{
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   "id": "interactive-link",
   "metadata": {},
   "source": [
    "> **This is a saved, working copy.** Sliders here are frozen at their\n",
    "> starting value — there's no marimo runtime in plain Jupyter to drive them.\n",
    "> For the live, drag-the-sliders version of this lecture, see\n",
    "> [Week 6 lecture — interactive](https://math4120.pages.dev/wasm/week06_lecture.html).\n"
   ]
  },
  {
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   "execution_count": 1,
   "id": "ipython-import",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-11-13T23:25:58.930641Z",
     "iopub.status.idle": "2026-11-13T23:25:58.935211Z",
     "shell.execute_reply": "2026-11-13T23:25:58.934349Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Markdown, HTML\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Hbol",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
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   },
   "source": [
    "# Week 6: The beavers of the Tay — logistic growth and stability\n",
    "## Computation lecture\n",
    "\n",
    "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "MJUe",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## Where are they?\n",
    "\n",
    "This lecture is about the beavers living on the river Tay in Scotland. The Tay flows from the Highlands through Perth (the marker) and into the sea at Dundee, about 165 miles north of Lancaster as the crow flies. Zoom out to find Lancaster, and zoom in to follow the Tay and the rivers that flow into it, such as the Earn, the Isla and the Tummel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "vblA",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-11-13T23:25:58.936725Z",
     "iopub.status.idle": "2026-11-13T23:25:58.941938Z",
     "shell.execute_reply": "2026-11-13T23:25:58.941259Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"100%\" height=\"450\" style=\"border:1px solid #ccc\" src=\"https://www.openstreetmap.org/export/embed.html?bbox=-6.0%2C55.6%2C-2.2%2C57.1&amp;layer=mapnik&amp;marker=56.396%2C-3.437\" title=\"Map of the Tay area\"></iframe><p style=\"font-size:0.8em\">Map © <a href=\"https://www.openstreetmap.org/copyright\" target=\"_blank\">OpenStreetMap</a> contributors. <a href=\"https://www.openstreetmap.org/?mlat=56.396&amp;mlon=-3.437#map=8/56.4/-4.0\" target=\"_blank\">Open a larger map</a>.</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(\n",
    "    '<iframe width=\"100%\" height=\"450\" style=\"border:1px solid #ccc\" '\n",
    "    'src=\"https://www.openstreetmap.org/export/embed.html?bbox=-6.0%2C55.6%2C-2.2%2C57.1&amp;layer=mapnik&amp;marker=56.396%2C-3.437\" '\n",
    "    'title=\"Map of the Tay area\"></iframe>'\n",
    "    '<p style=\"font-size:0.8em\">Map © <a href=\"https://www.openstreetmap.org/copyright\" target=\"_blank\">OpenStreetMap</a> contributors. '\n",
    "    '<a href=\"https://www.openstreetmap.org/?mlat=56.396&amp;mlon=-3.437#map=8/56.4/-4.0\" target=\"_blank\">Open a larger map</a>.</p>'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bkHC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "And here are the animals themselves, in a short film by NatureScot [7]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "lEQa",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-11-13T23:25:58.943213Z",
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     "shell.execute_reply": "2026-11-13T23:25:58.946744Z"
    },
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    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/buildhome/.asdf/installs/python/3.13.3/lib/python3.13/site-packages/IPython/core/display.py:448: UserWarning: Consider using IPython.display.IFrame instead\n",
      "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<iframe width=\"100%\" height=\"400\" src=\"https://www.youtube-nocookie.com/embed/BmDlnkIscLo\" title=\"Living with beavers (NatureScot)\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen></iframe>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(\n",
    "    '<iframe width=\"100%\" height=\"400\" '\n",
    "    'src=\"https://www.youtube-nocookie.com/embed/BmDlnkIscLo\" '\n",
    "    'title=\"Living with beavers (NatureScot)\" frameborder=\"0\" '\n",
    "    'allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" '\n",
    "    'referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen></iframe>'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "PKri",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "---\n",
    "\n",
    "Beavers were hunted to extinction in Britain centuries ago. In 2009 a licensed trial released a few families in Knapdale, Argyll. At about the same time, a wild population was growing on the river Tay from beavers that had escaped or been released without a licence. Scotland let both populations stay, and since 2019 beavers have been a protected species: they can only be moved or killed under licence [1, 6].\n",
    "\n",
    "NatureScot has surveyed the Tay beavers three times, in 2012, 2017/18 and 2020/21 [2, 3, 4]. A fourth survey was carried out in 2025, and its report is being finalised now [5].\n",
    "\n",
    "So what will the new survey show, and what would that tell us about the beavers' future? Today we use the maths from this week's lectures to make our own forecast, in five steps:\n",
    "\n",
    "1. plot the three surveys;\n",
    "2. warm up with Python functions, and work out the growth rate $\\alpha$ from the exponential model (5.2);\n",
    "3. code the logistic model (5.4) and find which carrying capacities $M$ fit the surveys;\n",
    "4. draw the phase portrait (Section 5.5);\n",
    "5. use stability and linearisation (Section 5.6) to see how fast the beavers recover after a flood."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Xref",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>How these numbers were found</b></summary>\n",
    "\n",
    "\n",
    "The data in this notebook were found and processed with an AI coding assistant (Claude Code). It searched NatureScot's reports, pulled out the numbers, and helped make sense of how they are reported. For example, a survey does not count beavers: people walk the rivers looking for feeding signs, dams, lodges and scent marks, work out how many family territories there are, and multiply by about 3.8 beavers per family [2]. Every number below is from a published report, listed at the end.\n",
    "\n",
    "One suggestion we did not keep. Three surveys look sparse on a plot, and when asked to make it look fuller, the AI suggested inventing values for the years in between. Made-up points on a plot look like data, so we left them out. Three surveys in nine years is a normal amount of data for a wild animal population.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "SFPL",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:58.949007Z",
