2_NEW_Bdiv by treatment and sex.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(phyloseq)\n",
    "library(ggplot2)\n",
    "library(vegan)\n",
    "library(readr)\n",
    "library(data.table)\n",
    "library(dplyr)\n",
    "library(stats)\n",
    "library(ggpubr)\n",
    "library(dunn.test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Read in NEW DATA NOVEMBER 2019\n",
    "alz_t = readRDS(\"/projects/gilbert_lab/Lutz/Alzheimers/Update_Oct2019/PS_for_analysis/alz_t.rds\")\n",
    "\n",
    "alz_t_fecal = subset_samples(alz_t, SampleType==\"Fecal\")\n",
    "alz_t_cecal = subset_samples(alz_t, SampleType==\"Cecal\")\n",
    "\n",
    "alz_t_cecal_control = subset_samples(alz_t_cecal, Treatment==\"Control\")\n",
    "alz_t_cecal_ABX = subset_samples(alz_t_cecal, Treatment==\"Abx\")\n",
    "\n",
    "alz_t_fec_M = subset_samples(alz_t_fecal, Sex==\"M\")\n",
    "alz_t_fec_F = subset_samples(alz_t_fecal, Sex==\"F\")\n",
    "alz_t_cec_M = subset_samples(alz_t_cecal, Sex==\"M\")\n",
    "alz_t_cec_F = subset_samples(alz_t_cecal, Sex==\"F\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- f6be0381fef70a81fd2fcb586ce0b3c7 -- in the phylogenetic tree in the data you provided.”\n",
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- f2a8ea26f8a95a9ca96507a89c0f82c1 -- in the phylogenetic tree in the data you provided.”\n"
     ]
    }
   ],
   "source": [
    "alz.dist.cecal = distance(alz_t_fecal, method = \"unifrac\", type = \"samples\")\n",
    "alz.dist.log.cecal = ordinate(alz_t_fecal, method = \"PCoA\", distance = \"wunifrac\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "'list'"
      ],
      "text/latex": [
       "'list'"
      ],
      "text/markdown": [
       "'list'"
      ],
      "text/plain": [
       "[1] \"list\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = unclass(alz.dist.log.cecal)\n",
    "class(x)\n",
    "#x2 = data.frame(x)\n",
    "write.csv(x, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/cecal.wuf.log.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 02a815f7142f217fd971f1941c3cb9ac -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- f2d95550080afa6b6007cd489af63c90 -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- e4e117cf82380ecda69190ad8320b5c4 -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 41e8f5e69f4f0d2bfce2d5658be3af79 -- in the phylogenetic tree in the data you provided.”"
     ]
    }
   ],
   "source": [
    "alz.dist.fecal = distance(alz_t_fecal, method = \"unifrac\", type = \"samples\")\n",
    "alz.dist.log.fecal = ordinate(alz_t_fecal, method = \"PCoA\", distance = \"wunifrac\")\n",
    "alz.dist.evals.fecal = alz.dist.log.fecal$values$Eigenvalues\n",
    "saveRDS(alz.dist.fecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/fecal.wuf.dist.rds\")\n",
    "saveRDS(alz.dist.log.fecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/fecal.wuf.log.rds\")\n",
    "saveRDS(alz.dist.evals.fecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/fecal.wuf.evals.rds\")\n",
    "\n",
    "alz.dist.cecal = distance(alz_t_cecal, method = \"unifrac\", type = \"samples\")\n",
    "alz.dist.log.cecal = ordinate(alz_t_cecal, method = \"PCoA\", distance = \"wunifrac\")\n",
    "alz.dist.evals.cecal = alz.dist.log.cecal$values$Eigenvalues\n",
    "saveRDS(alz.dist.cecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/cecal.wuf.dist.rds\")\n",
    "saveRDS(alz.dist.log.cecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/cecal.wuf.log.rds\")\n",
    "saveRDS(alz.dist.evals.cecal, \"/gpfs/data/gilbert-lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/cecal.wuf.evals.rds\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FECAL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unweighted UniFrac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- ec5aaf6c4c07befef14be9c35223ee07 -- in the phylogenetic tree in the data you provided.”\n",
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- aeac6a0b9012330bbfa09b8d75f37195 -- in the phylogenetic tree in the data you provided.”\n"
     ]
    },
    {
     "data": {
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dVlhw/tTE0VkRTDpaS08yISHRQkIpF+ful5eTpFebJeg5fXrEr89wt3+mQBAJrB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nNd5aoH+nQ3hSsROcmcPmg6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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<strong>png:</strong> 2"
      ],
      "text/latex": [
       "\\textbf{png:} 2"
      ],
      "text/markdown": [
       "**png:** 2"
      ],
      "text/plain": [
       "png \n",
       "  2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<strong>png:</strong> 2"
      ],
      "text/latex": [
       "\\textbf{png:} 2"
      ],
      "text/markdown": [
       "**png:** 2"
      ],
      "text/plain": [
       "png \n",
       "  2 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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PbUID8q2x3adEwikU76YuzTe89+WBYfdnQFVUEqkf4Zd/bWmXuEkJz0vEdXHxNC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GIoELNm4z2PQhssseBeErVnQL7pJee2lBid6mV0XQEQIAACAASURBVFs1WpvWZDfH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\nntptat9YF3sAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(viridis)\n",
    "\n",
    "alz.dist.fecal = distance(alz_t_fecal, method = \"unifrac\", type = \"samples\")\n",
    "alz.dist.log.fecal = ordinate(alz_t_fecal, method = \"PCoA\", distance = \"wunifrac\")\n",
    "alz.dist.evals.fecal = alz.dist.log.fecal$values$Eigenvalues\n",
    "\n",
    "p = plot_ordination(alz_t_fecal, alz.dist.log.fecal, color = \"Sex_Treatment\", shape = \"Sex_Treatment\", label=\"X.SampleID\") + \n",
    "    ggtitle(\"Unweighted UniFrac Treatment by Sex - FECAL\") +\n",
    "    geom_point(size=3, alpha=0.8) + \n",
    "    scale_colour_viridis(option=\"viridis\", discrete=TRUE, direction=1) +\n",
    "    #stat_ellipse(level=0.95, geom=\"polygon\",alpha = .2, aes(fill = Treatment), linetype=0) +\n",
    "    #scale_fill_viridis(option=\"viridis\", discrete=TRUE, direction=1)+\n",
    "    coord_fixed(sqrt(alz.dist.evals.fecal[2] / alz.dist.evals.fecal[1]))\n",
    "\n",
    "p = p + guides(colour = guide_legend(title = \"Treatment\", ncol = 2, keywidth = 1, keyheight = 1))\n",
    "\n",
    "p = p + theme_bw() + \n",
    "        theme(panel.grid.major = element_blank(),\n",
    "              axis.title.y=element_text(margin=margin(0,20,0,0)),\n",
    "              text=element_text(size=8, color=\"black\",family=\"Arial\"),\n",
    "              panel.grid.minor = element_blank(),\n",
    "              #axis.ticks = element_blank(),\n",
    "              #legend.key.size = unit(.1, \"in\"),\n",
    "              #legend.spacing.x = unit(.01,\"in\"),\n",
    "              legend.position = \"bottom\")\n",
    "\n",
    "p$layers <- p$layers[-1]\n",
    "\n",
    "p\n",
    "\n",
    "p2 = p + facet_wrap(~Sex, ncol=1)\n",
    "\n",
    "p2\n",
    "\n",
    "png('/projects/gilbert_lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/sex_by_treatment.png', width=6, height=5, units='in', res=300)\n",
    "plot(p)\n",
    "dev.off()\n",
    "\n",
    "png('/projects/gilbert_lab/Lutz/Alzheimers/Update_Oct2019/data_for_Hemraj/bdiv/sex_by_treatment.facet.png', width=6, height=5, units='in', res=300)\n",
    "plot(p2)\n",
    "dev.off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Weighted UniFrac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 9c8605abd883e27411e47085b89180df -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 4fc11f482ea4798c9c9d65db8f1ef1e8 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "image/png": 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13/XQoT1IJbrr3I440N5RFNJqW1ZqQdIoJgVyVo0fvy97t02QuXpzrSnF5nqiPN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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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etmbPx77lbnfXxN2jd44vWHqjeoWiKbSErOWLOp8MB08NjFf3ad3HjtAh/pGZbl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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(viridis)\n",
    "\n",
    "alz.dist.fecal = distance(alz_t_fecal, method = \"wunifrac\", type = \"samples\")\n",
    "alz.dist.log.fecal = ordinate(alz_t_fecal, method = \"PCoA\", distance = \"wunifrac\")\n",
    "alz.dist.evals.fecal = alz.dist.log.fecal$values$Eigenvalues\n",
    "\n",
    "p = plot_ordination(alz_t_fecal, alz.dist.log.fecal, color = \"Sex_Treatment\", shape = \"Sex_Treatment\") + #, label=\"X.SampleID\") + \n",
    "    ggtitle(\"Weighted UniFrac Treatment by Sex - FECAL\") +\n",
    "    geom_point(size=3, alpha=0.8) + \n",
    "    scale_colour_viridis(option=\"viridis\", discrete=TRUE, direction=1) +\n",
    "    #stat_ellipse(level=0.95, geom=\"polygon\",alpha = .2, aes(fill = Treatment), linetype=0) +\n",
    "    #scale_fill_viridis(option=\"viridis\", discrete=TRUE, direction=1)+\n",
    "    coord_fixed(sqrt(alz.dist.evals.fecal[2] / alz.dist.evals.fecal[1]))\n",
