{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Visualization\n",
"This notebook contains the code for all plots in the paper."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# DEPENDENCIES\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.cm as cm # colormaps\n",
"import matplotlib.lines as mlines # custom artist for legend across different axes\n",
"import numpy as np\n",
"import pandas as pd\n",
"from scipy.cluster import hierarchy\n",
"import seaborn as sns\n",
"\n",
"# OTHER USEFUL STUFF\n",
"# matplotlib default colour palette (Vega category 10 palette)\n",
"# can also be accessed with strings \"C0\", \"C1\", etc,\n",
"# but this is more comfortable for the dendrogram colouring\n",
"mpl_def_col_pal = [\"#1f77b4\", \"#ff7f0e\", \"#2ca02c\", \"#d62728\", \"#9467bd\", \"#8c564b\", \"#e377c2\", \"#7f7f7f\", \"#bcbd22\", \"#17becf\"]\n",
"\n",
"# unify plot sizes\n",
"plot_w = 8\n",
"plot_h = plot_w / 2\n",
"\n",
"# independent variables\n",
"IVs = [\"popsize\", \"host\", \"memsize\", \"numskills\"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Population size converging variation\n",
"The input for this plot is the output of the `popsize_solo` experiment in the Netlogo model's BehaviorSpace experiments, cleaned with the `clean_nl_csv()` function in `data_wrangling.jl()`.\n",
"Values are means of 25 runs.\n",
"The three data points at 2000, 2500, and 3000 were computed separately."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" max_pop_size \n",
" sig_len \n",
" stddev \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" 100 \n",
" 3.400405 \n",
" 0.440534 \n",
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" 0.487020 \n",
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" 2 \n",
" 120 \n",
" 4.264155 \n",
" 0.510706 \n",
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" 3 \n",
" 130 \n",
" 4.241522 \n",
" 1.428653 \n",
" \n",
" \n",
" 4 \n",
" 140 \n",
" 5.453127 \n",
" 0.238402 \n",
" \n",
" \n",
"
\n",
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(plot_w, plot_h), dpi=200)\n",
"\n",
"ax.plot(df[\"max_pop_size\"], df[\"sig_len\"], lw=0, marker=\"o\")\n",
"ax.plot(df[\"max_pop_size\"], df[\"stddev\"], label=\"standard deviation\")\n",
"\n",
"# grey lines\n",
"x = np.array([0, 1766])\n",
"y1 = 7.8-0.0015*x\n",
"y2 = 4+0.00065*x\n",
"ax.plot(x, y1, ls=\"--\", c=\"0.7\")\n",
"ax.plot(x, y2, ls=\"--\", c=\"0.7\")\n",
"\n",
"ax.legend()\n",
"\n",
"ax.set(\n",
" xlabel=\"population size\",\n",
" ylabel=\"signal length\",\n",
" xlim=(100, 3000),\n",
" ylim=(0,None),\n",
")\n",
"\n",
"plt.tight_layout()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Effects on signal length\n",
"The input for this plot is the output of the `hostility_solo` and `memory_solo` experiments in the Netlogo model's BehaviorSpace experiments, cleaned with the `clean_nl_csv()` function in `data_wrangling.jl()`.\n",
"Some unused columns have been removed."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" memory_mean \n",
" sig_len \n",
" \n",
" \n",
" \n",
" \n",
" 0 \n",
" 1 \n",
" 0.360000 \n",
" \n",
" \n",
" 1 \n",
" 1 \n",
" 0.430000 \n",
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" \n",
" 2 \n",
" 1 \n",
" 0.376667 \n",
" \n",
" \n",
" 3 \n",
" 1 \n",
" 0.320000 \n",
" \n",
" \n",
" 4 \n",
" 1 \n",
" 0.551667 \n",
" \n",
" \n",
"
\n",
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# initialise plot and axes\n",
"fig, ax1 = plt.subplots(figsize=(plot_w, plot_h), dpi=200)\n",
"ax2 = ax1.twiny()\n",
"\n",
"# do actual plotting\n",
"sns.lineplot(data=df_mem, x=\"memory_mean\", y=\"sig_len\",\n",