     "iopub.status.busy": "2026-11-13T23:25:58.948833Z",
     "iopub.status.idle": "2026-11-13T23:25:59.253436Z",
     "shell.execute_reply": "2026-11-13T23:25:59.252431Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "BYtC",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 1. The data\n",
    "\n",
    "Time $t$ is in years since the 2012 survey. Each survey gives a best estimate and a range, because the number of beavers per family varies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "RGSE",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.255804Z",
     "iopub.status.busy": "2026-11-13T23:25:59.255568Z",
     "iopub.status.idle": "2026-11-13T23:25:59.259181Z",
     "shell.execute_reply": "2026-11-13T23:25:59.258369Z"
    }
   },
   "outputs": [],
   "source": [
    "survey_t = np.array([0.0, 5.5, 8.5])         # years since the 2012 survey\n",
    "survey_N = np.array([146, 433, 954])         # best estimate of the number of beavers\n",
    "survey_low = np.array([106, 319, 602])       # lowest estimate in the report\n",
    "survey_high = np.array([187, 547, 1381])     # highest estimate in the report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "Kclp",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.260793Z",
     "iopub.status.busy": "2026-11-13T23:25:59.260602Z",
     "iopub.status.idle": "2026-11-13T23:25:59.425648Z",
     "shell.execute_reply": "2026-11-13T23:25:59.424804Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_fig_d, _ax_d = plt.subplots(figsize=(9, 4))\n",
    "_err = np.array([survey_N - survey_low, survey_high - survey_N])\n",
    "_ax_d.errorbar(2012 + survey_t, survey_N, yerr=_err, fmt=\"o\", color=\"#1a5276\",\n",
    "               markersize=9, capsize=6, linewidth=2)\n",
    "for _tt, _nn, _lab in zip(survey_t, survey_N, [\"2012\", \"2017/18\", \"2020/21\"]):\n",
    "    _ax_d.text(2012 + _tt + 0.25, _nn, f\"{_lab}: {_nn}\", va=\"center\", fontsize=11,\n",
    "               color=\"#1a5276\")\n",
    "_ax_d.set_xlim(2011, 2023)\n",
    "_ax_d.set_ylim(0, 1500)\n",
    "_ax_d.set_xlabel(\"year\", fontsize=12)\n",
    "_ax_d.set_ylabel(\"beavers on the Tay\", fontsize=12)\n",
    "_ax_d.set_title(\"Three surveys: best estimate and range\", fontsize=12)\n",
    "_ax_d.grid(True, alpha=0.3)\n",
    "_fig_d.tight_layout()\n",
    "_fig_d;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "emfo",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 2. Warm-up: functions, and the growth rate\n",
    "\n",
    "While a population is small compared with what its environment can hold, it grows like the exponential model from Monday, $$\\frac{dN}{dt} = \\alpha N, \\tag{5.1}$$ whose solution is $$N(t) = N_0 e^{\\alpha t}. \\tag{5.2}$$ If it goes from $N_\\text{start}$ to $N_\\text{end}$ in a number of years, then $N_\\text{end} = N_\\text{start}\\, e^{\\alpha \\times \\text{years}}$. Take logs and solve for $\\alpha$: $$\\alpha = \\frac{\\ln(N_\\text{end}/N_\\text{start})}{\\text{years}}.$$\n",
    "\n",
    "A **function** packages a formula so we can use it again with different numbers. In last week's poll, about 1 in 5 of you thought a cell like the one below shows nothing, because there is no `print`.\n",
    "\n",
    "**Predict** what the cell shows before you run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "Hstk",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.427451Z",
     "iopub.status.busy": "2026-11-13T23:25:59.427303Z",
     "iopub.status.idle": "2026-11-13T23:25:59.430943Z",
     "shell.execute_reply": "2026-11-13T23:25:59.430178Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.1976602011443915)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def growth_rate(N_start, N_end, years):\n",
    "    return np.log(N_end / N_start) / years    # equation (5.2), solved for alpha\n",
    "\n",
    "growth_rate(146, 433, 5.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "nWHF",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "A notebook cell shows the value of its **last line**, so you see the number without a `print`. `return` hands a value back to whoever called the function; `print` only puts text on the screen.\n",
    "\n",
    "The numbers go into the function **in order**: the first becomes `N_start`, the second `N_end`, the third `years`. **Predict:** what happens if we swap the first two?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "iLit",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.432429Z",
     "iopub.status.busy": "2026-11-13T23:25:59.432298Z",
     "iopub.status.idle": "2026-11-13T23:25:59.435680Z",
     "shell.execute_reply": "2026-11-13T23:25:59.434828Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(-0.1976602011443915)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "growth_rate(433, 146, 5.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ZHCJ",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The same size, but negative: Python has no idea which number you meant as the start, so it computed a population *shrinking* from 433 to 146. Now the two intervals, using positions in the arrays (counting from 0, as last week):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ROlb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.437290Z",
     "iopub.status.busy": "2026-11-13T23:25:59.437127Z",
     "iopub.status.idle": "2026-11-13T23:25:59.441112Z",
     "shell.execute_reply": "2026-11-13T23:25:59.440431Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alpha, 2012 to 2017/18:    0.198\n",
      "alpha, 2017/18 to 2020/21: 0.263\n",
      "growth per year, 2017/18 to 2020/21: 30 %\n"
     ]
    }
   ],
   "source": [
    "alpha_early = growth_rate(survey_N[0], survey_N[1], survey_t[1] - survey_t[0])\n",
    "alpha_recent = growth_rate(survey_N[1], survey_N[2], survey_t[2] - survey_t[1])\n",
    "print(\"alpha, 2012 to 2017/18:   \", round(alpha_early, 3))\n",
    "print(\"alpha, 2017/18 to 2020/21:\", round(alpha_recent, 3))\n",
    "print(\"growth per year, 2017/18 to 2020/21:\", round(100 * (np.exp(alpha_recent) - 1)), \"%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "qnkX",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "NatureScot reported 30% a year between the last two surveys [4]. Our $\\alpha = 0.263$ is the same thing written differently: growing by 30% a year means multiplying by 1.30 each year, and $e^{0.263} = 1.30$. The $\\alpha$ in (5.1) is a rate of change at each instant, $\\alpha = (dN/dt)/N$; the percentage is what that adds up to over a whole year, because the growth compounds.\n",
    "\n",
