{ "cells": [ { "cell_type": "markdown", "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 lab, see\n", "> [Week 6 lab — interactive](https://math4120.pages.dev/wasm/week06_lab.html).\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "ipython-import", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:01.672382Z", "iopub.status.busy": "2026-11-13T23:26:01.672141Z", "iopub.status.idle": "2026-11-13T23:26:01.676748Z", "shell.execute_reply": "2026-11-13T23:26:01.675843Z" } }, "outputs": [], "source": [ "from IPython.display import Markdown, HTML\n" ] }, { "cell_type": "markdown", "id": "Hbol", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "# Week 6 lab — Advising NatureScot on the Tay beavers\n", "\n", "**MATH4120 — Mathematical Modelling and Programming** Lancaster University, 2026–27\n", "\n", "---\n", "\n", "**Your brief.** In this lab you are a modeller advising NatureScot. Beavers are a protected species, but where they damage farmland NatureScot licenses their removal: since 2019 about 100 beavers a year in Scotland have been trapped and moved elsewhere, or killed [5, 6]. NatureScot has to make sure that it is not removing too many, so that the population stays safe. Your job is to tell them whether about 100 a year is safe, and how many would be too many.\n", "\n", "To answer, you need a model of how the beavers grow, and its two numbers: the growth rate $\\alpha$ and the carrying capacity $M$. The first four exercises are warm-ups that build these, and they follow the lecture closely. Aim to finish them in about half an hour, then move on to the main task.\n", "\n", "**Warm-ups**\n", "\n", "0. functions;\n", "1. the growth rate $\\alpha$ from the surveys, and how sure we are of it;\n", "2. which $M$ fit the surveys, and your forecast for the 2025 survey;\n", "3. equilibria and stability: how fast the beavers recover from a one-off loss.\n", "\n", "**The main task**\n", "\n", "4. removing beavers every year: how many can the Tay population take, and what do you advise?" ] }, { "cell_type": "code", "execution_count": 2, "id": "MJUe", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:01.678591Z", "iopub.status.busy": "2026-11-13T23:26:01.678425Z", "iopub.status.idle": "2026-11-13T23:26:01.992666Z", "shell.execute_reply": "2026-11-13T23:26:01.991724Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "id": "vblA", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "The data and the three functions from the lecture, unchanged. Time $t$ is in years since the 2012 survey." ] }, { "cell_type": "code", "execution_count": 3, "id": "bkHC", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:01.995029Z", "iopub.status.busy": "2026-11-13T23:26:01.994798Z", "iopub.status.idle": "2026-11-13T23:26:01.999706Z", "shell.execute_reply": "2026-11-13T23:26:01.998886Z" } }, "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\n", "\n", "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", "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": "markdown", "id": "lEQa", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "## Warm-up 0 — functions\n", "\n", "**Predict** what each of the next two cells shows, then run them." ] }, { "cell_type": "code", "execution_count": 4, "id": "PKri", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.001441Z", "iopub.status.busy": "2026-11-13T23:26:02.001275Z", "iopub.status.idle": "2026-11-13T23:26:02.006291Z", "shell.execute_reply": "2026-11-13T23:26:02.005560Z" } }, "outputs": [ { "data": { "text/plain": [ "np.float64(29.69300866657718)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def percent_per_year(alpha):\n", " return 100 * (np.exp(alpha) - 1)\n", "\n", "percent_per_year(0.26)" ] }, { "cell_type": "code", "execution_count": 5, "id": "Xref", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.007889Z", "iopub.status.busy": "2026-11-13T23:26:02.007725Z", "iopub.status.idle": "2026-11-13T23:26:02.010248Z", "shell.execute_reply": "2026-11-13T23:26:02.009415Z" } }, "outputs": [], "source": [ "x_percent = percent_per_year(0.2)" ] }, { "cell_type": "markdown", "id": "SFPL", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "
Answer\n", "\n", "\n", "The first shows about 29.7: the last line is a value, and a cell shows the value of its last line. The second shows **nothing**: its last line is an assignment, which stores the value in `x_percent` without showing it. Add a line with just `x_percent` (or `print(x_percent)`) to see it, 22.1.\n", "\n", "
