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Automated

De

Novo

Identification

of

Repeat

Sequence

Families

in

Sequenced

Genomes

Zhirong

Bao

and

Sean

R.

Eddy

Genome

Res

originally

published

online

Jul

Access

the

most

recent

version

at

doi

gr

References

This

article

cites

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of

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Press

Methods

Automated

De

Novo

Identification

of

Repeat

Sequence

Families

in

Sequenced

Genomes

Zhirong

Bao

and

Sean

R.

Howard

Hughes

Medical

Institute

and

Department

of

Genetics

Washington

University

School

of

Medicine

St.

Louis

Missouri

USA

Repetitive

sequences

make

up

a

major

part

of

eukaryotic

genomes

We

have

developed

an

approach

for

the

de

novo

identification

and

classification

of

repeat

sequence

families

that

is

based

on

extensions

to

the

usual

approach

of

single

linkage

clustering

of

local

pairwise

alignments

between

genomic

sequences

Our

extensions

use

multiple

alignment

information

to

define

the

boundaries

of

individual

copies

of

the

repeats

and

to

distinguish

homologous

but

distinct

repeat

element

families

When

tested

on

the

human

genome

our

approach

was

able

to

properly

identify

and

group

known

transposable

elements

The

program

RECON

should

be

useful

for

first-pass

automatic

classification

of

repeats

in

newly

sequenced

genomes

-LSB-

The

following

individuals

kindly

provided

reagents

samples

or

unpublished

information

as

indicated

in

the

paper

R.

Klein

-RSB-

A

significant

fraction

of

almost

any

genome

is

repetitive

Repetitive

sequences

fall

primarily

into

three

classes

local

repeats

-LRB-

tandem

repeats

and

simple

sequence

repeats

-RRB-

families

of

dispersed

repeats

-LRB-

mostly

transposable

elements

and

retrotransposed

cellular

genes

-RRB-

and

segmental

duplications

-LRB-

duplicated

genomic

fragments

-RRB-

The

role

of

repeated

transposed

and

duplicated

sequence

in

evolution

is

an

interesting

and

controversial

topic

-LRB-

Doolittle

and

Sapienza

Orgel

and

Crick

McClintock

-RRB-

but

repetitive

sequences

are

so

numerous

that

simply

annotating

them

well

is

an

important

problem

in

itself

This

is

particularly

the

case

for

repeat

sequence

families

which

often

carry

their

own

genes

-LRB-

e.g.

transposases

and

reverse

transcriptases

-RRB-

and

can

confuse

large-scale

gene

annotation

Computational

tools

have

been

developed

for

systematic

genome

annotation

of

repeat

families

Perhaps

the

best

known

is

the

program

RepeatMasker

-LRB-

A.F.A.

Smit

and

P.

Green

unpubl

-RRB-

which

uses

precompiled

representative

sequence

libraries

to

find

homologous

copies

of

known

repeat

families

RepeatMasker

is

indispensable

in

genomes

in

which

repeat

families

have

already

been

analyzed

However

it

does

not

pass

the

platypus

test

-LRB-

Marshall

-RRB-

Repeat

families

are

largely

species-specific

so

if

one

were

to

analyze

a

new

genome

-LRB-

like

the

platypus

-RRB-

a

new

repeat

library

would

first

need

to

be

manually

compiled

With

sequencing

efforts

moving

toward

large-scale

comparative

genome

sequencing

of

a

wide

variety

of

organisms

it

is

desirable

to

also

have

a

de

novo

method

that

automates

the

process

of

compiling

RepeatMasker

libraries

Several

de

novo

approaches

have

been

attempted

with

limited

success

They

generally

start

with

a

self-comparison

with

a

sequence

similarity

detection

method

to

identify

repeated

sequence

and

then

use

a

clustering

method

to

group

related

sequences

into

families

-LRB-

Agarwal

and

States

Parsons

Kurtz

et

al.

-RRB-

Detecting

repetition

by

sequence

alignment

methods

is

relatively

easy

Automatically

Corresponding

author

E-MAIL

eddy@genetics.wustl.edu

FAX

-LRB-314-RRB- 362 7855

Article

and

publication

are

at

gr

Article

published

online

before

print

in

July

defining

biologically

reasonable

families

is

more

difficult

Local

sequence

alignments

do

not

usually

correspond

to

the

biological

boundaries

of

the

repeats

because

of

degraded

or

partially

deleted

copies

related

but

distinct

repeats

and

segmental

duplications

covering

more

than

one

repeat

Difficulty

in

defining

element

boundaries

then

causes

a

variety

of

subsequent

problems

in

clustering

related

elements

into

families

Similar

problems

arise

in

automated

detection

of

conserved

protein

domains

Curated

databases

such

as

Pfam

-LRB-

Bateman

et

al.

-RRB-

play

a

role

equivalent

to

RepeatMasker

by

providing

precompiled

libraries

of

known

domains

Automated

clustering

approaches

are

used

to

help

detect

new

domains

-LRB-

Sonnhammer

and

Kahn

Gracy

and

Argos

-RRB-

These

automated

algorithms

combine

pairwise

alignments

with

a

variety

of

extra

information

to

try

to

define

biologically

meaningful

domain

boundaries

most

importantly

they

look

at

multiple

sequence

alignments

not

just

pairwise

alignments

to

find

significantly

conserved

boundaries

Here

we

describe

an

automated

approach

for

de

novo

repeat

identification

Our

approach

uses

multiple

alignment

information

to

infer

element

boundaries

and

biologically

reasonable

clustering

of

sequence

families

RESULTS

Given

a

set

of

genomic

sequences

-LCB-

Sn

-RCB-

our

goal

is

to

identify

the

repeat

families

therein

-LRB-

denoted

by

-LCB-

F

-RCB-

-RRB-

so

that

each

family

corresponds

to

a

particular

type

of

repeat

containing

all

and

only

copies

of

that

repeat

in

-LCB-

Sn

-RCB-

Each

individual

repeat

is

a

subsequence

Sn

-LRB-

sk

ek

-RRB-

where

sk

and

ek

are

start

and

end

positions

in

sequence

Sn

Therefore

the

output

is

-LRB-

F

-LCB-

Sn

-LRB-

sk

ek

-RRB-

-RCB-

We

define

the

following

terms

element

image

of

an

element

and

syntopy

An

individual

copy

of

a

repeat

Sn

-LRB-

sk

ek

-RRB-

is

called

an

element

A

subsequence

involved

in

an

alignment

is

called

an

image

-LRB-

Fig.

-RRB-

An

element

is

the

biological

entity

we

are

trying

to

infer

Images

are

observations

from

a

pairwise

comparison

of

the

genome

sequences

-LCB-

Sn

-RCB-

One

element

forms

many

images

because

of

its

repetitive

nature

We

call

two

images

of

the

same

element

syntopic

images

-LRB-

syntopy

is

a

by

Cold

Spring

Harbor

Laboratory

Press

ISSN

Genome

Research

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from

on

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Published

by

Cold

Spring

Harbor

Laboratory

Press

Bao

and

Eddy

a.

Construct

graph

H

-LRB-

V

E

-RRB-

where

V

represents

all

the

elements

and

E

represents

similarity

-LRB-

two

elements

are

connected

by

an

edge

if

they

form

alignments

in

Step

-RRB-

b.

Find

all

connected

components

of

H.

c.

For

each

connected

component

define

a

family

as

the

set

of

all

elements

in

the

component

Problem

Inference

of

Syntopy

The

main

problems

with

this

approach

arise

from

the

use

of

overlap

to

infer

syntopy

If

all

repeat

elements

were

full

length

well

conserved

and

well

separated

by

unique

sequence

in

the

genome

all

syntopic

images

would

be

equivalent

to

their

corresponding

element

and

single

linkage

clustering

would

work

fine

However

two

major

phenomena

distort

this

ideal

picture

One

is

drift

-LRB-

both

deletion

and

substitution

mutation

-RRB-

which

causes

partial

images

-LRB-

Fig.

-RRB-

and

the

other

is

segmental

duplication

and

juxtaposition

of

common

repeats

which

Figure

Flowchart

of

the

de

novo

strategy

Input

genomic

sequences

-LRB-

black

lines

on

top

-RRB-

contain

produce

images

containing

more

a

family

of

repeats

with

three

copies

-LRB-

i.e.

elements

-RRB-

two

full

length

-LRB-

blue

and

red

boxes

-RRB-

and

one

than

one

element

-LRB-

Fig.

