Kyle Rodman's Lab 1.ipynb

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    "## Looking Through Tree-Ring Data in the Southwestern USA Using Pandas\n",
    "\n",
    "**Pandas** provides a useful tool for the analysis of tabular data in Python, where previously we would have had to use lists of lists, or use R."
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    "## Bringing in necessary pckages\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats.mstats as stat"
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    "\n",
    "### The Data\n",
    "\n",
    "The dataset I included herein is an example of tree growth rates at many different sites in the southwestern United States (AZ, NM). Field crews used increment borers to core into live trees in these sites and extract core samples. These were then brought back to the lab and dated to determine tree age and growth rates. I obtained this during my master's work at Northern Arizona University.\n",
    "\n",
    "In this dataset, each individual row is a tree.\n",
    "The columns are as follows:\n",
    "* site: The code for either the plot name or study site at which the tree was surveyed\n",
    "* center.date: The innermost ring of the tree. The closes estimate for the establishment year of the tree\n",
    "* dbh: The diameter of the tree (cm) at 1.37m above ground level\n",
    "* dsh: The diameter of the tree (cm) at 0.4m above ground level\n",
    "* Age: Estimated age of the tree when the core was collected. $Age = inv.yr-center.date$\n",
    "* spp: Four letter species code for the tree. The first two letters of the genus and species\n",
    "* inv.yr: The year in which the core was collected\n",
    "* BA: The basal area of the tree. Basically the surface area of the top of a stump if the tree was cut at 1.37m. Given with the formula $BA = 0.00007854 * DBH^2$\n",
    "* BA/Age: Just what it sounds like\n",
    "* Annual BAI: An estimate of the square centimeters of basal area produced by the tree each year. A better measure of growth than annual growth on the core as it accounts for tree size in addition to ring thickness in the core.\n",
    "\n",
    "Similar datasets are available through the International Tree Ring Data Bank (ITRDB), and can be found on the [ITRDB Webpage](https://data.noaa.gov/dataset/international-tree-ring-data-bank-itrdb)\n",
    "\n",
    "The following codeblock reads in the data and displays the first few rows of the pandas data frame. The path should be changed to the location of the .csv file."
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>site</th>\n",
       "      <th>center.date</th>\n",
       "      <th>dbh</th>\n",
       "      <th>dsh</th>\n",
       "      <th>Age</th>\n",
       "      <th>spp</th>\n",
       "      <th>inv.yr</th>\n",
       "      <th>BA</th>\n",
       "      <th>BA/age</th>\n",
       "      <th>annual.bai</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CIBS2A</td>\n",
       "      <td>1978</td>\n",
       "      <td>42.200</td>\n",
       "      <td>45.2</td>\n",
       "      <td>19</td>\n",
       "      <td>PIPO</td>\n",
       "      <td>1997</td>\n",
       "      <td>0.139867</td>\n",
       "      <td>0.007361</td>\n",
       "      <td>84.453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Peaks</td>\n",
       "      <td>1956</td>\n",
       "      <td>62.600</td>\n",
       "      <td>68.1</td>\n",
       "      <td>44</td>\n",
       "      <td>ABLA</td>\n",
       "      <td>2000</td>\n",
       "      <td>0.307779</td>\n",
       "      <td>0.006995</td>\n",
       "      <td>82.781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>BM</td>\n",
       "      <td>1965</td>\n",
       "      <td>62.100</td>\n",
       "      <td>69.8</td>\n",
       "      <td>46</td>\n",
       "      <td>ABCO</td>\n",
       "      <td>2011</td>\n",
       "      <td>0.302882</td>\n",
       "      <td>0.006584</td>\n",
       "      <td>83.185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>COCS4A</td>\n",
       "      <td>1932</td>\n",
       "      <td>72.644</td>\n",
       "      <td>81.8</td>\n",
       "      <td>72</td>\n",
       "      <td>PIPO</td>\n",
       "      <td>2004</td>\n",
       "      <td>0.414467</td>\n",
       "      <td>0.005756</td>\n",
       "      <td>72.969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>BM</td>\n",
       "      <td>1907</td>\n",
       "      <td>83.800</td>\n",
       "      <td>89.5</td>\n",
       "      <td>104</td>\n",
       "      <td>PIPO</td>\n",
       "      <td>2011</td>\n",
       "      <td>0.551542</td>\n",
       "      <td>0.005303</td>\n",
       "      <td>60.493</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     site  center.date     dbh   dsh  Age   spp  inv.yr        BA    BA/age  \\\n",
       "0  CIBS2A         1978  42.200  45.2   19  PIPO    1997  0.139867  0.007361   \n",
       "1   Peaks         1956  62.600  68.1   44  ABLA    2000  0.307779  0.006995   \n",
       "2      BM         1965  62.100  69.8   46  ABCO    2011  0.302882  0.006584   \n",
