Targets Above The Level of The Individual

DNA encodes information that interacts with the environment to influence

phenotype

Among The Traits That Can Be Influenced By Genetically Determined Responses to the Environment Are:

1. The Viability in the Environment2. Given Alive, the Mating Success in the

Environment3. Given Alive and Mated, Fertility or

Fecundity in the Environment.

These two components are inherently a phenotype not ofAn individual, but a pair of individuals in a sexual population

DNA encodes information that interacts with the environment to influence

phenotype

Among The Traits That Can Be Influenced By Genetically Determined Responses to the Environment Are:

1. The Viability in the Environment2. Given Alive, the Mating Success in the

Environment3. Given Alive and Mated, Fertility or

Fecundity in the Environment.

Darwin felt that competition was a major determinant of viability, and competition is only manifest at the level of interacting

individuals.

Sexual Selection refers to the selection targeting the events that lead up to

successful mating or its failure. Many of these events emerge from interactions among

individuals and thereby constitute targets of selection above the level of the individual. Such targets under sexual selection are often split into

two types:

• Intrasexual selection that arises out of competition between individuals of the same sex for mates, and

• Intersexual selection that arises out of the interactions between individuals of opposite sex that lead to mating or its failure.

Intrasexual and intersexual selection are often interwoven, resulting in conflicts that direct selective responses to different units

of selection in the two sexes.

E.g., the butterfly Pieris napi. Males try to mate as often as possible. Females can also mate more than once, and if they do, there can be sperm competition. However, a female typically becomes non-receptive after mating for a time, and the length of this time depends on how full her spermatheca is.

Intrasexual and intersexual selection in Pieris napi.

To ensure mating success and avoid competition with sperm from other males, the males produce non-functional sperm to fill up the female’s spermatheca and make her non-receptive to other males. Thus, males have adapted to intrasexual competition with other males (via sperm competition) by manipulating female sexual receptivity (intersexual selection) and the quality of their ejaculate (the major male indicator of success in intersexual selection).

Intrasexual and intersexual selection in Pieris napi.

The inactive, apyrene sperm can serve as a source of nutrients that can affect the female reproductive success. Therefore, females can also select for males producing a high amount of apyrene sperm, and there is at least genetic variance for this female preference (perhaps additive?). Selection on the female preference further impacts on male intrasexual selection.

Common Theme

Constant fitness on a target of selection above the level of the individual induces frequency and/or density dependent selection when measured at the level of the individual. This is an artifact of attributing fitness to an individual when the true target is beyond the individual, but this has many important selective consequences.

E.g., Male Mating Success in Drosophila pseudoobscura (Ehrman, 1966, 1967)

• This species is polymorphic for two chromosomal inversions, AR and CH.

• This behaves as an autosomal, single-locus, two-allele unit of selection.

• The male mating success of AR/AR, AR/CH, and CH/CH was estimated by the number of matings each male genotype achieved divided by the expected number of matings for that genotype under a neutral, random mating model in many different populations over a range of genotype frequencies.


The male mating success in Ehrman’s data fit well to equations of the form:

0.6+ij/Gij

where Gij is the frequency of genotype ij and ij is an empirically derived constant that scales the frequency dependent mating success of males with genotype ij. Note that the success of any given male genotype is inversely proportional to its frequency, a result often described as a “rare male” mating advantage.


Male Genotype Frequency

AR/AR

AR/CH

CH/CH

0.2 0.4 0.6 0.8 1.0

1.

2.

3.

4.

5.

= 0.2

= 0.1

= 0.05


Assume neutrality in females, then:

€

wmale = GAR / AR 0.6 +x

GAR / AR

⎛

⎝ ⎜

⎞

⎠ ⎟+ GAR /CH 0.6 +

y

GAR /CH

⎛

⎝ ⎜

⎞

⎠ ⎟+ GCH /CH 0.6 +

z

GCH /CH

⎛

⎝ ⎜

⎞

⎠ ⎟

= 0.6 + x + y + z = 0.95 for the empirically determined values

The average female fitness is 1, so the total average fitness in a 50:50 sex ratio population is 0.975 – a flat fitness landscape! p0 1

0

1

€

w


Assume random mating, then the change in the male p is:

€

Δp = p '− p =0.6p + x + y / 2

0.6+ x + y + z− p

=x + y / 2− p x + y + z( )

0.6+ x + y + z

=p

w males

p 0.6+ xp2

⎛

⎝ ⎜

⎞

⎠ ⎟+ q 0.6+ y

2pq ⎛ ⎝ ⎜ ⎞

⎠ ⎟− w males

⎡

⎣ ⎢

⎤

⎦ ⎥

=p

w males

aAR Our familiar equation!


Despite the flat adaptive landscape, this system evolves until the average excesses of mating success are 0 at:

€

peq =x + y /2

0.6 + x + y + z= 0.71 for the empirical values

This is a stable, balanced polymorphism that does not change average fitness and that is not associated with an average fitness peak!


At Equilibrium:

Genotype: AR/AR AR/CH CH/CH

Fitness: 0.997 0.843 1.195

This is a stable, balanced polymorphism that appears to be associated with heterozygote inferiority and that appears to have two peaks at p=0 and p=1!

