(c)Ferdi Hellweger, Northeastern University, Boston.

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QUICK START: Click **setup**, then **go**.

Present biogeochemical models typically use a lumped-system (population-level) modeling (LSM) approach that assumes average properties of a population within a control volume. For modern models that formulate phytoplankton growth as a nonlinear function of the internal nutrient (e.g., Droop kinetics), this averaging assumption can introduce a significant error. Agent-based (individual-based) modeling (ABM) is an alternative approach that does not make the assumption of average properties.

This educational applet contrasts the agent-based and lumped-system modeling approaches. ABM and LSM models are constructed based on identical underlying sub-models of nutrient uptake (Michaelis-Menten) and growth (Droop). The models are applied to a scenario consisting of a point source nutrient discharge into a waterbody with advection and dispersion.

The details of the model can be found in the paper by Hellweger and Kianirad (2007a). More information on ABM vs. LSM comparison can be found in that and the other papers listed below.

1. Adjust the slider parameters (see below), or use the default settings.

2. Press the "setup" button.

3. Press the "go" button to begin the simulation.

4. View the "Phytoplankton" plot to watch the ABM and LSM populations develop over time.

5. View the Mean and Max. phytoplankton concentrations, and their differences.

Parameters:

VmaxPO4 (molP/molC/d): Max. PO4 uptake rate

KmPO4 (umol/L): PO4 uptake half-saturation constant

uPmax (1/d): Max. photosynthesis rate

q0P (mmolP/molC): P subsitence quota

uR (1/d): Respiration rate

uD (1/d): Death rate

vs (m/d): settling velocity

dt (d): Integration step size

xypatch (m): Grid cell x and y dimension

z (m): Water column depth

vx (m/s): Velocity in x-direction

Eu (m2/s): Dispersion coefficient

WPO4 (mol/s): PO4 loading rate

m0 (pmolC/cell): Min. cell size

rcv (): Randomization coefficent

ChlaC (ugChla/mgC): Chlorophyll a to carbon ratio

Notes:

Several parameters can be changed through the user interface, including VmaxPO4, KmPO4, uPmax, q0P, uR, uD and vs. Other are, for simplicity, are not included in the user interface, but hardwired into the code. This includes dt (0.005 d), xypatch (5,000 m), z (10 m), vx (0.1 m/s), Eu (50 m2/s), WPO4 (0.1 mol/s), m0 (1.0 pmolC/cell), rcv (0.1), ChlaC (30 ugChla/mgC).

Even though the ABM and LSM models are constructed based on identical underlying sub-models, they produce different results. Why is that? Read some of the papers in the reference list to learn more about this.

Try adjusting the parameters under various settings. How sensitive is the difference between the ABM and LSM models to the particular parameters?

Hellweger References:

Hellweger, F. L., Kianirad, E. 2007a. Accounting for Intra-Population Variability in Biogeochemical Models using Agent-Based Methods. Environmental Science & Technology, 41(8):2855-2860.

Hellweger, F. L., Kianirad, E. 2007b. Individual-Based Modeling of Phytoplankton: Evaluating Approaches for Applying the Cell Quota Model. Journal of Theoretical Biology, 249:554-565.

Hellweger, F. L. 2007. Is it time to abandon the chemistry approach to biogeochemistry? (Agent-based water quality modeling). In: Proceedings of WEFTEC 07, Water Environment Federation (WEF), Alexandria, VA., pp. 5646-5665.

Hellweger, F. L. 2008. Spatially Explicit Individual-Based Modeling Using a Fixed Super-Individual Density. Computers & Geosciences, 34(2):144-152.

Hellweger, F. L., Bucci, V. 2009. A bunch of tiny individuals – Individual-based modeling for microbes (review paper). Ecological Modelling, 220(1):8-22.

NetLogo References:

Wilensky, U. & Reisman, K. (1999). Connected Science: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. International Journal of Complex Systems, M. 234, pp. 1 - 12. (This model is a slightly extended version of the model described in the paper.)

Wilensky, U. & Reisman, K. (in press). Thinking like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. Cognition & Instruction.

