Reproductive Allocation Patterns in Different ...

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investigated in populations of the annuaI plant,spring wheat(Triticum aestivurn).A series of ... ation(IRA)in plants grown at high densities,It has also.
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Jour nal   of   I nt egr at i ve  P『 anf   Bi ol ogy 2008,50( 2) :141-146 

Reproducti ve  Al l ocati on Pat t erns i n Di ferent   Densi t y 

Popul ati ons of  Spri ng  W heat   Ji ng Li u’, 一,Gen- Xuan  W ang  ,Li ang  W ei ’and  Chun- Mi ng  W ang’   ( ’ Key  Labor at or y  ofAr i d  and  Gr ass l and  Agr oec ol ogy  at   Lanzhou  Uni v er si t y,Mi ni st y  r of   Educat i on.Lanzhou   730000.Chi na   Cof l ege   ofLi f e  Sci ences,Zhe j i ang  Uni ver si t y,Hangzhou   31 0027, Chi na;   。I nst i t ut e  ofModem  Physi cs t he   Chi nese  Academy  ofSci enc es.Lanzhou  730000.Chi na)   ,

Abstr act   The efects  of  i ncr eased i nt r aspeci ic com pet f i ti on  on si ze  hi er ar chi es ( si ze i nequal i t y1   and r epr oduct i ve  al l ocat i on wer e 

i nves t i ga t ed  i n   popul at i ons   of   t h e  annuaI   pl an t ,spr i ng   whe at( T r i t i cum  ae st i vur n) . A  ser i es   of   densi t i es( 10 0,300 ,1   00 0,   3  000  and  1   0  000  pl ant s/ m )al ong  a  gr adi ent   of   compet i t i on  i nt ensi t y  wer e  desi gned  i n  t hi s  experi ment .The  r esul t s  showed  t hat   aver age  shoot   bi omass  decr eased  wi t h i ncr eased  densi t y.Repr oduct i ve  al l ocat i on  was negat i vel y cor r el at ed  t o  Gi ni  

coe怖 ci ent( R2=0. 927) 。whi ch  suggest ed  t hat   r epr oduct i ve  al l ocati on i s i ncl i ned  t o  decr ease  as  si ze  i nequal i t y  i ncr eases.   These  resul t s  suggest   t hat   bot h  vege ̄ti ve  and  e pr r oducti ve  st r uct ur es  wer e  si gni icant f l y  afect ed  by  i nt ensi ve  com peti t i on.   How ever,r esul t s al so i ndi cat ed t hat  t her e w er e di fer ent  r el at i onshi ps bet w een pl ant  si ze and r eproduct i ve al l ocat i on 

pat ter n  i n  di fer ent   densi t i es.I n  the  I owest   densi t y  popul at i on,l acki ng  compet i t i on( 100  pl ant s/ m ) ,i ndi vi duaI   r epr oduct i ve  al l ocat i on  was  si ze  i ndependent   but ,i n  hi gh  densi ty  popul at i ons( 300,1   000,3  000  and  1   0  000  pl ant s/ m ) ,wher e  compet i t i on  occurr ed.i ndi vi duaI   repr oduct i ve al l ocati on  was  si ze  dependent :t he  smal I  pr opor ti on  of   I ar ger   i ndi vi dual s wer e wi nner s 

i n compet i ti on and got  hi gher  r epr oduc ti ve al l ocati on ( 1 ower  mar gi nal  r epr oducti ve al l ocati on;MRA) ,and t he l ar ger   pr opor ti on of  sm al l er  i ndi vi dual s were suppr essed and got  I ower  r epr oduct i ve al l ocat i on ( hi gher  MRA) .I n concl usi on。   our   r esul t s suppo ̄ the pr e di ti c on  t hat   el evat ed  i nt r aspeci ic  f com peti t i on  w oul d r e sul t   i n hi gher   I evel s  of  si ze i nequal i t y 

and  decr e ased r e pr oducti ve  al l ocat i on( wi t h a negati ve r el ati onshi p bet w een t hem) .However ,deeper   anal ysi s i ndi cat ed  that   t hese  f r equency-and si ze- dependent   r epr oduct i ve  st r at egi es  w er e  not   evoI uti ona  r i I V  st abl e  str at egi es.  

