Vol

January

doi

LETTERS

Infotaxis

as

a

strategy

for

searching

without

gradients

Massimo

Emmanuel

Boris

I.

Chemotactic

bacteria

rely

on

local

concentration

gradients

to

guide

them

towards

the

source

of

a

Such

local

cues

pointing

towards

the

location

of

the

source

are

not

always

available

at

macroscopic

scales

because

mixing

in

a

flowing

medium

breaks

up

regions

of

high

concentration

into

random

and

disconnected

patches

Thus

animals

sensing

odours

in

air

or

water

detect

them

only

intermittently

as

patches

sweep

by

on

the

wind

or

A

macroscopic

searcher

must

devise

a

strategy

of

movement

based

on

sporadic

cues

and

partial

information

Here

we

propose

a

search

algorithm

which

we

call

infotaxis

designed

to

work

under

such

conditions

Any

search

process

can

be

thought

of

as

acquisition

of

information

on

source

location

for

infotaxis

information

plays

a

role

similar

to

concentration

in

chemotaxis

The

infotaxis

strategy

locally

maximizes

the

expected

rate

of

information

gain

We

demonstrate

its

efficiency

using

a

computational

model

of

odour

plume

propagation

and

experimental

data

on

mixing

Infotactic

trajectories

feature

zigzagging

and

casting

paths

similar

to

those

observed

in

the

flight

of

The

proposed

search

algorithm

is

relevant

to

the

design

of

olfactory

but

the

general

idea

of

infotaxis

can

be

applied

more

broadly

in

the

context

of

searching

with

sparse

information

Chemotactic

search

strategies

based

on

local

concentration

gradients

require

the

concentration

to

be

high

enough

to

ensure

that

its

average

difference

measured

at

two

nearby

locations

is

larger

than

typical

-LRB-

see

also

Supplementary

Information

-RRB-

The

signal-to-noise

ratio

depends

of

course

on

the

averaging

time

and

might

be

improved

by

waiting

However

the

average

concentration

may

be

decaying

rapidly

-LRB-

for

example

exponentially

-RRB-

with

distance

away

from

the

source

and

in

this

weak

signal-to-noise

-LRB-

dilute

-RRB-

case

the

waiting

time

becomes

huge

An

example

of

organisms

performing

olfactory

search

in

a

dilute

limit

is

provided

by

moths

which

use

pheromones

to

locate

their

Moths

are

known

to

proceed

upwind

by

way

of

counterturning

patterns

of

extended

-LRB-

casting

-RRB-

or

limited

-LRB-

zigzagging

-RRB-

crosswind

width

thought

to

correlate

with

low

and

high

rates

of

odour

detection

A

practical

situation

involving

the

challenge

of

searching

in

dilute

conditions

is

encountered

in

the

design

of

sniffers

robots

that

track

chemicals

emitted

by

drugs

chemical

leaks

explosives

and

mines

Existing

methods

apply

to

high-concentration

conditions

where

or

plumetracking

might

be

used

In

the

dilute

limit

the

searcher

detects

odour

in

a

sporadic

sequence

of

distinct

events

arising

from

its

encounters

with

patches

of

fluid

-LRB-

or

air

-RRB-

where

turbulent

mixing

has

failed

to

dissipate

the

advected

odour

down

to

a

level

below

the

detectability

These

detection

events

or

hits

are

separated

by

wide

voids

with

no

detectible

signal

Because

the

probability

of

odour

encounter

depends

on

the

distance

from

the

source

the

set

of

encounters

that

occurred

at

times

-LCB-

ti

-RCB-

along

the

search

trajectory

r

-LRB-

t

-RRB-

carries

tion

about

the

source

location

We

shall

use

T

t

to

denote

times

and

coordinates

of

these

hits

In

the

spirit

of

coding

theory

the

trace

T

t

might

be

thought

of

as

a

message

sent

by

the

source

and

transmitted

to

the

searcher

with

strong

noise

due

to

the

random

nature

of

odour

propagation

in

the

turbulent

medium

Decoding

of

the

message

is

implemented

using

Bayes

formula

to

construct

given

the

received

signal

the

posterior

probability

distribution

Pt

-LRB-

-RRB-

for

the

unknown

location

of

the

source

-LRB-

see

Methods

and

similar

independent

arguments

in

ref

-RRB-

The

subscript

t

reminds

us

that

T

t

and

Pt

-LRB-

-RRB-

are

dynamical

objects

continuously

updated

with

time

The

specific

decoding

protocol

depends

of

course

on

the

nature

of

the

detection

events

and

the

transmitting

medium

For

concreteness

we

treat

here

two

cases

-LRB-

-RRB-

experimental

time-course

data

for

a

mixing

flow

and

-LRB-

-RRB-

a

model

where

detectable

particles

-LRB-

which

represent

patches

of

detectable

odours

-RRB-

are

emitted

by

the

source

at

rate

R

have

a

finite

lifetime

t

propagate

with

effective

diffusivity

D

and

are

advected

by

a

mean

current

or

wind

V

The

decoding

protocol

requires

knowing

the

probability

of

odour

encounters

as

a

function

of

the

distance

to

the

source

This

function

can

be

computed

analytically

for

model

-LRB-

-RRB-

or

estimated

from

experimental

data

for

case

-LRB-

-RRB-

as

detailed

in

Supplementary

Information

The

latter

method

is

quite

general

and

might

be

applied

to

other

cases

as

well

Given

a

probability

distribution

P

-LRB-

-RRB-

for

the

location

of

the

source

we

can

show

-LRB-

see

Supplementary

Information

-RRB-

that

the

expected

search

time

T

is

bounded

by

T

where

S

is

Shannon

's

entropy

for

the

distribution

S

dxP

x

ln

P

x

-LRB-

refs

-RRB-

The

latter

quantifies

how

spread-out

the

distribution

is

and

goes

to

zero

when

the

position

of

the

source

is

localized

to

one

site

that

is

is

known

The

rate

of

acquisition

of

information

is

quantified

by

the

rate

of

reduction

of

-LRB-

see

also

Supplementary

Information

-RRB-

The

main

problem

for

the

searcher

is

that

the

real

probability

distribution

is

unknown

-LRB-

to

it

-RRB-

and

must

be

estimated

from

the

available

data

the

history

of

its

odour

encounters

As

information

accumulates

the

entropy

of

the

estimated

distribution

decreases

and

with

it

the

expected

time

to

locate

the

source

The

searcher

is

faced

with

conflicting

choices

of

either

proceeding

with

its

current

information

-LRB-

that

is

going

to

the

estimated

most

probable

source

location

-RRB-

or

alternatively

pausing

to

gather

more

information

and

obtain

a

more

reliable

estimate

of

the

source

distribution

The

problem

of

dealing

with

only

partially

reliable

information

is

quite

general

and

has

received

a

systematic

formulation

in

learning

theory

in

terms

of

the

exploration

versus

exploitation

trade-off

to

be

struck

for

effective

In

the

search

context

exploitation

of

the

currently

estimated

Pt

-LRB-

-RRB-

by

chasing

locations

of

maximal

estimated

probability

is

very

risky

because

it

can

lead

off

the

track

The

most

conservative

exploration

approach

is

to

accumulate

information

before

taking

any

step

This

strategy

is

safe

but

not

productive

CNRS

URA

Institut

Pasteur

In

Silico

Genetics

Paris

Cedex

France

Aix

Marseille

IRPHE

Technopole

Chateau

Gombert

Marseille

France

Kavli

Institute

for

Theoretical

Physics

University

of

California

Santa

Barbara

California

USA

Nature

Publishing

Group

NATURE

Vol

January

LETTERS

and

is

inferior

to

more

active

exploration

for

example

systematic

search

in

a

particular

To

balance

exploration

and

exploitation

we

propose

the

following

infotaxis

strategy

At

each

time

step

the

searcher

chooses

the

direction

that

locally

maximizes

the

expected

rate

of

information

acquisition

Specifically

the

searcher

chooses

among

the

neighbouring

sites

on

a

lattice

and

standing

still

the

move

that

maximizes

the

expected

reduction

in

entropy

of

the

posterior

probability

field

Expectations

are

based

on

the

information

currently

available

that

is

the

field

Pt

-LRB-

-RRB-

itself

The

intuitive

idea

is

that

entropy

decreases

-LRB-

and

thus

information

accumulates

-RRB-

faster

close

to

the

source

because

cues

arrive

at

a

higher

rate

hence

tracking

the

maximum

rate

of

information

acquisition

will

guide

the

searcher

