7
1 !"#$% &’()*+,-./’01234567.89:;5<=> /’?@ABCDEFGHIIJ+KL7.MN OOPQ&R:ST;:GHKL0U7 VW XYZ 6 [\+]^_8 XYZ:‘abc XYZ:6d ef7.VW0gWLh c;iPjkh8J:0 ;5XYZI_l XYZ:6I VmI:nopqr 2 &’(:/’:s tuv&wR:;QK/7.:xy tuvz{|}O.:xy ~t5>Q:1ltJ:xy L:Qy H+,-.vvL:|2 H:5’:KL : :/’:s 3 #$ t™;%:;p¡¢C£¡ /¥ƒ;5&’% §¤'“ «‹ƒ› &fi:;5 fl–“ ²b‡· An Illustrated Guide to Theoretical Ecology Ted J. Case, Oxford University Press ¶•‚„”%»…‰ ;5&R% ST¿/’:;5XY£¡`´ ˆ˜¯˘“ ²b‡· 4 ST¿/’:s Gause 1934, Roughgarden 1971 From Case 2000 Paramecium aurelia Image from http://mtlab.biol.tsukuba.ac.jp/www/ PDB/Images/Ciliophora/Paramecium/aurelia/ Davidson 1938 From Case 2000 Sheep introduced into Tasmania

ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

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Page 1: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

1!

!"#$%!

&'()*+,-./'01234567.89:;5<=>!

/'?@ABCDEFGHIIJ+KL7.MN!

OOPQ&R:ST;:GHKL0U7!

VW! XYZ!

6!

[\+]^_8!

XYZ:`abc!

XYZ:6d!

ef7.VW0gWLh

c;iPjkh8J:0;5XYZI_l!

XYZ:6I!

VmI:nopqr!

2!

&'(:/':s!

•! tuv&wR:;QK/7.:xy!

•! tuvz{|}O.:xy!

•! ~�t���5�>Q�:1ltJ:xy!

•! �L:��Qy !

•! �H���+,-.�v��v�L:�|2!

•! �H:�5�':KL!

•! �:�!

��:/':s!

3!

��#$!

��t���;%:�;p���� ¡¢C£¡ !

¤¥¦�;5&'%"§¨©ª"«¬¦­!

&®:;5"¯°±ª"²b³´!

An Illustrated Guide to Theoretical Ecology!

Ted J. Case, Oxford University Press!

µ¶�·¸¹º�%»¼½¾!

;5&R%"ST¿/':;5XYÀ£¡ÁÂ!""ÃÄÅƪ"²b³´!

4!

ST¿/':s!

Gause 1934, Roughgarden 1971!

From Case 2000!

Paramecium aurelia!

Image from http://mtlab.biol.tsukuba.ac.jp/www/

PDB/Images/Ciliophora/Paramecium/aurelia/!

Davidson 1938!

From Case 2000!

Sheep introduced into Tasmania!

Page 2: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

5!

Voles in Sweden!

Hornfeldt 1994!

From Case 2000!

http://www.natuurbeleving.be/zoogdieren/

Rosgrijze_Woelmuis_Clethrionomys-rufocanus.html!

ÇÈC:ST¿/'s!

6!

CÉ£Ê! DZËÌÍ!

Image from!

http://hp.brs.nihon-u.ac.jp/~ocean/kenkyu/hormone.html!

Daphnia magna!

Image from!

http://dmc.utep.edu/rotifer/html/nsp1.html!

Pratt 1943!

From Case 2000!

Halbach 1979!

From Case 2000!

7!

Image from http://www.xeye.org/1995-2000/

LemmZoo.html!

Lemmings!Dicrostonyx groenlandicus!

·C£¡:ST;K/!

mÎ�mÏY¹ÐvÑÎ�XYZ+1.ÒÏ!

From Case 2000!

8!

ÓÔÕ:Ö!!

Raggett 1982, Brown and Rothery 1993!

Outbreak of the Great Plague

in a village in England, late

17th century.!

350 �:l×&wØÙ8:Q 83�!

ÚÛ�ÜÝÔÞ;mÏ!

ßÛ�ÝÔÞ;mÏ!

Page 3: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

9!

àáFQhxN:â�!

Bulmer 1994!

ÝÔÞ;Q 2 ãä»PK/!

Òåæç|mèéê.ëì!

10!

íç(:@ABCDEFîïGHN!

@ABCDEFdynamicsN�ð%v/ð%!

