When corn plants are too tall, they lodge (topple over) prior to harvest. this is bad since the grain is often lost when it cannot be picked up off of the ground by mechanical harvesters. you have a high-yielding strain of corn, but the plants often lodge. you want to estimate broad-sense heritability for % lodging in corn. you start by mating two inbred lines to produce an f1 generation. the f1 was allowed to intermate to produce an f2 generation. the variances for each generation are given below:

variance of inbred line 1 = 311
variance of inbred line 2 = 333
variance of f1 = 316
variance of f2 = 1153

what is the phenotypic variance?
what is the environmental variance? round to the nearest whole number.
what is the genetic variance? round to the nearest whole number.
what is the broad-sense heritability? round to three decimal places.

The phenotypic variance= 2113

The eenvironmenal variance= 644

The genetic variance= 1469

The broad-sense heritability = 0.695

Explanation:

To determine the phenotypic variance, we need to know the calculate the environmental variance and the genetic variance first;

because Phenotypic variance = V(p) such that;

V(p) = V(e) + V(g)                  

where V(e)  =  environmental variance and V(g)   =  genetic variance

Therefore, Environmental variance can be defined as a portion of phenotypic variance due to differences in the environments to which the individuals in a population have been exposed. The total amount of variance observed is dependent on the genetic component, determined by the variation that is inherited.

This implies that V(e)= initial variance which was there in the parents ( i.e  Variance of inbred line 1 = 311  and Variance of inbred line 2 = 333 )

V(e) = (311 + 333) = 644

Genetic Variance simply refer to the variance that occurs or preferrably , that is observed after inbreeding (i.e Variance of F1 = 316  and Variance of F2 = 1153)

V(g)  = (316 + 1153) = 1469

Now, back to phenotypic variance = V(e) + V(g)

substituting the parameters we have;  1469 + 644 = 2113

Broad-sense heritability can be calculated as the ratio of total genetic variance to total phenotypic variance.

= V(g)/ V(p)

= 1469/ 2113

= 0.695

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