APS 323 Social Insects: Lecture 8

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APS 323 Social Insects Lecture 8
Francis L. W. Ratnieks Laboratory of Apiculture
Social Insects
Department of Animal Plant Sciences University
of Sheffield
Lecture 8 Kin Structure Relatedness
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Aims Objectives
Aims 1. To show how to determine regression
relatedness among individuals using a pedigree
diagram. 2. 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. Objectives 1. To learn the methodology
covered in lecture.
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Determining Relatedness from a Pedigree Diagram
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Pedigree Diagram for Determining Relatedness
You must learn certain degrees of relatedness by
heart. For example, the regression relatedness
between full sisters is 0.75 and between half
sisters is 0.25. Mother to daughter is 0.5.
Mother to son is 1. But it is not possible to
learn all possible relatednesses. For example, to
your great-grandmothers 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.
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Pedigree Diagram for Determining Relatedness
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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, 0.5) x (a to e, 0.5) (d to b,
1) x (b to e, 0.5) 0.75 these two individuals
are connected via both mother and
father relatedness between half sisters (e.g., d
to f) (d to a, 0.5) x (a to f, 0.5) 0.25 these
two individuals are connected only via the
mother relatedness of a worker to a full-sister
worker's son (e.g., d to k) (d to a, 0.5) x (a to
e, 0.5) x (e to k, 1) (d to b, 1) x (b to e,
0.5) x (e to k, 1) 0.75
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Relatedness Among Female Offspring When Queens
Are Mated to Multiple Males, or Multiple Queens
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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 0.75 and
half sisters by 0.25. 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.
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Double Paternity
Full sisters are related by 0.75 and half sisters
by 0.25. If there are two fathers, what is the
average relatedness among all female
offspring? 0.5 The average of 0.75 and
0.25? 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.
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2 Fathers, Equal Paternity
Full sister interaction Half sister interaction
Relatedness among female offspring
0.75(0.250.25) 0.25(0.250.25) 0.5
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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. Patriline 1 with
Patriline 1 (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 0.5 x 0.5
0.25. Each interaction has an associated
relatedness. 0.75 for interactions between two
full sisters (blue), and 0.25 for half sisters
(white). From these we can determine the
average level of relatedness. 0.75(0.25 0.25)
0.25(0.25 0.25) 0.5 RelFullSisters(Prob 1
with 1 Prob 2 with 2) RelHalfSisters(Prob 1
with 2 Prob 2 with 1)
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2 Fathers, Unequal Paternity
Patriline 1 0.3
Patriline 2 0.7
Full sister interaction Half sister interaction
a)
b)
Patriline 1 0.3
0.75
0.25
c)
d)
With unequal paternity, the probabilities of full
sister interactions increase. The effect on
relatedness is quite small when the paternities
are 0.3 0.7.
Patriline 2 0.7
0.75
0.25
Relatedness among female offspring
0.75(0.090.49) 0.25(0.210.21) 0.54
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2 Fathers, Very Unequal Paternity
Patriline 1 0.1
Patriline 2 0.9
Full sister interaction Half sister interaction
Patriline 1 0.1
0.75
0.25
Patriline 2 0.9
0.75
With very unequal paternity, the probabilities of
full sister interactions increase almost to 100.
The situation approaches that of single paternity.
0.25
Relatedness among female offspring
0.75(0.010.81) 0.25(0.090.09) 0.68
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Many Fathers, Unequal Paternity
Patriline 1 0.3
Patriline 2 0.5
Patriline 3 0.2
Full sister interaction Half sister interaction
Patriline 1 0.3
0.75
0.25
0.25
Patriline 2 0.5
The same general idea can be extended to any
number of fathers with any paternity shares.
0.25
0.25
0.75
Patriline 3 0.2
0.75
0.25
0.25
Relatedness among female offspring 0.75(0.090.25
0.04) 0.25(0.150.060.150.10.060.1) 0.44
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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 0.75 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 0.25
0.5/n rearrange to give n 0.5/(b -
0.25) From this equation we get effective
paternities as follows Paternities Relatedness Ac
tual Paternity Effective Pat. 0.5, 0.5
0.75 2 2.00 0.7, 0.3 0.54
2 1.72 0.9, 0.1 0.68 2
1.16 0.3, 0.5, 0.2 0.44 3 2.63
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2 Full-Sister Mothers, Each Single Paternity
Matriline 1 0.3
Matriline 2 0.7
Full sister interaction Cousin interaction
a)
b)
Matriline 1 0.3
0.75
0.1875
c)
d)
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 0.1875.
Matriline 2 0.7
0.75
0.1875
Relatedness among female offspring
0.75(0.090.49) 0.1875(0.210.21) 0.51
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Pedigree Diagram Cousin Relatedness
Two full sister queens, each mated to a different
unrelated male
x
x
0.75
0.5
0.5
cousin relatedness 0.5 x 0.75 x 0.5 0.1875
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2 Unrelated Mothers, Each Single Paternity
Matriline 1 0.3
Matriline 2 0.7
Full sister interaction Non-kin interaction
a)
b)
Matriline 1 0.3
0.75
0
c)
d)
Here the relatedness between offspring of
different mothers is zero.
Matriline 2 0.7
0.75
0
Relatedness among female offspring
0.75(0.090.49) 0(0.210.21) 0.435
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2 Full-Sister Mothers, One Single One Double
Paternity
Matriline 2 0.7
Matriline 1 0.3
Pat 1 0.333
Pat 2 0.667
Full sister interaction Half sister
interaction Cousin interaction
Matriline 1 0.3
0.75
0.1875
0.1875
0.75
0.25
0.1875
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 0.333 and
0.667.
Matriline 2 0.7
0.75
0.25
0.1875
Relatedness among female offspring 0.75(0.09
((0.7)(0.333))2 ( (0.7)(0.667))2) 0.25(0.7 x
0.333 x 0.7 x 0.667 x 2) 0.1875(0.7 x 0.3 x
2) 0.405
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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 daughters son b. Regression relatedness
of two males, the queens mate and the son of one
of his daughter workers.