    "\n",
    "p = p + guides(colour = guide_legend(title = \"Treatment\", ncol = 2, keywidth = 1, keyheight = 1))\n",
    "\n",
    "p = p + theme_bw() + \n",
    "        theme(panel.grid.major = element_blank(),\n",
    "              axis.title.y=element_text(margin=margin(0,20,0,0)),\n",
    "              text=element_text(size=8, color=\"black\",family=\"Arial\"),\n",
    "              panel.grid.minor = element_blank(),\n",
    "              #axis.ticks = element_blank(),\n",
    "              #legend.key.size = unit(.1, \"in\"),\n",
    "              #legend.spacing.x = unit(.01,\"in\"),\n",
    "              legend.position = \"bottom\")\n",
    "\n",
    "p$layers <- p$layers[-1]\n",
    "\n",
    "p\n",
    "\n",
    "p2 = p + facet_wrap(~Sex, ncol=1)\n",
    "\n",
    "p2\n",
    "\n",
    "#png('sex_f_by_treatment.png', width=6, height=5, units='in', res=300)\n",
    "#plot(p)\n",
    "#dev.off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Unweighted Unifrac PERMANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- bb0cd1c91d415b92533a3dc96db88374 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 2       </td><td>0.6808427</td><td>0.2326271</td><td>3.940915 </td><td>0.001    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>26       </td><td>2.2459134</td><td>0.7673729</td><td>      NA </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>28       </td><td>2.9267561</td><td>1.0000000</td><td>      NA </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  2        & 0.6808427 & 0.2326271 & 3.940915  & 0.001    \\\\\n",
       "\tResidual & 26        & 2.2459134 & 0.7673729 &       NA  &    NA    \\\\\n",
       "\tTotal & 28        & 2.9267561 & 1.0000000 &       NA  &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  2        | 0.6808427 | 0.2326271 | 3.940915  | 0.001     |\n",
       "| Residual | 26        | 2.2459134 | 0.7673729 |       NA  |    NA     |\n",
       "| Total | 28        | 2.9267561 | 1.0000000 |       NA  |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs  R2        F        Pr(>F)\n",
       "Treatment  2 0.6808427 0.2326271 3.940915 0.001 \n",
       "Residual  26 2.2459134 0.7673729       NA    NA \n",
       "Total     28 2.9267561 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 2b7f00c067ed37d678b58707fcc56e50 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 1       </td><td>0.6031075</td><td>0.2746856</td><td>6.43811  </td><td>0.001    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>17       </td><td>1.5925212</td><td>0.7253144</td><td>     NA  </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>18       </td><td>2.1956287</td><td>1.0000000</td><td>     NA  </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  1        & 0.6031075 & 0.2746856 & 6.43811   & 0.001    \\\\\n",
       "\tResidual & 17        & 1.5925212 & 0.7253144 &      NA   &    NA    \\\\\n",
       "\tTotal & 18        & 2.1956287 & 1.0000000 &      NA   &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  1        | 0.6031075 | 0.2746856 | 6.43811   | 0.001     |\n",
       "| Residual | 17        | 1.5925212 | 0.7253144 |      NA   |    NA     |\n",
       "| Total | 18        | 2.1956287 | 1.0000000 |      NA   |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs  R2        F       Pr(>F)\n",
       "Treatment  1 0.6031075 0.2746856 6.43811 0.001 \n",
       "Residual  17 1.5925212 0.7253144      NA    NA \n",
       "Total     18 2.1956287 1.0000000      NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- a5c2e6ea2b146907392b65f681240928 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1        </td><td>0.1061556 </td><td>0.06567487</td><td>1.265242  </td><td>0.164     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>18        </td><td>1.5102252 </td><td>0.93432513</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>19        </td><td>1.6163808 </td><td>1.00000000</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1         & 0.1061556  & 0.06567487 & 1.265242   & 0.164     \\\\\n",
       "\tResidual & 18         & 1.5102252  & 0.93432513 &       NA   &    NA     \\\\\n",
       "\tTotal & 19         & 1.6163808  & 1.00000000 &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1         | 0.1061556  | 0.06567487 | 1.265242   | 0.164      |\n",
       "| Residual | 18         | 1.5102252  | 0.93432513 |       NA   |    NA      |\n",
       "| Total | 19         | 1.6163808  | 1.00000000 |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs  R2         F        Pr(>F)\n",
       "Sex       1 0.1061556 0.06567487 1.265242 0.164 \n",
       "Residual 18 1.5102252 0.93432513       NA    NA \n",
       "Total    19 1.6163808 1.00000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 5379fdb8eb917eca4fd878af89ff4115 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1       </td><td>0.2747353</td><td>0.1306782</td><td>2.555475 </td><td>0.014    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>17       </td><td>1.8276451</td><td>0.8693218</td><td>      NA </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>18       </td><td>2.1023804</td><td>1.0000000</td><td>      NA </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1        & 0.2747353 & 0.1306782 & 2.555475  & 0.014    \\\\\n",
       "\tResidual & 17        & 1.8276451 & 0.8693218 &       NA  &    NA    \\\\\n",
       "\tTotal & 18        & 2.1023804 & 1.0000000 &       NA  &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1        | 0.2747353 | 0.1306782 | 2.555475  | 0.014     |\n",
       "| Residual | 17        | 1.8276451 | 0.8693218 |       NA  |    NA     |\n",
       "| Total | 18        | 2.1023804 | 1.0000000 |       NA  |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs  R2        F        Pr(>F)\n",
       "Sex       1 0.2747353 0.1306782 2.555475 0.014 \n",
       "Residual 17 1.8276451 0.8693218       NA    NA \n",
       "Total    18 2.1023804 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Difference between treatment group within sex\n",
    "#Male\n",
    "alz_t_fec_M.dist.unif = distance(alz_t_fec_M, method = \"unifrac\", type = \"samples\")\n",
    "alz.fec.M.df = data.frame(sample_data(alz_t_fec_M))\n",
    "alz.fec.M.unif.adtest = adonis2(alz_t_fec_M.dist.unif ~ Treatment, data=alz.fec.M.df)\n",
    "alz.fec.M.unif.adtest\n",
    "#Female\n",
    "alz_t_fec_F.dist.unif = distance(alz_t_fec_F, method = \"unifrac\", type = \"samples\")\n",
    "alz.fec.F.df = data.frame(sample_data(alz_t_fec_F))\n",
    "alz.fec.F.unif.adtest = adonis2(alz_t_fec_F.dist.unif ~ Treatment, data=alz.fec.F.df)\n",
    "alz.fec.F.unif.adtest\n",
    "\n",
    "#Differences between sexes within treatment group\n",
    "#Control\n",
    "alz_t_fec.dist.unif = distance(alz_t_fecal_control, method = \"unifrac\", type = \"samples\")\n",
    "alz.fec.control.df = data.frame(sample_data(alz_t_fecal_control))\n",
    "alz.fec.control.unif.adtest = adonis2(alz_t_fec.dist.unif ~ Sex, data=alz.fec.control.df)\n",
    "alz.fec.control.unif.adtest\n",
    "#Abx\n",
    "alz_t_fec.dist.unif = distance(alz_t_fecal_ABX, method = \"unifrac\", type = \"samples\")\n",
    "alz.fec.abx.df = data.frame(sample_data(alz_t_fecal_ABX))\n",
    "alz.fec.abx.unif.adtest = adonis2(alz_t_fec.dist.unif ~ Sex, data=alz.fec.abx.df)\n",
    "alz.fec.abx.unif.adtest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Weighted Unifrac PERMANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 44ff22e644697df95cbb102298a748ea -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 2        </td><td>0.09029894</td><td>0.3311163 </td><td>6.435367  </td><td>0.001     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>26        </td><td>0.18241170</td><td>0.6688837 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>28        </td><td>0.27271064</td><td>1.0000000 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  2         & 0.09029894 & 0.3311163  & 6.435367   & 0.001     \\\\\n",
       "\tResidual & 26         & 0.18241170 & 0.6688837  &       NA   &    NA     \\\\\n",
       "\tTotal & 28         & 0.27271064 & 1.0000000  &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  2         | 0.09029894 | 0.3311163  | 6.435367   | 0.001      |\n",
       "| Residual | 26         | 0.18241170 | 0.6688837  |       NA   |    NA      |\n",
       "| Total | 28         | 0.27271064 | 1.0000000  |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs   R2        F        Pr(>F)\n",
       "Treatment  2 0.09029894 0.3311163 6.435367 0.001 \n",
       "Residual  26 0.18241170 0.6688837       NA    NA \n",
       "Total     28 0.27271064 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- ce41b5afe392b47adeab39d7fa943f0c -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 1        </td><td>0.03010591</td><td>0.266627  </td><td>6.180565  </td><td>0.001     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>17        </td><td>0.08280803</td><td>0.733373  </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>18        </td><td>0.11291393</td><td>1.000000  </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  1         & 0.03010591 & 0.266627   & 6.180565   & 0.001     \\\\\n",
