FUNCIÓN CATÁRTICA

The gene rat ion mean analys i s i s used t o s tudy gene e f fects by us ing dif f e rent generat ions de rive d f rom a cross between homo zygous

pa rent s . The analys i s a ims to detect the e f fect s of spe c i f i c t ypes o f

gene action and t o e s t imate the cont ribution o f a part ic u l a r component to the ove r a l l va riat ion ( Snape , 1 9 8 7 ) .

The most c ommon e xpe rimenta l st ructure i n wheat i s t o use t he e a rly f i l i a l generat ions der ived by intercros s ing and s e l f ing the p a rents and t he i r F 1 s . This produces s ix gene rations : P 1 ( t he h igher s co re parent ) , P 2 (the lowe r score pa rent ) , F 1 , F2 , B 1 (backcross o f t he F 1 to t he h i gher s core pa rent ) a n d B2 (backcross o f t he F 1 t o the lower-score pa rent ) . More c omplex expe r iment s can be p roduced by the

inter cross ing and sel f ing these gene rat ions f u rthe r ( Snape , 1 9 8 7 ) .

Hayman ( 1 9 5 8 ) proposed that if the t wo inbred lines d i f f e r by any

number o f unlinke d genes the expectat ions o f t he i r , and s ome o f t he i r

de scendant , f ami ly and gene ration means may be expressed a s

p 1 m + d ( 1 / 2 ) h + i - j + ( 1 / 4 ) l p 2 m - d ( 1 / 2 ) h + i + j + ( 1 / 4 ) l F 1 m + ( 1 / 2 ) h + _{( t /4) l} F 2 m B 1 m + ( 1 / 2 ) d + ( 1 / 4 ) i B2 m - ( 1 / 2 ) d + ( 1 / 4 ) i F 3 m - ( 1 /4 ) h + _{( 1 / '1 6 ) l} B 1 S m + ( 1 / 2 ) d - ( 1 / 4 ) h + ( 1 / 4 ) i - ( 1 / 4 ) j + ( 1 / 1 6 ) l B2 S m - ( 1 / 2 ) d - ( 1 / 4 ) h + ( 1 / 4 ) i + ( 1 / 4 ) j + ( 1 / 1 6 ) l F 4 m - ( 3 / 8 ) h + ( 9 / 6 4 ) l i . e . mean m + ad + �h + a2 i + 2 a� j + �2 1

P 1 and P 2 a re the means o f the two pa rent f amilies and F 1 i s the mea n of their p r ogeny . F2 , F 3 and F 4 a re t he means o f t he gene rat ions des cending f rom t h i s c ross by s e l f ing . s 1 and s2 are the means of the two backcrosse s . s 1 s and s2 s a re the means o f the progeny o f s e l f ing the f i rst two backc ross fami l ie s .

The gene t i c pa rameters d , h , i , j , 1 have the f o l owing

mean ings :

and

d pooled a dd i t i ve e f fec t s ; h pooled dominant e f fect s ;

i pooled interact ions between addit i ve e f fects ;

j pooled interact ions between addit i ve and dominance e f fe c t s

1 pooled interactions between dominance effect s .

When more than one loci a re invo lved i n t he charac t e r unde r

cons i de rat ion, the inc reas ing a l leles may occur togethe r in one o f the t rue breeding pa rent s and the decreas ing a l leles in the othe r . I n this case t he di s t r ibut ion o f the gene s a re a s soc iated . On the other hand if each pa rent c a r ies the increas ing a l le l e of one gene and the decreas i ng a l le l e o f the othe r , the dis t r ibut ion o f the gene s a re in the d i spe rs ion s t a te ( Hayman and Mathe r , 1 9 5 5 ; Mather and Jink s , 1 9 7 1 ) . Unde r t he d i spe rs ion s t a te the genes t end t o ba lance one anoth e r out , so the addit ive e f fect is the sum o f addit ive e f fe c t s at a l l l oc i , taking s ign into account . S imi l a r l y the dominant e f fect , i s the sum o f dominant e f fects o f individu a l genes tak ing s ign into account . But for dominant e f fect the s ign o f " h " does not depend on gene a s sociat ion n o r d i spers ion but on the d i rect ion o f the dominance i t sel f ( Hayman and Mathe r , 1 9 5 5 ; Mather and Jink s , 1 97 1 ) . Snape

( 1 9 8 7 ) po inted out a p roblem in interpret ing the ana lys i s o f

generat ion means i n that the e f fects a re the ba lanced e f fects o f a l l s egre ga t ing loc i .

