File:Gause's experiment and fitted logistic curves.svg

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日本語: ガウゼの実験結果[1]とレーベンバーグ・マーカート法でフィッティングさせたロジスティック曲線。

下記のScilab（lsqrsolve）を使用して各パラメータ（r, K, N0）を求めた。それらをもとにExcelでグラフ作成、InkscapeでSVG化。各曲線のパラメータは以下のとおり。

  • Saccharomyces cerevisiae: N0 = 0.2831294, K = 12.742142, r = 0.2586369
  • Schizosaccharomyces kefir: N0 = 0.4970908, K = 5.8802335, r = 0.0574421
  • Mixed population: N0 = 0.3796836, K = 10.690843, r = 0.2116539

グラフ中の各個体群成長データはガウゼの論文のTable Iのデータを使用した。

English: This figure shows Gause's experiment results[1] and logistic curves fitted with Levenberg-Marquardt Method. Logistic curve can be written as
.

Below Scilab (lsqrsolve) code was used to fit the parameters (r, K, N0). The fitted parameters of each curve are shown as follows:

  • Saccharomyces cerevisiae: N0 = 0.2831294, K = 12.742142, r = 0.2586369
  • Schizosaccharomyces kefir: N0 = 0.4970908, K = 5.8802335, r = 0.0574421
  • Mixed population: N0 = 0.3796836, K = 10.690843, r = 0.2116539
The population growth data used in this graph are derived from Table I of Gause's paper.
  1. ↑ a b Gause, G. F. (1932). "Experimental Studies on the Struggle for Existence". Journal of Experimental Biology 9 (4): 389-402. The Company of Biologists Ltd. ISSN 1477-9145.
Date
Source Own work
Author Yapparina
Other versions File:Gause's experiment and fitted logistic curves (single species).svg

Scilab source

Scilab source
Scilab source
 This media was created with Scilab, a free open-source software.

Here is a listing of the Scilab source used to create this file. 

clear all;

//data of Saccharomyces cerevisiae
t1=[6 7.5 15 16 24 24 29 31.5 33 40 44 48 51.5 53];
y1=[0.37 1.63 6.2 8.87 10.66 10.97 12.5 12.6 12.9 13.27 12.77 12.87 12.9 12.7];

//th(1)=N0, th(2)=K, th(3)=r
function e=fun1(th,m)
    e=y1-th(2)./(1+(th(2)/th(1)-1)*exp(-th(3)*t1));
endfunction

[parm, v]=lsqrsolve([0.1;12;0.1],fun1,size(t1,2));
parm

//data of Schizosaccharomyces kefir
t2=[15 16 29 31.5 48 51.5 72 93 117 141];
y2=[1.27 1 1.7 2.33 2.73 4.56 4.87 5.67 5.8 5.83];

//th(1)=N0, th(2)=K, th(3)=r
function e=fun2(th,m)
    e=y2-th(2)./(1+(th(2)/th(1)-1)*exp(-th(3)*t2));
endfunction

[parm, v]=lsqrsolve([0.1;6;0.1],fun2,size(t2,2));
parm

//data of Mixed population
t3=[6 7.5 15 16 24 24 29 31.5 33 44 48 51.5 53];
y3=[0.5 1.33 4.8 6.83 8.66 8.57 9.07 11.17 10.8 11.47 10.23 10.8 10.5];

//th(1)=N0, th(2)=K, th(3)=r
function e=fun3(th,m)
    e=y3-th(2)./(1+(th(2)/th(1)-1)*exp(-th(3)*t3));
endfunction

[parm, v]=lsqrsolve([0.1;11;0.1],fun3,size(t3,2));
parm

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