       "\tResidual & 17         & 0.08280803 & 0.733373   &       NA   &    NA     \\\\\n",
       "\tTotal & 18         & 0.11291393 & 1.000000   &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  1         | 0.03010591 | 0.266627   | 6.180565   | 0.001      |\n",
       "| Residual | 17         | 0.08280803 | 0.733373   |       NA   |    NA      |\n",
       "| Total | 18         | 0.11291393 | 1.000000   |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs   R2       F        Pr(>F)\n",
       "Treatment  1 0.03010591 0.266627 6.180565 0.001 \n",
       "Residual  17 0.08280803 0.733373       NA    NA \n",
       "Total     18 0.11291393 1.000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 5b0645f72373722861dd2953c6121d01 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1         </td><td>0.006271434</td><td>0.1055453  </td><td>2.123993   </td><td>0.045      </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>18         </td><td>0.053147917</td><td>0.8944547  </td><td>      NA   </td><td>   NA      </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>19         </td><td>0.059419352</td><td>1.0000000  </td><td>      NA   </td><td>   NA      </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1          & 0.006271434 & 0.1055453   & 2.123993    & 0.045      \\\\\n",
       "\tResidual & 18          & 0.053147917 & 0.8944547   &       NA    &    NA      \\\\\n",
       "\tTotal & 19          & 0.059419352 & 1.0000000   &       NA    &    NA      \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1          | 0.006271434 | 0.1055453   | 2.123993    | 0.045       |\n",
       "| Residual | 18          | 0.053147917 | 0.8944547   |       NA    |    NA       |\n",
       "| Total | 19          | 0.059419352 | 1.0000000   |       NA    |    NA       |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs    R2        F        Pr(>F)\n",
       "Sex       1 0.006271434 0.1055453 2.123993 0.045 \n",
       "Residual 18 0.053147917 0.8944547       NA    NA \n",
       "Total    19 0.059419352 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 1d5ab75b320aeb74c80516e444077755 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1        </td><td>0.04768720</td><td>0.3472297 </td><td>9.042853  </td><td>0.001     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>17        </td><td>0.08964896</td><td>0.6527703 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>18        </td><td>0.13733616</td><td>1.0000000 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1         & 0.04768720 & 0.3472297  & 9.042853   & 0.001     \\\\\n",
       "\tResidual & 17         & 0.08964896 & 0.6527703  &       NA   &    NA     \\\\\n",
       "\tTotal & 18         & 0.13733616 & 1.0000000  &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1         | 0.04768720 | 0.3472297  | 9.042853   | 0.001      |\n",
       "| Residual | 17         | 0.08964896 | 0.6527703  |       NA   |    NA      |\n",
       "| Total | 18         | 0.13733616 | 1.0000000  |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs   R2        F        Pr(>F)\n",
       "Sex       1 0.04768720 0.3472297 9.042853 0.001 \n",
       "Residual 17 0.08964896 0.6527703       NA    NA \n",
       "Total    18 0.13733616 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Difference between treatment group within sex\n",
    "#Male\n",
    "alz_t_fec_M.dist.wunif = distance(alz_t_fec_M, method = \"wunifrac\", type = \"samples\")\n",
    "alz.fec.M.df = data.frame(sample_data(alz_t_fec_M))\n",
    "alz.fec.M.wunif.adtest = adonis2(alz_t_fec_M.dist.wunif ~ Treatment, data=alz.fec.M.df)\n",
    "alz.fec.M.wunif.adtest\n",
    "#Female\n",
    "alz_t_fec_F.dist.wunif = distance(alz_t_fec_F, method = \"wunifrac\", type = \"samples\")\n",
    "alz.fec.F.df = data.frame(sample_data(alz_t_fec_F))\n",
    "alz.fec.F.wunif.adtest = adonis2(alz_t_fec_F.dist.wunif ~ Treatment, data=alz.fec.F.df)\n",
    "alz.fec.F.wunif.adtest\n",
    "\n",
    "#Differences between sexes within treatment group\n",
    "#Control\n",
    "alz_t_fec.dist.wunif = distance(alz_t_fecal_control, method = \"wunifrac\", type = \"samples\")\n",
    "alz.fec.control.df = data.frame(sample_data(alz_t_fecal_control))\n",
    "alz.fec.control.wunif.adtest = adonis2(alz_t_fec.dist.wunif ~ Sex, data=alz.fec.control.df)\n",
    "alz.fec.control.wunif.adtest\n",
    "#Abx\n",
    "alz_t_fec.dist.wunif = distance(alz_t_fecal_ABX, method = \"wunifrac\", type = \"samples\")\n",
    "alz.fec.abx.df = data.frame(sample_data(alz_t_fecal_ABX))\n",
    "alz.fec.abx.wunif.adtest = adonis2(alz_t_fec.dist.wunif ~ Sex, data=alz.fec.abx.df)\n",
    "alz.fec.abx.wunif.adtest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CECAL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 95d45246fb908dbc68e9c057df584d01 -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 2a248c8ca446856290e3cd3a7a1e9ea4 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "image/png": 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z2g4lT8SMn5r859XsxNVcLrXRue0LWZiMei86KvSOoktm6RLhEIJrVg56c7Pr+1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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Z7r0Ou0RS7KNltNRoOX8wAAUNE4ecLnDezXaP6cKFkIIZzb5s5r3G+gECI+Pr64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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(viridis)\n",
    "\n",
    "alz.dist.cecal = distance(alz_t_cecal, method = \"unifrac\", type = \"samples\")\n",
    "alz.dist.log.cecal = ordinate(alz_t_cecal, method = \"PCoA\", distance = \"unifrac\")\n",
    "alz.dist.evals.cecal = alz.dist.log.cecal$values$Eigenvalues\n",
    "\n",
    "p = plot_ordination(alz_t_cecal, alz.dist.log.cecal, color = \"Sex_Treatment\", shape = \"Sex_Treatment\") + #, label=\"X.SampleID\") + \n",
    "    ggtitle(\"Unweighted UniFrac Treatment by Sex - CECAL\") +\n",
    "    geom_point(size=3, alpha=0.8) + \n",
    "    scale_colour_viridis(option=\"viridis\", discrete=TRUE, direction=1) +\n",
    "    #stat_ellipse(level=0.95, geom=\"polygon\",alpha = .2, aes(fill = Treatment), linetype=0) +\n",
    "    #scale_fill_viridis(option=\"viridis\", discrete=TRUE, direction=1)+\n",
    "    coord_fixed(sqrt(alz.dist.evals.cecal[2] / alz.dist.evals.cecal[1]))\n",
    "\n",
    "p = p + guides(colour = guide_legend(title = \"Treatment\", ncol = 2, keywidth = 1, keyheight = 1))\n",
    "\n",
    "p = p + theme_bw() + \n",
    "        theme(panel.grid.major = element_blank(),\n",
    "              axis.title.y=element_text(margin=margin(0,20,0,0)),\n",
    "              text=element_text(size=8, color=\"black\",family=\"Arial\"),\n",
    "              panel.grid.minor = element_blank(),\n",
    "              #axis.ticks = element_blank(),\n",
    "              #legend.key.size = unit(.1, \"in\"),\n",
    "              #legend.spacing.x = unit(.01,\"in\"),\n",
    "              legend.position = \"bottom\")\n",
    "\n",
    "p$layers <- p$layers[-1]\n",
    "\n",
    "p\n",
    "\n",
    "p2 = p + facet_wrap(~Sex, ncol=1)\n",
    "\n",
    "p2\n",
    "\n",
    "#png('sex_f_by_treatment.png', width=6, height=5, units='in', res=300)\n",
    "#plot(p)\n",
    "#dev.off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 9de39561caafff948608dc50267dea53 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 2       </td><td>0.4474468</td><td>0.1318139</td><td>1.973748 </td><td>0.009    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>26       </td><td>2.9470880</td><td>0.8681861</td><td>      NA </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>28       </td><td>3.3945348</td><td>1.0000000</td><td>      NA </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  2        & 0.4474468 & 0.1318139 & 1.973748  & 0.009    \\\\\n",
       "\tResidual & 26        & 2.9470880 & 0.8681861 &       NA  &    NA    \\\\\n",
       "\tTotal & 28        & 3.3945348 & 1.0000000 &       NA  &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  2        | 0.4474468 | 0.1318139 | 1.973748  | 0.009     |\n",
       "| Residual | 26        | 2.9470880 | 0.8681861 |       NA  |    NA     |\n",
       "| Total | 28        | 3.3945348 | 1.0000000 |       NA  |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs  R2        F        Pr(>F)\n",
       "Treatment  2 0.4474468 0.1318139 1.973748 0.009 \n",
       "Residual  26 2.9470880 0.8681861       NA    NA \n",