    "Notice that the rate went *up* between the two intervals. The logistic model says it should go down as the population grows. The lab asks you why that might be.\n",
    "\n",
    "**What if 30% a year carried on?** Before you run the next cell, guess how many beavers there would be on the Tay by 2050."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "TqIu",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.442512Z",
     "iopub.status.busy": "2026-11-13T23:25:59.442358Z",
     "iopub.status.idle": "2026-11-13T23:25:59.445704Z",
     "shell.execute_reply": "2026-11-13T23:25:59.444866Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2025 3120\n",
      "2030 11639\n",
      "2040 161973\n",
      "2050 2254117\n"
     ]
    }
   ],
   "source": [
    "for year in [2025, 2030, 2040, 2050]:\n",
    "    N_projected = survey_N[2] * np.exp(alpha_recent * (year - 2020.5))\n",
    "    print(year, round(N_projected))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Vxnm",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "Over two million beavers by 2050. The Tay can't hold that: each family needs a stretch of river with enough trees to eat, and the 2020/21 survey already found them spreading into neighbouring catchments [4]. Sooner or later the growth has to slow down.\n",
    "\n",
    "Is there any sign of a slowdown in the three surveys yet? The curve below is the exponential model (5.2) started from the 2012 survey, so $N_0 = 146$, and the slider sets $\\alpha$. The hollow circles are what the curve predicts at the two later surveys.\n",
    "\n",
    "**Before you move the slider:**\n",
    "\n",
    "- Which $\\alpha$ do you expect to fit best: 0.198 (from the first two surveys), 0.263 (from the last two), or something in between?\n",
    "- Is there any $\\alpha$ for which the curve passes through all three ranges?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "DnEU",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.447164Z",
     "iopub.status.busy": "2026-11-13T23:25:59.446992Z",
     "iopub.status.idle": "2026-11-13T23:25:59.449532Z",
     "shell.execute_reply": "2026-11-13T23:25:59.449020Z"
    }
   },
   "outputs": [],
   "source": [
    "alpha_exp_slider = type('_W', (), {'value': 0.26})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ulZA",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.451283Z",
     "iopub.status.busy": "2026-11-13T23:25:59.451154Z",
     "iopub.status.idle": "2026-11-13T23:25:59.632317Z",
     "shell.execute_reply": "2026-11-13T23:25:59.630593Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_alpha = alpha_exp_slider.value\n",
    "_t_curve = np.linspace(0, 13, 300)\n",
    "_N_curve = survey_N[0] * np.exp(_alpha * _t_curve)       # equation (5.2), N_0 = 146\n",
    "_N_at_surveys = survey_N[0] * np.exp(_alpha * survey_t)\n",
    "\n",
    "_fig_e, _ax_e = plt.subplots(figsize=(9, 4.5))\n",
    "_err_e = np.array([survey_N - survey_low, survey_high - survey_N])\n",
    "_ax_e.errorbar(2012 + survey_t, survey_N, yerr=_err_e, fmt=\"o\", color=\"#1a5276\",\n",
    "               markersize=9, capsize=6, linewidth=2, label=\"surveys (best estimate and range)\")\n",
    "_ax_e.plot(2012 + _t_curve, _N_curve, color=\"#c0392b\", linewidth=2.5,\n",
    "           label=f\"exponential (5.2), α = {_alpha:.2f}\")\n",
    "_ax_e.plot(2012 + survey_t[1:], _N_at_surveys[1:], \"o\", markersize=11,\n",
    "           markerfacecolor=\"none\", markeredgecolor=\"#c0392b\", markeredgewidth=2)\n",
    "_ax_e.set_xlim(2011, 2026)\n",
    "_ax_e.set_ylim(0, 2500)\n",
    "_ax_e.set_xlabel(\"year\", fontsize=12)\n",
    "_ax_e.set_ylabel(\"beavers on the Tay\", fontsize=12)\n",
    "_ax_e.set_title(f\"α = {_alpha:.2f}, that is {100 * (np.exp(_alpha) - 1):.0f}% a year:   \"\n",
    "                f\"{_N_at_surveys[1]:.0f} in 2017/18,  {_N_at_surveys[2]:.0f} in 2020/21\", fontsize=12)\n",
    "_ax_e.legend(loc=\"upper left\", fontsize=10)\n",
    "_ax_e.grid(True, alpha=0.3)\n",
    "_fig_e.tight_layout()\n",
    "_fig_e;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecfG",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>What to notice (open after you have tried the slider)</b></summary>\n",
    "\n",
    "\n",
    "With $\\alpha = 0.26$ the curve overshoots the 2017/18 range: it predicts about 610 beavers when the survey says at most 547. Any $\\alpha$ from about 0.17 to 0.24 passes through all three ranges, and $\\alpha = 0.22$ hits 954 almost exactly.\n",
    "\n",
    "So the three surveys **do not** show a slowdown: an exponential curve fits them fine. With only three surveys we cannot tell whether the growth has started to slow. We come back to this at the end of Section 3. Notice also how far apart the fitting curves are by 2025: from about 1300 beavers ($\\alpha = 0.17$) to about 3300 ($\\alpha = 0.24$).\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "Pvdt",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The simplest model whose growth slows down by itself is the logistic.\n",
    "\n",
    "## 3. The logistic model\n",
    "\n",
    "On Monday: $$\\frac{dN}{dt} = \\alpha\\left(1 - \\frac{N}{M}\\right)N, \\tag{5.4}$$ where $M$ is the **carrying capacity**. Nobody knows $M$ for the Tay. For now we guess $M = 3000$, and use $\\alpha = 0.26$ from the two most recent surveys.\n",
    "\n",
    "**This line is equation (5.4):**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ZBYS",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.634516Z",
     "iopub.status.busy": "2026-11-13T23:25:59.634335Z",
     "iopub.status.idle": "2026-11-13T23:25:59.637812Z",
     "shell.execute_reply": "2026-11-13T23:25:59.636774Z"
    }
   },
   "outputs": [],
   "source": [
    "alpha_beaver = 0.26     # per year, from the two most recent surveys\n",
    "M_beaver = 3000         # carrying capacity: a guess for now\n",
    "\n",
    "def beaver_rate(t, N):\n",
    "    return alpha_beaver * (1 - N / M_beaver) * N    # equation (5.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aLJB",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The function takes `t` as well as `N`, even though (5.4) doesn't use `t`. That is so it fits the Week 4 loop, which always asks for the slope at a time and a value.\n",
    "\n",
    "**Predict** before you run: for which of these populations is the rate negative? Which gives the biggest rate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "nHfw",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.639465Z",
     "iopub.status.busy": "2026-11-13T23:25:59.639290Z",
     "iopub.status.idle": "2026-11-13T23:25:59.642858Z",
     "shell.execute_reply": "2026-11-13T23:25:59.642111Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N = 146   dN/dt = 36.1\n",
      "N = 1500   dN/dt = 195.0\n",
