Food web input file for: 

The Ecoflat C-balance food web as in:

Van Oevelen, D., Soetaert, K., Middelburg, J.J., Herman, P.M.J., Moodley, L., Hamels, I., Moens, T., Heip, C.H.R., 2006b. 
Carbon flows through a benthic food web: Integrating biomass, isotope and tracer data. J. Mar. Res. 64, 1-30.


Data	: Molenplaat, Station 2, June 1996 
Data Sources	:	Moens et al (ECOFLAT summary report) -> biomass data
		           	Middelburg et al (L&O) --> organic content of sediment
          			Spreadsheet Ilse: "Data Ilse Hamels C-cyclus.xls"

Units	:	Fluxes:				mgC/m2/d
			Standing stocks:	mgC/m2

Implementation: Dick van Oevelen

#####################################################################





!=============================================================!
!                                                             !
!                           PARAMETERS                        !
!                                                             !
!=============================================================!
########################### PARAMETERS ########################


!~~~~~~~~~~~~~~~~~~~~~~~~~~
!   MEASUREMENTS       
!~~~~~~~~~~~~~~~~~~~~~~~~~~

GPP						=	714  	 {mgC/m2/d}        !7*102 = GPP on hourly basis * emersion period/tide (Report ECOFLAT, 6 in Middelburg et al) = GPP on daily basis (only 1 emersion in daylight)
BNP						=	600      {mgC/m2/d}        !from upper 5mm, from upper 4 cm with exponential decrease, spreadsheet Ilse
SedResp					=	2112     {mgC/m2/d}        !176 mmolC/m2/d * 12 = 2112 mgC/m2/d
MicroBactGraz           =   13.2     {mgC/m2/d}        !From Hamels, 1998 




!~~~~~~~~~~~~~~~~~~~~~~~~~~
!   CONSTRAINTS
!~~~~~~~~~~~~~~~~~~~~~~~~~~
MinMPBRes               =   0.16     {-}
MinMPBDocRelease        =   0.42     {-}
MaxMPBDocRelease        =   0.73     {-}
MinBGE                  =   0.28     {-}               !Minimal Bact Growth Efficiency
MaxBGE                  =   0.48     {-}               !Maximal Bact Growth Efficiency
MinProdMicro            =   0.2      {/d}              !Minimal Production by microbenthos
MaxProdMicro            =   0.5      {/d}              !Maximal Production by microbenthos
BasRespMin              =   0.01     {/d}              !Minimal resp per day
BasRespMax              =   0.10     {/d}              !Maximal resp per day
GrowthRespMin           =   0.4      {-}               !Minimal respiration per production
GrowthRespMax           =   0.6      {-}               !Maximal respiration per production  
MeioGrazMin             =   0.1      {/d}              !Minimal meiofauna grazing rate
MeioGrazMax             =   1.0      {/d}              !Maximal meiofauna grazing rate
MicroGrazMin            =   1.0      {/d}              !Minimal microfauna grazing rate
MicroGrazMax            =   2.0      {/d}              !Maximal microfauna grazing rate

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!                                    !
!       CARBON ISOTOPE RATIOS        !
!                                    !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

13C_MPB             =      -15.0
13C_Phytoplankton   =      -20.0
13C_Refrac          =      -24.2
13C_Detritus        =      -21.2
13C_Bacteria        =      -17.9
13C_Micro           =      -20.95
13C_Meio            =      -17.4
13C_Macro           =      -17.8


!!!!!!!!!!!!!!!!!!!!!!!!!!
!                        !
!       BIOMASSES        !
!                        !
!!!!!!!!!!!!!!!!!!!!!!!!!!