\n", "\n", "**Task.** A population growing at rate $\\alpha$ doubles in a fixed time, whatever its size. **On paper first:** using (5.2), $N(t) = N_0 e^{\\alpha t}$, find the time $t$ at which $N = 2N_0$. Then replace the placeholder so that `doubling_time` returns it." ] }, { "cell_type": "code", "execution_count": 6, "id": "BYtC", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.012013Z", "iopub.status.busy": "2026-11-13T23:26:02.011812Z", "iopub.status.idle": "2026-11-13T23:26:02.015451Z", "shell.execute_reply": "2026-11-13T23:26:02.014759Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "doubling time at alpha = 0.26: 0.0 years\n" ] } ], "source": [ "def doubling_time(alpha):\n", " return 0.0 # ← replace\n", "\n", "print(\"doubling time at alpha = 0.26:\", doubling_time(0.26), \"years\")" ] }, { "cell_type": "code", "execution_count": 7, "id": "RGSE", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.017013Z", "iopub.status.busy": "2026-11-13T23:26:02.016843Z", "iopub.status.idle": "2026-11-13T23:26:02.020667Z", "shell.execute_reply": "2026-11-13T23:26:02.019912Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/markdown": [ "- doubling time: not yet" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_ok = abs(doubling_time(0.26) - np.log(2) / 0.26) < 1e-9 and abs(doubling_time(0.1) - np.log(2) / 0.1) < 1e-9\n", "Markdown(\"- doubling time: \" + (\"✓\" if _ok else \"not yet\"))" ] }, { "cell_type": "markdown", "id": "Kclp", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "## Warm-up 1 — the growth rate, and how sure we are of it\n", "\n", "Your advice will depend on how fast the beavers can replace the ones that are removed: that is $\\alpha$.\n", "\n", "**Task (a).** Using `growth_rate` and positions in `survey_N` and `survey_t`, compute $\\alpha$ for 2012 to 2017/18 and for 2017/18 to 2020/21. Don't type the numbers in yourself." ] }, { "cell_type": "code", "execution_count": 8, "id": "emfo", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.022415Z", "iopub.status.busy": "2026-11-13T23:26:02.022225Z", "iopub.status.idle": "2026-11-13T23:26:02.025710Z", "shell.execute_reply": "2026-11-13T23:26:02.024963Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "alpha_early: 0.0\n", "alpha_recent: 0.0\n" ] } ], "source": [ "alpha_early = 0.0 # ← replace: 2012 to 2017/18\n", "alpha_recent = 0.0 # ← replace: 2017/18 to 2020/21\n", "print(\"alpha_early: \", alpha_early)\n", "print(\"alpha_recent:\", alpha_recent)" ] }, { "cell_type": "code", "execution_count": 9, "id": "Hstk", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.027325Z", "iopub.status.busy": "2026-11-13T23:26:02.027185Z", "iopub.status.idle": "2026-11-13T23:26:02.031293Z", "shell.execute_reply": "2026-11-13T23:26:02.030424Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/markdown": [ "- alpha_early: not yet\n", "- alpha_recent: not yet" ], "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_ok_e = abs(alpha_early - growth_rate(survey_N[0], survey_N[1], survey_t[1] - survey_t[0])) < 1e-9\n", "_ok_r = abs(alpha_recent - growth_rate(survey_N[1], survey_N[2], survey_t[2] - survey_t[1])) < 1e-9\n", "Markdown(f\"- alpha_early: {'✓' if _ok_e else 'not yet'}\\n- alpha_recent: {'✓' if _ok_r else 'not yet'}\")" ] }, { "cell_type": "markdown", "id": "nWHF", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "Each survey is a best estimate inside a range. The slowest growth between the last two surveys that the ranges allow is from the *top* of the 2017/18 range to the *bottom* of the 2020/21 range.\n", "\n", "**Task (b).** Compute that slowest $\\alpha$, and the fastest one the ranges allow. Use `survey_low` and `survey_high`." ] }, { "cell_type": "code", "execution_count": 10, "id": "iLit", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.032778Z", "iopub.status.busy": "2026-11-13T23:26:02.032614Z", "iopub.status.idle": "2026-11-13T23:26:02.035679Z", "shell.execute_reply": "2026-11-13T23:26:02.034941Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "slowest: 0.0\n", "fastest: 0.0\n" ] } ], "source": [ "alpha_recent_slowest = 0.0 # ← replace\n", "alpha_recent_fastest = 0.0 # ← replace\n", "print(\"slowest:\", alpha_recent_slowest)\n", "print(\"fastest:\", alpha_recent_fastest)" ] }, { "cell_type": "markdown", "id": "ZHCJ", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "
Check\n", "\n", "\n", "$\\alpha \\approx 0.198$ for 2012 to 2017/18 and $0.263$ for 2017/18 to 2020/21. The ranges allow anything from about $0.03$ (`growth_rate(survey_high[1], survey_low[2], 3)`) to $0.49$ (`growth_rate(survey_low[1], survey_high[2], 3)`) for the recent interval: from 3% a year to 63% a year.\n", "\n", "
\n", "\n", "**Questions.**\n", "\n", "1. In the logistic model the growth rate per beaver, $\\alpha(1 - N/M)$, goes *down* as $N$ grows. The best estimates went *up*, from 0.198 to 0.263. Does that mean the logistic model is wrong? Use your answer to (b).\n", "2. Suggest two other reasons why the measured rate might go up between surveys.\n", "\n", "
Answers (open after you have discussed them)\n", "\n", "\n", "1. Not necessarily. The ranges are so wide that the recent rate could be anywhere from 0.03 to 0.49, so the surveys can't tell us whether the rate really went up.\n", "2. For example: the later surveys covered more ground as the beavers spread, so they may have found a larger share of the animals; or the population really did grow faster later on. A very small population can grow slowly because animals struggle to find mates; the exercise at the end of Section 5.6 is a model of exactly that. Licensed removals, which started in 2019, would slow the growth down, so they make the rise more surprising, not less.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "ROlb", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "## Warm-up 2 — fitting the logistic model by eye\n", "\n", "It will also depend on how many beavers the Tay can hold: that is $M$.\n", "\n", "In the lecture we kept $\\alpha = 0.26$ and changed $M$. Now change both. The curve starts at the 2012 estimate, 146. A survey point turns red when the curve misses its range. The hollow circle is the curve's forecast for the 2025 survey.\n", "\n", "**Before you start:** if you make $\\alpha$ bigger, do you expect the $M$ that fits to get bigger or smaller?" ] }, { "cell_type": "code", "execution_count": 11, "id": "qnkX", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.037307Z", "iopub.status.busy": "2026-11-13T23:26:02.037157Z", "iopub.status.idle": "2026-11-13T23:26:02.039889Z", "shell.execute_reply": "2026-11-13T23:26:02.039085Z" } }, "outputs": [], "source": [ "alpha_fit_slider = type('_W', (), {'value': 0.26})() # static default\n", "M_fit_slider = type('_W', (), {'value': 3000})() # static default" ] }, { "cell_type": "code", "execution_count": 12, "id": "TqIu", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.041328Z", "iopub.status.busy": "2026-11-13T23:26:02.041176Z", "iopub.status.idle": "2026-11-13T23:26:02.257923Z", "shell.execute_reply": "2026-11-13T23:26:02.256692Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_alpha = alpha_fit_slider.value\n", "_M = M_fit_slider.value\n", "_t = np.linspace(0, 23, 500)\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_f, _ax_f = plt.subplots(figsize=(10, 4.8))\n", "_err = np.array([survey_N - survey_low, survey_high - survey_N])\n", "_ax_f.plot(2012 + _t, logistic_formula(_t, 146.0, _alpha, _M), color=\"#1e8449\", linewidth=2.5)\n", "if _M <= 6000:\n", " _ax_f.axhline(_M, color=\"#1e8449\", linestyle=\":\", linewidth=1)\n", "for _i in range(3):\n", " _col = \"#1a5276\" if _inside[_i] else \"#922b21\"\n", " _ax_f.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_f.plot(2012 + 13.5, _N_2025, \"o\", markersize=12, markerfacecolor=\"white\",\n", " markeredgecolor=\"#1e8449\", markeredgewidth=2.5, zorder=6)\n", "_ax_f.text(2012 + 13.5, _N_2025 + 250, f\"2025: {_N_2025:.0f}\", ha=\"center\", fontsize=10,\n", " color=\"#1e8449\")\n", "_ax_f.set_xlim(2011, 2035)\n", "_ax_f.set_ylim(0, 5000)\n", "_ax_f.set_xlabel(\"year\", fontsize=12)\n", "_ax_f.set_ylabel(\"beavers\", fontsize=12)\n", "_verdict = \"inside all three ranges\" if _inside.all() else f\"misses {3 - _inside.sum()} of the 3 ranges\"\n", "_ax_f.set_title(rf\"$\\alpha = {_alpha:.2f}$, $M = {_M}$: {_verdict}\", fontsize=12)\n", "_ax_f.grid(True, alpha=0.3)\n", "_fig_f.tight_layout()\n", "_fig_f;" ] }, { "cell_type": "markdown", "id": "Vxnm", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**Task (a).