" color=\"C0\",\n",
" ci=\"sd\", # ribbon standard deviation\n",
" ax=ax1,\n",
" )\n",
"sns.lineplot(data=df_host, x=\"hostility_mean\", y=\"sig_len\",\n",
" color=\"C1\",\n",
" ci=\"sd\",\n",
" ax=ax2,\n",
" )\n",
"\n",
"# set limits and labels\n",
"ax1.set(\n",
" xlim=(1, 26),\n",
" xlabel=\"memory size\",\n",
" ylabel=\"signal length\"\n",
")\n",
"ax2.set(\n",
" xlim=(0, 1),\n",
" xlabel=\"hostility\"\n",
")\n",
"\n",
"# get legend across both axes done\n",
"lab1 = mlines.Line2D([], [], color=\"C0\", label=\"memory size\")\n",
"lab2 = mlines.Line2D([], [], color=\"C1\", label=\"hostility\")\n",
"plt.legend(handles=[lab1, lab2], loc=\"upper left\")\n",
"\n",
"# wrap up and save\n",
"plt.tight_layout()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Effects on population size\n",
"The input for this plot is the output of the `memory_solo` experiment in the Netlogo model's BehaviorSpace experiments with a very high value for `max-pop-size` (~ 100000), cleaned with the `clean_nl_csv()` function in `data_wrangling.jl()`."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
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" \n",
" \n",
" memory_mean \n",
" pop_size \n",
" \n",
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" 0 \n",
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" 153 \n",
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(plot_w, plot_h), dpi=200)\n",
"\n",
"sns.lineplot(\n",
" data=df, x=\"memory_mean\", y=\"pop_size\",\n",
" color=\"C0\",\n",
" ax=ax,\n",
")\n",
"\n",
"ax.set(\n",
" xlabel=\"memory size\",\n",
" ylabel=\"population size\",\n",
" xlim=(0,20.5),\n",
")\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Longest segment\n",
"The input for this plot is explained in `longest_dist_metric.ipynb`."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" popsize \n",
" host \n",
" memsize \n",
" numskills \n",
" maxsegment \n",
" \n",
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" 0 \n",
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# ACTUAL PLOTTING\n",
"fig, ax = plt.subplots(figsize=(plot_w, plot_h), dpi=200)\n",
"\n",
"# line plots\n",
"for i in range(len(y_IVs)):\n",
" ax.plot(x, y_IVs[i])\n",
"\n",
"# transparent bar plot\n",
"ax.bar(x, y_IVs[3], width=step, color=\"#fbf5f5\", edgecolor=\"C3\", lw=0.2, ls=\"dotted\")\n",
"\n",
"# add legend\n",
"ax.legend([\"population size\", \"hostility\", \"memory size\", \"numskills\"])\n",
"\n",
"# add labels, title, etc\n",
"ax.set(\n",
" title=\"(c) parameters influencing community strength\",\n",
" xlabel=\"linguistic community strength\",\n",
" ylabel=\"IVs, normalized\",\n",
" xlim=(0, 1.015),\n",
" ylim=(0, 1),\n",
")\n",
"\n",
"# add grid\n",
"ax.grid(True, ls=\"--\", c=\"0.8\")\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dendrograms explaining longest segment metric\n",
"This plot uses random data."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# HELPER FUNCTIONS\n",
"\n",
"def normalize_distances(Z):\n",
" \"\"\"\n",
" normalises distances for dendrogram to ]0, 1[\n",
" \"\"\"\n",
" max_clust_dist = max([i[2] for i in Z])\n",
" for i in Z:\n",
" i[2] /= max_clust_dist\n",
" return Z\n",
"\n",
"\n",
"def longest_segment(dendline):\n",
" \"\"\"\n",
" returns tuple of start and end of longest segment\n",
" \"\"\"\n",
" ms = 0.0\n",
" ms_start = -1\n",
" ms_end = -1\n",
" for i in range(len(dendline)-1):\n",
" s = dendline[i+1] - dendline[i]\n",
" if s > ms:\n",
" ms = s\n",
" ms_start = dendline[i]\n",
" ms_end = dendline[i+1]\n",
" return (ms_start, ms_end)\n",
