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Xuhua Xia Slide 2
Objectives• Comprehend one of the two major components in
molecular phylogenetics, dating speciation events. (What is the other component?)
• Understand the concept of a molecular clock and its two meanings:– as a measure of time (after calibration)– as a measure of the rate of change
• Learn to calibrate the molecular clock and how to use it to solve practical biological problems
Xuhua Xia Slide 3
The Origin of Darwin’s Fox
Chiloé Island
Yahnke, C. J., W. E. Johnson, E. Geffen, D. Smith, F. Hertel, M. S. Roy, C. F. Bonacic et al. 1996. Darwin's fox: A distinct endangered species in a vanishing habitat. Conservation Biology 10:366-375.
Xuhua Xia Slide 4
Dusicyon fulvipesIn the evening we reached the island of S. Pedro...two of the officers landed to take a round of angles with the theodilite. A fox, of a kind said to be peculiar to the island, and very rare in it, and which is an undescribed species, was sitting on the rocks. He was so intently absorbed in watching their manoeuvres, that I was able, by quietly walking up behind, to knock him on the head with my geological hammer. This fox, more curious or more scientific, but less wise, than the generality of his brethren, is now mounted in the museum of the Zoological Society.
--C. Darwin. 1839. Journal of researches in the geology and natural history of the various countries visited by H.M.S. Beagle, under the command of Captain Fitzroy, R. N. from 1832-1836. Henry Colburn, London. P. 341.
Xuhua Xia Slide 5
Conventional Hypothesis• Gray foxes on the mainland have frequently migrated to the
island during the ice ages when the sea level was much lower than it is today
• After the last glaciation period which ended about 15000 years ago, the sea level rose isolating the island from the mainland. The gray fox population on the island then evolved independently from that of the mainland and the two gradually diverge from each other.
• The Darwin’s fox is the product of this isolated evolution of the ancestral gray fox on the Chiloé Island.
• Prediction: The genetic difference should be small and comparable to the divergence time of ~15000 years.
Xuhua Xia Slide 6
The Challenge to the Hypothesis• Differences between Darwin’s fox and gray fox
– Morphological– Behavioral
• A mainland population was found (Medel, R. G., J. E. Jimenez, F. M. Jaksic, J. L. Yanez, and J. J. Armesto. 1990. Discovery of a continental population of the rare Darwin's fox, Dusicyon fulvipes, new record (Martin, 1837) in Chile. Biological Conservation 51:71-78.): Reproductive isolation
• Ancient origin of Darwin’s fox?– Scientific significance: the two criteria of species conservation.– Methodology: molecular clock
Xuhua Xia Slide 7
Mechanical Clock
We can obtain the length of time by counting the number of ticks. How does a molecular clock tick?
Xuhua Xia Slide 8
Factors Affecting DNA Evolution• Types of Mutation
– Point mutation– Insertion– Deletion– Inversion– Duplication
ATG AAA CCC CGG GGC CCC TAT TTT TTG
ATG AAA CCC CGA GGC CCC TAT TTT TTG
ATG AAA CCC CGG AAA AAA GGC CCC TAT TTT TTG
ATG AAA CCC CGG GGC CCC TAT TTT TTG
ATG AAA CCC CGG CCC CGG TAT TTT TTG
ATG AAA CCC CGG GGC CCC TAT TTT TTT TTT TTG
Xuhua Xia Slide 9
How Does a Molecular Clock Tick?ATGACCCCGACACGCAAAATTAACCCACTAATAAAATTAATTAATCACTCATTTATCGAC
ATGACCTCGACACGCAAAATTAACCCACTAATAAAGTTAATTAATCACTCATTTATCGAC
ATGACCTCGACACGCAAAATGAACCCACTAATAAAGTTAATTAATCACTCATTTATCGAC
ATGACCCCGACACGCAAAATTAACCCACTAATAAAGTTAATTAATCACTCATTTATCGAC
ATGACCTCGACACGCAAAATGAACCCACTAATAAAGTTAATTAATCACTCATTTATCGAC
Each nucleotide substitution is equivalent to one tick in a mechanical clock. The more nucleotide substitutions, the longer the time is.
Xuhua Xia Slide 10
A Major Difference
• The Molecular clock is an irregular (or even sporadic) clock.
• However, we could still say that, on average, this particular DNA clock, or that particular protein clock, ticks once every million years.
• But how do we know when is the beginning of the time? We don’t have the ancestral sequence available for comparison.
Xuhua Xia Slide 11
Divergence from a Common AncestorAAA CCC CGG GGC CCC TAT TTT TTG AAA CCC CGG GGC CCC TAT TTT TTG
AAA CCC CGG GGC CCC TAT TTT TTT
AAT CTC CGG GGC CCC TAT TTT TTT
AAT CTC CGG GGC CTC TAT TTT TTT
AAG CCT CGG GGC CCC TAT TTT TTG
AAG CCT CGG GGC CCT TAT TTT TTG
AAG CCC CGG GGC CCC TAT TTT TTG
Xuhua Xia Slide 12
Sequence Divergence
• Sequence length: 24• Identical pairs: 18• Number of nucleotide differences per site:
d = (24-18)/24 = 0.25 or d’ = -ln(1-d) = 0.288, called the Poisson-corrected P-distance, is a better estimate because it partially corrects for multiple hits (partially because it does not correct for substitutions such as AG A)
• How can we translate this 0.288 into divergence time, i.e., how many years have Species 1 and 2 diverged from each other?
