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On note dans la suite cette probabilité $p$. + \item Pour simuler le fait qu'un individu re-capturé soir marqué ou non, on utiliser la formule suivante: \calc{=Si(ALEA() < p; 1; 0)} où $p$ est à remplacer par la valeur trouvée à la questions précédente. Compléter votre tableau pour simuler 50 re-captures. + \item Calculer le nombre d'individus marqué puis estimer la population avec la méthode CMR. + \end{enumerate} + En appuyant sur la touche \texttt{F9}, la simulation (tous les \texttt{ALEA()}) sera rejouée. + \item Repoduire ce qui a été fait avant pour simuler 50 re-captures. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.25\textwidth} + \includegraphics[scale=0.25]{./fig/haut_tableur} + + ... + + \includegraphics[scale=0.25]{./fig/bas_tableur} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{3} + \item Tracer un graphique représentant les populations estimées lors de vos 50 simulations. Décrire les valeurs obtenus. Que peut-on en conclure sur la précision de la méthode CMR? + \item Changer les paramètres \texttt{Population totale} et \texttt{Individus marqués} puis décrire le comportement des simulations. Dans quelles conditions, la méthode CMR donne de bons résultats? De mauvais résultats? + \end{enumerate} +\end{exercise} + +\vfill + +\printexercise{exercise}{1} +\vfill + +\end{document} diff --git a/EnseignementsScientifique/02_Biodiversite_evolution/3B_confiance.pdf b/EnseignementsScientifique/02_Biodiversite_evolution/3B_confiance.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5a723a8d5d35132f09245aa74d237870da9b08f4 GIT binary patch literal 72900 zcmce7V|XR)mUi5+?R4zy*ha^;ZQHgxwmNnv-LY-kw(YO`#mt$RbA2;^&e>OXr5;r6 zTBxAmt06G?E(#hGrMQCP120~i{3uta`XnG}gJ7Yq6HCY1-V?!rsdPQdg zr$2f`Z5^zk=>-LC-3T=qe$59k{PER>rvE+i$58-idTD(p2lHPu0KaDZ8vnihHABJJ z(bn0)(AbfX1Fgf_M@`fKFZ-tS9i`*q@fj|lAlDiJvTZ6W}E8|PnQ z2EcEV|9k8JVEmT}@$Yjcz`x9!7=PRN-(v~J-$wtJxDzAOzfXwYLGWKA1na*~h~J+3 zFA;+2A9KXt;hP=6`e*$9-^2HrmZa^9C}R7G>Sg=A~@8j<(oF|%t4t-xZ}P$t}+56xah=@QDV>W zWcQ8^1#0L|K$7`(93XidOUGM9t`xPC7R7LUt7&>}qnp#f6sbd53Gi>~oUKASY!lGI z;@_G7a!c=E@W?Ca!zBW%vT15>i{aPx6>~&BS`^tXp`WTr`g9zq>p)+b;Ryko7KI>R z6PF1x6V}iJYL9S6!NRmE3Car07*@VQFMpk}PWu`*j%G)I{GvU=>!Qxcg9p?Tb^pBN=q3k|Ci)rwlh2bh`UP(3m(Af@1`^G)NYb zH${HRd$-ksScCAZM)$IX;2P&JKLO-z3)lwOf(&|s*7p^wiS0Xlg`Cc1yN`^fRxv}6 zn^etxY*NZt$tk^(WzqIx(nOw7L0^^4w`0WDqjr0y){hK5D+%V~Zc{ zl`10)>#u!9_QuWG<6hAL8baxxXATpmdXFtY_iq=~JKGh|64g=(Lh&MKqmBn&EkWkY zf2a$keYQHKR^@r4^l~t4IoqpmhV#szxKcj9adOw3b1q<^4<(Gl#aR)o!S&-ev{WyU zqdk~Qv1o5Hw|4Pa3+cusX@i20$I7bEl_Iep4^^iQYdn+nV68OG@EFupbFJyjXG#eK z-U%oIcAR^g7VGkNXrnZA+(ghq6n~xqgNl~!BV$Diyt>7n*^{2Vx`}1=TpU=04$c$cI{Sf3NIdCYpM!VSGn>Ct}4sOU{sr8MZJqWwxRxJ9tLT3Q7@>2J|DDFcO43B zm)4Cvk8h@DvJJwOg}NN23t`Q^$YPr4pPYeAf{K%Ak<3%mu{-vp%4^OXvUSyl<2~`vG~TH zO8bo`3`%P^w4N_(V|HdsP_snSdS>TqVKvHVN^35tHjc^I-rck^(IK>r5B$^X?Fn@k z;*fN}Obj}nMAz*NJu=XLg32Z5s7 zv}sderoxHDcR7iR_x%yt4e=v1ClRVWk+d08nH&!9{o4HY8| zoijaeS2afO-aT(+WRDG33l7k`?|QM`0EjkLXCmwlSHy&?8qJ}0`?s1L-U^2~JjECx z{U3%KGDpGw9K!?6A{*|Bl-~a!qkdvG(x9Hf1CIy1v_H`k{x9i%i}~S}nGH3_x6S@= znCAIa>AXX1!f$@cP|kzm6F+y(v-Ptf|LW2*sQtI?P@z>!>;U$<=gJD+(z}W5Imdp0 zzNZ;aXgsYiiAs)JqPcg`UE2IFl~zvFzw6iQ010~H7Zrmr3?s~#D&&ZJlikIN9Y

