source-code/numpy/genetic_drift.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4955d8ae-54b0-40da-baa3-c1766c8fb4c0",
   "metadata": {},
   "source": [
    "# Requirements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6621f06c-50f7-4ebf-9aaa-a63ad29c0bb2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import itertools\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fcaf1d4-1491-4ddf-ad90-52d6fcd9c99b",
   "metadata": {},
   "source": [
    "# Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3330efdd-6c7c-4ff3-955e-471012390188",
   "metadata": {},
   "source": [
    "The model consists of agents that have a fixed position in space.  They can be in several gene variants, represented by integers.  At each time step, an agent is selected, as well as a random neighbour (von Neuman neighbourhood).  The agent's gene variant is then changed to that of its neighbour.  The simulation ends when all agents have the same gene variant.\n",
    "\n",
    "The space can have any dimension, and periodic boundary conditions are applied.  So in 1D this is a ring, in 2D a torus, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "916c196b-0cc3-40a8-9e30-0ec2bb171dd4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class Population:\n",
    "    '''Class representing a system to study genetic drift.  Agents have fixed positions\n",
    "    on a Carthesian grid and can have any of a fixed set of gene variants, represented as\n",
    "    integers.\n",
    "    '''\n",
    "    \n",
    "    def __init__(self, shape, nr_variants=2, p=None):\n",
    "        '''Create a new population\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        shape: tuple[int]\n",
    "            defines the number of dimentions and the size in each dimension\n",
    "        nr_variants: int\n",
    "            the number of gene variants to be present initially\n",
    "        p: array-like\n",
    "            probabilities for the gene variants\n",
    "        '''\n",
    "        if p is not None and nr_variants != len(p):\n",
    "            raise ValueError('number of variants and length of probability vector should match')\n",
    "        self._space = np.random.choice(nr_variants, size=shape, p=p)\n",
    "        self._neighbours = self._compute_neighbours()\n",
    "        self._reshape = tuple([-1] + [1]*(self.ndim - 1))\n",
    "        self._index = tuple([0]*(self.ndim - 1))\n",
    "        self._nr_steps = None\n",
    "        self._counts = {variant: [np.count_nonzero(self._space == variant)] for variant in range(nr_variants)}\n",
    "    \n",
    "    @property\n",
    "    def ndim(self):\n",
    "        '''Return the number of dimensions of the model\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        int\n",
    "            number of dimensions of the system\n",
    "        '''\n",
    "        return self._space.ndim\n",
    "    \n",
    "    @property\n",
    "    def shape(self):\n",
    "        '''Return the shape of the system\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        tuple[int]\n",
    "            shape of the system\n",
    "        '''\n",