** Find three pairs $(\\alpha, M)$ that pass through all three ranges, as different from each other as you can: try a small $\\alpha$, a middling one and a large one. Write them into `my_fits`, replacing the two placeholder pairs." ] }, { "cell_type": "code", "execution_count": 13, "id": "DnEU", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.260111Z", "iopub.status.busy": "2026-11-13T23:26:02.259825Z", "iopub.status.idle": "2026-11-13T23:26:02.262895Z", "shell.execute_reply": "2026-11-13T23:26:02.262184Z" } }, "outputs": [], "source": [ "my_fits = [(0.26, 3000), (0.0, 0), (0.0, 0)] # ← replace the two (0.0, 0) pairs" ] }, { "cell_type": "code", "execution_count": 14, "id": "ulZA", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.264630Z", "iopub.status.busy": "2026-11-13T23:26:02.264442Z", "iopub.status.idle": "2026-11-13T23:26:02.426618Z", "shell.execute_reply": "2026-11-13T23:26:02.425957Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/markdown": [ "| $\\alpha$ | $M$ | inside all 3 ranges? | 2025 forecast | growth per year, 2020/21 to 2025 |\n", "|---|---|---|---|---|\n", "| 0.26 | 3000 | yes | 1893 | 15% |" ], "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_fig_m, _ax_m = plt.subplots(figsize=(10, 4.5))\n", "_err = np.array([survey_N - survey_low, survey_high - survey_N])\n", "_ax_m.errorbar(2012 + survey_t, survey_N, yerr=_err, fmt=\"o\", color=\"#1a5276\",\n", " markersize=9, capsize=6, linewidth=2, zorder=5)\n", "_t = np.linspace(0, 23, 500)\n", "_cols = [\"#1e8449\", \"#e67e22\", \"#7d3c98\", \"#922b21\", \"#17a589\"]\n", "_rows = [\"| $\\\\alpha$ | $M$ | inside all 3 ranges? | 2025 forecast | growth per year, 2020/21 to 2025 |\", \"|---|---|---|---|---|\"]\n", "for _k, (_a, _M) in enumerate(my_fits):\n", " if _a <= 0 or _M <= 146:\n", " continue\n", " _c = _cols[_k % len(_cols)]\n", " _ax_m.plot(2012 + _t, logistic_formula(_t, 146.0, _a, _M), color=_c, linewidth=2.2,\n", " label=rf\"$\\alpha = {_a:g}$, $M = {_M}$\")\n", " _Ns = logistic_formula(survey_t, 146.0, _a, _M)\n", " _ok = bool(np.all((_Ns >= survey_low) & (_Ns <= survey_high)))\n", " _N25 = logistic_formula(13.5, 146.0, _a, _M)\n", " _ax_m.plot(2012 + 13.5, _N25, \"o\", markersize=11, markerfacecolor=\"white\",\n", " markeredgecolor=_c, markeredgewidth=2.5, zorder=6)\n", " _pct = 100 * ((_N25 / _Ns[2]) ** (1 / 5) - 1)\n", " _rows.append(f\"| {_a:g} | {_M} | {'yes' if _ok else '**no**'} | {_N25:.0f} | {_pct:.0f}% |\")\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", "_ax_m.set_title(\"your fits, and their forecasts for 2025 (hollow circles)\", 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", "Markdown(\"\\n\".join(_rows))" ] }, { "cell_type": "markdown", "id": "ecfG", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**Questions.**\n", "\n", "1. What are the smallest and the largest $M$ you can make fit? What happens to the $\\alpha$ that goes with it?\n", "2. Can three surveys tell us $M$?\n", "\n", "
Answers\n", "\n", "\n", "1. Small $M$ needs a big $\\alpha$, and large $M$ a small one: the curve has to rise fast early to reach the 2020/21 range before it flattens. With $\\alpha \\approx 0.45$–$0.5$, $M$ as small as about 650 fits. With $\\alpha \\approx 0.17$–$0.24$, $M$ can be as large as you like, even 100,000: the curve is then still exponential through 2020.\n", "2. No. Very different pairs fit equally well, and their 2025 forecasts run from about 650 (already flat) to over 3500.\n", "\n", "
\n", "\n", "**Task (b): your forecast.** Replace the placeholder with the range you expect the 2025 survey's best estimate to fall in, using your fits and the questions above. Write it down somewhere you will find it when the report comes out. It matters for your advice in Exercise 4." ] }, { "cell_type": "code", "execution_count": 15, "id": "Pvdt", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.428788Z", "iopub.status.busy": "2026-11-13T23:26:02.428606Z", "iopub.status.idle": "2026-11-13T23:26:02.432133Z", "shell.execute_reply": "2026-11-13T23:26:02.431315Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "my forecast for the 2025 survey: 0 to 0 beavers\n" ] } ], "source": [ "my_forecast = [0, 0] # ← replace: [lowest, highest] for the 2025 survey's best estimate\n", "print(\"my forecast for the 2025 survey:\", my_forecast[0], \"to\", my_forecast[1], \"beavers\")" ] }, { "cell_type": "markdown", "id": "ZBYS", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**The reveal.** NatureScot hasn't published the 2025 survey yet, but its management report for 2025/26 [5] says something about what the surveyors found. Only open it once you have written your forecast.\n", "\n", "