Targets of selection above the level of the individual lead to many paradoxes when we try to assign the fitnesses to individuals rather than interacting sets of individuals.

The Fertility/Fecundity Target Is a Mated Pair:

E.g., ABO incompatibility.

If there is leakage of blood across the placenta, a mother can mount an immunological reaction against a developing fetus that bears antigens not found in the mother. This results in a significant increase in the rate of spontaneous abortions in those couples that have ABO genotypes that yield ABO maternal-fetal incompatible combinations. For example, a type O woman married to a type O man would not be at risk for any ABO induced spontaneous abortions, but a type O woman married to a type AB man would have every pregnancy at risk. Therefore, fertility is not an individual attribute but rather is an attribute of a mating pair of individuals.

The Fertility/Fecundity Target Is a Mated Pair:

Pair Frequency b AA Aa aa

AA AA

p2p2=p4 b1 1 0 0

AA Aa 2p22pq=4p3q b21/2

1/2 0

AA aa 2p2q2=2p2q2 b3 0 1 0

Aa Aa 2pq2pq=4p2q2 b41/4

1/21/4

Aa aa 22pqq2=4pq3 b5 0 1/21/2

aa aa q2q2=q4 b6 0 0 1

Genotype Frequency in Next Generation:

€

p4b1 + 2p3qb2 + p2q2b4

b

= p2 bAA

b

€

2p3qb2 + 2p2q2b3 + 2p2q2b4 + 2pq3b5

b

= 2pq bAa

b

€

p2q2b4 + 2pq3b5 + q4b6

b

= q2 baa

b

Where the bij =

And:€

p2b1 + 2pqb2 + q2b4

€

p2b2 + 2pq 12 b3 + 1

2 b4( ) + q2b5

€

p2b4 + 2pqb5 + q2b6

€

b = p4b1 + 4 p3qb2 + 2p2q2b3 + 4 p2q2b4 + 4 pq3b5 + q4b6

The Fertility/Fecundity Target Is a Mated Pair:the average fertilities,

€

bij’ , s of the individuals with genotype ij under random :mating

€

b AA = p2b1 + 2pqb2 + q2b3

b Aa = p2b2 + 2pqb4 + q2b5

b aa = p2b3 + 2pqb5 + q2b6

€

p2b1 + 2pqb2 + q2b4

€

p2b2 + 2pq 12 b3 + 1

2 b4( ) + q2b5

€

p2b4 + 2pqb5 + q2b6

Fertilities that determine the selective response:

It is only the average fertilities of the mating pairs that matter, and the genotypic averages are for their offspring;

hence this can involve mating pairs that do not even include the focal genotype.

FertilityOf aaWhenMated To AA

FertilityOf aaWhenMated To Aa

FertilityOf aaWhenMated To aa

FertilityOf AaWhenMated To Aa

FertilityOf aaWhenMated To Aa

FertilityOf aaWhenMated To aa

Plots of average fertility over all mating pairs and average excess across p for the special case of:

b1=1

b2=0.7

b3=0.8

b4=1.3

b5=0.7

b6=0.75

Competition

• Darwin thought that competition was an important contributor to fitness

• An individual does not have a competitive ability.

• Competitive abilities are manifest only at the level of interacting individuals

• A constant fitness model at the level of competing individuals results in frequency dependent selection at the individual level.

CompetitionRandom mating, random encounter model of

Cockerham et al. 1972

Genotype

AA Aa aa

Competing With: AA w22 w12 w02

Competing With: Aa w21 w11 w01

Competing With: aa w20 w10 w00

Average Competitive

Fitness

w2 =

p2w22+2pqw21+q2w20

w1 =

p2w12+2pqw11+q2w10

w0 =

p2w02+2pqw01+q2w00

Note that the individual fitnesses are frequency dependent, and hence can display complex evolutionary dynamics.



Because of the potential complex evolutionary dynamics, Cockerham et al analyzed this model using the concept of a protected polymorphism that occurs when at least one allele at a locus is favored by natural selection when very rare and selected against when very common.

To see if a selective regime results in protecting an allele from loss, all you need to do is look at the average excess of the allele when it is rare. If the average excess of the allele is positive, it is protected. If two or more alleles are protected, the polymorphism is protected.



aA=p[p2w22+2pqw21+q2w20]+q[p2w12+2pqw11+q2w10]-

€

w

€

w =p2[p2w22+2pqw21+q2w20]+2pq[p2w12+2pqw11+q2w10]+q2[p2w02+2pqw01+q2w00]

As p 0, woo and aA w10 - w00

€

w

As q 0, w22 and aa w12 - w22

€

w

When there is no dominance or recessiveness

So the polymorphism is protected whenever:

€

w10 > w00 and w12 > w22

Kin and Family Selection• Individuals in many species interact strongly with

their offspring, their parents, and their siblings.• Fitness effects often emerge at the level of a

family. • When a group of interacting relatives is the target

of selection, kin selection is the result.• Kin selection has to be frequency dependent and

non-linear, in contrast to the linear inequality of Hamilton’s rule that the cost(alturistic ind.)<benefit(to recipient) X relatedness of recipient to the alturist