GHIIJ+KL7.�'vJh4QOê0ñò7.óÄ!

1 ST|)\:GHHôõ+ö»hcó÷hc2

ST+t.øù0ú2û7&Rüý0¥þ.ÿ !

G!"t! 0! 1! 2! 3!

O:1lt&R|m#7.xQOO

PQ$%Iht_ÿ&4'PXYZ:[\P&.ÿhxhv(D)À*t

�:�&R|+cQ'.xJhêt_ÿ !

11!

ST;:GHKL!

G!"t P:ST;0"Nt I¦4Iv,-GH+ 1 STQ 2 ST+ó÷7.x.v !

Nt+1 = 2 Nt!

/»ST;0"N0 I7ê0v ! Nt = N0 2t!

,-GH+ö»hc 2 ST+ó÷7.I_l[\+]^4XYZ !

I6-.ÿ !

12)*<+v1 ST|,-GH+"r 1+237.I[\7ê0v !

Nt+1 = r Nt! Nt = N0 rt! 04.ÿ !

12!

ST;5ST67!

86+Qv&R:ST;Q9::;;<P&.=wÿhxhv,->�&82:ST670¥þê0v? Jh4Q@:m;P&ÙcJ1_ÿABQST67+efh8@ABCDE0¥þ.ÿ !

Nt+1 = r Nt!r : 1 ST&82:CD:; (r > 0)!

mE:&RPQv !

ó÷23QFG+Qö»hc_t_!

&.STQ�ST12J12H4237.IJ|&.!

ST67|K4t.ILMó:NOvPQRR+1.STUV

:WLt�P23X"r QYZ7.!

Olh8Vm[QO:XYZ+Q\]éêc_t_^!

r > 1 :GvU;2_!

STQ`3Bab7.I¥þ.!

Page 4: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

13!

U;2_XYZ:s!

{1, 1.5, 2.25, 3.375, 5.0625, 7.59375, 11.3906, 17.0859, 25.6289, 38.4434, 57.665,

86.4976, 129.746, 194.62, 291.929, 437.894, 656.841, 985.261, 1477.89, 2216.84,

3325.26}!

r = 1.5, N0 = 1 :IJ! Nt = N0 rt! 12! Nt = 1.5t!

0 5 10 15 20

500

1000

1500

2000

2500

3000

3500

4000

G!"t!

!"#$!

14!

Nt = N0 rt! :cd:e;0I.Iv !

!

logNt

= logN0 + t log r

U;2_:IJvST67:e;QGH"t +nshc2_7.!

0 5 10 15 20

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20

2

4

6

8

10

G!"t! G!"t!

e;Ef¹Z:¡¢gQhÎIt2viwQ log r !

r = 1.5 :U;2_!jk0e;Ef¹ZPl_8J:!

iwQ log 1.5 = 0.41!

e;Ef¹Z!

15!

!mn:23s!

ST67|U;<+KLhc_.x�lx0o.+Qve;Ef¹Z+ef

7.ÿU;<+KL7.t.hÎ+t.Qpÿ !

Brown and Rothery 1993!

16!

�H:;:2_!

�qQvU;2_12Jrs+2_hc_.^!

「新人口論-生態学的アプローチ」 農山漁村文化協会 1998 Joel E. Cohen著 重定・瀬野・高須共訳

Page 5: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

17!

1_GH Doubling Time!

U;2_XYZPvST67| 2 1+2_7.:+�7.GH01_GH (Doubling Time) Ituÿ !

Nt = N0 rt!

1_GH0"Td I7.I\�x.! Nt+Td = 2 Nt!

0�Áhcv ! N0 rt+Td = 2 N0 r

t!

vwv ! rTd = 2! It2v ! Td = log 2 / log r!

r = 1.5 / day :IJvTd = log 2 / log1.5 = 1.71 day!

r = 4 / hour :IJv1_GHQ_4.xy!

18!

U;xyXYZ!

,-GH&82:ST:&zX0"s I¦4Iv !

Nt+1 = s Nt! (0 < s < 1)!

{'2vG! t +&wØÙc_.ST67Q!

Nt = N0 st! N0 Q/»ST67!

Nt = N0 rt!

r > 1 :GvU;2_XYZ!0 < r < 1 :GvU;xyXYZ!

19!

ÊË|À Robin :s!ÊË|À:µ}+O~0{-c;ã+�82µ}:&zX0�=8ñòLack

1965!

ST;! 129! 49! 20! 8! 2!