Key  w or ds: c ompet i t i on;dens i t y;r epr oduc t i ve  al l ocat i on 

Li u  J,Wang GX,Wei   L,Wang  CM ( 2008) .Repr oduct i ve  al l oc at i on  p a ̄er ns   i n   di f f er en t   densi  ̄ popul at i ons  of   spr i ng  wh eat ,   I nt egr .P『 anf   Bi ol   50( 2) .1 41—146  Avai l abl e  onl i ne  at   wwW  j i pb, net  

I n pl ant  popul at i ons,i ncr easi ng densi t y  can i nt ensi f y pl ant - 

2000;van Kl eumen et  a1 .2001) .Among t hese com ponent s,  

pl ant  compet i t i on di ect r l y( Pi anka 1981) .Compet i t i on among 

si ze hi er ar chi es and r e pr oduct i ve out put  have been m ost l y  

pl ant s  i s  an  i m por tant   f act or   i n  af fect i ng  si ze  hi er ar chi es  f W ei ner  

i nvest i gat ed bec ause t hey ar e of  t r emendous ec o l ogi a l c  and 

1   985;Bonan 1   988;Pan  et   a1 . 2003alb) ,gr owt h  r at e( Ehl er i nger  

evol ut i onar y  si gni ic f a nce.  

1   984;W ei ner  and Thomas  1   992) 。sur vi vor shi p( W hi t e 1   98  1:  

I t  has l ong been r ec o gni zed t hat  si ze i nequal i t y al ways  

Tanner   1   997;van   Kl eunen  et   a1 . 2001),and  e pr r oduct i ve  out put  

l ncr eases  wi t h  l ncr easi ng  densi t y( W ei ner  1   985) .The  l ncr ease 

fEhl ennger  1   984;W ei ner   and  Thomas 1   992;Sot o— Pi nt o  et   a1 .  

of   si ze i nequal i t y may  afect  t ot al  r epr oduct i ve out put( Wei ner   1   985;Sugi yama  and  Bazzaz  1   997;Pan  et   a1 . 2003a,b) .W ei ner  

Rec ei ved 12  Sept.2006  Accept ed  20  M ar .2007 

( 1   988) pr esent ed a si mpl e l i near  model  of  si ze— dependent  

Suppor t ed   by   t h e  Nat i on al   Nat ur al   Sci enc e  Found at i on   of   Chi na( 30 730020.  

r epr oduct i ve out put  t o expl ai n t he decr e ase i n r e pr oduct i ve 

901 02015) ,863   pr oj ec t( 200 6AA100 202)an d  Coop er at i on   Pr oj e ct   Bet ween  

al l oc at i on( I RA)i n  pl ant s gr own at  hi gh densi t i es,I t  has al so 

Chi na   and   Gr eec e( 2003 DFB00034) .  

been r epor t ed t hat 。i n  wat er  def ici t  and m ul chi ng wi t h cl ear  

Aut hor   f or  Co ̄espondenc e.  

pl ast i c f ¨m condi t i ons i n spr i ng wheat( Tr i t i cum aest i vum)  

Tel : +8 6( 0) 571  8 820  6590;  

popul at i ons,t her e i s a negat i ve c o r r el at i on bet w een I RA and 

Fax:+86( 0) 571  88 20  6590;  

Gi ni  coef ici f ent( G)(Pan et  al ,2003a,b) .I t  was  suspect ed 

E・ mai l :<wanggx @z j u. edu   cn>.  

t hat   t hi s  negat i ve  cor el r at i on  w oul d  exi st   al ong an  el evat ed i n-  

⑧ 2008 I nst i tut e  of   Bot any.t he  Chi nese  Academy  of   Sci enc e s 

t r aspeci ic  f o m pet c i t i on  gr adi ent .Unf or t unat el y,di e ct r   evi dence 

doi :10. 1111   1744. 7909 2007. 00602, x 

i s  st i l l  l acki ng  t o  pr ove  t hi s  pr edi ct i on.Ther ef or e,i n  t he  pr e sent  

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142  Jour n al   ofI nt egr at i ve  P| ant   Bi ol ogy  Vo1 .50  No.2  2008 

∞∞母E o一 口 ooI |∞ c母 = 

exper i m ent 。we  desi gned a  wi de r ange  of   densi t i es  f or   f ur t her  

一 芒日I d, 6一  

anal ysi s.  

