HGMHybrid networks with

Gene Evolution

Ali Tofigh, KTH

Jens Lagergren, KTH

Bengt Sennblad

Why?

• Lateral gene transfer– Important process in prokaryote evolution

– Less common in eukaryotes• Polyploidic hybridization, e.g., in plants• Endosymbionts -- mitochondria &chloroplasts

– Source of incongruence among gene trees

What?

• An integrated model for:

– Species evolution through speciation and polyploidic hybridization

• Yields species networks

– Gene evolution in species networks by gene duplication and loss

• Yields binary gene trees

A hybrid evolution model

Species evolution through speciation and polyploidic hybridization

How?

• Polyploidic hybridization– Hybridization followed by

polyploidization• Avoid hybrid sterility

– Parental genomes retained in hybrid

– Yields a network

• Endosymbiosis– Both symbiont genomes

’retained’ in host

A hybrid evolution model• Extended BD model

– -- extinction rate– = +– -- speciation rate – -- hybridization parent 1

parent 2 ~U([n]), n=#lineages at ti

• Generation simple• Reconctruction Pr[S] non-trivial

– Dependencies– Ghosts

The probability of a hybrid network• Scenario:

– Network– Ghost specification

• Between events – Birth-death process– Keep ploidy level

• Sum over scenarios– Upper limit of k ghosts– Dynamic programming– Prior of j ghosts at root

Summary

• Algorithm for Pr[S] given maximmum k ghosts– Event-based model– Efficient o(nk3)

• Approximation– k 100 good approximation

Hybrid species network Gene evolution Model

Gene evolution in hybrid networks

How?

• Gene evolution by– Duplication– Loss

• Species tree constraints– Speciation splits genes– Hybrid has one gene

copy from each parent

Idea: treat genomes individually and use gene evolution model

1) Extract binary homeolog tree from the hybrid species network

2) Enumerate all possible gene tree leaf-mappings w.r.t. homeolog tree

S G

H G+gs1 G+gs2 G+gs3 G+gs4

gs:G S

Probability of gene tree in hybrid network

• For each enumerated pair (G,gsi)– Compute probability Pr[G, gsi|H]

using the gene evolution model

• Probability of original gene tree is

i.e., the expectation over enumerated trees

Summary

• Naive brute force algorithm for Pr[G|S]– Enumeration of gs-maps exponential

• Reasonable for small problems, bad for larger

– Can be done efficiently with DP

• Model extensions– Gene loss probabilities after hybridization– Use prior information about ploidy level

Combining the models

Integrated analysis -- primeHGM

• Aim: identify hybrid species network given a set of gene trees {G1, G2,…,Gn}

• Bayesian framework

– Pr[G|S] - Extended gene evolution model– Pr[S]- Model for hybrid networks

Search for best hybrid network• Ideally -- MCMC over S

– Branch-swapping on networks problematic

– Maximum a posteriori (MAP) comparison

– Probabilistic pseudo-enumeration

• Synthetic data

Probabilistic pseudo-enumeration• Generate a set S of networks from hybrid model

• Select ’true’ S’ from S and generate set G of gene trees

• For each S S– Compute MAP of Pr[S |G] over div. time space of S

• Evaluate rank of S’ w.r.t. MAP

• Repeat with different true S’ and compute frequencies of different ranks of S’

Preliminary results

data subset 1 2 3 5 10

Easy 2G 0.81 0.97 1 1 1

10G 0.87 1 1 1 1

Hard 2G 0.41 0.56 0.66 0.77 0.85

10G 0.6 0.8 0.85 0.93 0.99

• 4-leaved species networks– S size of 100 covers 90% of prior prob

• Gene tree with 4-12 leaves– two sizes of G: 2 and 10 gene trees– Two parameter settings: Hard and Easy

Summary

• primeHGM– Integrated model

• Hybrid species network• GEM in hybrid network

– MAP estimation of net work divergence times

• Future– include sequence data– Branchswapping– Inclusion of prior information

Acknowledgements

• Gene evolution model– Lars Arvestad, Ann-Charlotte Berglund-

Sonnhammer, Jens Lagergren, Örjan Åkerborg

• Hybrid species network model– Ali Tofigh, Jens Lagergren

’Pseudo-visible’ extinction vertices