      "N = 3000   dN/dt = 0.0\n",
      "N = 4000   dN/dt = -346.7\n"
     ]
    }
   ],
   "source": [
    "for N_test in [146, 1500, 3000, 4000]:\n",
    "    print(\"N =\", N_test, \"  dN/dt =\", round(beaver_rate(0, N_test), 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "xXTn",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>Answer</b></summary>\n",
    "\n",
    "\n",
    "Below $M = 3000$ the bracket $1 - N/M$ is positive and the population grows; at $M$ it is 0; above $M$ it is negative and the population shrinks. The biggest rate is at $N = 1500 = M/2$, about 195 beavers a year. At $N = 146$ the bracket is $0.95$, almost 1, so the population grows almost exponentially: that is why the exponential model was good for estimating $\\alpha$ from the early surveys (the key idea in Section 5.4).\n",
    "\n",
    "</details>\n",
    "\n",
    "### 3.1 Follow the arrows (Week 4)\n",
    "\n",
    "In Week 4 we traced a solution by standing at a point, taking a small step $h$ along the slope, and looking again: $N_\\text{new} = N + h \\times \\text{slope}$. **On paper:** one step of a whole year, $h = 1$, starting from $N = 146$. You need the slope at 146 from the cell above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "AjVT",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.644929Z",
     "iopub.status.busy": "2026-11-13T23:25:59.644732Z",
     "iopub.status.idle": "2026-11-13T23:25:59.648178Z",
     "shell.execute_reply": "2026-11-13T23:25:59.647419Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "after one step of h = 1 year: 182.1\n"
     ]
    }
   ],
   "source": [
    "h_hand = 1.0\n",
    "N_after_one_year = 146 + h_hand * beaver_rate(0, 146)\n",
    "print(\"after one step of h = 1 year:\", round(N_after_one_year, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pHFh",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The loop from Week 4 does the same with 2000 small steps. On Monday you also saw the exact solution, $$N(t) = \\frac{M N_0}{(M - N_0)e^{-\\alpha t} + N_0}. \\tag{5.5}$$ **This line is equation (5.5):** `return M * N0 / ((M - N0) * np.exp(-alpha * t) + N0)`. The two should agree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "NCOB",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.649755Z",
     "iopub.status.busy": "2026-11-13T23:25:59.649597Z",
     "iopub.status.idle": "2026-11-13T23:25:59.653584Z",
     "shell.execute_reply": "2026-11-13T23:25:59.652898Z"
    }
   },
   "outputs": [],
   "source": [
    "def follow_arrows(f, t_start, y_start, t_stop, n_steps=2000):\n",
    "    \"\"\"Trace a solution curve: take a tiny step along the arrow, then look again.\"\"\"\n",
    "    h = (t_stop - t_start) / n_steps\n",
    "    t_values = [t_start]\n",
    "    y_values = [y_start]\n",
    "    for step in range(n_steps):\n",
    "        t_now = t_values[-1]\n",
    "        y_now = y_values[-1]\n",
    "        t_values.append(t_now + h)\n",
    "        y_values.append(y_now + h * f(t_now, y_now))\n",
    "    return np.array(t_values), np.array(y_values)\n",
    "\n",
    "def logistic_formula(t, N0, alpha, M):\n",
    "    return M * N0 / ((M - N0) * np.exp(-alpha * t) + N0)    # equation (5.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aqbW",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.655126Z",
     "iopub.status.busy": "2026-11-13T23:25:59.654979Z",
     "iopub.status.idle": "2026-11-13T23:25:59.658819Z",
     "shell.execute_reply": "2026-11-13T23:25:59.658109Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "largest gap between loop and formula: 2.06 beavers\n"
     ]
    }
   ],
   "source": [
    "t_loop, N_loop = follow_arrows(beaver_rate, 0.0, 146.0, 25.0)\n",
    "N_exact = logistic_formula(t_loop, 146.0, alpha_beaver, M_beaver)\n",
    "print(\"largest gap between loop and formula:\", round(np.max(np.abs(N_loop - N_exact)), 2), \"beavers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "TRpd",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "About 2 beavers apart, on a population of up to 3000. That was for $\\alpha = 0.26$ and $M = 3000$. Does the loop work for any $\\alpha$ and $M$? In the cell below, `rate_any` is (5.4) with the two numbers taken from the sliders, and the loop is run again.\n",
    "\n",
    "**Before you move the sliders:** if you make $\\alpha$ bigger, will the gap between the loop and the formula grow or shrink? What about a bigger $M$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "TXez",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.660298Z",
     "iopub.status.busy": "2026-11-13T23:25:59.660144Z",
     "iopub.status.idle": "2026-11-13T23:25:59.662829Z",
     "shell.execute_reply": "2026-11-13T23:25:59.662198Z"
    }
   },
   "outputs": [],
   "source": [
    "alpha_arrows_slider = type('_W', (), {'value': 0.26})()  # static default\n",
    "M_arrows_slider = type('_W', (), {'value': 3000})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dNNg",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.664290Z",
     "iopub.status.busy": "2026-11-13T23:25:59.664096Z",
     "iopub.status.idle": "2026-11-13T23:25:59.831250Z",
     "shell.execute_reply": "2026-11-13T23:25:59.830561Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_any = alpha_arrows_slider.value\n",
    "M_any = M_arrows_slider.value\n",
    "\n",
    "def rate_any(t, N):\n",
    "    return alpha_any * (1 - N / M_any) * N    # equation (5.4), with the slider values\n",
    "\n",
    "t_any, N_any = follow_arrows(rate_any, 0.0, 146.0, 25.0)\n",
    "N_any_exact = logistic_formula(t_any, 146.0, alpha_any, M_any)\n",
    "gap_any = np.max(np.abs(N_any - N_any_exact))\n",
    "\n",
    "_fig_l, _ax_l = plt.subplots(figsize=(9, 4))\n",
    "_ax_l.plot(2012 + t_any, N_any_exact, color=\"#1a5276\", linewidth=6, alpha=0.3,\n",
    "           label=\"formula (5.5)\")\n",
    "_ax_l.plot(2012 + t_any, N_any, color=\"#922b21\", linewidth=1.8,\n",
    "           label=\"following the arrows (2000 steps)\")\n",
    "_top = 1.15 * max(np.max(N_any), np.max(N_any_exact))\n",
    "if M_any <= _top:\n",
    "    _ax_l.axhline(M_any, color=\"grey\", linestyle=\":\", linewidth=1.2)\n",
    "    _ax_l.text(2012.3, M_any + 0.02 * _top, f\"M = {M_any}\", color=\"grey\", fontsize=10)\n",
    "_ax_l.set_xlim(2012, 2037)\n",
    "_ax_l.set_ylim(0, _top)\n",
    "_ax_l.set_xlabel(\"year\", fontsize=12)\n",
    "_ax_l.set_ylabel(\"beavers\", fontsize=12)\n",
    "_ax_l.set_title(f\"largest gap between loop and formula: {gap_any:.1f} beavers\", fontsize=12)\n",
    "_ax_l.legend(fontsize=10, loc=\"lower right\")\n",
    "_ax_l.grid(True, alpha=0.3)\n",
    "_fig_l.tight_layout()\n",