    "        return self._space.shape\n",
    "    \n",
    "    @property\n",
    "    def size(self):\n",
    "        '''Return the size of the system\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        int\n",
    "            size of the system, i.e., the number of agents\n",
    "        '''\n",
    "        return self._space.size\n",
    "    \n",
    "    def _compute_neighbours(self):\n",
    "        '''Initialize the neighbour deltas for the given number of dimentions\n",
    "        '''\n",
    "        neighbours = set()\n",
    "        for coordinate in itertools.permutations([1] + [0]*(self.ndim - 1),\n",
    "                                                 self.ndim):\n",
    "            neighbours.add(coordinate)\n",
    "        for coordinate in itertools.permutations([-1] + [0]*(self.ndim - 1),\n",
    "                                                 self.ndim):\n",
    "            neighbours.add(coordinate)\n",
    "        return list(map(np.array, neighbours))\n",
    "    \n",
    "    def _step(self):\n",
    "        '''Perform an individual step in the simulation\n",
    "        \n",
    "        Randomly select an agent by coordinate, randomly select a neighbour delta,\n",
    "        if the species are different, update the selected agent, and increment the\n",
    "        number of steps.\n",
    "        '''\n",
    "        coordinate = np.empty((self._space.ndim, ), dtype=np.int32)\n",
    "        for i, dim in enumerate(self.shape):\n",
    "            coordinate[i] = np.random.choice(dim, size=1)\n",
    "        old_variant = self._space[tuple(coordinate)]\n",
    "        neighbour = np.mod(coordinate + random.choice(self._neighbours), self.shape)\n",
    "        new_variant = self._space[tuple(neighbour)]\n",
    "        if old_variant != new_variant:\n",
    "            self._space[tuple(coordinate)] = new_variant\n",
    "            for variant in self._counts:\n",
    "                if variant == old_variant:\n",
    "                    self._counts[variant].append(self._counts[variant][-1] - 1)\n",
    "                elif variant == new_variant:\n",
    "                    self._counts[variant].append(self._counts[variant][-1] + 1)\n",
    "                else:\n",
    "                    self._counts[variant].append(self._counts[variant][-1])\n",
    "            self._nr_steps += 1\n",
    "        \n",
    "    def run(self):\n",
    "        '''Run the simulation until all agents have the same state\n",
    "        '''\n",
    "        self._nr_steps = 0\n",
    "        while self.nr_variants > 1:\n",
    "            self._step()\n",
    "    \n",
    "    @property\n",
    "    def nr_variants(self):\n",
    "        '''Return the number of gene variants\n",
    "        \n",
    "        Returs\n",
    "        ------\n",
    "        int\n",
    "            number of gene variants\n",
    "        '''\n",
    "        count = 0\n",
    "        for series in self.history.values():\n",
    "            if series[-1] > 0:\n",
    "                count += 1\n",
    "        return count\n",
    "\n",
