556    0.1504       0.1447       0.1409       0.1421       0.1734       0.1348    0.1903       0.2334       0.1908     0.1495       0.1532      0.1952    0.1141    0.1197       0.1583    0.1498       0.0979        0.1969      0.1371       0.2180       0.1434    0.0000        0.2620     0.1470    0.1697    0.2786       0.1602      0.2693       0.1495      0.1391        0.3973    0.1229    0.2740    0.1560    0.1142       0.2126       0.2297    0.1490        0.0999    0.2896     0.1460       0.2114       0.1778    0.3899\n",
       "Madagascar      0.2410       0.2388      0.2592       0.2395       0.4458       0.4407    0.2709        0.2599    0.2857    0.2829      0.2758    0.2216       0.2761       0.2706       0.2587       0.2795       0.2757    0.2961       0.2991       0.2420     0.2588       0.2517      0.3169    0.2696    0.2605       0.2613    0.2603       0.2635        0.2911      0.2740       0.2826       0.2798    0.2620        0.0000     0.2234    0.2844    0.3537       0.2643      0.3608       0.2618      0.2740        0.4391    0.2759    0.3506    0.2651    0.2529       0.2741       0.3299    0.2531        0.2650    0.1332     0.2783       0.2764       0.2854    0.4245\n",
       "Manatee         0.1144       0.0753      0.1363       0.0762       0.3905       0.3931    0.1563        0.1464    0.1823    0.1733      0.1632    0.0152       0.1534       0.1528       0.1344       0.1641       0.1543    0.1879       0.1881       0.1262     0.1460       0.1208      0.2037    0.1580    0.1351       0.1571    0.1492       0.1481        0.1865      0.1527       0.1632       0.1625    0.1470        0.2234     0.0000    0.1802    0.2685       0.1367      0.2703       0.1464      0.1478        0.3738    0.1661    0.2635    0.1508    0.1273       0.1332       0.2387    0.1292        0.1491    0.2466     0.1585       0.1323       0.1759    0.3715\n",
       "Mole            0.2045       0.1898      0.1929       0.1903       0.4175       0.4223    0.1793        0.1750    0.1955    0.1917      0.1831    0.1794       0.1794       0.1681       0.1718       0.1976       0.1693    0.2190       0.2605       0.2165     0.1757       0.1826      0.2113    0.1782    0.1553       0.1864    0.1778       0.1642        0.2181      0.1759       0.2461       0.1803    0.1697        0.2844     0.1802    0.0000    0.3087       0.1932      0.2976       0.1761      0.1720        0.4028    0.1876    0.3015    0.1830    0.1496       0.2345       0.2596    0.1831        0.1707    0.3102     0.1785       0.2347       0.1987    0.4008\n",
       "Mouse           0.2955       0.2898      0.2851       0.2891       0.4541       0.4560    0.2901        0.2556    0.2868    0.2989      0.2991    0.2686       0.2929       0.2884       0.2597       0.2616       0.2762    0.3021       0.3433       0.3069     0.2563       0.2740      0.3399    0.2718    0.2674       0.2666    0.2582       0.2783        0.2955      0.2793       0.3236       0.2836    0.2786        0.3537     0.2685    0.3087    0.0000       0.2825      0.3474       0.2563      0.2796        0.4525    0.2893    0.1133    0.2584    0.2709       0.3171       0.3405    0.2778        0.2794    0.3633     0.2948       0.3137       0.2874    0.4407\n",
       "NineBande       0.1634       0.1486      0.1134       0.1504       0.3916       0.3963    0.1669        0.1550    0.1878    0.1800      0.1718    0.1374       0.1681       0.1571       0.1381       0.1753       0.1617    0.1996       0.2267       0.1771     0.1553       0.0614      0.2230    0.1668    0.1482       0.1629    0.1575       0.1539        0.1921      0.1641       0.2151       0.1660    0.1602        0.2643     0.1367    0.1932    0.2825       0.0000      0.2774       0.1568      0.1637        0.3814    0.1751    0.2757    0.1598    0.1396       0.2003       0.2557    0.0971        0.1555    0.2867     0.1658       0.2007       0.1827    0.3741\n",
       "OldWorld        0.2960       0.2782      0.2774       0.2801       0.4654       0.4796    0.2817        0.2678    0.2967    0.2935      0.2937    0.2684       0.2858       0.2843       0.2594       0.2627       0.2769    0.3043       0.3485       0.3046     0.2667       0.2667      0.3357    0.2786    0.2660       0.2803    0.2686       0.2776        0.2935      0.2760       0.3394       0.2822    0.2693        0.3608     0.2703    0.2976    0.3474       0.2774      0.0000       0.2675      0.2826        0.4547    0.2850    0.3407    0.2714    0.2650       0.3167       0.3235    0.2719        0.2764    0.3694     0.2886       0.3189       0.3104    0.4498\n",