!---DOC---!
TotDoc                 =   100

!---Detritus---!
TotDetritus            =   130660     !2/3 of total in upper 5 cm

!---MPB---!
TotMPB                 =   2090    ! estimate Jack: 2090 estimate Ilse: 1287   

!---BACTERIA---!
TotBact                =   4097

!---MICROBENTHOS---!
Flagellates            =   132
CiliatesCarn           =   4.1
CiliatesBact           =   0.9
CiliatesOmn            =   1.1
CiliatesUnk            =   1.7
TotCiliates            =   CiliatesCarn + CiliatesBact + CiliatesOmn   &
                           + CiliatesUnk
TotMicro               =   Flagellates + TotCiliates

!---MEIOBENTHOS---!
MeioMicrovores          =	4
MeioCiliates			=	59.2
MeioDeposit				=	27.6
MeioEpistrate			=	25.6
MeioPredators			=	7.2
MeioFacPredators		=	32.8
TotMeio                 =	MeioMicrovores + MeioCiliates + MeioDeposit	+ MeioEpistrate	+   &
                            MeioPredators  + MeioFacPredators

!---MACROBENTHOS---!
!distinction among feeding types not further used
MacroSuspension			=	3650
MacroDeposit			=	6250
MacroSurface			=	2250
TotMacro				=	MacroSuspension	+ MacroDeposit + MacroSurface	

! variable only defined for dynamical TracerSimulation
 TotTracer      = totMPB + totDOC + totBact + totMicro + totMeio + totDetritus + totMacro

################################### END PARAMETERS




!=============================================================!
!                                                             !
!                    VARIABLES                                !
!                                                             !
!=============================================================!
############################ VARIABLES ########################

!---------------!
!   DETRITUS    !
!---------------!
 DetritusDOCRelease		=	Flow(Detritus,DOC)


!---------------!
!     MPB       !
!---------------!
 PrimProd				=	Flow(CO2,MPB)
 MPBRespiration      	=	Flow(MPB,CO2)
 MPBDOCRelease	        =	Flow(MPB,DOC)


!---------------!
!   BACTERIA    !
!---------------!
 BacteriaRespiration	=	Flow(Bacteria,CO2)
 BacteriaUptake			=	Flow(DOC,Bacteria) ! + Flow(Detritus,Bacteria)
 BacteriaProduction		=	BacteriaUptake - Flow(Bacteria,CO2) - Flow(Bacteria,DOC)


!---------------!
! MICROBENTHOS  !
!---------------!
 MicroBacterivory       =   Flow(Bacteria,Micro))
 MicroRespiration		=	Flow(Micro,CO2)
 MicroUptake			=	Flow(MPB,Micro) + Flow(Bacteria,Micro) + Flow(Detritus,Micro)
 MicroAssimilation		=	MicroUptake - Flow(Micro,Detritus)
 MicroProduction        =   MicroAssimilation - Flow(Micro,CO2)



!---------------!
!  MEIOBENTHOS  !
!---------------!
 MeioRespiration		=	Flow(Meio,CO2)
 MeioUptake				=	Flow(Detritus,Meio) + Flow(MPB,Meio) + Flow(Bacteria,Meio) + &
							Flow(Micro,Meio) + Flow(Meio,Meio)
 MeioAssimilation		=	MeioUptake - Flow(Meio,Detritus)
 MeioProduction         =   MeioAssimilation - MeioRespiration


!---------------!
! MACROBENTHOS  !
!---------------!
 MacroRespiration		=	Flow(Macro,CO2)
 MacroUptake			=	Flow(Detritus,Macro) + Flow(MPB,Macro) + Flow(Micro,Macro) + &
							Flow(Meio,Macro) + Flow(Phytoplankton,Macro)
 MacroAssimilation		=	MacroUptake - Flow(Macro,Detritus)
 MacroProduction        =   MacroAssimilation - MacroRespiration


 SedimentRespiration  = BacteriaRespiration + MicroRespiration + MeioRespiration + Macrorespiration + MPBRespiration
################################### END VARIABLES






!=============================================================!
!                                                             !
!                    EQUALITY CONSTRAINTS                     !
!                                                             !
!=============================================================!
############################ STOCK ############################

