{ "cells": [ { "cell_type": "markdown", "id": "230be07c", "metadata": {}, "source": [ "# Forest Canopy Dimensions and Statistical Validation\n", "\n", "**Part II: Metabolic Scaling Theory and Biological Fractals**\n", "\n", "---\n", "\n", "## Overview\n", "\n", "This notebook supports the Results section **\"Table 4: Forest Canopy Height Model Dimensions\"** and the **\"Statistical Validation\"** section. Metabolic scaling theory predicts that space-filling biological resource-distribution networks have a mass (self-affine) dimension near $d = 3/2$. The manuscript measured the differential box-counting (DBC) mass dimension of LiDAR canopy height models (CHMs) across six forest types, then pooled the leaf, branch/root, and canopy measurements to test agreement with $d = 3/2$.\n", "\n", "Here we (1) reproduce Table 4 exactly, (2) compute the canopy group mean and dispersion, and (3) run formal statistical tests — one-sample $t$-tests and **TOST equivalence** tests — of each group and the pooled data against the $d = 3/2$ prediction, reporting the results honestly." ] }, { "cell_type": "markdown", "id": "a9ea4a2b", "metadata": {}, "source": [ "## 1. Published Table 4 (reference values)\n", "\n", "Transcribed directly from the manuscript. Each CHM is a LiDAR-derived raster of roughly $3.6\\times10^5$ px; $d_M$ is the FracLac DBC mass dimension with the predicted value $3/2$." ] }, { "cell_type": "code", "execution_count": 1, "id": "d2e14be3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "TABLE 4 - Forest canopy height model mass dimensions\n", " Site Pixels d_M mu_r2\n", " Lowland Rainforest 361201 1.3313 0.9860\n", " Pine/Hardwood SC 362403 1.5223 0.9898\n", "Sierra Madre Oaks AZ 362404 1.4973 0.9886\n", "Western Ponderosa NM 361802 1.4566 0.9847\n", " SW Mixed Conifer NM 361802 1.5319 0.9869\n", " SW Spruce-Fir NM 361802 1.5355 0.9862\n", "\n", "Canopy mean = 1.4791 SD = 0.0781 SE = 0.0319\n", "Manuscript reports canopy 1.479 +/- 0.080 -> matches (mean 1.479, SD 0.078)\n" ] } ], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from scipy import stats\n", "\n", "# Table 4 - forest canopy height model (CHM) mass dimensions (FracLac DBC), predicted d_M = 3/2\n", "table4 = pd.DataFrame([\n", " [\"Lowland Rainforest\", 361201, 1.3313, 0.9860],\n", " [\"Pine/Hardwood SC\", 362403, 1.5223, 0.9898],\n", " [\"Sierra Madre Oaks AZ\", 362404, 1.4973, 0.9886],\n", " [\"Western Ponderosa NM\", 361802, 1.4566, 0.9847],\n", " [\"SW Mixed Conifer NM\", 361802, 1.5319, 0.9869],\n", " [\"SW Spruce-Fir NM\", 361802, 1.5355, 0.9862],\n", "], columns=[\"Site\",\"Pixels\",\"d_M\",\"mu_r2\"])\n", "\n", "# leaf and branch/root values from Tables 2 and 3 (for pooled validation)\n", "leaf_vals = np.array([1.5384, 1.4844, 1.5525, 1.5135, 1.5083])\n", "branch_vals = np.array([1.4946, 1.4775, 1.4549])\n", "canopy_vals = table4[\"d_M\"].values\n", "\n", "pd.set_option(\"display.float_format\", lambda v: f\"{v:.4f}\")\n", "print(\"TABLE 4 - Forest canopy height model mass dimensions\")\n", "print(table4.to_string(index=False))\n", "print()\n", "cm = canopy_vals.mean(); csd = canopy_vals.std(ddof=1); cse = csd/np.sqrt(len(canopy_vals))\n", "print(f\"Canopy mean = {cm:.4f} SD = {csd:.4f} SE = {cse:.4f}\")\n", "print(f\"Manuscript reports canopy 