       "3  COCS4A         1932  72.644  81.8   72  PIPO    2004  0.414467  0.005756   \n",
       "4      BM         1907  83.800  89.5  104  PIPO    2011  0.551542  0.005303   \n",
       "\n",
       "   annual.bai  \n",
       "0      84.453  \n",
       "1      82.781  \n",
       "2      83.185  \n",
       "3      72.969  \n",
       "4      60.493  "
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   "source": [
    "## Change the path below if being run on a different computer\n",
    "data = pd.read_csv(r\"/Users/kyle/Google Drive/UC Boulder PhD Stuff/Classes/Fall 2016/Spatiotemporal Methods/Combined_BaiData.csv\")\n",
    "data.head()"
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     "name": "stdout",
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     "text": [
      "There are cores for 9913 trees\n"
     ]
    }
   ],
   "source": [
    "print \"There are cores for \"+str(len(data))+\" trees\""
   ]
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     "text": [
      "After removing rows with missing values, there are cores for 8952 trees. \n",
      "So, there were 961 rows that had NaN's\n"
     ]
    }
   ],
   "source": [
    "filtered_data = data.dropna()\n",
    "print (\"After removing rows with missing values, there are cores for \"+str(len(filtered_data))+\n",
    "\" trees. \\nSo, there were \"+str(len(data)-len(filtered_data))+\" rows that had NaN's\")"
   ]
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   "source": [
    "#### A logical question may be: \n",
    "\n",
    "*What species is growing the fastest across the sites?*\n",
    "So, we can produce a simple boxplot to help visualize this."
   ]
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   "source": [
    "filtered_data.boxplot(column = 'annual.bai', by = 'spp')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears that *Abies lasiocarpa* - subalpine fir - may be the fastest growing species overall. We can also look at the median values for the different species to verify this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>spp</th>\n",
       "      <th>annual.bai</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ABCO</td>\n",
       "      <td>4.1280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ABLA</td>\n",
       "      <td>14.9410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ACGR</td>\n",
       "      <td>3.3930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>JUOS</td>\n",
       "      <td>1.9330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>PIAR</td>\n",
       "      <td>10.0035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>PIED</td>\n",
       "      <td>1.5950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>PIEN</td>\n",
       "      <td>13.6570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>PIPO</td>\n",
       "      <td>7.6180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>PIST</td>\n",
       "      <td>2.8570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>POTR</td>\n",
       "      <td>6.6650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>PSME</td>\n",
       "      <td>1.3510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>QUGA</td>\n",
       "      <td>2.7400</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     spp  annual.bai\n",
       "0   ABCO      4.1280\n",
       "1   ABLA     14.9410\n",
       "2   ACGR      3.3930\n",
       "3   JUOS      1.9330\n",
       "4   PIAR     10.0035\n",
       "5   PIED      1.5950\n",
       "6   PIEN     13.6570\n",
       "7   PIPO      7.6180\n",
       "8   PIST      2.8570\n",
       "9   POTR      6.6650\n",
       "10  PSME      1.3510\n",
       "11  QUGA      2.7400"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "filtered_data.groupby('spp', as_index=False)['annual.bai'].median()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Kruskal-Wallis H-statistic is: 817.16 and... \n",
      "The p-value is: 3.91295661264e-168\n"
     ]
    }
   ],
   "source": [
    "## Adapted from http://stackoverflow.com/questions/35816865/create-vectors-for-kruskal-wallis-h-test-python\n",
    "groupednumbers = {}\n",
    "for grp in filtered_data['spp'].unique(): \n",
    "    groupednumbers[grp] = filtered_data['annual.bai'][filtered_data['spp']==grp].values\n",
    "args = groupednumbers.values()\n",
    "h,p = stat.kruskalwallis(*args)\n",
    "print(\"The Kruskal-Wallis H-statistic is: \"+str(round(h,2))+\" and... \\nThe p-value is: \"+str(p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the species have very different growth rates. We could take this a step further and perform pairwise comparisons between groups using Mann-Whitney tests with Bonferroni correction for multiple comparison, but a more robust analysis would likely use mixed-effects models or partial regression to account for the different growing conditions between sites, and perhaps to account for age and tree size as additional covariates."
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