What NatureScot said (2026)\n", "\n", "\n", "The population is still increasing, but not at the 30% a year measured between 2017/18 and 2020/21. 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", "
\n", "\n", "**Questions.**\n", "\n", "1. Does that rule out the exponential model at 30% a year? How many beavers would that have given by 2025?\n", "2. Look at the last column of the table above. Does the statement rule out any of your logistic fits?\n", "3. Would you change your forecast?\n", "\n", "
Answers\n", "\n", "\n", "1. Yes: $954 e^{0.263 \\times 4.5} \\approx 3100$ beavers by 2025, and NatureScot says the growth is slower than that.\n", "2. Strictly, none. Every logistic curve that fits the surveys grows more slowly than 30% a year between 2020/21 and 2025 (at most about 26%), because logistic growth always slows down. And every one is still increasing, even if only by 1–3% a year for the smallest $M$. So the statement agrees with the logistic model, but \"more slowly\" doesn't say how much more slowly, and that narrows $M$ down very little. The number in the survey report will.\n", "3. Probably not by much: the statement is too vague to move a forecast far. If your forecast was near the top of the range, above about 3000, the curves behind it barely slow down (about 25% a year from 2020/21 to 2025), so the report nudges it lower.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "aLJB", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**Question.** Suppose the 2025 survey's best estimate is 1300. Use the sliders: which $M$ (with a matching $\\alpha$) fit all four points? What if it is 2500?\n", "\n", "
Answer\n", "\n", "\n", "Allowing about 10% either way: an estimate near 1300 fits $M = 1500$ with a large $\\alpha$, but also $M = 50{,}000$ with a small one, so it rules out only the small values of $M$ (below about 1500). An estimate near 2500 rules out every $M$ below about 5000. So one more survey helps, but it does not settle $M$ on its own. What pins down $M$ is seeing the growth level off, and that takes several more surveys.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "nHfw", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "## Warm-up 3 — equilibria and stability\n", "\n", "Taking beavers away knocks the population below where it would be, a bit like a small flood. First, how does a population recover from a one-off loss?\n", "\n", "**Task (a), on paper.** For $f(N) = \\alpha\\left(1 - \\frac{N}{M}\\right)N$:\n", "\n", "1. find the equilibria;\n", "2. differentiate to find $f'(N)$, then $f'$ at each equilibrium;\n", "3. use the linearised stability criterion (Section 5.6) to say which is stable.\n", "\n", "
Check\n", "\n", "\n", "Equilibria $N = 0$ and $N = M$. $f'(N) = \\alpha(1 - 2N/M)$, so $f'(0) = \\alpha > 0$ (unstable) and $f'(M) = -\\alpha < 0$ (stable).\n", "\n", "
\n", "\n", "### A flood\n", "\n", "Near $M$ the gap $\\tilde N = N - M$ obeys $d\\tilde N/dt = -\\alpha \\tilde N$ (5.7), so $\\tilde N = \\tilde N(0) e^{-\\alpha t}$. **On paper:** how long does the gap take to halve? You already have a function that computes this number.\n", "\n", "**Task (b).** Below, a flood removes a fraction of the beavers when they are at $M = 3000$. Replace the placeholder in `flood_rate` with the logistic model (5.4), using `alpha_flood` and `M_flood`. The next cell then follows the arrows and measures how long the gap from $M$ really takes to halve." ] }, { "cell_type": "code", "execution_count": 16, "id": "xXTn", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.433902Z", "iopub.status.busy": "2026-11-13T23:26:02.433705Z", "iopub.status.idle": "2026-11-13T23:26:02.436688Z", "shell.execute_reply": "2026-11-13T23:26:02.435944Z" } }, "outputs": [], "source": [ "alpha_flood = 0.26\n", "M_flood = 3000\n", "\n", "def flood_rate(t, N):\n", " return 0.0 # ← replace" ] }, { "cell_type": "code", "execution_count": 17, "id": "AjVT", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.438372Z", "iopub.status.busy": "2026-11-13T23:26:02.438217Z", "iopub.status.idle": "2026-11-13T23:26:02.447661Z", "shell.execute_reply": "2026-11-13T23:26:02.446757Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "linearisation: the gap halves every 0.0 