to

the

source

much

like

concentration

gradients

in

chemotaxis

Suppose

that

the

searcher

has

arrived

at

r

at

time

t

and

gathered

information

is

stored

into

the

field

Pt

-LRB-

-RRB-

having

entropy

S

The

variation

of

entropy

expected

upon

moving

to

one

of

the

neighbouring

points

rj

-LRB-

or

standing

still

-RRB-

is

DS

r.rj

Pt

rj

-LCB-

Sz

-LCB-

Pt

rj

rj

rj

z

The

first

term

on

the

right-hand

side

corresponds

to

finding

the

source

that

is

becoming

a

d-function

and

entropy

becoming

zero

which

occurs

with

estimated

probability

Pt

-LRB-

rj

-RRB-

The

second

term

on

the

right-hand

side

corresponds

to

the

alternative

case

when

the

source

is

not

found

at

rj

Symbols

rk

-LRB-

rj

-RRB-

denote

the

probability

that

k

detections

be

made

at

rj

during

a

time-step

Dt

given

by

a

Poisson

law

rk

for

independent

detections

The

expected

number

of

hits

is

estimated

as

h

rj

Dt

Pt

R

rj

with

R

-LRB-

-RRB-

denoting

the

mean

rate

of

hits

at

position

r

if

the

source

is

located

in

-LRB-

see

Methods

-RRB-

The

symbols

DSk

in

equation

-LRB-

-RRB-

denote

the

change

of

entropy

between

the

fields

-LRB-

-RRB-

and

Pt

-LRB-

-RRB-

Two

effects

contribute

to

DSk

first

-LRB-

rj

-RRB-

because

the

source

was

not

found

and

second

the

estimated

posterior

probabilities

are

modified

by

the

k

cues

received

The

first

term

on

the

right-hand

side

of

equation

-LRB-

-RRB-

is

the

exploitative

term

weighing

only

the

event

that

the

source

is

found

at

the

point

rj

and

favouring

motion

to

maximum

likelihood

points

The

second

term

on

the

right-hand

side

of

equation

-LRB-

-RRB-

is

the

information

gain

from

receiving

additional

cues

It

appears

even

when

the

searcher

does

not

move

and

thus

represents

conservative

exploration

Thus

we

explicitly

see

that

infotaxis

naturally

combines

exploitative

and

exploratory

tendencies

-LRB-

see

Supplementary

Information

for

details

of

this

point

and

for

quantitative

comparisons

among

different

strategies

-RRB-

a

Average

search

time

800 600 400

Initial

distance

80 90 100 110

b

PDF

c

Residual

search

time

Search

time

Residual

entropy

Figure

Typical

infotactic

trajectories

a

Without

wind

b

with

wind

Simulations

are

performed

for

a

model

of

odour

spreading

where

detectable

particles

are

emitted

at

rate

R

have

a

lifetime

t

propagate

with

diffusivity

D

-LRB-

combining

turbulent

and

molecular

diffusion

-RRB-

and

are

advected

by

a

mean

wind

V

The

wind

in

b

is

directed

downwards

The

greyscale

represents

the

mean

detection

rate

decaying

exponentially

at

large

distances

In

each

panel

the

searcher

starts

from

the

black

filled

triangle

the

colour

code

on

the

trajectories

is

linear

in

the

elapsed

time

and

odour

detections

are

indicated

by

black

filled

circles

Note

the

long

lags

with

no

particle

detections

characteristic

of

searches

in

dilute

conditions

Figure

Quantitative

characterization

of

infotaxis

searches

a

Scaling

of

the

average

search

time

with

the

initial

distance

to

the

source

The

mean

path

of

particles

during

their

lifetime

is

The

linear

scaling

at

large

distances

compares

favourably

with

the

exponential

time

needed

to

average

out

concentration

noise

Error

bars

indicate

s.d.

b

The

exponential

decay

of

the

search

time

probability

distribution

function

-LRB-

PDF

-RRB-

indicating

that

infotaxis

is

not

plagued

by

strong

fluctuations

c

The

residual

time

to

locate

the

source

plotted

against

the

entropy

of

the

estimated

source

location

PDF

The

exponential

dependence

of

the

residual

time

indicates

that

reducing

entropy

is

effective

in

ensuring

a

rapid

search

process

Nature

Publishing

Group

LETTERS

NATURE

Vol

January

Infotactic

paths

are

illustrated

in

Fig.

which

presents

the

result

of

a

numerical

simulation

using

the

model

of

odour

propagation

described

in

Methods

In

the

absence

of

wind

-LRB-

Fig.

-RRB-

Pt

-LRB-

r

-RRB-

is

rotationally

symmetric

around

the

starting

point

and

the

searcher

starts

spiralling

around

it

-LRB-

as

is

observed

with

sea

urchin

-RRB-

Interestingly

in

the

absence

of

hits

the

radius

of

the

spiral

increases

in

a

scale

invariant

manner

making

an

approximately

Archimedean

spiral

As

time

progresses

and

information

is

gathered

along

the

trajectory

the

direction

towards

the

source

emerges

as

the

preferential

one

finally

leading

the

searcher

to

the

source

In

the

presence

of

wind

-LRB-

Fig.

-RRB-

the

search

alternates

phases

of

consistent

progression

upwind

with

phases

of

wider

crosswind

excursion

and

even

downwind

movements

similar

to

the

classical

casting

and

zigzagging

patterns

observed

during

bird

and

moth

To

quantify

the

performance

of

the

proposed

search

algorithm

we

examine

-LRB-

Fig.

-RRB-

the

scaling

of

the

average

search

time

with

the

initial

distance

to

the

source

for

the

model

without

wind

-LRB-

the

most

difficult

one

-RRB-

The

linear

dependence

found

for

large

initial

distances

should

be

contrasted

with

the

exponential

dependence

needed

to

average

out

the

concentration

noise

-LRB-

see

Supplementary

Information

-RRB-

Furthermore

random

walking

searchers

would

often

attain

the

boundaries

of

the

box

where

the

search

is

taking

place

The

corresponding

probability

distribution

of

search

times

would

have

a

long

tail

decaying

as

contrary

to

the

exponential

decay

shown

in

Fig.

Figure

shows

the

relation

between

search

times

and

the

entropy

of

the

posterior

field

Pt

-LRB-

-RRB-

which

supports

the

theoretical

bound

mentioned

above

Figure

presents

an

infotactic

path

generated

in

a

simulation

using

experimental

measurements

of

dye

concentration

in

a

turbulent

Hits

occur

when

the

searcher

encounters

concentration

above

a

threshold

which

we

chose

sufficiently

high

to

keep

the

number

of

hits

low

Simulations

indicate

that

the

infotactic

strategy

is

robust

with

respect

to

the

searcher

's

model

of

the

turbulent

medium

and

to

fluctuations

and

inhomogeneities

of

the

medium

Indeed

even

the

simplistic

hypothesis

of

time-independent

odour

encounters

does

not

hinder

the

search

Modelling

of

the

turbulent

medium

might

be

further

improved

by

accounting

for

temporal

correlations

of

odour

plume

encounter

and

velocity

fluctuations

-LRB-

see

Supplementary

Information

-RRB-

We

have

presented

an

olfactory

search

algorithm

that

works

in

the

dilute

limit

corresponding

to

weak

sources

in

realistic

flows

These

are

the

conditions

encountered

in

applications

of

olfactory

robots

and

by

various

living

creatures

When

comparing

our

results

with

the

behaviour

of

living

creatures

we

need

to

bear

in

mind

that

similarity

in

trajectories

does

not

imply

identity

of

causal

mechanisms

and

decision

Still

it

is

worth

remarking

that

the

olfactory

search

motion

observed

with

moths

and

birds

exhibits

a

pattern

of

extended

crosswind

casts

and

zigzags

similar

to

the

one

generated

in

Fig.

by

the

general

principle

of

local

maximization

of

information

gain

We

note

that

the

dilute

limit

also

describes

the

case

of

odour

diffusion

at

the

molecular

scale

provided

that

the

searcher

can

detect

single

molecules

This

situation

may

apply

for

example

in

the

case

of

sea

urchin

sperm

which

responds

to

a

single

molecule

of

resact

a

chemoattractant

It

is

difficult

to

imagine

a

single

cell

Figure

Simulation

of

infotaxis

using

mixing

flow

experimental

Snapshots

-LRB-

false

colours

red

corresponds

to

high

concentrations

-RRB-

of

dye

concentration

levels

are

acquired

from

mixing

flow

experimental

data

and

the

trajectory

of

the

searcher

is

numerically

simulated

in

the

resulting

sequence

of

fields

Snapshots

and

trajectories

are

shown

at

four

successive

times

in

panels

a

d.

