{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pylab as plt\n", "import seaborn as sbn\n", "from scipy.optimize import fmin" ] }, { "cell_type": "markdown", "metadata": { "code_folding": [] }, "source": [ "Note: this post has been updated for newer versions of python. Content-wise it is mostly identical to the earlier version except for some minor editorial changes. You can interact with this post [live on Google Colab](https://colab.research.google.com/drive/1qJKw_LPo1Dmykye3PJm3qgixHtDXr4Aq?usp=sharing)." ] }, { "cell_type": "markdown", "metadata": { "code_folding": [] }, "source": [ "## Fisheries Simulation Model\n", "\n", "In this notebook, we examine the workings of the Gordon-Schaefer Fisheries Model for a single species.\n", "\n", "Denoting $S(t)$ as the stock at time $t$, we can write the population growth function as\n", "\n", "$$\\frac{\\Delta S}{\\Delta t} = \\frac{\\partial S}{\\partial t} = r S(t) \\left(1- \\frac{S(t)}{K} \\right)$$\n", "\n", "where \n", "$S(t)$ = stock size at time $t$ \n", "$K$ = carrying capacity \n", "$r$ = intrinsic growth rate of the population\n", "\n", "\n", "\n", "Notice that growth $\\left(\\frac{\\partial S}{\\partial t}\\right)$ is stock dependent:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "jupyter": { "outputs_hidden": false } }, "outputs": [ { "data": { 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\n", 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