-RRB-

partially

deleted

-LRB-

green

box

-RRB-

These

elements

unknown

at

this

point

will

yield

three

alignments

in

an

Various

strategies

have

been

all

versus

all

pairwise

comparison

of

the

genomic

sequences

The

aligned

fragments

-LRB-

i.e.

images

-RRB-

colored

as

their

corresponding

elements

for

clarity

are

sorted

to

their

corresponding

genomic

region

suggested

for

inferring

syntopy

and

those

coming

from

the

same

element

-LRB-

i.e.

syntopic

images

-RRB-

can

be

grouped

together

according

from

image

overlap

Two

typical

to

their

overlaps

On

the

basis

of

the

syntopic

sets

elements

can

be

defined

These

defined

elements

measurements

termed

single

coverare

then

clustered

into

one

family

because

they

are

all

similar

to

each

other

age

method

and

double

coverage

method

require

the

overlap

to

be

longer

than

a

certain

fraction

of

either

or

both

of

the

images

neologism

from

syn

same

tope

site

-RRB-

Because

observed

respectively

When

overlapping

images

are

of

different

alignments

may

extend

well

beyond

the

bounds

of

an

elelength

the

two

methods

make

different

inference

of

syntopy

ment

and

may

even

include

unrelated

elements

-LRB-

e.g.

because

which

leads

to

different

definitions

of

elements

-LRB-

Fig.

-RRB-

The

of

segmental

duplication

or

coincidental

juxtaposition

of

single

coverage

method

is

suitable

for

the

scenario

in

Figure

abundant

repeats

-RRB-

syntopy

can

not

be

inferred

just

by

image

whereas

the

double

coverage

is

suitable

for

that

in

Figure

overlap

and

this

is

the

problem

we

must

address

However

either

strategy

leads

to

errors

When

the

double

coverage

method

is

applied

to

partial

images

-LRB-

Fig.

-RRB-

The

Existing

Single

Linkage

Clustering

Algorithms

it

yields

many

spurious

overlapping

elements

for

one

true

The

existing

de

novo

repeat

identification

algorithms

can

be

biological

copy

When

the

single

coverage

method

is

applied

summarized

in

our

terms

as

single

linkage

clustering

algoto

multielement

images

-LRB-

Fig.

-RRB-

it

yields

a

composite

elerithms

as

follows

ment

corresponding

to

the

whole

segmental

duplication

which

will

lump

families

together

later

in

family

definition

Obtain

pairwise

local

alignments

between

sequences

in

Simply

tuning

the

thresholds

of

these

methods

will

not

solve

-LCB-

Sn

-RCB-

the

problem

The

two

biological

scenarios

require

opposite

Define

elements

-LCB-

Sn

-LRB-

sk

ek

-RRB-

-RCB-

from

the

obtained

alignments

measurements

of

overlap

to

correctly

infer

syntopy

-LRB-

Agarwal

or

images

and

States

I.

Holmes

pers

comm

-RRB-

Furthermore

bea

Construct

graph

G

-LRB-

V

E

-RRB-

where

V

represents

all

the

imcause

these

algorithms

use

only

pairwise

relationships

beages

and

E

represents

the

syntopy

between

images

Two

tween

images

they

are

not

able

to

distinguish

the

two

bioimages

are

considered

syntopic

if

they

overlap

regardlogical

scenarios

and

choose

the

proper

criterion

The

exless

of

strand

beyond

some

threshold

ample

in

Figure

therefore

indicates

that

no

algorithm

of

this

b.

Find

all

connected

components

in

G

-LRB-

Skiena

-RRB-

type

can

work

c.

For

each

connected

component

define

an

element

However

one

also

sees

in

Figure

that

there

is

useful

Sn

-LRB-

sk

ek

-RRB-

as

the

shortest

fragment

that

covers

all

images

information

in

the

pattern

of

the

multiple

alignment

of

the

in

the

component

images

In

both

cases

most

image

endpoints

agree

on

the

Group

defined

elements

into

families

on

the

basis

of

their

boundaries

of

an

independent

repeat

The

key

distinction

lies

sequence

similarity

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

De

Novo

Repeat

Identification

-LRB-

Fig.

B

-RRB-

which

may

lead

to

an

incorrect

splitting

of

an

element

Unlike

those

in

Figure

these

misleading

image

endpoints

do

not

occur

at

the

termini

of

either

of

the

two

elements

involved

-LRB-

Fig.

open

circles

-RRB-

We

use

this

difference

to

filter

the

misleading

endpoints

before

the

element

reevaluation

and

update

procedure

-LRB-

see

image

end

selection

rule

in

Methods

-RRB-

Problem

Interfamily

Similarity

Many

repeat

families

are

evolutionarily

related

-LRB-

e.g.

the

autonomous

DNA

transposons

and

the

smaller

nonautonomous

elements

in

Caenorhabditis

elegans

Fig.

-RRB-

Although

the

reality

is

that

repeats

like

Pfam

's

protein

domain

families

or

biological

species

are

a

hiFigure

Different

biological

scenarios

require

different

methods

of

syntopy

inference

-LRB-

A

-RRB-

For

three

images

-LRB-

thin

black

lines

-RRB-

in

a

genomic

region

-LRB-

top

bold

black

line

-RRB-

the

single

and

double

coverage

erarchical

evolutionary

continuum

methods

lead

to

different

definitions

of

elements

-LRB-

B

-RRB-

A

full-length

element

and

its

images

-LRB-

black

and

that

defies

classification

it

is

still

degrey

lines

below

-RRB-

The

top

long

image

is

formed

with

another

full-length

member

in

its

family

sirable

to

impose

a

simplistic

classifiwhereas

the

shorter

images

are

formed

with

the

fragmented

members

-LRB-

C

-RRB-

A

segmental

duplication

cation

that

pretends

that

repeat

famicovering

two

kinds

of

elements

The

top

long

image

is

formed

with

the

other

copy

of

this

segmental

lies

are

distinct

for

the

purpose

of

duplication

whereas

the

shorter

images

are

formed

with

other

members

in

the

two

families

respecpractical

genome

annotation

Inastively

much

as

related

families

may

form

significant

sequence

alignments

we

in

the

endpoints

of

the

shorter

images

In

Figure

these

will

have

to

impose

arbitrary

criteria

to

avoid

lumping

related

endpoints

are

quasi-randomly

dispersed

throughout

the

mulbut

distinct

families

together

tiple

alignment

whereas

in

Figure

the

endpoints

pile

up

We

consider

two

elements

to

be

distinct

if

the

length

Biologically

this

distinction

will

hold

true

as

long

as

the

inof

the

nonconserved

regions

adds

up

to

more

than

certain

dependent

replication

of

repeats

is

more

frequent

than

the

ratio

of

both

of

the

two

sequences

-LRB-

Fig.

dashed

lines

-RRB-

The

generation

of

composite

elements

-LRB-

e.g.

by

segmental

duplifamily

relationship

determination

procedure

-LRB-

see

Methods

-RRB-

cations

-RRB-

and

deletion

is

a

random

process

which

are

usually

implements

this

definition

When

constructing

the

graph

-LRB-

but

not

always

-RRB-

the

case

for

clustering

-LRB-

Step

in

the

above

algorithm

-RRB-

elements

Our

approach

to

the

problem

is

based

on

the

above

obbelonging

to

the

same

family

are

linked

with

primary

servation

-LRB-

Fig.

-RRB-

After

an

initial

definition

using

the

single

edges

and

those

belonging

to

different

families

but

still

formcoverage

method

elements

are

split

according

to

significant

ing

significant

alignments

are

linked

with

secondary

edges

aggregations

of

image

endpoints

As

shown

in

Figure

a

Families

-LRB-

connected

components

-RRB-

are

defined

by

primary

composite

element

will

be

split

into

several

pieces

-LRB-

right

edges

panel

five

pieces

in

this

case

-RRB-

whereas

a

full-length

element

Incorrect

primary

edges

can

arise

in

the

presence

of

cerwill

be

preserved

-LRB-

left

panel

-RRB-

Details

are

specified

in

the

eletain

partially

deleted

elements

-LRB-

Fig.

-RRB-

As

shown

in

Figure

ment

reevaluation

and

update

procedure

-LRB-

see

Methods

-RRB-

primary

and

secondary

edges

are

properly

constructed

beCertain

images

complicate

the

above

splitting

process

tween

full-length

copies

of

and

by

the

family

relasuch

as

those

formed

between

related

but

distinct

elements

tionship

determination

procedure

However

edges

between

the

partial

copy

of

and

the

are

rendered

primary

as

there

are

no

nonconserved

regions

in

this

compared

with

These

false

primary

edges

will

lump

the

two

families

Such

a

situation

can

be

recognized

by

finding

triangles

involving

two

primary

edges

and

a

secondary

edge

-LRB-

e.g.

-RRB-

Once

an

element

yielding

incorrect

primary

edges

is

recognized

all

its

primary

edges

are

removed

except

for

the

one

linking

to

its

most

closely

related

element

-LRB-

Fig.

-RRB-

More

rules

are

specified

in

the

family

graph

construction

procedure

with

edge

reevaluation

-LRB-

see

Methods

-RRB-

Figure

The

RECON

algorithm

uses

the

aggregation

of

endpoints

in

the

multiple

alignment

of

images

to

distinguish

between

different

biological

scenarios

The

RECON

Algorithm

Our

algorithm

is

summarized

as

follows

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

Bao

and

Eddy

random

sample

of

Mb

or

of

the

human

genome

-LRB-

Lander

et

al.