MPB		        =	TotMPB	!	(iso=-15)	!upper ? cm, include: cyanobacteria, diatoms and (dino)flagellates
Bacteria		=	TotBact	!	(iso=-17.9)	!upper 4 cm, spreadsheet Ilse
Micro			=	TotMicro	!(iso=-20.95)	!upper 4 cm, include: (dino)flagellates and ciliates
Meio			=	TotMeio		!(iso=-17.4)    !upper 6 cm, include: deposit-,ciliate-, micro-, epistratefeeders and (faculatative) predators
	                                !include biomass of forams
Macro			=	TotMacro	!(iso=-17.8)	!upper ? cm, include: (surface) deposit- and suspension feeders
DOC				=	TotDOC    		!not available, assumed
Detritus		=	TotDetritus  !(iso=-21.3)   !total orgC = 196 g/m2 in upper 5cm (Middelburg, 2000)

################################### END STOCK





!=============================================================!
!                                                             !
!                    EXTERNALS                                !
!                                                             !
!=============================================================!
############################## EXTERNALS ######################
CO2		!(iso=-15)
Burial
Export
Phytoplankton   ! (iso=-20)                   !it is considered external since its 'unlimited' supply						
Refrac			!(iso=-24.2)

################################### END EXTERNALS






!=============================================================!
!                                                             !
!                    RATE DECLARATION                         !
!                                                             !
!=============================================================!
############################# RATE  ###########################

! model is assumed to be in steady state -> all rates are zero

################################### END RATE






!=============================================================!
!                                                             !
!                    FLOW DECLARATION                         !
!                                                             !
!=============================================================!
################################ FLOW #########################

!---------------!
!     DOC       !
!---------------!
DOC				->		Bacteria    ! (DELT=1e-8)


!---------------!
!   Detritus    ! no burial since only assimilable detritus is considered
!---------------!
Detritus		->		DOC           
!Detritus		->		Bacteria  ! (FR=-15)
Detritus		->		Micro      
Detritus		->		Meio       
Detritus		->		Macro      


!---------------!
! PHYTOPLANKTON !
!---------------!
Phytoplankton   ->      Detritus   !simulation of deposition of phytodetritus
Phytoplankton   ->		Macro
Refrac          ->      Detritus

!---------------!
!    MPB        !
!---------------!
CO2				->		MPB        !primary production
MPB     		->		CO2
MPB	        	->		DOC       
MPB      		->		Detritus
MPB		        ->		Micro        
MPB	         	->		Meio        
MPB	        	->		Macro       


!---------------!
!   BACTERIA    !
!---------------!
Bacteria		->		CO2
Bacteria		->		DOC
Bacteria		->		Detritus
Bacteria		->		Micro       
Bacteria		->		Meio        
Bacteria        ->      Burial


!---------------!
! MICROBENTHOS  !
!---------------!
Micro			->		CO2
Micro			->		Detritus
Micro			->		Meio        
Micro			->		Macro       


!---------------!
!  MEIOBENTHOS  !
!---------------!
Meio			->		CO2
Meio			->		Detritus
Meio            ->      Meio        
Meio			->		Macro       


!---------------!
! MACROBENTHOS  !
!---------------!
Macro			->		CO2
Macro			->		Detritus
Macro			->		Export

################################### END FLOW








!=============================================================!
!                                                             !
!                    EQUALITY CONSTRAINTS                     !
!                                                             !
!=============================================================!
############################### EQUATION ######################

! If primprod = net production then exudation and respiration have to be added in stead of 
! subtracted!!!!!!!!!