       "Orangutan       0.1708       0.1552      0.1577       0.1563       0.4028       0.4076    0.1605        0.0137    0.1801    0.1737      0.1695    0.1468       0.1598       0.1551       0.1259       0.1552       0.1523    0.1681       0.2444       0.1896     0.0134       0.1444      0.2160    0.1598    0.1399       0.0679    0.0173       0.1498        0.1841      0.1563       0.2157       0.1570    0.1495        0.2618     0.1464    0.1761    0.2563       0.1568      0.2675       0.0000      0.1527        0.3886    0.1677    0.2528    0.0395    0.1331       0.2044       0.2427    0.1520        0.1487    0.2838     0.1651       0.2037       0.1683    0.3855\n",
       "Pangolin        0.1788       0.1625      0.1608       0.1622       0.4114       0.4178    0.1354        0.1531    0.1651    0.1599      0.1498    0.1508       0.1411       0.1377       0.1377       0.1671       0.1365    0.1967       0.2434       0.1910     0.1534       0.1491      0.2032    0.1440    0.1195       0.1627    0.1538       0.1267        0.1933      0.1397       0.2226       0.1483    0.1391        0.2740     0.1478    0.1720    0.2796       0.1637      0.2826       0.1527      0.0000        0.4003    0.1517    0.2746    0.1597    0.1153       0.2164       0.2366    0.1578        0.1293    0.2970     0.1405       0.2134       0.1790    0.3875\n",
       "Phascogale      0.3896       0.3798      0.3894       0.3798       0.1828       0.2004    0.3951        0.3881    0.4114    0.4025      0.4088    0.3722       0.4121       0.4010       0.3819       0.4014       0.4001    0.4048       0.4164       0.3983     0.3894       0.3799      0.4186    0.4037    0.3820       0.3990    0.3903       0.3966        0.4050      0.4028       0.4025       0.3983    0.3973        0.4391     0.3738    0.4028    0.4525       0.3814      0.4547       0.3886      0.4003        0.0000    0.4033    0.4485    0.3934    0.3833       0.4007       0.4492    0.3799        0.4016    0.4537     0.4005       0.4023       0.3872    0.1358\n",
       "Pig             0.1914       0.1806      0.1767       0.1818       0.4137       0.4232    0.1620        0.1688    0.1499    0.1804      0.1687    0.1656       0.1613       0.1540       0.1538       0.1885       0.1517    0.2154       0.2513       0.2080     0.1681       0.1653      0.2199    0.1224    0.1411       0.1812    0.1699       0.1065        0.2082      0.1528       0.2305       0.1644    0.1229        0.2759     0.1661    0.1876    0.2893       0.1751      0.2850       0.1677      0.1517        0.4033    0.0000    0.2888    0.1807    0.1348       0.2270       0.2404    0.1695        0.1073    0.2941     0.1566       0.2266       0.2004    0.3938\n",
       "Rat             0.2902       0.2800      0.2779       0.2792       0.4515       0.4502    0.2797        0.2532    0.2877    0.2878      0.2899    0.2644       0.2833       0.2805       0.2549       0.2563       0.2719    0.2928       0.3368       0.2955     0.2532       0.2639      0.3307    0.2709    0.2606       0.2631    0.2550       0.2752        0.2852      0.2747       0.3180       0.2797    0.2740        0.3506     0.2635    0.3015    0.1133       0.2757      0.3407       0.2528      0.2746        0.4485    0.2888    0.0000    0.2583    0.2619       0.3091       0.3439    0.2721        0.2770    0.3610     0.2915       0.3079       0.2841    0.4382\n",
       "Rhesus          0.1775       0.1604      0.1614       0.1612       0.4093       0.4120    0.1667        0.0381    0.1896    0.1813      0.1749    0.1513       0.1664       0.1584       0.1275       0.1582       0.1600    0.1697       0.2490       0.1946     0.0378       0.1482      0.2151    0.1682    0.1479       0.0690    0.0410       0.1564        0.1871      0.1636       0.2238       0.1631    0.1560        0.2651     0.1508    0.1830    0.2584       0.1598      0.2714       0.0395      0.1597        0.3934    0.1807    0.2583    0.0000    0.1374       0.2123       0.2460    0.1572        0.1564    0.2896     0.1675       0.2112       0.1700    0.3899\n",