    "    @property\n",
    "    def nr_steps(self):\n",
    "        '''Return the number of steps\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        int\n",
    "            number of steps taken in the simulation\n",
    "        '''\n",
    "        return self._nr_steps\n",
    "    \n",
    "    @property\n",
    "    def history(self):\n",
    "        '''Return the gene variant counts for all time steps\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        dict[int, int]\n",
    "            dictionary containing for each variant (integer ID) a list of counts, one per time step\n",
    "        '''\n",
    "        return self._counts"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1c7e885-fe62-486f-8a91-43157d85fe2c",
   "metadata": {},
   "source": [
    "# Visualisation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4af81c-e653-499c-a3b4-ce2926a5a587",
   "metadata": {},
   "source": [
    "We can define a simple function to visualize the evolution of the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1237a089-e058-4f05-be34-0bc094acbcdb",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_history(population):\n",
    "    '''Create a visualization of the population's evolution as a stack plot\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    population: Population\n",
    "        population to visualize the evolution of\n",
    "    '''\n",
    "    plt.stackplot(list(range(len(population.history[0]))),\n",
    "                  *list(map(\n",
    "                      lambda x: list(map(lambda y: y/population.size, x)),\n",
    "                      population.history.values())));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "692bad37-9677-4b07-9aee-2581d0df7638",
   "metadata": {},
   "source": [
    "# Runs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "727f3209-098c-47a4-b85a-2fb3ebbcae71",
   "metadata": {},
   "source": [
    "Create a new population on a $5 \\times 5$ grid with two distinct gene variants.  Run the simulation and return the number of steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "91ac8411-ed32-46c1-b310-16d70cb58786",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "population = Population((5, 5), 2)\n",
    "population.run()\n",
    "population.nr_steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6636053a-8332-4f69-acbb-b1db51a0b822",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_history(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98ead8d4-0768-4ea8-87d8-e0209bd5b13c",
   "metadata": {},
   "source": [
    "Create a new population on a $25 \\times 25$ grid with two distinct gene variants.  Run the simulation and return the number of steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7b0f7960-b712-4305-b99f-d67973a4fe3e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = Population((25, 25), 2)\n",
    "population.run()\n",
    "plot_history(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f64fbd00-e251-4382-92a0-81f9c94d7875",
   "metadata": {},
   "source": [