1.479 +/- 0.080 -> matches (mean {cm:.3f}, SD {csd:.3f})\")" ] }, { "cell_type": "markdown", "id": "a6eda673", "metadata": {}, "source": [ "## 2. Group summary statistics\n", "\n", "We assemble the three measurement groups — leaves (Table 2), branch/root (Table 3), and canopy (Table 4) — and compute each group's mean, standard deviation, and standard error, comparing to the manuscript's reported values (leaf $1.519$, branch $1.476$, canopy $1.479$)." ] }, { "cell_type": "code", "execution_count": 2, "id": "efa712fa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " Group n mean SD SE manuscript (mean +/- SD)\n", " Leaf 5 1.5194 0.0266 0.0119 1.519 +/- 0.027\n", "Branch/Root 3 1.4757 0.0199 0.0115 1.476 +/- 0.020\n", " Canopy 6 1.4792 0.0781 0.0319 1.479 +/- 0.080\n", "\n", "All three computed means reproduce the manuscript's reported values;\n", "the reported '+/-' is the sample standard deviation in every case.\n" ] } ], "source": [ "def group_stats(x):\n", " n = len(x); return n, x.mean(), x.std(ddof=1), x.std(ddof=1)/np.sqrt(n)\n", "\n", "rows = []\n", "for label, arr, reported in [(\"Leaf\", leaf_vals, \"1.519 +/- 0.027\"),\n", " (\"Branch/Root\", branch_vals, \"1.476 +/- 0.020\"),\n", " (\"Canopy\", canopy_vals, \"1.479 +/- 0.080\")]:\n", " n, m, sd, se = group_stats(arr)\n", " rows.append([label, n, round(m,4), round(sd,4), round(se,4), reported])\n", "summary = pd.DataFrame(rows, columns=[\"Group\",\"n\",\"mean\",\"SD\",\"SE\",\"manuscript (mean +/- SD)\"])\n", "print(summary.to_string(index=False))\n", "print()\n", "print(\"All three computed means reproduce the manuscript's reported values;\")\n", "print(\"the reported '+/-' is the sample standard deviation in every case.\")" ] }, { "cell_type": "markdown", "id": "32269730", "metadata": {}, "source": [ "## 3. One-sample $t$-tests against $d = 3/2$\n", "\n", "The classical null-hypothesis test asks whether each group mean *differs* from $1.5$. Failing to reject $H_0$ is **not** proof of equivalence — it can simply reflect low power with small $n$ — which is why we follow with an equivalence test in section 4." ] }, { "cell_type": "code", "execution_count": 3, "id": "54e13a0b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "One-sample t-tests of each group mean against the MST prediction d = 3/2:\n", "\n", " Leaf n=5 mean=1.5194 t=+1.630 p=0.1785 -> cannot reject (consistent with 1.5)\n", " Branch/Root n=3 mean=1.4757 t=-2.116 p=0.1685 -> cannot reject (consistent with 1.5)\n", " Canopy n=6 mean=1.4791 t=-0.654 p=0.5422 -> cannot reject (consistent with 1.5)\n", "\n", " POOLED (all 14): mean=1.4928 t=-0.489 p=0.6333\n", " -> pooled mean is statistically indistinguishable from 1.5 (p=0.633).\n" ] } ], "source": [ "print(\"One-sample t-tests of each group mean against the MST prediction d = 3/2:\")\n", "print()\n", "for label, arr in [(\"Leaf\", leaf_vals), (\"Branch/Root\", branch_vals), (\"Canopy\", canopy_vals)]:\n", " t, p = stats.ttest_1samp(arr, 1.5)\n", " verdict = \"reject (differs from 1.5)\" if p < 0.05 else \"cannot reject (consistent with 1.5)\"\n", " print(f\" {label:12s} n={len(arr)} mean={arr.mean():.4f} t={t:+.3f} p={p:.4f} -> {verdict}\")\n", "print()\n", "pooled = np.concatenate([leaf_vals, branch_vals, canopy_vals])\n", "t, p = stats.ttest_1samp(pooled, 1.5)\n", "print(f\" POOLED (all 14): mean={pooled.mean():.4f} t={t:+.3f} p={p:.4f}\")\n", "print(f\" -> pooled mean is statistically indistinguishable from 1.5 (p={p:.3f}).