       "Total     28 3.3945348 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- b071cfbe7f44435b348de7ad1688d73c -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 1       </td><td>0.8131942</td><td>0.3350372</td><td>8.061496 </td><td>0.001    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>16       </td><td>1.6139818</td><td>0.6649628</td><td>      NA </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>17       </td><td>2.4271760</td><td>1.0000000</td><td>      NA </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  1        & 0.8131942 & 0.3350372 & 8.061496  & 0.001    \\\\\n",
       "\tResidual & 16        & 1.6139818 & 0.6649628 &       NA  &    NA    \\\\\n",
       "\tTotal & 17        & 2.4271760 & 1.0000000 &       NA  &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  1        | 0.8131942 | 0.3350372 | 8.061496  | 0.001     |\n",
       "| Residual | 16        | 1.6139818 | 0.6649628 |       NA  |    NA     |\n",
       "| Total | 17        | 2.4271760 | 1.0000000 |       NA  |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs  R2        F        Pr(>F)\n",
       "Treatment  1 0.8131942 0.3350372 8.061496 0.001 \n",
       "Residual  16 1.6139818 0.6649628       NA    NA \n",
       "Total     17 2.4271760 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 7670f7777bd47d3fcb4e3c8b7308b72d -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1        </td><td>0.1548327 </td><td>0.09136821</td><td>1.810005  </td><td>0.011     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>18        </td><td>1.5397686 </td><td>0.90863179</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>19        </td><td>1.6946013 </td><td>1.00000000</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1         & 0.1548327  & 0.09136821 & 1.810005   & 0.011     \\\\\n",
       "\tResidual & 18         & 1.5397686  & 0.90863179 &       NA   &    NA     \\\\\n",
       "\tTotal & 19         & 1.6946013  & 1.00000000 &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1         | 0.1548327  | 0.09136821 | 1.810005   | 0.011      |\n",
       "| Residual | 18         | 1.5397686  | 0.90863179 |       NA   |    NA      |\n",
       "| Total | 19         | 1.6946013  | 1.00000000 |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs  R2         F        Pr(>F)\n",
       "Sex       1 0.1548327 0.09136821 1.810005 0.011 \n",
       "Residual 18 1.5397686 0.90863179       NA    NA \n",
       "Total    19 1.6946013 1.00000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, ...):\n",
      "“Randomly assigning root as -- 2e02a71a929cd85d4404619c72f7baa0 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1       </td><td>0.4437071</td><td>0.1531905</td><td>2.894451 </td><td>0.012    </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>16       </td><td>2.4527323</td><td>0.8468095</td><td>      NA </td><td>   NA    </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>17       </td><td>2.8964394</td><td>1.0000000</td><td>      NA </td><td>   NA    </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1        & 0.4437071 & 0.1531905 & 2.894451  & 0.012    \\\\\n",
       "\tResidual & 16        & 2.4527323 & 0.8468095 &       NA  &    NA    \\\\\n",
       "\tTotal & 17        & 2.8964394 & 1.0000000 &       NA  &    NA    \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1        | 0.4437071 | 0.1531905 | 2.894451  | 0.012     |\n",
       "| Residual | 16        | 2.4527323 | 0.8468095 |       NA  |    NA     |\n",
       "| Total | 17        | 2.8964394 | 1.0000000 |       NA  |    NA     |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs  R2        F        Pr(>F)\n",
       "Sex       1 0.4437071 0.1531905 2.894451 0.012 \n",
       "Residual 16 2.4527323 0.8468095       NA    NA \n",
       "Total    17 2.8964394 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Difference between treatment group within sex\n",
    "#Male\n",
    "alz_t_cec_M.dist.unif = distance(alz_t_cec_M, method = \"unifrac\", type = \"samples\")\n",
    "alz.cec.M.df = data.frame(sample_data(alz_t_cec_M))\n",
    "alz.cec.M.unif.adtest = adonis2(alz_t_cec_M.dist.unif ~ Treatment, data=alz.cec.M.df)\n",
    "alz.cec.M.unif.adtest\n",
    "#Female\n",
    "alz_t_cec_F.dist.unif = distance(alz_t_cec_F, method = \"unifrac\", type = \"samples\")\n",
    "alz.cec.F.df = data.frame(sample_data(alz_t_cec_F))\n",
    "alz.cec.F.unif.adtest = adonis2(alz_t_cec_F.dist.unif ~ Treatment, data=alz.cec.F.df)\n",
    "alz.cec.F.unif.adtest\n",
    "\n",
    "#Differences between sexes within treatment group\n",
    "#Control\n",
    "alz_t_cec.dist.unif = distance(alz_t_cecal_control, method = \"unifrac\", type = \"samples\")\n",
    "alz.cec.control.df = data.frame(sample_data(alz_t_cecal_control))\n",
    "alz.cec.control.unif.adtest = adonis2(alz_t_cec.dist.unif ~ Sex, data=alz.cec.control.df)\n",
    "alz.cec.control.unif.adtest\n",
    "#Abx\n",
    "alz_t_cec.dist.unif = distance(alz_t_cecal_ABX, method = \"unifrac\", type = \"samples\")\n",
    "alz.cec.abx.df = data.frame(sample_data(alz_t_cecal_ABX))\n",
    "alz.cec.abx.unif.adtest = adonis2(alz_t_cec.dist.unif ~ Sex, data=alz.cec.abx.df)\n",
    "alz.cec.abx.unif.adtest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 87cf1196d21c2399750fa4498439c3dd -- in the phylogenetic tree in the data you provided.”Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 8fe6312f1bcde84da7bd3adc0f2eb0f4 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
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kr1IWvHB3pj0jf/HHVvnDusixDi6dVn\nB0f7fisC2Un/5NikZm+WeuEbTZJMCV2KruLyew+AhvELzguXvXmMUQjR8tESAeiemrFCiJTO\n490bjyx5yRBV4z/DP50+e86Un7+6o2MNnT7uow0nVMmPkGOrRuj1sYOGf/b77Fmj3n4kufoV\nRROlKp8f+VLK7+csXrlime9j5ez9oYpB1/Zfj46eOHX6lHHP9b/SlNjJ2wfYsZXvxel1rXvf\n89aHX/405qcvP3zz7msv0RurfbX57PRgQQp2d9aIuea/Xy1dvnz6mA+vqJ1i1Mkp/6wv+rg9\nuvwVvbHqY++Mmjl7xgfP3CyEGDB5r7c9eztu2UYf3x0fxZR62wMPdgH+MJR6YanDle3WIi7h\n/lc/S/v9tw+evytKb3zfbSK3QwvvkLqoOL3u4bWZHl+es++XpjHG6pf0fOrVkaO+//GnH797\n4/nB9cyGARP3BFC267UuKYlNHrS5lFKulzvUiK93T76zfONi1ZTHO+v0MTfe/9Tn34z+/qsP\nB93cTgjRtO+Hpb7YMV4EspOiqYiunVR6PPXOsVcJIV7dccrbIcr3FQFAZUOw8+qn9jWFEM/t\nPOXeuPShFkKIqyfvKdV53fg3ulxUxyClKb5G5+v6TfjnSFF7qc/yNWNebZ2aKHWmlt3/Pf/A\nCZ0hyWM395bXel8kpTTFVfV7rEOLvruxU/Nog84QXbXLzf9ZcsTiI3IdXTnpvpu6piTGSCnj\nqtbt2fc/00tO+hqkYJe58uuODapKnbFJxxt/Wn7k5U61DOaqx87cubXi+xdb16sqpb5mo3bP\nfv6Ht936OK7HRm/vmI9iSr3t53QCL8AfBuXzu1yq24l1P/duW98gddUatBs+boP7VkfBnhi9\nzhjdLM973rIcXfXaw3e1alzLpNfpDNENW3Ub/t3iQN6lnWPvlvrosWem4rNkzkwy6LqPXOnt\nQP44Z33+3yta1jfppT4qtnHrK5/94NdSpxIDuLzgayd/P9JS6kzrywzZseUs00vZ8NbfvR2i\nvF8RAFQuLK0TOsd271D1miSfubPNnrcyvu6z1qyFYS0KWnBnzdiVXX/ZM+WGcBcCAAgznf8u\nqCBpt17x78l7i58eWfx+lUb3hrEeaIPt1JxfjhfcPbJLuAsBAIQfo2JD5/oPbx9y83XvuT69\nvm3dg2tmPfnQ1IELPw13UYhgypmzbuuBZf971JR49bCmieEuBwAQflyKDanZHzz61P/GbDuc\nW7NR24EvfPLmIM6yoPzs+WtrVu0oa7d755eZgztUD3c5AIDwI9gBAABoBPfYAQAAaATBDgAA\nQCMIdgAAABpBsAMAANAIgh0AAIBGEOwAAAA0gmAHAACgEQQ7AAAAjWBJsRIyMjLS09PDXQUA\nAIBXycnJ9evX97iJYFfC3LlzP/vss169eoW7EAAAgNLmz58vhLjpppuGDRvmsQPBrrSuXbuO\nHDky3FUAAACU9sQTTyxZssRHh0gNdsplmfz5e7NW7xdC1e/Q59mhfWN0slSXD/rf+dSYSYF1\nBgAAiHiROnhi59iX5hV0+HL0d9+N/rK9Zc6LY3a6b90xd9qnbzy2MNsaSGcAAABtiNRgN2nO\nwX4PXWOSUkrzNQ/1S587yX1rfEq9zr3vDbDzVjd5eXkh+gIAAAAqWqReil2fb38mwVj0OCqh\nkz3/M/ettVq1qxVw5/79+xc/bt++fXR0dHBKBgAACK5IPWMnhBDK65Pz7QwAABCBIvWMXetY\n4+o8+xUJUUIIe+4aY2ybcnceM2ZM8eM//vhj165dwSkZAAAguCL1jN0dvVPH/rBECSGEa+mP\nY+r1vkMI4W1uYY+di7VwExcXF+zKAQAAgiRSz9g17fdmj0/efnDIryZhr9ai1xv9mgohhg4d\nmpaWFmBnAAAAjYnUYCd1MXc+8fqdJRtLpbripx47AwAAaEykXooFAABAKZF6xi5yKOHYIZTN\nTy9pEoZmQrAeBgAAKD+CXXCpguki7y0hawqp99rJlSWEQyR+JY0tQ1gaAADQGoJdcEllV6pA\n6Fwy7nmhi/fQwzpbWacL4ZLKGvLqAACAphDsgszQQOiShXCpgvEy4XWhSyqx1fKzKlwmjB2E\nY2+Y6gMAANrB4Ingk7Ey+t/CdVTlvCJcp862W35WBZNFVCcZ/W8hubsOAACcL4JdSBgulnHP\nlMh2xaku7hlft98BAAAEjGAXKkUZrijb5Y9yS3VcDQcAABWDYBdCRUnOsVnlfy2MrUl1AACg\nYhHsQsuxSwijkCbhyhQqN9zVAAAATSHYhVDRfXWmnjLhPeE6VnosBQAAwPkh2IWK+2gJU5fS\nYykAAADOG8EuJKxzS4+WcB9L4eKaLAAAqADcvB98rpPKNlNEXSZNvYVjy9l2GS3N/1IFY1X+\n+0KRsAEAwPki2AWXcmwXrlNCxgr7buUY4amHXbiOCmFS0swkxQAA4HwQ7IJLmrsLV7aI6uxr\nFmLHbqXypPHiENYFAAA0iGAXZLo6Im6Inz7GVpyrAwAA549gB0SY/VlZdpfTRwe9TtcwMSlk\n9QAAKg+CHRBhRvz1Z6Yl30eHGKNxwu13hqweAEDlwWBMAAAAjSDYAQAAaATBDgAAQCMIdgAA\nABpBsAMAANAIgh0AAIBGEOwAAAA0gmAHAACgEUxQDAAA4N+hnYdXz9uQsfuIcqkaqdXbXNWy\nSduG4S6qNIIdAACAL3abffzbU/+ZsUYpVdy4YNziFp2b3TfizviqcWGsrRSCHRBhOtSpk2Oz\n+ehg0utDVgwAaJ7D7vziiR+2r9xVdtPW5Tv+N+jL5358JCY+OvSFeUSwAyLMkA6XhbsEALiA\n/DF2kcdUV+TYgeOT/zf93uF3hLIkHxg8AQAA4JlyqfljF/nus2LmmuzMnNDU4xdn7AAAADzb\nv+VgfrbF4ya7zZ57Kt+ab3M5nS/1ebvdNa2u7Nu5abswD6cg2AGovFZnZGw6dtR3n6sbNa6b\nkBCaegBcaLK8nIrLOZGblZkjVHG37FVz1q2as67rbZfd8dytBmPY7nUm2AGovDZnHv1162bf\nfVrWrEmwAxAk5lhz2cack3lZx0oEPp1OFj1YMnWF0+HqP+z/QlGcJ9xjBwAA4Fm9i+roDSVO\nvznszuxj2aW6RUWbih8vm75q2wqvgy2CjWAHAADgWUxCdJurWrq35Gflu01mJ4QQUWZDlNno\n3rLol2UhqM0jgh0AAIBXtz56fVxibPFTW0Gh+1YpRVJKUqmX7F6/LwSFeUSwAwAAESZ9x+EV\ns9b+M2PNng37lUv5f8F5qFa76pAP7yteXsLldBVv0ulk9TpVTdFRpV6Sn5Uf1JJ8YPAEAACI\nGBsXb5368Ywj+zKLW6rUSLjxoWuuuDWIk7c3vLTeK5OemvvjX6vnrjt24LgQQqfXxcSbE6on\neBwAG8ZFxgh2AAAgMvzx8+IpH81QJe9xy87M+fmNX/duPHDPy32llEE6dFxi7L8ev+Ffj98w\nY9T86V/M0el9XfNs3rFJkMrwi0uxAAAgAmxZtqNsqiv2928rQzNkoVvfzjEJvlaGlVL2uOuK\nEFTiEcEOAABEgGmfzvSW6opM/2qu3WYPdhnxVePufP5WHx169e/WoGVqsMvwhmAHAAAqu8yD\nx9N3HPbdx5JTsPWfnSEoptMN7Qa8dqcpxlSqXafX3TC4162PXh+CGrzhHjsAAFDZHd1/PJBu\nx/Zn+u9UETr1aXdRp6ZLpizfsWp39vHcuMTYRq3qd7mlY0rDmqEpwBuCHYDK65pGTVqn1PLd\np2Fi6RmkAFxQCq2FhTa7crr0RkNhgS1kx61SPb7Pg9f0efCakB0xEAQ7AJVXrfj4WvHx4a4C\nQPjVrFe9bKOtoPDkkSy79ex9dVM+npWfa7t5aO+yc8tdILjHDgAAVHY161Wv26y2e0tBbsGx\n/ZnuqU6n1xlNxj/HL/nwwa8L8qwhr7FSINgBAIAIcMsj1xVPU2cvdBzPOFlqjGyV6vFSJ4UQ\nB7am//zGr6GvsDIg2AEAgAjQskvzm4f2Lsp2OSfylKvE1tjEGPf1HtbM33Bwe0aIK6wMCHYA\nACAy9L7/qkHv9KuRWr0gt6C4UW/QVa2VWK1W6XFU6xZsDG11lQKDJwAAQMRo2/OSRq3qP939\nVXuhQylliDKYoqM8riQW4AwpGkOwAwAAkUSnk1HRUVH+xr3qdMFaN7Yy41IsAACIJHFJsfFJ\nsX67hX2u4LAg2AEAgEgipWx79aW+++h0/vtoEsEOAABEmOse6BkdZ/bR4fKbO9ZqlByyeioP\ngh0AAIgwiTWrPPT+vaYYk8etTds3+r9nbg5xSZUEwQ4AAESeZh0aP/fDwy06N3MfEhsdZ755\naO/HPh8UZTaGsbYwYlQsAACISLUaJT/62cBTR7PTtx8qyLMmpSQ1uCTVGHVBZ5sL+osHAACR\nLim5SlJylXBXUVlwKRYAAEAjCHYAAAAaQbADAADQCO6xA4DK4u+DByZv2ey7z+0Xt+ySWi80\n9QCIOAQ7AKgssq3WXSdP+O0TmmIARCIuxQIAAGgEwQ4AAEAjCHYAAAAaQbADAADQCIIdAACA\nRhDsAAAANIJgBwAAoBEEO6AiKaGOWI8qocJdCADgQkSwAyrS/vwDX+z6Zn/+gXAXAgC4EBHs\ngIpU6Cos/hsAgBBjSTEAqCx6NWp8Zf36vvuY9PzeBuAVvyAAoLIw6vVGvT7cVQCIYFyKBQAA\n0AiCHQAAgEYQ7AAAADSCe+yAc6aESrccsit72U0Z1sM2ly3DetigK/2PyyiNdWPqSCFDUiMA\n4EJEsAPO2RHr0VF7RnvcZHNaTxSempUxx6Q3l906pMngWuaUIFcHALhwEeyAc5ZiTh7c6H6P\nZ+wOWA7OOjz3+lrX1otJLbXJKI0p5uSQFAgACLXDR7Oz8wouahzm/70T7IBzJoVMjanrcZPD\n5TDpTLXNtRrFNgxxVQCAMBqftiorxzL8yRt1unDecsPgCQAAgPOybkv65h0Zh45kLVy2I7yV\nEOwAAADKz+5wTvp9ddHjaXPX51tsYSwmUi/FKpdl8ufvzVq9XwhVv0OfZ4f2jTlz5tPjpi0f\nDXlx0TG9FEKImpe99uXzl4SzegAAoBULlm4/mplT9DjfYkubt+Hft3QMVzGRGux2jn1pXkGv\nL0e/GiVsM9579MUxrT4a0MzHpiM7c+7+Zuwd1aPDWzYAANCS7NyCtHkb3FsW/L29e+dmtZOr\nhKWeSA12k+Yc7PfFNSYphTBf81C/H4ZOEgNe9rFpQ679uhijx1298MILxY91Oq5NAwCAQE2b\ns85qKzFJgsulJqStemrw1WGpJ1KD3fp8+zMJp4NaVEIne/5nvjetzy8sGDZ0xY7MGo3bDnz+\n2U7JZ0/dzZ8/v/hx+/bto6M5qwcAAPzbl35iyYrdZds378hYt/lgm5al570KgUgNdkIIoYTb\nHP7KxyblzG3TvfdVfe9+Ptm4+vcP3//v6InfDy3e3KtXr+LHOp3OYrEEsWZoXZQuqvhvAICG\nKaUmpq1yKeVx66QZa1o2r2006ENcVaQGu9axxtV59isSooQQ9tw1xtg2PjZJffzjjw0p2trh\n5ieto+8V4mywGzlyZPHjH374Yd26dSH6GqBF9WPrDW3yYLK5ZnjLsDkdqw4d8t0nKTr64hph\nrhMAItfK9ft37D3mbevRzJw/lmy7rkfLUJYkIjfY3dE79cMflnR5rKcUrqU/jqnX+0khRHp6\net26dctusmX/2f/hvz769pXaZn3G6onRyb3DXT40SwpZGZaXyLHZ3lm62HefDrXrvNqdYAcA\n5VFod/wyY43vPtPnb7y8faMq8SG9xStSg13Tfm/2+OTtB4f8ahL2ai16vdGvqRBi6NChaWlp\nZTeZdM1eun3bGw8/WKhcUTUuemHkE+EuHwAARLBZf24+mZXvu4/VZp8ya+39d3QJTUlFIjXY\nSV3MnU+8fmfJxrS0NG+bWt865ItbQ1YdAADQrJNZ+bMXbgmk59+r9lx1efMGqdWCXVKxSA12\nAAAAYTFzwSajUW80BjQwYvr8DY/ef1WwSypGsAMAADgH/f7Vqd+/OoW7Cs+YjxcAAEAjCHYA\nAAAaQbADAADQCIIdAACARhDsAAAANIJgBwAAoBFMdwJoUKwxakCbtr771L78xLsAACAASURB\nVIqLD00xAICQIdgBGhRjNPZtEeqVpwEAYcelWAAAAI0g2AEAAGgEwQ4AAEAjCHYAAAAaQbAD\nAADQCIIdAACARhDsAAAANIJgB6AyUkIdsR5VQoW7EACIJAQ7AJXR/vwDX+z6Zn/+gXAXAgCR\nhGAHoDIqdBUW/w0ACBDBDgAAQCMIdgAAABpBsAMAANAIgh0AAIBGEOwAAAA0whDuAgBURp+v\n+GfpQT9TjQzrflXz6tXP80BKqHTLIbuyl2rPsB62uWwZ1sMGXelfU0ZprBtTRwp5nocGAO0h\n2AHwwOqw5xXafPdxKtf5H+iI9eioPaPLttuc1hOFp2ZlzDHpzWW3DmkyuJY55fyPDgAaQ7AD\nEE4p5uTBje4ve8bugOXgrMNzr691bb2Y1FKbjNKYYk4OVYEAEEkIdgDCSQqZGlO3bLvD5TDp\nTLXNtRrFNgx9VQAQoRg8ASDoWPgVAEKDYAcg6Fj4FQBCg2AHIOhY+BUAQoN77ABcKMZsWLf2\n8GHffR7t1LlhYlJo6gGACkewA3ChOJaXt+vkCd99Cuylx+cCQAThUiwAAIBGcMYOQGUUpYsq\n/hsAKqdP/1m+8dgR331G9rq2anRMaOoRBDsAHiWao1Pi4nz3Mer0wSugfmy9oU0eTDbXDN4h\nAOA8nbIWHMnL893HqUI60xPBDoAHA9u1H9iu/Tm9xNuqr6JcC79KIVleAgDOFcEOQMXwtuqr\nYOFXAAgVgh2AiuFt1VfBwq/l9fy8OQdzcnz3Gdf3/0JTDICIQLADUDG8rfoqWPi1vCwOe16h\nLdxVAIgkTHcCAACgEQQ7AAAAjSDYAQAAaAT32AG4UDzdpevTXbqGuwoACCLO2AEAAGgEwQ5A\n0LE+GACEBpdiAQQd64MB0KRXu18V7hJKI9gBCDrWBwOA0OBSLAAAgEZwxg4AKqnq0TE2hyPc\nVQCIJAQ7AKikhvXoGe4SAEQYLsUCAABoBMEOAABAIwh2AAAAGsE9dgAARCIl7BsD6mi8VAgZ\n5GIqhsvp+mfmmnV/bj6efkJKUbtxStterdpc1VLKyKi/MiDYAQAQeVThRpF1r5SxSlfDW25T\nrmzpOiGqjJTm60NcXjkc3Z/59dM/HtmXWdySsfvoqrnrm7ZrNPDtuxOqxYextghCsAMAIPJI\nYVcyXgkhjC1k9J1l761StsWyYKKUZqGrGo4Cz03WsewPBn+VezKv7Kada/Z8PGTUM98PjY4z\nh76wiMM9dgAARCZddWG6Wti3KdufwniJMLYq/qMc+4XtD2m8WOlTIuIkzviR0zymuiKH9xyd\n8c28UNYTuQh2AABEKmm+UZj7CNsilfexEK6iRlUwXVhGS+PFInpARHzQn8g4tXHRFt99lk5d\nYbfZQ1NPRIuA7zcAAPBCytiB7tnubKqLf1nIqHCXF5Adq3f77WMrKNy3OT0ExUS6CDg9CwAA\nvJMydqASQlhnKMdO4TwsjS1F/MtCRswdaT4uwpbslhvsSjSAM3YAAEQ6KWMHKn1DYVsihEvE\nvxhBqU4IEZ8UF0i32Coxwa5EAwh2AABEPFXwu3TuE4ZmQgiV/3Xx/XYRoVHr+n77GKMMDVqm\nhqCYSEewAwAgshXfVyerjhHmm0qNpaj8kuvXuOiyJr77dOrTzhRjCk09EY1gBwBABCs5WiK6\n1FiKcFcXqDufv9XHNHVVayXd/PB1oawnchHsAACIVMq21C3VFQUjt3GyBb8IocJcYmCS69d4\n9PNBiTWrlN1Uq1Hy418MikuMDX1VkcjXqNgAl2ZTKjJ+aAAA0BLlypbWydJ4iTDfKhw73DfJ\nqI7KeVjY5grhipTzdg1apg6b/PTCScvW/7kpM/2ETq9LaVCj43VtO9/UwWDUh7u6iOFnuhO/\noY11eQEACD0ljNJ1Qkqzch4SuW966SOkK1e5MiPlo9oUY+p9X4/e9/UIdyERzFewGzVqlN/X\nB9IHAABULBl1qUr8RMh4Kb1+lEuhhOukiOoWysIQXr6C3aBBg0q1nFj7zdU3PrPL1fCj2X8O\nal3VYx8AABB8Upq6h7sGVDrnNnji6Rueumb0uq0Tbnvy+ueCVBAAAADKx889drvzHY1jz/aZ\neMxyolfDGN2rjsw4Ib4Ncm0AAOAMVSgc2/x3M1wUKUvEIhj8BLu+F3fo++bnL/e7oui+y3uS\nY4cv2P+Y6SdDjTtDUBwAACjiyh0prVOFvrYQXnKbsgvnIRF9k0wYEdrSUIn4CXartvz6zuMP\nNv+h4TejPuzRMP7d2R9dfUOrz+31Ppj9V2jqAwAAQgidsY0qmCKUXcY/JnS1Sm92HVM57wih\npLF9OKpDZeEn2BliG7/07R/9l4x96KZWP90x4uOXHlibPjA0lQEAgLP0dZS+thRGZRkvE14T\nerf1VZ3pKvcDoYtWopbU1w1wf0op5izTnoAGT9Tr2m/m+o299ItaX3rdj3/tC3JJAADAAylN\nIvYBoRwqZ5hw7j/d6kxX2S8LYRfR90md11W5SrHa7N9P/DtYhSJ8/AS742u+bl07oUrdtqO3\nFN790qgNs17++63rr7p/xI5ce2jqAwAAxaS+rkgYfjbbFae6+Fekob7/158xff7Gv1fv2bD1\nUPBKRVj4CXbP9nn6tnEb137X8/Hr/yuEiKt/5ddztr59reGuS7iEDwBAGEhDk9PZLvsFlf3M\n6VRnvCjwPRzNzPljyTYhxITpq5zOyFhwDAHyE+wmHXe+2qN+w17DLUd+Lm7s/O8XV2xNC3Jh\nAADAM2loImKHCPtO4dglYgedU6oTQkyascbucAohjmbmzF8SwBQqiBx+gt1dNQyv/3Vw3x+v\nxST/273dENMgiEUBAAAfnOkif5Qy1BP6esLy49n77QKweUfGus0Hi5+mzduQm2cNQokIDz/B\n7t2ZH/x618WtH/jjo9nvhKYgAADgy5n76mTCW6LKu6XHUvjkcqmJ01e7t1ht9imz1wanUISB\nn+lOqrUZvOHw4NCUAgDQHCXsW4Sw+zmPIHXC0FIIpt4IgCtT5X3qfl+dShgucoarnGEy+v/8\nvnrB39sPHckq1bhkxe6eXS5KrZ0UlIIRWn6CnZSy/b+HT/7upQbRfnoCAFCKsm+RWQOVyyn0\ntYTUe+lkE64METtIxj4S2uoikLKrvG+ELtp9tIQ0NDmd7fK/E6LQx6vzLba0eRvKtruUGjdt\nxXNDrmVaOw3wH9fatsu9vlnne0d+9Pw9XQOa9Q4AACGEEFJZlUwQOpvQV5Mxg4UurnQP50GV\n94EQUuqbhKPAiOLKFM5DQl9VRN8nRaGwn41oUggVc7fI/Z9QJ4XrqLcdTJu7Pt9i87hpx95j\nqzce6NDqHCZMQeXkP9i1vvu1z+7f+crQ/9R6p8ozTz9x313X1jB5+V9XCCmXZfLn781avV8I\nVb9Dn2eH9o3RSW+bokWBt84AgOCSsTLm36rgd2X9RcYPF7oqZzc5dirLOCGrCL1Z6GqEr8TI\n4LL9I4VSKkpaRitPHZQ0SZdStmXSfEPZrYeOZC1ctsPH/idOX926RV2jMfwf8TgfAV1gNVVr\n8+7E5Y8s+3XEW8NSHxrQ+drePbp2Hv7cw8EuzoedY1+aV9Dry9GvRgnbjPcefXFMq48GNPO2\naaj80ltnAEDQGVrJ+KYq90OVO/xstnPsVDnDhTTKmH4q/5twlxgBdAnPiug+UkZ56yCFEMIu\nDJ6nPhmfttLl8hgITzuZlT/7r8039Wp1fmUizM7h4mq9y/t+O33F8V3z77+6yba/JgWvpkBM\nmnOw30PXmKSU0nzNQ/3S507ysclHZyHEITc2m+dz1ACA8xLVVcY/KRwHVO5w4co+m+oSXhe6\nmuEuLkLIGBHVQRhb+fzTXsjYsi9du+ng1p1H/B5h5oLNp7ItQSgdoXPOQyLi6rYa8HirAY8P\nC0Y1gVufb38mwVj0OCqhkz3/Mx+b1guvnYUQt9xyS/Hj9u3bR0dHB7d0ALgwRXWV8ULlfqhy\nnhbOXKGLlgmvC32qcB4Ld2UaZ3c4J81Y7b+fEIV2xy8z1jx4d9dgl4Tg8RPslPJ12jbMlPvQ\neOVnk4/OAIDQiOoqYw6pnJFCFy0TvhX61HAXVGGUUEetx5LNNWXlm7Rl2+6j1ZJiqyV5OJNX\nVm6e9WSWpWpiTLCrQpBE6iQmrWONq/PsVyRECSHsuWuMsW18bGot1nnrLIQYM2ZM8eM//vhj\n165dIfoaAOBC49ipCtKEsb5wOZVlVOmxFJFsf/6B7/f+9EDDexvEVrqBpZc2r31p89rhrgIh\nEqkTmNzRO3XsD0uUEEK4lv44pl7vO4QQ6enpHjd57FyshZu4uDJD8QEAFaL4vroqn8qE58/e\nb6cJha7C4r+BMCrPGbsdP17Z/L4l4b1K27Tfmz0+efvBIb+ahL1ai15v9GsqhBg6dGhaWlrZ\nTdHCQ2cAQOi4j5bQpwp96un77XKHS9Ot4S4O0I7yBLtmAxarARVeybmRupg7n3j9zpKNaWlp\nXjZ56AwACBFnusqbdDbVFSkeS+H6XihnWOsDtCNS77EDAEQGZVP5nwhdkoy5T7hOCdeps5tk\ngoy+VeV/K5RFuPLCVyKgHQQ7AECwKGmWrhNKFAppVnlfeO4ko4QrSznWStE9tNUBGkSwAwAE\nizReLKp8LIVT6OJ9dFOuUzKqY8iqKmYpKDSbjTpWvoeG+Al23S9JXrTZ89SRlXqKOwBApSCF\nqXMAncJjyqy19epU69apSeAvUUKlWw7Zlb1Ue4b1sM1ly7AeNug8fLAapbFuTJ1KOMUdtMdP\nsPtr0+HRtzd53fndnqlXhaYgAABC4ODhUwuX70yIO3hZm/pmk7G4fdafm6/q0sy9xd0R69FR\ne0aXbbc5rScKT83KmGPSmz2+cEiTwbXMKRVSOeCD30uxulte7/n6i6EoBQCAkJnw2yqlVHZu\nQdq8DXfc2L6o8fCx7Klz1hVYC/91fVuPr0oxJw9udH/ZM3YHLAdnHZ57fa1r68V4WE7DKI0p\n5uSKrR/wyP89dknNPlj8dVQISgEAIDRWbzywbfeRoscLlm7v3qlpco0EIcSEtFVOp2vuoq3d\nOjWtXtXDlPVSyNSYumXbHS6HSWeqba7VKLZhUCsHfPO/8oTUJ9Sp6fnEMgAAEcfucE76fXXZ\npxu2Htq0PaNsByCCROqSYgAAlM+cv7YcP1li2rx1W9I3bkufkLayuMX9lB4QQfwEu8KcNYN6\nt401Gmq16P7dP6eHx+ZnfCYZHA4AiECnsi2z/txctv2T0X8dPZ7r3jL+t5XM/4CI4yfYfdH7\nhr9TH9yXbVn09YA3endZlsPyxgCACDZl9jqrrfTQB6fTtS/9eE6e1b0x/XDWwuU7Q1gaUAH8\nBLsRqzK//N8DNWKimnZ7YOa7TfoNnh6asgAAqHC792cuW72nbHtWrkW5VHZOgctV4hTdtDnr\nLAWc0UAk8RPsYvW6Q7bTazNfNPCXhvMHTs7ID35VAABUMKXUxOmry15dLbQ78/IKhRAulysr\nx+K+KS/f9tvc9aErEThvfoLdG91rPX790GkLlmU7ldTH/zTpwQeu6L9g89HQFAcAQEVZtmbv\n7v2ZZdtPnsoX4nTay8232e1O961/Lttx+Fi2351H6aKK/wbCyE+wu2fqvH/X3XbvdV3nn7IK\nIWpf/e7vT6YMvuntkNQGAEDFsNrsU2atLdtuKSi0FbrdcqfUyawSF6acTteEtFV+918/tt7Q\nJg/Wj6133pUC58VPsDPENP/kt+U5tsLbqkcXtXR77IuMnGPrVywNfm0AAFSMWX9uPpVtKdWo\nlDqZVbrRarOXuq9u0/aMDVsP+d6/FDLFnMxqsAg7XytPSClP34sg9e4BUBdVtVXHLqX7AADg\nmRKOHULZ/PSSJmFoJgLORkqoo9ZjyeaafuOUUiou1nT7De1Kta/bfLDUSNgz/Uu3TJi+qmWz\nWno9k7+isvO/pBgAAEKIYweO79t0oCDPmlA9oVn7RrFVYgJ8oSr4VeS8JfQpQpq8dVHO41IU\niqTR0tgywN3uzz/w/d6fHmh4b4PY+r57SimvubJFqcZ8i23Zmj1N6tcI5Fgup2vl+v2d27Fc\nGCo7P8GOiYgBABm7jkx6P23Hqt3FLTq9rsstHW977IbouADWnJSJQiohbDJ2iNCXDWEuUTBJ\nuBYLYZbKw/kzbwpdhcV/l