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1!
!"#$%!
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/'?@ABCDEFGHIIJ+KL7.MN!
OOPQ&R:ST;:GHKL0U7!
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6!
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2!
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��t���;%:�;p���� ¡¢C£¡ !
¤¥¦�;5&'%"§¨©ª"«¬¦!
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An Illustrated Guide to Theoretical Ecology!
Ted J. Case, Oxford University Press!
µ¶�·¸¹º�%»¼½¾!
;5&R%"ST¿/':;5XYÀ£¡ÁÂ!""ÃÄÅƪ"²b³´!
4!
ST¿/':s!
Gause 1934, Roughgarden 1971!
From Case 2000!
Paramecium aurelia!
Image from http://mtlab.biol.tsukuba.ac.jp/www/
PDB/Images/Ciliophora/Paramecium/aurelia/!
Davidson 1938!
From Case 2000!
Sheep introduced into Tasmania!
5!
Voles in Sweden!
Hornfeldt 1994!
From Case 2000!
http://www.natuurbeleving.be/zoogdieren/
Rosgrijze_Woelmuis_Clethrionomys-rufocanus.html!
ÇÈC:ST¿/'s!
6!
CÉ£Ê! DZËÌÍ!
Image from!
http://hp.brs.nihon-u.ac.jp/~ocean/kenkyu/hormone.html!
Daphnia magna!
Image from!
http://dmc.utep.edu/rotifer/html/nsp1.html!
Pratt 1943!
From Case 2000!
Halbach 1979!
From Case 2000!
7!
Image from http://www.xeye.org/1995-2000/
LemmZoo.html!
Lemmings!Dicrostonyx groenlandicus!
·C£¡:ST;K/!
mÎ�mÏY¹ÐvÑÎ�XYZ+1.ÒÏ!
From Case 2000!
8!
ÓÔÕ:Ö!!
Raggett 1982, Brown and Rothery 1993!
Outbreak of the Great Plague
in a village in England, late
17th century.!
350 �:l×&wØÙ8:Q 83�!
ÚÛ�ÜÝÔÞ;mÏ!
ßÛ�ÝÔÞ;mÏ!
9!
àáFQhxN:â�!
Bulmer 1994!
ÝÔÞ;Q 2 ãä»PK/!
Òåæç|mèéê.ëì!
10!
íç(:@ABCDEFîïGHN!
@ABCDEFdynamicsN�ð%v/ð%!
GHIIJ+KL7.�'vJh4QOê0ñò7.óÄ!
1 ST|)\:GHHôõ+ö»hcó÷hc2
ST+t.øù0ú2û7&Rüý0¥þ.ÿ !
G!"t! 0! 1! 2! 3!
O:1lt&R|m#7.xQOO
PQ$%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.!
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
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!
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.!
25!
$% 1!
Lack (1954) +1.©É:ST;2_:Y¹Ð!
ã! 1937! 1938! 1939! 1940! 1941! 1942!
ST;! 8! 30! 81! 282! 705! 1325!
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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!