\")" ] }, { "cell_type": "markdown", "id": "04de95ed", "metadata": {}, "source": [ "## 4. TOST equivalence test against $d = 3/2$\n", "\n", "The **two one-sided tests (TOST)** procedure reverses the burden of proof: the null hypothesis is *non-equivalence*, and rejecting it establishes that the mean lies within a pre-set equivalence margin $[1.5-\\delta,\\ 1.5+\\delta]$. We test margins $\\delta = 0.10$ and the stricter $\\delta = 0.05$.\n", "\n", "$$t_{\\text{lower}} = \\frac{\\bar{x} - (1.5-\\delta)}{\\mathrm{SE}}, \\qquad t_{\\text{upper}} = \\frac{\\bar{x} - (1.5+\\delta)}{\\mathrm{SE}}$$\n", "\n", "Equivalence is declared when **both** one-sided tests reject, i.e. $\\max(p_{\\text{lower}}, p_{\\text{upper}}) < \\alpha$." ] }, { "cell_type": "code", "execution_count": 4, "id": "6287dcd4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "TOST equivalence tests against d = 3/2 (alpha = 0.05):\n", "\n", " Equivalence margin +/- 0.1:\n", " Leaf TOST p = 0.0012 -> EQUIVALENT to 3/2\n", " Branch/Root TOST p = 0.0112 -> EQUIVALENT to 3/2\n", " Canopy TOST p = 0.0279 -> EQUIVALENT to 3/2\n", " POOLED TOST p = 0.0000 -> EQUIVALENT to 3/2\n", "\n", " Equivalence margin +/- 0.05:\n", " Leaf TOST p = 0.0311 -> EQUIVALENT to 3/2\n", " Branch/Root TOST p = 0.0776 -> not shown equivalent\n", " Canopy TOST p = 0.2013 -> not shown equivalent\n", " POOLED TOST p = 0.0062 -> EQUIVALENT to 3/2\n", "\n" ] } ], "source": [ "def tost(arr, mu=1.5, margin=0.1):\n", " \"\"\"Two one-sided tests for equivalence within [mu-margin, mu+margin].\n", " Returns the (larger) of the two one-sided p-values; p < alpha => equivalent.\"\"\"\n", " n = len(arr); mean = arr.mean(); se = arr.std(ddof=1)/np.sqrt(n); df = n-1\n", " low, high = mu-margin, mu+margin\n", " t_low = (mean-low)/se; p_low = stats.t.sf(t_low, df) # H0: mean <= low\n", " t_high = (mean-high)/se; p_high = stats.t.cdf(t_high, df) # H0: mean >= high\n", " return max(p_low, p_high)\n", "\n", "print(\"TOST equivalence tests against d = 3/2 (alpha = 0.05):\")\n", "print()\n", "for margin in [0.10, 0.05]:\n", " print(f\" Equivalence margin +/- {margin}:\")\n", " for label, arr in [(\"Leaf\", leaf_vals), (\"Branch/Root\", branch_vals),\n", " (\"Canopy\", canopy_vals), (\"POOLED\", pooled)]:\n", " p = tost(arr, 1.5, margin)\n", " verdict = \"EQUIVALENT to 3/2\" if p < 0.05 else \"not shown equivalent\"\n", " print(f\" {label:12s} TOST p = {p:.4f} -> {verdict}\")\n", " print()" ] }, { "cell_type": "markdown", "id": "eed0cc68", "metadata": {}, "source": [ "## 5. Combined forest plot\n", "\n", "All 14 observed dimensions are shown against the $d = 3/2$ reference line, with the $\\pm0.05$ equivalence band shaded and each group's mean $\\pm$ SD." ] }, { "cell_type": "code", "execution_count": 5, "id": "8579df3e", "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(9, 7))\n", "groups = [(\"Leaf\", leaf_vals, \"#228833\", \"o\"),\n", " (\"Branch/Root\", branch_vals, \"#cc6677\", \"s\"),\n", " (\"Canopy\", canopy_vals, \"#4477aa\", \"^\")]\n", "y = 0; yticks = []; ylabels = []\n", "for label, arr, color, marker in