    "_fig_l;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "yCnT",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>What to notice (open after you have tried the sliders)</b></summary>\n",
    "\n",
    "\n",
    "The loop works for every $\\alpha$ and $M$: nothing in `follow_arrows` knows about beavers, it only asks `rate_any` for a slope. The gap grows with both $\\alpha$ and $M$, because a steeper curve bends more within each small step, but it never gets above about half a percent of $M$. With $\\alpha = 0.8$ and $M = 10{,}000$ it is about 36 beavers out of 10,000. In Chapter 6 you will see why the gap behaves like this, and how to make it smaller.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "wlCL",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "The loop and the formula agree, so from here on we use whichever is handier.\n",
    "\n",
    "### 3.2 Which $M$ fits the surveys?\n",
    "\n",
    "Keep $\\alpha = 0.26$ and start from the 2012 survey. The slider changes $M$. The dashed line is the exponential model ($M$ infinitely large), and the hollow circle is what the curve predicts for the 2025 survey.\n",
    "\n",
    "**Before you move the slider:**\n",
    "\n",
    "1. Can a small $M$, say 1000, still pass through all three ranges?\n",
    "2. Which $M$ goes closest to the 2020/21 estimate of 954?\n",
    "3. How much do the possible $M$ disagree about the 2025 survey?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "kqZH",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.833922Z",
     "iopub.status.busy": "2026-11-13T23:25:59.833703Z",
     "iopub.status.idle": "2026-11-13T23:25:59.836714Z",
     "shell.execute_reply": "2026-11-13T23:25:59.835963Z"
    }
   },
   "outputs": [],
   "source": [
    "M_fit_slider = type('_W', (), {'value': 1500})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "wAgl",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:25:59.838762Z",
     "iopub.status.busy": "2026-11-13T23:25:59.838571Z",
     "iopub.status.idle": "2026-11-13T23:26:00.099045Z",
     "shell.execute_reply": "2026-11-13T23:26:00.097971Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_M = M_fit_slider.value\n",
    "_alpha = 0.26\n",
    "_t = np.linspace(0, 23, 500)\n",
    "_N = logistic_formula(_t, 146.0, _alpha, _M)\n",
    "_N_surveys = logistic_formula(survey_t, 146.0, _alpha, _M)\n",
    "_inside = (_N_surveys >= survey_low) & (_N_surveys <= survey_high)\n",
    "_N_2025 = logistic_formula(13.5, 146.0, _alpha, _M)\n",
    "\n",
    "_fig_m, _ax_m = plt.subplots(figsize=(10, 4.8))\n",
    "_err = np.array([survey_N - survey_low, survey_high - survey_N])\n",
    "_ax_m.plot(2012 + _t, 146 * np.exp(_alpha * _t), \"--\", color=\"grey\", linewidth=1.3,\n",
    "           label=\"exponential (no limit)\")\n",
    "_ax_m.plot(2012 + _t, _N, color=\"#1e8449\", linewidth=2.5, label=f\"logistic, M = {_M}\")\n",
    "_ax_m.axhline(_M, color=\"#1e8449\", linestyle=\":\", linewidth=1)\n",
    "for _i in range(3):\n",
    "    _col = \"#1a5276\" if _inside[_i] else \"#922b21\"\n",
    "    _ax_m.errorbar(2012 + survey_t[_i], survey_N[_i], yerr=_err[:, _i:_i + 1], fmt=\"o\",\n",
    "                   color=_col, markersize=9, capsize=6, linewidth=2, zorder=5)\n",
    "_ax_m.plot(2012 + 13.5, _N_2025, \"o\", markersize=12, markerfacecolor=\"white\",\n",
    "           markeredgecolor=\"#1e8449\", markeredgewidth=2.5, zorder=6)\n",
    "_ax_m.text(2012 + 13.5, _N_2025 + 220, f\"2025 survey?\\n{_N_2025:.0f}\", ha=\"center\",\n",
    "           fontsize=10, color=\"#1e8449\")\n",
    "_ax_m.set_xlim(2011, 2035)\n",
    "_ax_m.set_ylim(0, 5000)\n",
    "_ax_m.set_xlabel(\"year\", fontsize=12)\n",
    "_ax_m.set_ylabel(\"beavers\", fontsize=12)\n",
    "_verdict = \"inside all three ranges\" if _inside.all() else f\"misses {3 - _inside.sum()} of the 3 ranges (red)\"\n",
    "_ax_m.set_title(rf\"$\\alpha = 0.26$, $M = {_M}$: {_verdict}\", fontsize=12)\n",
    "_ax_m.legend(fontsize=10, loc=\"upper left\")\n",
    "_ax_m.grid(True, alpha=0.3)\n",
    "_fig_m.tight_layout()\n",
    "_fig_m;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rEll",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>What to notice (open after you have tried the slider)</b></summary>\n",
    "\n",
    "\n",
    "1. Every $M$ from about 1000 to 4000 passes through all three ranges. Below that, the curve flattens too early to reach the 2020/21 range; above it, it overshoots.\n",
    "2. $M \\approx 3000$ goes through 954 almost exactly.\n",
    "3. Those curves disagree a lot about 2025: from about 850 beavers ($M = 1000$, already levelling off) to over 2200 ($M = 4000$). The three surveys can't tell them apart, but the 2025 survey will. In the lab you also change $\\alpha$, and find that the range of possible $M$ gets wider still.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dGlV",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "### 3.3 What NatureScot has said since\n",
    "\n",
    "The 2025 survey report is not out yet, but NatureScot's management report for 2025/26 [5] gave one hint about what the surveyors found on the Tay.\n",
    "\n",
    "**Before you open it:** which of these do you think it said? Which curves from the slider above could go with each?\n",
    "\n",
    "- (a) still growing at about 30% a year;\n",
    "- (b) still growing, but more slowly;\n",
    "- (c) levelled off;\n",
    "- (d) falling.\n",
    "\n",
    "<details><summary><b>What NatureScot said (2026)</b></summary>\n",
    "\n",
    "\n",
    "The population is still increasing, but not at the 30% a year previously reported. Its growth appears to follow a natural curve, as in other reintroduced beaver populations in Europe. The 2025 survey is complete and its report is being finalised [5].\n",
    "\n",
    "</details>\n",
    "\n",
    "<details><summary><b>What this tells us (open after the reveal)</b></summary>\n",
    "\n",
    "\n",
    "Answer (b). That rules out the exponential model carrying on at 30% a year, which would mean about 3100 beavers by 2025. It is just what the logistic model predicts: as $N$ grows, the factor $1 - N/M$ in (5.4) shrinks, and so does the growth rate. On the curves from the slider ($\\alpha = 0.26$, $M$ from 1000 to 4000), the growth in 2025 is down to between about 4% a year ($M = 1000$) and 12% a year ($M = 4000$).\n",
    "\n",
    "But \"more slowly\" doesn't say *how much* more slowly, so it can't tell us $M$. The number in the survey report will. Below, you can try out what that number might be.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "SdmI",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "#### Waiting for the fourth point\n",
    "\n",
