{"id":1562,"date":"2023-07-25T21:11:46","date_gmt":"2023-07-25T21:11:46","guid":{"rendered":"https:\/\/statorials.org\/pl\/wskaznik-roznorodnosci-shannona\/"},"modified":"2023-07-25T21:11:46","modified_gmt":"2023-07-25T21:11:46","slug":"wskaznik-roznorodnosci-shannona","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/wskaznik-roznorodnosci-shannona\/","title":{"rendered":"Indeks r\u00f3\u017cnorodno\u015bci shannona: definicja i przyk\u0142ady"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Indeks r\u00f3\u017cnorodno\u015bci Shannona<\/strong> (czasami nazywany indeksem Shannona-Wienera) to spos\u00f3b pomiaru r\u00f3\u017cnorodno\u015bci gatunk\u00f3w w obr\u0119bie zbiorowiska.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznaczone <em>H<\/em> , wska\u017anik ten oblicza si\u0119 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>H<\/em> = -\u03a3 <em>p<\/em> <sub>ja<\/sub> * <em>ln(p<\/em> <sub>ja<\/sub> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3:<\/strong> grecki symbol oznaczaj\u0105cy \u201esum\u0119\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>ln<\/em> :<\/strong> Log naturalny<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>p<\/em> <sub>i<\/sub> :<\/strong> Proporcja ca\u0142ej spo\u0142eczno\u015bci z\u0142o\u017conej z gatunk\u00f3w <em>i<\/em><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Im wy\u017csza warto\u015b\u0107 <em>H<\/em> , tym wi\u0119ksze zr\u00f3\u017cnicowanie gatunkowe w danym zbiorowisku. Im ni\u017csza warto\u015b\u0107 <em>H<\/em> , tym mniejsze zr\u00f3\u017cnicowanie. Warto\u015b\u0107 <em>H<\/em> = 0 oznacza zbiorowisko sk\u0142adaj\u0105ce si\u0119 z tylko jednego gatunku.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Wska\u017anik r\u00f3wno\u015bci Shannona to spos\u00f3b pomiaru r\u00f3wno\u015bci gatunk\u00f3w w spo\u0142eczno\u015bci. Termin \u201ejednolito\u015b\u0107\u201d odnosi si\u0119 po prostu do podobie\u0144stwa liczebno\u015bci r\u00f3\u017cnych gatunk\u00f3w w obr\u0119bie spo\u0142eczno\u015bci.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznaczono <em>jako <sub>EH<\/sub><\/em> , wska\u017anik ten oblicza si\u0119 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><em>mi <sub>H.<\/sub><\/em> = <em>H.<\/em> \/ <em>ln<\/em> ( <em>S<\/em> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><em>H<\/em> :<\/strong> Wska\u017anik r\u00f3\u017cnorodno\u015bci Shannona<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>S<\/em> :<\/strong> Ca\u0142kowita liczba unikalnych gatunk\u00f3w<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Warto\u015b\u0107 ta mie\u015bci si\u0119 w zakresie od 0 do 1, gdzie 1 oznacza ca\u0142kowit\u0105 r\u00f3wno\u015b\u0107.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje krok po kroku jak obliczy\u0107 Indeks R\u00f3\u017cnorodno\u015bci Shannon i Indeks Kapita\u0142u Shannon dla danej spo\u0142eczno\u015bci.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 1: Zbierz dane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Za\u0142\u00f3\u017cmy, \u017ce biolog chce zmierzy\u0107 r\u00f3\u017cnorodno\u015b\u0107 gatunkow\u0105 w lokalnym lesie. Gromadzi nast\u0119puj\u0105ce dane:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15477 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon1.png\" alt=\"\" width=\"158\" height=\"186\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 2: Oblicz proporcje<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie biolog mo\u017ce obliczy\u0107 odsetek spo\u0142eczno\u015bci sk\u0142adaj\u0105cej si\u0119 z ka\u017cdego gatunku.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad \u0142\u0105cznie jest 105 osobnik\u00f3w, a 40 jest sklasyfikowanych jako gatunek A. Zatem gatunek A reprezentuje 40\/105 = <strong>0,38<\/strong> ca\u0142ej spo\u0142eczno\u015bci.