       "Rhino           0.1542       0.1406      0.1388       0.1403       0.3997       0.4049    0.1216        0.1320    0.1480    0.1360      0.1279    0.1298       0.1210       0.1134       0.1164       0.1544       0.1119    0.1750       0.2170       0.1754     0.1316       0.1281      0.1829    0.1197    0.0729       0.1454    0.1338       0.1084        0.1745      0.1155       0.2021       0.1233    0.1142        0.2529     0.1273    0.1496    0.2709       0.1396      0.2650       0.1331      0.1153        0.3833    0.1348    0.2619    0.1374    0.0000       0.1924       0.2036    0.1321        0.1117    0.2746     0.1200       0.1917       0.1604    0.3790\n",
       "RockHyrax       0.1726       0.1414      0.2020       0.1418       0.4163       0.4196    0.2167        0.2055    0.2375    0.2257      0.2190    0.1310       0.2177       0.2054       0.1914       0.2165       0.2085    0.2395       0.2435       0.1945     0.2059       0.1844      0.2575    0.2210    0.2007       0.2126    0.2085       0.2118        0.2355      0.2114       0.2224       0.2176    0.2126        0.2741     0.1332    0.2345    0.3171       0.2003      0.3167       0.2044      0.2164        0.4007    0.2270    0.3091    0.2123    0.1924       0.0000       0.2879    0.1911        0.2158    0.3009     0.2145       0.0135       0.2325    0.4037\n",
       "RoundEare       0.2596       0.2434      0.2471       0.2442       0.4497       0.4592    0.2400        0.2419    0.2555    0.2560      0.2203    0.2360       0.2234       0.2112       0.2362       0.2530       0.1975    0.2840       0.3184       0.2832     0.2408       0.2461      0.2852    0.2341    0.2124       0.2459    0.2434       0.2301        0.2652      0.2121       0.3012       0.2014    0.2297        0.3299     0.2387    0.2596    0.3405       0.2557      0.3235       0.2427      0.2366        0.4492    0.2404    0.3439    0.2460    0.2036       0.2879       0.0000    0.2402        0.2285    0.3451     0.1964       0.2875       0.2651    0.4361\n",
       "Sloth           0.1529       0.1418      0.0934       0.1425       0.3904       0.3991    0.1582        0.1499    0.1784    0.1736      0.1604    0.1299       0.1664       0.1486       0.1318       0.1686       0.1483    0.1909       0.2206       0.1712     0.1506       0.0853      0.2148    0.1608    0.1418       0.1609    0.1524       0.1452        0.1879      0.1557       0.2073       0.1578    0.1490        0.2531     0.1292    0.1831    0.2778       0.0971      0.2719       0.1520      0.1578        0.3799    0.1695    0.2721    0.1572    0.1321       0.1911       0.2402    0.0000        0.1497    0.2775     0.1545       0.1919       0.1780    0.3746\n",
       "SpermWhale      0.1788       0.1619      0.1550       0.1635       0.4171       0.4234    0.1391        0.1484    0.1124    0.1636      0.1474    0.1492       0.1398       0.1351       0.1374       0.1740       0.1315    0.1917       0.2308       0.1933     0.1484       0.1463      0.1985    0.0817    0.1183       0.1587    0.1477       0.0254        0.1917      0.1326       0.2179       0.1433    0.0999        0.2650     0.1491    0.1707    0.2794       0.1555      0.2764       0.1487      0.1293        0.4016    0.1073    0.2770    0.1564    0.1117       0.2158       0.2285    0.1497        0.0000    0.2845     0.1404       0.2147       0.1772    0.3961\n",
       "Tenrec          0.2696       0.2559      0.2816       0.2558       0.4609       0.4598    0.2894        0.2823    0.3031    0.3037      0.3061    0.2449       0.3034       0.2965       0.2737       0.3014       0.2960    0.3216       0.3198       0.2626     0.2812       0.2730      0.3335    0.2868    0.2770       0.2903    0.2845       0.2848        0.3101      0.2952       0.3009       0.2977    0.2896        0.1332     0.2466    0.3102    0.3633       0.2867      0.3694       0.2838      0.2970        0.4537    0.2941    0.3610    0.2896    0.2746       0.3009       0.3451    0.2775        0.2845    0.0000     0.2993       0.3024       0.3042    0.4385\n",