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new file mode 100644 index 0000000..e2cc2d2 --- /dev/null +++ b/EnseignementsScientifique/02_Biodiversite_evolution/3B_confiance.tex @@ -0,0 +1,37 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{wasysym} + +\author{Benjamin Bertrand} +\title{Intervalle de confiance} +\date{Décembre 2021} +\tribe{Enseignements Scientifiques} + +\newcommand\cours{% +\begin{bclogo}[barre=none, arrondi=0.1, logo=]{Cours: Intervalle de confiance} + \begin{minipage}{0.6\linewidth} + On cherche à estimer $p$ la proportion d'un caractère d'une population. Pour cela, on fait un échantillon de $n$ individus de cette population et l'on calcule $f$ la fréquence (proportion) du caractère dans cet échantillon. + + On peut définir \textbf{l'intervalle de confiance à 95\%} + \[ + IC_{95\%} = \intFF{f - \frac{1}{\sqrt{n}}}{f+\frac{1}{\sqrt{n}}} + \] + Alors $p$ est dans cet intervalle avec une probabilité de 95\%. + \end{minipage} + \hfill + \begin{minipage}{0.3\linewidth} + \includegraphics[scale=0.6]{./fig/confiance} + \end{minipage} +\end{bclogo} +} + +\begin{document} + +\cours +\cours +\cours +\cours +\cours + + +\end{document} diff --git a/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance.pdf b/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance.pdf new file mode 100644 index 0000000000000000000000000000000000000000..50e8436aa6e695c4918381930807be4972fbda2a GIT binary patch literal 32924 zcmce;bF45=wZ;%FrI9r#76JwWJ0nXd9v&!q6%Tt;0(uR3BTG|bXDE7Q7bEBY zXc4n>w1J`*60&nA&}R6@o{`}{Ze1w)fA##wTZ~ZjvWCu%7XMf<{$ue^|G%F9SSXn~ z*||6xn>rD&{?noaMK5D&YwrAqfRUBpKd*mAv9NYFbtIq{vo>@#6)`ooGckqY`OltzO8@$F_J0QcpMk*f?}EVjKL&yEU*!B- zXkh#o<^MB0Ff#qyK>W`+6XUQ#B{uKoOJs{Zr=Ro|+ zbN?+MnEyKy{~5lSSQ**>SN#6Jhwp3c?YK=gB){E0A-jeE=BeAb1N$(NRcI}oNZUrY z*ZJ!pV=HzlYme2&myO>aGYP3eYt63NPCzW02SHDf85r}>A$)P98C&Mep04~)TEhj! z1jWK)qj?RwQqecB%UkMf^F==R^76YNS8g+{|q_d~(<&kgD zKahSJRWVAzS~;{U=o09e$kZxi5he^nJY5~_GQ~=^#Xzaqj6u~Mjj7-jLup9T90x3` z6@kXzUDNQPlu+iXFMTi*cdtzE_~1y9$}=nAy2b+)YIoKtx*)_{ zgmDTEJP3TSu^_&`Gjx+80p&>qIuQ0Voh2BOG{bpfX0VdTh7~86LG{dJ%%OkIX{>H- zA)(`IasH}st}6EAMl%dGOW1<3mK3Wwe<3RsjSx+fD`0z6C1a#qkgzCQp+W#j^y~`p2Zyf&OBwnad}~pto;-|&i0N~tC4mjP zWU`Zpta%uzT}vj>`EbLmRmpPX?3)2*tRspVG3x>Q>#p7I*jCZjuGl|q7L8a|SQ#bH zNns?!jl9CLP_SCjPLnAMeonoWQNJi#peMU+f_@@7IC86A0LvwKYNj`=rz)-qqheJY z3h61lwAnu_$Ktl%nKx;~3h(J(0(Ro4-$$j^ZXtEy!k#o!