-RRB-

and

compared

the

results

with

RepeatMasker

annotation

as

a

gold

standard

For

purpose

of

comparison

we

also

implemented

and

tested

the

basic

single

linkage

clustering

algorithm

using

both

the

single

or

double

coverage

element

definition

methods

All

three

de

novo

methods

use

the

same

set

of

pairwise

alignments

generated

by

WU-BLASTN

-LRB-

W.

Gish

unpubl

-RRB-

-LRB-

see

Methods

-RRB-

It

took

RECON

central

processing

unit

-LRB-

CPU

-RRB-

hr

and

a

maximum

of

MB

randomaccess

memory

-LRB-

RAM

-RRB-

to

analyze

this

set

of

alignments

on

a

single

Intel

Xeon

GHz

processor

A

RECON

analysis

of

a

set

of

alignments

from

a

three-fold

larger

sample

-LRB-

Mb

-RRB-

took

CPU

hr

and

MB

RAM

We

can

not

give

a

useful

asymptotic

analysis

of

memory/CPU

usage

in

terms

of

genome

or

sample

size

because

RECON

's

computational

complexity

is

strongly

dependent

on

repeat

density

and

composition

For

example

an

analysis

of

the

alignments

from

the

same

sample

with

known

repeats

Figure

Complications

because

of

sequence

similarity

between

related

families

-LRB-

A

-RRB-

masked

out

by

RepeatMasker

took

min

and

The

schematic

structure

of

and

two

related

DNA

transposons

that

are

similar

at

KB

of

RAM

This

indicates

that

for

a

large

the

end

of

their

terminal

inverted

repeats

-LRB-

black

and

grey

blocks

-RRB-

but

not

in

the

rest

of

the

sequences

-LRB-

Plasterk

and

von

Luenen

-RRB-

-LRB-

B

-RRB-

A

element

and

its

images

-LRB-

C

-RRB-

repeat-rich

genome

it

will

be

possible

-LRB-

and

necImages

in

B

are

filtered

and

only

those

ends

labeled

with

closed

circles

will

be

collected

essary

-RRB-

to

carry

out

an

iterative

RECON

analysis

to

determine

whether

the

element

should

be

split

Open

circles

in

Box

b

mark

the

for

example

first

find

the

most

abundant

famimisleading

ends

Dashed

lines

link

the

pairs

of

images

formed

with

the

same

copy

of

lies

in

a

small

sample

of

the

genome

and

then

and

represent

the

unalignable

sequences

between

a

and

a

Although

not

shown

analyze

progressively

larger

samples

after

maskin

the

figure

the

two

TIRs

of

also

form

alignments

in

the

opposite

strands

and

images

from

these

alignments

are

also

filtered

ing

families

that

have

already

been

confidently

identified

In

regard

to

the

quality

of

the

results

we

Obtain

pairwise

local

alignments

between

the

input

sefirst

looked

specifically

at

the

definition

of

Alu

which

is

the

quences

most

numerous

repeat

element

and

therefore

the

most

prone

Define

elements

from

the

obtained

alignments

to

many

sorts

of

clustering

artifacts

-LRB-

Table

-RRB-

We

identified

a.

Elements

are

first

defined

using

the

single

coverage

each

de

novo

constructed

family

that

contained

one

or

more

method

as

described

in

Step

of

the

existing

algorithm

sequences

that

overlapped

Alu

elements

defined

by

Repeatb

Each

element

defined

is

reevaluated

after

the

image

end

Masker

For

the

largest

family

defined

by

each

method

we

selection

rule

-LRB-

Fig.

-RRB-

and

the

element

reevaluate

and

also

counted

how

many

of

the

defined

elements

contained

update

procedure

-LRB-

Fig.

-RRB-

non-Alu

repeat

sequences

as

defined

by

RepeatMasker

A

c

If

an

element

defined

is

considered

composite

and

is

correct

result

would

be

that

a

de

novo

method

would

idensplit

elements

forming

alignments

with

the

composite

tify

a

single

family

of

Alu

elements

covering

element

will

be

reevaluated

The

process

continues

until

bases

of

the

genome

sample

exactly

matching

the

Repeatall

definitions

of

elements

stabilize

Masker

annotation

Group

elements

defined

into

families

on

the

basis

of

their

The

single

coverage

method

defined

elements

that

sequence

similarity

overlapped

the

Alus

defined

by

RepeatMasker

The

number

a.

Elements

and

their

family

relationship

are

determined

is

because

some

Alu

copies

are

broken

into

several

fragand

converted

to

a

graph

H

-LRB-

V

E

-RRB-

according

to

the

famments

by

the

method

The

elements

covered

too

much

ily

relationship

determination

procedure

and

the

graph

of

the

genome

-LRB-

bp

-RRB-

because

some

of

the

elements

construction

procedure

with

edge

reevaluation

-LRB-

Fig.

-RRB-

are

actually

segmental

duplications

that

happen

to

contain

b.

Find

all

connected

components

of

H

according

to

the

Alus

This

method

overclusters

In

the

largest

family

defined

primary

edges

constructed

For

each

connected

compoit

mixed

of

non-Alu

sequences

-LRB-

most

of

which

are

nent

define

a

family

as

a

set

of

all

elements

in

the

elements

the

second

most

abundant

human

repeat

family

-RRB-

component

with

the

Alu

elements

The

double

coverage

method

underclusters

images

defining

many

elements

that

comThe

algorithm

has

been

implemented

as

RECON

a

set

of

C

pletely

overlap

each

other

leading

to

a

huge

number

of

elprograms

and

Perl

scripts

The

RECON

package

including

a

ements

-LRB-

-RRB-

clustered

into

too

many

families

-LRB-

-RRB-

REdemo

and

more

materials

is

available

at

CON

minimizes

both

problems

leading

to

two

Alu-containing

families

-LRB-

one

of

which

dominates

-RRB-

with

elements

covering

bp

with

minimal

contamination

from

other

Assessment

repeat

families

Some

Alu

elements

are

still

inappropriately

To

assess

the

performance

of

RECON

we

used

it

to

analyze

a

broken

into

two

or

more

fragments

-LRB-

leading

to

significantly

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

De

Novo

Repeat

Identification

posed

protein-coding

genes

which

are

a

class

of

repeats

not

annotated

by

RepeatMasker

An

important

usage

of

a

de

novo

method

is

to

generate

repeat

libraries

for

the

incremental

analysis

of

a

genome

To

evaluate

how

useful

RECON

families

would

be

for

genome

annotation

of

elements

in

a

subsequent

sample

of

human

sequence

we

compared

the

consensus

sequence

of

each

RECON

family

to

their

most

similar

sequences

used

in

RepeatMasker

-LRB-

Table

see

Methods

-RRB-

Bases

in

RECON

's

consensus

that

are

not

in

RepeatMasker

's

sequence

are

counted

as

false

positives

-LRB-

consensus

fp

column

-RRB-

measuring

to

what

extent

RECON

defines

too

large

of

a

consensus

element

Bases

in

RepeatMasker

's

sequence

that

are

not

in

RECON

's

consensus

are

counted

as

false

negatives

-LRB-

consensus

fn

column

-RRB-

measuring

to

what

extent

RECON

Figure

False

primary

edges

because

of

partial

elements

-LRB-

A

-RRB-

The

schematic

structure

of

full-length

only

recovers

part

of

the

consensus

and

-LRB-

see

also

Fig.

-RRB-

and

a

partially

deleted

which

preserves

only

the

region

similar

to

element

For

four

of

the

six

known

-LRB-

B

-RRB-

Graph

constructed

for

and

Closed

nodes

represent

full-length

elements

Solid

and

transposable

elements

found

the

dashed

lines

represent

primary

and

secondary

edges

respectively

-LRB-

C

-RRB-

Certain

primary

edges

are

removed

from

the

partial

to

eliminate

the

false

ones

canonical

sequence

is

reconstructed

essentially

intact

-LRB-

and

-RRB-

For

and

however

only

part

of

the

canonical

elements

-RRB-

The

somewhat

lower

genomic

coverage

of

sequence

is

recovered

in

families

and

Manual

inRECON

compared

with

RepeatMasker

results

from

the

higher

spection

indicates

that

this

is

due

to

the

truly

fragmented

sensitivity

of

RepeatMasker

's

similarity

search

algorithm

nature

of

the

copies

in

our

sample

rather

than

erroneous

and

threshold

-LRB-

CROSSMATCH

with

an

aggressive

threshold

as

splittings

by

RECON

opposed

to

RECON

's

use

of

WU-BLAST

with

a

conservative

The

canonical

Alu

sequence

is

dimeric

containing

a

left

threshold

-RRB-

-LRB-

L

-RRB-

and

a

right

-LRB-

R

-RRB-

monomer

-LRB-

Jurka

and

Zuckerkandl

-RRB-

It

To

evaluate

how

reliable

RECON

annotation

is

overall

we

is

interesting

that

the

consensus

sequence

identified

by

REsystematically

compared

every

RECON

family

containing

CON

family

contains

exactly

one

and

a

half

Alu

elements

in

elements

to

RepeatMasker

annotation

-LRB-

Table

-RRB-

Each

RECON

the

configuration

LLR

The

longest

six

elements

in

are

all

in

family

was

labeled

according

to

which

RepeatMasker

annothis

configuration

Such

trimeric

Alus

have

been

noted

before

tation

made

up

the

majority

of

its

elements

Any

element

that

-LRB-

Perl

et

al.