    "The slider sets how fast the population grew each year between the 2020/21 survey and the 2025 survey. That gives a *what if* fourth point (the hollow star): it is not data, just a number we try out. The green curve is the logistic curve, started from 146 in 2012, that passes closest to all four points.\n",
    "\n",
    "**Before you move the slider:** it starts at the old rate, 30% a year. What $M$ do you expect the best curve to have there? As you slide down towards 1% a year, what happens to $M$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "lgWD",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.101123Z",
     "iopub.status.busy": "2026-11-13T23:26:00.100917Z",
     "iopub.status.idle": "2026-11-13T23:26:00.103826Z",
     "shell.execute_reply": "2026-11-13T23:26:00.103106Z"
    }
   },
   "outputs": [],
   "source": [
    "growth_2025_slider = type('_W', (), {'value': 30})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "yOPj",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.105677Z",
     "iopub.status.busy": "2026-11-13T23:26:00.105489Z",
     "iopub.status.idle": "2026-11-13T23:26:00.306468Z",
     "shell.execute_reply": "2026-11-13T23:26:00.305409Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_pct = growth_2025_slider.value\n",
    "_N4 = survey_N[2] * (1 + _pct / 100) ** 5          # five years after the 2020/21 survey\n",
    "_t4 = np.append(survey_t, 13.5)\n",
    "_N_all = np.append(survey_N, _N4)\n",
    "\n",
    "# try many (alpha, M) pairs and keep the one closest to all four points\n",
    "_A, _Mg = np.meshgrid(np.linspace(0.10, 0.80, 141),\n",
    "                      np.exp(np.linspace(np.log(500), np.log(100000), 400)), indexing=\"ij\")\n",
    "_miss = np.zeros_like(_A)\n",
    "for _tk, _Nk in zip(_t4, _N_all):\n",
    "    _miss = _miss + (np.log(logistic_formula(_tk, 146.0, _A, _Mg)) - np.log(_Nk)) ** 2\n",
    "_best = np.unravel_index(np.argmin(_miss), _miss.shape)\n",
    "_a_best, _M_best = _A[_best], _Mg[_best]\n",
    "\n",
    "_fig_w, _ax_w = plt.subplots(figsize=(10, 4.8))\n",
    "_err_w = np.array([survey_N - survey_low, survey_high - survey_N])\n",
    "_t_w = np.linspace(0, 23, 500)\n",
    "_ax_w.plot(2012 + _t_w, logistic_formula(_t_w, 146.0, _a_best, _M_best), color=\"#1e8449\",\n",
    "           linewidth=2.5, label=\"logistic curve closest to all four points\")\n",
    "if _M_best < 5000:\n",
    "    _ax_w.axhline(_M_best, color=\"#1e8449\", linestyle=\":\", linewidth=1)\n",
    "_ax_w.errorbar(2012 + survey_t, survey_N, yerr=_err_w, fmt=\"o\", color=\"#1a5276\",\n",
    "               markersize=9, capsize=6, linewidth=2, zorder=5, label=\"the three surveys\")\n",
    "_ax_w.plot(2012 + 13.5, _N4, \"*\", markersize=22, markerfacecolor=\"white\",\n",
    "           markeredgecolor=\"#c0392b\", markeredgewidth=2, zorder=6, label=\"what if? (not data)\")\n",
    "_ax_w.text(2012 + 14.0, _N4, f\"{_N4:.0f}?\", va=\"center\", fontsize=11, color=\"#c0392b\")\n",
    "_ax_w.set_xlim(2011, 2035)\n",
    "_ax_w.set_ylim(0, 5000)\n",
    "_ax_w.set_xlabel(\"year\", fontsize=12)\n",
    "_ax_w.set_ylabel(\"beavers\", fontsize=12)\n",
    "if _M_best > 50000:\n",
    "    _M_text = \"M above 50,000: no limit in sight\"\n",
    "else:\n",
    "    _M_text = f\"M ≈ {_M_best:,.0f}\"\n",
    "_ax_w.set_title(f\"{_pct}% a year gives {_N4:.0f} beavers in 2025.   Best fit: α ≈ {_a_best:.2f}, {_M_text}\",\n",
    "                fontsize=12)\n",
    "_ax_w.legend(fontsize=10, loc=\"upper left\")\n",
    "_ax_w.grid(True, alpha=0.3)\n",
    "_fig_w.tight_layout()\n",
    "_fig_w;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fwwy",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>What to notice (open after you have tried the slider)</b></summary>\n",
    "\n",
    "\n",
    "At 30% a year (about 3500 beavers in 2025) the best curve has no limit in sight: it is the exponential model again. Slide down and $M$ comes down with it: about 4700 at 15% a year, 2400 at 10%, 1600 at 5% and 1200 at 1%. The slower the growth, the closer the population already is to its carrying capacity.\n",
    "\n",
    "So the single number in the survey report will tell us far more than \"more slowly\" did. Write down the growth rate you expect; the lab asks for your forecast too.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "LJZf",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "## 4. The phase portrait\n",
    "\n",
    "The logistic equation is **autonomous**: the right-hand side depends on $N$ only, $dN/dt = f(N)$ as in (5.6). So we can learn a lot from the graph of $f$ alone, without solving anything (Section 5.5):\n",
    "\n",
    "- where $f(N) > 0$ the population grows: arrow to the right;\n",
    "- where $f(N) < 0$ it shrinks: arrow to the left;\n",
    "- where $f(N) = 0$ it stays put: an **equilibrium**. For the logistic model, $N = 0$ and $N = M$.\n",
    "\n",
    "Below, $M = 3000$ and $\\alpha = 0.26$ again. Four populations start at 146 (the 2012 survey), 954 (2020/21), 2000 and 4500. The last one is above $M$: more beavers than the river can feed. Drag the time slider. Each population is a dot on the phase line (left) and on its curve $N(t)$ (right).\n",
    "\n",
    "**Before you drag:**\n",
    "\n",
    "1. Which way does each dot move, and where does it stop?\n",
    "2. The dot that starts at 146: where on the phase line does it move fastest? What does $N(t)$ look like at that moment?\n",
    "3. Can the dot from 4500 end up below 3000?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "urSm",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.308659Z",
     "iopub.status.busy": "2026-11-13T23:26:00.308433Z",
     "iopub.status.idle": "2026-11-13T23:26:00.311648Z",
     "shell.execute_reply": "2026-11-13T23:26:00.310763Z"
    }
   },
   "outputs": [],
   "source": [
    "t_phase_slider = type('_W', (), {'value': 0.0})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "jxvo",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.313566Z",
     "iopub.status.busy": "2026-11-13T23:26:00.313328Z",
     "iopub.status.idle": "2026-11-13T23:26:00.664935Z",
     "shell.execute_reply": "2026-11-13T23:26:00.663940Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1300x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_t_now = t_phase_slider.value\n",
    "_starts = [146.0, 954.0, 2000.0, 4500.0]\n",
    "_cols = [\"#1a5276\", \"#7d3c98\", \"#e67e22\", \"#922b21\"]\n",
    "\n",
    "_fig_p, (_axf, _axn) = plt.subplots(1, 2, figsize=(13, 4.8),\n",
    "                                    gridspec_kw={\"width_ratios\": [1.15, 1]})\n",
    "# left: f(N) and the phase line\n",
    "_N_grid = np.linspace(-200, 5000, 500)\n",
    "_axf.plot(_N_grid, beaver_rate(0, _N_grid), color=\"#555\", linewidth=2)\n",
    "_axf.axhline(0, color=\"black\", linewidth=1.2)\n",
    "for _x0, _x1 in [(400, 900), (1700, 2200), (4300, 3800)]:\n",
