In a large herd of cattle, three different characters...

In a large herd of cattle, three different characters showing continuous distribution are measured, and the variances in the following table are calculated: a. Calculate the broad- and narrow-sense heritabilities for each character. b. In the population of animals studied, which character would respond best to selection? Why? c. $A$ project is undertaken to decrease mean fat content in the herd. The mean fat content is currently 10.5 percent. Animals with a mean of 6.5 percent fat content are interbred as parents of the next generation. What mean fat content can be expected in the descendants of these animals?

In a large herd of cattle, three different characters showing continuous distribution are measured, and the variances in the following table are calculated:
a. Calculate the broad- and narrow-sense heritabilities for each character.
b. In the population of animals studied, which character would respond best to selection? Why?
c. $A$ project is undertaken to decrease mean fat content in the herd. The mean fat content is currently 10.5 percent. Animals with a mean of 6.5 percent fat content are interbred as parents of the next generation. What mean fat content can be expected in the descendants of these animals?

Key Concepts

Genetic Variance Components

This concept involves understanding that the total phenotypic variance of a trait can be partitioned into genetic variance and environmental variance. The genetic variance is further broken down into additive (the cumulative effect of individual genes), dominance (interaction between alleles at the same locus), and epistatic (interaction between different genes) components. In the context of selection, additive genetic variance is particularly important as it is the heritable portion that directly affects the response to selection.

Broad-sense Heritability

Broad-sense heritability is defined as the ratio of the total genetic variance (including additive, dominance, and epistatic variances) to the overall phenotypic variance. It measures the overall genetic influence on a trait but does not distinguish between the different types of genetic effects, making it less directly predictive of how a trait will respond to selection.

Narrow-sense Heritability

Narrow-sense heritability is the ratio of additive genetic variance to the total phenotypic variance. It specifically captures the portion of genetic variance that is passed from parent to offspring, making it a critical parameter for predicting the response to selection. A high narrow-sense heritability indicates that selection based on the trait will effectively shift the population mean in the desired direction.

Response to Selection

The response to selection is the change in the population mean of a trait as a result of selecting individuals with extreme phenotypes. It is calculated as the product of the narrow-sense heritability and the selection differential, which is the difference between the mean of the selected parents and the population mean. This concept explains how artificial selection can incrementally modify the trait distribution in successive generations.

Selection Differential

The selection differential represents the difference between the mean value of the trait in the selected group and the overall population mean. It quantifies the intensity of selection applied and, when multiplied by the narrow-sense heritability, predicts the expected change (response) in the trait in the next generation.

Transcript

00:01 All right, guys.

00:01 So this, my goodness, is a longer question.

00:05 So we're looking at a large herd of cattle, and we're looking at three different characters that could show a continuous distribution, and we actually calculate that variance.

00:17 And that was calculating the table that, again, you can't see here, but you can't see in your book.

00:21 So we want to do two things.

00:23 We want to do two things.

00:24 A, we want to calculate the broad and narrow and narrow since hair buildings of each character.

00:27 We want a b, and the population animal studied, which character will respond best to selection, and then that's a while, of course, and then c, a project is undertaking to describe what to decrease mean fat content i heard.

00:38 The mean fat content is currently at 10 .5 % and so eat animal with a mean of 6 .5 % fat content are interbreed as parents for the next generation of what mean fat content can be expected in the descendants of these animals.

00:51 So this is literally a combination of a lot of questions we've already answered already.

00:57 The first one is brides since harry bill to remember just to keep in mind measures the the portion of total variance that's due to genetic variance.

01:55 And so this is, this looks mathematical as h2 equals genetic variance, gdp divided by phenotypic variance, which is pv.

02:08 And then this further is broken down to h square equals s2p minus s to b divided by this.

02:25 The narrow sense just tells us the total variation of population that's due to additive genes alone.

03:04 And so that's usually looks like low -case h.

03:06 So h -square equals additive gene variation, hb, divided by, additive gene variation plus dumbness variation plus the environmental variation.

03:17 So db plus e.

03:21 And then mathematically, this looks like, now i'm going to refresh this page, so you may want to stop here if you need to roll this down.

03:43 So we have a lot of math to it.

03:47 So the first thing we want to calculate, since we're looking at those three characters, is shank length.

03:56 So the h2, and i thought i worked with one, i can speed this up so equals.

04:10 Divide that by this.

04:12 And all these figures are coming from.

04:15 That gives us 0 .200.

04:17 And now narrow sense.

04:34 And really, like i said, you just need to find the values from the table, which i've already mentioned...

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