Add formula for response.

Next: Delete some of the other stuff given that we want a fully
connected graph.

src/simulate_world.ipynb

@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -37,7 +37,28 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The response variable is total population size after SIMULATION_YEARS."
+    "The response variable is the arithmetic mean of the normalized coefficients of variation for the population sizes.\n",
+    "\n",
+    "$$\n",
+    "z_{i} = \\frac{1}{T + 1}\n",
+    "\\sum_{t=0}^{T}\n",
+    "    \\frac{\n",
+    "        \\sqrt{\n",
+    "            \\hat{V} \\left(\n",
+    "            \\mathrm{logpopsize}_{i,t}\n",
+    "            \\right)\n",
+    "        }\n",
+    "    }\n",
+    "    {\n",
+    "        \\underset{j}{\\mathrm{median}}\\left(\\mathrm{logpopsize}_{i,j,t}\\right)\n",
+    "    } \n",
+    "         \n",
+    "                \n",
+    "$$\n",
+    "\n",
+    "where $i=1,2,\\dots,k$ indexes the treatment, $j=1,2,\\dots n_i$ indexes the replicate for the $i^{\\text{th}}$ treatment, and $t=1,2,\\dots,T$ indexes the time.\n",
+    "\n",
+    "$\\hat{V}$ denotes the unbiased sample variance which is taken of the natural logarithms of the population sizes observed for treatment $i$ at time $t$."
    ]
   },
   {