{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Relation proie- prédateur ou hôte -pathogène selon Lotka et Volterra\n", "\n", "*Notebook d'Alix Helme-Guizon, à partir d'un Notebook d'Olivier Ricou (EPITA) issu de l'excellent MOOC [«Python pour les scientifiques»](https://courses.ionisx.com/courses/EPITA/002-001-002/2014-FALL/course/)*\n", "\n", "Public visé : BCPST1, Préparation à l'agrégation et au CAPES. **À simplifier pour le lycée.**\n", "\n", "*Vous pouvez écrire dans ce ficher (ou sur papier) et sauver ce ficher entier avec vos réponses en utilisant File/Download as/ (PDF ou python).*\n", " \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ces équations s'appliquent à une \n", "* une population de proies n'ayant qu'un seul prédateur et une cette population de prédateur n'ayant pour source de nourriture que cette proie.\n", "* une population d'hôtes parasitée par un parasite spécifique.\n", "\n", "Prenons d'exemple célèbre est celui du **lièvre à raquettes d'Amérique et du Lynx du Canada.**\n", "![An image](https://images.math.cnrs.fr/local/cache-vignettes/L492xH350/arton1144-84fc7.png?1605704237)\n", "L’évolution des populations de lièvres et de lynx, leurs prédateurs, en fonction du temps t, a été modélisée par Alfred Lotka et Vito Volterra au début du xxe siècle. Ce modèle a été repris par l’écologiste canadien Crawford Holling qui en a proposé une version plus élaborée : elle contient notamment un nouveau terme qui rend compte de la mortalité des prédateurs. \n", "\n", "## 1. Établissons les équations qui contrôlent les effectifs de ces deux populations\n", "\n", "\n", "On rappelle que l'équation logistique de l'effectif N d'une population est \n", "$$\\frac{dN}{dt} = rN(t)*(1 - {N}/{K})$$\n", "\n", "### 1.1. Équation de l'effectif de la population de proie, noté H (pour Herbivore).\n", "Sachant qu'il s'agit d'une proie, très chassée par ce prédateur (puisque c'est sa seule source de nourriture), comment pensez-vous qu'il faut modifier cette équation ?\n", "\n", ">1. Il n'y a rien à modifier, car cette équation rend compte de la mortalité par prédation dans le terme *r*\n", "2. La capacité biologique du milieu n'est jamais atteinte, donc on peut supprimer le terme N/K;\n", "3. Il faut modifier *r*, car cela représente la différence entre natalité et mortalité en absence d'interaction avec une autre espèce, donc sans prédateur" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">*Vos réponses ici*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">Exprimez l'accroissement d'effectif du à la natalité de la proie et à sa mort **de vieillesse ou de maladie.**\n", "\n", ">*votre réponse : * $\\frac{dH}{dt} =$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La proie meurt (1) si elle rencontre le prédateur, **et** (2) si le prédateur est assez habile pour la tuer.\n", "Appelons «P» l'effectif des prédateurs. \n", ">Comment pourriez-vous exprimer simplement et mathématiquement la probabilité de rencontre entre la proie et son prédateur ?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">*votre réponse :*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Appelons $\\beta$ la probabilité que le prédateur tue la proie, **sachant** que la rencontre proie-prédateur a eu lieu.\n", "> Exprimez la mortalité de la proie causée par la prédation\n", "\n", ">*Votre réponse :*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2. Équation de l'effectif de la population de prédateurs, noté P.\n", "Soit $\\gamma$ le taux de mortalité individuel des prédateurs, indépendemment de tout problème de nourriture.\n", "> Exprimez les variations d'effectifs de prédateurs dus à là vieillesse et à la maladie\n", "\n", ">*Votre réponse :*\n", "\n", "La nourriture des carnivores contrôle très fortement leur fertilité. on appelera $\\delta$ la probabilité que la consommation d'un lièvre donne naissance à un petit lynx. \n", "> En réutilisant l'expression que vous aviez établi pour la probabilité que le lièvre soit tué par le lynx (et donc consommé par celui-ci), exprimez l'augmentation d'effectif obtenu par la reproduction des lynx :\n", "\n", ">*Votre réponse :*\n", "\n", "> Regroupez les deux éléments pour estimer la variation des effectifs de la population de lynx.