    "Create a new population on a $5 \\times 5$ grid with two distinct gene variants, the first is much more likely than the second.  Run the simulation and plot the distribution of gene variants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "df5f3513-d311-4ecd-97c1-5778075dbcce",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = Population((5, 5), 2, p=(0.85, 0.15))\n",
    "population.run()\n",
    "plot_history(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "559f6451-8d9e-4d46-bc73-1fb17c881a90",
   "metadata": {},
   "source": [
    "Create a new population on a $5 \\times 5 \\times 5$ grid with two distinct gene variants.  Run the simulation and plot the evolution of the distribution of gene variants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ce22a855-0d39-437b-978b-49e48eafdac5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = Population((5, 5, 5), 2)\n",
    "population.run()\n",
    "plot_history(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bb46b00-249b-4333-b0bf-6552234f636b",
   "metadata": {},
   "source": [
    "Create a new population on a $10 \\times 10$ grid with 5 distinct gene variants.  Run the simulation and plot the distribution of gene variants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9193a6d9-3e37-4d94-9c9f-e24089e125e6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = Population((10, 10), 5)\n",
    "population.run()\n",
    "plot_history(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c903fd40-a347-470d-9933-5459d016e16d",
   "metadata": {},
   "source": [
    "# Scaling"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dfbb893-6cfd-476f-ad78-b6aa5bee19fd",
   "metadata": {},
   "source": [
    "How does the number of steps required to reach equilibrium change as a function of the system size?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "07198b5d-fe35-4b3d-83f4-ee5dc29863ec",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "size = 10\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "size = 20\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "size = 30\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "size = 40\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "size = 50\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "for size in range(10, 51, 10):\n",
    "    print(f'size = {size}')\n",
    "    data.append([])\n",
    "    for i in range(10):\n",
    "        print(f'\\trun {i}')\n",
    "        population = Population((size, size), 2)\n",
    "        population.run()\n",
    "        data[-1].append(population.nr_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "84513dd9-0e56-4759-bd3c-fb47737798e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(data)\n",
    "plt.xticks(ticks=[1, 2, 3, 4, 5], labels=list(range(10, 51, 10)))\n",
    "plt.yscale('log')\n",
    "plt.xlabel(r'N, size is $N \\times N$')\n",
    "plt.ylabel('nr. of steps');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3d42a3e-0017-4f48-aa33-80d1b6596f5a",
   "metadata": {},
   "source": [
