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heritability

  • Heritability and stature

    Mon, 2011-09-12 01:42 -- John Hawks
    Synopsis: 
    Heritability is the proportion of variance in a phenotype explained by additive genetic variance.

    Tall parents tend to have tall children.

    That's a simple generalization, not an absolute statement. You may be a short person with two tall parents. If you know many families, you'll probably know someone who is an exception to the rule. Two short parents may have a very tall daughter, and two siblings may be very different heights.

    Still, if we look at many families we will find that the stature of the parents lets us make some fair predictions about the statures of their children. We can look at data to quantify just how parent and offspring heights are related.

    For example, here is a plot of the statures of students in my Anthropology 105 class in 2010, compared to the mean of their mothers' and fathers' statures. The average of mother and father's heights are the midparent stature.

    Young men in this class have a taller average stature than young women. The picture separates men and women, and both taller sons and daughters tend to come from taller parents.

    We can do a bit better than this to quantify the relationship of the parents' and sons' and daughters' statures: We can put lines on the graph to show how the sons' and daughters' heights tend to increase with the midparent stature:

    Each of these lines is called a linear regression between midparent stature and offspring stature. The linear regression is the line that has the smallest squared distance from all of the points, added together.

    The squared distance is special. In statistics, the average squared distance from all points to the mean is called the variance. When we consider a trait like stature, there are many possible biological causes that can contribute to individuals being taller or shorter than the average. In statistical terms, these causes are all factors that contribute to the variance of stature.

    In the chart above, the linear regression represents the amount of the variance of the stature of the offspring that was contributed by the variance of their midparent statures. Parent statures can predict offspring statures and the linear regression is the prediction.

    It's not a perfect prediction. Take a look at the midparent value of 160 cm. When the midparent average is 160 cm, the regressions predict that daughters will be 156 cm and sons will be 168 cm. Out of Anthropology 105 students last year, two men had parents with an average of 160 cm, and both of them were very close to 168 cm in height — a good prediction! But the two women with parents this stature have very different heights. One is only 148 cm, the other 162, both more than 2 inches from the predicted value, in different directions. The regression gives the best prediction we can make from the parents, but there is obviously a lot of variation that can't be predicted in that way.

    Let's look more closely at the female students. The following chart adds together females from several years of Anthropology 105, with their midparent statures.

    The slope of the regression across these 300 women is 0.72. That means that roughly 72 percent of the variance of the students' stature can be attributed to variance in their midparent stature.

    This regression is special in genetics. Daughters resemble their parents because they inherit genes from them. The regression between the midparent and daughters' statures gives us a way to estimate the effects of those genes. In fact, the proportion of variance in a trait that can be explained by genes is the same as the slope of the regression. Geneticists call this proportion the heritability of stature. In my Anthropology 105 classes over the last few years, we would estimate the heritability of stature as 0.72, or 72%.

    Again, there are exceptions. Sometimes parents give other things to their children besides genes. The right foods, the right resources can make a difference to growth and development. And some genes can have unexpected effects. Most obviously, some genes make sons a lot taller than daughters, which is why we've considered the two sexes separately.

    The heritability of a trait is a powerful concept. It's important to understand some of its strengths and limits:

    1. Heritability refers to a population. A female in my Anthropology 105 class may be taller or shorter than her parents. We can't predict 72% of that student's stature; instead, 72% of the variance in the students can be explained by the variance among their parents.
    2. Traits with higher heritability have a lower influence from the environment. Traits that are highly influenced by the environment have a lower heritability.
    3. The response of a population to selection on a trait is determined by the heritability.
    4. Geneticists can look at other relatives besides parents to estimate heritability. Some of the strongest estimates come from comparing identical twins (who have the same genes) to fraternal twins (who share on average half their genes).
    5. Estimating heritability doesn't require us to know anything about the actual genes themselves.

    The last point is very important. We can quantify the influence of genes without knowing anything about which genes even affect a trait. Francis Galton invented the parent-offspring method of estimating heritability, more than twenty years before the word "gene" was coined. Remembering this helps to remind us that the concept of heritability is limited. It is not a guide to how genes work, it is a simple scale of which traits have a stronger or weaker genetic influence.

    Because it is a proportion, heritability varies only between zero and one. A trait with zero heritability is one for which none of the variance can be explained by the parents' variance.

    Heritability may be very low because the individuals in the population have little genetic variability. For example, an orchard of apple trees may consist of genetically identical individuals that are clones of a single parent tree. The apples (hopefully) all taste the same. But the trees may be very different in height, branch form, and the number of apples. These traits may be strongly influenced both by the environments of individual trees and by chance. By contrast, wild populations of oak trees are not made up of clones. The heights of individual trees are still strongly influenced by environments, but they may also be influenced by differences in genes.