0NsjGnE0zeV77VApeUr2HGNFQCwY9XuL5/60WYpcSHV5XQtmfLP\nrjV7nhw1JD4p1vcepC5J6eoIaVKWCTLhVWFo7r4nkfepsm8VpquFnYlFgPPF7QIAAK9yT+aN\nen5sqVRX7Mi+zO/++3NAO5JGGTtYyCiVM0I4tp9pdYm8T5VtoTDfIM03VkzFwIWNYAcA8Gr+\n2EX5ZQaTutuxave2FbsC2peuhkx43S3buaW62EGBj5mICLmn8tcu2LRkyj/rFmzKPZkX7nJw\nAWHwBADAq3ULNvnts2b+hosuaxLQ7vR1ZcLrKucVlTNCGhor+0btpbqcE7m/fvj7qrnr1ZnV\nyXQ62bZXq75P9EmsWSW8teFCwBk7AIBnTofz+KGTfrtlHjzhbZNyqYPbM7atPHxgh3A6XEIU\nZbvXhOuIKkgTUR01luoyDx4f2f/TlbPXKbc1Z10utXru+ncGfHZkn4d1L4CKxRk7AIBnUkop\nPUzqVqabh8ZCq33O6AWLJi/Pz7YIZRFOfUyVCVf0zbxh0FUm11QhooW+hrBvFo4dJcdSVDqB\nz5bncrq+fuanLC/rj2Vn5nz99I8vjn/CGMUnL4KIHy8AgGc6va563WrHDhz33S25zFRwuafy\nP3v0u4PbSqzWYMkrnPfTX5sWTn/k7SOJdW+R5utUzqsqZ0SZcbKlKaHSLYfsyl6qPcN62Oay\nZVgPG3QePsuM0lg3ps75LwUR+Gx5/8xck7Hb11rqR/dnLp++6sq+nc+zJMAHgh0AwKv217Sa\n9d0CP32ube3+VCn1/YvjSqW6oi3Cdezwntxv36j3zI8DhU539n67hFd97P+I9eioPaPLttuc\n1hOFp2ZlzDHpPc+lN6TJ4FrmFN/F+xX4bHlr/9gYSB+CHYKKYAcA8Orqe65cOm1lzolcbx0u\nvbJFk7Yl1mPYtHjr9pWexsm6soSyCl2VvVvNK2av63RDuxJjKaJv93aIFHPy4Eb3lz1jd8By\ncNbhudfXurZeTGrZVxmlMcWc7Purq1h+T20KIbjNDsFGsAMAeBWTEPOf/9372WOjLTkeJj1J\nbV57wIg7SzWumLW2TEclhEOoPCEThIwVqmDVzPmdrjn9ASRj7lH5X6n8z4TwvOCYFDI1pm7Z\ndofLYdKZaptrNYplpS/gNIIdAMCXBpfUe/6nRyZ/8PvmJVtdZwZ7RpmN3W6/vM9D15iio0r1\n93CfmbIJ5RRSL5RFOC1CiEPbM1TOMrcOduE6KZRU0hy5Q2ST69fwe9IupUFAS9MC5UawAwD4\nUaNutSEfDMg+nntgy8G8bEtijYTGbRpGmY0eOzsdztJNukQhpJBn74RzimiZcE/Jl2UJmSeM\nF1dw6SHU9upLNy7e6rtPu16tQlMMLlgEOwC4sLiU0nmcocSfKtXjL+3mP3hVr1O1zIkrndAl\nuT+vkVpfGEtGHM8pMZJcdn3bBeMWp+847K1DSoManW/qEMqScAFigmIAuLD8+Mvy7NyC4O2/\nVfeWAfSJ4DNz3uj0usHv9EtK9ry8RGLNKv/54D6DUR/iqnCh8RPsCnPWDOrdNtZoqNWi+3f/\nHCtqzM/4TJbrf3sAgPDatvvIkpW7ps5eF7xDdLm5Q7XaVX10SKgW3+32y4NXQDkooQ5a0vfk\n7y37p3i2vLKbDlrSlSgxfXON1OovjHms0w3tpO7sp6TUyQ692zz/06M161UP+VeGC46fS7Ff\n9L7h75bD9mUPzFo19treXS4+sOXyhNL3yQIAIoJSasJvq4QQS1fu7tG5WYPUasE4iiHK8OB7\n/T/+zzcWT+cFTTGmwe/2N8d6HgB7TqJ0UcV/nydvU+UJf7PllZ0qL75q3IARd/Z96sY96/fn\nnMiNS4pt3KZhfFLs+RcJBMJPsBuxKnPq7AdqxETV6PbAzHcn3Th4+u6JfUNTGQCgYi1cvvPg\n4VNCCJdSE6evem7ItUG6/JLavPYzox8e/9aUnWv2uLc3vLTePS/1rd3kfCcNLlI/tt7QJg8m\nm2ue/668TZUnfM6W52OqvLjEWE1ebkbl5yfYxep1h2ynxzddNPCXhv9NnZxx3fXBLwsAULEs\nBYW/zV1f/HTH3mMr1++/rE2DIB0upUGNJ7956OD2jJ2rd+ecyItLim3arlG9FnUqMEpKIStq\nCmJvU+UJZstDpPET7N7oXuvx64fGvPfQVd07V9HH/zTpwYuu6P/zN/5vjAUAVCpp8zbk5lnd\nW36ZsaZNy7pRRoMQYvf+zGMnci9v16hiD5ravHZq89oVu08APvgZPHHP1Hn/rrvt3uu6zj9l\nFULUvvrd359MGXzT2yGpDQBQMQ4fy17w9/ZSjSez8mf9uVkIoZQaN23lrzPXWm0erkUCiCB+\ngp0hpvknvy3PsRXeVj26qKXbY19k5Bxbv2Jp8GsDAFSMidNXO52usu2zF245mZW/bPWefekn\nTmVbZv65KfS1AahAgc1jJ/Xu/XRRVVt17BKcegAAFWzD1kMbtx3yuKnQ7hiftnLymdVd5/61\n9fjJvBCWBqCCMUExAGiZ0+maOH2Vjw4Lluw4mplb9NjucE76fXVI6gIQFOUJdjt+vJIJigEg\nIsxfsu1IZo63rQ6HMyev4FR2fnHL6o0Htu0+EpLSIkMFzpYHhEB5gl2zAYuVUv77AQDCKjfP\n+vsfG310OJltUUoVFjry8m3FjRPSVvNLvljRbHn1Y+uFuxAgIFyKBQDNmjJ7naWg0NtWq81e\ncGZrVo7FdSbMHcw4uXD5zlDUFwmKZsuTgutUiAwBBbv9vw1rWiNur9V5ZNGbqQmmhNqXfrCI\nE/UAUKnl5llPZuW3aJri7Y/D6TKbjUV/jEZ9QcHZuU5+m7veRyIEUGn5maC4yMD73r1tyraG\nZv0z/d7tP3vv4Pz3W/Yd+lTmlGAXBwDwJivHkpgQ46NDfJz5yUFXe9v657IdW3ceiYvxvGZr\nbp41bd6Gu27ucL5VAgitgILdkhzbJ53quOzHvsqMP3F5bX3BIOvJNsGuDAAqB6Usvwhlk1Gt\nffQRhcuFqYcwNA9NTfkW21ufzXnpkeuqJESX7+VTZ6/z3WfB39u7d25aq2aVchUIIDwCCna3\nVY/+fMnBJywvRzf7r0mKQ8s/NyV6/V8gAGiJsm+R+R8rV67SVRc6zylHOTOlylHKoYsLUbCb\nOmf9iVN5k2etHXhneWYVTZu3Id9i893H6XRNnL76iYE9y1VgZXcyK3/91kNXXd4s3IUAFSyg\nYPfRr6/3uK3lt/bkD5Z+lrP/lTb9/nxpzJxgVwYAlYFUVqWrLnS1hMqX5mtF1BUltytl+VW6\n/lQiQRfVKTQlHTqS9dfyHUKIZav39OzSvGFqtXN6+eGjHpYX82jjtkMbth5q1aJOeaqs3H6Z\nsWbT9owOl9aLjzOHuxagIgUU7JK7PrU186kzz17PzHg9eAUBQOWjk3FPKevvyjpP6usJc58z\n7UrlfSEcG0VUN+nYIkI1cHJC2iqXSwkhlFLjf1v534d7n9PcoktX765Xu2qAnZev2aO9YLdj\n77GV6/crpabMXjvg9svDXQ5QkQIKdgBwoZMmmfCKynld5X8nhRDmPqdTnW2+MPWSUZ1U7pbQ\nFLJ208EtOw8XP929P3P5mr2Xt28U+B5uv6FdEOqKGC6lJqatKpqob/GK3T27XJRaOyncRQEV\nxtd0J1LKS59cUfSgrFBVCACVg4yWCa8Iw0Uq/zth/f1sqosbGrJzdXaHs+z6YL/OWmu12T32\nR1lLVuzel36i6HHRKc/w1gNULF/BTim18cPLih6UFaoKAaDSKM52uSNFwa8hTnVCiHmLt2ae\nzCvVeCrbMnthiM4XRjqrzT519lr3lu17jq7asD9c9QAVLqBLsVtzClsklFgmz3J4eUytzsEp\nCQAqMWkWuppCFQoppKF+KFNddm7BDC/rg81euLlrx8bVq8aFrJhzYrHb1x7O8N0nKTr64upJ\nKv9DaWwndDW9dVOuTFG4SsY/IYTnGfh8S5u3ISfPWqpx0u9rWl9c12jQl2OHQGUTULBrV7/j\nu+MnP3pdUyGEEGrhty/2f/SDgwV+hsoDgOYolfeFKPxLRN8tXMdU/vdSSLexFME1eeZaq83h\ncZPd4fxlxpoh/buFppJzlZmf/87Sxb77dKhd55XL40T+OCXGK31tKaM89bILZ4ZQLmXqIc99\nDPLRzJwFSz0MBz5xKm/2ws039Wp1rjsEKqGAgt2GCQ/d3b/NzLtGfvdil7cfuPuHzcmfzmEZ\nQQAXGlXivjplPTuWQpcS7GPvO3hi+eo9Pjqs2rB/++6jzRsnB7uS4JFCp/S1hCiUMlrEPiT1\nJb8Wlanyvha6JCGjZLlG/k36fbXd4fS4aeaCzV07Nkmq4mslDyAiBLRWbNPeQ5ft31Jtxst1\na3ec5rx7986F93WrF+zKAKAyUaVHS7iPpSj8O8jHVuN+W+nyd3Pz+LSVZW6Adoq8L5XtL2Hf\n4PWPbYnK/1yoyjH8Qppl7CNCmoTlZyWThLHV6T/66ip/nBCGrUcGKVWemec278hYtyXd29ZC\nu+OXGWvOo26gsgjoPz323O2vDrx7WmGrD7+59qun33vstXqjRtwXr2dgLIALhSqYKhxbSo+W\nkNGn50CxzhCqMHhHX7Fu3+79mX67Hcw4teifXd07Ny1uUYVrhOVrIXRKX8fjL3wlHNKRIaRD\nGdpKU3kWsah4+noy4VWVM0LkvKISXpeGVOHKUNmvCFWQp3vhywkr7r0useNl57ZLl0uNTys9\nmriUFev2XX1F88b1a5S/cqASCOiMXZvU1ssS7tixa+Hjg15Zt29pXjcQPgAAIABJREFU8tq3\n67e6KdiVAUAloVwnROEiYbhUmroK+8YSp7scO2X0bULGCddx4dgQjKOf08mkqXPWWQrORkwp\ndEKXInRVhC5Wxj8hE15z/yPinpKiitDHKV2KlOUZixAshuYy4VUh7CLnFVW4qijVyYRXpszP\nt1idk+bVtttd57S/BX9vP3w023efotOizPmASBfQGbvBY9Y+cVOLosempEs/nrmtz+dPB7Mq\nAKgslDQLoVfCKR0bVY7nQalCuIQuXglzMC5kZOdab+p16bn0L4iJdht5IKNl9APKOkVZfpYJ\nbxQPOFWuEyLvayFtwjxYWn+t2JorgKG5THhV5bwsTg1V+lRd4hsHj6UsXrFaCHEyxzh78ZGb\nrgt0T/kWW9q8gDL3voMnlq3e06VD43JXDYRdQMGuONUJIVz2rEXTJ/+6cMO1DwetKACoNKTx\nYpn0lVD+5gGQJmEIyoryNarGde98fns2NJbxL6rct1TOy0XZTrlOiOxXhTom4p6TQqdKTwBS\nOejihdAL6ZBSp0TceLfTaTP/OtL1ckuAYx0WLt8ZYzbGmI0Bdu7UtqFeH9DlLKASCnRgkXIV\nrJw7dcL48RMnzzls1bW96uaglgUAlYYUhubhruG8GVsVZzsR97TI/eR0qovqKApXh7s4T4ru\nqxM6WeVNlT921T/vbN/dVpyZA6XQ7vplxpoH7+4ayJ769LykT89LglkrUIn4C3bKsXnJjPHj\nx0+Y9Nuekw6lHG98Mf6O/7u1afXyDEoCAITN6Ww3Qpy6X+hririXZFTHcNfkxZnREjLhFWFo\n4VANJs0bJ5wZQl+7uAtjHQCPfJ1tfuuZB1qlJl7a484Z2x2D3vxpy/4VQoiXhtxFqgOASKT0\ndYSIFsoiRJQ01A93OV6o4+6pTggxe4n9ZF49IZRwZhRPyxLgFDDAhcbXGbuX/jc6tu6VPy4e\n379LHSGEw7I1VFUBwIVlxaH0kwUFvvv0atTYoCv/vV+n76sTVhH3grBOK77frtw7DA67yv1A\nSLOMHSiUXdg3nMounPnHOiGU0FUVruPCdax4upl9B08sW7Xnio6MdQDO8hXsxn48bNy4cQO6\npr7W8bp+/frdcctFISsLAC4oU7Zu2ZJ5zHefbvUblDvYlRgtEdVRGC8+O5Yi+BLM5r4tWvru\nUzchQYnsohXDhKGWyh9d1P7Lb/ULrYlnermEsruvz/vrrLXtW9UzmwIaGAFcCHwFu3seG37P\nY8Oz9qwaP27cuC+fGvH4CSHEsI/H3HlH34trse4KAEQGpbJLpDpRYiyFjL4j2AUkmc0D2rQN\noFCLMF8noi4X+tOXiXcfyF2xbYvQu11vVYVC5Ql5+o6g7NyC3//YePsN7Sq+aCAy+f/PX2Kj\nDkNe/mDxliP718wZ+ezAae8PvaROYuse/wpBcQCA86SEQ+R9VyLVFTG2kvEvCleOyh8lhCN8\nBbqRMSLhLWG+qWgZMZfh0nEzspUwCxl99o+uitDXcf/wmr9427HjuWGsGqhUzuGsfmqbns+/\n++36g1kbF0668aLyLMAMACgfq82ek+fnJjxP7NKRIVS6MPeV0lR6lVghZPQdwnVMOA/5n6gv\n5Jav3rPv4Am/3ewO56QZlXLGFiAcypHP9C273fpmt1srvhYAgBcnsyzT5mz4z10BzdxWTIko\nIQ1CmEXBROUlFiphksKopKFSrf9ttTkmz1wbYOe1mw5u3XmkRdOUoJYERAROvAFAZZebZ7Xb\nHSvW7r3uihYNUqsF/kIZ1VZU/cn32TgpgrhsRrnpdfK/jwS8apgQ0YyfAIQQBDsAqORcLpWV\nUyCEcAk17reV/324t5SBn1yL1GUzjEZ9japx4a4CiDwshwcAlVpWjsXlchU93r0/c8W6fWEt\nB0ClRrADgMrLbnfm5pe4kPrLjDWF9soxiBVA5UOwA4DK62S2RZRcNetUtmXmgs3hqgdAJUew\nA4BKylJQaLUWlm2fvXDzyaz80NcDoPJj8AQAhN+/Wlzco0FD9xan0zVh+qroXFdxi06dHjNh\ndzgnTl89pH+3kJYIIBIQ7AAg/C6rU7dUy+yFm6OOumoKk8f+qzbs37H3WLOGNYNfGoBIwqVY\nAKh0snMLps/f6LvPuGkrVMnb7wCAYAcAlc7U2eusNrvvPgczTi1esTs09QCIFAQ7AKhc9h08\nsXRlQIltyuy1BVY/+Q/ABYVgBwCViFJqwvRVrsCusebmWafP3xDskgBEEAZP/H979x0eVZX/\ncfycKZlJJgkJARJagEhHuqKuWBBpiiAiuOuC7iKggEhRERVBEUVBRUXhJypdLKvoooIUxZVi\npasgQTqhhJBA6tTz+2NwCCEzGUKSSU7er4cnz8295577PZPJ5MOtAFC+jPzXjcE3Nhj4/zmA\ncwh2AFCOSCltEYVfCQsAReK/egAAAJqoqHvslCfn4zenr9h0QAhV74pbHx3eN8IgAyz6/dVh\nT3x3wiiFEKJGh2dmP3Z5KKsHAAAoBRU12CUvfnJ17s2z500ME/Yvp498YlGrV+9tHGDRseQz\nd89Z3L9aeGjLBgAAKD0VNdh9tPLQgFldLFIKYe1y/4D5wz8S904IsGh7prN7hLnQrsaPH++b\n5jRkAABQcVXUYLct2/lI9NmgFhZ9lTP7jcCLtmU7cicN/2l3avXL2t732KNXxZ/bdbdmzRrf\ndPv27cPD2asHAAAqpIoU7Hr16uWdWLZsmRBCKCGkb+H593w6f5FyZ7a5oVunvnc/Fm/e9MWM\nlx6f9+Hc4b7FHTp08E1HRkY6HI5SqR4AAKCUVaRgdzbPCSGEaG0zb8pyXhsdJoRwZm4229oE\nWCSNUaMeGuZdekWvMXnz7hHiXLCbNWuWb3r+/Plbt24t7YEAAACUhop6Sln/bnUXz1+vhBDC\ns2HBosRu/YUQhw8fLnSR/fTa/gOeTslzCyFSNn0YHt8thJUDAACUkoq0xy6/RgOeu/H1qUOH\nfWIRzrhmN08Z0EgIMXz48GXLll24yGJo/OSdu6aMGOpQnrDqTce/MDrU5QMAAJS8ihrspCHi\nrtHP3nX+TO+x2kIXtb592Kzby6w6AACAEKioh2IBAABQAMEOAABAEwQ7AAAATRDsAAAANEGw\nAwAA0ATBDgAAQBMEOwAAAE0Q7AAAADRBsAMAANAEwQ4AAEATBDsAAABNEOwAAAA0QbADAADQ\nBMEOAABAEwQ7AAAATRDsAAAANEGwAwAA0ATBDgAAQBMEOwAAAE0Q7AAAADRBsAMAANAEwQ4A\nAEATBDsAAABNEOwAAAA0QbADAADQBMEOAABAEwQ7AAAATRDsAAAANEGwAwAA0ATBDih3lFDH\n8o4roUJdCACggjGFugAABR3IPjh338JBDe6pb6sX6loAVHJK5CwQxgbCEOu/SZ5ybpe2gUJY\nyrAwFI5gB5Q7Do/D9xUAQkg5toisV4UwKENtKQvNDB7hThHKrkyXSUunsq4PFyDYAQCAwkmh\nlCFBCLs02kTEMFlgv53KU9lvC0+6MERLGR2iGnEezrEDAAD+yXAZ8YBQQuS+pwwJwtzq7D9T\nQ5X7sfCkyYi7Bamu3CDYAQCAgEwNZdTjwnNGZE5Q7hNCCKFy1JmnhWuPjBwmzFeGuj6cQ7AD\nAABFMbc+l+1cB86lOkuXUFeG8xDsAABAEM5muwyRMUA5d5HqyieCHQAACI6pkZBVhCdTGozK\n1DrU1aAQXBULhIwS6nDOEadyFpifknfU7rGn5B01GQr+hpqluU5EbSlkWdUIAH/xnlfnSZOR\nI1Te1yJzgoqaIo01Ql0WzkOwA0LmWN7xt/fOu3C+3Z2X5khfkbLSYrReuHRYwyE1rQmlXx0A\n5JP/aglLF2nuoDKnns12oS4N+RHsgJBJsMYPSfr3hXvsDuYcWnF0VY+aXRMj6hZYZJbmBGt8\nWRUIAEIIIVRewaslzK1l1ONns521