-RRB-

and

RECON

's

annotation

indicates

that

they

was

annotated

as

a

different

family

or

not

annotated

at

all

was

have

been

actively

transposed

in

the

human

genome

considered

a

false

positive

element

-LRB-

cluster

and

cluster

columns

in

the

Table

respectively

-RRB-

These

results

indicate

that

RECON

's

families

are

almost

completely

pure

with

very

little

DISCUSSION

contamination

from

unrelated

repeat

families

The

families

The

problem

of

automated

repeat

sequence

family

classificaare

usually

a

subset

of

their

corresponding

biological

families

tion

is

inherently

messy

and

ill-defined

and

does

not

appear

for

example

one

large

family

with

the

majority

of

the

to

be

amenable

to

a

clean

algorithmic

attack

The

heuristic

elements

is

found

-LRB-

-RRB-

along

with

several

smaller

families

of

approach

we

have

taken

in

RECON

appears

to

be

satisfactory

partial

elements

-LRB-

and

-RRB-

which

are

not

for

many

practical

purposes

Our

use

of

multiple

sequence

clustered

with

a

new

family

is

a

family

of

retroalignment

information

specifically

the

clustering

of

observed

alignment

endpoints

is

a

significant

improvement

over

single

linkage

clustering

on

the

basis

of

pairTable

Definition

of

the

Alu

Family

wise

sequence

relationships

alone

Largest

Family

Several

aspects

of

the

RECON

algoNo

of

Total

Genomic

No

of

rithm

are

probabilistic

in

nature

Method

elements

length

bp

coverage

bp

families

Non-Alus

Alus

For

example

the

split

ratio

n/m

in

the

element

reevaluation

and

upRepeatMasker

date

procedure

is

correlated

with

Single

Double

the

probability

of

two

repeats

being

RECON

adjacent

by

chance

We

could

take

a

more

formal

approach

evaluating

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

Bao

and

Eddy

the

significance

of

n/m

However

a

simple

cutoff

value

appears

to

be

sufficient

The

evaluation

of

RECON

's

performance

indicates

several

issues

that

could

use

improvement

It

slightly

underclusters

elements

failing

to

appropriately

link

some

small

fragmentary

families

to

a

large

full-length

family

This

might

be

addressed

by

a

postprocessing

step

that

merges

RECON

families

when

the

consensus

of

one

family

covers

the

consensus

of

the

other

RECON

is

sometimes

unable

to

recover

a

highly

fragmented

family

in

one

piece

To

overcome

this

we

could

use

a

statistical

test

to

identify

RECON

families

whose

copies

tend

to

be

physically

adjacent

to

each

other

The

more

diverged

families

such

as

the

ancient

human

family

was

not

recovered

in

our

test

because

of

the

chosen

sensitivity

settings

of

WUBLAST

RECON

can

also

fail

when

its

simple

assumptions

about

alignment

end

clustering

are

violated

For

example

when

a

particular

form

of

partial

copy

is

generated

preferentially

-LRB-

e.g.

solo

long

terminal

repeats

-LSB-

LTRs

-RSB-

for

retrovirus-like

elements

-LSB-

Kim

et

al.

-RSB-

formed

by

high-frequency

deletion

between

the

directly

repeated

LTRs

-RRB-

it

can

lead

to

an

erroneous

splitting

of

the

full-length

copies

Also

if

a

particular

combination

of

repeat

elements

can

itself

be

duplicated

at

high

frequency

-LRB-

e.g.

the

composite

bacterial

element

-LSB-

Berg

-RSB-

-RRB-

it

may

not

be

recognized

as

composite

Different

repeat

composition

may

require

tuning

of

parameters

For

example

if

elements

are

largely

fragmented

one

may

lower

the

requirements

of

overlap

between

images

at

the

risk

of

producing

more

composite

elements

When

solo

LTRs

are

predominant

one

may

raise

the

ratio

cutoff

for

element

splitting

at

the

risk

of

failing

to

break

truly

composite

elements

One

can

only

hope

to

optimize

among

conflicting

situations

in

a

genome-scale

analysis

We

envision

using

RECON

as

a

tool

for

initial

analysis

of

a

genome

sequence

Much

like

automatically

identified

ProDom

protein

domain

families

aid

the

construction

of

curated

Pfam

multiple

alignments

the

families

identified

by

RECON

can

be

the

basis

of

a

higher

quality

level

of

analysis

such

as

using

RECON

families

to

build

a

RepeatMasker

library

or

using

RECON

multiple

alignments

to

build

a

library

of

profile

hidden

Markov

models

METHODS

Components

of

RECON

Image

End

Selection

Rule

This

rule

filters

misleading

images

-LRB-

Fig.

-RRB-

by

considering

the

length

and

arrangement

of

the

aligned

and

unaligned

sequences

between

two

elements

as

follows

For

each

pair

of

defined

elements

that

form

alignments

find

all

maximal

groups

of

alignments

in

which

all

alignments

are

part

of

one

-LRB-

but

not

necessarily

the

optimal

-RRB-

global

alignment

of

the

two

given

elements

This

is

performed

by

finding

maximal

cliques

-LRB-

Skiena

-RRB-

in

a

graph

in

which

the

vertices

represent

the

alignments

and

two

vertices

are

linked

if

the

two

corresponding

alignments

can

be

seen

as

part

of

one

global

alignment

of

the

two

given

elements

For

each

group

found

above

order

the

alignments

according

to

their

coordinates

eliminate

the

group

if

the

sequences

outside

the

outermost

alignment

or

between

any

two

adjacent

alignments

in

the

group

are

longer

than

a

given

length

cutoff

in

both

elements

and

if

not

eliminated

assign

a

score

to

the

group

as

the

sum

of

scores

of

all

alignments

in

the

group

The

length

cutoff

is

chosen

so

that

sequences

shorter

than

the

cutoff

can

be

considered

as

generated

by

the

random

extension

of

true

alignments

by

the

pairwise

alignment

tool

If

more

than

one

group

remains

take

the

one

with

the

highest

score

and

discard

the

others

Ends

of

the

images

in

the

remaining

group

-LRB-

if

any

-RRB-

are

collected

for

further

analysis

Element

Reevaluation

and

Update

Procedure

Table

The

Larger

Human

Repeat

Families

Defined

by

RECON

Clusterb

RECON

family

a

Consensusc

fp

fn

RepeatMasker

family

Alu

Alu

MaLR

-LRB-

LTR

-RRB-

MaLR

-LRB-

LTR

internal

-RRB-

MaLR

-LRB-

LTR

-RRB-

New

Copya

number

This

procedure

updates

the

definition

of

a

given

element

-LRB-

Fig.