    "How does the number of steps vary as a function of the number of gene variants in the system?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b857d916-6d4c-4e5e-9365-2b4f0d161629",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variants = 2\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 3\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 4\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 5\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 6\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 7\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "variants = 8\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n"
     ]
    }
   ],
   "source": [
    "size = 10\n",
    "data_variants = []\n",
    "for nr_variants in range(2, 9):\n",
    "    print(f'variants = {nr_variants}')\n",
    "    data_variants.append([])\n",
    "    for i in range(10):\n",
    "        print(f'\\trun {i}')\n",
    "        population = Population((size, size), nr_variants)\n",
    "        population.run()\n",
    "        data_variants[-1].append(population.nr_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e66710b7-696f-4d97-95ee-f0453c2961ff",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(data_variants)\n",
    "plt.xticks(list(range(1, 8)), labels=list(range(2, 9)))\n",
    "plt.xlabel('nr. of variants')\n",
    "plt.ylabel('nr. of steps');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f55f052a-6c5f-45ce-924c-20f443a90f09",
   "metadata": {},
   "source": [
    "How does the number of steps vary as a function of the number of dimensions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a26088c4-ef50-4e0b-871c-8d946940da54",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim = 1\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "dim = 2\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "dim = 3\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "dim = 4\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n"
     ]
    }
   ],
   "source": [
    "size = 10\n",
    "nr_variants = 2\n",
    "data_dims = []\n",
    "for dims in range(1, 5):\n",
    "    print(f'dim = {dims}')\n",
    "    data_dims.append([])\n",
    "    for i in range(10):\n",
    "        print(f'\\trun {i}')\n",
    "        population = Population((size,)*dims, nr_variants)\n",
    "        population.run()\n",
    "        data_dims[-1].append(population.nr_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "19413d0e-bd64-434f-beb8-bc9d8edda007",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(data_dims)\n",
    "plt.yscale('log')\n",
    "plt.xticks(list(range(1, 5)), labels=list(range(1, 5)))\n",
    "plt.xlabel('nr. of dimensions')\n",
    "plt.ylabel('nr. of steps');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "107d33e9-8a42-4a4c-a0b3-d029ad904571",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dim = (64,)\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "dim = (8, 8)\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n",
      "dim = (4, 4, 4)\n",
      "\trun 0\n",
      "\trun 1\n",
      "\trun 2\n",
      "\trun 3\n",
      "\trun 4\n",
      "\trun 5\n",
      "\trun 6\n",
      "\trun 7\n",
      "\trun 8\n",
      "\trun 9\n"
     ]
    }
   ],
   "source": [
    "shapes = [(2**6, ), (2**3, )*2, (2**2, )*3]\n",
    "nr_variants = 2\n",
    "data_dims_same = []\n",