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017ce wykona\u0107 podobne obliczenia dla ka\u017cdego gatunku:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15478 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon2.png\" alt=\"\" width=\"251\" height=\"194\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz logarytm naturalny proporcji<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie mo\u017ce obliczy\u0107 logarytm naturalny ka\u017cdej proporcji:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15479 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon3.png\" alt=\"\" width=\"299\" height=\"179\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 4: Pomn\u00f3\u017c proporcje przez logarytm naturalny proporcji<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie mo\u017ce pomno\u017cy\u0107 proporcje przez logarytm naturalny proporcji:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15480 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon4.png\" alt=\"\" width=\"376\" height=\"181\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 5: Oblicz wska\u017anik r\u00f3\u017cnorodno\u015bci Shannona<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017ce zastosowa\u0107 nast\u0119puj\u0105cy wz\u00f3r do obliczenia wska\u017anika r\u00f3\u017cnorodno\u015bci Shannona:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>H<\/em> = -\u03a3 <em>p<\/em> <sub>ja<\/sub> * <em>ln(p<\/em> <sub>ja<\/sub> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym przyk\u0142adzie mo\u017ce wzi\u0105\u0107 sum\u0119 z ostatniej kolumny i pomno\u017cy\u0107 przez ujemn\u0105:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15481 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/shannon5.png\" alt=\"Przyk\u0142ad wska\u017anika r\u00f3\u017cnorodno\u015bci Shannona\" width=\"397\" height=\"220\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Indeks r\u00f3\u017cnorodno\u015bci Shannona dla tej spo\u0142eczno\u015bci wynosi <strong>1,49<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017ce r\u00f3wnie\u017c skorzysta\u0107 z poni\u017cszego wzoru do obliczenia Indeksu Shannon Equity Index:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>mi <sub>H.<\/sub><\/em> = <em>H.<\/em> \/ <em>ln<\/em> ( <em>S<\/em> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym przyk\u0142adzie jest \u0142\u0105cznie <em>S<\/em> = 5 gatunk\u00f3w, wi\u0119c mo\u017cemy obliczy\u0107 ten wska\u017anik w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><sub>EH<\/sub><\/em> = 1,49 \/ <em>ln<\/em> (5) = <strong>0,92<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Mo\u017cesz skorzysta\u0107 z kalkulatora Indeksu R\u00f3\u017cnorodno\u015bci Shannona, aby automatycznie obliczy\u0107 Indeks R\u00f3\u017cnorodno\u015bci Shannona dla dowolnego zbioru danych.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Indeks r\u00f3\u017cnorodno\u015bci Shannona (czasami nazywany indeksem Shannona-Wienera) to spos\u00f3b pomiaru r\u00f3\u017cnorodno\u015bci gatunk\u00f3w w obr\u0119bie zbiorowiska. Oznaczone H , wska\u017anik ten oblicza si\u0119 w nast\u0119puj\u0105cy spos\u00f3b: H = -\u03a3 p ja * ln(p ja ) Z\u0142oto: \u03a3: grecki symbol oznaczaj\u0105cy \u201esum\u0119\u201d ln : Log naturalny p i : Proporcja ca\u0142ej spo\u0142eczno\u015bci z\u0142o\u017conej z gatunk\u00f3w i Im [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1562","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Indeks r\u00f3\u017cnorodno\u015bci Shannona: definicja i przyk\u0142ad \u2013 Statologia<\/title>\n<meta name=\"description\" content=\"Ten samouczek zawiera wyja\u015bnienie Indeksu R\u00f3\u017cnorodno\u015bci Shannona, w tym formaln\u0105 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