Computational Modelling of the Plankton Ecosystem

Tony Field

Angelo Maggiore

Reza Adams

Samir Al-Battran

Massoud Aref

Wolfgang Barkmann

Tim Barrell

Alan Brice

Matt Booth

Cheng-Hua Chang

James Duggin

Lucas Partridge

Simon Smith

Kevin Stratford

Sarah Talbot

Jana Tharmaratnam

Dave Turner

Stephen Warren

Uli Wolf

 

Pak-Wing Fok

Sam Gratrix

Chris Harris

Chris Hurt

Ben Jefferys

Cheng-Chien Liu

Katrina Lythgoe

Camille Maclet

Enrique Nogueira

Darren Osborne

John WoodsRoger WileyTony FieldSilvana Vallerga

Wes HinsleyMatteo SinnerchiaJeremy CopeMohammad Raza

Contributors

Goals“Improved scientific understanding”

– Stability– Climate– Toxic blooms– Disease– Fisheries– Environmental managementetc.

Phytoplankton

• Fix atmospheric carbon via photosynthesis– Basis of the “carbon pump”– Influence atmosphere and climate

• Form the base of the food chain– Key to fisheries ‘recruitment’

• Nasty surprises– Red tides

Diatom

Zooplankton

• Grazers– Dominant consumers of phytoplankton

• Transporters– Eat at one depth, excrete at another

• Nasty surprises– Cholera

Copepod

Modelling the Ecosystem

• Traditionally population-based– Coupled ODEs– Each defines one continuous “compartment”

• The seminal model is Fasham’s (1990)– Compartments are Phyto, Zoo, Bact, Detritus,

Nit, Amm, DON– The “currency” is nitrogen (mmol N/m^3)…

= Growth – Grazing – Mortality – Mixing/dilution

M

Pthm

Pk

PGPrNnNPMt

dt

dP ))((),,,,()1(

21

1

M

Zth

Zk

ZGGG

dt

dZ )(

2

22

332211

M

Bthm

Zk

ZBGU

dt

dB ))((

2

22

32

= Grazing – Predation – Dilution

= Uptake – Grazing – Mortality – Mixing/dilution

Etc.

BUT… Demography is not an artefact of nature!

• Individual-based Models (IBMs)– Primitive phenotypic equations based on

experimental observation– Models compute individuals’ trajectories– Bio-chemical/bio-optical feedback from

individuals– Demography is an emergent property– Sound scientific basis– Demonstrably stable over a

wide range of parameterisations

• IBMs are expensive– interactions per time step

• A compromise: Lagrangian Ensemble (LE)– Agents represent subpopulations– Interactions between agents and fields

)( 2nO

Concentration

Populationsin

i

sin

TP

Agents Ingestion

The 1D LE Metamodel• Models a single “water column”

(mesocosm)– Horizontal correlations >> vertical

• Mesocosm advected by ocean circulation• External forcing by sun and atmosphere

– Equations for solar elevation– ERA40 data for atmosphere (from ECMWF)– Other ‘scenario’ factors, e.g. ApCO2, Fe…– Initial conditions from NOAA world ocean

atlas

• Cannot assume ‘homogeneity’

WindSunCloud

Mixing layer

Laminar flow

Turbocline

Temperature

Thermocline

Irradiance

Turbidity (bio-optical feedback)

Surface

+Upwelling(ignored)

• LE Metamodel Encapsulated by the Virtual Ecology Workbench (VEW)

• Supports building of new models and archiving of old models

• End users: ecologists, students…– Configure & integrate models; analyse data…

• Model designers: biological oceanographers– Define “agent” behaviour and chemistry via

primitive equations

The “VEW”

VEW Components• Data viewer

• Model designer

• Planktonica

• Compiler

• Species builder

• Scenario builder

• Controller

• Particle manager

• Output controller

• Run manager

• LiveSim

• VEWAnalyser

• VEWDocumenter

• The VEW assumes a stratified virtual mesocosm…

…

1

2

L

3

…Physics Biology

• Agents move between layers (by swimming, turbulence, gravity, …)

• “Visible” model ingredients…

Layer i

Irradiance

ChemistryPhysics (fixed)

vI

Temp T

Ambient concC

MLDepth

poolCingestC

uptakeCz

Other vars

User-defined, each with specified units

User-defined Cx defined automatically for each C

Globals

t timestep

Agents and Biodiversity• New agent types (Functional Groups, FGs)

may be defined in the VEW

• FGs may have several life cycle stages1 2 3 4

• FGs can be parameterised to define species

• Behaviour in each stage specified by rules- Each rule modifies agent’s internal state- Special functions control LE integration- Essentially a “single-assignment” language

The Curtain “API”

