Download ppt - Comparing phylogenetic and statistical classification methods for DNA barcoding Frederic Austerlitz, Olivier David, Brigitte Schaeffer, Sisi Ye, Michel

Comparing phylogenetic and statistical classification methods

for DNA barcoding

Frederic Austerlitz, Olivier David, Brigitte Schaeffer, Sisi Ye, Michel

Veuille & Catherine Laredo

Testing the assignation methods

• Individual to be tested:– X1 : ATATGTACCTAGTA

– X2 : TTATCTACCTAGAA

• Reference sample :– 1_1: ATATGTACGTAGTA

– 1_2: ATATCTACGAAGTA

– 1_3: ATATCTACTAAGTA

– 2_1: ATATGTACGTAGTT

– 2_2: ATATGTACGAAGTT

– 2_3: ATTTCTACTAAGTT

Species 1

Species 2

Phylogenetic methods

1_1 1_3 2_1 1_2 2_2 2_3X1

• Unanimity rule: X1 classified as ambiguous, X2 classified as species 1

• Majority rule: X1 and X2 classified as belonging to species 1

• Two methods tested: neighbor joining and maximum likelihood (PhyML, Guindon and Gascuel 2003)

X2

Node 0 Start with all the individualsto reach:

« individuals in each leave belong to the same species »

A: 5 B: 3 C: 8

CART (Classification And Regression Tree)

• Builds a classification tree from the reference sample

(Breiman et al., 1984, 1996)

Node 1

A: 5 B: 0 C: 4

Node 2

A: 0 B: 3 C: 4

Leave 1

A: 5 B: 0 C: 0

Leave 2

A: 0 B: 0 C: 4

Leave 3

A: 0 B: 0 C: 4

Leave 1

A: 0 B: 3 C: 0

node t = subset of individualsp (j | t) = relative proportion of individuals of class j in node t

JJ

1,...,

1 maximum

1,0,...,0,...,0,...,0,1 minimum for

Computing the impurity of the nodes

Impurity criterion at node t:

I(t) = - ∑j p(j|t) log p(j|t) entropy

I(t) = 1 - ∑j p(j|t)² Gini index

))(),...,(),...,1(()( tJptjptptI

PL + PR = 1

t

tLtR

s PRPL s SS: set of variables

t: set of individuals

Finding the best split

ΔI(s*,t) = max { ΔI(s,t), s S }

ΔI(s,t) = I(t) - pL I(tL) - pR I(tR)

Rule to select a splitting candidate:

Decrease in impurity:

s* selected as

Stop splitting rule: e.g. threshold β

max { ΔI(s,t), s S } < β

Example:

I(t) = I(node0) = - ∑j p(j|t) log p(j|t)At node 0:

I(node0) = - [3/10 × log(3/10) + 3/10 × log(3/10) + 4/10 × log(4/10)]

3 species, 10 individuals, 4 variables

I(node0) = 1.0889

Species x1 x2 x3 x4 A a g c g A a g c g A a a a g B t t a g B t t a g B t a c g C a c a g C g c a g C a c a g C a c c g

Node 0A: 3/10, B: 3/10, C: 4/10

I(t) = - ∑j p(j|t) log p(j|t)

Splitting according to x1


At node L: Ix1(nodeL) = - [0 + 3/3× log(3/3) + 0] = 0

Ix1(nodeR) = - [3/7× log(3/7) + 0 + 4/7× log(4/7)]At node R:

Ix1(nodeR) = 0.6829

A: 0, B: 3/3, C: 0 A: 3/7, B: 0, C: 4/7

Node 0A: 3/10, B: 3/10, C: 4/10

x1= t

Node L Node R

PR= 7/10PL= 3/10

ΔI(x1,t) = I(node0) - PL *Ix1(nodeL) - PR *Ix1(nodeR)

ΔI(x1,t) = 1.0889 - 0.3 × 0 - 0.7 × 0.6829 = 0.6109


At node L:

Ix2(nodeR) = - [0 + 0 + 4/4*log(4/4)] = 0


Ix2(nodeL) = - [3/6*log(3/6) + 3/6*log(3/6) +0]

At node R:

Node 0A: 3/10, B: 3/10, C: 4/10

x2 = a,g,t

Node L Node RA: 3/6, B: 3/6, C: 0 A: 0, B: 0, C: 4/4

PR= 4/10PL= 6/10


ΔI(x2,t) = 1.0889 - 0.6 *0.6931 - 0.4*0 = 0.6730

Ix2(nodeL) = 0.6931



Ix3(nodeR) = - [2/4*log(2/4) + 1/4*log(1/4) + 1/4*log(1/4)] = 1.040


At node L: Ix3(nodeL) = - [1/6*log(1/6) + 2/6*log(2/6) + 2/6*log(2/6)] = 1.031

At node R:

Node 0A: 3/10, B: 3/10, C: 4/10

x3 = a

Node L Node RA: 1/6, B: 2/6, C: 1/6 A: 2/4, B: 1/4, C: 1/4

PR= 4/10PL= 6/10


ΔI(x3,t) = 1.0889 - 0.6 *1.031 - 0.4*1.040 = 0.0662



ΔI(x2,t) = 0.6730

ΔI(s*,t) = max ΔI(s,t)s S

ΔI(x1,t) = 0.6109

ΔI(x3,t) = 0.0662

x4 no division

x2 is selected

Choosing the best split

Criterion: entropy

Software: RPackage: rpart

Implementation

Bagging or bootstrap aggregation

N bootstrap samples from original data

N classification trees

N assignements for a new individual

Majority rule → class of the new individual

Simulation method

• one haploid population that splits into two (or more), T generations in the past.

• The ancestral population and the two new populations of constant size N.

• Sequences with mutation rate parameter of interest = 2N• Simulations performed with simcoal 2.1.2 (Excoffier et al)

T

Evaluation of the different classification methods

• We simulate n +1 individuals in each species.

• n individuals are considered as the reference samples, and the last one as the individual to test.

• Using repeated simulations, we compute the proportion of cases in which each test individual is correctly assigned to its species.

T

Parameters assumed for the simulation study

• = 3 (e.g. Litoria) or 30 (e.g. Astraptes)

• Reference sample size n = 3, 5, 10, 25

• Effective population size: N = 1000

• Separation time T = N/10, N/2, N, 5N or 10N

• Number of newly founded populations: from 2 to 5 In all cases, all populations assumed to be founded

simultaneously.

Comparison between phylogenetic methods

0.0%

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reference sample size

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neighbor joining

PhyML

• 2 populations • Separation time = 500, = 3.

Effect of the number of populations

• = 3

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bagging

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(Separation time: 500 generations, Reference sample size = 10)

Effect of the separation time

• = 3

• = 30

(4 populations, Reference sample size = 10)

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Separation time

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Bagging

Effect of the size of the reference sample

• = 3

• = 30

(4 populations, Separation time = 500)

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Bagging

Adding nuclear genes

• We considered the case where polymorphism of nuclear genes are also available.

• We assumed that– these genes were independent.– they all have the same (= 4N) value, equal

to the value for the cytoplasmic genes.– They do not show intragenic recombination or

they show it at a rate equal to the mutation rate (c = , i.e. 4Nc = ).


• Phylogenetic method• 2 populations• = 3, separation time = 500, reference sample size = 10

0%

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number of nuclear loci

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without recombination no cyto

with recombination no cyto

without recombination + cyto

with recombination + cyto


• Phylogenetic method• = 30, separation time = 500, reference sample size = 10

0%

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0 1 2 3 4 5

number of nuclear loci

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without recombination no cyto

with recombination no cyto

without recombination + cyto

with recombination + cyto

Application to real data

• Litoria (Schneider et al, 1998, Mol. Ecol. 7, 487–498).

– 4 species– Average sample size: 43.75– average = 1.54

92%

93%

94%

95%

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97%

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100%

0 2 4 6 8 10 12


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Application to real data

• Astraptes (Hebert et al 2004. Proc. Natl Acad. Sci. USA 101,14812–14817)

– 12 species– Average sample size: 38.8– average = 23.5

90%

91%

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3 4 5 6 7 8 9 10

Reference Sample size

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Application to real data• Cowries (Meyer et al (2005) PLoS Biol 3: e422)

– 357 taxa (species/subspecies)– Average sample size: 5.7– average = 2.93

90%91%92%

93%94%95%96%97%98%

99%100%101%

0 5 10 15 20 25 30


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Conclusions• Regarding phylogenetic methods, the maximum

likelihood method performs better than the neighbor joining.

• CART performs better than phylogenetic methods for poorly informative data (low value)

• but not for more polymorphic data (high value)

• Adding nuclear loci can help, but at a quite high cost.

• Recombination improves the phylogenetic method for low values (Ongoing work for CART).

Perspectives

• Developing a statistical method to put a confidence level on a given assignation.

• Evaluating other classification methods (learning methods)