Functional Mapping1. Model2. Material – rice doubled haploid (DH) population

Tall (AA) x short (aa)

Aa A a

AA aa 124 DH lines were planted in a randomized block

design in Hangzhou and Hainan

g(t) is the plant height;a is the asymptotic value;b is the parameter that describes the initial growth of plant height;r is the relative growth rate;k is the power at which the metabolic rate of an organ scales as the kth power of its weight.

Functional Mapping

lili gt ,

lkll

l

l

l

kak

b

r1

1

,1

ln1

=

Three developmental landmarks

First, Pi, the inflection point of growth curve

Hypothesis testsH0: How to estimate the parameters?

H0:

1

ln1

1ln

1

2

2

21

1

1 k

b

rk

b

r

21 1

1

221

1

11kk kaka

Second, P1, the first inflection point of growth rate curve

ll gt 11 ,

llkl

kll

l

li a

k

rt

l

l

111

11 ,

1

)1(ln

1

=

Third, P2, the second inflection point of growth rate curve

ll gt 22 ,

llkl

kll

l

li a

k

rt

l

l

212

12 ,

1

)1(ln

1

=

1

1

2,1 )12(2

)4()1()1(

lk

ll

llllll kk

kkkkk

Developmental Processes

(1) Exponential growth (0 to P1)(2) Linear growth (P1 to P2)(3) Ageing (P2 to the infinite)

Homework 3You have analyzed the rice data and obtained significant QTLs.

You draw genotypic curves using growth parameters

Next, you need to test the genetic effects of the QTL on

- Pi, the inflection point of growth curve- P1, the first inflection point of growth rate curve - P2, the second inflection point of growth rate curve- Exponential growth (0 to P1)- Linear growth (P1 to P2)- Ageing (P2 to the infinite)