The pur pose  of   t hi s  st udy  was  t o  expl or e( 1)t he  el r at i onshi p 

2  

O  

8  

6  

4  

2  

O  

bet ween  si ze i nequal i t y  and RA i n  a wi de r ange o f  densi t i es  f r 0m no com pet i t i on t o  i nt ensi ve com pet i t i on f i n whi ch pl ant s 

under went   sel f - t hi nni ng)and( 2)si ze- dependent  r epr oduct i ve  al l ocat i on pat t er ns   i n  di fer e nt   densi t i es.  

Pl ant   si ze( g)  

Resul t s  Si ze  i nequal i t y  Aver age shoot  bi om ass  per  pl ant   decr e ased w i t h i ncr easi ng 



 

densi t y at  20 June ( Fi gur e 1) ,whi ch means t he i ncr eased 

: } :  

st r engt h of  i nt r aspeci ic  f com pet i t i on suppr essed pl ant   gr owt h.  

j}   五  ‘, ,  

Pl ant   si ze( g)   1  000 pl ants Derm2 



 

器 

一 6)  zI ∞m兰A∞ 

里  ‘, , 

100 

300  1 00o 30o0  10000 

Densi t y 

Fi gur e  1.Mean pl ant  bi omass ( ab ove- gr ound)i n  di fer ent  densi t y  

、一

 

器 

tr eatment s  at  20 June.  

旦 

0. 加 

■ 10  000,m 2 

◆ 3 000,m 2 

O 300,m 2 

口 100/m 2 

▲ 1 000/m 2 

五  ‘ , ,  

0.35 

0. 30  一

《 

 

器 

芷  0. 25 

丽 

卫  0. 20 

五  ‘ , ,  

0. 15 

Pl ant   si ze( g)   0.10  0 

0. 1  

0. 2 

0. 3 

Gi n  i  coeffi clent 

Fi gur e  3.Li near   r el at i ons hi p  bet ween   s pi ke  si ze  and   pl ant   si z e( above-   gr oun d  bi omass)i n  di fer ent   sp r i ng   wheat   popul at i ons   at   20  June.  

Fi gure 2.Rel ati onshi ps bet ween Gi ni  coeff ici ent s of spri ng wheat  

O i ndi cates i ndi vi dual s wi t h spi kes whi ch were  used i n f it t i ng t he l i ne;口 

popul at i ons and  r epr oduct i ve  al l oc at i on( RA)( dat a at  20  Jun e) .The 

i ndi a t c es  bar ren i ndi vi dual s  whi ch wer e excl uded i n f iti ng  the l i ne.See 

regr essi on l i nei sy=一1. 464x+ 0. 5221,R2= 0 927.  

Tabl e  2  for   regressi on c o ef i ci ent s.  



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Repr oduct i ve  Al l ocat i on  Pat t er ns  i n  Di fer ent   Popul at i ons  1   43 

Tabl e 1.The mean cl i mat i c condi t i ons of  t he  exper i ment aI  si t e i n  Chi na( dat a fr 0m  Lanzhou met eor ol oai caI  adm i ni st r ati on 

Tabl e  2.Par amet er s   of   l i near   r egr essi on bet ween   spi k e  s i ze( Y)an d  pl ant   s i ze( above— gr oun d  bi omass,x)f or   i ndi vi dual s   of   spr i ng  wheat   i n  di f f er ent   densi t i es at   20 June 

Themodeli sY= alx+ bl  

“ Number   of  baden i ndi vi dual s  i n  the sampl e To f it   t he  model ,t he baden  i ndi vi dual s  wer e excl uded 

I RA was negat i vel y cor r el at ed t o G  of  t he popul at i on  

Reproduc ti ve  al l ocat i on  and  si ze  st ruct ur e 

( 尺 =0. 927,Fi gur e 2) .The negat i ve corel at i on suggest s  t hat   I RA  i s i ncl i ned t o decr ease as  si ze i nequal i t y i ncr eases.Thi s 