    "for shape in shapes:\n",
    "    print(f'dim = {shape}')\n",
    "    data_dims_same.append([])\n",
    "    for i in range(10):\n",
    "        print(f'\\trun {i}')\n",
    "        population = Population(shape, nr_variants)\n",
    "        population.run()\n",
    "        data_dims_same[-1].append(population.nr_steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1194fd67-8527-405f-89f0-4b0dc26f0b21",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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x+u53v6uGhgZJUnFxsRYtWhTygOHAWlcAAEQG20XnoYceUr9+/XT48GG53e7A9lmzZmnz5s0hDRcuJSUl2rdvn3bt2uV0FAAAEEa2r9F5++239dZbb2nEiBGdto8ePVp//OMfQxYMAACgp2yf0Wlubu50JqfDl19+qQEDBoQkFAAAQCjYLjrXX3+9Xn311cBjl8slv9+v8vJyFRQUhDQcAABAT9j+6qq8vFxTpkxRdXW1zp49q0ceeUQff/yxvvrqK/3ud78LR0YAAICg2D6jk5mZqb179+qaa67R1KlT1dzcrBkzZujDDz/UlVdeGY6MAAAAQbF9Rufw4cNKSUnRE0880eVzI0eODEkwAACAnrJ9RictLU1ffPHFeduPHTumtLS0kIQCAAAIBdtFx7KsLtexOnXqlAYOHBiSUAAAAKHQ7a+uOlYld7lceuyxxzrdYt7e3q7f//73mjBhQsgDAgAABKvbRefDDz+UdO6MzkcffaT+/fsHnuvfv7+uvvpq/ehHPwp9QvSYq+20vjMsSrEnDkifBb28meNiTxzQd4ZFydV22ukoAIBLRLeLTseq5T/4wQ/0/PPPKyEhIWyhEFoDTx3W7vvipKr7pCqn0wQvQ9Lu++LkPXVYUr7TcQAAlwDbd12tXr260+PGxka9++678ng88ng8IQsWThUVFaqoqFB7e7vTUXrF6biRyn7plNauXauMS+TvqCveujrNnj1bL3+XO/sAAN1ju+jccccduv766zVv3jy1trYqNzdXPp9PlmXp9ddf1+233x6OnCFVUlKikpISNTY2KjEx0ek4YWfFDNSHR/1qvWyMNHyC03GC1nrUrw+P+mXFcNE7AKB7bF+wUVVVpcmTJ0uSNmzYIMuydOLECf3bv/2blixZEvKAAAAAwbJddE6ePKmkpCRJ0ubNm3X77bfL7XZr+vTpqq+vD3lAAACAYNkuOikpKdqxY4eam5u1efNm3XTTTZKk48ePM48OAADoU2xfo1NaWqrZs2crLi5Oo0aN0pQpUySd+0orKysr1PkAAACCZrvoPPjgg/rbv/1bHT58WFOnTlVU1LmTQt/+9re5RgcAAPQptouOJOXk5CgnJ6fTtunTp4ckEAAAQKhcutPkAgAAXARFBwAAGIuiAwAAjNWtojNjxgw1NjZKkl599VWdOXMmrKEAAABCoVtFZ9OmTWpubpZ0blHPkydPhjUUAABAKHTrriuPx6PFixeroKBAlmXpjTfeuODq5XfffXdIAwIAAASrW0XnxRdf1MKFC/XrX/9aLpdL//zP/yyXy3Xefi6Xi6IDAAD6jG4Vnfz8fO3cuVOSFBUVpQMHDmjIkCFhDQYAANBTtu+6OnTokK644opwZOk1FRUVyszMVF5entNRAABAGNmeGXnUqFE6ceKEXn75ZXm9XrlcLmVkZGju3LlKTEwMR8aQKykpUUlJiRobGy+ZzAAAwD7bZ3Sqq6t15ZVXavny5frqq6/05Zdfavny5bryyiu1e/fucGQEAAAIiu0zOg899JBuu+02rVq1SjEx517e1tam4uJilZaWqqqqKuQhAQAAgmG76FRXV3cqOZIUExOjRx55RLm5uSENBwAA0BO2i05CQoIOHz4sj8fTafuRI0cUHx8fsmAInZaWFkkK61eLra2t8vl8Sk1NVWxsbFiO4fV6wzIuAMBctovOrFmzNHfuXC1dulT5+flyuVx6//339fDDD+v73/9+ODKih+rq6iRJ9957r8NJQoNCDQDoLttFZ+nSpYGJAdva2iRJ/fr10wMPPKBnnnkm5AHRc4WFhZLOzXDtdrvDcgyv16uioiKtWbNGGRkZYTmGdK7kjB49OmzjAwDMYrvo9O/fX88//7zKysp08OBBWZal9PT0sH2AoucGDx6s4uLiXjlWRkaGsrOze+VYAABcjO2i08HtdisrKyuUWQAAAELK9jw6AAAAlwqKDgAAMBZFBwAAGIuiAwAAjBWyotPQ0KDDhw+HajgAAIAeC1nRufHGG5WWlhaq4QAAAHrMVtFpa2vTE088oSNHjpz33Kuvvqp33303ZMEAAAB6ytY8OjExMSovL9ecOXPOey4vLy9koQAA6G2uttP6zrAoxZ44IH126V7CGnvigL4zLEquttNOR+kTbE8Y+Pd///faunWr7rnnnjDEAQDAGQNPHdbu++KkqvukKqfTBC9D0u774uQ9dVhSvtNxHGe76EybNk2LFy9WbW2tcnJyNGjQoE7P33bbbSELFy4VFRWqqKhQe3u701EAAH3E6biRyn7plNauXasMj8fpOEHz1tVp9uzZevm7I52O0ifYLjoPPPCAJOnZZ5897zmXy3VJlIeSkhKVlJSosbFRiYmJTscBAPQBVsxAfXjUr9bLxkjDJzgdJ2itR/368KhfVsxAp6P0CbaLjt/vD0cOAACAkLt0r7YCAAC4iKBWL9+yZYu2bNmizz///LwzPP/5n/8ZkmAAAAA9ZbvoPPHEE3ryySeVm5ur5ORkuVyucOQCAADoMdtF58UXX9Qrr7yiu+66Kxx5AAAAQsb2NTpnz55Vfj735QMAgL7PdtEpLi7Wa6+9Fo4sAAAAIWX7q6vTp09r5cqV+u1vf6vx48erX79+nZ7van