Light

blue

regions

correspond

to

concentrations

below

the

detection

threshold

The

black

star

denotes

an

isolated

odour

detection

event

The

infotactic

strategy

is

robust

with

respect

to

fluctuations

and

inhomogeneities

of

the

medium

-LRB-

for

example

of

the

wind

direction

-RRB-

and

its

modelling

by

the

searcher

Robustness

stems

from

the

tracking

of

information

rather

than

estimated

maximum

likelihood

locations

Nature

Publishing

Group

NATURE

Vol

January

LETTERS

performing

complex

computations

like

those

required

for

infotaxis

as

described

above

It

will

be

interesting

to

explore

heuristic

approximations

simple

enough

to

be

plausible

for

single

cells

Finally

we

note

that

the

general

information-theoretic

approach

described

above

in

the

olfactory

search

context

applies

more

broadly

to

any

situation

where

competing

demands

of

exploration

and

exploitation

must

be

efficiently

balanced

METHODS

Estimation

of

the

posterior

probability

distribution

The

probability

distribution

posterior

to

experiencing

a

trace

T

t

of

uncorrelated

odour

encounters

is

given

by

t

exp

-LCB-

R

r

t

dt

PH

R

r

ti

Lr

T

t

i

t

H

Pt

Lx

T

t

dx

exp

-LCB-

R

r

t

jx

dt

Pi

R

r

ti

jx

dx

Here

H

is

the

number

of

hits

along

the

trajectory

the

tis

are

the

corresponding

times

and

-LRB-

T

t

-RRB-

is

the

likelihood

of

observing

the

trace

T

t

of

odour

encounters

for

a

source

located

at

This

expression

is

supplemented

by

the

prescription

that

visited

regions

where

the

source

was

not

found

have

zero

probability

Note

that

-LRB-

-RRB-

factorizes

as

Pt

-LRB-

-RRB-

times

a

term

that

depends

on

the

hits

received

in

the

Dt

interval

Thus

keeping

track

of

the

whole

trajectory

and

the

history

of

detections

is

not

required

The

expression

for

Pt

-LRB-

-RRB-

is

derived

by

taking

the

mean

hit

rate

during

an

infinitesimal

interval

dt

to

be

R

-LRB-

-RRB-

dt

and

the

number

of

hits

to

be

Poisson

distributed

The

function

R

-LRB-

-RRB-

appearing

in

equation

-LRB-

-RRB-

denotes

the

mean

rate

of

hit

encounters

at

position

r

for

a

source

located

at

For

the

model

where

detectable

particles

are

emitted

by

the

source

at

rate

R

have

a

finite

lifetime

t

propagate

with

isotropic

effective

diffusivity

D

-LRB-

which

parameterizes

the

combined

effect

of

turbulent

and

molecular

diffusion

-RRB-

and

are

-LRB-

possibly

-RRB-

advected

by

a

mean

current

or

wind

V

the

function

can

be

computed

analytically

as

described

in

Supplementary

Information

The

result

for

the

three

dimensional

case

is

sffiffiffiffiffiffiffiffiffiffiffiffiffiffi

aR

-LCB-

jr

-LCB-

j

-LCB-

y

-LCB-

V

Dt

l

e

e

l

R

jr

-LCB-

j

V

t

where

a

is

the

size

of

the

searcher

and

the

coordinates

are

chosen

to

have

the

wind

blowing

along

the

y

axis

in

the

negative

direction

A

similar

expression

holds

in

two

dimensions

In

both

cases

the

rate

function

decreases

exponentially

at

large

distances

-LRB-

anisotropically

in

the

presence

of

wind

-RRB-

For

experimental

data

on

mixing

flows

the

parameters

in

the

rate

function

are

estimated

from

the

data

as

detailed

in

Supplementary

Information

Mixing

flow

experiment

and

simulation

parameters

Parameters

used

in

the

simulations

are

as

follows

Figs

and

emission

rate

of

the

source

R

particle

lifetime

t

and

diffusivity

D

The

typical

travel

distance

durpffiffiffiffiffiffi

ing

a

lifetime

is

approximately

Dt

The

search

space

is

a

grid

and

equation

-LRB-

-RRB-

was

evaluated

for

five

possible

actions

at

each

time

step

-LRB-

moves

to

the

four

neighbours

and

standing

still

-RRB-

Figure

wind

blows

downwards

with

unit

speed

the

emission

rate

R

5 1/2

and

the

lifetime

of

particles

t

the

initial

vertical

separation

to

the

source

Figure

experimental

data

are

generated

injecting

dye

by

a

mm

tube

in

the

far

field

of

a

jet

a

large-scale

-LRB-

integral

scale

cm

-RRB-

sustained

turbulent

flow

The

pictures

in

the

figure

show

the

random

advection

of

the

dye

downstream

of

the

injection

point

-LRB-

for

about

three

integral

scales

-RRB-

Dye

is

passively

transported

by

the

flow

as

odours

are

Odour

detection

events

correspond

to

encounters

with

dye

concentrations

above

a

threshold

fixed

at

about

five

times

the

average

intensity

level

The

mean

velocity

-LRB-

pointing

downward

in

Fig.

-RRB-

is

about

cm

-LRB-

its

measurement

by

olfactory

robots

might

be

realized

using

standard

anemometers

-RRB-

and

the

root-meansquare

velocity

is

about

of

the

mean

velocity

giving

a

Reynolds

number

of

Snapshots

of

the

field

are

acquired

at

a

frequency

of

Hz

Coherent

odour

patches

make

the

searcher

spiral

around

the

location

of

the

encounters

due

to

correlations

among

the

detections

Yet

the

resulting

search

process

is

just

twice

as

long

as

for

a

model

with

independent

hits

and

might

be

further

accelerated

by

accounting

for

time-correlations

as

detailed

in

Supplementary

Information

Received

May

accepted

November

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B.

C.

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T.

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Birch

M.

C.

Kennedy

M.

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-RRB-

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Olfaction

-LRB-

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Murlis

J.

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Carde

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T.

Odor

plumes

and

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insects

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Annu

Rev.

Entomol

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Dusenbery

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B.

Sensory

Ecology

How

Organisms

Acquire

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Respond

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-LRB-

Freeman

New

York

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Fine-scale

structure

of

pheromone

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upwind

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flying

moths

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-LRB-

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Olfaction

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Berlin

-RRB-

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as

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Rev.

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preprogrammed

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Physiol

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-LRB-

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mobile

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olfaction

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Supplementary

Information

is

linked

to

the

online

version

of

the

paper

at

Acknowledgements

This

work

was

done

during

the

visits

of

M.V.

and

E.V.

to

KITP

and

was

supported

by

the

ARO

E.V.

is

a

member

of

the

Institut

Universitaire

de

France

Author

Information

Reprints

and

permissions

information

is

available

at

The

authors

declare

no

competing

financial

interests

Correspondence

and

requests

for

materials

should

be

addressed

to

B.I.S.

-LRB-

shraiman@kitp.ucsb.edu

-RRB-

Nature

Publishing

Group

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


Emergent

Biogeography

of

Microbial

Communities

in

a

Model

Ocean

Michael

J.

Follows

et

al.

Science

-LRB-

-RRB-

DOI

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REPORTS

germ

insects

not

only

uncovers

those

features

essential

to

this

developmental

mode

but

also

sheds

light

on

how

the

bcd-dependent

anterior

patterning

program

might

have

evolved

Through

analysis

of

the

regulation

of

the

trunk

gap

gene

Kr

in

Drosophila

and

Nasonia

we

have

been

able

to

demonstrate

that

anterior

repression

of

Kr

is

essential

for

head

and

thorax

formation

and

is

a

common

feature

of

long-germ

patterning

Both

insects

accomplish

this

task

through

maternal

anteriorly

localized

factors

that

either

indirectly

-LRB-

Drosophila

-RRB-

or

directly

-LRB-

Nasonia

-RRB-

repress

Kr

and

hence

trunk

fates

In

Drosophila

the

terminal

system

and

bcd

regulate

expression

of

gap

genes

including

Dm-gt

that

repress

Dm-Kr

Nasonia

's

bcd-independent

long-germ

embryos

must

solve

the

same

problem

but

they

employ

a

maternally

localized

repression

system

in

which

maternal

Nv-gt

is

localized

to

the

oocyte

's

anterior

where

it

represses

Nv-Kr

In

the

dipteran

lineage

whereas

gt

retained

the

ability

to

repress

Kr

maternal

regulation

of

Kr

's

position

was

taken

over

by

two

novel

features

bcd

a

specific

dipteran

innovation

and

the

terminal

pathway

which

although

present

ancestrally

appears

to

function

less

extensively

in

the

anterior

of

nondipteran

insects

-LRB-

-RRB-

In

addition

to

activating

anterior

patterning

genes

such

as

otd

and

hb

bcd

also

acquired

regulation

of

gt

which

became

a

strictly

zygotic

gene

with

a

reduced

role

in

repressing

Kr

Our

findings

thus

identify

two

independent

mechanisms

for

long-germ

anterior

patterning

one

using

two

maternally

localized

genes

and

gt

that

respectively

activate

anterior

zygotic

patterning

genes

and

repress

trunk

fates

and

a

second

using

bcd

for

these

same

functions

thereby

demoting

otd

and

gt

to

zygotic

gap

genes

Interestingly

it

appears

that

long-germ

embryos

use

RNA

localization

for

a

number

of

different

developmental

processes

-LRB-

-RRB-

By

contrast

in

short-germ

insects

although

some

localized

RNAs

have

been

identified

there

is

as

yet

no

evidence

of

their

contribution

to

anterior-posterior

patterning

-LRB-

-RRB-

mRNA

localization

indeed

appears

to

be

an

important

component

of

long-germ

embryogenesis

perhaps

even

playing

a

role

in

the

transition

from

the

ancestral

short-germ

to

the

derived

longgerm

fate

References

and

Notes

G.