    "    _axf.annotate(\"\", xy=(_x1, 0), xytext=(_x0, 0),\n",
    "                  arrowprops={\"arrowstyle\": \"-|>\", \"color\": \"black\", \"lw\": 1.5})\n",
    "_axf.plot(0, 0, \"o\", markersize=11, markerfacecolor=\"white\", markeredgecolor=\"black\",\n",
    "          markeredgewidth=2, zorder=6)\n",
    "_axf.plot(M_beaver, 0, \"o\", markersize=11, color=\"black\", zorder=6)\n",
    "_axf.text(0, -70, \"0\", ha=\"center\", va=\"top\", fontsize=11)\n",
    "_axf.text(M_beaver, -70, \"M\", ha=\"center\", va=\"top\", fontsize=11)\n",
    "for _N0, _c in zip(_starts, _cols):\n",
    "    _N_now = logistic_formula(_t_now, _N0, alpha_beaver, M_beaver)\n",
    "    _axf.plot(_N_now, 0, \"o\", color=_c, markersize=11, zorder=7)\n",
    "    _axf.plot(_N_now, beaver_rate(0, _N_now), \"o\", color=_c, markersize=7, alpha=0.6, zorder=7)\n",
    "    _axf.plot([_N_now, _N_now], [0, beaver_rate(0, _N_now)], color=_c, linewidth=1,\n",
    "              alpha=0.6)\n",
    "_axf.set_xlim(-200, 5000)\n",
    "_axf.set_ylim(-650, 260)\n",
    "_axf.set_xlabel(r\"$N$\", fontsize=12)\n",
    "_axf.set_ylabel(r\"$f(N) = dN/dt$  (beavers per year)\", fontsize=11)\n",
    "_axf.set_title(\"phase line: where each population is now\", fontsize=12)\n",
    "_axf.grid(True, alpha=0.3)\n",
    "\n",
    "# right: N(t) for each start\n",
    "_t_all = np.linspace(0, 30, 400)\n",
    "_past = _t_all <= _t_now\n",
    "for _N0, _c in zip(_starts, _cols):\n",
    "    _N_all = logistic_formula(_t_all, _N0, alpha_beaver, M_beaver)\n",
    "    _axn.plot(_t_all, _N_all, color=_c, linewidth=1.2, alpha=0.3)\n",
    "    _axn.plot(_t_all[_past], _N_all[_past], color=_c, linewidth=2.5, label=f\"start {_N0:.0f}\")\n",
    "    _axn.plot(_t_now, logistic_formula(_t_now, _N0, alpha_beaver, M_beaver), \"o\",\n",
    "              color=_c, markersize=9, zorder=5)\n",
    "_axn.axhline(M_beaver, color=\"grey\", linestyle=\":\", linewidth=1)\n",
    "_axn.axhline(M_beaver / 2, color=\"grey\", linestyle=\":\", linewidth=1)\n",
    "_axn.text(30.3, M_beaver / 2, \"M/2\", va=\"center\", fontsize=10, color=\"grey\")\n",
    "_axn.text(30.3, M_beaver, \"M\", va=\"center\", fontsize=10, color=\"grey\")\n",
    "_axn.set_xlim(0, 30)\n",
    "_axn.set_ylim(0, 4700)\n",
    "_axn.set_xlabel(r\"$t$ (years)\", fontsize=12)\n",
    "_axn.set_ylabel(r\"$N$\", fontsize=12)\n",
    "_axn.set_title(rf\"$t = {_t_now:g}$ years\", fontsize=12)\n",
    "_axn.legend(fontsize=9, loc=\"upper right\")\n",
    "_axn.grid(True, alpha=0.3)\n",
    "_fig_p.tight_layout()\n",
    "_fig_p;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mWxS",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "<details><summary><b>What to notice</b></summary>\n",
    "\n",
    "\n",
    "1. The dots below $M$ move right and the one above moves left; all of them end at $M$. None of them can reach $M$ in finite time, and none can cross it: at $M$ the speed is 0.\n",
    "2. A dot's speed is the height of the curve above it. The dot from 146 is slow at first, fastest as it passes $N = M/2 = 1500$ (the top of the parabola), then slows down near $M$. So $N(t)$ is steepest when it crosses $M/2$: that is the bend in the middle of the S-shape.\n",
    "3. The dot from 4500 falls fast at first (the curve is far below the axis there) and slows down as it nears 3000, but never goes below it.\n",
    "4. $N = 0$ is an equilibrium too, but the arrows point away from it: any small population grows. $N = M$ is the one everything heads towards. Section 5.6 makes this precise.\n",
    "\n",
    "</details>\n",
    "\n",
    "## 5. Stability: recovering from a flood\n",
    "\n",
    "Suppose the beavers have reached $M$, and a bad flood takes away part of the population. How quickly does it recover?\n",
    "\n",
    "Near an equilibrium, the curve $f(N)$ is close to its tangent line. Write $\\tilde N = N - M$ for the gap from $M$. The linearisation (5.7) says $$\\frac{d\\tilde N}{dt} = f'(M)\\,\\tilde N.$$ Differentiating (5.4) gives $f'(N) = \\alpha(1 - 2N/M)$. **This line is $f'(N)$:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "CcZR",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.666587Z",
     "iopub.status.busy": "2026-11-13T23:26:00.666438Z",
     "iopub.status.idle": "2026-11-13T23:26:00.669825Z",
     "shell.execute_reply": "2026-11-13T23:26:00.669140Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f'(0) = 0.26\n",
      "f'(M) = -0.26\n"
     ]
    }
   ],
   "source": [
    "def beaver_rate_slope(N):\n",
    "    return alpha_beaver * (1 - 2 * N / M_beaver)    # f'(N), from differentiating (5.4)\n",
    "\n",
    "print(\"f'(0) =\", beaver_rate_slope(0))\n",
    "print(\"f'(M) =\", beaver_rate_slope(M_beaver))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "YWSi",
   "metadata": {
    "marimo": {
     "config": {
      "hide_code": true
     },
     "md_prefix": "r"
    }
   },
   "source": [
    "$f'(M) = -\\alpha < 0$, so $M$ is **stable**: the gap obeys $d\\tilde N/dt = -\\alpha \\tilde N$, so it shrinks like $e^{-\\alpha t}$ and halves every $\\ln 2/\\alpha \\approx 2.7$ years. $f'(0) = \\alpha > 0$, so $0$ is **unstable**, and near 0 the linearisation is $d\\tilde N/dt = \\alpha \\tilde N$: exactly the exponential model again.\n",
    "\n",
    "The slider sets how much of the population the flood takes. On the left, the tangent line at $M$ (slope $-\\alpha$) is what the linearisation uses instead of the curve. On the right, the recovery from the full model (5.4) and from the linearisation.\n",
    "\n",
    "**Before you move it:** for a small flood, will the linearisation be close? What about a flood that takes 80% of the beavers: will the linearisation say the recovery is faster or slower than it really is?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "zlud",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.671608Z",
     "iopub.status.busy": "2026-11-13T23:26:00.671478Z",
     "iopub.status.idle": "2026-11-13T23:26:00.673942Z",
     "shell.execute_reply": "2026-11-13T23:26:00.673290Z"
    }
   },
   "outputs": [],
   "source": [
    "flood_slider = type('_W', (), {'value': 20})()  # static default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "tZnO",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-13T23:26:00.675298Z",
     "iopub.status.busy": "2026-11-13T23:26:00.675175Z",
     "iopub.status.idle": "2026-11-13T23:26:00.956840Z",
     "shell.execute_reply": "2026-11-13T23:26:00.955781Z"
    },
    "jupyter": {
     "source_hidden": true
    },
    "marimo": {
     "config": {
      "hide_code": true
     }
    },
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1300x460 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_p = flood_slider.value / 100\n",