-RRB-

by

evaluating

the

aggregation

of

image

endpoints

collected

according

to

the

rule

above

Choose

a

length

cutoff

so

that

sequences

shorter

than

the

cutoff

are

considered

generated

by

the

random

extension

of

true

alignments

by

the

pairwise

alignment

tool

Slide

a

window

of

the

chosen

length

cutoff

along

the

given

element

Within

each

window

cluster

the

collected

image

ends

as

follows

Seed

a

cluster

with

the

leftmost

end

not

yet

clustered

if

an

end

is

within

a

certain

distance

to

any

member

in

the

cluster

it

is

assigned

to

the

cluster

and

when

no

more

ends

can

be

assigned

to

the

cluster

start

a

new

cluster

if

necessary

until

all

ends

in

the

window

are

clustered

For

each

cluster

found

above

let

n

denote

the

number

of

ends

in

Number

of

defined

elements

in

RECON

family

Number

of

elements

in

RECON

family

corresponding

to

a

different

RepeatMasker

family

Number

of

elements

in

RECON

family

not

annotated

by

RepeatMasker

c

fp

False

positive

positions

vs

length

of

the

consensus

fn

False

negative

positions

vs

length

of

the

RepeatMasker

sequence

The

consensus

of

the

families

match

different

sequences

in

RepeatMasker

as

do

the

MaLR-corresponding

families

b

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

De

Novo

Repeat

Identification

the

cluster

c

denote

the

mean

position

of

these

n

ends

and

m

denote

the

number

of

images

of

the

given

element

spanning

position

c

If

n/m

is

greater

than

a

given

threshold

c

is

considered

a

significant

aggregation

point

If

no

significant

aggregation

point

is

accepted

the

original

definition

of

the

given

element

is

maintained

Otherwise

update

the

given

element

as

follows

Split

the

element

and

its

alignments

at

the

aggregation

points

discard

the

original

definition

of

the

given

element

discard

the

split

products

-LRB-

new

elements

and

alignments

-RRB-

that

are

shorter

than

the

chosen

length

cutoff

at

the

beginning

and

assign

alignments

to

proper

new

elements

If

more

than

one

new

element

remains

the

original

element

is

considered

composite

tially

defined

elements

that

have

images

and

in

which

the

number

of

partner

elements

is

less

than

one

fifth

of

the

number

of

images

Furthermore

because

we

discard

short

elements

generated

during

splitting

-LRB-

element

reevaluation

and

update

procedure

-RRB-

the

whole

family

can

suddenly

disappear

when

it

decreases

below

the

minimum

element

length

cutoff

In

addition

to

the

threshold

and

parameter

choices

in

the

initial

pairwise

comparison

RECON

has

four

tunable

parameters

The

cutoff

for

fractional

overlap

between

images

which

is

used

in

the

initial

inference

of

syntopy

by

the

single

coverage

method

-LRB-

Default

-RRB-

The

minimum

length

of

an

element

for

example

the

maximal

length

that

we

expect

the

pairwise

alignment

tool

to

spuriously

extend

by

chance

from

a

true

element

boundary

used

in

the

image

end

selection

rule

and

the

element

reevaluation

and

update

procedure

-LRB-

Default

nt

-RRB-

The

ratio

cutoff

for

splitting

an

element

at

a

given

position

used

in

the

element

reevaluation

and

update

procedure

-LRB-

Default

-RRB-

The

minimal

fraction

of

alignable

sequences

between

two

elements

before

they

are

considered

to

belong

the

same

family

-LRB-

Default

-RRB-

To

guide

parameter

optimization

we

have

developed

an

objective

function

that

measures

errors

in

the

recovery

of

known

families

in

a

genome

-LRB-

Z.

Bao

and

S.

Eddy

unpubl

-RRB-

A

detailed

description

of

the

function

is

available

at

http

The

default

parameters

were

hand

optimized

on

the

basis

of

the

recovery

of

four

experimentally

verified

DNA

transposons

-LRB-

and

-LSB-

Plasterk

and

von

Luenen

-RSB-

-RRB-

from

the

C.

elegans

genome

sequence

-LRB-

The

C.

elegans

Sequencing

Consortium

-RRB-

The

human

genome

is

dominated

by

retro-transposons

-LRB-

Alu

and

MaLR

-RRB-

and

old

fragmented

DNA

transposons

-LRB-

Lander

et

al.

-RRB-

and

these

families

yield

different

patterns

in

multiple

alignments

than

the

young

DNA

transposons

in

the

C.

elegans

training

set

so

the

test

on

human

data

was

reasonably

independent

of

our

training

of

these

few

parameters

Family

Relationship

Determination

Procedure

This

procedure

determines

for

a

given

pair

of

defined

elements

that

form

alignments

whether

the

two

belong

to

the

same

family

or

to

two

related

but

distinct

families

-LRB-

Fig.

-RRB-

The

procedure

which

considers

the

relative

length

of

the

aligned

sequences

compared

with

the

length

of

the

elements

is

as

follows

For

a

given

pair

of

defined

elements

that

form

alignments

find

all

maximal

groups

of

alignments

in

which

all

alignments

are

part

of

one

-LRB-

but

not

necessarily

the

optimal

-RRB-

global

alignment

of

the

two

given

elements

See

Step

in

the

image

end

selection

rule

for

detail

The

total

length

of

each

group

found

above

is

calculated

as

the

sum

of

the

length

of

all

alignments

in

the

group

The

longest

total

length

among

the

groups

is

treated

as

the

alignable

length

between

the

two

elements

If

the

alignable

length

is

longer

than

a

certain

fraction

of

the

length

of

either

element

the

two

elements

are

considered

to

belong

to

the

same

family

Otherwise

they

are

not

Family

Graph

Construction

Procedure

with

Edge

Reevaluation

Each

element

defined

is

represented

by

a

vertex

Edges

are

constructed

as

follows

If

two

elements

are

considered

to

belong

to

the

same

family

by

the

family

relationship

determination

procedure

a

primary

edge

is

constructed

between

the

two

corresponding

vertices

if

two

elements

form

significant

alignments

but

do

not

belong

to

the

same

family

a

secondary

edge

is

constructed

between

the

two

if

two

elements

do

not

form

significant

alignments

no

edge

is

constructed

between

the

two

For

each

vertex

v

its

primary

edges

are

reevaluated

as

follows

-LRB-

Fig.

-RRB-

Let

N

-LRB-

v

-RRB-

denote

the

set

of

vertices

directly

connected

to

v

via

primary

edges

If

any

pair

in

N

-LRB-

v

-RRB-

is

connected

by

a

secondary

edge

then

v

N

-LRB-

v

-RRB-

the

primary

edge

between

v

and

v

is

removed

unless

v

is

the

most

closely

related

element

to

v

in

N

-LRB-

v

-RRB-

-LRB-

on

the

basis

of

alignment

score

and/or

percent

identity

-RRB-

or

v

is

the

most

closely

related

element

to

v

in

N

-LRB-

v

-RRB-

In

the

latter

case

the

primary

edges

of

v

will

be

updated

as

just

described

Remove

all

secondary

edges

Human

Genome

Analysis

A

total

of

Mb

of

sequence

was

randomly

sampled

as

chunks

from

the

contigs

in

the

December

release

of

the

human

genome

-LRB-

Lander

et

al.

-RRB-

-LRB-

http

-RRB-

All-versus-all

comparison

of

the

sampled

sequences

was

performed

using

WU-BLASTN

-LRB-

W.

Gish

unpubl

-RRB-

-LRB-

http

blast.wustl.edu

-RRB-

with

options

M

N

Q

R

kap

E

wordmask

dust

wordmask

seg

maskextra

hspmax

Known

repeats

were

identified

using

the

July

version

of

RepeatMasker

-LRB-

-RRB-

with

default

options

Consensus

sequences

of

RECON

families

were

made

by

aligning

the

longest

members

of

the

family

with

-LRB-

Morgenstern

-RRB-

with

default

options

then

selecting

a

simple

majority

rule

consensus

residue

for

each

column

Implementation

Details

RECON

starts

from

a

datafile

containing

pairwise

alignments

which

allows

a

user

to

choose

a

tool

other

than

WU-BLAST

to

do

the

initial

all-versus-all

comparison

of

the

genome

to

itself

A

major

issue

is

memory

usage

To

avoid

holding

all

alignments

from

a

genome-scale

analysis

in

RAM

at

once

RECON

manipulates

files

on

disk

-LRB-

including

a

separate

file

for

each

currently

defined

element

-RRB-

It

is

therefore

extremely

input/output

intensive

RECON

is

not

useful

for

processing

short-period

tandem

repeats

these

are

split

down

to

shorter

forms

or

even

monomers

a

process

that

can

take

many

iterations

to

converge

To

improve

time

efficiency

we

filter

these

by

ignoring

the

ini

ACKNOWLEDGMENTS

We

thank

Dr.

Elena

Rivas

for

discussions

and

advice

The

sequence

sampling

tool

was

provided

by

Mr.

Robert

Klein

We

gratefully

acknowledge

financial

support

from

the

National

Science

Foundation

-LRB-

Grant

No

-RRB-

and

the

Howard

Hughes

Medical

Institute

The

publication

costs

of

this

article

were

defrayed

in

part

by

payment

of

page

charges

This

article

must

therefore

be

Genome

Research

Downloaded

from

on

May

Published

by

Cold

Spring

Harbor

Laboratory

Press

Bao

and

Eddy

hereby

marked

advertisement

in

accordance

with

USC

section

solely

to

indicate

this

fact

REFERENCES

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P.

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States

D.J.

The

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Pattern

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RPT

-RRB-

Analyzing

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structure

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evolution

of

the

C.

elegans

genome

In

Proceedings

of

the

Second

International

Conference

on

Intelligent

Systems

for

Molecular

Biology

-LRB-

eds

R.

Altman

et

al.

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pp.

AAAI

Press

Menlo

Park

CA

Bateman

A.

Birney

E.

Durbin

R.

Eddy

S.R.

Howe

K.L.

and

Sonnhammer

E.L.L.

The

Pfam

protein

families

database

Nucleic

Acids

Res

Berg

D.E.

Transposon

In

Mobile

DNA

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ed

D.E.

Berg

et

al.

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pp.

American

Society

for

Microbiology

Washington

DC

Doolittle

W.F.

and

Sapienza

C.

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evolution

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Gracy

J.

and

Argos

P.