_g>pXyTH5P|6+)&D1j4u za^Ith6Yoxkpch8A`#c63QrUk!F};Jp4@ee~1Y~9yj!ZOtP(~?L;ifD~-Xx1TI_JP4 zk}F3fKe&WjyB6ipfIi0hq{AWK&M{7;!e*@pKkhJmp_b;M z(y8|b@bbmanorlhkGcWvJ?Tc9oxma@$eY6`NA7pKp9wNIjG9(GIYoy#EyR}Ia=ynT zy*L_C5hAQNiBR8vl$WH{nGDo{8hHq-b zK9yheJN2lfWx?BD2L!I~3)hrQ3!YFI5UWtuVui+`id=51FhBhTi4RGFMGmLD)LaYmvZ zFw$M-5sX^?TI&E9-9)ss{ZdbMDk4xflxYM2Y`LZ+%M7Lu66qhrw-@m3wkEi{yMDwkD=(nxXWk-q0}18>nl8Z znhze12f$t9Qp|lmCOC(Ujfq2hdUCMJ5fdSwJ)8A%3G`3z+(-%|I!DdnBxSfseW7Fd)x4t^$YfxF3TqD2RLo ziA(!)94!eWD2Mjuqgo;fntd={9f@Q$$wYw=Qd~%}LgVNTU#cwLT&`|)d(4FEdk}1`}mY8AO!^bUw6M(9B9ZY zvo9`sHEQo%Oy5xQpx#xX!mc+Nr_C)b@cbUXqo+An1TNkq)kkmIX8coVB+uUrOYlW4 zl$jx3`VJo%kGt}hJrC3JtYp$yYrN&-&Bil=&HD=oCx4BxH~|^#+nS$LL@gc zzJoV*;#mG5yqZI0(P~VGFV0}LSoshr-h;QK5IiotOXx!yJU5=O0$xqR@XNQIM+$ojveesC2rr(Q~9JbsPy!gIjTwQrQU{8}4EF#45h`cFOO z>MrX&QOSXWZy)NY+^~(@?RI)@3U`nrWgz`O1Iy%e;RYw&%jC1H4olJMc^vA)Y;Rrq zzDNyUPiVBQn!6rF=s(}2@?inzmp5So-xj20A~OMr%I4{Hg-0R|9#A|)To-p$5SzZ8 zjL!StT_%Wg0Ob}@Y=*<>H`tJCZNV*??VYbNBIdJq1%TNTAc{S!rUM^hYe&N2m?Stu zOLt)i_2F>*!TqS1e8K)ZJ7EX{_xM8oV6*p-(8YE_Loeuizkno
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a/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance.tex b/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance.tex new file mode 100644 index 0000000..97337a5 --- /dev/null +++ b/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance.tex @@ -0,0 +1,63 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} +\usepackage{wasysym} + +\author{Benjamin Bertrand} +\title{Intervalle de confiance} +\date{Novembre 2021} +\tribe{Enseignements Scientifiques} + +\setlength{\columnseprule}{0pt} +\setlength\columnsep{5pt} + +\geometry{left=10mm,right=10mm, top=5mm, bottom=5mm} + +\begin{document} + +\maketitle + +\begin{doc}{Sondage d'élection} + Deux candidats se présentent à une élection. Un sondage est commandé pour chercher à prédire les résultats. Il est fait sur 1302 électeurs. 629 déclarent qu'ils projettent de voter pour le candidat A et le reste pour le candidat B. + \medskip + + Peut-on affirmer que le candidat $A$ a aucune chance d'être élu? +\end{doc} + +\begin{doc}{Deux phénotypes de l’épervier strié} + % Issu du livre scolaire + L’épervier strié est un poisson qui vit dans les récifs coralliens. Il existe sous deux phénotypes : sombre et clair. Un recensement des formes claires et sombres a été effectué le long de cinquante-quatre transects, de la surface jusqu’au fond du lagon. + + \begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|} + \hline + Nombre de Poissons & Profondeur < 5m & Profondeur > 5m \\ + \hline + Sombre & 538 & 20 \\ + \hline + Clairs & 310 & 238 \\ + \hline + \end{tabular} + + \medskip + Peut-on affirmer que les poissons sombres préfèrent vivre proche de la surface? +\end{doc} + +\begin{doc}{Compétition entre établissements} + Trois établissements scolaires revendiquent être les meilleurs pour préparer leurs élèves au