PrimProd				=	GPP
BacteriaProduction		=	BNP
SedimentRespiration		=	SedResp
MicroBacterivory        =   MicroBactGraz
!Flow(detritus,doc)      =   0.0








!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 13C balance of Bacteria     !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!Flow(Detritus,Bacteria)*13C_Detritus - Flow(Detritus,Bacteria)*13C_Bacteria +     &
!Flow(DOC,Bacteria)*13C_DOC           - Flow(DOC,Bacteria)     *13C_Bacteria = 0


!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 13C balance of Microbenthos !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 Flow(Bacteria,Micro)*13C_Bacteria - Flow(Bacteria,Micro)*13C_Micro  +    &
 Flow(MPB,Micro)     *13C_MPB      - Flow(MPB,Micro)     *13C_Micro  +    &
 Flow(Detritus,Micro)*13C_Detritus - Flow(Detritus,Micro)*13C_Micro  = 0 



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 13C balance of Meiobenthos  !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 Flow(Detritus,Meio)*13C_Detritus - Flow(Detritus,Meio)*13C_Meio  +       &
 Flow(Bacteria,Meio)*13C_Bacteria - Flow(Bacteria,Meio)*13C_Meio  +       &
 Flow(MPB,Meio)     *13C_MPB      - Flow(MPB,Meio)     *13C_Meio  +       &
 Flow(Micro,Meio)   *13C_Micro    - Flow(Micro,Meio)   *13C_Meio  = 0



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 13C balance of Macrobenthos !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 Flow(MPB,Macro)          *13C_MPB           - Flow(MPB,Macro)          *13C_Macro  +     &
 Flow(Meio,Macro)         *13C_Meio          - Flow(Meio,Macro)         *13C_Macro  +     &
 Flow(Detritus,Macro)     *13C_Detritus      - Flow(Detritus,Macro)     *13C_Macro  +     &
 Flow(Phytoplankton,Macro)*13C_Phytoplankton - Flow(Phytoplankton,Macro)*13C_Macro  +     &
 Flow(Micro,Macro)        *13C_Micro         - Flow(Micro,Macro)        *13C_Macro  = 0



!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!   13C balance of Detritus   !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 Flow(MPB,Detritus)          *13C_MPB           - Flow(MPB,Detritus)          *13C_Detritus +  &
 Flow(Bacteria,Detritus)     *13C_Bacteria      - Flow(Bacteria,Detritus)     *13C_Detritus +  &
 Flow(Meio,Detritus)         *13C_Meio          - Flow(Meio,Detritus)         *13C_Detritus +  &
 Flow(Phytoplankton,Detritus)*13C_Phytoplankton - Flow(Phytoplankton,Detritus)*13C_Detritus +  &
 Flow(Refrac,Detritus)       *13C_Refrac        - Flow(Refrac,Detritus)       *13C_Detritus +  &
 Flow(Macro,Detritus)        *13C_Macro         - Flow(Macro,Detritus)        *13C_Detritus +  &
 Flow(Micro,Detritus)        *13C_Micro         - Flow(Micro,Detritus)        *13C_Detritus =  0  


################################### END EQUATION









!=============================================================!
!                                                             !
!                    INEQUALITY CONSTRAINTS                   !
!                                                             !
!=============================================================!
############################## CONSTRAINT #####################


!---------------!
!    MPB        !
!---------------!
 MPBRespiration		       >	   MinMPBRes * GPP                                 ! Langdon (1993)
 MPBDOCRelease	           =       [MinMPBDocRelease, MaxMPBDocRelease] * GPP      ! Goto (1999)
 

!---------------!
!   BACTERIA    !
!---------------!
 BacteriaProduction		   =       [MinBGE,MaxBGE]*BacteriaRespiration +          &
                                   [MinBGE,MaxBGE]*BacteriaProduction
  
!---------------!
! MICROBENTHOS  !
!---------------!
 MicroProduction            =       [MinProdMicro, MaxProdMicro]*Micro
 MicroAssimilation			=		[0.5, 0.75]*MicroUptake
 MicroRespiration			=		[BasRespMin, BasRespMax]*TotMicro +    & 
                                    [GrowthRespMin, GrowthRespMax]*MicroAssimilation