Wei ner( 1988)pr esent ed a  si mpl e  I i near  modeI( WR= aVVp+ 

r esul t  suppor ts  t he  t heo ̄ t hat   st and  uni f or mi t y  of   iel f d cr ops  i s 

b) bet w een wei ght  of  pl ant  r epr oduct i ve st r uct ur e( spi ke  bi omass,WR)and pl ant  si ze( shoot  bi omass,Wp)t o expl ai n 

an  i mpor tant   aspect   of   hi gh  yi el d  f or mat i on( Gl enn  and  Daynar d  1974) .  

t he decr ease i n I RA i n pl ant s gr own  i n hi gh densi t i es.He  suggest ed  t hat   pl ant s   m us t   r each  a  cer t ai n  si ze  bef or e  t hey  can  devot e  ener gy  t o  r epr oduct i ve  bi om ass.Thus,t he  sl ope  and  t he 

Si ze- dependent   r epr oduct i ve  al l ocat i on 

x- i nt er cept  of   t he I i near  m odeI  shoul d be posi t i ve.The I i near   r el at i onshi p was  conf ir m ed i n al I  of  t he f ive densi t i es i n  t he 

To i nvest i gat e t he r el at i onshi ps bet w een I RA  and pl ant  si ze 

pr esent  st udy.except  t hat  t he x- i nt er cept  f or  1   00 pl ant s/ m 

and bet w een  spi ke si ze and pl ant  si ze.dat a f r Om 20 June 

was   negat i ve( Fi gur e  5,Tabl e  3) .Pan  et   a1 .( 2003a)devel oped 

w er e anal yzed,w hen spr i ng wheat   i s  at   t he  gr ai n  il f l i ng st age 

W ei ner ’ s   t heor y   and t r ansf or m ed  t he  f or m ul a  as  bel ow :  

and no i ndi vi dual s  have di ed because of   r i peni ng.For  al I  f ive 

RA = VV R/VV p = e+ b}VV p  

popul at i ons,spi ke  si ze  i ncr eased  l i near l y  wi t h  pl ant   si ze( above-   gr ound bi omass)( Fi gur e 3,Tabl e  2) .Meanwhi l e,I RA  i ncr eased 

W her e  e  i s  def ined  as  i nnat e  I RA . w hi ch   r epr esent s   t he  m axi m um 

i nver sel y  wi t h  pl ant   si ze i n  t he f our   com pet i t i ve  densi t i es ( 300,  

I RA ( I RAma x)of   t he speci es.The sl ope of   t he i nver se  cur ve i s 

1   000,3  000,and 1   0  000 pl ant s/ m )( Fi gur e  4,Tabl e  3) .Appar -  

t he  addi t i onaI  I RA  f r om each addi t i onaI  uni t   of   t he W  ,w hi ch  i s  

ent l y.i ndi vi duaI  spi ke  si ze and RA  i n com pet i t i ve popul at i ons  

def ined  as   mar gi na  J   r epr oduct i ve  al l ocat i on( MRA。侧

i n spr i ng wheat  w er e si ze- dependent .However .at  a densi t y 



/dWp= 

6/x2) .MI RA i s  an i ndi cat or  of  r epr oduct i ve pot ent i al i t y.The 

Of  1   00 pl ant s/ mz. I RA  kept  c o nst ant  i n di fer ent  pl ant  si zes 

decl i ne i n M I RA  as pl ant  si ze i ncr eases  i s  cal l ed di mi ni shi ng 

( Fi gur e  4,Tabl e 3) .So,when  t he  popul at i on l acks   compet i t i on,  

mar gi naI   r epr oduct i ve  al l ocat i on  f Pan  et   a1 .2003a) .I t   i s   bel i eved 

i ndi vi duaI   I RA  i s  si ze- i ndependent .  

t hat  t her e i s a t r ade- of bet w een pl ant  si ze and MI RA.and a  popul at i on  m ust   consi s t   of   a  I ar ge  pr opor ti on   of   sm al Ii ndi vi dual s  wi t h hi gh  MI RA   and a  sm al I   pr opor ti on of   I ar ge i ndi vi dual s  wi t h  

Di scussi on 

I ow  MI RA .These  f r equency-and si ze- dependent  r epr oduct i ve  st r at egi es i n pl ant  popul at i ons  ar e consi der ed t o be a good 