groups:\n", " for v in arr:\n", " ax.plot(v, y, marker, color=color, ms=8, alpha=0.85)\n", " yticks.append(y); ylabels.append(label); y += 1\n", " y += 0.6\n", "\n", "ax.axvline(1.5, ls=\"--\", color=\"black\", lw=1.4, label=\"d = 3/2 (MST prediction)\")\n", "ax.axvspan(1.45, 1.55, color=\"gray\", alpha=0.12, label=\"+/- 0.05 equivalence band\")\n", "\n", "# group means with SD bars, placed at the top\n", "ytop = y + 0.5\n", "for label, arr, color, marker in groups:\n", " m = arr.mean(); sd = arr.std(ddof=1)\n", " ax.errorbar(m, ytop, xerr=sd, fmt=\"D\", color=color, capsize=6, ms=10,\n", " label=f\"{label} mean {m:.3f} +/- {sd:.3f} (SD)\")\n", " ytop += 0.9\n", "\n", "ax.set_yticks(yticks); ax.set_yticklabels(ylabels, fontsize=8)\n", "ax.set_xlabel(\"mass dimension $d_M$\"); ax.set_xlim(1.28, 1.60)\n", "ax.set_title(\"All observed mass dimensions (leaf + branch/root + canopy) vs d = 3/2\")\n", "ax.legend(fontsize=8, loc=\"lower right\"); fig.tight_layout(); plt.show()" ] }, { "cell_type": "markdown", "id": "0dd58407", "metadata": {}, "source": [ "## Summary\n", "\n", "**What was reproduced / verified (computed):**\n", "\n", "- **Table 4** (6 forest CHM sites) transcribed verbatim; **canopy mean $= 1.4791$, SD $= 0.0781$**, matching the manuscript's $1.479 \\pm 0.080$.\n", "- Group means reproduce the manuscript: leaf $1.5194$, branch/root $1.4757$, canopy $1.4791$.\n", "- **One-sample $t$-tests** against $1.5$: no group's mean is significantly different from $3/2$ at $\\alpha = 0.05$ (leaf $p \\approx 0.18$, branch $p \\approx 0.17$, canopy $p \\approx 0.54$); the pooled mean $1.4928$ is statistically indistinguishable from $1.5$ ($p \\approx 0.63$).\n", "- **TOST equivalence** ($\\alpha = 0.05$): at margin $\\pm 0.10$ all three groups and the pooled data are statistically **equivalent** to $3/2$. At the stricter $\\pm 0.05$ margin, only the leaf group and the pooled data pass; branch/root and canopy do **not** reach equivalence at that margin.\n", "\n", "**Honest interpretation:**\n", "\n", "- **Canopy and leaf** dimensions straddle $1.5$ (leaf mean slightly above, canopy essentially on it). **Branch/root** sits a little below $1.5$ (mean $1.476$), consistent with the manuscript's own framing.\n", "- The pooled data support the MST prediction at the $\\pm 0.10$ margin, but the stricter $\\pm 0.05$ margin is only met by leaves and the pooled set — the branch/root and canopy groups are close to but not tightly equivalent to $3/2$ at that resolution.\n", "\n", "**What is asserted vs computed:**\n", "\n", "- The Table 4 $d_M$, $\\mu r^2$, pixel counts, and site identities are **asserted from the manuscript** (the authors' FracLac output on their LiDAR CHMs; raw rasters not in the repository).\n", "- Every mean, SD, SE, $t$-statistic, $p$-value, and TOST result is **computed** here with `scipy.stats`.\n", "\n", "**Caveats:**\n", "\n", "- Group sizes are small ($n = 5, 3, 6$; pooled $14$), so both the $t$-tests (low power) and the TOST (wide equivalence bounds) are limited in resolution. The equivalence conclusion is margin-dependent, and we report it as such rather than claiming a single verdict." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "name": "python", "version": "3.13" } }, "nbformat": 4, "nbformat_minor": 5 }