G amble ( 1 9 6 2 ) used the s ymbols " a " f o r a dditive e f fect s , " d" f o r dominance e f fect , " aa " f o r addit ive b y add i t i ve interact ion, " ad" f o r a ddi t ive x dominance inte ract ion , and " dd" f o r dominance x dominance

interact ion . The pa rameters for the v a r ious gene e f fects used by Gamble ( 1 9 62 ) can be re lated with those used by Anderson and Kemptho rne ( 1 9 5 4 ) and by Hayman ( 1 9 5 8 ) as f o llows :

Gene e f fe c t Gamble

Mean m

Addit ive a

Dominance d

Additive X addit ive a a

Addit ive X dominance ad

Dominance x dominance dd

Ande rson and Kempthorne K2 E + F 2 E G + L + 2 G + L 4 G Hayman m d h M i j 1

Ande rson and Kempthorne ( 1 9 5 4 ) set t he genet ic a s s umpt ions i n the development of t he i r gene t ic mode l a s f o l lows :

1 ) multiple a l le les absent ; 2 ) linkage absent ;

3 ) _{lethal genes absent ;}

4 ) constant viability for a l l genotypes and

5 ) envi ronment e f fects addit ive with genotypic va lue .

Assumpt i on 5 cou ld ha rdly be va l i d in many experiments when genotype x envi ronment int e raction is impo rtant . The use o f

population means ave raged ove r environment s w i l l reduced the b i a s i n e s t imates the gene e f fects (Gamble , 1 9 6 2 ) .

When genotype x environment inte ract i on exi s t s , the mode l f o r

gene rat ion means can include new pa ramete r s . The parameters a re

e = _{environment a l e f fect s ;}

ae addit i ve x environment e f fect ;

de dominance x envi ronment e f fect ;

aae = ( addit ive x addit ive ) x envi ronment e f fect

etc .

Mather and Jinks ( 1 9 7 1 ) expre ssed the expected gene rat ion means with a mode l s imi l a r t o the m9del proposed by Hayma n ; but us ing Fro gene ration, which is t he populat ion o f all i nb red l ines de rived f rom the cross of two i nb re ds , as a background mean instead o f the F2 gene rat ion .

Gene ration mea n a na lys i s has been w ide ly used t o est imate the

genet ic pa rame t e r s f o r va rious cha racte rs in many crops . In whea t it

has been used to s t udy the inhe rit ance of phot ope riod response and ve rn a l i zat ion response (Klaimi and Qua l s e t , 1 9 7 3 , 1 9 7 4 ) , the

inhe r i t a nce o f ke rne l we ight ( Bhat t , 1 9 7 2 ; Sun et al . , 1 9 7 2 ) ; t o s t udy

gene e f fect s f o r heading date and plant height (Amaya e t al . , 1 9 7 2 ;

Bhatt , 1 9 7 2 ; Edwa rds e t al . , 1 9 7 6 ; Keta t a e t a l . , 1 9 7 6 ) , yield and yie l d component s ( Chapman and McNe a l , 1 9 7 1 ; Amaya et a l . , 1 97 2 ;

Edwa rds et al . , 1 9 7 6 ; Ketata et al . , 1 9 7 6 ) , and grain p rote in ( Ch apman

and McNea l , 1 9 7 0 ) ; and to est imate the gene e f fects f o r a-amylase in the wheat grains ( Ga le , 1 9 7 6 ) .

Gale ( 1 97 6 ) p roposed the mode l for gene rat ion mea n analys i s o f GA3 - i nduced a-amy l a se i n the wheat gra i n . H i s model cons idered the inhe rit ance o f this cha racter i n t riploid s c a le . The ma i n d i f fe rence in t he endosperm model ( or t riploid sca le ) f rom the diploid model i s that heterozygotes c a n deviate f rom the mid-pa rent even in the absence of dominance , and that there a re two di st inct intra a l le le int e ract ion component s , " h 1 " and " h2 " . The two mode l s a re presented in Figu re 2 .

scale a a aA 0 AA r - - -- - r - - - -- - - r - - - --- - - - - r < - - - h- - - -> < - - - -- - -a - - - ->< -- - - -- - +a--- - - -> scale

a a a aaA 0 aAA AAA

r - - - r - - - --- r - - - r - - - r - - -- - - - r - - - r

< --h2 --> < --h 1 - -- >

< - - - -a - - - ->< - - - - +a -- --- - - - -- ->

2 . The genotypic va lues o f the homo z ygote s and t he

The triploid model f itted the data bet t e r than t he diploid mode l f o r GA3 i nduced a-amylase (Gale, 1 9 7 6 ) .