Four  com pet i t i on I evel s wer e i nves t i gat ed i n t hi s st udy:(1)  

exampl e  of   evol ut i onar i l y  st abl e  st r at egy( ESS) .However ,t her e 

no compet i t i on ( popul at i on sown at  1   00 pl ant s / m  ( 2)sl i ght   compet i t i on( popul at i on sown  at  300 pl ant s/ m  ( 3)i nt er medi -   at e compet i t i on( popul at i on  sown at  1   000 pl ant s/ m2) :and ( 4)  

ar e s ever aI   de ci enci es  i n  t hi s  cont ent i on.  

i nt ensi ve  o m pet c i t i on  f popul at i on  sown at  3  000 pl ant s / m  and 

r epr oduct i ve abi l i t y. The di mi ni shed M I RA m eans t hat  l ar ge 

1   0  000 pl ant s/ m   w hi ch  under w ent  sel f . t hi nni ng i n t he  gr owth  

i ndi vi dual s  have hi gher  i ndi vi duaI  f it ness.and c a n gener at e 

per i od) . The  r esul t s   i ndi at c ed  t hat   t he  r el at i onshi p  bet w een  pl ant  

ofspr i ng mor e successf ul l y.Smal Ii ndi vi dual s ar e  weak com-  

si ze  and  I RA   of   t hese  popul at i ons  devel oped i n   di fer ent   w ays.  

pet i t or s   wi t h  hi gh  MRA.I f   ot her   i ndi vi dual s   gi ve  up  o mpet c i t i on.  

I   n  com pet i t i ve popul at i ons.1 ar ge i ndi vi dual s  ar e st r ong c o m-   pet i t or s  and t hey have t he chance t o ut i l i ze al I   t hei r  pot ent i aI  

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144  Joumal   ofI nt egr at i ve  f anf   Bi ol ogy  Vo1 .50  No.2  2008 

t hey  wi l Ii m pr ove  t hei r   RA.However ,i n  dense  popul at i ons.sm al I  

100 pl ants per  m 2 

i ndi vi dual s  r i sk  densi  ̄- dependent  mor t al i t y mor e t han I ar ge 

i ndi vi dual s( Wei ner   1   985) .Mor eover ,spr i ng  wheat   i s  an  annuaI   sem el par ous   speci es.and  t hi s  det er mi nes  t hat   sm al I i ndi vi dual s   wi t h  hi gh  M RA  have  I i t t l e  chance  t o  i m pr ove  t hei r   RA.So i n  t hi s  .

exper i m ent .t he  di mi ni shed MRA  i s  not   bad  f or   I ar ge  i ndi vi dual s  and  hi gh  M RA  i s  not   good  f or   sm al Ii ndi vi dual s.That   i s.t r ade. of 

bet ween  pl ant   si ze and  MRA  i s  i nval i d.  

A  st r at egy  or   st r at egy   mi xt ur e  t hat   cannot   be  i nvaded  by   novel  

Pl ant   s‘ i ze( g)  

st r at egi es  i s  cal l ed  an  evol ut i onar i l y  st abl e  st r at egy(ESS  or   ESS 

300 pl antsp e rm2 

mi xt ur e;Fal st er   and  W est oby   20031. So  we  can  t est   a  popul at i on 

0. 4  O. 35 

f 0r  ESS by  whet her  i t  has t he c a paci t y  t o excl ude al t er nat i ve 

O. 3 

st r at egi es f r Om i nvadi ng.Pot ent i al  i nvadi ng st r at egi es  a n be  c

叠。 震 

t hought  of  as  r ar e mut ant s wi t hi n t he exi st i ng popul at i on,or   as  i ni t i al l y  r ar e speci es  col oni zi ng f r Om el sew her e.I t   has  been 

O. 15  O.1  

wi del y  r ecogni zed t hat   m oder n seed cr ops,w hi ch ar e  seeki ng 

O. O5 

m axi m um popul at i on yi el d, ar e evol ut i onar i l y unst abl e. and 

O 

r equi r e  ongoi ng ar t i ici f aI   sel ect i on  t o  mai nt ai n  t he  evol ut i onar i l y 