       "TombBat         0.1808       0.1677      0.1672       0.1685       0.4062       0.4232    0.1482        0.1622    0.1743    0.1659      0.1361    0.1586       0.1333       0.1245       0.1450       0.1738       0.0956    0.2009       0.2396       0.2034     0.1622       0.1571      0.2051    0.1520    0.1299       0.1677    0.1640       0.1392        0.1950      0.1272       0.2245       0.1108    0.1460        0.2783     0.1585    0.1785    0.2948       0.1658      0.2886       0.1651      0.1405        0.4005    0.1566    0.2915    0.1675    0.1200       0.2145       0.1964    0.1545        0.1404    0.2993     0.0000       0.2114       0.1898    0.3926\n",
       "TreeHyrax       0.1741       0.1409      0.2006       0.1412       0.4165       0.4211    0.2152        0.2041    0.2378    0.2245      0.2171    0.1302       0.2172       0.2059       0.1893       0.2168       0.2074    0.2394       0.2445       0.1949     0.2044       0.1834      0.2570    0.2213    0.1985       0.2103    0.2066       0.2106        0.2351      0.2095       0.2242       0.2172    0.2114        0.2764     0.1323    0.2347    0.3137       0.2007      0.3189       0.2037      0.2134        0.4023    0.2266    0.3079    0.2112    0.1917       0.0135       0.2875    0.1919        0.2147    0.3024     0.2114       0.0000       0.2312    0.4052\n",
       "TreeShrew       0.1983       0.1848      0.1851       0.1867       0.4024       0.4070    0.1816        0.1632    0.2010    0.2016      0.1942    0.1739       0.1966       0.1814       0.1573       0.1836       0.1824    0.1953       0.2513       0.2134     0.1646       0.1675      0.2351    0.1867    0.1697       0.1798    0.1680       0.1753        0.2042      0.1914       0.2328       0.1918    0.1778        0.2854     0.1759    0.1987    0.2874       0.1827      0.3104       0.1683      0.1790        0.3872    0.2004    0.2841    0.1700    0.1604       0.2325       0.2651    0.1780        0.1772    0.3042     0.1898       0.2312       0.0000    0.3834\n",
       "Wombat          0.3888       0.3758      0.3806       0.3758       0.1503       0.1740    0.3914        0.3831    0.4039    0.3962      0.4018    0.3684       0.4035       0.3916       0.3786       0.3956       0.3899    0.3976       0.4157       0.3943     0.3831       0.3720      0.4192    0.3976    0.3771       0.3934    0.3882       0.3928        0.4053      0.3911       0.3950       0.3940    0.3899        0.4245     0.3715    0.4008    0.4407       0.3741      0.4498       0.3855      0.3875        0.1358    0.3938    0.4382    0.3899    0.3790       0.4037       0.4361    0.3746        0.3961    0.4385     0.3926       0.4052       0.3834    0.0000\n",
       "---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pair_distance = aln.distance_matrix()\n",
    "pair_distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_coll = aln.degap()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "seq_coll.write(\"seq_coll.fasta\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = seq_coll.to_dict()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Mash distance "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Firstly, I test two sets of mash distance calculated by me, compared with distance reported by MASH. My results are very close to MASH's."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05332165358294851"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "##some tests\n",
    "##sketch two seqs\n",
    "flyingfox = data[\"FlyingFox\"]\n",
    "dogfaced = data[\"DogFaced\"]\n",
    "\n",
    "hash1, hash2 = sketch_genome_64(flyingfox, dogfaced, kmer = 21, sketch=1000)\n",
    "##dis\n",
    "mash_d(hash1, hash2, kmer=21, sketch=1000) ##mash report: 0.0519203 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14977748270692326"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#more tests\n",
    "##sketch two seqs\n",
    "cat = data[\"Cat\"]\n",
    "Aardvark = data[\"Aardvark\"]\n",
    "\n",
    "hash5, hash6 = sketch_genome_64(cat, Aardvark, kmer = 21, sketch=1000)\n",
    "##dis\n",
    "mash_d(hash5, hash6, kmer=21, sketch=1000) ##mash report: 0.149777"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29598131422644164"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#another test\n",
    "##sketch two seqs\n",
    "Rat = data[\"Rat\"]\n",
    "GiantElep = data[\"GiantElep\"]\n",
    "\n",
    "hash3, hash4 = sketch_genome_64(Rat, GiantElep, kmer = 21, sketch=1000)\n",