• Nutrient uptake/release– uptake(c,x) – requests uptake of of

chemical c from ambient environment– release(c,x) - similarly

These affect internal and external

• Ingestion (food web)– ingest( ) – both arguments are vectors

gx

poolC concC

rV ,

Encodes agent/field interaction, nutrient budgeting, logging, emergence…

• change(s) – changes the stage to s• pchange(p,s) – changes the stage to s with

probability p.

p

1-p

ss’

s

User view

ss’

s

Behind the curtain

Pop n

Pop mean np

Pop mean n(1-p)

• divide(m) – duplicate the agent m-fold

m

1

…

Pop n Pop mn

User view Behind the curtain

• create(s,m,as) – creates m new instances of the agent, each in stage s with internal state set by list of assignments as

User view Behind the curtain

Pop n

Pop mn

Pop n

vs’

v’s

v’s

v’s

…

0

1

2

m

v’s

v’ = internal state set by as

vs’

vs’

vs’

Some examples (from “WB”)Diatom energetics…

)(),)(min(

)(7.03.0

)(3600

)(

max

1

1)/(2

2

JEtEEEE

JhT

TRE

JheIrkE

Wmtt

IIII

respphoto

rLresp

IIvFphoto

a

mvmm

mv

Imported(reusable)

Some examples (from “WB”)Diatom energetics…

)(),)(min(

)(7.03.0

)(3600

)(

max

1

1)/(2

2

JEtEEEE

JhT

TRE

JheIrkE

Wmtt

IIII

respphoto

rLresp

IIvFphoto

a

mvmm

mv

Some examples (from “WB”)Diatom energetics…

)(),)(min(

)(7.03.0

)(3600

)(

max

1

1)/(2

2

JEtEEEE

JhT

TRE

JheIrkE

Wmtt

IIII

respphoto

rLresp

IIvFphoto

a

mvmm

mv

Some examples (from “WB”)Diatom energetics…

)(),)(min(

)(7.03.0

)(3600

)(

max

1

1)/(2

2

JEtEEEE

JhT

TRE

JheIrkE

Wmtt

IIII

respphoto

rLresp

IIvFphoto

a

mvmm

mv

0

50

100

150

200

250

300

350

0 4 8 12 16Time (hrs)

W/m

^2

0

10

20

30

40

50

60

Ep

ho

to (

J/h

* 1

0^

6)

IvImEphoto

Diatom nutrient uptake…

),(then0if

),(then0if

)(,1min

)(

max

1

AtdAsuptakedN

NtdNsuptakedN

tdN

ANNs

gNhkAA

Au

kN

NudN

poolpool

conc

concA

Nconc

concN

Modifies droop ‘pools’by uptake from environment

concA

concNdN spoolNpoolA

Death and decay…)(then0if DeadchangeE

Then, in the ‘Dead’ stage…

),(

),(

tNNNrelease

tAAArelease

poolrem

poolrem

Bacterial remineralisation(from droop pool to environment)

Diatom reproduction…

)2(then)(andif divideNANEE divpoolpooldiv

Copepod ingestion of diatoms…

Imin

min

maxGT

grazed

grazedingest

ingestmin

kPP

PPf

Rzz

fFWP

RPR

RPPP

*

)*(

,),10max(

)(integratemin

),min(

)0elsethen*if*,(ingest

2

15

max

Prey vector Vector expression

Sums over trajectory

Function of ‘satiation’

Copepod ageing and reproduction…

)(thenif AdultchangeGC

tAgeAge

maxpool

0

0

5.0with

R

GC

A

S

minpool

r

),(thenif nNewborncreateAgeAge

G

GCn

rep

min

maxpool

Then, when Adult…

Some ResultsTaken from 6-year integrations at the Azores (41’N, 27’W)

Concluding remarks• First attempt at LE modelling environment

– Scientifically sound basis– Stable ecosystems (=> prediction)– Results already inform scientific understanding

• BIG advantages– Robust, well engineered, domain-specific– Many really useful tools– Modular, re-usable components– Static checking (consistency, units, types…)– Good housekeeping (budgeting, emergence…)

Q: Is “computational model” right?

A: Possibly not…– Think IBMs; LE is behind the scenes– Model food webs properly (A eats B!)– Derive interaction rates– Introduce stochastic time delays (currently

history-based)– Fix the “language”– Turbulent advection

etc.

Warning!• Interdisciplinary projects are slippery beasts

– Avoid offering a programming ‘service’!– Stick to focused science/computing agenda

• BUT, interesting CS can emerge, e.g.Languages

Type systems

Type mutation (Fickle)

Memory management

Meshing (AFEM)

Parallelisation

Code optimisation

Radiation transport

etc.

A Quick Tour of the VEW

• Ambient grazing/predation “rate”

If T is time to next interaction and target interactions areWhat is niITP n ,...,1),,( ?

nII ,...,1