4dAAAAJ9guOnv37tWECRMkSbW1tZ2e48JkAADQl9guOu+99144cgAAAIQcEwYCAABjUXQAAICxKDoAAMBYFB0AAGAsig4AADAWRQcAABiLogMAAIxF0QEAAMai6AAAAGNRdAAAgLEisuhUVFQoMzNTeXl5TkcBAABhFJFFp6SkRPv27dOuXbucjgIAAMIoIosOAACIDBQdAABgLIoOAAAwFkUHAAAYi6IDAACMRdEBAADGougAAABjUXQAAICxYpwOAABAX9DS0iJJ2r17d9iO0draKp/Pp9TUVMXGxoblGF6vNyzjXqooOgAASKqrq5Mk3XvvvQ4nCY34+HinI/QJFB0AACQVFhZKkjwej9xud1iO4fV6VVRUpDVr1igjIyMsx5DOlZzRo0eHbfxLCUUHAABJgwcPVnFxca8cKyMjQ9nZ2b1yrEjHxcgAAMBYnNEB4AhX22l9Z1iUYk8ckD67NH/mij1xQN8ZFiVX22mnowC4AIoOAEcMPHVYu++Lk6ruk6qcThOcDEm774uT99RhSflOxwHQBYoOAEecjhup7JdOae3atcrweJyOExRvXZ1mz56tl7870ukoAC6AogPAEVbMQH141K/Wy8ZIwyc4HScorUf9+vCoX1bMQKejALiAS/OLcQAAgG6g6AAAAGNRdAAAgLEoOgAAwFgUHQAAYCyKDgAAMBZFBwAAGIuiAwAAjEXRAQAAxqLoAAAAY1F0AACAsSKy6FRUVCgzM1N5eXlORwEAAGEUkUWnpKRE+/bt065du5yOAgAAwigiiw4AAIgMFB0AAGAsig4AADAWRQcAABiLogMAAIxF0QEAAMai6AAAAGNRdAAAgLEoOgAAwFgUHQAAYCyKDgAAMBZFBwAAGIuiAwAAjEXRAQAAxqLoAAAAY1F0AACAsSg6AADAWBQdAABgLIoOAAAwFkUHAAAYi6IDAACMRdEBAADGougAAABjxTgdAACAS1FLS4vq6upsvcbr9Xb6vbs8Ho/cbret1+Acig4AAEGoq6tTTk5OUK8tKiqytX9NTY2ys7ODOlako+gAABAEj8ejmpoaW69pbW2Vz+dTamqqYmNjbR0LwaHoAAAQBLfbHdRZlkmTJoUhDS6Ei5EBAICxKDoAAMBYFB0AAGAsig4AADAWRQcAABiLogMAAIxF0QEAAMai6AAAAGNRdAAAgLGYGRmAI1paWiRJu3fvDsv4wU61b4fdhRkB9D6KDgBHdKz6fO+99zqcpOfi4+OdjgDgAig6ABxRWFgo6dxihW63O+Tje71eFRUVac2aNcrIyAj5+B3i4+M1evTosI0PoGcisuhUVFSooqJC7e3tTkcBItbgwYNVXFwc9uNkZGQEtfAiADNE5MXIJSUl2rdvn3bt2uV0FAAAEEYRWXQAAEBkoOgAAABjUXQAAICxKDoAAMBYFB0AAGAsig4AADAWRQcAABiLogMAAIxF0QEAAMai6AAAAGNRdAAAgLEoOgAAwFgUHQAAYCyKDgAAMBZFBwAAGIuiAwAAjEXRAQAAxqLoAAAAY1F0AACAsSg6AADAWDFOB0Df1NLSorq6um7v7/V6O/1uh8fjkdvttv06AAAuhqKDLtXV1SknJ8f264qKimy/pqamRtnZ2bZfBwDAxVB00CWPx6Oamppu79/a2iqfz6fU1FTFxsbaPhYAAOFA0UGX3G637bMskyZNClMaAACCw8XIAADAWBQdAABgLIoOAAAwFkUHAAAYi6IDAACMRdEBAADGougAAABjUXQAAICxKDoAAMBYFB0AAGAsig4AADAWRQcAABiLogMAAIxF0QEAAMai6AAAAGNRdAAAgLEoOgAAwFgUHQAAYCyKDgAAMBZFBwAAGCvG6QAA0B0tLS2qq6vr9v5er7fT73Z4PB653W7brwPQ91B0AFwS6urqlJOTY/t1RUVFtl9TU1Oj7Oxs268D0PdQdABcEjwej2pqarq9f2trq3w+n1JTUxUbG2v7WADM4LIsy3I6hFMaGxuVmJiokydPKiEhwek4AACgG+x8fnMxMgAAMBZFBwAAGIuiAwAAjEXRAQAAxqLoAAAAY1F0AACAsSg6AADAWBQdAABgLIoOAAAwFkUHAAAYi6IDAACMRdEBAADGougAAABjxTgdwEkdC7c3NjY6nAQAAHRXx+d2x+f4N4nootPU1CRJSklJcTgJAACwq6mpSYmJid+4j8vqTh0ylN/v12effab4+Hi5XC6n41zSGhsblZKSoiNHjighIcHpOAD/JtEn8e8yNCzLUlNTk4YPH66oqG++Cieiz+hERUVpxIgRTscwSkJCAv/xok/h3yT6Iv5d9tzFzuR04GJkAABgLIoOAAAwFkUHITFgwAD95Cc/0YABA5yOAkji3yT6Jv5d9r6IvhgZAACYjTM6AADAWBQdAABgLIoOAAAwFkUHAAAYi6KDHqmqqtKtt96q4cOHy+VyaePGjU5HQoQrKytTXl6e4uPjNWTIEBUWFmr//v1Ox0IEW7FihcaPHx+YJHDixIn6zW9+43SsiEHRQY80Nzfr6quv1s9+9jOnowCSpG3btqmkpEQ7d+7UO++8o7a2Nt10001qbm52Ohoi1IgRI/TMM8+ourpa1dXVuvHGG/W9731PH3/8sdPRIgK3lyNkXC6XNmzYoMLCQqejAAFffPGFhgwZom3btun66693Og4gSUpKSlJ5ebnmzp3rdBTjRfRaVwDMd/LkSUnnPlgAp7W3t+tXv/qVmpubNXHiRKfjRASKDgBjWZalhQsX6rrrrtO4ceOcjoMI9tFHH2nixIk6ffq04uLitGHDBmVmZjodKyJQdAAYa968edq7d6/ef/99p6Mgwo0dO1Z79uzRiRMntH79es2ZM0fbtm2j7PQCig4AI82fP1///d//raqqKo0YMcLpOIhw/fv3V3p6uiQpNzdXu3bt0vPPP6+XXnrJ4WTmo+gAMIplWZo/f742bNigrVu3Ki0tzelIwHksy9KZM2ecjhERKDrokVOnTumTTz4JPD506JD27NmjpKQkjRw50sFkiFQlJSV67bXX9F//9V+Kj4/X0aNHJUmJiYmKjY11OB0i0aOPPqpp06YpJSVFTU1Nev3117V161Zt3rzZ6WgRgdvL0SNbt25VQUHBedvnzJmjV155pfcDIeK5XK4ut69evVr33HNP74YBJM2dO1dbtmxRQ0ODEhMTNX78eP34xz/W1KlTnY4WESg6AADAWMyMDAAAjEXRAQAAxqLoAAAAY1F0AACAsSg6AADAWBQdAABgLIoOAAAwFkUHAAAYi6IDoFf97ne/U1ZWlvr166fCwsJuvy41NVXPPfdc4LHL5dLGjRtDni+Utm7dKpfLpRMnTjgdBYhYrHUFoFctXLhQEyZM0G9+8xvFxcUFPU5DQ4Muv/zyECYLvfz8/MC0/wCcwRkdAN3y9ddfh2ScgwcP6sYbb9SIESN02WWXBT3OsGHDNGDAgJBkCpf+/ftr2LBhF1x/C0D4UXSACDRlyhQtWLBAjzzyiJKSkjRs2DA9/vjjnfZxuVx68cUX9b3vfU+DBg3SkiVLLjrumTNntGDBAg0ZMkQDBw7Uddddp127dkmSfD6fXC6Xjh07ph/+8IdyuVwXXPj1888/16233qrY2FilpaVp7dq15+3zl19ddYz9xhtvaPLkyYqNjVVeXp4OHDigXbt2KTc3V3Fxcbr55pv1xRdfdBpn9erVysjI0MCBA+XxePTCCy8EnusYt7KyUgUFBXK73br66qu1Y8eOwD5//OMfdeutt+ryyy/XoEGDdNVVV+nNN9+U1PVXV+vXr9dVV12lAQMGKDU1VcuWLeuUJzU1VU8//bR++MMfKj4+XiNHjtTKlSsDz589e1bz5s1TcnKyBg4cqNTUVJWVlV307waIWBaAiHPDDTdYCQkJ1uOPP24dOHDA+vnPf265XC7r7bffDuwjyRoyZIj18ssvWwcPHrR8Pt9Fx12wYIE1fPhw680337Q+/vhja86cOdbll19uHTt2zGpra7MaGhqshIQE67nnnrMaGhqslpaWLseZNm2aNW7cOOuDDz6wqqurrfz8fCs2NtZavnx5p3wbNmywLMuyDh06ZEmyPB6PtXnzZmvfvn3Wtddea2VnZ1tTpkyx3n//fWv37t1Wenq6df/99wfGWLlypZWcnGytX7/e+vTTT63169dbSUlJ1iuvvHLeuJs2bbL2799vzZw50xo1apT19ddfW5ZlWdOnT7emTp1q7d271zp48KD1P//zP9a2bdssy7Ks9957z5JkHT9+3LIsy6qurraioqKsJ5980tq/f7+1evVqKzY21lq9enUg06hRo6ykpCSroqLCqq+vt8rKyqyoqCjL6/ValmVZ5eXlVkpKilVVVWX5fD5r+/bt1muvvXbRvxsgUlF0gAh0ww03WNddd12nbXl5edaPf/zjwGNJVmlpabfHPHXqlNWvXz9r7dq1gW1nz561hg8fbv30pz8NbEtMTOz0wf7X9u/fb0mydu7cGdjm9XotSRctOv/xH/8ReP4Xv/iFJcnasmVLYFtZWZk1duzYwOOUlJTzSsJTTz1lTZw48YLjfvzxx5akQPHIysqyHn/88S7fy18XnTvvvNOaOnVqp30efvhhKzMzM/B41KhRVlFRUeCx3++3hgwZYq1YscKyLMuaP3++deONN1p+v7/LYwLojK+ugAg1fvz4To+Tk5P1+eefd9qWm5vb7fEOHjyor7/+WpMmTQps69evn6655hp5vd5uj+P1ehUTE9Pp2B6Pp1vX8/zlexo6dKgkKSsrq9O2jvf4xRdf6MiRI5o7d67i4uICv5YsWaKDBw9ecNzk5GRJCoyzYMECLVmyRJMmTdJPfvIT7d279xvf21/++UjSpEmTVF9fr/b29i6P53K5NGzYsMDx7rnnHu3Zs0djx47VggUL9Pbbb1/0zwWIZBQdIEL169ev02OXyyW/399p26BBg7o9nmVZgXH+erudi3EvNE53/OV76nj9X2/reI8dv69atUp79uwJ/KqtrdXOnTsvOm7H64uLi/Xpp5/qrrvu0kcffaTc3Fz9+7//+wXfW1d/Pt/0Pv46d3Z2tg4dOqSnnnpKra2tuuOOOzRz5swL/ZEAEY+iAyAk0tPT1b9/f73//vuBbV9//bWqq6uVkZHR7XEyMjLU1tam6urqwLb9+/eHfC6aoUOH6lvf+pY+/fRTpaend/qVlpZma6yUlBTdf//9qqys1KJFi7Rq1aou98vMzOz05yNJH3zwgcaMGaPo6OhuHy8hIUGzZs3SqlWr9Mtf/lLr16/XV199ZSszECmYRwdAt/zhD3/Q3XffrS1btuhb3/rWec8PGjRIDzzwgB5++GElJSVp5MiR+ulPf6qWlhbNnTu328cZO3asbr75Zt17771auXKlYmJiVFpaqtjY2FC+HUnS448/rgULFighIUHTpk3TmTNnVF1drePHj2vhwoXdGqO0tFTTpk3TmDFjdPz4cb377rsXLHaLFi1SXl6ennrqKc2aNUs7duzQz372s053el3M8uXLlZycrAkTJigqKkq/+tWvNGzYsB7dqg+YjKIDoFtaWlq0f//+b5xP55lnnpHf79ddd92lpqYm5ebm6q233rI9sd/q1atVXFysG264QUOHDtWSJUv02GOP9fQtnKe4uFhut1vl5eV65JFHNGjQIGVlZam0tLTbY7S3t6ukpER/+tOflJCQoJtvvlnLly/vct/s7Gy98cYb+pd/+Rc99dRTSk5O1pNPPql77rmn28eLi4vTv/7rv6q+vl7R0dHKy8vTm2++qagoTtADXXFZXX1BDAAAYAB+BAAAAMai6AAAAGNRdAAAgLEoOgAAwFgUHQAAYCyKDgAAMBZFBwAAGIuiAwAAjEXRAQAAxqLoAAAAY1F0AACAsf4fqiAPUmo0LioAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.boxplot(data_dims_same)\n",
    "plt.yscale('log')\n",
    "plt.xticks(list(range(1, 4)), labels=list(range(1, 4)))\n",
    "plt.xlabel('nr. of dimensions')\n",
    "plt.ylabel('nr. of steps');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92e2fce0-ef60-46e9-a7df-2b4bca50d50d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}