    "##dis\n",
    "mash_d(hash3, hash4, kmer=21, sketch=1000) ##mash report:  0.295981  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, calculate all MASH distance and wrap in matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmer=21\n",
    "# Because 4**kmer > 2**32, we can use 64-bit hash.\n",
    "mash_distance = pair_mash_distance(data, kmer=21, sketch=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0.09813753018019467, 0.1457271806995982, 0.09684626213555463,\n",
       "        0.29598131422644164, 0.21953132035710143, 0.14977748270692326,\n",
       "        0.1309794155758673, 0.18676063506101495, 0.1338642904272318,\n",
       "        0.15422278343639906, 0.10299743304193935, 0.16466155834946195,\n",
       "        0.14977748270692326, 0.12960392142344132, 0.14200853843568037,\n",
       "        0.1477073033077396, 0.15914648850735036, 0.1744083317251048,\n",
       "        0.1369476059660776, 0.1369476059660776, 0.1110725979806038,\n",
       "        0.24376149136828001, 0.18676063506101495, 0.12330024592426836,\n",
       "        0.1457271806995982, 0.1338642904272318, 0.15661861302363517,\n",
       "        0.14977748270692326, 0.1477073033077396, 0.1338642904272318,\n",
       "        0.16182151768725705, 0.13857232167999814, 0.21089670004150873,\n",
       "        0.09378288792692892, 0.16466155834946195, 0.19173063154559256,\n",
       "        0.13239861250865886, 0.21089670004150873, 0.12330024592426836,\n",
       "        0.15914648850735036, 0.29598131422644164, 0.14977748270692326,\n",
       "        0.26302185335832945, 0.13239861250865886, 0.11676011876517363,\n",
       "        0.16182151768725705, 0.26302185335832945, 0.11990859159380944,\n",
       "        0.15422278343639906, 0.26302185335832945, 0.16182151768725705,\n",
       "        0.16182151768725705, 0.1353795009048372, 0.26302185335832945],\n",
       "       [0.09813753018019467, 0, 0.11990859159380944, 0.00399628587810372,\n",
       "        0.29598131422644164, 0.24376149136828001, 0.1402577696840135,\n",
       "        0.13239861250865886, 0.1744083317251048, 0.13857232167999814,\n",
       "        0.15422278343639906, 0.06158387907426547, 0.15661861302363517,\n",
       "        0.16182151768725705, 0.1221404455934065, 0.1457271806995982,\n",
       "        0.13857232167999814, 0.16768792903874916, 0.23010979802723042,\n",
       "        0.1369476059660776, 0.1309794155758673, 0.1157590508369442,\n",
       "        0.1744083317251048, 0.16768792903874916, 0.1110725979806038,\n",
       "        0.15194610475625225, 0.1369476059660776, 0.15422278343639906,\n",
       "        0.14200853843568037, 0.1477073033077396, 0.12960392142344132,\n",
       "        0.14977748270692326, 0.14200853843568037, 0.23010979802723042,\n",
       "        0.06371235196890539, 0.18676063506101495, 0.23010979802723042,\n",
       "        0.11990859159380944, 0.26302185335832945, 0.12449132016378583,\n",
       "        0.13857232167999814, 0.29598131422644164, 0.15914648850735036,\n",
       "        0.24376149136828001, 0.13857232167999814, 0.11019321400744202,\n",
       "        0.11990859159380944, 0.26302185335832945, 0.14200853843568037,\n",
       "        0.14200853843568037, 0.29598131422644164, 0.14382975648306484,\n",
       "        0.1157590508369442, 0.15661861302363517, 0.26302185335832945],\n",
       "       [0.1457271806995982, 0.11990859159380944, 0, 0.11990859159380944,\n",
       "        0.29598131422644164, 0.26302185335832945, 0.1402577696840135,\n",
       "        0.15422278343639906, 0.15914648850735036, 0.1477073033077396,\n",
       "        0.16182151768725705, 0.11676011876517363, 0.1781728580714031,\n",
       "        0.1744083317251048, 0.12330024592426836, 0.15661861302363517,\n",
       "        0.16466155834946195, 0.16768792903874916, 0.24376149136828001,\n",
       "        0.1457271806995982, 0.15422278343639906, 0.09813753018019467,\n",
       "        0.21089670004150873, 0.16466155834946195, 0.13857232167999814,\n",
       "        0.1457271806995982, 0.15194610475625225, 0.15914648850735036,\n",
       "        0.1744083317251048, 0.1457271806995982, 0.16182151768725705,\n",
       "        0.16768792903874916, 0.13857232167999814, 0.21953132035710143,\n",