ã! 0! 1! 2! 3! 4+!

hÎ:iwQ!log r = –0.97!

r = e–0.97 = 0.38!

Brown and Rothery 1993!

20!

�xGH Half Life!

U;xyPST67|�x7.:+�7.GH0�xGH"(Half Life) Ituÿ !

Nt = N0 st!

�xGH0"Th I¦4I\�12v ! Nt+Th = 1/2 Nt!

0�Áhc! N0 st+Th = 1/2 N0 s

t!

vwv ! sTh = 1/2! It2v ! Th = – log 2 / log s!

(0 < s < 1)!

s = 0.8 / year :IJv�xGHQ –log 2 / log 0.8 = 3.11 year!

Page 6: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

21!

���®:��!

0! 1! 2! 3! ...! i!

�ã'P:&zX|"s P&2vã�I:&a|�b�WP&.IJ!

1 �Pab7.�X� 1 – s!

2 �Pab7.�X�"s (1 – s) !

i �Pab7.�X�""si–1 (1 – s)!

...!

���®!

ÊË|ÀFs = 0.38 /yearN:IJv!

���®Q 1.61 ã!

22!

Í¢Ê(º:s!

(Z�£����:Í¢Ê(º| 1955 ãA�ÀE+�

×�'êc!`3ÿ10 ãHP 4 �x. 18,855 �+2_ÿ !

hÎ:iw! log r = 0.98!

õã:2_X�!e0.98 ~ 2.66!

Image from http://www.mbr-

pwrc.usgs.gov/id/framlst/i3153id.html!

Brown and Rothery 1993!

23!

Í¢Ê(º:@ABCDEXYZ !

t ã+,-.Í¢Ê(º:ST670"Nt I¦4ÿ !

Í¢Ê(ºµ}:�ã'P:&zX0"sa!!

�B:&zX0"sb v1 ãH+���BF�N:;0"b I7.I!

sa = 0.86, sb = 0.6, b = 4~6 :Gv2_XQ!

:GvU;2_!

2.06 ~ 2.66!

µ}:!

&wØ2!

��+�'ê8!

�}!

24!

îïGHXYZ!

`3�ab|ö»hc}O.&R:ST67@ABCDE:XYZIhc14�_.ê.F���}t�Nÿ !

�ó�ùiF LiNPjkéê.ÿ !

r > 1 :GvST67|¡ïhch'lÿ !

Vm:&RüýPQvr Q)\PQt_ÿ !

¢:NOvSTUV:WLt�+12vST67|K4t.I"r QYZ7

.I��ê.ÿ !

U;2_XYZ:£Ñ�!

67�¤0¥¥h8XYZ|��!

U;2_XYZQvµ¦øù+&.&Rüý014§¨Pw.!

Page 7: ST¿/’:sgi.ics.nara-wu.ac.jp/~takasu/lecture/global/H21-global-1.pdf · 17! 1_GH Doubling Time! U;2_XYZPvST67| 2 1+2_7.:+Š7.GH01 _GH (Doubling Time) Ituÿ! N t = N 0 trt! 1_GH0"T

25!

$% 1!

Lack (1954) +1.©É:ST;2_:Y¹Ð!

ã! 1937! 1938! 1939! 1940! 1941! 1942!

ST;! 8! 30! 81! 282! 705! 1325!

ST;Q2þc_.|v�:1lt2þ�xª«¬1!

G(­Y¹Ð6d:)*=®!

íN¯°+GHv±°+Y¹Ð<0IÙ8¡¢g0l4!²Ne;Ef¹ZPl_ca.!³Ne;Ef¹ZP´µhÎ+tê0vU;<+KLhc_.I¶·!

26!

$% 2!

double pop_density = 1.0, r=1.1;!

int t;!

for(t=0; t<100; t++){!

pop_density *= r;!

printf("%f\n", pop_density);!

}!

U;2_XYZ0¸+t2_X"rv/»67P��7.� ¡¢Ì0¹µhv@ABCDE0º»L¬1ÿe;Ef¹ZPJº»L7.�ÿ !

� ¡¢Ì:¼½!

27!

% ./a.out > data!

% gnuplot!

G N U P L O T!

Linux version 3.7!

patchlevel 1!

Terminal type set to 'x11'!

gnuplot> plot 'data'!

gnuplot> !

À@A·D;£+12v¤0g¿AZÀ³ð!

g¿AZ data 0¡¢g+l4!

gnuplot 0�_cY¹Ð0º»L!