\n", "\n", "\n", ">*Votre réponse :*\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3. Analyser et critiquer les équations de Lotka et Volterra\n", "\n", "Dans l'excellent MOOC [«Python pour les scientifiques»](https://courses.ionisx.com/courses/EPITA/002-001-002/2014-FALL/course/) d'Olivier Ricou (EPITA), j'ai trouvé ce Notebook, que j'ai modifié pour vous. Il présente le modèle proies-prédateurs ainsi :" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les équations de Lotka-Volterra permette de simuler l'évolution de populations\n", "de proies et de prédateurs. Elles sont :\n", "$$\\frac{dH}{dt} = (\\alpha * H - \\beta \\; H*P)$$\n", "\n", "$$\\frac{dP}{dt} = - P(\\gamma - \\delta \\; H)$$\n", "\n", "Où $H$ représente le nombre de proies herbivores et $P$ celui des prédateurs. On note que :\n", "\n", " * $\\alpha$ représente la capacité de reprodution des proies\n", " * $\\beta$ représente l'appétit des prédateurs\n", " * $\\gamma$ représente le taux de morts de faim chez les prédateurs\n", " * $\\delta$ représente le taux de reproduction des prédateurs bien nourris\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">Comparez ces équations aux vôtres, et montrez que ces équations répondent bien aux contraintes données dans les parties 1.1 et 1.2.\n", "\n", ">Critiquez cette la validité biologique de cette présentation des équations de Lotka et Volterra. Comparez en particulier vos coefficients et ceux utilisés ici, et le fonctionnement d'une équation par rapport au fonctionnement d'organismes biologiques.\n", "\n", ">Pourquoi dit-on qu'il s'agit **d'équations différentielles couplées ?** Savez-vous résoudre mathématiquement ce type d'équations ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Visualiser les solutions de deux équations différentielles couplées\n", "\n", "Cliquer sur la flèche située après Entrée pour exécuter le code Python de la cellule, directement dans le Notebook." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline \n", "#installer matplotlib si cette bibliothèque n'est pas déjà installée.\n", "#Vous pouvez le faire directement en ouvrant la console ou par cliquer sur CMD direct Prompt dans Anaconda\n", "#taper «conda install matplotlib»\n", "from matplotlib.pyplot import * #importer la bibliothèque permettant de tracer des graphiques mathématiques sous python" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "a = 3 # on choisit le paramètre $\\alpha$ et on le stocke en variable globale\n", "b = 2 # on choisit le paramètre $\\beta$ et on le stocke en variable globale\n", "c = 3 # on choisit le paramètre $\\gamma$ et on le stocke en variable globale\n", "d = 0.3 # on choisit le paramètre $\\delta$ et on le stocke en variable globale\n", "#n'oubliez pas d'éxécuter, ou les paramètres n'auront pas ces valeurs !" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1. Tracer les courbes qui montrent l'evolution du nombre de proies et de prédateurs dans le temps" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour tracer les courbes des effectifs des proies et des prédateurs en fonction du temps, on ne va pas résoudre mathématiquement ce système de deux équations à deux inconnues, mais découper le temps en moments élémentaires. À chaque instant, on peut calculer $\\frac{dH}{dt}$ et $\\frac{dP}{dt}$ et les intégrer. \n", "la fonction f renvoie deux valeurs qui sont $\\frac{dP}{dt}$ et $\\frac{dH}{dt}$. \n", "puis on intègre cette fonction (avec `odeint`) en lui donnant le temps défini par t et H(0) et P(0), c'est à dire les populations de proies et de prédateurs initiales au temps 0." ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint #importer la fonction intégrale\n", "from numpy import linspace, arange #importer la fonction linspace pour découper le temps en moments élémentaires\n", "#import numpy as np\n", "#from matplotlib.text import OffsetFrom\n", "\n", "def f(Y,t,a,b,c,d):\n", " return Y[0]*(a-b*Y[1]), -Y[1]*(c-d*Y[0]) # attention à la porté des variables, a b c d doivent être des variables globales\n", "#le paramètre Y est utilisé ainsi : Y(0)=H(t) et Y(1)=P(t)\n", "#la fonction f renvoie dH/dt , dP/dt à l'instant t, pour les paramètres a b c d choisis.\n", "\n", "t = linspace(0,10,1000) #débuter t à 0, finir à 10, en faisant 1000 pas\n", "res = odeint(f, (10,4), t, args=(a,b,c,d)) #res renvoie la valeur de l'intégrale de f avec H(0)=10 et P(0)=4. \n", "# (10=10 000 lièvres et 4=4000 lynx au démarrage, on a un facteur 1000)\n", "# pour le temps t et en utilisant les arguments a b c d défini globalement dans la cellule précédente.