       "        0.11990859159380944, 0.20360350300491922, 0.23010979802723042,\n",
       "        0.10299743304193935, 0.24376149136828001, 0.15194610475625225,\n",
       "        0.1477073033077396, 0.29598131422644164, 0.16466155834946195,\n",
       "        0.23010979802723042, 0.1744083317251048, 0.1338642904272318,\n",
       "        0.16466155834946195, 0.21953132035710143, 0.099469842006639,\n",
       "        0.16768792903874916, 0.29598131422644164, 0.17092636542742498,\n",
       "        0.15194610475625225, 0.14382975648306484, 0.29598131422644164],\n",
       "       [0.09684626213555463, 0.00399628587810372, 0.11990859159380944, 0,\n",
       "        0.29598131422644164, 0.24376149136828001, 0.14200853843568037,\n",
       "        0.1338642904272318, 0.18676063506101495, 0.13857232167999814,\n",
       "        0.15422278343639906, 0.06426446625444529, 0.15661861302363517,\n",
       "        0.16768792903874916, 0.12330024592426836, 0.14382975648306484,\n",
       "        0.13857232167999814, 0.16466155834946195, 0.23010979802723042,\n",
       "        0.14200853843568037, 0.13239861250865886, 0.11778466447449416,\n",
       "        0.18676063506101495, 0.1781728580714031, 0.10848650009414704,\n",
       "        0.15194610475625225, 0.13857232167999814, 0.15194610475625225,\n",
       "        0.1477073033077396, 0.1477073033077396, 0.12826959350714812,\n",
       "        0.15194610475625225, 0.1457271806995982, 0.23010979802723042,\n",
       "        0.06745841661757743, 0.20360350300491922, 0.23010979802723042,\n",
       "        0.12330024592426836, 0.26302185335832945, 0.12571533881073133,\n",
       "        0.1369476059660776, 0.29598131422644164, 0.16768792903874916,\n",
       "        0.24376149136828001, 0.13857232167999814, 0.11019321400744202,\n",
       "        0.1221404455934065, 0.26302185335832945, 0.1457271806995982,\n",
       "        0.1477073033077396, 0.29598131422644164, 0.14382975648306484,\n",
       "        0.11883376946415547, 0.15194610475625225, 0.26302185335832945],\n",
       "       [0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0, 0.23010979802723042, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.1744083317251048, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.19173063154559256],\n",
       "       [0.21953132035710143, 0.24376149136828001, 0.26302185335832945,\n",
       "        0.24376149136828001, 0.23010979802723042, 0, 0.26302185335832945,\n",
       "        0.21089670004150873, 0.26302185335832945, 0.24376149136828001,\n",
       "        0.23010979802723042, 0.24376149136828001, 0.26302185335832945,\n",
       "        0.23010979802723042, 0.21953132035710143, 0.21953132035710143,\n",
       "        0.29598131422644164, 0.24376149136828001, 0.23010979802723042,\n",
       "        0.29598131422644164, 0.26302185335832945, 0.21089670004150873,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.21953132035710143,\n",
       "        0.21953132035710143, 0.21089670004150873, 0.24376149136828001,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.24376149136828001,\n",
       "        0.29598131422644164, 0.24376149136828001, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.24376149136828001, 0.23010979802723042,\n",
       "        0.21953132035710143, 0.29598131422644164, 0.21089670004150873,\n",
       "        0.23010979802723042, 0.1744083317251048, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.21953132035710143, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.26302185335832945,\n",
       "        0.24376149136828001, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.1457271806995982],\n",
       "       [0.14977748270692326, 0.1402577696840135, 0.1402577696840135,\n",
       "        0.14200853843568037, 0.29598131422644164, 0.26302185335832945, 0,\n",
       "        0.15194610475625225, 0.16182151768725705, 0.10604721607027343,\n",
       "        0.12960392142344132, 0.1402577696840135, 0.15422278343639906,\n",
       "        0.1353795009048372, 0.12697410970492254, 0.14200853843568037,\n",
       "        0.12826959350714812, 0.18226917931724548, 0.23010979802723042,\n",
       "        0.16768792903874916, 0.15194610475625225, 0.12826959350714812,\n",