    Study questions: 
    1. Make a list of three traits that have low heritability in humans. Why are these mostly influenced by the environment and not genes?
    2. Are there environments inhabited by human populations that would make the influence of genes seem to be less on some traits?
    3. Suppose that the linear regression between midparent and offspring for a trait has a slope of 0.56. What would you estimate as the heritability of this trait?
    Study terms: 
    stature
    heritability
    variance
    Tags: 
    heritability
    explainer
    Anthropology 105
    stature

  • What does it mean for a trait to be heritable?

    Fri, 2011-08-05 00:57 -- John Hawks
    Synopsis: 
    Heritability is the proportion of variation in a phenotype that can be explained by variation in genes.

    Tall people tend to have tall parents. The height of the body, called stature, is one of the most obvious phenotypic traits in human populations. Anyone who knows very many families can see that some families tend to have a lot of tall members, and others tend to be relatively short.

    Still, there is more to being tall than having tall parents. A child may grow to be taller than either of his parents, sometimes much taller. A very tall father and short mother don't always have children that are in between their statures: sometimes a daughter may match her mother's height, or even be shorter. Relatives resemble each other in height, but we cannot say that a woman's stature is determined by the statures of her parents.

    There are two key reasons why most phenotypes are not inherited as simple Mendelian traits. Many traits are affected not by one, but by multiple genes. At present, more than 300 genes are known to influence the variation in stature within populations of European ancestry. Other genes may be responsible for differences within other populations and between very different populations such as the short-statured Biaka Pygmies and tall-statured Dinka of equatorial Africa. The combination of so many genes helps to explain why stature is not a Mendelian trait with only two or three distinct forms. Instead, stature is a \term{continuous} trait, in which a person may be 62 inches tall, 61.5 inches, 61.25 inches, 61.0003 inches, or any measurable value in between.

    Another reason for variation is that different people may have experienced different environments. The effects of environmental variation are plain in many fields of corn. The corn plants in a single field generally have very little genetic variation: they are hybrids bred for their high yields with adequate fertilizer, pesticide, and water. But many fields have low spots where water pools, or drier spots on the edge of the field. Here, the plants do not grow as tall or yield as much, because their environment is not ideal for high yield by the planted strain. The variation in plant height visible in such fields is entirely the result of environmental variation, because the plants are genetically uniform.

    Environmental variation may come in at many points during an individual's life, from early embryonic development to childhood nutrition and disease. At all stages, this environmental variation can have a major effect on some phenotypes --- sometimes more extensive than variation in genes.

    Heritability is the proportion of phenotypic variation that is explained by genetic variation.

    \begin{figure}
    \includegraphics[width=\textwidth]{female_stature_heritability.png}
    \label{fig:female_stature_heritability}
    \caption[Female stature heritability]{Relationship of student stature to midparent stature in a sample of 100 female college students. The midparent stature is the average of the mother's and father's heights. Taller parents tend to have taller offspring, although some women are taller than the average of their parents, and others are shorter. The slope of the line relating the two reflects the heritability of stature in the sample, which for these students is estimated at 0.89. }
    \end{figure}

    For a phenotype like stature, it can be important to know how much of the variation results from genetic variation, and how much of the variation results from the environment. This is important because genetic changes can affect a phenotype only to the degree that the phenotypic variation is influenced by those genes. Geneticists also want to discover if phenotypic similarities among people are the result of shared alleles, or whether instead they are the effect of shared environments. The concept that relates genetic variation and phenotypic variation is called \term{heritability}, which is the proportion of phenotypic variation that can be explained by genetic variation in the population (Falconer and Mackay 1996). Because it is a proportion, heritability varies between 0 and 1.

    Phenotypic traits with heritabilities near zero are very weakly affected by genetic variation, while heritabilities near 1 indicate a very strong genetic influence. Very different traits can have similar heritabilities. For example, near-sighted, or myopic, parents are substantially more likely to have children with myopia. In Western populations, genetic variation accounts for more than 80 percent of the variation in juvenile-onset myopia (Gilmartin 2004). Likewise, variation in the many genes that influence stature accounts for approximately 80 percent of the phenotypic variation in stature, at least in Western societies with relatively stable childhood nutrition (Silventoinen 2003). Some human traits have heritabilities very near 1. One example is the mass of the brain, which has a heritability of approximately 0.94 (Bartley et al. 1997).

    Study questions: 
    1. Tall parents don't always have tall children. Why not?
    2. What does the heritability of a trait enable geneticists to predict?
    3. What explains the regression to the mean?
    Study terms: 
    heritability
    phenotype
    genotype
    genetic variation
    Mendelian
    Tags: 
    genetics
    explainer
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