Pl ant   si ze( gJ  

unst abl e st r at egy ( Zhang et  a1 .1   999;Fal st er  and West oby  2003) .I n t hi s  st udy.t he  ̄equency.and si ze. dependent  r e.   pr oduct i ve s t r at egi es i n dense spr i ng w heat  popul at i ons  ar e  evol ut i onar i l y unst abl e t oo.bec a use nei t her  l ar ge pl ant  si ze  wi t h hi gh  r epr oduct i ve capaci t y nor   sm al I  pl ant  si ze wi t h  I ow 

《  正 

r epr oduct i ve capaci t y i s  a successf uI  st r at egy. Fur ther m or e.   i n sel f - t hi nni ng popul at i ons, t he l at t er  st r at egy w i l l  be el i mi -   nat ed f r Om ser i ousl y com pet i t i ve popul at i ons.and t he f or m er   st r at egy w i l I  f a. 1  w hen i t  f aces a m or e com pet i t i ve st r at egy   such as  a m ut ant  t hat  has devel oped l ar ge pl ant  si ze and 

Pl ant   si ‘ ze( g)  

I ow RA.So t hes e st r at egi es at e not  st abl e agai nst  i nvasi on 

3000pl antsp e rm 2  

by r ar e mut ant  or   devi ant  st r at egi es.I n f act .wi t hout  ar t i ici f aI   m anagement ,most   cr op popul at i ons  wi l l  be  r epl aced by ot her   wi l d speci es,or   wi l I  be  r epl aced by  m or e  com pet i t i ve m ut ant s.   《  正 

Si ze- dependent   r epr oduct i ve  al l ocat i on paRer ns  i n  di fer ent   densi t i es 

Pl ant   si ze( g)   I n  t hi s  st udy.di fer ent   si ze- dependent   r epr oduct i ve  pa ̄er ns  ar e 

10000 pl antsp e rm 2  O. 4 

show n am ong t he di fer ent  densi t i es, J n popul at i ons w i t hout  

compet i t i on( 1   OO  pl ant s / m2) ,al l   member s( 1 ar ge  ones  and  smal l  

O. 3 

ones)c a n  devel op  t hei r   maxi mum  pot ent i al   r epr oduct i ve  abi l i t y,  

《 

n- 0 2 

so MRA i s  equal   t o zer o(Fi gur e 4,Tabl e 3)and t hei r   r epr o-  



duct i ve pa ̄er ns ar e si ze- i ndependent .Thi s i m pl i es  t hat  pl ant  

O. 1  

RA i s  det er mi ned by i nt r i nsi c pr oper ti es w hen com pet i t i on  i s   O  O 

O.5 

1 

1. 5 

Pl ant   si ze( g)  

l acki ng.I n  t he  hi gher   densi  ̄ popul at i ons( 300,1   000, 3  000,and 

1   0  000  pl ant s/ m )wi t h  compet i t i on,as   f ound by  W ei ner(1   988)   and Pan  et   a1 .( 2003a,b) ,t her e ar e si gni ic f a nt   cor r el at i ons  be-  

Fi gur e 4.I nver se r el at i onshi p bet ween  RA and  pl ant  s i ze ( above-   gr ound   bi omas s)i n  di fer ent   spr i ng   wh eat   popul at i ons   at   20  Jun e.  

teen  w pl ant   si ze and r epr oduct i ve  st r uct ur e( Fi gur e  3,Tabl e  2)   and bet w een pl ant  si ze and RA ( Fi gur e 4,Tabl e 3).Among  t he hi gher  densi t y t r eat m ent s, t he i ncr eased si ze i nequal i t y 

◇i ndi cates i ndi vi dual s wi t h spi kes  whi ch  were used i n  it f ti ng  the l i ne;口 

suggest s  t he pr opor ti on of  sm al I  pl ant s i ncr eased and t he 

i ndi cates barr en i ndi vi dual s whi ch  wer e excl uded i n f iti ng  the  l i ne.See 

pr opor ti on of   I ar ge pl ant s decr eased.So i t  i s  t he sm al I  ones  

Tabl e  3  f or   e gressi r on coef ici f ents.  

t hat  m ai nl y cont r i but e t o t he gr eat  gr owt h r edundancy, f or  

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Repr oduct i ve  Al l ocat i on  Pat t er ns  i n  Di f f er ent   Popul at i ons   145 