Automated

protein

sequence

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classification

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Delineation

of

domain

boundaries

from

sequence

similarities

Bioinformatics

Jurka

J.

and

Zuckerkandl

E.

Free

left

arms

as

precursor

molecules

in

the

evolution

of

Alu

sequences

J.

Mol

Evol

Kim

J.M.

Vanguri

S.

Boeke

J.D.

Gabriel

A.

and

Voytas

D.F.

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elements

and

genome

organization

A

comprehensive

survey

of

retrotransposons

revealed

by

the

complete

Saccharomyces

cerevisiae

genome

sequence

Genome

Res

Kurtz

S.

Ohlebusch

E.

Schleiermacher

C.

Stoye

J.

and

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R.

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and

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et

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analysis

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teams

adjust

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shotgun

marriage

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B.

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significance

of

responses

of

the

genome

to

challenge

Science

Morgenstern

B.

DIALIGN

Improvement

of

the

segment-to-segment

approach

to

multiple

sequence

alignment

Bioinformatics

Orgel

L.E.

and

Crick

F.H.

Selfish

DNA

The

ultimate

parasite

Nature

Parsons

J.D.

Miropeats

Graphical

DNA

sequence

comparisons

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Appl

Biosci

Perl

A.

Colombo

E.

Samoilova

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Butler

M.C.

and

Banki

K.

Human

transaldolase-associated

repetitive

elements

are

transcribed

by

RNA

polymerase

III

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Biol

Chem

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R.H.A.

and

von

Luenen

H.G.A.M.

Transposons

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C.

elegans

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ed

D.

Riddle

et

al.

-RRB-

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Skiena

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algorithm

design

manual

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E.L.

and

Kahn

D.

Modular

arrangement

of

proteins

as

inferred

from

analysis

of

homology

Protein

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The

C.

elegans

Sequencing

Consortium

Genome

sequence

of

the

nematode

C.

elegans

A

platform

for

investigating

biology

Science

WEB

SITE

REFERENCES

WU-BLAST

Repeat

Masker

University

of

California

Santa

Cruz

Human

Genome

Project

Working

Draft

RECON

Received

January

accepted

in

revised

form

May

Genome

Research

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O


Empirical

Analysis

of

an

Evolving

Social

Network

Gueorgi

Kossinets

et

al.

Science

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science

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following

subject

collections

Sociology

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REPORTS

Empirical

Analysis

of

an

Evolving

Social

Network

Gueorgi

and

Duncan

J.

Social

networks

evolve

over

time

driven

by

the

shared

activities

and

affiliations

of

their

members

by

similarity

of

individuals

attributes

and

by

the

closure

of

short

network

cycles

We

analyzed

a

dynamic

social

network

comprising

students

faculty

and

staff

at

a

large

university

in

which

interactions

between

individuals

are

inferred

from

time-stamped

e-mail

headers

recorded

over

one

academic

year

and

are

matched

with

affiliations

and

attributes

We

found

that

network

evolution

is

dominated

by

a

combination

of

effects

arising

from

network

topology

itself

and

the

organizational

structure

in

which

the

network

is

embedded

In

the

absence

of

global

perturbations

average

network

properties

appear

to

approach

an

equilibrium

state

whereas

individual

properties

are

unstable

ocial

networks

have

attracted

great

interest

in

recent

years

largely

because

of

their

likely

relevance

to

various

social

processes

such

as

information

processing

-LRB-

-RRB-

distributed

search

-LRB-

-RRB-

and

diffusion

of

social

influence

-LRB-

-RRB-

For

many

years

however

social

scientists

have

also

been

interested

in

social

networks

as

dynamic

processes

in

themselves

-LRB-

-RRB-

Over

time

individuals

create

and

deactivate

social

ties

thereby

altering

the

structure

of

the

networks

in

which

they

participate

Social

network

formation

is

a

complex

process

in

which

many

individuals

simultaneously

attempt

to

satisfy

their

goals

under

multiple

possibly

conflicting

constraints

For

example

individuals

often

interact

with

others

similar

to

themselves

a

tendency

known

as

homophily

-LRB-

-RRB-

and

attempt

to

avoid

conflicting

relationships

-LRB-

-RRB-

while

exploiting

cross-cutting

circles

of

acquaintances

-LRB-

-RRB-

However

the

realization

of

these

intentions

is

subject

to

spatial

and

social

proximity

of

available

others

-LRB-

-RRB-

In

circumstances

where

individuals

may

benefit

from

cooperative

relationships

they

may

emphasize

embedded

ties

those

belonging

to

locally

dense

clusters

-LRB-

-RRB-

For

example

they

may

choose

new

acquaintances

who

are

friends

of

friends

a

process

known

as

triadic

closure

-LRB-

-RRB-

They

may

however

also

seek

access

to

novel

information

and

resources

and

hence

benefit

from

access

to

bridges

-LRB-

-RRB-

connections

outside

their

circle

of

acquaintances

or

by

spanning

structural

holes

-LRB-

-RRB-

precisely

between

others

who

do

not

know

one

another

Finally

social

ties

may

dissolve

for

various

reasons

such

as

when

they

are

not

supported

by

other

relations

-LRB-

-RRB-

or

else

conflict

with

them

-LRB-

-RRB-

To

what

extent

each

of

these

individually

plausible

mechanisms

manifests

itself

in

Department

of

Sociology

and

Institute

for

Social

and

Economic

Research

and

Policy

Columbia

University

West

Street

MC

New

York

NY

USA

Santa

Fe

Institute

Hyde

Park

Road

Santa

Fe

NM

USA

To

whom

correspondence

should

be

addressed

E-mail

-LRB-

G.K.

-RRB-

-LRB-

D.J.W.

-RRB-

JANUARY

VOL

SCIENCE

Downloaded

from

on

May

S

various

social

and

organizational

contexts

is

largely

an

empirical

matter

requiring

longitudinal

-LRB-

i.e.

collected

over

time

-RRB-

network

data

-LRB-

-RRB-

combined

with

information

about

individuals

attributes

and

group

affiliations

-LRB-

-RRB-

Yet

longitudinal

network

data

are

rare

and

the

best

known

examples

are

for

small

groups

-LRB-

-RRB-

Recent

studies

of

much

larger

networks

by

contrast

have

tended

to

focus

on

cross-sectional

-LRB-

i.e.

