Pi = Ai + Di + Ei

VP = VA + VD + VE + some other stuff (covariances)

Parents

Off

sprin

g What is parental phenotype?Pi = Ai + Di + EiPWhat is offspring phenotype? Oi = 1/2 Ai + EiO

CovO,P = 1/2 VA + 1/2 Cov (A,D) + 1/2 Cov (A,EP ) + Cov (A,EO ) + Cov (D,EO ) + Cov (EP,EO )

CovO,P = 1/2 VA + “G by E terms” + covariance in environment

Sibling

Sibl

ing

Siblings have the same parents

They have resemblance throughboth parents---AND it is possible forboth to get the same alleles. In that case their phenotypes will be influencedby Dominance in the same way.

Covsiblings = 1/2 VA + 1/4 VD

Mid-Parent

Off

sprin

g

How does a populationrespond to selection?

On average, Offspring = h2 Parents

If we only allow some parents to breed (e.g. above the mean)

Then the offspring will be larger. By how much? offspring = h2 Parents

R = h2 s

Mean of Parents Threshold for Survival

Mean of Surviving Parents

Mean of Offspring

s

R

R = h2 s Often: h2 = R / s

s -- Selection Differential

With a single gene the change in phenotype is the change inallele frequency:

qsq q

sq

2

2

11

( )

With a quantitative trait: R = h2 s

Selection differentials

How big are selection differentials?

R = h2 s

R = h2 sOr resemblance among relatives

How much heritability is there?

Why is that important?

How do traits differ?

Graph of successive generations of phenotype.

Change in ‘oil content’ = R = h2 s

R1 ~ R30 ~ R70

Closer look shows decline in rateof change

the selection differential and the selection gradient:

s, selection differential = XS - X

, selection gradient = slope of best fit line for relative fitness, w, as a function of trait value, z

= [cov(w, z)]/var (z)

s = cov (w, z)

the selection gradient enables measurement of selection independentof trait size (otherwise, larger trait=stronger selection)

important when considering multiple traits simultaneously

Different Types of Selection

Directional Selection in the Blackcap, Sylvia atriacapilla

novel route

change in migratory direction is heritable, h2: 0.58 – 0.9

non-migratory

num

ber o

f 30-

min

ute

peri o

ds

of

mi g

r ato

ry r e

stl e

ssne

s s

populations from southern Germany are migratory, those from the Canary Is. are not

artificial selection increased and decreased migratory tendency

Stabilizing selection in the goldenrod gallfly, Eurosta solidiginis

females insert an egg into a goldenrod bud

larva induces gall formation ---> protection summer: parasitoid waspswinter (pupa): woodpeckers and chickadees

infer predator from type of damage to gall

16 populations, each for four yearsmeasure galls of survivors and dead each spring

sources of mortality intensity, direction of selection

parasitoids attack small galls; birds attack large galls

opposing directional selection is equivalent to stabilizing selection

Stabilizing selection in the goldenrod gallfly, Eurosta solidiginis

females insert an egg into a goldenrod bud

larva induces gall formation ---> protection summer: parasitoid waspswinter (pupa): woodpeckers and chickadees

infer predator from type of damage to gall

16 populations, each for four yearsmeasure galls of survivors and dead each spring

---> sources of mortality---> intensity, direction of selection

*great variation in intensity of selection among populationsand among years

Disruptive Selection in the large cactus finch, Geospiza conirostris

Geospiza conirostris on Genovese Is.

four dry season feeding modes:

bark-stripping to obtain arthropods

cracking seeds of Opuntia helleri

extracting seeds from ripe Opuntia fruits to obtain the surrounding arils

tearing open rotting Opuntia pads to obtain arthropods

extracting seeds from ripe Opuntia fruits to obtain the surrounding arils

tearing open rotting Opuntia pads to obtain arthropods

Grant 1986

stripping bark to obtain insects and other arthropods

Geospiza conirostris on Genovese Is.

four dry season feeding modes:bark-stripping to obtain arthropodscracking seeds of Opuntia helleriextracting seeds from ripe Opuntia fruits to

obtain the surrounding arilstearing open rotting Opuntia pads to obtain arthropods

birds that stripped bark had significantly deeper beaks thanthose that did not

birds that cracked seeds had significantly larger beaks than those that did not

birds that opened opuntia fruits had significantly longer bills than those that fed on arils in already opened fruits

seed-size hardiness

feed

ing

efficie

ncy

resource gradient

utiliz

atio

n effi

cienc

y

Evolution of correlated characters

selection acts on individuals, not traits

few traits are completely independent—

e.g., forelimbs and hindlimbssimilar developmental pathways, similar genes

e.g., size of red shoulder patch on a Red-Winged Blackbirdpigment precursor may be involved in multiplebiochemical pathways