years\n", "lose 10 %: the gap never halves (check flood_rate)\n", "lose 20 %: the gap never halves (check flood_rate)\n", "lose 50 %: the gap never halves (check flood_rate)\n", "lose 80 %: the gap never halves (check flood_rate)\n" ] } ], "source": [ "print(\"linearisation: the gap halves every\", round(doubling_time(alpha_flood), 2), \"years\")\n", "for fraction_lost in [0.1, 0.2, 0.5, 0.8]:\n", " N_after_flood = (1 - fraction_lost) * M_flood\n", " t_flood, N_flood = follow_arrows(flood_rate, 0.0, N_after_flood, 30.0, n_steps=6000)\n", " gap = M_flood - N_flood\n", " halved = np.where(gap <= gap[0] / 2)[0]\n", " if len(halved) > 0:\n", " print(\"lose\", round(100 * fraction_lost), \"%: the gap halves after\", round(t_flood[halved[0]], 2), \"years\")\n", " else:\n", " print(\"lose\", round(100 * fraction_lost), \"%: the gap never halves (check flood_rate)\")" ] }, { "cell_type": "markdown", "id": "pHFh", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**Questions.**\n", "\n", "1. Why is the halving time from the linearisation the same as the doubling time from Exercise 0?\n", "2. The bigger the flood, the longer the real halving time. Why? (The lecture's tangent-line picture helps.)\n", "\n", "
Answers\n", "\n", "\n", "1. Doubling is $e^{\\alpha t} = 2$ and halving is $e^{-\\alpha t} = 1/2$: the same equation, so both give $t = \\ln 2 / \\alpha \\approx 2.67$ years.\n", "2. Real halving times: about 2.9 years (10%), 3.1 (20%), 4.2 (50%) and 6.9 (80%). Below $M$ the parabola $f(N)$ sits below its tangent line, so the real population climbs back more slowly than the linearisation says, and the further from $M$ it starts, the bigger the difference.\n", "\n", "
\n", "\n", "### A new river (if you have time)\n", "\n", "NatureScot now moves some Tay families to other catchments [5]. Suppose a family of 4 beavers is released on a river with room for $M = 60$, and grows with the same $\\alpha = 0.26$.\n", "\n", "**Task (c).** On paper, set $N(t) = M/2$ in the solution (5.5) and solve for $t$. Then replace the placeholder, using `np.log`." ] }, { "cell_type": "code", "execution_count": 18, "id": "NCOB", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.449184Z", "iopub.status.busy": "2026-11-13T23:26:02.449035Z", "iopub.status.idle": "2026-11-13T23:26:02.452050Z", "shell.execute_reply": "2026-11-13T23:26:02.451348Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "years until the river is half full: 0.0\n" ] } ], "source": [ "N0_new = 4\n", "M_new = 60\n", "alpha_new = 0.26\n", "\n", "time_to_half_full = 0.0 # ← replace\n", "print(\"years until the river is half full:\", time_to_half_full)" ] }, { "cell_type": "code", "execution_count": 19, "id": "aqbW", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.453446Z", "iopub.status.busy": "2026-11-13T23:26:02.453276Z", "iopub.status.idle": "2026-11-13T23:26:02.456867Z", "shell.execute_reply": "2026-11-13T23:26:02.456063Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "text/markdown": [ "Check: the formula (5.5) at your time gives **4.00** beavers; half of $M$ is 30." ], "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_check = logistic_formula(time_to_half_full, N0_new, alpha_new, M_new)\n", "Markdown(f\"Check: the formula (5.5) at your time gives **{_check:.2f}** beavers; half of $M$ is {M_new / 2:g}.\")" ] }, { "cell_type": "markdown", "id": "TRpd", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "
Answer\n", "\n", "\n", "$\\dfrac{M N_0}{(M - N_0)e^{-\\alpha t} + N_0} = \\dfrac{M}{2}$ gives $(M - N_0)e^{-\\alpha t} = N_0$, so $$t = \\frac{1}{\\alpha}\\ln\\frac{M - N_0}{N_0} = \\frac{\\ln 14}{0.26} \\approx 10.2 \\text{ years.}$$ In code: `time_to_half_full = np.log((M_new - N0_new) / N0_new) / alpha_new`. A new population takes a decade to get going, and then fills the second half of the river much faster.\n", "\n", "