K.

Davis

N.

H.

Patel

Annu

Rev.

Entomol

-LRB-

-RRB-

T.

Berleth

et

al.

EMBO

J.

-LRB-

-RRB-

W.

Driever

C.

Nusslein-Volhard

Cell

-LRB-

-RRB-

J.

Lynch

C.

Desplan

Curr

Biol

-LRB-

-RRB-

J.

A.

Lynch

A.

E.

Brent

D.

S.

Leaf

M.

A.

Pultz

C.

Desplan

Nature

-LRB-

-RRB-

J.

Savard

et

al.

Genome

Res

-LRB-

-RRB-

G.

Struhl

P.

Johnston

P.

A.

Lawrence

Cell

-LRB-

-RRB-

A.

Preiss

U.

B.

Rosenberg

A.

Kienlin

E.

Seifert

H.

Jackle

Nature

-LRB-

-RRB-

M.

Hulskamp

C.

Pfeifle

D.

Tautz

Nature

-LRB-

-RRB-

X.

Wu

R.

Vakani

S.

Small

Development

-LRB-

-RRB-

R.

Kraut

M.

Levine

Development

-LRB-

-RRB-

J.

A.

Lynch

C.

Desplan

Nat

Protocols

-LRB-

-RRB-

R.

Kraut

M.

Levine

Development

-LRB-

-RRB-

M.

A.

Pultz

et

al.

Development

-LRB-

-RRB-

G.

F.

Hewitt

et

al.

Development

-LRB-

-RRB-

J.

A.

Lynch

E.

C.

Olesnicky

C.

Desplan

Dev

Genes

Evol

-LRB-

-RRB-

R.

Schroder

C.

Eckert

C.

Wolff

D.

Tautz

Proc

Natl.

Acad

Sci

U.S.A.

-LRB-

-RRB-

E.

C.

Olesnicky

et

al.

Development

-LRB-

-RRB-

A.

Bashirullah

R.

L.

Cooperstock

H.

D.

Lipshitz

Annu

Rev.

Biochem

-LRB-

-RRB-

G.

Bucher

L.

Farzana

S.

J.

Brown

M.

Klingler

Evol

Dev

-LRB-

-RRB-

The

authors

wish

to

thank

members

of

the

Desplan

and

Small

laboratories

for

support

and

advice

This

project

was

supported

by

NIH

grants

awarded

to

C.D.

and

awarded

to

S.S.

A.E.B

is

a

Damon

Runyon

Fellow

supported

by

the

Damon

Runyon

Cancer

Research

Foundation

-LRB-

-RRB-

Nv-gt

and

green

fluorescent

protein

-LRB-

gfp

-RRB-

and

observed

the

expected

Nv-gt

phenotype

deletion

of

head

and

thorax

as

well

as

loss

of

anterior

Nv-hb

expression

-LRB-

Fig.

D

and

E

-RRB-

Knockdown

of

Nv-gt

and

Nv-Kr

yielded

striking

results

In

of

examined

embryos

the

head

and

thorax

-LRB-

-RRB-

were

restored

-LRB-

Fig.

-RRB-

and

the

resulting

cuticular

phenotypes

were

essentially

identical

to

those

after

Nv-Kr

RNAi

alone

-LRB-

Fig.

-RRB-

Consistent

with

rescued

head

and

thorax

development

anterior

zygotic

Nv-hb

was

also

restored

although

not

to

wild-type

levels

-LRB-

Fig.

-RRB-

Nonetheless

the

amount

of

Nv-hb

present

in

Nv-gt

Kr

RNAi

embryos

was

sufficient

to

direct

head

and

thorax

development

demonstrating

that

Nv-Kr

expansion

impedes

anterior

patterning

and

that

maternally

localized

Nv-gt

confines

Nv-Kr

to

the

embryo

's

center

Thus

whereas

in

Drosophila

bcd-activated

Dm-gt

plays

only

a

moderate

role

in

positioning

Nv-Kr

-LRB-

Fig.

-RRB-

in

Nasonia

maternal

Nv-gt

is

sufficient

to

perform

this

function

This

distinction

led

us

to

consider

whether

Dm-gt

's

role

in

Drosophila

would

be

enhanced

if

the

Drosophila

embryo

were

reengineered

to

develop

like

Nasonia

with

Dm-gt

maternally

provided

and

anteriorly

localized

We

found

that

whereas

Dm-gt

was

sufficient

to

repress

Dm-Kr

anteriorly

in

the

absence

of

bcd

-LRB-

fig

-RRB-

head

and

thoracic

structures

were

not

rescued

-LRB-

fig

-RRB-

an

unsurprising

result

given

that

in

addition

to

permitting

anterior

development

by

regulating

Kr-repressing

gap

genes

bcd

also

functions

instructively

to

activate

genes

required

for

head

and

thorax

formation

In

Nasonia

by

contrast

the

instructive

and

permissive

anterior

patterning

functions

are

discrete

Head

and

thoraxspecific

genes

are

triggered

by

an

instructive

anterior

determinant

maternal

which

is

localized

independently

of

the

permissively

acting

maternal

repression

system

Nv-gt

A

comparison

of

the

molecular

mechanisms

employed

by

two

independently

evolved

-LRB-

-RRB-

long

Supporting

Online

Material

Materials

and

Methods

SOM

Text

Fig

References

November

accepted

March

science

Emergent

Biogeography

of

Microbial

Communities

in

a

Model

Ocean

Michael

J.

Follows

Stephanie

Dutkiewicz

Scott

Grant

Sallie

W.

A

marine

ecosystem

model

seeded

with

many

phytoplankton

types

whose

physiological

traits

were

randomly

assigned

from

ranges

defined

by

field

and

laboratory

data

generated

an

emergent

community

structure

and

biogeography

consistent

with

observed

global

phytoplankton

distributions

The

modeled

organisms

included

types

analogous

to

the

marine

cyanobacterium

Prochlorococcus

Their

emergent

global

distributions

and

physiological

properties

simultaneously

correspond

to

observations

This

flexible

representation

of

community

structure

can

be

used

to

explore

relations

between

ecosystems

biogeochemical

cycles

and

climate

change

significant

challenge

in

understanding

the

changing

earth

system

is

to

quantify

and

model

the

role

of

ocean

ecosystems

in

the

global

carbon

cycle

The

structure

of

microbial

communities

in

the

surface

ocean

is

A

known

to

regulate

important

biogeochemical

pathways

including

the

efficiency

of

export

of

organic

carbon

to

the

deep

ocean

Although

there

is

extraordinary

diversity

in

the

oceans

the

biomass

of

local

microbial

communities

at

SCIENCE

VOL

MARCH

Downloaded

from

on

May

Fig.