bac. Voici leurs résultats pour l'année dernière. + + \begin{tabular}{|c|c|c|} + \hline + Nombre d'élèves & Reçut & Refusé \\ + \hline + Lycée A & 40 & 13 \\ + \hline + Lycée B & 87 & 36 \\ + \hline + Lycée C & 140 & 16 \\ + \hline + \end{tabular} + + \medskip + Peut-on affirmer qu'un établissement est meilleur qu'un autre? +\end{doc} + +\end{document} diff --git a/EnseignementsScientifique/02_Biodiversite_evolution/4E_Hardy_Weinberg.pdf b/EnseignementsScientifique/02_Biodiversite_evolution/4E_Hardy_Weinberg.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b3c1908499397696721ece33e2b237501809d859 GIT binary patch literal 70362 zcmce;W2|t^wk5o6+qP}{*|u%_*|u%lwr$(CZL{BV``$18qm!@yoU@X(QkYe#kuft< zRdZyK%8Q86GSaa^kaD0(3wJ2wI?hJWlC8UE|lfujFc&wq_#grb)*aCWr#$Aa-6i+}q6_5H^}(ZtE_ zucMKP69MZ#Es9X|(k8ZM&gKM+tOWo4{4DfwPH-iIJVL2^1e6l#{cg ziGdB2+r}dNj6B869uNTdH{czViLLQ}_xw}(*V5VlnfN~gf#cr=f%88Gf$?AD{99;X 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b/EnseignementsScientifique/02_Biodiversite_evolution/index.rst @@ -0,0 +1,57 @@ +Biodiversité évolution +###################### + +:date: 2021-11-08 +:modified: 2021-11-08 +:authors: Benjamin Bertrand +:tags: Proportion, Tableur, Echantillonnage +:category: EnseignementsScientifique +:summary: Outils pour estimer une population et des proportions d'une population + +Étape 1: (SVT) mesure de la biodiv +================================== + +Zoologie de ce qu'il y a dans un océan. + +Étape 2: (MATH) Évaluer la taille des populations: CMR +====================================================== + +Calculs de proportion avec la méthode de Capture-Marquage-Recapture. + +On récupère doc 2 p174 avec ajout de la formule. Refonte des docs pour plus de clarté. + +.. image:: ./1E_methode_CMR.pdf + :height: 200px + :alt: Découverte de la méthode CMR + + +Simulation de la variation de la taille de la population trouvée avec cette méthode pour commencer à voir le comportement de l'intervalle de confiance. La formule de cet intervalle n'est pas à connaître mais cette activité prépare l'étude de l'intervalle de confiance sur une proportion. + +.. image:: ./2E_simulation_CMR.pdf + :height: 200px + :alt: Simulation de la fluctuation avec de la méthode CMR + +Étape 3: (MATH) Évaluer la taille des populations: échantillonnage +================================================================== + +Estimation d'une proportion d'une population avec l'échantillonnage. + +.. image:: ./4B_confiance.pdf + :height: 200px + :alt: Cours sur l'intervalle de confiance + +.. image:: ./4E_confiance.pdf + :height: 200px + :alt: Documents pour travailler l'intervalle de confiance + + +Simulation de l'intervalle de confiance? + +Étape 4: Hardy-Weinberg +======================= + +.. image:: ./4E_Hardy_Weinberg.pdf + :height: 200px + :alt: Étude du modèle d'équilibre de HW + +