Determining Relatedness from a Pedigree Diagram

Transcription

1 Kin structure & relatedness Francis L. W. Ratnieks Aims & Objectives Aims 1. To show how to determine regression relatedness among individuals using a pedigree diagram. Social Insects: C To show how to determine relatedness among offspring females in colonies headed by a queen mated to more than one male, or by several queens. Laboratory of Apiculture & Social Insects Department of Biological & Environmental Science University of Sussex Objectives 1. To learn the methodology covered in lecture. Determining Relatedness from a Pedigree Diagram Pedigree Diagram for Determining Relatedness You must learn certain degrees of relatedness by heart. For example, the regression relatedness between full sisters is and between half sisters is. Mother to daughter is. Mother to is 1. But it is not possible to learn all possible relatednesses. For example, to your great-grandmother s aunt. Fortunately, these can be calculated from the pedigree diagram following. The method is based on the four degrees of regression relatedness below, from which all others can be calculated. Donor Recipient Reg. Relatedness Male Female (daughter, mother) Male Male (, father) 0 (has no father) Female Female (daughter, mother) Female Male (, father) 1

2 Pedigree Diagram for Determining Relatedness d) worker b) queen s mate 1 a) mother queen c) queen s mate e) h) i) f) worker queen s queen s worker Parents Queen s offspring g) worker Pedigree Diagram for Determining Relatedness Relatedness can be calculated from the diagram in the previous slide. (We will only consider cases where outbreeding occurs.) The method is based on the four degrees of regression relatedness given before this. Each arrow goes from donor to recipient. When the arrow connects a male with a female the numbers at the two ends are different, so be careful you know which "way" you are going. relatedness between full sisters (e.g., d to e) (d to a, ) x (a to e, ) + (d to b, 1) x (b to e, ) = these two individuals are connected via both mother and father j) k) l) m) Workers s relatedness between half sisters (e.g., d to f) (d to a, ) x (a to f, ) = these two individuals are connected only via the mother relatedness of a worker to a full-sister worker's (e.g., d to k) (d to a, ) x (a to e, ) x (e to k, 1) + (d to b, 1) x (b to e, ) x (e to k, 1) = Pedigree Diagram: Cousin Relatedness Two full sister queens, each mated to a different unrelated male x cousin relatedness x x = x Relatedness Among Female Offspring When Queen is Mated to Multiple Males, or there are Multiple Queens Heading the Colony

3 Multiple Paternity/Mating If the queen mates with more than one male, how does this affect relatedness among female offspring? Full sisters are related by and half sisters by. But what is the average relatedness among all female offspring? In many species, the female offspring of a single queen are fathered by more than one male: there is more than one patriline in the colony. When multiple paternity occurs, paternity is usually not equal. For example, the female offspring may have two fathers, one fathering 80% and the other 20%. Double Paternity Full sisters are related by and half sisters by. If there are two fathers, what is the average relatedness among all female offspring? The average of and? Yes. But only if the two males have equal paternity. If their paternity is unequal, relatedness is higher. To understand things work through the next slides. 2 Fathers, Equal Paternity Prop.= cell Rel = = (+) + (+) = 2 Fathers, Equal Paternity The previous diagram enables us to calculate the relatedness among female offspring. It works in exactly the same way as the Punnet square used to calculate diploid genotype frequencies from gene frequencies. We assume that offspring interact at random. The four cells represent the four types of interaction possible. with (a), 1 with 2 (c), 2 with 1 (b), 2 with 2 (d) These have probabilities that depend on the proportion of offspring in each patriline. In this case each probability = x =. Each interaction has an associated relatedness. for interactions between two full sisters (blue), and for half sisters (white). From these we can determine the average level of relatedness. ( + ) + ( + ) = RelFullSisters(Prob 1 with 1 + Prob 2 with 2) + RelHalfSisters(Prob 1 with 2 + Prob 2 with 1)

4 2 Fathers, Unequal Paternity With unequal paternity, the probabilities of full sister interactions increase. The effect on relatedness is quite small when the paternities are &. = ( ) + ( ) = Fathers, Very Unequal Paternity With very unequal paternity, the probabilities of full sister interactions increase almost to 100%. The situation approaches that of single paternity. = ( ) + ( ) = 0.68 Patriline Many Fathers, Unequal Paternity Patriline The same general idea can be extended to any number of fathers with any paternity shares. =( ) + ( ) = 0.44 Effective Paternity The previous slides show that when a queen is mated to two males, relatedness among female offspring depends on their paternity shares. As these become more unequal the situation approaches that of single mating. For example, with paternities of 0.9 and 0.1 relatedness among is 0.68, quite close to the for single paternity. Even though there may be two fathers in a sense the effective paternity is less than two. We can determine effective paternity from the equation below, where n is effective paternity and b is relatedness. b = + /n rearrange to give n = /(b - ) From this equation we get effective paternities as follows Paternities Relatedness Actual Paternity Effective Pat., , , ,,

5 2 Full-Sister Mothers, Each Single Paternity = ( ) + ( ) = 1 Cousin interaction The same method can be extended to multiple queens. Here we have a colony headed by two full-sister queens each mated to a different male. From the pedigree diagram we know that relatedness between cousin females is. 2 Unrelated Mothers, Each Single Paternity 0 = ( ) + 0( ) = Non-kin interaction Here the relatedness between offspring of different mothers is zero. 2 Full-Sister Mothers, One Single & One Double Paternity Pat 1 Pat Cousin interaction Here we have a more complex situation. Two full sister queens, one mated to a single male and one to two males, with paternities of 33 and = ( (()(33)) 2 +(()(0.667)) 2 ) + ( x 33 x x 2) + ( x x 2) = Self Test The only way to be sure that you understand this is to work through some examples. First work through the examples in the slideshow. Then work out some more, such as these. 1. Determine relatedness among offspring females when a. Single queen mated to 2 unrelated males, paternities 0.2, 0.8 b. Single queen mated to 10 unrelated males, equal paternity c. Single queen mated to 20 unrelated males, equal paternity d. Two queens, mother and daughter, each single paternity e. 5 queens, all are unrelated, each single paternity 2. Using a pedigree diagram determine a. Regression relatedness of mother queen to daughter s b. Regression relatedness of two males, the queen s mate and the of one of his daughter workers.