" ] }, { "cell_type": "markdown", "id": "TXez", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "## Exercise 4 — the main task: how many can be removed?\n", "\n", "Back to your brief. Since May 2019, beavers that damage farmland can be removed under licence: trapped and moved elsewhere, or killed. These are the real numbers for each year NatureScot has reported [6, 7, 8, 9, 5]. They are for all of Scotland; we treat them as coming from the Tay population, which is by far the largest." ] }, { "cell_type": "code", "execution_count": 20, "id": "dNNg", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.458338Z", "iopub.status.busy": "2026-11-13T23:26:02.458205Z", "iopub.status.idle": "2026-11-13T23:26:02.460954Z", "shell.execute_reply": "2026-11-13T23:26:02.460282Z" } }, "outputs": [], "source": [ "removal_periods = [\"May–Dec 2019\", \"2020\", \"2021\", \"2022\", \"Jan 2023–Apr 2024\",\n", " \"Apr 2024–Mar 2025\", \"Apr 2025–Mar 2026\"]\n", "removal_years = np.array([0.67, 1.0, 1.0, 1.0, 1.33, 1.0, 1.0]) # length of each period\n", "removed = np.array([87, 115, 120, 108, 85, 102, 84]) # beavers removed" ] }, { "cell_type": "code", "execution_count": 21, "id": "yCnT", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.462381Z", "iopub.status.busy": "2026-11-13T23:26:02.462171Z", "iopub.status.idle": "2026-11-13T23:26:02.606725Z", "shell.execute_reply": "2026-11-13T23:26:02.606022Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_fig_r, _ax_r = plt.subplots(figsize=(10, 3.6))\n", "_x = np.arange(len(removed))\n", "_ax_r.bar(_x, removed / removal_years, color=\"#1a5276\")\n", "_ax_r.set_xticks(_x)\n", "_ax_r.set_xticklabels([_p.replace(\" \", \"\\n\", 1) for _p in removal_periods], fontsize=9)\n", "_ax_r.set_ylabel(\"removed per year\", fontsize=12)\n", "_ax_r.set_title(\"Beavers removed under licence in Scotland, per year\", fontsize=12)\n", "_ax_r.grid(True, alpha=0.3, axis=\"y\")\n", "_fig_r.tight_layout()\n", "_fig_r;" ] }, { "cell_type": "markdown", "id": "wlCL", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "About 100 a year. Next week's lectures add this to the model: removing $H$ beavers a year gives $$\\frac{dN}{dt} = \\alpha\\left(1 - \\frac{N}{M}\\right)N - H,$$ equation (5.9) in Section 5.9. Here you just run it.\n", "\n", "**Task.** Replace the placeholder in `harvest_rate` with the right-hand side above, using `alpha_h`, `M_h` and `H_h`. The plot then starts from the 2020/21 survey (954 beavers) and removes $H$ beavers every year from then on." ] }, { "cell_type": "code", "execution_count": 22, "id": "kqZH", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.609035Z", "iopub.status.busy": "2026-11-13T23:26:02.608878Z", "iopub.status.idle": "2026-11-13T23:26:02.611615Z", "shell.execute_reply": "2026-11-13T23:26:02.611005Z" } }, "outputs": [], "source": [ "H_slider = type('_W', (), {'value': 100})() # static default\n", "M_harvest_slider = type('_W', (), {'value': 3000})() # static default" ] }, { "cell_type": "code", "execution_count": 23, "id": "wAgl", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.613353Z", "iopub.status.busy": "2026-11-13T23:26:02.613217Z", "iopub.status.idle": "2026-11-13T23:26:02.616004Z", "shell.execute_reply": "2026-11-13T23:26:02.615288Z" } }, "outputs": [], "source": [ "alpha_h = 0.26\n", "M_h = M_harvest_slider.value\n", "H_h = H_slider.value\n", "\n", "def harvest_rate(t, N):\n", " if N <= 0:\n", " return 0.0 # no beavers left to remove\n", " return 0.0 # ← replace" ] }, { "cell_type": "code", "execution_count": 24, "id": "rEll", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.617617Z", "iopub.status.busy": "2026-11-13T23:26:02.617453Z", "iopub.status.idle": "2026-11-13T23:26:02.782248Z", "shell.execute_reply": "2026-11-13T23:26:02.781183Z" }, "jupyter": { "source_hidden": true }, "marimo": { "config": { "hide_code": true } }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_t_h, _N_h = follow_arrows(harvest_rate, 0.0, 954.0, 40.0, n_steps=8000)\n", "_N_h = np.clip(_N_h, 0, None)\n", "_gone = np.where(_N_h <= 0)[0]\n", "if len(_gone) > 0:\n", " _verdict = f\"dies out around {2020.5 + _t_h[_gone[0]]:.0f}\"\n", "else:\n", " _verdict = f\"{_N_h[-1]:.0f} beavers in 2060\"\n", "\n", "_fig_h, _ax_h = plt.subplots(figsize=(10, 4.5))\n", "_ax_h.plot(2020.5 + _t_h, _N_h, color=\"#922b21\", linewidth=2.5, label=f\"removing {H_h} a year\")\n", "_ax_h.axhline(M_h, color=\"grey\", linestyle=\":\", linewidth=1)\n", "_ax_h.text(2021, M_h, f\"M = {M_h}\", va=\"bottom\", fontsize=10, color=\"grey\")\n", "_ax_h.set_xlim(2020, 2061)\n", "_ax_h.set_ylim(0, 10500 if M_h > 5000 else 5300)\n", "_ax_h.set_xlabel(\"year\", fontsize=12)\n", "_ax_h.set_ylabel(\"beavers\", fontsize=12)\n", "_ax_h.set_title(rf\"$\\alpha = 0.26$, $M = {M_h}$, $H = {H_h}$: {_verdict}\", fontsize=12)\n", "_ax_h.legend(fontsize=10, loc=\"upper right\")\n", "_ax_h.grid(True, alpha=0.3)\n", "_fig_h.tight_layout()\n", "_fig_h;" ] }, { "cell_type": "markdown", "id": "dGlV", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**Questions.