Repression

of

Nv-Kr

by

maternal

Nv-gt

is

required

for

head

and

thorax

formation

in

Nasonia

-LRB-

A

-RRB-

Two

models

for

maternal

Nv-gt

function

Cuticular

analysis

-LRB-

B

D

and

F

-RRB-

and

Nv-hbzyg

expression

-LRB-

C

E

and

G

-RRB-

after

knockdown

for

Nv-Kr

-LSB-

-LRB-

B

-RRB-

and

-LRB-

C

-RRB-

-RSB-

Nv-gt

gfp

-LSB-

-LRB-

D

-RRB-

and

-LRB-

E

-RRB-

-RSB-

and

Nv-gt

Kr

-LSB-

-LRB-

F

-RRB-

and

-LRB-

G

-RRB-

-RSB-

REPORTS

any

location

is

typically

dominated

by

a

smaller

subset

of

strains

Their

relative

fitness

and

ecosystem

community

structure

are

regulated

by

a

variety

of

factors

including

physical

conditions

dispersal

predation

competition

for

resources

and

the

variability

of

the

environment

-LRB-

-RRB-

Models

reflecting

this

conceptual

view

have

been

examined

in

idealized

ecological

settings

-LRB-

-RRB-

and

have

been

applied

to

studies

of

terrestrial

ecosystems

-LRB-

-RRB-

We

have

used

this

approach

in

a

marine

ecosystem

model

that

embraces

the

diversity

of

microbes

and

their

genomic

underpinnings

a

model

in

which

microbial

community

structure

emerges

from

a

wider

set

of

possibilities

and

thus

mimics

aspects

of

the

process

of

natural

selection

The

system

is

flexible

enough

to

respond

to

changing

ocean

environments

and

can

be

used

to

interpret

the

structure

and

development

of

marine

microbial

communities

and

to

reveal

critical

links

between

marine

ecosystem

structure

global

biogeochemical

cycles

and

climate

change

Recent

ocean

models

have

begun

to

resolve

community

structure

by

the

explicit

representation

of

three

or

four

classes

or

functional

groups

of

phytoplankton

-LRB-

-RRB-

but

significant

challenges

remain

-LRB-

-RRB-

First

the

specification

of

functional

groups

and

diversity

of

the

model

ecosystem

is

subjective

and

somewhat

arbitrary

Second

it

is

difficult

to

evaluate

the

parameters

controlling

such

models

because

quantitative

physiological

information

from

laboratory

cultures

is

extremely

limited

Third

observations

of

microbial

community

structure

with

which

to

evaluate

global-scale

models

are

still

relatively

sparse

Finally

model

ecosystem

structures

optimized

to

reflect

today

's

ocean

may

not

be

sufficiently

dynamic

to

adapt

appropriately

to

a

changing

climate

where

radical

shifts

in

community

structure

might

be

possible

To

circumvent

some

of

these

difficulties

we

formulated

a

marine

ecosystem

model

that

represents

a

large

number

of

potentially

viable

phytoplankton

types

whose

physiological

characteristics

were

determined

stochastically

The

initialized

organism

types

interacted

with

one

another

and

their

environment

evolving

into

a

sustainable

ecosystem

where

community

structure

and

diversity

were

not

imposed

but

were

emergent

properties

The

ecosystem

model

consisted

of

a

set

of

coupled

prognostic

equations

-LRB-

eqs

to

-RRB-

with

idealized

representations

of

the

transformations

of

inorganic

and

organic

forms

of

phosphorus

nitrogen

iron

and

silica

Many

tens

of

phytoplankton

types

-LRB-

here

-RRB-

were

initialized

in

each

simulation

each

type

distinguished

by

Fig.

Annual

mean

biomass

and

biogeography

from

single

integration

-LRB-

A

-RRB-

Total

phytoplankton

biomass

-LRB-

mM

P

to

m

average

-RRB-

-LRB-

B

-RRB-

Emergent

biogeography

Modeled

photo-autotrophs

were

categorized

into

four

functional

groups

color

coding

is

according

to

group

locally

dominating

annual

mean

biomass

Green

analogs

of

Prochlorococcus

orange

other

small

photo-autotrophs

red

diatoms

and

yellow

other

large

phytoplankton

-LRB-

C

-RRB-

Total

biomass

of

Prochlorococcus

analogs

-LRB-

mM

P

to

m

average

-RRB-

Black

line

indicates

the

track

of

Department

of

Earth

Atmospheric

and

Planetary

Sciences

Massachusetts

Institute

of

Technology

MIT

Cambridge

MA

USA

of

Oceanography

University

of

Hawaii

Pope

Road

Honolulu

HI

USA

of

Civil

and

Environmental

Engineering

and

Biology

Massachusetts

Institute

of

Technology

MIT

Cambridge

MA

USA

To

whom

correspondence

should

be

addressed

E-mail

mick@mit.edu

MARCH

VOL

SCIENCE

Downloaded

from

on

May

its

physiological

capabilities

and

the

values

of

coefficients

that

control

the

rates

and

sensitivities

of

metabolic

processes

These

were

provided

by

random

drawing

from

broad

ranges

guided

by

laboratory

and

field

studies

-LRB-

table

-RRB-

We

focused

these

choices

on

light

temperature

and

nutrient

requirements

-LRB-

fig

-RRB-

the

niche

dimensions

for

phytoplankton

thought

to

be

most

important

in

regulating

growth

To

facilitate

a

test

of

the

approach

we

also

specifically

addressed

functions

that

differentiate

Prochlorococcus

spp.

from

other

phytoplankton

including

their

small

size

and

inability

to

assimilate

nitrate

Other

functions

could

be

emphasized

depending

on

the

aim

of

the

study

Ecological

trade-offs

were

imposed

through

highly

simplified

allometric

constraints

-LSB-

see

supporting

online

material

-LRB-

SOM

-RRB-

-RSB-

To

reflect

the

extra

energetic

expense

of

using

nitrate

relative

to

other

inorganic

nitrogen

sources

we

allowed

the

maximum

growth

rate

to

increase

slightly

when

nitrate

was

not

the

major

nitrogen

source

-LRB-

-RRB-

Organisms

incapable

of

utilizing

nitrate

were

given

a

slightly

lower

nutrient

half-saturation

We

explicitly

represented

predation

by

two

classes

of

grazer

and

for

the

action

of

heterotrophic

microbes

we

used

a

simple

remineralization

rate

-LRB-

SOM

-RRB-

A

global

ocean

circulation

model

constrained

by

observations

-LRB-

-RRB-

provided

flow

fields

and

mixing

coefficients

that

transport

all

biological

and

chemical

tracers

All

phytoplankton

types

were

initialized

with

identical

distributions

of

biomass

and

the

model

was

integrated

forward

for

years

over

which

time

a

repeating

annual

cycle

in

ecosystem

structure

emerged

We

repeated

the

integration

times

each

time

with

a

different

random

selection

of

phytoplankton

physiologies

forming

an

ensemble

of

members

Although

each

ensemble

member

produced

a

unique

emergent

ecosystem

the

broad-scale

patterns

of

productivity

community

structure

and

biogeography

were

robust

across

all

Global

patterns

of

open-ocean

biomass

-LRB-

Fig.

-RRB-

primary

production

and

nutrients

-LRB-

fig

-RRB-

were

qualitatively

consistent

with

in

situ

and

remote

observations

The

ensemble

mean

globally

integrated

annual

primary

production

was

gigatons

C

per

year

with

a

standard

deviation

of

less

than

This

small

standard

deviation

suggested

that

sufficient

phytoplankton

types

were

initialized

for

consistent

emergent

solutions

and

also

reflects

the

large-scale

regulation

by

the

physical

transport

of

nutrients

After

an

initial

adjustment

the

biomass

of

some

phytoplankton

types

fell

below

the

threshold

of

numerical

noise

and

these

types

were

assumed

to

have

become

extinct

In

all

ensemble

members

about

phytoplankton

types

accounted

for

almost

all

of

the

total

global

biomass

-LRB-

fig

-RRB-

We

classified

the

phytoplankton

types

into

four

broad

functional

groups

each

a

REPORTS

composite

of

several

types

according

to

aspects

of

their

physiology

-LRB-

i

-RRB-

diatom

analogs

large

phytoplankton

that

require

silica

-LRB-

ii

-RRB-

other

large

eukaryotes

-LRB-

iii

-RRB-

Prochlorococcus

analogs

small

phytoplankton

that

can

not

assimilate

nitrate

and

-LRB-

iv

-RRB-

other

small

photo-autotrophs

The

large-scale

biogeography

of

the

emergent

phytoplankton

community

was

plausible

with

respect

to

observations

-LRB-

Fig.

-RRB-

and

consistent

among

the

ensemble

members

The

model

successfully

captured

the

domination

of

annual

biomass

by

large

phytoplankton

in

subpolar

upwelling

regions

where

both

light

and

macronutrients

are

seasonally

plentiful

The

subtropical

oceans

were

dominated

by

small

phytoplankton

functional

types

-LRB-

-RRB-

Large

areas

of

the

tropics

and

subtropics

were

dominated

by

several

Prochlorococcus

analogs

-LRB-

Fig.

-RRB-

also

in

accord

with

observations

-LRB-

-RRB-

Along

the

cruise

track

of

Atlantic

Meridional

Transect

-LRB-

-RRB-

total

Prochlorococcus

abundance

-LRB-

the

sum

of

all

Prochlorococcus

analogs

-RRB-

qualitatively

and

quantitatively

reflected

the

major

features

of

the

observed

distribution

with

highest

abundances

in

the

most

oligotrophic

-LRB-

nutrient-depleted

-RRB-

waters

-LRB-

-RRB-

-LRB-

Fig.

A

to

D

-RRB-

Real-world

Prochlorococcus

exhibit

genetic

diversity

which

leads

to

differences

in

light

and

temperature

sensitivities

-LRB-

-RRB-

as

well

as

nitrogen

assimilation

abilities

-LRB-

-RRB-

The

strains

or

ecotypes

of

Prochlorococcus

exhibit

distinct

patterns

of

abundance

along

ocean

gradients

-LRB-

-RRB-

and

observations

on

-LRB-

-RRB-

-LRB-

Fig.

E

G

I

and

K

-RRB-

provide

an

ideal

test

for

the

stochastic

modeling

strategy

Do

the

emergent

model

analogs

of

Prochlorococcus

reflect

the

geographic

distributions

relative

abundances

and

physiological

properties

of

their

real-world

counterparts

Of

the

Prochlorococcus

analogs

initialized

in

each

model

solution

between

three

and

six

variants

persisted

with

significant

abundances

-LRB-

fig

-RRB-

We

grouped

the

analogs

by

defining

three

model

ecotypes

based

only

on

distinct

geographic

habitats

without

regard

to

physiology

which

had

a

qualitative

resemblance

to

the

observed

distributions

of

ecotypes

along

In

any

ensemble

member

more

than

one

emergent

Prochlorococcus

analog

may

fall

into

a

particular

model-ecotype

classification

and

some

were

ambiguous

Model

ecotype

-LRB-

Fig.