Tabl e  3.Par amet er s( 士SE)of   i nver se  r egr essi on  bet ween  RA( y)and  pl ant   si ze( ab ove- gr ound  bi omass, x)f or   i ndi vi dual s  of   spr i ng   wheat   i n  di fer ent   densi t i es  at  20  June 

The modeli s Y = b2i 1+ a2   ” Number   of   barr en i ndi vi dual s i n t he  sam pl e.To  it f   the  model ,the  baren i ndi vi dual s wer e  excl uded 

t he sm al I  ones  had r el at i vel y I ow er  RA I n t he hi gher  densi t y 

ur ea  and  O. 2% pot assi um  di hydr o gen  phosphat e  per   pl ot   ever y 

t r eat m ent s. Fur t her m or e. t he i ncr easi ng pr opor ti on  of  sm al I  

w o  t weeks)wer e  added  dur i ng  t he  gr owt h  st age.  

pl ant s( wi t h  l ower  RA)caused t he aver age RA t o decr ease 

Pl ant s gr ow n I n t he c e nt r aI  pl ot   w er e har v est ed at  gr ound 

al ong t he densi t y gr adi ent .So I t  c a n be concl uded t hat   t her e 

I eve1 .1   OO一1   5O  I i ve  I ndi vi dual s  wer e  r andom l y  col l ect ed  f r 0m  t he 

ar e  negat i ve  cor r el at i ons  bet ween  si ze  i nequal i t y( as   measur ed  by Gi ni   coef ici ent )and  RA ( Fi gur e  2)wi t hi n  t hese  compet i t i ve 

t hr ee  pl ot s.The  i ndi vi dual s  wer e  put  i n paper   bags  separ at el y,  

popul at i ons.  

was  c al cul at ed f or  each pl ot  f t ot aI  sam pl e si ze 1   OO一1   5O i n 

I n  concl usi on,t hi s  st udy  suppor ted t he  pr edi ct i on( Pan  et   a1 .  

dr i ed( 65。C,48  h) ,and wei ghed.Dr y shoot  bi omass  per   pl ant   each t r eat m ent  f or  c a l cul at i ng G i nI  c o ef i ci f ent . but  40-70 I n 

2003a1  t hat  el evat ed i nt r aspeci ic com pet f i t i on woul d r esul t  I n  

1   OO  pl ant s/ m  pl ot s) .Shoot  bi omass  and spi ke bi omass ( f or  

hi gher   I evel s  of   si ze  i nequal i y  t and  decr eased  RA.Ther e  wer e 

cal cul at i ng RA  whi ch  I s   equaI   t o  spi ke bi omass/ shoot   bi omass1  

al so  I nver se  cor r el at i ons  bet w een  pl ant   si ze  and RA  I n  com pet .  

of   each pl ant   wer e  w ei ghed  separ at el y.  

i t i ve  popul at i ons.These  f act s  i m pl y  t hat   r epr oduct i ve  st r at egi es 

Hi er ar chi es  wer e  def ined  I n  t er ms  of   t he  degr ee  of   i nequal i y  t

i n  o m pet c i t i ve  popul at i ons  ar e  f r equency—and si ze— dependent .  

G  I n  t he  f r equency  di st r i but i on  as   m easur ed  by  t he  Gi nI   coef i ci f ent  

However .we ar e not  yet  cer tai n t hat  t hey ar e evol ut i onar i l y 

f Wei ner  and Sol br i g 1   984) .Gi nI  c o ef ici ent s r ange f r 0m O 

st abl e,bec a use  t her e  was no evi dence  t o pr ove  t hat  t hey  a n  c

∑  ( absol ut e  equal i t y i n  t he  f r equency  di st r i but i on)t o 1( absol ut e 

excl ude ot her  com pet i t i ve st r at egi es, especi al l y i n ar ti ici f al l y 

i nequal i t y)( Bonan 1988).The Gi ni  c∑  oef ici ent( G)was  cal cu-  

m anaged  popul at i ons.  

