Use the Above Family Tree to Calculate R Between Individual D and Individual H

Relatedness

Overview

This tutorial shows how to calculate the relatedness of two family members. Information technology is meant to complement the Cooperation tutorial just can also stand on its own. The basic tutorial requires no groundwork in game theory and takes less than x minutes. The optional department on circuitous relatedness patterns takes another ten minutes.

Introduction

When studying the evolution of cooperation and conflict or lack thereof, we oft want to know how closely two individuals are related, since that may affect the costs and benefits of their actions1. For this purpose, relatedness is defined equally follows:

Relatedness is the probability that two individuals share an allele due to recent common beginnings.

This probability is expressed as the coefficient of relatedness, denoted by the symbol r. Information technology ranges from 0 (unrelated) to 1 (clones or identical twins). The definition excludes alleles that are shared simply by virtue of beingness members of the aforementioned species or population within a species.

Calculating Relatedness

In diploid organisms, each kid receives half of its genes from its mother and half from its father3. Thus each parent shares half its alleles with a child, and we say that parents and offspring are related by ½. Whatsoever two siblings are as well related by ½. Each sibling receives half its genes from each parent. As a outcome, siblings could share no alleles (in the unlikely case that each child got the half of the genes from each parent that the other didn't), all alleles (in the unlikely case that both children got the same set up of genes from each parent), or anywhere in between. That averages to (0+i)/two, so siblings share half their alleles on boilerplate and r = ½. This example illustrates the betoken:

This hypothetical diploid organism has 4 chromosomes, R, Southward, T, and U. Each parent has ii copies of each chromosome and each gamete (egg or sperm) carries only one of those copies. A child gets half its chromosomes from each gamete, then parent and kid are related past ½. Since chromosomes segregate randomly into gametes, the bodily proportion of alleles shared by any two siblings tin vary. In this example, A and C share all alleles while B and D share none. A and B share ½ their alleles, as do B and C. A and D share only ¼, as practice C and D. Considering all possible combinations of gametes, siblings share ½ of their alleles on average.

Given that parents and offspring are related by ½ and siblings are related by ½, we can summate the relatedness of whatsoever family members. The reasoning well-nigh parents and children shows that a grandparent and grandchild are related by ¼, since 1 parent received half of its genes from that grandparent and then passed half of those genes on to its children. Nosotros tin can as well follow that reasoning to prove that you are related to an uncle or aunt by ¼. Your parent and his or her sibling share half their alleles, and half of those shared alleles were passed on to you from your parent.

If tracing genes from one generation to the adjacent seems complicated, in that location is a simple graphical fashion to accomplish the same thing by looking at a family tree. Describe the tree as in the instance below. Then mark the shortest possible path between two family members and count the number of steps between them. Each step across generations (parent to child) or between siblings counts equally one. Once you lot accept this number of steps (n), r = ½^northward, or ½ multiplied by itself due north times.

Family tree: A is a parent of B and C, B is a parent of D and E, so on. Simply two siblings per generation are shown; if at that place are more than, they are all related to each other by the same amount. Solid lines connect parent and child; dashed lines connect siblings.

For example, how are D and K related (niece or nephew to aunt or uncle)? There are two steps, D-E and E-M, so r = ½×½, or ¼. How are H and J related (first cousins)? There are three steps, H-D, D-E, and E-J, so r = ½×½×½, or ⅛. If you want more practise, endeavour these examples. All refer to the above tree.

This concludes the basic relatedness tutorial, which is sufficient for almost purposes.

Complications

Inbreeding

What if the parents are related4? Suppose r′ is the coefficient of relatedness betwixt the parents. A kid gets half of its genes from the father and one-half from the female parent. Amongst the genes that it gets from the female parent, at that place is a probability of r′ that those alleles are shared with the father. So the relatedness of child to father is ½ (genes from the father) plus ½ (genes from the female parent) × r′ (probability that alleles inherited from the female parent are also present in the father). The same reasoning applies to relatedness to the female parent. Offspring are related to each parent by ½+½ r′.

What about siblings when parents are related? Each sibling receives half its genes from each parent. Even if each child got merely the genes from the mother that it didn't get from the begetter and vice versa, they would still share r′ of their alleles because of relatedness of the parents. At the other farthermost, they could share all of their alleles in the unlikely event that both children got the same sets of genes from each parent. And so their shared alleles could range from r′ to 1 or anywhere in between. That averages to (r′+i)/two, so r = (r′+1)/two, or r = ½+½ r′.