-RRB-

was

defined

to

include

emergent

analogs

with

significant

biomass

in

the

upper

m

along

the

transect

between

N

and

S

qualitatively

corresponding

to

the

habitat

of

real-world

ecotype

-LRB-

Fig.

-RRB-

Model

ecotype

-LRB-

Fig.

-RRB-

included

analogs

that

had

significant

biomass

in

surface

waters

polewards

of

but

low

biomass

within

of

the

equator

broadly

reflecting

-LRB-

Fig.

-RRB-

Finally

model

ecotype

-LRB-

Fig.

-RRB-

was

defined

to

include

analogs

that

had

a

subsurface

maximum

biomass

in

common

with

and

-LRB-

Fig.

I

and

K

-RRB-

The

observed

widespread

distribution

of

deep

maxima

with

low

abundance

associated

with

and

was

not

clearly

reflected

in

the

model

analogs

This

might

be

explained

by

the

tendency

toward

unrealistically

complete

competitive

exclusion

typical

in

ecosystem

models

-LRB-

-RRB-

precluding

persistent

populations

at

low

abundance

There

is

a

deep

high

biomass

layer

in

the

model

made

up

of

other

nitrate-consuming

small

phytoplankton

This

may

partially

reflect

a

contribution

from

nitrate-utilizing

Prochlorococcus

which

have

recently

been

inferred

from

ocean

observations

-LRB-

-RRB-

but

which

have

not

yet

been

seen

in

culture

Fig.

Observed

and

modeled

properties

along

the

cruise

track

Left

column

shows

observations

-LRB-

-RRB-

right

column

shows

results

from

a

single

model

integration

-LRB-

A

and

B

-RRB-

Nitrate

-LRB-

mmol

-RRB-

-LRB-

C

and

D

-RRB-

total

Prochlorococcus

abundance

-LSB-

log

-LRB-

cells

-RRB-

-RSB-

-LRB-

E

G

I

and

K

-RRB-

Distributions

of

the

four

most

abundant

Prochlorococcus

ecotypes

-LSB-

log

-LRB-

cells

-RRB-

-RSB-

ranked

vertically

-LRB-

F

H

and

J

-RRB-

The

three

emergent

model

ecotypes

ranked

vertically

by

abundance

Model

Prochlorococcus

biomass

was

converted

to

cell

density

assuming

a

quota

of

fg

P

-LRB-

-RRB-

Black

lines

indicate

isotherms

SCIENCE

VOL

Fig.

Optimum

temperature

and

light

intensity

for

growth

Topt

and

Iopt

of

all

initialized

Prochlorococcus

analogs

-LRB-

all

circles

-RRB-

from

the

ensemble

of

model

integrations

Large

circles

indicate

the

analogs

that

exceeded

a

total

biomass

of

mol

P

along

in

the

year

Colors

indicate

classification

into

model

ecotypes

-LRB-

see

main

text

-RRB-

Red

circles

blue

circles

green

circles

Mixedcolor

and

solid

black

circles

denote

ambiguity

in

model-ecotype

classification

Bold

diamonds

indicate

real-world

Prochlorococcus

ecotypes

-LRB-

red

blue

green

and

yellow

-RRB-

MARCH

Downloaded

from

on

May

REPORTS

Within

each

ensemble

member

emergent

model

ecotypes

typically

followed

the

abundance

ranking

of

their

geographically

identified

real-world

counterparts

-LRB-

Fig.

and

fig

-RRB-

Model

ecotypes

and

ranked

first

and

second

-LRB-

compare

these

with

and

respectively

-RRB-

with

consistently

at

lower

abundances

-LRB-

compare

this

with

ecotypes

and

-RRB-

There

is

a

simultaneous

correspondence

between

the

physiological

characteristics

of

emergent

modeled

ecotypes

and

cultured

representatives

of

the

wild

population

Each

cultured

strain

of

Prochlorococcus

and

the

emergent

model

ecotypes

from

all

ensemble

members

were

characterized

by

an

optimal

temperature

-LRB-

Topt

-RRB-

and

photon

flux

-LRB-

Iopt

-RRB-

for

growth

the

temperature

or

light

intensity

at

which

growth

rates

are

greatest

if

all

other

limitations

are

set

aside

-LRB-

fig

-RRB-

Potentially

viable

Prochlorococcus

analogs

were

seeded

in

the

model

over

wide

ranges

of

optimal

temperature

and

photon

fluxes

-LRB-

all

circles

Fig.

-RRB-

but

those

that

maintained

significant

abundances

along

the

AMT

transect

-LRB-

solid

large

circles

Fig.

-RRB-

were

all

characterized

by

Topt

C

This

is

consistent

with

the

observations

of

Prochlorococcus

in

warmer

waters

and

with

the

warm

Topt

of

cultured

strains

-LRB-

-RRB-

Our

model

indicates

that

the

oligotrophic

conditions

confined

Prochlorococcus

analogs

to

warmer

waters

and

selected

for

warm

Topt

an

emergent

adaptation

driven

by

other

environmental

factors

In

the

cooler

waters

of

the

model

nutrients

are

typically

abundant

and

so

larger

phytoplankton

with

higher

intrinsic

maximum

growth

rates

have

an

advantage

In

the

highly

oligotrophic

-LRB-

typically

warmer

-RRB-

regions

the

Prochlorococcus

analogs

lower

half-saturation

-LRB-

consistent

with

their

very

small

size

-RRB-

is

advantageous

Across

the

ensemble

of

integrations

the

geographically

defined

model

ecotypes

were

clustered

in

optimal

temperature

and

light

parameter

space

-LRB-

Fig.

-RRB-

Model

ecotype

-LRB-

red

circles

-RRB-

generally

occupied

the

warmest

area

of

parameter

space

over

a

broad

upper

range

of

optimal

photon

fluxes

-LRB-

blue

circles

-RRB-

generally

had

a

lower

Topt

but

a

similar

range

of

Iopt

This

is

consistent

with

their

surface-oriented

habitats

and

latitudinal

-LRB-

or

temperature

-RRB-

separation

In

contrast

-LRB-

green

circles

-RRB-

occupied

a

wider

range

of

Topt

but

only

in

the

region

of

lowest

Iopt

consistent

with

its

expression

of

subsurface

maxima

Although

there

were

exceptions

the

clustering

of

geographically

defined

model

ecotypes

in

physiological

parameter

space

indicated

that

robust

ecological

controls

were

operating

across

the

integrations

The

physiological

characteristics

-LRB-

Topt

Iopt

-RRB-

of

real-world

ecotypes

-LRB-

colored

diamonds

Fig.

-RRB-

are

notably

consistent

with

the

grouping

of

their

model

counterparts

This

correspondence

was

not

imposed

but

emerged

as

a

feature

of

the

model

solution

Significantly

there

was

simultaneous

consistency

between

the

geographical

habitat

rank

abundance

and

physiological

specialization

of

the

emergent

Prochlorococcus

model

ecotypes

and

their

real-world

counterparts

These

parallels

indicate

that

the

stochastic

self-organizing

representation

of

marine

ecosystems

reflects

real-world

processes

and

is

suitable

for

application

in

ecological

and

biogeochemical

studies

This

approach

circumvents

some

of

the

obstacles

facing

most

current

ocean

ecosystem

models

such

as

the

a

priori

imposition

of

low

diversity

the

prescription

of

dominant

functional

types

and

the

difficulty

of

specifying

the

physiological

rate

coefficients

that

define

them

This

functionbased

approach

can

naturally

evolve

to

exploit

the

growing

body

of

genomic

and

metagenomic

data

mapping

the

oceans

in

terms

of

genes

and

their

encoded

physiological

functionality

-LRB-

-RRB-

Finally

because

the

ecosystem

structure

and

function

are

by

design

emergent

and

not

tightly

prescribed

this

modeling

approach

is

ideally

suited

for

studies

of

the

relations

between

marine

ecosystems

evolution

biogeochemical

cycles

and

past

and

future

climate

change

References

and

Notes

D.

Tilman

Ecology

-LRB-

-RRB-

R.

Margalef

Perspectives

in

Ecological

Theory

-LRB-

Univ.

of

Chicago

Press

Chicago

-RRB-

C.

Pedr

s-Ali

Trends

Microbiol

-LRB-

-RRB-

S.

L.

Pimm

J.

H.

Lawton

Nature

-LRB-

-RRB-

A.

Kleidon

H.

A.

Mooney

Glob

Change

Biol

-LRB-

-RRB-

J.

K.

Moore

S.

Doney

J.

Kleyplas

D.

Glover

I.

Fung

Deep-Sea

Res

II

-LRB-

-RRB-

W.

W.

Gregg

P.

Ginoux

P.

S.

Schopf

N.

W.

Casey

Deep-Sea

Res

II

-LRB-

-RRB-

E.

Litchman

C.

A.

Klausmeier

J.

R.

Miller

O.

M.

Schofield

P.

G.

Falkowski

Biogeosciences

-LRB-

-RRB-

C.