       "        0.17092636542742498, 0.11990859159380944, 0.12330024592426836,\n",
       "        0.1369476059660776, 0.16466155834946195, 0.106844980617672,\n",
       "        0.15422278343639906, 0.1157590508369442, 0.17092636542742498,\n",
       "        0.1353795009048372, 0.11019321400744202, 0.26302185335832945,\n",
       "        0.13857232167999814, 0.16182151768725705, 0.26302185335832945,\n",
       "        0.1309794155758673, 0.29598131422644164, 0.1457271806995982,\n",
       "        0.12101037244527219, 0.29598131422644164, 0.13239861250865886,\n",
       "        0.29598131422644164, 0.15194610475625225, 0.10526406768151808,\n",
       "        0.17092636542742498, 0.21089670004150873, 0.1369476059660776,\n",
       "        0.10933140085818609, 0.29598131422644164, 0.1402577696840135,\n",
       "        0.15914648850735036, 0.15194610475625225, 0.29598131422644164],\n",
       "       [0.1309794155758673, 0.13239861250865886, 0.15422278343639906,\n",
       "        0.1338642904272318, 0.29598131422644164, 0.21089670004150873,\n",
       "        0.15194610475625225, 0, 0.15422278343639906, 0.1338642904272318,\n",
       "        0.15422278343639906, 0.1309794155758673, 0.15661861302363517,\n",
       "        0.16768792903874916, 0.11478044898097774, 0.11990859159380944,\n",
       "        0.1457271806995982, 0.14200853843568037, 0.20360350300491922,\n",
       "        0.13857232167999814, 0.00567497319151483, 0.1457271806995982,\n",
       "        0.23010979802723042, 0.15661861302363517, 0.13857232167999814,\n",
       "        0.05790331050540797, 0.009937674002860502, 0.14977748270692326,\n",
       "        0.20360350300491922, 0.16768792903874916, 0.16182151768725705,\n",
       "        0.1477073033077396, 0.1369476059660776, 0.20360350300491922,\n",
       "        0.1338642904272318, 0.18676063506101495, 0.1781728580714031,\n",
       "        0.15422278343639906, 0.23010979802723042, 0.014870959042618736,\n",
       "        0.12960392142344132, 0.29598131422644164, 0.16182151768725705,\n",
       "        0.29598131422644164, 0.043329584932794055, 0.1353795009048372,\n",
       "        0.16466155834946195, 0.21953132035710143, 0.14200853843568037,\n",
       "        0.14382975648306484, 0.29598131422644164, 0.17092636542742498,\n",
       "        0.1477073033077396, 0.1744083317251048, 0.24376149136828001],\n",
       "       [0.18676063506101495, 0.1744083317251048, 0.15914648850735036,\n",
       "        0.18676063506101495, 0.29598131422644164, 0.26302185335832945,\n",
       "        0.16182151768725705, 0.15422278343639906, 0, 0.14200853843568037,\n",
       "        0.16182151768725705, 0.15661861302363517, 0.16466155834946195,\n",
       "        0.17092636542742498, 0.15194610475625225, 0.15422278343639906,\n",
       "        0.14200853843568037, 0.18226917931724548, 0.21089670004150873,\n",
       "        0.17092636542742498, 0.16182151768725705, 0.16466155834946195,\n",
       "        0.20360350300491922, 0.12101037244527219, 0.1781728580714031,\n",
       "        0.14977748270692326, 0.15661861302363517, 0.11883376946415547,\n",
       "        0.21953132035710143, 0.15914648850735036, 0.17092636542742498,\n",
       "        0.1477073033077396, 0.11778466447449416, 0.29598131422644164,\n",
       "        0.14977748270692326, 0.16466155834946195, 0.20360350300491922,\n",
       "        0.16182151768725705, 0.29598131422644164, 0.15661861302363517,\n",
       "        0.14382975648306484, 0.29598131422644164, 0.14200853843568037,\n",
       "        0.23010979802723042, 0.18676063506101495, 0.16466155834946195,\n",
       "        0.20360350300491922, 0.20360350300491922, 0.17092636542742498,\n",
       "        0.1110725979806038, 0.29598131422644164, 0.1781728580714031,\n",
       "        0.17092636542742498, 0.1781728580714031, 0.29598131422644164],\n",
       "       [0.1338642904272318, 0.13857232167999814, 0.1477073033077396,\n",
       "        0.13857232167999814, 0.29598131422644164, 0.24376149136828001,\n",
       "        0.10604721607027343, 0.1338642904272318, 0.14200853843568037, 0,\n",
       "        0.15914648850735036, 0.14200853843568037, 0.18226917931724548,\n",
       "        0.18226917931724548, 0.1157590508369442, 0.11883376946415547,\n",