f6jrwzkEOyBkpJB1I+pcON/lcVkMllrWmkm2BmVfFQCc\nz6Ny5gpPesGrJXzZLudtpVzstysnCHYAAMAP5ZGeo8qTLm0DhSFeOLefv1jK8H4q+w3pOS1U\nbmgqxPkIdgAAoHBKmoQSSoaJ3OUid7mfVhYhjEoqdtqVBwQ7AEA5o/KUY500BDydVOUIYRdh\n1wsuEi9NMqyNqLpIKntR7SzC1LhMKkIRCHYAgPJF5Xwosl5WhjhhiPHTxClcKVJKFbtQmluU\naXGVjhSmJqGuAReBYAcAKF+kqYmS4UK4pKWTsNxYcLEnXWX9nzBEK2mRKi8E9QHlGMEOKHfC\nDGG+r0BlJM3CmCCMdZR9rTTWFeF9zi3ypKqsN4VwS9v9Kvej0JUIlFMEO6DcqWdLHN5waLyV\n+7mjMjPI8IHK/pXKWSiFOJvtPKnq9AThSZfRjwvlCXGBQLnEs2KBckcKmWCN57lhqOykWUY9\nLsytVc5CkfvpeanO3DbUxQHlFMEOAFBeSctf2W6uOjWYVAcUiWAHACjHpEXahghPpnDvl5a/\nkeqAwAh2AIByzJOqzkwWhmrCcp2y/0/kfhrqgoByjYsnAADl1bnz6p4UpuYqc+p511IAuADB\nDgBQLqkMdXpO/vPqvI+cP5vtjImhrg8ojzgUCwAoh5wq6+2CV0ucu5ZiobB/F9LygHKKPXYA\ngHLGc0a4UoQhWkaOEMIonNvzL5TWnsqTpvKWCsmfMKAgfisAAOWLx50ipUdIi8pZ4q+JUE6h\ncpW0cr9HID+CHQCgfDHY7hZhbYRwF9XQJMzNyqIgoOIg2AEAyhspzC1CXQNQIXHxBAAAgCYI\ndgAAAJog2AEAAGiCYAcAAKAJgh0AAIAmCHYAAACaINgBAABogmAHAACgCYIdAACAJgh2AAAA\nmiDYAQAAaIJgBwAAoAmCHQAAgCYIdgAAAJog2AEAAGiCYAcAAKAJgh0AAIAmCHYAAACaINgB\nAABogmAHAACgCYIdAACAJgh2AAAAmiDYAQAAaIJgBwAAoAmCHQAAgCZMoS6gmJQn5+M3p6/Y\ndEAIVe+KWx8d3jfCIAs0eWXgXWMXfRRcYwAAgAqvou6xS1785OrcK2bPe/fdebPb56x8YlFy\n/qW7V302c8pD357OC6YxAACAHipqsPto5aEB93exSCmltcv9Aw6v+ij/0qiExKu73RNk4yP5\n2O32MhoAAABASauoh2K3ZTsfiTZ7p8Oir3Jmv5F/ac1W7WoG3bh3796+6fbt24eHh5dOyQAA\nAKWrIgW7Xr16eSeWLVsmhBBKiHNnyqkiVr6oxgAAABVQRQp2Z/OcEEKI1jbzpizntdFhQghn\n5mazrU2AFQM3njVrlm/6+++/37dvXwnXDQAAUCYq6jl2/bvVXTx/vRJCCM+GBYsSu/UXQhw+\nfDj4xj4d8qlSpUppVw4AAFBKKtIeu/waDXjuxtenDh32iUU445rdPGVAIyHE8OHD8+/VC9wY\nAABAMxU12ElDxF2jn73r/JkFUp3v20IbAwAAaKaiHooFAABAAQQ7AAAATRDsAAAANEGwAwAA\n0ATBDgAAQBMEOwAAAE0Q7AAAADRBsAMAANAEwQ4AAEATBDsAAABNEOwAAAA0QbADAADQBMEO\nAMqCEupY3nElVKgLAaAzgh0AlIUD2Qdn7ZlzIPtgqAsBoDOCHQCUBYfH4fsKAKWEYAcAAKAJ\ngh0AAIAmCHYAAACaINgBAABogmAHAACgCVOoCwAAfSihDucccSrnhYtS8o7aPfaUvKMmQ8EP\nXrM014moLYUskxoB6IxgBwAl5lje8bf3zit0kd2dl+ZIX5Gy0mK0Xrh0WMMhNa0JpVwdAP0R\n7ACgxCRY44ck/bvQPXYHcw6tOLqqR82uiRF1CywyS3OCNb5MCgSgOYIdAJQYKWTdiDqFLnJ5\nXBaDpZa1ZpKtQRlXBaDy4OIJAKh4ePIsgEIR7ACg4uHJswAKRbADgIqHJ88CKBTBDgAAQBME\nOwAAAE0Q7AAAADRBsAOAshBmCPN9BYBSwn3sAKAs1LMlDm84NN5aI9SFANAZwQ4AyoIU8mIf\nL8GTZwFcLIIdAJRTPHkWwMUi2AFAOcWTZwFcLIIdAJRTPHkWwMXiqlgAAABNEOwAAAA0QbAD\nAADQBMEOAABAEwQ7AAAATRDsAAAANEGwA4CKhyfPAigU97EDgIqHJ88CKBTBDgAqnmI8eRZA\nZcChWAAAAE0Q7AAAADRBsAMAANAEwQ4AAEATBDsAAABNEOwAAAA0QbADAADQBMEOAABAE9yg\nuKD169ePHz8+1FUAAAAUtH79+sANCHaFWLNmTahLAAAAKJzNZvO3SCqlyrKUcs7lcjmdzlBX\ngcrurbfeWrx4cVJS0oIFC0JdC3DRVq9ePXnyZCHEunXrQl0LcNH27t177733CiEWLFiQlJQU\n6nIKZ7FYDIbCz6Zjj915TCaTycRrghDzvgkNBkN4eHioawEuWlhYmHeCNzAqIovF4puoiO9h\nLp4AAADQBHungHKnYcOGN998c0JCQqgLAYojISHh5ptvDnUVQDFFRkZ638CRkZGhrqU4OMcO\nAABAExyKBQAA0ATBDgAAQBOcYweUC8qT8/Gb01dsOiCEqnfFrY8O7xthkAWavDLwrrGLPgpN\nfYAfAd66QbyrgRDT77OXPXZAuZC8+MnVuVfMnvfuu/Nmt89Z+cSi5PxLd6/6bOaUh749nReq\n8gB/Arx1A7+rgfJAv89egh1QLny08tCA+7tYpJTS2uX+AYdXnfe/w6iExKu73ROq2oAAArx1\nA7+rgfJAv89egh1QLmzLdnaINnunw6KvcmZvy7+0Zqt2V155ZSjqAooQ4K0b+F0NlAf6ffZy\njh0QMr169fJOLFu2TAghlBDnTu3gPkSoOAK8dXlXo/zT611KsANC5myeE0II0dpm3pTlvDY6\nTAjhzNxstrUJXV3ARQjw1uVdjfJPv3cph2KBcqF/t7qL569XQgjh2bBgUWK3/kKIw4cPh7gs\noCgB3rqFLgLKFf0+e3nyBFAuKE/OR69PXfPHKYtwxjW7+bEH+0UYZK9evfLv1SvwLVAeBHjr\nFroo1PUC59Hvs5dgBwAAoAkOxQIAAGiCYAcAAKAJgh0AAIAmCHYAAACaINgBAABogmAHAACg\nCYIdAACAJgh2AAAAmiDYAQAAaIJgB0BPyQtvklI2H7ahyJZSlsVzruRfymBbhTq0smtoCwBQ\nBgh2APT01lOb4m+svff9x1xFPTfxscceu8i+1YD4yGKUpJTyPsXR7Tj8xICutWJtRpOlXssb\nZq496m3gb35+ab/dI/NJ6rNWCHHyl/ld2tS3Wq2JrTrP/SnV29KVm9w+vv3uXJf327rdVvEM\nSUB7PCsWgIbs6avC47p/vP/7fzS4ZsLu9Kcuq1Ii3Sr3mbWrVv9v6auT31l/sR+eUp77vP3h\nwRa3fPO3z//zRNN466+rZ3a9f7X9zM8B5uf3+5vXXD+r71cLbvR+a4lp0rJh1HUx1tv/s3XM\nzY13r3m5Tb9leRnrhBAfDmy0os+q+Xc08FcGAP2wxw6Ahna/PSGy9kN3JF41qWHMgid/8s48\n+u0TlsjWv+e4hBDHv3/GGtVuR7ZT5DsUe2zd7BsuTwwzGuMSWz+zdO+F3bodRz/67+rjxhaX\nWF78LVM++OSla1s0iK0SU6NOwyLn53fk85S6d9zUrlXThk1bX3HFFS0bRgkhjELYHQ6Xx2V3\nOL0f7Kd+e3XUzrvmnZ/qAOhPAYB2/lEj4sZ5fyil9n7czWxrkeP2eOe/d0/jxFtnuvL2X1vF\nOvG7o96Zvk/Ca6Itz336/fGTqZtXTDfbWgbovxgfnheucvSHW4QQUhrHf5MSzHyvifWiE268\nOtJokNLQ5IaBP2fYlVInf5nfuWWiyWBKbNl5/i8nPe6s/nVrf348p0QqB1CBsE8egG5yjs2L\nrDV09b6DrW1mV87vdevf+OD21BmXxwkhPI6UbrUaOlpWOdV01o7ZfbztfUcnm9rC/v72ypF9\nro8LN2ZkZMTExPjbRDEOaF64inKdSU09tfKNex/6qEN68vQi53sN7nyds8uolx/qHZ59cPbD\nPV9KHnbs+4cKtPnlhRtGOadteOqqEqkcQEUS0lgJACXv+4cKHipN7LbUt3TnWx2llCvScn1z\nfJ+ER9cvuLv7NTUio5pd3WPmigMBNlGMD8/8q2zeuGFPrss77XYcMxhtgef748z5w2CKLTAz\n9+TKOrX7nHF5Tm5a0LlVoslgqtvyprk/pxa7cgAVCOfYAdCMe/yCPde/s8v3MffnB11Svh2d\n7lJCCGfWln6PbBt212WDbn/pwt1W2/Oavrdi47HTqUue7jGmT6fSK/Gl27uMWHvEO+1xnZam\nmMDzfZxZP7/44vRcj692j8EcV6DNtFvvGfnl21FG2eemoTc9998se9ay5zoNu/mO0hkKgPKF\nYAdAK6f3vvDdGff0/ucuGqjb82Wj89DDv5wQwvPCrbdGPPj5zIUbWu18/p+LdhdY9+m+nV/9\n/IfUjGzlzjGGxXtnvvrqqyVe5Oghzdb9a+jyn/84dnTv2w/3q3ndlMDzfTUYrQ3enzKh88Nv\n/XHo6OHkzVMG9kzqf155B78YuqDeS+NaxwkhHErYbDaLyRJhixTKWeKjAFAehXBvIQCUuJX9\nL4u5bFKBmS80rVrzb/N/nXNHZJ3+Z1wepdTJLS+FWet8eypP5Ts6eeDz59rUi5PSUD3pyhlr\njnhnFvo5WYwPz/yreFxnpg/rVauK1WAMb9t9yK9ZzsDz86+b/tvSfje0ijQbwiJr3Dr4uTSn\n27fIlbu3Q43Wv2efXev4D+/e2KK2xWKp3aLTuz8cL3blACoQzqIFgLJQTq5aKCdlACglHIoF\nAADQBMEOAMpIeXhWbKi2DqBssE8eAABAE+yxAwAA0ATBDgAAQBMEOwAAAE0Q7AAAADRBsAMA\nANAEwQ4AAEATBDsAAABNEOwAAAA0QbADAADQBMEOAABAEwQ7AAAATRDsAAAANEGwAwAA0ATB\nDgAAQBMEOwAAAE0Q7AAAADRBsAMAANAEwQ4AAEATBDsAAABNEOwAAAA0QbADAADQBMEOAABA\nEwQ7AAAATRDsAAAANEGwAwAA0ATBDgAAQBMEOwAAAE0Q7AAAADRBsAMAANAEwQ4AAEATBDsA\nAABNEOwAAAA0QbADAADQhCnUBQBlZ+/evUlJSaGuAqVFKZWcnNyoUSMpZahrASqS1MNpGz79\n6beNu9KOnLJGhl/Wut4V3dq0vL65waDzr1Ke2741Y9vvZ3Ydt58QQiRY45tHNW0T29piCAt1\naZdEKqVCXQNQFtLT0/v27Tt79uwmTZqEuhaUis2bNw8dOnTOnDnt2rULdS1AxeBxez6bueLL\nt9ecSctUHmUwGpTHo5SwRFiaX9Vo8LQB8fWqh7rGUvHr6d8/Pbws1ZHq9niklEIJJZVRGmuE\nVb+jbu/m0U1DXWDxsccOlcXs2bPPnDnz0ksvzZkzhz06WsrJyfF9RX5Kqe3bt9vt9sDNLBZL\nq1at+O2oPJRS8ya8v2bxOo/bXTUh1mg6e3aWEiInI3vzNzuev/v1J98fVSOxWmjrLHGb07d+\nePDjLHdWlCk6zGz2zXd4HEftRxfsW/yPev3bxLQKYYWXgmCHczIzM1evXr1p06b09PTY2Nj2\n7dt37do1MjIy1HWVgN27d3/22WdCiC1btnz99dc333xzqCsqI5mZmTt37gzcpkaNGvXr1y+T\nchAaW7Zs6dGjhxCidu3aBkPhp1bn5eUdOnRo4sSJDz/8cNlWh5D5ftkvaz/YIKWIq1U1/3wp\nhC3GZraGHUk+8vb4955476Fg4r6UMi4uzvftyZMn/bV0Zv0cWeWqmrd+tn9ZL9+6ZXb8MMOZ\nsfTIf7Nc2bGWqgZx3rjCDGFVw2LTHBkfH/q0ga1eFXOVYDqUUtbsuCBl3T2+OYuuq3XP+qP+\nRlRSwy/0BZdSEuxw1tdffz116tSMjAzfnJUrV86aNevJJ5/s1KlTCAsrES+//LLH4/FOv/rq\nqx07drRaraEtqWz8+eefw4cPD9zmzjvvHD9+fNnUg5DIycmx2WxOpzMpKWn06NFhYQVPITp4\n8ODjjz+ulEpMTAxJhSh7Ho9aNmulPdte3c8OuTCrOSI6YufGP3as29nq+ubB9BkgzOW3Z9GY\nmCvvP7L6oXTXbbGmst5D/F3qhnR7RhVzlQKpzksKQ6y5Sobr9LrUjT1r9Qiyz4Qdj+7L+2cD\nq1EI4bYfGvdrghBH/TUuweEX+oLrfFWs23Hk+WF3XJYQYzaa4+o0vXvsjDSXp6Q6P7N/gizM\nlIOZJbWJsrRixYrx48fnT3VeGRkZ48aN++qrr0JSVUlZs2bNpk2bfN8eO3Zs8eLFIawHKHtV\nq1b917/+tX///iVLlrRq1apDPjExMbNnz46Ojk5MTKxZs2aoK0UZ2f/rwSPJRyNibAHaRMbY\n7Dn2Tau2leymp0/eOuCdKffEnBzz43HfzLeG3tSgXkKdll0/P5S198N763Z5VQiRdejDGjV7\npjpL7G+3R3i2pm8zSoPJYPTXxiiNUoltGduVCHYv2oy+sSO+POidPvL1yOjbXw7QuLSHr3Ow\nW9D7msUZl89f9cvhlIP/+3hG7LaXOtz9cUl1HllnbPJfhBC+6eG1LvXApclU1rtRU1NTn3vu\nOX/7gZVSzz//fJD/D8tPSlktnwAtnVk/W4yG+r2W5V/3Yjfnj8PheP311wvMnD9//vHjxwtt\nX6Tgx7VlyZSOLepVqx4XU71+/zFv5Ab9uzl48OAgKwm2x5Impax13cL8cxZdVytAPaX6Iy5Z\noRpaoe8rf8V8ck0jbzPfWo2v/bLITXTr1m3UqFE//fTTmDFj8vLyvDN37949bNgwpdTDDz9c\njN3YF/tyafxLUeEc3HnEkee0WM2Bm9ntzh+Xbw6yT98+jjaPb/LXJuf4wsWZSVOaxz00sumK\n0f/1zf/qqlf2HTi2dJj5X91eSbprwTDHtAeX//lIl5GT1iwo41VdAAAeDElEQVSqbi6xrJJu\nT890ZZkNRYzaZDBlOE+fcqQH2W37yaM2PvqOd3rJw+sefPZKfy1LdviFvuA6B7txX6esXfj0\nda0axsfXvPzqHq8uW3H4ixI7d8RgqtrwL0II33TVS96r7Ha7S6LAi/DRRx/5PuULlZOT85//\n/KcYPZ/MJ0CzfPulS/4ci4ULF6akpBSYmZeXN3PmzGL3Gcy4jm+YcP0jG59ZuvlkatqxXavr\n//xc1+nbg+z/3XffLXZtZSZhx6P78s6+V/869OBXqf6IS1yohlbo+6rQYvp+n+xr5p3YveHW\nYDYxcODAUaNG/fzzz95s50t1s2fPLvZB2OBfLu1/KSoWe67D4/HIom5o4nF5lCfY97b6y9ap\n7f212TplWr3eM8INovHQcSe3PJqc6/LOn31PKyFE+8FvZSTPEEI88vmny/u1/eG2JSNaxAa5\n9WA4lFMpJWUR4cftcSuhMhwFj2L5E1l7WPfs11al251ZP09Nu2FkHb+7eEp2+IW+4DoHu8us\nxvFvrTjz16et2dbKnnPIO6082S8P6xkfZQmPqX3HgzMy3UoIcfTbJyyRrX/PcQkhjn//jDWq\n3Y5sZzG2K6VM+WZaUoxlxJ4Mf9sSQhxe9dr1LRItRkNUjcvun/G9d2ZMTIzvq7erHQvHNaxu\nM9vi73vtl2XP3Vu7itVsqzHwhQ2+zfnrX0p5ctPCbm2TrCZjbJ2WE5bs8lfwjz/+WOSgfvjh\nh2K8FEEqvf3SJ06cWLhwYaGLVq5cuW1bCR9fyO/Ne94csXJR5yZxQghrXKOnP3mjmzHVlfPH\n6Duvr1PvsqR6da7rO2pnjksIIaX84IGeLerW6D76UyFEx44dfV+llBun/SOuetdCVwytEB56\n8F7j+dMFdu7cmZ2dvXPnzgsXbd++Pfhzk8vVUZWLKiYYvmw3aNCg+++/35vqLuUeQMFXqP0v\nRcUSUyPaZDK6nEXsSrDawpJa1y+xrSrnwwv37Flys5QyovpdHnfmyC/Ovnm86VEKozRYhBDO\n7JQsc3T6zuQS27QQQogq5mijweRWRYzaII1GaawVfhFnJkwY1+LxN3b+uWRso4cm+m1UNsNX\n+jr01bRWNSNM4TU63vKPZ2bM/WXfGd+iXyZe1egfz/964Pj+X78d0Dy25YPfeOe/d0/jxFt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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bnDko4nu6EYqBvBDgCAqlVUaHJlmMVsqepKoHoEOwAAqlb90LoajVTusLqN6rih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\nnmxHnx6eeW9cNTfOo9/z9q3O+EYtqJSi+92QnBz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jvI/EVuTIJ7K6a+bMnsOFUKb5Z7U2ShHac5zoLxcAAAYkSURBVELE7nWKUf3ClV66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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(viridis)\n",
    "\n",
    "alz.dist.cecal = distance(alz_t_cecal, method = \"wunifrac\", type = \"samples\")\n",