LeQuere

et

al.

Glob

Change

Biol

-LRB-

-RRB-

T.

R.

Anderson

J.

Plankton

Res

-LRB-

-RRB-

R.

R.

Hood

et

al.

Deep-Sea

Res

II

-LRB-

-RRB-

P.

A.

Thompson

et

al.

Limnol

Oceanogr

-LRB-

-RRB-

C.

Wunsch

P.

Heimbach

Physica

D

j.physd

-LRB-

-RRB-

Y.

Dandonneau

Y.

Montel

J.

Blanchot

J.

Giraudeau

J.

Neveux

Deep-Sea

Res

I

-LRB-

-RRB-

M.

V.

Zubkov

M.

A.

Sleigh

P.

H.

Burkill

R.

J.

G.

Leakey

Prog

Oceanogr

-LRB-

-RRB-

H.

A.

Bouman

et

al.

Science

-LRB-

-RRB-

Z.

I.

Johnson

et

al.

Science

-LRB-

-RRB-

L.

R.

Moore

G.

Rocap

S.

W.

Chisholm

Nature

-LRB-

-RRB-

G.

Rocap

et

al.

Nature

-LRB-

-RRB-

L.

R.

Moore

S.

W.

Chisholm

Limnol

Oceanogr

-LRB-

-RRB-

L.

R.

Moore

A.

F.

Post

G.

Rocap

S.

W.

Chisholm

Limnol

Oceanogr

-LRB-

-RRB-

G.

E.

Hutchinson

Am

Nat

-LRB-

-RRB-

R.

A.

Armstrong

R.

McGehee

Am

Nat

-LRB-

-RRB-

M.

W.

Lomas

F.

Lipschultz

Limnol

Oceanogr

-LRB-

-RRB-

J.

C.

Venter

et

al.

Science

-LRB-

-RRB-

E.

F.

DeLong

et

al.

Science

-LRB-

-RRB-

S.

Bertilsson

O.

Berglund

D.

M.

Karl

S.

W.

Chisholm

Limnol

Oceanogr

-LRB-

-RRB-

Thanks

to

J.

Marshall

R.

Williams

P.

Falkowski

J.

Cullen

and

J.

Bragg

for

inspiration

and

encouragement

Thanks

also

to

M.

Coleman

R.

Hood

and

three

anonymous

reviewers

for

stimulating

comments

on

the

manuscript

to

C.

Hill

for

computing

guidance

and

to

P.

Heimbach

C.

Wunsch

and

the

ECCO

group

for

ocean

circulation

state

estimates

We

are

grateful

for

funding

from

the

PARADIGM

consortium

of

the

National

Ocean

Partnership

Program

NSF

-LRB-

M.J.F.

S.D.

-RRB-

NSF

DOE

-LRB-

S.W.C.

-RRB-

and

the

Gordon

and

Betty

Moore

Foundation

-LRB-

S.W.C.

M.J.F.

-RRB-

M.J.F.

is

also

grateful

for

the

MIT

Global

Habitat

Longevity

Award

We

acknowledge

the

Atlantic

Meridional

Transect

consortium

-LRB-

NER/O/S

-RRB-

which

enabled

the

biogeographical

observations

first

published

in

-LRB-

-RRB-

-LRB-

AMT

contribution

no.

-RRB-

Supporting

Online

Material

Materials

and

Methods

SOM

Text

Figs

to

Table

References

and

Notes

December

accepted

March

science

Cascading

Effects

of

the

Loss

of

Apex

Predatory

Sharks

from

a

Coastal

Ocean

Ransom

A.

Myers

Julia

K.

Baum

Travis

D.

Shepherd

Sean

P.

Powers

Charles

H.