I at ed  usi ng  t he  f or m ul a:  

= 

坼 

|  

、  

f /( 2 n   - x )  

Mat er i al s and Met hods 

l  

W her e  xi   and xj  r epr esent   t he masses of   al I  possi bl e pai r s  of  

Fi el d exper i ment s wer e conduct ed I n t he year  of  2003 at  

Yuzhong  exper i ment al   st at i on   of   Lanzhou  Uni ver si t y( 36。O3 N,  

1O3。53 E and 1517 m I n al t i t ude) .The mai n cl i mat i c c o ndi .   t i ons ar e pr esent ed I n Tabl e 1.The sol I  I s a I oess. 1 i ke I oam .  

wi t h a bul k densi y of t  1. 37 g/ cm3,and a f iel d wat er - h0I dI nq 

l ndi vi dual s.and  n  I s  t he  sampl e  si ze.Cal cul at ed  G  val ues  wer e 

mul t i pl i ed  by  n/( n一 1   1   t o  gi ve unbi ased  val ues  G  .Conf idenc e  I nt er v al s f or  Gi nI  c o ef i ci f ent s  w er e  det er mi ned usi ng a ‘ boot —  

st r appi ng’t echni que f Wei ner  1   985;Di xon  et  a1 .1   987) .I n  t hi s  st udy.G was  a l c cul at ed f or   each of  200 ar ti ici f aI  sam pl es  of  

a paci c t y( FW HC,maxI mum  a pi c l l ar y— hel d  wat er )of   25% ( gr avi —  

t he same si ze as  t he or i gi naI  sam pl e.whi ch ar e t aken f r om 

met r i al c l y) .Hi gh or gani c f er ti l i zer  i nput s wer e added t o t he 

t he  or i gi nal  sampl e  wi t h  r epl ac e ment .Conf idence  I nt er v al s  f or  

exper i m ent al   pl ot   bef or e  sow i ng.  

Seeds  of   spr i ng wheat(   衔cum aest i vum L. ,cv.Longchun  No. 151  wer e spr i nkl ed I n pl ot s  each 50 cm  x  50  cm  at  f ive 

G val ues  ar e det er mi ned f r 0m t he  di st r i but i on  of   G val ues   f or  

t hese boot st r apped sam pl es  usi ng a  bi as— corect ed per cent i l e  m et hod.  

densi t i es ( t hr ee r epl i at c es wer e used I n each densi y) t :1   OO,   300.1   000.3  000  and 1   0  000  seeds/ m 2.The  t ot aI   I r r i gat i on  was  5O m m  x  5.Rai nf a¨dur i ng t he per i od f r 0m sowi ng  t o t he I ast  

Ref erences 

har vest  was 229  mm ( Tabl e 1).Sowi ng occur r ed 0n 1   8—2O  M ar ch 2003,and har v est  was t aken on 20 June.The pl ot s  wer e sur rounded by suppor ts of  wi r e net ti ng t o pr event  t he 

pl ant s  f r 0m l odgi ng ( especi al l y i n hi gh  densi t i es)and 25  cm  guar d  r ows   wer e  pl ant ed  t o  avoi d mar gi naI   efect s.Pl ant s   wer e 

spr ayed wi t h chl or pyr i phos( Dow Agr osci ences,USA)agai nst  

Bonan  GB ( 1 988) .The  si z e  st r uct ur e  of   t heor et i cal  pl ant  p opul at i ons   spati al  pat ter n s  and nei ghbor hood efect s.Ecol ogy  69,1721-1730 

Di xon   PM, W ei ner   J,Mi t chel I - OI ds  T, W oodl ey  R( 1987) .Boot st sr ap-   pi ng t he  gi ni  c o ef ici f ent   of   i nequal i t y.Ecol ogy  68.1   548—1   551.  

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pest  atack and st r ept omyci n sol ut i on  agai nst  bact eri a.Hi gh 

t i ons,gr owt h and repr oduct i on i n Encel i a f ari nosa.Oec ol ogi a 63,  

f er ti l i zer  i nput s( i r r i gat ed wi t h 500  mL sol ut i on c o nt ai ni ng 1% 

153—158.  

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van  Kl eumen  M。Fi scher   M。Schmi d  B( 2001) .Efec ts   of   i n t r aspeci i f c 

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competi t i on  on si ze var i ati on and  reproduct i ve al l oc a t i on i n a cl onal  

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on wi thi n-pl ot   vanabi l i t y i n gr ow t h and gr ai n yi el d of  spri ng wheat   i n 

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( Handl i ng  edi t or :Da- Yong  Zhang)  

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