    "alz.dist.log.cecal = ordinate(alz_t_cecal, method = \"PCoA\", distance = \"wunifrac\")\n",
    "alz.dist.evals.cecal = alz.dist.log.cecal$values$Eigenvalues\n",
    "\n",
    "p = plot_ordination(alz_t_cecal, alz.dist.log.cecal, color = \"Sex_Treatment\", shape = \"Sex_Treatment\") + #, label=\"X.SampleID\") + \n",
    "    ggtitle(\"Weighted UniFrac Treatment by Sex - CECAL\") +\n",
    "    geom_point(size=3, alpha=0.8) + \n",
    "    scale_colour_viridis(option=\"viridis\", discrete=TRUE, direction=1) +\n",
    "    #stat_ellipse(level=0.95, geom=\"polygon\",alpha = .2, aes(fill = Treatment), linetype=0) +\n",
    "    #scale_fill_viridis(option=\"viridis\", discrete=TRUE, direction=1)+\n",
    "    coord_fixed(sqrt(alz.dist.evals.cecal[2] / alz.dist.evals.cecal[1]))\n",
    "\n",
    "p = p + guides(colour = guide_legend(title = \"Treatment\", ncol = 2, keywidth = 1, keyheight = 1))\n",
    "\n",
    "p = p + theme_bw() + \n",
    "        theme(panel.grid.major = element_blank(),\n",
    "              axis.title.y=element_text(margin=margin(0,20,0,0)),\n",
    "              text=element_text(size=8, color=\"black\",family=\"Arial\"),\n",
    "              panel.grid.minor = element_blank(),\n",
    "              #axis.ticks = element_blank(),\n",
    "              #legend.key.size = unit(.1, \"in\"),\n",
    "              #legend.spacing.x = unit(.01,\"in\"),\n",
    "              legend.position = \"bottom\")\n",
    "\n",
    "p$layers <- p$layers[-1]\n",
    "\n",
    "p\n",
    "\n",
    "p2 = p + facet_wrap(~Sex, ncol=1)\n",
    "\n",
    "p2\n",
    "\n",
    "#png('sex_f_by_treatment.png', width=6, height=5, units='in', res=300)\n",
    "#plot(p)\n",
    "#dev.off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 1e40d6d32efb5f1d289ebe33ebdb0738 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 2        </td><td>0.03619592</td><td>0.1275203 </td><td>1.90006   </td><td>0.065     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>26        </td><td>0.24764840</td><td>0.8724797 </td><td>     NA   </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>28        </td><td>0.28384432</td><td>1.0000000 </td><td>     NA   </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  2         & 0.03619592 & 0.1275203  & 1.90006    & 0.065     \\\\\n",
       "\tResidual & 26         & 0.24764840 & 0.8724797  &      NA    &    NA     \\\\\n",
       "\tTotal & 28         & 0.28384432 & 1.0000000  &      NA    &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  2         | 0.03619592 | 0.1275203  | 1.90006    | 0.065      |\n",
       "| Residual | 26         | 0.24764840 | 0.8724797  |      NA    |    NA      |\n",
       "| Total | 28         | 0.28384432 | 1.0000000  |      NA    |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs   R2        F       Pr(>F)\n",
       "Treatment  2 0.03619592 0.1275203 1.90006 0.065 \n",
       "Residual  26 0.24764840 0.8724797      NA    NA \n",
       "Total     28 0.28384432 1.0000000      NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 457c750f9a11cb1ddaeea49b2967685d -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Treatment</th><td> 1        </td><td>0.03417163</td><td>0.243912  </td><td>5.161559  </td><td>0.004     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>16        </td><td>0.10592654</td><td>0.756088  </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>17        </td><td>0.14009816</td><td>1.000000  </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tTreatment &  1         & 0.03417163 & 0.243912   & 5.161559   & 0.004     \\\\\n",
       "\tResidual & 16         & 0.10592654 & 0.756088   &       NA   &    NA     \\\\\n",
       "\tTotal & 17         & 0.14009816 & 1.000000   &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Treatment |  1         | 0.03417163 | 0.243912   | 5.161559   | 0.004      |\n",
       "| Residual | 16         | 0.10592654 | 0.756088   |       NA   |    NA      |\n",
       "| Total | 17         | 0.14009816 | 1.000000   |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "          Df SumOfSqs   R2       F        Pr(>F)\n",
       "Treatment  1 0.03417163 0.243912 5.161559 0.004 \n",
       "Residual  16 0.10592654 0.756088       NA    NA \n",
       "Total     17 0.14009816 1.000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- 2d452c8b095e9566a790c023bc2bceed -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1        </td><td>0.01271197</td><td>0.05571963</td><td>1.062135  </td><td>0.374     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>18        </td><td>0.21542967</td><td>0.94428037</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>19        </td><td>0.22814164</td><td>1.00000000</td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1         & 0.01271197 & 0.05571963 & 1.062135   & 0.374     \\\\\n",
       "\tResidual & 18         & 0.21542967 & 0.94428037 &       NA   &    NA     \\\\\n",
       "\tTotal & 19         & 0.22814164 & 1.00000000 &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1         | 0.01271197 | 0.05571963 | 1.062135   | 0.374      |\n",
       "| Residual | 18         | 0.21542967 | 0.94428037 |       NA   |    NA      |\n",
       "| Total | 19         | 0.22814164 | 1.00000000 |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs   R2         F        Pr(>F)\n",
       "Sex       1 0.01271197 0.05571963 1.062135 0.374 \n",
       "Residual 18 0.21542967 0.94428037       NA    NA \n",
       "Total    19 0.22814164 1.00000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in UniFrac(physeq, weighted = TRUE, ...):\n",
      "“Randomly assigning root as -- d3f6e5ee86aaf936f5dcc50d43a06d43 -- in the phylogenetic tree in the data you provided.”"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>Df</th><th scope=col>SumOfSqs</th><th scope=col>R2</th><th scope=col>F</th><th scope=col>Pr(&gt;F)</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Sex</th><td> 1        </td><td>0.03441813</td><td>0.2576411 </td><td>5.552919  </td><td>0.003     </td></tr>\n",
       "\t<tr><th scope=row>Residual</th><td>16        </td><td>0.09917127</td><td>0.7423589 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "\t<tr><th scope=row>Total</th><td>17        </td><td>0.13358940</td><td>1.0000000 </td><td>      NA  </td><td>   NA     </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & Df & SumOfSqs & R2 & F & Pr(>F)\\\\\n",
       "\\hline\n",
       "\tSex &  1         & 0.03441813 & 0.2576411  & 5.552919   & 0.003     \\\\\n",
       "\tResidual & 16         & 0.09917127 & 0.7423589  &       NA   &    NA     \\\\\n",
       "\tTotal & 17         & 0.13358940 & 1.0000000  &       NA   &    NA     \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | Df | SumOfSqs | R2 | F | Pr(>F) |\n",
       "|---|---|---|---|---|---|\n",
       "| Sex |  1         | 0.03441813 | 0.2576411  | 5.552919   | 0.003      |\n",
       "| Residual | 16         | 0.09917127 | 0.7423589  |       NA   |    NA      |\n",
       "| Total | 17         | 0.13358940 | 1.0000000  |       NA   |    NA      |\n",
       "\n"
      ],
      "text/plain": [
       "         Df SumOfSqs   R2        F        Pr(>F)\n",
       "Sex       1 0.03441813 0.2576411 5.552919 0.003 \n",
       "Residual 16 0.09917127 0.7423589       NA    NA \n",
       "Total    17 0.13358940 1.0000000       NA    NA "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Difference between treatment group within sex\n",
    "#Male\n",
    "alz_t_cec_M.dist.wunif = distance(alz_t_cec_M, method = \"wunifrac\", type = \"samples\")\n",
    "alz.cec.M.df = data.frame(sample_data(alz_t_cec_M))\n",
    "alz.cec.M.wunif.adtest = adonis2(alz_t_cec_M.dist.wunif ~ Treatment, data=alz.cec.M.df)\n",
    "alz.cec.M.wunif.adtest\n",
    "#Female\n",
    "alz_t_cec_F.dist.wunif = distance(alz_t_cec_F, method = \"wunifrac\", type = \"samples\")\n",
    "alz.cec.F.df = data.frame(sample_data(alz_t_cec_F))\n",
    "alz.cec.F.wunif.adtest = adonis2(alz_t_cec_F.dist.wunif ~ Treatment, data=alz.cec.F.df)\n",
    "alz.cec.F.wunif.adtest\n",
    "\n",
    "#Differences between sexes within treatment group\n",
    "#Control\n",
    "alz_t_cec.dist.wunif = distance(alz_t_cecal_control, method = \"wunifrac\", type = \"samples\")\n",
    "alz.cec.control.df = data.frame(sample_data(alz_t_cecal_control))\n",
    "alz.cec.control.wunif.adtest = adonis2(alz_t_cec.dist.wunif ~ Sex, data=alz.cec.control.df)\n",
    "alz.cec.control.wunif.adtest\n",
    "#Abx\n",
    "alz_t_cec.dist.wunif = distance(alz_t_cecal_ABX, method = \"wunifrac\", type = \"samples\")\n",
    "alz.cec.abx.df = data.frame(sample_data(alz_t_cecal_ABX))\n",
    "alz.cec.abx.wunif.adtest = adonis2(alz_t_cec.dist.wunif ~ Sex, data=alz.cec.abx.df)\n",
    "alz.cec.abx.wunif.adtest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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