Impacts

of

chronic

overfishing

are

evident

in

population

depletions

worldwide

yet

indirect

ecosystem

effects

induced

by

predator

removal

from

oceanic

food

webs

remain

unpredictable

As

abundances

of

all

great

sharks

that

consume

other

elasmobranchs

-LRB-

rays

skates

and

small

sharks

-RRB-

fell

over

the

past

years

of

of

these

prey

species

increased

in

coastal

northwest

Atlantic

ecosystems

Effects

of

this

community

restructuring

have

cascaded

downward

from

the

cownose

ray

whose

enhanced

predation

on

its

bay

scallop

prey

was

sufficient

to

terminate

a

century-long

scallop

fishery

Analogous

top-down

effects

may

be

a

predictable

consequence

of

eliminating

entire

functional

groups

of

predators

E

cological

impacts

of

eliminating

top

predators

can

be

far-reaching

-LRB-

-RRB-

and

include

release

of

mesopredator

prey

populations

VOL

SCIENCE

from

predatory

control

-LRB-

-RRB-

and

induction

of

subsequent

cascades

of

indirect

trophic

interactions

-LRB-

-RRB-

In

the

oceans

fishing

has

dispropor

MARCH

Downloaded

from

on

May

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

ecosystem phytoplankton ocean biogeography biology models


# 2003 Oxford University Press Nucleic Acids Research , 2003 , Vol . 31 , No. 13 3429 3431 DOI : 10.1093 / nar/gkg599 Vienna RNA secondary structure server Ivo L. Hofacker * Institut fur Theoretische Chemie und Molekulare Strukturbiologie , Universitat Wien , Wahringerstra e 17 , A-1090 Wien , Austria Received February 15 , 2003 ; Revised and Accepted April 5 , 2003 ABSTRACT The Vienna RNA secondary structure server provides a web interface to the most frequently used functions of the Vienna RNA software package for the analysis of RNA secondary structures . It currently offers prediction of secondary structure from a single sequence , prediction of the consensus secondary structure for a set of aligned sequences and the design of sequences that will fold into a predefined structure . All three services can be accessed via the Vienna RNA web server at http : / / rna.tbi.univie.ac.at / . The Vienna RNA web site tries to address these shortcomings by offering access to the most popular features via an easy to use web interface . It consists of three CGI scripts equivalent to the RNAfold , RNAalifold and RNAinverse command line programs , respectively . While the servers have to limit request sizes for performance reasons , they return for each request an equivalent command line invocation . This makes it easier for users to make the transition to locally installed software , should their requirements exceed the limits of the web service . THE RNAfold SERVER Of the three services , the RNAfold server provides both the most basic and most widely used function . Input consists of a single sequence that has to be typed or pasted into a text field of the input form . In the simplest case , the server predicts only the minimum free energy -LRB- mfe -RRB- structure of a single sequence using the classic algorithm of Zuker and Stiegler -LRB- 1 -RRB- . In addition to mfe folding the server can calculate equilibrium base pairing probabilities via John McCaskill 's partition function algorithm -LRB- 4 -RRB- . By default the RNA energy parameters of the Turner group -LRB- 13 -RRB- are used , but single stranded DNA sequences can be handled as well , by selecting the DNA parameter set provided by John SantaLucia -LRB- 14 -RRB- . The fold server output consists of a static html page presenting the predicted mfe structure as a string in bracket notation and links to the plots generated for visualization . Three types of plots can be produced . Firstly , the predicted mfe structure is plotted as a conventional secondary structure graph using the naview layout method -LRB- 15 -RRB- . The pair probabilities can be visualized in a so-called ` dot plot ' : on a square grid of n n we draw for each possible pair -LRB- i , j -RRB- a box with area proportional to its probability . Finally , we produce a mountain plot depicting both the predicted mfe and pair probabilities . A mountain plot is an xy-graph that plots the number of base pairs enclosing a sequence position -LRB- for pair probabilities the average number of enclosing pairs -RRB- . See Figure 1 for examples of all three representations . Secondary structure drawing and dot plots are always produced in Postscript format . Postscript is used not only because it gives the highest print quality , but also because it allows the actual data to be embedded in the file , e.g. all pair probabilities are contained in the dot plot in an easy to parse INTRODUCTION Biomolecules exhibit a close interplay between structure and function . Therefore the growing number of RNA molecules with complex functions , beyond that of encoding proteins , has brought increased demand for RNA structure prediction methods . While prediction of tertiary structure is usually infeasible , the area of RNA secondary structures is an example where computational methods have been highly successful . The first practical dynamic programming algorithms to predict the optimal secondary structure of an RNA sequence date back over 20 years -LRB- 1 -RRB- . Since then they have been extended to allow prediction of suboptimal structures -LRB- 2,3 -RRB- and thermodynamic ensembles -LRB- 4 -RRB- , which allow to assign a confidence level or ` well definedness ' to the predictions -LRB- 5 -RRB- . Recently , several methods have addressed the problem of predicting a consensus structure for a group of related RNA sequences -LRB- 6 11 -RRB- . Such conserved structures are of particular interest , since conservation of structure in spite of sequence variation implies that the structure must be functionally important . By enhancing energy rules with sequence covariation these methods also obtain much better prediction accuracies . The Vienna RNA package -LRB- 12 -RRB- is a free software package that implements a variety of algorithms for the prediction and analysis of RNA secondary structures . The package is , however , strongly geared toward Unix command-line users and programmers . For the less computer savvy , or occasional user , it provides neither a point-and-click graphical user interface nor even pre-compiled binaries . * Tel : 43 1 4277 52738 ; Fax : 43 1 4277 52793 ; Email : ivo@tbi.univie.ac.at Nucleic Acids Research , Vol . 31 , No. 13 # Oxford University Press 2003 ; all rights reserved 3430 Nucleic Acids Research , 2003 , Vol . 31 , No. 13 Figure 1 . Three representations for secondary structure and structure ensembles as produced by the RNAfold service : structure graph , mountain plot and dot plot . As can be seen clearly in the dot plot , the sequence has two almost equally good but very dissimilar foldings . format . On the other hand , Postscript files can not be used for inline images on web pages and require additional software for viewing -LRB- e.g. gsview , http://www.ghostscript.com/ -RRB- . A suitable alternative is the new standard for Scalable Vector Graphics , SVG -LRB- http://www.w3.org/Graphics/SVG -RRB- . Users with SVG enabled browsers -LRB- typically through the use of Adobe 's SVG plugin , http://www.adobe.com/svg/ -RRB- can request structure drawings in SVG , which allows some interactivity such as toggling annotation . Currently the server accepts sequences up to a maximum length of 4000 nt , sequences up to 300 nt will be processed immediately while longer jobs are submitted to a batch queue , in which case the user is notified by email after completion . THE Alifold SERVER The Alifold service predicts the consensus secondary structure for a set of aligned RNA or DNA sequences by using modified dynamic programming algorithms that add a covariance term to the standard energy model -LRB- 11 -RRB- , again it supports prediction of mfe structures and pair probabilities . Usage is almost identical to that of the RNAfold service . Instead of typing an input sequence , a precomputed sequence alignment is uploaded via the input form . Currently , only alignments in Clustal format are accepted . The server restricts both the size of the upload and the length of the alignment , current limits being 10 Kb and 2000 nt , respectively . Results are again visualized in Postscript plots that are enhanced by information on sequence variation . In the structure drawings mutations supporting the predicted structure are marked by circles , in the dot plots and mountain plots , color is used to indicate the number of different pair types . Examples and detailed explanation of these representations can be found on the online help page -LRB- http://www.tbi.univie.ac.at/~ivo/RNA/ alifoldcgi.html -RRB- . THE INVERSE FOLD SERVER Finding sequences that fold into a predefined structure is the inverse of structure prediction problem . Often it is useful to design such sequences , e.g. in order to experimentally test an hypothesis about functional structures . While this is often done manually for very short sequences , it quickly becomes tedious and error prone . Our inverse folding service treats sequence design as an optimization problem in sequence space that is solved heuristically -LRB- 12 -RRB- . There are again two variants based on mfe and partition function folding . In the first case we minimize the dissimilarity between the predicted mfe structure and the desired target structure . In the second case we optimize the frequency of the target structure in the thermodynamic ensemble . While the mfe optimization typically yields sequences that are marginally stable , i.e. have many alternative foldings , optimization via the partition function produces sequences with a very strong preference for the target structure . Input consists simply of the desired structure in bracket notation . The maximum structure length is currently 100 nt . The time needed for the search varies widely depending on the ubiquity of the target structure . Most valid secondary structure strings never occur as mfe structure of some sequence -LRB- i.e. many sequence design problems have no solution -RRB- , while some others are extremely common -LRB- for example see 16 -RRB- . Conversely , the number of search steps performed by the algorithm is a good indicator for the frequency of a structure in sequence space . FUTURE PLANS The Vienna RNA secondary structure server presented here provides only basic access to a subset of the functions in the Vienna RNA software package . Nevertheless they provide a convenient interface for users that need RNA structure prediction only occasionally and a shallow learning curve for those new to the field . Work is underway to further improve the visualization of the results , e.g. by producing structure drawings annotated with various measures of well-definedness . As SVG enabled browsers become more widespread , a combination of SVG graphics and client side javascript should allow users to explore the predicted structures interactively . Nucleic Acids Research , 2003 , Vol . 31 , No. 13 3431 The output web page produced by the server is designed for the interactive user and thus is not ideal for automatic parsing and further processing of the results . To facilitate such interoperation with other programs and web services we plan to offer input and output in a standardized data exchange format . A promising candidate for this is the recently proposed RNAML format -LRB- 17 -RRB- , an XML based language for the storage of information on RNA sequence and structure . While the server currently runs on a somewhat dated dual Pentium II 450 MHz machine , the use of a batch queuing system allows jobs to be distributed to other machines should that become necessary . ACKNOWLEDGEMENTS This work is supported by the Austrian Fonds zur Forderung der Wissenschaftlichen Forschung , Projects FWF 15893 and P-13545-MAT . REFERENCES 1 . Zuker , M. and Stiegler , P. -LRB- 1981 -RRB- Optimal computer folding of larger RNA sequences using thermodynamics and auxiliary information . Nucleic Acids Res. , 9 , 133 148 . 2 . Zuker , M. -LRB- 1989 -RRB- The use of dynamic programming algorithms in RNA secondary structure prediction . In Waterman , M.S. -LRB- ed . -RRB- , Mathematical Methods for DNA Sequences , CRC Press , Boca Raton , FL , pp. 159 184 . 3 . Wuchty , S. , Fontana , W. , Hofacker , I.L. and Schuster , P. -LRB- 1999 -RRB- Complete suboptimal folding of RNA and the stability of secondary structures . Biopolymers , 49 , 145 165 . 4 . McCaskill , J.S. -LRB- 1990 -RRB- The equilibrium partition function and base pair binding probabilities for RNA secondary structure . Biopolymers , 29 , 1105 1119 . 5 . Zuker , M. and Jacobson , A.B. -LRB- 1995 -RRB- ` Well-determined ' regions in RNA secondary structure prediction : analysis of small subunit ribosomal RNA . Nucleic Acids Res. , 23 , 2791 2798 . 6 . Gorodkin , J. , Heyer , L.J. and Stormo , G.D. -LRB- 1997 -RRB- Finding the most significant common sequence and structure motifs in a set of RNA sequences . Nucleic Acids Res. , 25 , 3724 3732 . 7 . Hofacker , I.L. , Fekete , M. , Flamm , C. , Huynen , M.A. , Rauscher , S. , Stolorz , P.E. and Stadler , P.F. -LRB- 1998 -RRB- Automatic detection of conserved RNA structure elements in complete RNA virus genomes . Nucleic Acids Res. , 26 , 3825 3836 . 8 . Luck , R. , Graf , S. and Steger , G. -LRB- 1999 -RRB- Construct : a tool for thermodynamic controlled prediction of conserved secondary structure . Nucleic Acids Res. , 27 , 4208 4217 . 9 . Juan , V and Wilson , C. -LRB- 1999 -RRB- RNA secondary structure prediction . based on free energy and phylogenetic analysis . J. Mol . Biol. , 289 , 935 947 . 10 . Knudsen , B. and Hein , J. -LRB- 1999 -RRB- RNA secondary structure prediction using stochastic context-free grammars and evolutionary history . Bioinformatics , 15 , 446 454 . 11 . Hofacker , I.L. , Fekete , M. and Stadler , P.F. -LRB- 2002 -RRB- Secondary structure prediction for aligned RNA sequences . J. Mol . Biol. , 319 , 1059 1066 . 12 . Hofacker , I.L. , Fontana , W. , Stadler , P.F. , Bonhoeffer , S. , Tacker , M. and Schuster , P. -LRB- 1994 -RRB- Fast folding and comparison of RNA secondary structures . Monatsh . Chem. , 125 , 167 188 . 13 . Mathews , D. , Sabina , J. , Zucker , M. and Turner , H. -LRB- 1999 -RRB- Expanded sequence dependence of thermodynamic parameters provides robust prediction of RNA secondary structure . J. Mol . Biol. , 288 , 911 940 . 14 . SantaLucia , J. Jr. -LRB- 1998 -RRB- A unified view of polymer , dumbbell , and oligonucleotide DNA nearest-neighbor thermodynamics . Proc . Natl Acad . Sci . USA , 95 , 1460 1465 . 15 . Bruccoleri , R.E. and Heinrich , G. -LRB- 1988 -RRB- An improved algorithm for nucleic acid secondary structure display . CABIOS , 4 , 167 173 . 16 . Schuster , P. , Fontana , W. , Stadler , P.F. and Hofacker , I.L. -LRB- 1994 -RRB- From sequences to shapes and back : a case study in RNA secondary structures . Proc . Royal Society London B , 255 , 279 284 . 17 . Waugh , A. , Gendron , P. , Altman , R. , Brown , J. , Case , D. , Gautheret , D. , Harvey , S. , Leontis , N. , Westbrook , J. , Westhof , E. et al. -LRB- 2002 -RRB- RNAML : a standard syntax for exchanging RNA information . RNA , 8 , 707 717 .

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prediction bioinformatics rna structures secondary