       "        0.12697410970492254, 0.16466155834946195, 0.21953132035710143,\n",
       "        0.15422278343639906, 0.1338642904272318, 0.12697410970492254,\n",
       "        0.1972921298281682, 0.1309794155758673, 0.13857232167999814,\n",
       "        0.14977748270692326, 0.1402577696840135, 0.12960392142344132,\n",
       "        0.18676063506101495, 0.12571533881073133, 0.15661861302363517,\n",
       "        0.1477073033077396, 0.1110725979806038, 0.24376149136828001,\n",
       "        0.1402577696840135, 0.17092636542742498, 0.26302185335832945,\n",
       "        0.1338642904272318, 0.26302185335832945, 0.1309794155758673,\n",
       "        0.11883376946415547, 0.26302185335832945, 0.15422278343639906,\n",
       "        0.29598131422644164, 0.15422278343639906, 0.10933140085818609,\n",
       "        0.18226917931724548, 0.20360350300491922, 0.1369476059660776,\n",
       "        0.13239861250865886, 0.24376149136828001, 0.15914648850735036,\n",
       "        0.15661861302363517, 0.1477073033077396, 0.23010979802723042],\n",
       "       [0.15422278343639906, 0.15422278343639906, 0.16182151768725705,\n",
       "        0.15422278343639906, 0.29598131422644164, 0.23010979802723042,\n",
       "        0.12960392142344132, 0.15422278343639906, 0.16182151768725705,\n",
       "        0.15914648850735036, 0, 0.15661861302363517, 0.1309794155758673,\n",
       "        0.05332165358294851, 0.1338642904272318, 0.15661861302363517,\n",
       "        0.12960392142344132, 0.21089670004150873, 0.20360350300491922,\n",
       "        0.1744083317251048, 0.16768792903874916, 0.13857232167999814,\n",
       "        0.23010979802723042, 0.1744083317251048, 0.1338642904272318,\n",
       "        0.16466155834946195, 0.15422278343639906, 0.13857232167999814,\n",
       "        0.23010979802723042, 0.1309794155758673, 0.1972921298281682,\n",
       "        0.1457271806995982, 0.14977748270692326, 0.29598131422644164,\n",
       "        0.15914648850735036, 0.1781728580714031, 0.21953132035710143,\n",
       "        0.1402577696840135, 0.29598131422644164, 0.1457271806995982,\n",
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       "        0.29598131422644164, 0.29598131422644164, 0.24376149136828001,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.26302185335832945, 0.24376149136828001,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.26302185335832945,\n",
       "        0.29598131422644164, 0.26302185335832945, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.1402577696840135,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.26302185335832945,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.26302185335832945, 0.29598131422644164, 0.29598131422644164,\n",
       "        0.29598131422644164, 0.29598131422644164, 0.29598131422644164, 0]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mash_distance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scatter plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "dim = len(pair_distance)\n",
    "list_cog3=[]\n",
    "list_mash=[]\n",
    "for x, y in itertools.product(range(dim), range(dim)):\n",
    "    list_cog3.append(pair_distance[x,y])\n",
    "    list_mash.append(mash_distance[x,y])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 720x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(list_cog3, list_mash, c =\"lightblue\", s=10)\n",
    "ident = [0.0, 0.5]\n",
    "plt.plot(ident,ident)\n",
    "plt.xlabel(\"fraction difference\")\n",
    "plt.ylabel(\"mash distance\")\n",
    "plt.figure(figsize=(10, 10))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When sequences become more divergent, Mash distance seems underestimate their difference. The reason may be the estimation of Jaccard similarity they used. \n",
    "\n",
    "In MASH, two randomly obtained sets of hashed k-mers are used to estimate the jaccard similarity. So, the number of their intersections must be discrete, which reduces the accuracy of distance. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.12 (main, Apr  5 2022, 01:53:17) \n[Clang 12.0.0 ]"
  },
  "vscode": {
   "interpreter": {
    "hash": "273e328cce5cd07063760b650b4406bb6af8be0e8ac4c3ff00be44b2191ce4de"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}