static

-RRB-

analysis

-LRB-

-RRB-

or

they

have

emphasized

either

the

interactions

between

individuals

-LRB-

-RRB-

or

their

group

affiliations

-LRB-

-RRB-

but

not

both

We

analyzed

a

longitudinal

network

data

set

created

by

merging

three

distinct

but

related

data

structures

First

we

compiled

a

registry

of

e-mail

interactions

in

a

population

of

undergraduate

and

graduate

students

faculty

and

staff

of

a

large

university

over

the

course

of

one

academic

year

For

each

e-mail

message

the

timestamp

sender

and

list

of

recipients

-LRB-

but

not

the

content

-RRB-

were

recorded

Second

for

the

same

population

we

gathered

information

specifying

a

range

of

personal

attributes

-LRB-

status

gender

age

departmental

affiliation

and

number

of

years

in

the

community

-RRB-

Third

we

obtained

complete

lists

of

the

classes

attended

and

taught

respectively

by

students

and

instructors

in

each

semester

For

privacy

protection

all

individual

and

group

identifiers

were

encrypted

we

can

determine

for

example

whether

two

individuals

were

in

the

same

class

together

but

not

which

class

that

was

Because

in

a

university

setting

class

attendance

provides

essential

opportunities

for

faceto-face

interaction

-LRB-

at

least

for

students

-RRB-

we

used

classes

to

represent

the

changing

affiliation

structure

Our

use

of

e-mail

communication

to

infer

the

underlying

network

of

social

ties

is

supported

by

recent

studies

reporting

that

use

of

e-mail

in

local

social

circles

is

strongly

correlated

with

face-to-face

and

telephone

interactions

-LRB-

-RRB-

Individuals

and

groups

of

individuals

may

differ

in

their

e-mail

usage

thus

inferences

drawn

on

a

small

sample

of

communicating

pairs

may

be

confounded

by

the

idiosyncrasies

of

particular

personalities

and

relationships

However

by

averaging

over

thousands

of

such

relationships

we

expect

that

our

results

will

represent

only

the

most

general

regularities

-LRB-

at

least

within

the

environment

of

a

university

community

-RRB-

governing

the

initiation

and

progression

of

interpersonal

communication

To

ensure

that

our

data

do

indeed

reflect

interpersonal

communication

as

opposed

to

ad

hoc

mailing

lists

and

other

mass

mailings

we

filtered

out

messages

with

more

than

four

recipients

-LRB-

of

all

messages

had

four

or

fewer

addressees

-RRB-

After

filtering

there

were

messages

exchanged

by

the

users

during

days

of

observation

Ongoing

social

relationships

produce

spikes

of

e-mail

exchange

that

can

be

observed

and

counted

-LRB-

-RRB-

The

stronger

the

relationship

between

two

individuals

the

more

spikes

will

be

observed

for

this

particular

pair

on

average

within

a

given

time

interval

We

approximate

instantaneous

strength

wij

of

a

relationship

between

two

individuals

i

and

j

by

the

geometric

rate

of

bilateral

e-mail

exchange

within

a

window

of

t

days

-LRB-

-RRB-

The

instantaneous

network

at

any

point

in

time

includes

all

pairs

of

individuals

that

sent

one

or

more

messages

in

each

direction

during

the

past

days

Using

daily

network

approximations

we

calculated

-LRB-

i

-RRB-

shortest

path

length

dij

and

-LRB-

ii

-RRB-

the

number

of

shared

affiliations

sij

for

all

pairs

of

individuals

in

the

network

on

consecutive

days

spanning

most

of

the

fall

and

spring

semesters

-LRB-

-RRB-

By

identifying

new

ties

that

appear

in

the

network

over

time

we

can

compute

two

sets

of

measures

-LRB-

i

-RRB-

cyclic

closure

and

-LRB-

ii

-RRB-

focal

closure

biases

For

some

specified

value

of

dij

cyclic

closure

bias

is

defined

as

the

empirical

probability

that

two

previously

unconnected

individuals

who

are

distance

dij

apart

in

the

network

will

initiate

a

new

tie

Thus

cyclic

closure

naturally

generalizes

the

notion

of

triadic

closure

-LRB-

-RRB-

i.e.

formation

of

cycles

of

length

three

By

analogy

we

define

focal

closure

bias

as

the

empirical

probability

that

two

strangers

who

share

an

interaction

focus

-LRB-

in

the

present

case

a

class

-RRB-

will

form

a

new

tie

Because

class

attendance

is

relevant

mostly

for

students

the

results

on

focal

and

cyclic

closure

are

presented

here

for

a

subset

of

graduate

and

undergraduate

students

-LRB-

-RRB-

Figure

-LRB-

triangles

-RRB-

shows

that

in

the

absence

of

a

shared

focus

-LRB-

i.e.

class

-RRB-

cyclic

closure

diminishes

rapidly

in

strength

with

dij

implying

that

individuals

who

are

far

apart

in

the

network

have

no

opportunity

to

interact

and

hence

are

very

unlikely

to

form

ties

For

example

individuals

who

are

separated

by

two

intermediaries

-LRB-

dij

-RRB-

are

about

times

less

likely

to

initiate

a

new

tie

REPORTS

Fig.

Cyclic

and

focal

closure

-LRB-

A

-RRB-

Average

daily

empirical

probability

pnew

of

a

new

tie

between

two

individuals

as

a

function

of

their

network

distance

dij

Circles

pairs

that

share

one

or

more

interaction

foci

-LRB-

attend

one

or

more

classes

together

-RRB-

triangles

pairs

that

do

not

share

classes

-LRB-

B

-RRB-

pnew

as

a

function

of

the

number

of

mutual

acquaintances

Circles

pairs

with

one

or

more

shared

foci

triangles

pairs

without

shared

foci

-LRB-

C

-RRB-

pnew

as

a

function

of

the

number

of

shared

interaction

foci

Circles

pairs

with

one

or

more

mutual

acquaintances

triangles

pairs

without

mutual

acquaintances

Lines

are

shown

as

a

guide

for

the

eye

standard

errors

are

smaller

than

symbol

size

Fig.

Results

of

multivariate

survival

analysis

of

triadic

closure

for

a

sample

of

pairs

of

graduate

and

undergraduate

students

Shown

are

the

hazard

ratios

and

confidence

intervals

from

Cox

regression

of

time

to

tie

formation

between

two

individuals

since

their

transition

to

distance

dij

Hazard

ratio

g

means

that

the

probability

of

closure

changes

by

a

factor

of

g

with

a

unit

change

in

the

covariate

or

relative

to

the

reference

category

We

treat

a

covariance

as

significant

if

the

corresponding

confidence

interval

does

not

contain

g

-LRB-

no

effect

-RRB-

Predictors

sorted

by

effect

magnitude

strong

indirect

-LRB-

if

indirect

connection

strength

is

above

sample

median

otherwise

-RRB-

classes

-LRB-

number

of

shared

classes

-RRB-

acquaintances

-LRB-

number

of

mutual

network

neighbors

less

-RRB-

same

age

-LRB-

if

absolute

difference

in

age

is

less

than

year

otherwise

-RRB-

same

year

-LRB-

if

absolute

difference

in

number

of

years

at

the

university

is

less

than

otherwise

-RRB-

gender

-LSB-

effects

of

male-male

-LRB-

MM

-RRB-

and

female-female

-LRB-

FF

-RRB-

pair

respectively

relative

to

a

female-male

-LRB-

FM

-RRB-

pair

-RSB-

acquaint

classes

-LRB-

interaction

effect

between

acquaintances

and

classes

-RRB-

and

obstruction

-LRB-

if

no

mutual

acquaintance

has

the

same

status

as

either

member

of

the

pair

otherwise

-RRB-

-LRB-

-RRB-

than

individuals

who

are

separated

by

only

one

intermediary

-LRB-

dij

-RRB-

Figure

-LRB-

circles

-RRB-

however

demonstrates

that

when

two

individuals

share

at

least

one

class

they

are

on

average

times

more

likely

to

interact

if

they

also

share

an

acquaintance

-LRB-

dij

-RRB-

and

about

times

more

likely

if

they

do

not

-LRB-

dij

-RRB-

In

addition

Fig.

shows

that

the

empirical

probability

of

tie

formation

increases

with

the

number

of

mutual

acquaintances

both

for

pairs

with

-LRB-

circles

-RRB-

and

without

-LRB-

triangles

-RRB-

shared

classes

becoming

independent

of

shared

affiliations

for

large

numbers

of

mutual

acquaintances

-LRB-

six

and

more

-RRB-

Figure

displays

equivalent

information

for

shared

classes

indicating

that

while

the

effect

of

a

single

shared

class

is

roughly

interchangeable

with

a

single

mutual

acquaintance

the

presence

of

additional

acquaintances

has

a

greater

effect

than

additional

foci

in

our

data

set

These

findings

imply

that

even

a

minimally

accurate

generative

network

model

would

need

to

account

separately

for

-LRB-

i

-RRB-

triadic

closure

-LRB-

ii

-RRB-

focal

closure

and

-LRB-

iii

-RRB-

the

compounding

effect

of

both

biases

together

Our

data

can

also

shed

light

on

theoretical

notions

of

tie

strength

-LRB-

-RRB-

and

attributebased

homophily

-LRB-

-RRB-

We

found

-LRB-

Fig.

-RRB-

that

the

likelihood

of

triadic

closure

increases

if

the

average

tie

strength

between

two

strangers

and

their

mutual

acquaintances

is

high

which

supports

commonly

accepted

theory

-LRB-

-RRB-

By

contrast

homophily

with

respect

to

individual

attributes

appears

to

play

a

weaker

role

than

might

be

expected

Of

the

attributes

we

considered

in

this

and

other

models

-LRB-

-RRB-

status

-LRB-

undergraduate

graduate

student

faculty

or

staff

-RRB-

gender

age

and

time

in

the

community

has

a

significant

effect

on

triadic

closure

The

significant

predictors

are

tie

strength

number

of

mutual

acquaintances

shared

classes

the

interaction

of

shared

classes

and

acquaintances

and

status

obstruction

which

we

define

as

the

effect

on

triadic

closure

of

a

mediating

individual

who

has

a

different

status

than

either

of

the

potential

acquaintances

For

example

two

students

connected

through

a

professor

are

less

likely

to

form

a

direct

tie

than

two

students

connected

through

another

student

ceteris

paribus

We

suspect

however

that

status

obstruction

may

be

an

indicator

of

unobserved

focal

closure

beyond

class

attendance

Thus

although

homophily

has

often

been

observed

with

respect

to

individual

attributes

in

cross-sectional

data

-LRB-

-RRB-

these

effects

may

be

mostly

indirect

operating

through

the

structural

constraint

of

shared

foci

-LRB-

-RRB-

such

as

selection

of

courses

or

extracurricular

activities

Our

results

also

have

implications

for

the

utility

of

cross-sectional

network

analysis

which

relies

on

the

assumption

that

the

network

properties

of

interest

are

in

equilibrium

-LRB-

-RRB-

Figure

shows

that

different

network

measures

exhibit

varying

levels

of

stability

over

time

and

with

respect

to

the

smoothing

window

t.

Average

vertex

degree

bk

fractional

size

of

the

largest

component

S

and

mean

shortest

path

length

L

all

exhibit

seasonal

changes

and

produce

different

measurements

for

different

choices

of

t

where

bk

is

especially

sensitive

to

t

The

clustering

coefficient

C

-LRB-

-RRB-

however

stays

virtually

constant

as

bk

changes

suggesting

perhaps

surprisingly

that

averages

of

local

network

properties

are

more

stable

than

global

properties

such

as

L

or

S.