---> many loci, many traits

geneticcorrelations

pleiotropy (one gene, many traits)

polygeny (many genes, one trait)

linkage disequilibrium can produce genetic correlations

locus A only affects trait z1, locus B only affects trait z2

D = 0 D = +0.15 D = -0.15

no positive negative correlation correlation correlation

pleiotropy can produce genetic correlationslocus A (with additive alleles) affects both trait z1 and z2

phenotypic correlations may also arise from environmental effects

rG and rE positive rG no rG

both positive negative rE negative rE

initial selection study --- measure several features

problems of interpretation: how important is what you’ve measured?

observe change in trait-- selection on measured trait-- selection on a correlated trait that wasn’t measured

failure of trait to change-- no selection-- no additive variance-- opposing selection-- genetic correlation

easy to measure phenotypic variance and covariance but only genetic variance and covariance relevant to evolution

Evolution of correlated characters

selection on any trait can be partitioned into a directcomponent (changes due to phenotypic/genotypicvariation in the trait) and an indirect component dueto genetic covariation with other traits

the magnitude and direction of direct selection may differfrom overall selection because of indirect effects

consequently:

a trait may change solely because of selection on some other trait -- correlated response to selection

a trait may fail to change (despite measurable selection) because of opposing selection on some other, correlated trait --- constraints on trait evolution

Model for quantitative trait evolution

single trait: R = h2s amount of phenotypic change (R), depends on amount of VA (h2) and strength of selection (s)

several traits: z = GP-1s z is the trait vector (z1 z2 z3 …zn) = Gs is still selection differential (z – zs)

G, P are the genotypic and phenotypicvariance-covariance matrices

is the selection gradient

si = Pijij = Pi11 + Pi22 + Pi33 + …… + Pinn

direct indirect

is the partial regression coefficient

Directional natural selection on Geospiza fortis in 1976-77 and 1984-86.

standardized selection coefficientsdifferential gradient s SE

1976-77 (n=632) weight +0.74 +0.477 0.146 wing length +0.72 +0.436 0.126 tarsus length +0.43 +0.005 0.110 bill length +0.54 -0.144 0.174 bill depth +0.63 +0.528 0.214 bill width +0.53 -0.450 0.197

1984-86 (n=549) weight -0.11 -0.040 0.101 wing length -0.08 -0.015 0.084 tarsus length -0.09 -0.047 0.076 bill length -0.03 +0.245 0.095 bill depth -0.16 -0.135 0.136 bill width -0.17 -0.152 0.125

Grant & Grant 1995 Evolution 49:241

Evolutionary genetics of feeding behavior in the garter snake, Thamnophis elegans

two populations:coastal -- eat slugsinland -- no slugs occur; eats fish and aquatic amphibians

(Arnold 1981)

feeding response to slugs is influenced by genes

coastal – eat slugs inland – avoid slugs

Genetic correlations between responses to different prey odors in twopopulations of Thamnophis elegans

Hyla Batrachoseps Taricha fish slug leech

Hyla --- 1.10 -0.24 0.18 0.88 1.01

Batrachoseps 0.81 --- 0.07 1.00 1.34 0.98

Taricha -0.45 0.57 --- 0.09 -0.55 -0.88

fish 0.89 1.27 0.02 --- 0.59 0.84

slug -0.03 0.56 -0.79 0.19 --- 0.89

leech 0.07 0.77 -0.01 -0.38 0.89 ---

coastal = above diagonal; inland = below diagonal

Response to slugs (food)

avoid accept

avoi

d

a

ccep

t

Res

pons

e to

leec

hes (

risk)

Response to slugs (food)avoid accept

avoi

d

a

ccep

tRe

spon

se to

leec

hes (

risk)

H

L

Response to slugs (food)

avoid accept

avoi

d

a

ccep

t

Res

pons

e to

leec

hes (

risk)

H

L

Selection against eating leeches is stronger than selection for eating slugs (slugs are rare)

Response to slugs (food)

avoid accept

avoi

d

a

ccep

t

Res

pons

e to

leec

hes (

risk)

H

L

Selection for eating slugs is stronger than selection against eating leeches (slugs are common)

Traits may not evolve independently because of geneticcorrelations due to pleiotropy or linkage disequilibirum

A trait may change as a consequence of direct selection, oras a correlated response to selection on a different trait

A trait undergoing selection may fail to change because of aconstraint operating through a genetically correlatedcharacter

Partial regression is a statistical method that enables us to separate direct selection on a trait () from totalselection (s)

The selection gradient () and the selection differential (s) maydiffer in magnitude and sign