Sp1: AAG CCT CGG GGC CCT TAT TTT TTG
|| | ||| ||| | ||| ||| ||
Sp2: AAT CTC CGG GGC CTC TAT TTT TTT
3
41ln
4
3 pK JC
80
1 1ln ln
1 2 1 2
2 4K
P Q QK
Xuhua Xia Slide 13
Sedimentary Rocks and Fossils
If fossils of rats and mice are found in one stratum, but not in any older strata, then, if the stratum is found to be 15 million years old, we can infer that mice and rats must have diverged 15 millions years ago.
Sedimentary rocks form on top of older rocks, with fossils buried inside.
Xuhua Xia Slide 14
Calibration of the Molecular Clock: I
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 2 4 6 8 10
Divergence Time (myr)G
enet
ic D
ista
nce
SpeciesPair
DivergenceTime (my) d’
1 1 0.05
2 2 0.12
3 3 0.11
4 4 0.2
5 5 0.21
6 6 0.27
7 7 0.35
8 8 0.33
9 9 0.41
11 ? 0.288
The same calibration can be made with any genetic distances (e.g., those calculated from DNA hybridization or allelic frequencies)
Xuhua Xia Slide 15
Different ways of calibration: II
IAU79453
IAU79450
IAU05331
IAU79451
IAU37172
IAU37171
IAU37176
IAU37181
IAU37180
FLAHAOHF
FLAHA1N
IAU11858
IVHATG391
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 2 4 6 8 10
Divergence Time (10000)
Ge
ne
tic
Dis
tan
ce
90000 years
Xuhua Xia Slide 16
The Challenge to the Hypothesis• Mitochondrial DNA genes were sequenced from
Darwin’s fox, the gray fox and other related foxes.
• According a calibrated molecular clock, the divergence time is estimated to be ~2 million years, which is much greater than the expected divergence time of ~15000 years.
Darwin’s fox
Mainland gray fox
2 myr
Xuhua Xia Slide 17
Conclusions• Darwin’s fox had diverged from the gray fox
millions of years ago on the mainland, long before the Chiloé island was formed.
• After the formation of Chiloé Island, some Darwin’s foxes, not gray foxes, migrated to the island and became established. Meanwhile, the mainland population had gone extinct.
• Darwin’s fox is an independent species and its conservation is urgent (only about 500 left).
Xuhua Xia Slide 18
Divergence time
Island Darwin’s fox
Mainland Darwin’s fox
Mainland gray fox
2 myr
Afternoon Lab: Testing the validity of the molecular hypothesis
Xuhua Xia Slide 19
Testing the Molecular Clock• Distance-based tests
• Likelihood ratio tests– The tree-based test– The relative-rate test
• Nucleotide-based analysis (Muse and Gaut 1992)• Codon-based analysis (Muse and Gaut 1994)
Xuhua Xia Slide 20
Relative-rate tests
Outgroup
Ingroup 2
Ingroup 1
1
1
2
2
Constraint both: 1= 2 = , 1 = 2 = (2 parameters)
General model: 1, 2 , 1 , 2 (4 parameters)
Constrain : 1= 2 = , 1, 2 (3 parameters)
Constrain : 1, 2 , 1 = 2 = (3 parameters)
Likelihood ratio test: 2 = 2lnL, DF = Parameter
3
3
Xuhua Xia Slide 21
Tree-based tests
BosTaurus
BalaenopteraMusculus
PongoPygmaeus
PanTroglodytes
HomoSapiens
GallusGallus
AlligatorMississippiensis
x1
x5
x7 x2
x6
x5
x4
x3
x2
x6
x1x4
x3
x8
x10
x11
x9
AlligatorMississippiensis
GallusGallus
BalaenopteraMusculus
BosTaurus
PongoPygmaeus
PanTroglodytes
HomoSapiens
DF for LRT: n - 2
Xuhua Xia Slide 22
Tree-based tests
ln2
ncRSS n pAICu
n p n p
S5
S4
S3
S2
S1
S6
S7
x5
x7 x2
x6
x1x4
x3
x8
x10
x11
x9
d’12 = x1 + x2
d’13 = x1 + x4 + x3
...
d’67 = x10 + x11
RSSnc = (dij – d’ij)2
d’12 = 2 x1
d’13 = 2 (x1 + x2)
...
d’67 = 2 ( x5 + x6)
RSSc = (dij – d’ij)2
x1
x5
x4
x3
x2
x6
S7
S6
S5
S4
S3
S2
S1
ln2
cRSS n pAICu
n p n p
Xia, X. 2009. Molecular Phylogenetics and Evolution 52:665-676