Nevertheless

these

results

suggest

that

as

long

as

the

smoothing

window

t

is

chosen

appropriately

and

care

is

taken

to

avoid

collecting

data

in

the

vicinity

of

exogenous

changes

-LRB-

e.g.

end

of

semester

-RRB-

average

network

measures

remain

stable

over

time

and

thus

can

be

recovered

with

reasonable

fidelity

from

network

snapshots

The

relative

stability

of

average

network

properties

however

does

not

imply

equivalent

stability

of

individual

network

properties

for

which

the

empirical

picture

is

more

complicated

On

the

one

hand

we

find

that

distributions

of

individual-level

properties

are

stable

with

the

same

caveats

that

apply

to

averages

For

example

-LRB-

Fig.

A

to

C

-RRB-

the

shape

of

the

degree

distribution

p

-LRB-

k

-RRB-

is

relatively

constant

across

the

duration

of

our

SCIENCE

VOL

JANUARY

Downloaded

from

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May

REPORTS

Fig.

Network-level

properties

over

time

for

three

choices

of

smoothing

window

t

days

-LRB-

dashes

-RRB-

days

-LRB-

solid

lines

-RRB-

and

days

-LRB-

dots

-RRB-

-LRB-

A

-RRB-

Mean

vertex

degree

bk

-LRB-

B

-RRB-

Fractional

size

of

the

largest

component

S.

-LRB-

C

-RRB-

Mean

shortest

path

length

in

the

largest

component

L.

-LRB-

D

-RRB-

Clustering

coefficient

C.

of

network

evolution

are

generic

and

which

are

specific

to

the

cultural

organizational

and

institutional

context

in

question

We

note

that

the

methods

we

introduced

here

are

generic

and

may

be

applied

easily

to

a

variety

of

other

settings

We

conclude

by

emphasizing

that

understanding

tie

formation

and

related

processes

in

social

networks

requires

longitudinal

data

on

both

social

interactions

and

shared

affiliations

-LRB-

-RRB-

With

the

appropriate

data

sets

theoretical

conjectures

can

be

tested

directly

and

conclusions

previously

based

on

cross-sectional

data

can

be

validated

or

qualified

appropriately

References

and

Notes

P.

S.

Dodds

D.

J.

Watts

C.

F.

Sabel

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

J.

M.

Kleinberg

Nature

-LRB-

-RRB-

T.

W.

Valente

Network

Models

of

the

Diffusion

of

Innovations

-LRB-

Hampton

Press

Cresskill

NJ

-RRB-

P.

Doreian

F.

N.

Stokman

Eds.

Evolution

of

Social

Networks

-LRB-

Gordon

and

Breach

New

York

-RRB-

P.

Lazarsfeld

R.

Merton

in

Freedom

and

Control

in

Modern

Society

M.

Berger

T.

Abel

C.

Page

Eds

-LRB-

Van

Nostrand

New

York

-RRB-

pp.

M.

McPherson

L.

Smith-Lovin

J.

M.

Cook

Annu

Rev.

Sociol

-LRB-

-RRB-

J.

A.

Davis

Am

J.

Sociology

-LRB-

-RRB-

T.

M.

Newcomb

The

Acquaintance

Process

-LRB-

Holt

Rinehart

and

Winston

New

York

-RRB-

P.

M.

Blau

J.

E.

Schwartz

Crosscutting

Social

Circles

-LRB-

Academic

Press

Orlando

FL

-RRB-

S.

L.

Feld

Am

J.

Sociology

-LRB-

-RRB-

J.

S.

Coleman

Sociol

Theory

-LRB-

-RRB-

A.

Rapoport

Bull

Math

Biophys

-LRB-

-RRB-

M.

S.

Granovetter

Am

J.

Sociology

-LRB-

-RRB-

R.

S.

Burt

Am

J.

Sociology

-LRB-

-RRB-

M.

Hammer

Soc

Networks

-LRB-

-RRB-

M.

T.

Hallinan

E.

E.

Hutchins

Soc

Forces

-LRB-

-RRB-

M.

E.

J.

Newman

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

S.

Wasserman

K.

Faust

Social

Network

Analysis

Methods

and

Applications

-LRB-

Cambridge

Univ.

Press

Cambridge

-RRB-

M.

E.

J.

Newman

SIAM

Review

-LRB-

-RRB-

J.

P.

Eckmann

E.

Moses

D.

Sergi

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

C.

Cortes

D.

Pregibon

C.

Volinsky

J.

Comp

Graph

Stat

-LRB-

-RRB-

P.

Holme

C.

R.

Edling

F.

Liljeros

Soc

Networks

-LRB-

-RRB-

B.

Wellman

C.

Haythornthwaite

Eds.

The

Internet

in

Everyday

Life

-LRB-

Blackwell

Oxford

-RRB-

N.

K.

Baym

Y.

B.

Zhang

M.

Lin

New

Media

Soc

-LRB-

-RRB-

Materials

and

methods

are

available

as

supporting

material

on

Science

Online

H.

Louch

Soc

Networks

-LRB-

-RRB-

G.

Kossinets

D.

J.

Watts

data

not

shown

M.

E.

J.

Newman

S.

H.

Strogatz

D.

J.

Watts

Phys

Rev.

E

-LRB-

-RRB-

We

thank

P.

Dodds

and

two

anonymous

reviewers

for

helpful

comments

and

B.

Beecher

and

W.

Bourne

for

assistance

with

data

collection

and

anonymization

This

research

was

supported

by

NSF

-LRB-

SES

-RRB-

the

James

S.

McDonnell

Foundation

Legg

Mason

Funds

and

the

Institute

for

Social

and

Economic

Research

and

Policy

at

Columbia

University

Fig.

Stability

of

degree

distribution

and

individual

degree

ranks

-LRB-

A

-RRB-

Degree

distribution

in

the

instantaneous

network

at

day

logarithmically

binned

-LRB-

B

-RRB-

Same

at

day

-LRB-

C

-RRB-

The

Kolmogorov-Smirnov

statistic

D

comparing

degree

distribution

in

the

instantaneous

network

at

day

and

in

subsequent

daily

approximations

-LRB-

D

-RRB-

Dissimilarity

coefficient

for

degree

ranks

z

where

rS

is

the

Spearman

rank

correlation

between

individual

degrees

at

day

and

in

subsequent

approximations

z

varies

between

and

and

measures

the

proportion

of

variance

in

degree

ranks

that

can

not

be

predicted

from

the

ranks

in

the

initial

network

data

set

except

during

natural

spells

of

reduced

activity

such

as

winter

break

-LRB-

Fig.

-RRB-

On

the

other

hand

as

Fig.

illustrates

individual

ranks

change

substantially

over

the

duration

of

the

data

set

Analogous

results

-LRB-

-RRB-

apply

to

the

concept

of

Bweak

ties

-LSB-

-LRB-

-RRB-

The

distribution

of

tie

strength

in

the

network

is

stable

over

time

and

bridges

are

on

average

weaker

than

embedded

ties

Econsistent

with

-LRB-

-RRB-

However

they

do

not

retain

their

bridging

function

or

even

remain

weak

indefinitely

Our

results

suggest

that

conclusions

relating

differences

in

outcome

measures

such

as

status

or

performance

to

differences

in

individual

network

position

-LRB-

-RRB-

should

be

treated

with

caution

Bridges

for

example

may

indeed

facilitate

diffusion

of

information

across

entire

communities

-LRB-

-RRB-

However

their

unstable

nature

suggests

that

they

are

not

Bowned

-LSB-

by

particular

individuals

indefinitely

thus

whatever

advantages

they

confer

are

also

temporary

Furthermore

it

is

unclear

to

what

extent

individuals

are

capable

of

strategically

manipulating

their

positions

in

a

large

network

even

if

that

is

their

intention

-LRB-

-RRB-

Rather

it

appears

that

individual-level

decisions

tend

to

Baverage

out

-LSB-

yielding

regularities

that

are

simple

functions

of

physical

and

social

proximity

Sharing

focal

activities

-LRB-

-RRB-

and

peers

-LRB-

-RRB-

for

example

greatly

increases

the

likelihood

of

individuals

becoming

connected

especially

when

these

conditions

apply

simultaneously

It

may

be

the

case

of

course

that

the

individuals

in

our

population

mostly

students

and

faculty

do

not

strategically

manipulate

their

networks

because

they

do

not

need

to

not

because

it

is

impossible

Thus

our

conclusions

regarding

the

relation

between

local

and

global

network

dynamics

may

be

specific

to

the

particular

environment

that

we

have

studied

Comparative

studies

of

corporate

or

military

networks

could

help

illuminate

which

features

Supporting

Online

Material

Materials

and

Methods

References

July

accepted

November

science

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O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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