\n", "\n", "figure(figsize=(10,3), dpi=100) # taille en inchs et résolution de la figure à tracer\n", "plot(t,res) #trace le graphique \n", "\n", "#Annotation du graphique\n", "import numpy as np\n", "import matplotlib.pyplot as plt #importer la bibliothèque plot pour légender les axes\n", "#plt.legend(loc='best', fontsize=8) #au meilleur emplacement\n", "plt.title(\"Évolution de la population de proies et de prédateurs, selon Lotka et Volterra\", fontsize=12)\n", "plt.xlabel(\"Temps en multiple de 5 ans\", fontsize=10) #titre des abscisses\n", "plt.ylabel(\"Effectifs des populations en milliers\", fontsize=10)\n", "plt.text(-0.4,10,\"Proies\", color='b', fontsize=12, fontfamily=\"arial\", bbox=dict(facecolor='blue', alpha=0.1)) \n", "#position x,y, texte, couleur, taille, police, rectangle transparent en fond\n", "plt.text(-0.4,0,\"Prédateurs\", color='orange', fontsize=12, fontfamily=\"arial\", bbox=dict(facecolor='orange', alpha=0.1))\n", "#si vous voulez changer la longueur de l'axe des abscisses, ordonnées plt.axis([0,10,0,25])\n", "grid() #par défaut montre un quadrillage gris. grid(b=None) supprime le quadrillage\n" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.savefig(\"mon_graphique.png\", dpi=200) #sauve le graphique sous forme d'image au même endroit que le notebook\n", "plt.savefig(\"mon_graphique.pdf\", format = \"pdf\") # en PDF\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On voit qu'il s'agit de courbe périodiques ce qui implique que dans un **repère nombre de proies en fonction du nombre de prédateurs**, on repasse toujours par les mêmes points et donc qu'on tourne en rond. \n", "\n", "Pouvons-nous tracer une figure qui montre cet aspect cyclique ?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2. Tracer la courbe paramétrique proies/prédateur\n", "\n", "\n", "Pour tracer ce cycle, regardons la variable `res` afin de comprendre sa structure :" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[10. , 4. ],\n", " [ 9.51200644, 3.99704519],\n", " [ 9.04888295, 3.98839291],\n", " ...,\n", " [ 2.37116055, 1.30247454],\n", " [ 2.38126123, 1.27299365],\n", " [ 2.39279978, 1.24422046]])" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il s'agit d'un tableau donnant H(t) en 1ère position et P(t) en 2ème, pour différentes valeurs de t.\n", "On peut donc dessiner la seconde colonne P(t) en fonction de la première H(t), soit `res[:,1]` en fonction de `res[:,0]` :" ] }, { "cell_type": "code", "execution_count": 204, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = linspace(0,3,100) # pas trop de cycles \n", "init_pred= 3 # effectif de predateurs pour 10 proies, en milliers\n", "a = 3 # réattribué au cas ou l'utilisateur les aurait modifié précédemment.\n", "b = 2 \n", "c = 3 \n", "d = 0.3\n", "res = odeint(f, (10,init_pred), t, args=(a,b,c,d)) \n", "\n", "plot(res[:,0],res[:,1],'.',label=\"%2.1f\"%(init_pred)) # trace H(t) en fonction de P(t).\n", "#label met une légende qui donne l'effectif de predateurs pour 10 proies avec deux chiffes avant la virgule et 1 après.\n", "# '.' demande de mettre un point par valeur. \n", "xlabel(u'Effectifs des proies en milliers')\n", "ylabel(u'Effectifs des prédateurs en milliers')\n", "plt.title(\"Effectifs des proies en fonction des effectifs de prédateurs, selon Lotka et Volterra\", fontsize=14)\n", "legend()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Pourquoi cette représentation est-elle plus fiable pour dire que les oscillations des effectifs des deux populations sonst bien cycliques ?\n", "> Pourquoi prend-on le ratio prédateurs/proies et non leurs valeurs absolues ? Faites une ou plusieurs simulations pour montrer que c'est ce ration et non les valeurs absolues qui déterminent les effectifs.\n", "\n", "Faisons varier le rapport initial du nombre de prédateurs par rapport au nombre de proies pour en tester les conséquences." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3. La variation du ratio proies / prédateurs et son impact " ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = linspace(0,3,100) # pas trop de cycles \n", "for init_pred in range(1,7): # on fait varier effectif initial de predateurs pour 10 proies entre 1 et 7\n", " res = odeint(f, (10,init_pred), t, args=(a,b,c,d)) \n", " #res renvoie la valeur de l'intégrale de f avec H(0)=10 et P(0)=init_pred. \n", " plot(res[:,0],res[:,1],'.',label=\"%2.1f\"%(init_pred)) \n", "xlabel(u'Effectifs des proies en milliers')\n", "ylabel(u'Effectifs des prédateurs en milliers')\n", "plt.title(\"Effectifs des proies en fonction des effectifs de prédateurs, selon Lotka et Volterra\", fontsize=14)\n", "legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> En négligeant pour le moment les cas correspondant à 1 ou 2 prédateurs pour 10 proies, expliquez l'emboitement des différentes courbes paramétriques." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4. Trouver la valeur d'équilibre qui fait que les deux populations restent constantes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Surprise__ La courbe correspondant à 2 prédateurs pour 10 proies est incluse dans la courbe 1.0 alors qu'ensuite chaque courbe est incluse dans celle de ratio plus petit !\n", "\n", "Zoomons en choisissant des ratios proie/prédateur dans la zone d'inversion :" ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t = linspace(0,2.5,100) # temps pas assez long pour avoir des cycles complets\n", "for init_pred in arange(0.5,3,0.5): # arange pour avoir des réels, on avance d'un pas de 0.5\n", " res = odeint(f, (10,init_pred), t, args=(a,b,c,d)) \n", " plot(res[:,0],res[:,1],'.',label=\"%2.1f\"% (init_pred)) \n", "xlabel(u'proies')\n", "ylabel(u'prédateurs')\n", "legend()\n", "grid() # on commence les cycles en x = 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Quand il y a 1,5 prédateurs pour 10 proies (avec les coefficients choisis), aucune des deux populations ne fluctue plus !" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Partie facultative\n", "\n", "Calculons la ratio qui mène au cercle le plus petit c.a.d à l'équilibre naturel. On note qu'il s'agit du cycle le plus court, on va donc cherche à minimiser le cycle et pour cela on va utiliser `minimize` de `scipy.optimize`.\n", "\n", "Pour commencer définissons la fonction à optimiser :" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Minimum pour le ratio proies/prédateurs= 6.666669\n" ] } ], "source": [ "def ecart(ratio):\n", "\n", " t = linspace(0,9,1000)\n", " res = odeint(f, (10., 10./ratio), t, args=(a,b,c,d))\n", " return max(res[:,0]) - min(res[:,0])\n", "\n", "from scipy.optimize import minimize # attention, demande la version 0.11 ou + de Scipy\n", "\n", "mini = minimize(ecart,[3],method='TNC',bounds=[(1,10)])\n", "print (\"Minimum pour le ratio proies/prédateurs= %f\" % mini.x[0])\n", "t = arange(0,5,0.01)\n", "res = odeint(f, (10., 10./mini.x[0]), t, args=(a,b,c,d))\n", "#plot(res[:,0],res[:,1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le ratio de 20 proies /3 prédateurs donne la position d'équilibre. " ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 186, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot(t,res) #graphique pour le ratio à l'équilibre\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Cet équilibre mathématique est-il atteint dans la réalité ? Pourquoi ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.5. Limites du modèle proie-prédateur\n", "\n", "Dans la réalité, les populations de proies et de prédateurs ne sont pas isolées. \n", "- Il y a des migrations qui peuvent faire fluctuer les effectifs.\n", "- des pathogènes qui peuvent tuer le prédateur ou la proie \n", "- Les Mammifères ont une fertilité qui dépend de la densité de population. les femelles ont des interactions aggressives qui réduisent leur fertilité. Les lynx ont un grand territoire et peuvent avoir des difficultés à rencontrer un partenaire quand la densité de population se réduit. \n", "\n", "> Pour chacun de ces phénomènes biologiques, identifiez le paramètre des équations de Lotka et Volterra qu'il faudrait modifier. \n", "> Proposer une expression mathématique pour cette modification. Est-il possible d'écrire un programme «résolvant» ces équantions modifiées, selon vous ?\n", "\n", "Cette jolie animation montre une dynamique proie-prédateur. \n", "Les paramètres modifiables sont :\n", "-Predator death probability\n", "-Prey reproduction probability\n", "-Predator reproduction probability\n", "-Neighbor max number\n", "\n", "> Quelle modification a été faite par rapport aux équations de Lotka et Volterra ? En quoi est-ce important biologiquement ?\n", "> Quelles autres améliorations pourraient être faites ?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 1 }