"\n",
"\n",
"def link_color_func(old_col):\n",
" \"\"\"\n",
" map ugly dendrogram colours to default matplotlib colours\n",
" \"\"\"\n",
" if old_col == \"b\":\n",
" return \"C0\"\n",
" elif old_col == \"r\":\n",
" return \"C1\"\n",
" elif old_col == \"g\":\n",
" return \"C2\""
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# ACTUAL PLOTTING\n",
"\n",
"# generate random data\n",
"np.random.seed(4)\n",
"mean_a = [0, 0]\n",
"mean_b = [10, 10]\n",
"cov = [[2, 1], [1, 2]]\n",
"size = 25\n",
"\n",
"a = np.random.multivariate_normal(mean_a, cov, 2*size)\n",
"b = np.random.multivariate_normal(mean_a, cov, size)\n",
"c = np.random.multivariate_normal(mean_b, cov, size)\n",
"\n",
"# collect data for weak and strong plot\n",
"X_weak = a\n",
"X_strong = np.concatenate((b, c),)\n",
"Xs = [X_weak, X_strong]\n",
"\n",
"titles = [\"(a) weak linguistic communities\", \"(b) strong linguistic communities\"]\n",
"fig, axes = plt.subplots(\n",
" nrows=1,\n",
" ncols=2,\n",
" figsize=(plot_w, plot_h),\n",
" dpi=200,\n",
" sharey=True,\n",
")\n",
"\n",
"# do both dendrograms at once\n",
"for i in range(2):\n",
" \n",
" # perform clustering and plot dendrogram\n",
" Z = hierarchy.linkage(Xs[i], method=\"average\")\n",
" Z = normalize_distances(Z)\n",
" if i == 0:\n",
" # weak clusters: one colour\n",
" hierarchy.dendrogram(Z, no_labels=True, link_color_func=lambda x: \"C0\", ax=axes[i])\n",
" else:\n",
" # strong clusters: default colour palette\n",
" hierarchy.set_link_color_palette(mpl_def_col_pal[1:])\n",
" hierarchy.dendrogram(Z, no_labels=True, above_threshold_color=\"C0\", ax=axes[i])\n",
" \n",
" # grey line\n",
" dendline = Z[:,2]\n",
" \n",
" # x-position for grey line (11 has no special meaning, purely based on aesthetic aspects)\n",
" line_x = -axes[i].get_xlim()[1]/11\n",
" \n",
" # start and end of longest segment\n",
" l_seg = longest_segment(dendline)\n",
" \n",
" # recalculate limit for x-axis to fit grey line\n",
" # (similarly to 11 above, 8 has no special meaning)\n",
" new_xmin = -axes[i].get_xlim()[1]/8\n",
" \n",
" # plot grey line\n",
" axes[i].plot(np.full(len(dendline), line_x), dendline,\n",
" marker=\"o\",\n",
" markersize=4,\n",
" linestyle=\"dashed\",\n",
" c=\"0.7\",\n",
" )\n",
" \n",
" # plot red longest segment\n",
" axes[i].plot(np.full(2, line_x), l_seg,\n",
" marker=\"o\",\n",
" markersize=5,\n",
" color=\"C3\"\n",
" )\n",
" \n",
" # dark grey annotation of longest segment\n",
" ant_line_x = line_x+15\n",
" ant_c = \"0.4\"\n",
" hammer_w = 5\n",
" hammer_x = [ant_line_x-hammer_w, ant_line_x+hammer_w]\n",
" length = l_seg[1] - l_seg[0]\n",
" midpoint = l_seg[1] - (length / 2)\n",
" \n",
" axes[i].plot(np.full(2, ant_line_x), l_seg, c=ant_c, ls=\"dashed\")\n",
" axes[i].plot(hammer_x, [l_seg[0], l_seg[0]], c=ant_c)\n",
" axes[i].plot(hammer_x, [l_seg[1], l_seg[1]], c=ant_c)\n",
" axes[i].text(ant_line_x+5, midpoint, \"{:.2f}\".format(length), rotation=90, ha=\"left\", va=\"center\", c=ant_c)\n",
" \n",
" # set limits and title\n",
" axes[i].set_xlim(new_xmin)\n",
" axes[i].set(title=titles[i])\n",
"\n",
"\n",
"axes[0].set(ylabel=\" \") # for correct vertical alignment with other .png in tex document\n",
"plt.tight_layout()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"@webio": {
"lastCommId": null,
"lastKernelId": null
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"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
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"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
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