** Predict each answer before you use the sliders.\n", "\n", "1. With $M = 3000$, compare $H = 0$ and $H = 100$. Is removing 100 a year making much difference?\n", "2. With $M = 3000$, what is the largest $H$ the beavers survive, starting from 954?\n", "3. Now $M = 1500$ and $H = 100$. What happens, and why could it fool someone watching the numbers for a few years?\n", "4. Removals have been about 100 a year since 2019, and NatureScot says the population is still increasing [5]. What does that suggest about $M$?\n", "5. **Your advice.** Should NatureScot remove more beavers each year, fewer, or about the same? What would you want to know from the 2025 survey before deciding? Discuss with your neighbour, then write your advice in the cell below: two or three sentences, using numbers from the model.\n", "\n", "
Answers\n", "\n", "\n", "1. Not much. The population still grows, to about 2500 instead of 3000 by 2060: removals lower the level it settles at, but don't stop the growth.\n", "2. About 160–170 a year. At 170 the population sinks slowly and dies out after 2060; at 200 it is gone by the early 2030s. The limit is the growth rate at 954 beavers, $f(954) \\approx 169$ a year: remove more than the population adds and it shrinks, which makes it add even fewer. Next week's lectures (Section 5.9) explain this properly, together with a related number, the critical rate $\\alpha M/4$.\n", "3. It shrinks, but very slowly: there are still about 775 beavers in 2060. 100 a year is only just more than the most this population can ever add ($\\alpha M/4 \\approx 97.5$ for $M = 1500$), so there is no level where it can settle and it does die out in the end, but the counts barely change for decades. A few years of steady counts would look reassuring.\n", "4. With $\\alpha = 0.26$ and 100 a year removed, the population would already be shrinking if $M$ were below about 1600. So $M$ is probably larger than that, unless $\\alpha$ is too. (The surveys' counts already include the removals since 2019, so the $\\alpha$ and $M$ from Exercise 2 are a little off.)\n", "5. There is no single right answer; good answers use the model (an example is in the answers version of the cell below). If $M$ is large, 100 a year barely changes where the population ends up, so the removals are about local damage, not numbers. If $M$ is small, the same 100 a year could eventually wipe the population out. So the first thing to know is $M$, and the 2025 survey is the best evidence we will have for it.\n", "\n", "
" ] }, { "cell_type": "code", "execution_count": 25, "id": "SdmI", "metadata": { "execution": { "iopub.execute_input": "2026-11-13T23:26:02.784367Z", "iopub.status.busy": "2026-11-13T23:26:02.784165Z", "iopub.status.idle": "2026-11-13T23:26:02.787330Z", "shell.execute_reply": "2026-11-13T23:26:02.786756Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "my_advice = \"\" # ← replace with your advice, in two or three sentences\n", "print(my_advice)" ] }, { "cell_type": "markdown", "id": "lgWD", "metadata": { "marimo": { "config": { "hide_code": true }, "md_prefix": "r" } }, "source": [ "**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).\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.\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.\n", "\n", "[5] [*Beaver Management Report 2025/26*](https://www.nature.scot/doc/beaver-management-report-202526), NatureScot.\n", "\n", "[6] [*Beaver Management Report for 2020*](https://www.nature.scot/doc/beaver-management-report-2020), NatureScot.\n", "\n", "[7] [*Beaver Management Report for 2022*](https://www.nature.scot/doc/beaver-management-report-2022), NatureScot.\n", "\n", "[8] [*Beaver Management Report, January 2023 to April 2024*](https://www.nature.scot/doc/beaver-management-report-january-2023-april-2024), NatureScot.\n", "\n", "[9] [*Beaver Management Report, 01 April 2024 to 31 March 2025*](https://www.nature.scot/doc/beaver-management-report-01-april-2024-31-march-2025), NatureScot." ] } ], "metadata": { "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.3" }, "marimo": { "app_config": { "app_title": "Week 6 Lab — Advising NatureScot on the Tay beavers", "width": "medium" }, "marimo_version": "0.25.2" } }, "nbformat": 4, "nbformat_minor": 5 }