Population: The term can refer to a breed, an entire species, a single herd or flock, or even a small group of animals within a herd.

(1)

POPULATION PARAMETERS

 Population: The term can refer to a

breed, an entire species, a single herd or flock, or even a small group of

animals within a herd.

(2)

 Sample: A sample is defined as a

smaller set of data that is chosen and/or selected from a larger population by using a predefined selection method. The sample usually represents a manageable size from the population.

(3)

1 n

)2 x n - (x 2 ...

) x 2 - x 2 ( ) x 1- 2 (x

s 



 

Variance

s2

s 

n )2 x1 x s Σ( 

Standart deviation 

Variation coefficient .100 x

%v  S

Standart error

n S Sx

n S2

S_x2    Variation range R = X_max – X_min

POPULATION AND SAMPLE

(4)

DISTRIBUTIONS

Normal distribution

(5)

CORRELATIONS

 Phenotypic correlations (r_P)

 Genetic correlations (r_G, r_A)

 Environmental correlations (r_E)

(6)

1. Phenotypic correlations

Cow number

X trait chest girth

(cm)

Y trait Live weight

(kg)

1 136 200

2 138 208

3 130 190

4 135 202

5 138 200

6 140 220

7 132 190

8 150 190

2 2

2

Sy Sx

n y xy x

n y y

n x x

n y xy x

rxy





 





 

 





 







 







 





r_xy = + 0.965

(7)

2 2

Sx

n y xy x

n x x

n y xy x

bxy



 



 





 







 





b_yx = 2.658 kg

Regression

Cow number

X trait chest girth

(cm)

Y trait Live weight

(kg)

1 136 200

2 138 208

3 130 190

4 135 202

5 138 200

6 140 220

7 132 190

8 150 190

(8)

2. Genetic correlations

The reasons for

genetic correlations

 pleiotropy

 linkage

 selection

(9)

3. Environmental correlations

 Environmental factors can affect any two characters in the same or opposite direction, causing positive or negative correlations between these characters.

(10)

r_p=h_x h_y r_A+e_x e_y r_E

1 hx2

ex   ^e_y ^ ¹^^h_y²