Kin and Family Selection Mendelian Probabilities of Offspring (Zygotes) Times wij

Mating

Pair

Frequency AA Aa aa

1. AA × AA p4 1•w21 0 0

2. A A× Aa 4p3q 1/2•w22 1/2•w12 0

3. AA × aa p2q2 0 1•w13 0

4. A a× Aa 4p2q2 1/4•w24 1/2•w14

1/4•w04

5. Aa × aa 4pq3 0 1/2•w15 1/2•w05

6. a a× aa q4 0 0 1•w06

Frequency in Next

:Generation

€

p4w21+2p3qw22+p2q2w24w

=p2wAA w

€

2p3qw12+2p2q2w13+2p2q2w14+2pq3w15 w

=2pqwAa w

€

p2q2w04+2pq3w05+q4w06 w

=q2waa w

Where

€

wAA=p2w21+2pqw22+q2w24

€

wAa=p2w12+2pq12w13+12w14( )+q2w15

€

waa=p2w04+2pqw05+q2w06

Random mating, 1-locus model

Kin and Family Selection

Fitness Matrix wij

Mating Pair Frequency AA Aa aa

1. AA × AA p4 w21=0.9

2. A A× Aa 4p3q w22=0.9 w12=0.9

3. AA × aa p2q2 w13=0.9

4. A a× Aa 4p2q2 w24=1 w14=1 w04=0.76

5. Aa × aa 4pq3 w15=1.1 w05=0.8

6. a a× aa q4 w06=1


A recessive, alturistic allele

€

w

p0.2 0.4 0.6 0.8 1.0

0.92

0.94

0.96

0.98

1.00

0.2 0.4 0.6 0.8 1.0

0.92

0.94

0.96

0.98

1.00

p

aA

Note, in this case selection drives A to fixation, which

always lowers average fitness

Kin and Family Selection

Fitness Matrix wij

Mating Pair Frequency AA Aa aa

1. AA × AA p4 w21=0.8

2. A A× Aa 4p3q w22=0.8 w12=0.8

3. AA × aa p2q2 w13=0.8

4. A a× Aa 4p2q2 w24=1 w14=1 w04=0.76

5. Aa × aa 4pq3 w15=1.1 w05=0.8

6. a a× aa q4 w06=1


A recessive, alturistic allele

€

w

p

p

aA

Note, in this case selection results in a balanced (and protected)

polymorphism for a recessive allele, but does not optimize average fitness!

0.2 0.4 0.6 0.8 1.0

0.85

0.90

0.95

1.00

0.2 0.4 0.6 0.8 1.0

0.02

0.04

0.06

0.08

0.10

Stable polymorphism

Frequency-Dependent Selection In General

• does not maximize average fitness• evolutionary outcomes are not predictable

from apparent individual-level fitness projections

• the course of evolution violates Fisher’s fundamental theorem

• The average excess still correctly predicts the course of adaptive evolution

THINK LIKE A GAMETE!

A Unit of Selection Can Have Targets Below, At and Above the Individual Simultaneously

Huntington’s Disease: An Autosomal Dominant, Late Onset Neurodegenerative

Disease

Huntington’s Disease

Huntington’s DiseaseCAG repeats in subject’s HD allele

Number of Repeats in Single Sperm From Subject

Once the 27 repeat threshold has been passed, there is strong molecular drive to increase the repeat number during male germ line mitosis. This causes “anticipation”

– the disease tends to occur earlier and earlier with passing generations, which increases the deleterious fitnesses consequences at the individual level.


Fitnesses consequences at the individual level.

neutral

Intense selection against


Reed and Neel (1959) found that the relative fitness of affected sibs is 1.12 when the fitness of non-

affected sibs is set to 1 (Hh sibs had more children despite the disease). Hence, both germline level

selection and individual fertility selection operating within families seem to favor this disease.

However, families with this disease are often discriminated against, and since (until recently) the at-risk sibs could not

be identified, all children of a choreic individual had reduced chances of mating or having children, often by choice.

Huntington’s Disease Mendelian Probabilities of OffspringTimes The Fitness in the

Context of Familyj For Each Offspring Genotype

Mating

Pair &

Number

Freq. of

Mating

Pair

Hh

hh

5. Hh × hh 4pq3 1/2•(1.12)

1/2•(1)

6. h h× hh q4 0 1•(1.2)

OffspringFrequency in

:Next Generation

€

2pq3(1.12) w ≈2pqq21.121.2

⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

2pq3(1)+q4(1.2) w ≈q22pq+q21.2

1.2 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

(<1) (>1)


Natural selection upon this one unit of selection involves

1. strong germ line selection favoring HD below the level of the individual

2. increasing individual selection operating in opposition to germ line selection against HD

3. individual-level fertility selection within families favoring HD

4. strong family level selection against choreic families.

Units of Selection Can Have Multiple Targets of Selection,

andTargets of Selection Can

Have Multiple Units of Selection

Targets Above The Level of The Individual

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