In full general, when parents are related to each other by r′, they are related to their offspring by ½+½ r′ and these offspring are related to their siblings by ½+½ r′. When there is no inbreeding, r′ = 0 and nosotros get the usual r = ½ for parent-child and sibling-sibling relatedness.

Mixed Families

What about half-siblings, who share just one parent? Parents are nevertheless related to offspring by ½, but siblings are related by only ¼. At a minimum, they might share no alleles (in the unlikely event that they become completely different sets of genes from the shared parent). At most, they could share ½ of their alleles (in the unlikely event that they both get the same genes from their shared parent). So allele sharing ranges from 0 to ½, which averages to ¼, and so r = ¼ among half-siblings.

Haplodiploidy

In bees, wasps, and ants, females are diploid and males are haploid5. A reproductive female (or queen) passes one-half of her genes to her offspring, while a male person passes all of his genes to daughters. (He has no sons, since males come up from unfertilized eggs.) Males are related by ½ to their mothers and by ½ to siblings. Sisters are related by ¾. At a minimum, sisters share ½ of their alleles (all inherited from their male parent, with no shared genes from the queen). At about, they could share all of their alleles (half from their father, plus completely identical genes from the queen). So allele sharing ranges from ½ to ane, which averages to ¾, so r = ¾ amid sisters.

Queens in many species of social insects mate with multiple males, so relatedness through the father is reduced. Sisters in these colonies are related past more ½ only less than ¾ on average. In some cases, in that location are even multiple queens, reducing boilerplate relatedness still further. Both of these complications have interesting effects on cooperation and conflict in social insects.

Calculating Relatedness

How can we calculate relatedness in inbred, mixed, or haplodiploid families? The procedure is essentially the same as with regular diploid families. We tin can trace genes from generation to generation and calculate the probability that they are shared or nosotros can use a graphical technique like to the ane higher up. Withal, we can no longer assume that all steps reduce relatedness by a factor of 2 (multiplying by ½). Instead, we must label our family tree with the known relatedness at each step. As you make your path through the tree, write down the relatedness at each step. At the cease, multiply all of the r values to obtain the coefficient of relatedness. The four copse below illustrate this for sample unrelated, inbred, mixed, and haplodiploid cases.

Unrelated. This tree only adds the relatedness of ½ between parents and offspring and between siblings when there is no inbreeding.

Inbred. A was related to its mate by ½ (siblings) and B was related to its mate past ⅛ (first cousins). No other parents are related.

Mixed. In this tree, B and C share only one parent, A, reducing their relatedness to ¼. Similarly, D and East share only one parent, B.

Haplodiploid. This tree shows a family of wasps with multiple queens. Only G is male person; all the others are female. (Non-reproductive females are non shown.)

For example, what is the relatedness betwixt D and One thousand in the Inbred tree? Following the path D-B-C-G, we cross relatednesses of ^nine⁄_xvi, ¾, and ½, giving a relatedness of ²⁷⁄₁₂₈ (about 0.211). For comparison, D and G are related by ⅛ (0.125) in the Unrelated tree. In the Mixed tree, how are D and Chiliad related? The path D-East-G has ¼ and ½, for a relatedness of ⅛. For more do, try the problems beneath,which refer to the family trees above unless otherwise indicated. (For other families, you need to draw customized trees using the parent-offspring and sibling-sibling relatednesses given earlier in this tutorial.)

1. Run across Wikipedia essays on kin selection and inclusive fitness.
2. Almost traits are polygenic, controlled by multiple genes. However, the concept of alleles and relatedness yet applies. The trait that is expressed is determined by the mixture of alleles in the relevant genes.
3. The maternal contribution is actually slightly larger, since all mitochondrial Dna comes from the mother and since, in XX daughters, paternal genes on the Ten chromosome are often deactivated.
4. This isn't merely hypothetical. In some human societies, the only acceptable mate is a cousin, while some animals may become through several generations of inbreeding or asexual reproduction before dispersing widely.
5. A diploid organism has ii copies of each chromosome and thus 2 copies of each factor. A haploid organism has only 1 copy of each chromosome.

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Source: http://pages.nbb.cornell.edu/Gamebug/relatedness.html