Question

Many characters are found to have a significant hereditary component, without knowing the exact genetic mechanism. To assess if a character past on genetically we can compare parents and their offspring. In the European barn swallow (Hirunde rustica), it has been shown that the length of the tail feathers has great influence fitness of male birds. The question is: do fathers with long tail feathers have offspring with long tail feathers? You measured the tail length several male birds, and then measured the tail length in one of their male offspring as they grew to adult size Table 2. Adult tail length in millimeters for male European barn swallow (Hiruade ustica), and one of their offspring f#Father's tailSon's tail lengtlh length (mm 52 48 72 68 48 53 62 60 49 51 40 53 60 68 71 68 9 68 68 10 53 50 49 12 53 13 67 65 14 64 68 15 60 Using the data you collected estimate the Covariance for the tail length. Make sure to show your work

Answer 1

​​​​Answer:

Covariance determine the type of relationships (positive, negative or no relations) between two variables. Here, the two variables are father's tail length and son's tail length of European barn swallow (Hirundo rustica).

Let assume the variable father's tail length be X and son's tail length be Y.

Calculation-

The formula for determining covariance and calculations are given in the two images below-

y-Neam of all,data, in vanjable. Y Mean of ait dot inble Y 5 48 6 53 a.4t 다2- 13 53 128.1 92 3 4S 531052 5. 47 57 . S99 1 6 2 0 3.47 1.53 5.309子 | 51 G. 4 +1 2091 1847 5: 5 3 O2 1391 14.009 118 31 G8 .5 2 68 13-41 9.4t 9:32 68 10 S 1.5 3 1.53 5. 3091 11 S3 12 453 5- 53 8 1 SO 46.8 39 S2.191 5S. 3091 9.5 3 S.47 65 6.5 3 S2 1291 69 9.53 -3.53 862-2665

So, the covariance for tail length is positive (i.e. 61.59); it means there is a positive relation between two variables (father's tail length and son's tail length), thus it can be said that father's with long tail feathers have greater chance of having offspring with long tail feathers.

978 %다구- 151 스 一 15 IS 58.53 So to 52-.53 6.52 aud hence sest Similahl GQ. 266 15-1 G2.266S 61.59