    "_N_start = (1 - _p) * M_beaver\n",
    "_t = np.linspace(0, 25, 500)\n",
    "_N_full = logistic_formula(_t, _N_start, alpha_beaver, M_beaver)\n",
    "_N_lin = M_beaver - _p * M_beaver * np.exp(-alpha_beaver * _t)\n",
    "\n",
    "def _back_within_5pc(N_curve):\n",
    "    _ok = np.abs(N_curve - M_beaver) <= 0.05 * M_beaver\n",
    "    _bad = np.where(~_ok)[0]\n",
    "    return 0.0 if len(_bad) == 0 else _t[min(_bad[-1] + 1, len(_t) - 1)]\n",
    "\n",
    "_fig_s, (_axt, _axr) = plt.subplots(1, 2, figsize=(13, 4.6),\n",
    "                                    gridspec_kw={\"width_ratios\": [1, 1.15]})\n",
    "_N_grid = np.linspace(0, 3600, 400)\n",
    "_axt.plot(_N_grid, beaver_rate(0, _N_grid), color=\"#555\", linewidth=2, label=r\"$f(N)$\")\n",
    "_axt.plot(_N_grid, -alpha_beaver * (_N_grid - M_beaver), \"--\", color=\"#e67e22\",\n",
    "          linewidth=2, label=r\"tangent at $M$: $-\\alpha(N - M)$\")\n",
    "_axt.axhline(0, color=\"black\", linewidth=1)\n",
    "_axt.plot(M_beaver, 0, \"o\", color=\"black\", markersize=10, zorder=6)\n",
    "_axt.plot(_N_start, beaver_rate(0, _N_start), \"o\", color=\"#1a5276\", markersize=10, zorder=6)\n",
    "_axt.plot(_N_start, -alpha_beaver * (_N_start - M_beaver), \"o\", color=\"#e67e22\",\n",
    "          markersize=10, zorder=6)\n",
    "_axt.axvline(_N_start, color=\"#1a5276\", linewidth=1, alpha=0.5)\n",
    "_axt.set_xlim(0, 3600)\n",
    "_axt.set_ylim(-200, 750)\n",
    "_axt.set_xlabel(r\"$N$\", fontsize=12)\n",
    "_axt.set_ylabel(r\"$dN/dt$\", fontsize=12)\n",
    "_axt.set_title(f\"just after the flood: N = {_N_start:.0f}\", fontsize=12)\n",
    "_axt.legend(fontsize=10, loc=\"upper left\")\n",
    "_axt.grid(True, alpha=0.3)\n",
    "\n",
    "_axr.axhspan(0.95 * M_beaver, 1.05 * M_beaver, color=\"#1e8449\", alpha=0.12)\n",
    "_axr.plot(_t, _N_full, color=\"#1a5276\", linewidth=2.5, label=\"full model (5.4)\")\n",
    "_axr.plot(_t, _N_lin, \"--\", color=\"#e67e22\", linewidth=2.2, label=\"linearisation (5.7)\")\n",
    "_axr.axhline(M_beaver, color=\"grey\", linestyle=\":\", linewidth=1)\n",
    "_axr.set_xlim(0, 25)\n",
    "_axr.set_ylim(0, 3300)\n",
    "_axr.set_xlabel(\"years after the flood\", fontsize=12)\n",
    "_axr.set_ylabel(r\"$N$\", fontsize=12)\n",
    "_axr.set_title(f\"back within 5% of M (green): full {_back_within_5pc(_N_full):.1f} yr, \"\n",
    "               f\"linearised {_back_within_5pc(_N_lin):.1f} yr\", fontsize=11)\n",
    "_axr.legend(fontsize=10, loc=\"lower right\")\n",
    "_axr.grid(True, alpha=0.3)\n",
    "_fig_s.tight_layout()\n",
    "_fig_s;"
   ]
  },
  {
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    "<details><summary><b>What to notice</b></summary>\n",
    "\n",
    "\n",
    "- For a small flood (5–20%) the two curves almost coincide: close to $M$ the parabola and its tangent line are nearly the same, so the linearisation is a good model.\n",
    "- For a big flood the linearisation is far too optimistic. Look at the left plot: below $M$ the tangent line sits *above* the parabola, so it overestimates how fast the beavers come back, and the further from $M$, the bigger the error. After an 80% flood the linearisation says about 10 years; the full model says about 17.\n",
    "- After a big flood the population is small compared with $M$, so for a while it grows like the *other* linearisation, the one at 0: exponential growth at rate $\\alpha$. A population knocked far down behaves like the early Tay beavers.\n",
    "\n",
    "</details>\n",
    "\n",
    "## Summary\n",
    "\n",
    "- A function packages a formula: `def`, then `return`. A cell shows the value of its last line. Arguments go in by position, so their order matters.\n",
    "- From two surveys and the exponential model (5.2), $\\alpha = \\ln(N_\\text{end}/N_\\text{start})/\\text{years}$: about 0.26 per year, the same as NatureScot's 30% a year.\n",
    "- The logistic model (5.4) is one line of code. Following the arrows reproduces the formula (5.5).\n",
    "- The three surveys fit a wide range of carrying capacities $M$, and those $M$ disagree a lot about 2025. The 2025 survey will narrow it down.\n",
    "- NatureScot's 2026 report says the growth has slowed, as the logistic model predicts, but not by how much.\n",
    "- The phase portrait shows where the population goes without solving anything; the sign of $f'$ at an equilibrium decides whether it is stable (5.7).\n",
    "\n",
    "**In the lab:** you advise NatureScot on how many beavers it can safely remove each year. After some warm-ups that follow this lecture (including your own forecast for the 2025 survey), you add the real removals under licence to the model, which is where next week's lectures go (harvesting, Section 5.7)."
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    "## References\n",
    "\n",
    "[1] Scottish Wildlife Trust, [*Policy briefing: Beaver conservation and conflict*](https://scottishwildlifetrust.org.uk/wp-content/uploads/2025/01/Scottish-Wildlife-Trust_Policy-Briefing_Beaver-conservation-and-conflict_December-2024.pdf) (December 2024).\n",
    "\n",
    "[2] R. Campbell, A. Harrington, A. Ross and L. Harrington, [*Distribution, population assessment and activities of beavers in Tayside*](https://www.nature.scot/naturescot-commissioned-report-540-distribution-population-assessment-and-activities-beavers-tayside), Scottish Natural Heritage Commissioned Report 540 (2012): 38–39 family groups, about 146 beavers (106–187), at 3.8 beavers per group.\n",
    "\n",
    "[3] [*Survey of the Tayside area beaver population 2017–2018*](https://www.nature.scot/doc/naturescot-research-report-1013-survey-tayside-area-beaver-population-2017-2018), NatureScot Research Report 1013: 114 territories, about 433 beavers (319–547).\n",
    "\n",
    "[4] R. Campbell-Palmer et al., [*Survey of the Tayside area beaver population 2020–2021*](https://www.nature.scot/doc/naturescot-research-report-1274-survey-tayside-area-beaver-population-2020-2021), NatureScot Research Report 1274: 251 territories, about 954 beavers (602–1381).\n",
    "\n",
    "[5] [*Beaver Management Report 2025/26*](https://www.nature.scot/doc/beaver-management-report-202526), NatureScot: the 2025 survey of Tayside and surrounding catchments is complete and its report is being finalised; the population is still increasing, but not at the 30% a year previously reported, and its growth appears to follow a natural curve.\n",
    "\n",
    "[6] [*Beaver Management Report for 2020*](https://www.nature.scot/doc/beaver-management-report-2020), NatureScot.\n",
    "\n",
    "[7] NatureScot, [*Living with beavers*](https://www.youtube.com/watch?v=BmDlnkIscLo) (video, February 2026)."
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