; ABMvsLSM.nlogo ; ferdi hellweger ; ferdi@coe.neu.edu ; 12/30/2009 globals [ dt time dtp ntp skipABM xypatch z acpatch vpatch vx vy Qx Qy Eu Ep pXa pXb pXt pYa pYb pYt idx idy r1 r2 xcor2 ycor2 isx isy WPO4 vS2 linear? VmaxPO42 KmPO42 VPO4t uPmax2 q0P2 uR2 uD2 nq m0 SR nb mt sf rcv ChlaC meanLSM meanABM meandiff maxLSM maxABM maxdiff G1 Cmin Cmax ccolmin ccolmax ccolslope LSM_PCt LSM_PPt LSM_PO4t ABM_PO4t PC0 PP0 PO40 PC0s PP0s PO40s LSM_RPCt LSM_RPPt LSM_RPO4t ABM_RPO4t PO4t plotx ploty ] breed [ bguys bguy ] patches-own [ itype LSM_PC LSM_PP LSM_PO4 LSM_TP ABM_PC ABM_PP ABM_PO4 ABM_TP LSM_RPC LSM_RPP LSM_RPO4 ABM_RPO4 LSM_VPO4 LSM_qP LSM_uP ] bguys-own [ m VPO4 uP qP RqP ] to setup clear-all set dt 0.005 set time 0 set dtp 1 set ntp 0 set skipABM 0 set xypatch 5000 set z 10 set acpatch xypatch * z set vpatch ( xypatch ^ 2 ) * z set vx 0.1 * 86400 set vy 0 set Qx vx * acpatch set Qy vy * acpatch set Eu ( 50 * 86400 ) set Ep ( Eu * acpatch / xypatch ) set isx -13 set isy 0 set WPO4 0.1 * 86400 * ( max-pycor - min-pycor + 1) * xypatch / 1000 set linear? false set m0 1.0e-12 set rcv 0.1 if linear? [set KmPO42 KmPO42 / 100] set nq 1 do-input set PC0 0 set PP0 0 set PO40 0 set PC0s 1 set PP0s PC0s * q0P2 set PO40s KmPO42 * 0.01 set nb 300 set SR PC0s * vpatch / (nb * m0 * 1.5) set ChlaC 30 set ccolmax 69 set ccolmin 61 ;random-seed 1 ask patches [ set itype 0 set LSM_PC PC0 set LSM_PP PP0 set LSM_PO4 PO40 set ABM_PO4 PO40 ] ask patch isx isy [ set itype 1 set LSM_PC PC0s set LSM_PP PP0s set LSM_PO4 PO40s set ABM_PO4 PO40s set plabel "S " set plabel-color black ] set-default-shape bguys "circle" create-bguys nb [ set color 15 set size 0.15 ask one-of patches with [itype = 1] [ set xcor2 pxcor set ycor2 pycor ] setxy xcor2 ycor2 set m m0 * 1.5 set qP PP0s / PC0s ] do-output do-plot end to go do-input if skipABM = 0 [ if not any? turtles [ stop ] ] if skipABM = 0 [ ask bguys [ set idx 0 set idy 0 set pXb ( Qx / vpatch * dt ) set r1 random-float 1.0 if ( r1 < pXb ) [ set idx 1 ] set pXa ( Ep / vpatch * dt ) set pXb ( Ep / vpatch * dt ) set pXt pXa + pXb set r1 random-float 1.0 if ( r1 < pXt ) [ set r2 random-float 1.0 ifelse (r2 < pXa / pXt) [set idx ( idx - 1 )] [set idx ( idx + 1 )] ] set pYa ( Ep / vpatch * dt ) set pYb ( Ep / vpatch * dt ) set pYt pYa + pYb set r1 random-float 1.0 if ( r1 < pYt ) [ set r2 random-float 1.0 ifelse (r2 < pYa / pYt) [set idy ( idy - 1 )] [set idy ( idx + 1 )] ] set xcor2 ( [pxcor] of patch-here + idx ) set ycor2 ( [pycor] of patch-here + idy ) ifelse xcor2 > (min-pxcor - 0.5) and xcor2 < (max-pxcor + 0.5) and ycor2 > (min-pycor - 0.5) and ycor2 < (max-pycor + 0.5) [ setxy xcor2 ycor2 setxy (xcor - 0.5 + random-float 1.0) (ycor - 0.5 + random-float 1.0) ] [die] ] ask bguys [ set PO4t [ABM_PO4] of patch-here set uP 0 ifelse linear? [ set uP ( uPmax2 * PO4t / KmPO42 ) set VPO4 ( (uP - uR2 ) * q0P2 ) ] [ if qP > q0P2 [ set uP ( uPmax2 * ( (qP - q0P2) ^ nq / (q0P2 ^ nq + (qP - q0P2) ^ nq ) ) ) ] set VPO4 ( VmaxPO42 * ( PO4t / ( KmPO42 + PO4t ) ) ) ] set VPO4t VPO4 set mt m ask patch-here [ set ABM_PO4 ( ABM_PO4 - VPO4t * mt * SR / vpatch * dt ) ] set RqP ( VPO4 - ( uP - uR2 ) * qP) set qP ( qP + RqP * dt ) set m ( m + (uP - uR2) * m * dt ) if m > 2 * m0 [ ;type "Division: " type uP type ", " type m type ", " print m0 set mt m set sf random-normal 0.5 rcv if sf <= 0 [set sf 0.5] set m ( mt * sf) hatch 1 [ set m ( mt * (1 - sf ) ) ] ] ] ask bguys [ if random-float 1.0 < ( ( uD2 + vs2 / z) * dt ) [ die ] ] ] ;skipABM ask patches [ set LSM_RPC 0 set LSM_RPP 0 set LSM_RPO4 0 set ABM_RPO4 0 ] ask patches [ set LSM_PCt [LSM_PC] of self set LSM_PPt [LSM_PP] of self set LSM_PO4t [LSM_PO4] of self set ABM_PO4t [ABM_PO4] of self ask neighbors4 [ set LSM_RPC ( LSM_RPC + ( Ep / vpatch * LSM_PCt ) ) set LSM_RPP ( LSM_RPP + ( Ep / vpatch * LSM_PPt ) ) set LSM_RPO4 ( LSM_RPO4 + ( Ep / vpatch * LSM_PO4t ) ) set ABM_RPO4 ( ABM_RPO4 + ( Ep / vpatch * ABM_PO4t ) ) ] set LSM_RPC ( LSM_RPC - ( 4 * Ep / vpatch * LSM_PCt ) ) set LSM_RPP ( LSM_RPP - ( 4 * Ep / vpatch * LSM_PPt ) ) set LSM_RPO4 ( LSM_RPO4 - ( 4 * Ep / vpatch * LSM_PO4t ) ) set ABM_RPO4 ( ABM_RPO4 - ( 4 * Ep / vpatch * ABM_PO4t ) ) ] ask patches [ set LSM_PCt [LSM_PC] of self set LSM_PPt [LSM_PP] of self set LSM_PO4t [LSM_PO4] of self set ABM_PO4t [ABM_PO4] of self ask patches at-points [[1 0]] [ set LSM_RPC ( LSM_RPC + ( Qx / vpatch * LSM_PCt ) ) set LSM_RPP ( LSM_RPP + ( Qx / vpatch * LSM_PPt ) ) set LSM_RPO4 ( LSM_RPO4 + ( Qx / vpatch * LSM_PO4t ) ) set ABM_RPO4 ( ABM_RPO4 + ( Qx / vpatch * ABM_PO4t ) ) ] set LSM_RPC ( LSM_RPC - ( Qx / vpatch * LSM_PCt ) ) set LSM_RPP ( LSM_RPP - ( Qx / vpatch * LSM_PPt ) ) set LSM_RPO4 ( LSM_RPO4 - ( Qx / vpatch * LSM_PO4t ) ) set ABM_RPO4 ( ABM_RPO4 - ( Qx / vpatch * ABM_PO4t ) ) ] ask patches with [itype = 1] [ set LSM_RPO4 ( LSM_RPO4 + WPO4 / vpatch ) set ABM_RPO4 ( ABM_RPO4 + WPO4 / vpatch ) ] ask patches [ set LSM_VPO4 ( VmaxPO42 * ( LSM_PO4 / ( KmPO42 + LSM_PO4 ) ) ) set LSM_qP 0 if LSM_PC > 0 [ set LSM_qP ( LSM_PP / LSM_PC ) set LSM_uP 0 ifelse linear? [ set LSM_uP ( uPmax2 * LSM_PO4 / KmPO42 ) set LSM_VPO4 ( (LSM_uP - uR2) * q0P2 ) ] [ if LSM_qP > q0P2 [ set LSM_uP ( uPmax2 * ( (LSM_qP - q0P2) ^ nq / (q0P2 ^ nq + (LSM_qP - q0P2) ^ nq ) ) ) ] ] set LSM_RPC ( LSM_RPC + (LSM_uP - uR2 - uD2 - vs2 / z) * LSM_PC ) set LSM_RPP ( LSM_RPP + LSM_VPO4 * LSM_PC + (- uD2 - vs2 / z) * LSM_PP ) set LSM_RPO4 ( ( LSM_RPO4 - LSM_VPO4 * LSM_PC ) ) ] ] ask patches [ set LSM_PC ( LSM_PC + LSM_RPC * dt) set LSM_PP ( LSM_PP + LSM_RPP * dt ) set LSM_PO4 ( LSM_PO4 + LSM_RPO4 * dt ) set ABM_PO4 ( ABM_PO4 + ABM_RPO4 * dt ) ] if min [LSM_PC] of patches < 0 [show "Error: Negative LSM_PC."] if min [LSM_PP] of patches < 0 [show "Error: Negative LSM_PP."] if min [LSM_PO4] of patches < 0 [show "Error: Negative LSM_PO4."] if ntp >= time [ set ntp time + dtp do-output do-plot ] set time ( time + dt ) end to do-input set VmaxPO42 VmaxPO4 ; 0.5 set KmPO42 KmPO4 * 1e-3 ; 2.5 * 1e-3 set uPmax2 uPmax ; 2.0 set q0P2 q0P * 1e-3 ; 1e-3 set uR2 uR ; 0.1 set uD2 uD ; 0.15 set vs2 vs ;0.5 end to do-output ask patches [ set LSM_TP ( LSM_PP + LSM_PO4 ) ] set Cmin min [LSM_PC] of patches set Cmax max [LSM_PC] of patches set ccolslope 0 if not (Cmax = 0) [ set ccolslope (ccolmax - ccolmin) / ( Cmax - Cmin) ] ask patches [ set G1 ( Ccolmax - ( LSM_PC - Cmin ) * ccolslope ) set pcolor G1 ] ask patches [ set ABM_PC 0 set ABM_PP 0 if any? bguys-here [ set ABM_PC ( sum [m] of bguys-here ) * SR / vpatch set ABM_PP ( ABM_PC * mean [qP] of bguys-here ) ] set ABM_TP ( ABM_PP + ABM_PO4 ) ] set meanLSM mean [LSM_PC] of patches * 12 * ChlaC set meanABM mean [ABM_PC] of patches * 12 * ChlaC ifelse ( ( meanLSM + meanABM ) > 0 ) [set meandiff abs (meanLSM - meanABM) / ((meanLSM + meanABM) / 2 ) * 100] [set meandiff 0] set maxLSM max [LSM_PC] of patches * 12 * ChlaC set maxABM max [ABM_PC] of patches * 12 * ChlaC ifelse ( ( meanLSM + meanABM ) > 0 ) [set maxdiff abs (maxLSM - maxABM) / ((maxLSM + maxABM) / 2 ) * 100] [set maxdiff 0] end to do-plot set-current-plot "Nutrient" set-current-plot-pen "LSMTP" plotxy time mean [LSM_TP] of patches * 1e3 set-current-plot-pen "LSMPP" plotxy time mean [LSM_PP] of patches * 1e3 set-current-plot-pen "LSMPO4" plotxy time mean [LSM_PO4] of patches * 1e3 set-current-plot-pen "ABMTP" plotxy time mean [ABM_TP] of patches * 1e3 set-current-plot-pen "ABMPP" plotxy time mean [ABM_PP] of patches * 1e3 set-current-plot-pen "ABMPO4" plotxy time mean [ABM_PO4] of patches * 1e3 set-current-plot "Phytoplankton" set-current-plot-pen "LSM" plotxy time meanLSM set-current-plot-pen "ABM" plotxy time meanABM end