p i = a i + d i + e i
DESCRIPTION
Offspring. Parents. P i = A i + D i + E i. V P = V A + V D + V E + some other stuff (covariances). What is parental phenotype? P i = A i + D i + E iP. What is offspring phenotype? O i = 1/2 A i + E iO. - PowerPoint PPT PresentationTRANSCRIPT
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