!---------------!
! MEIOBENTHOS   !
!---------------!
 MeioAssimilation           =       [0.10, 0.25]*MeioUptake
 MeioRespiration			=		[BasRespMin, BasRespMax]*TotMeio +    & 
                                    [GrowthRespMin, GrowthRespMax]*MeioAssimilation

!Feeding constraints
 Flow(Meio,Meio)            =       [0.25, 1.]*MeioPredators    + [0.025, 0.20]*MeioFacPredators
 Flow(Micro,Meio)           =       [MeioGrazMin, MeioGrazMax]*MeioCiliates      &
                                  + [MeioGrazMin, MeioGrazMax]*MeioEpistrate
 Flow(Bacteria, Meio)       =       [MeioGrazMin, MeioGrazMax]*MeioMicrovores    &
                                  + [MeioGrazMin, MeioGrazMax]*TotMeio
 Flow(Detritus,Meio)        =       [MeioGrazMin, MeioGrazMax]*MeioDeposit

 
!---------------!
! MACROBENTHOS  !
!---------------!
 MacroAssimilation			=		[0.4, 0.8]*MacroUptake
 MacroProduction            =       [0.01, 0.05]*Macro
 MacroRespiration			=		[BasRespMin, BasRespMax]*Macro + [0.20, 0.26]*MacroProduction





!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!                                      !
!      INEQUALITIES BASED ON 13C       !
!                                      !
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!  Doc is unknown, therefore splitted in upper and lower constraint
!  Bacteria  !  Minimal DOC is MPB and max DOC is Det
!!!!!!!!!!!!!!  

! MAXIMAL DOC CONSTRAINT gives: 13C_Bact > 13C_Detritus 
! As this is NOT TRUE -> cannot be used
 
 !Flow(Detritus,Bacteria)*13C_Detritus - Flow(Detritus,Bacteria)*13C_Bacteria <   &
!      Flow(DOC,Bacteria)*13C_Bacteria - Flow(DOC,Bacteria)*13C_MPB
 
!!!!!!!!!!!!!!
!  Meio      !
!!!!!!!!!!!!!!

! Flow(Detritus,Meio)*13C_Detritus - Flow(Detritus,Meio)*13C_Meio +    &
! Flow(Bacteria,Meio)*13C_Bacteria - Flow(Bacteria,Meio)*13C_Meio +    &
! Flow(MPB,Meio)*13C_MPB           - Flow(MPB,Meio)*13C_Meio      +    &
! Flow(Micro,Meio)*13C_Micro       - Flow(Micro,Meio)*13C_Meio   > 0

! MAXIMAL CONSTRAINT: IMPOSSIBLE

! Flow(Detritus,Meio)*13C_Detritus - Flow(Detritus,Meio)*13C_Meio    +    &
! Flow(Bacteria,Meio)*13C_Bacteria - Flow(Bacteria,Meio)*13C_Meio    +    &
! Flow(MPB,Meio)*13C_MPB           - Flow(MPB,Meio)*13C_Meio         >    &
! Flow(Micro,Meio)*13C_Meio        - Flow(Micro,Meio)*13C_MPB


!!!!!!!!!!!!!!
!  Macro     !
!!!!!!!!!!!!!!

! Flow(MPB,Macro)          *13C_MPB           - Flow(MPB,Macro)          *13C_Macro  +     &
! Flow(Meio,Macro)         *13C_Meio          - Flow(Meio,Macro)         *13C_Macro  +     &
! Flow(Detritus,Macro)     *13C_Detritus      - Flow(Detritus,Macro)     *13C_Macro  +     &
! Flow(Phytoplankton,Macro)*13C_Phytoplankton - Flow(Phytoplankton,Macro)*13C_Macro  <     &
! Flow(Micro,Macro)        *13C_Macro         - Flow(Micro,Macro)        *13C_MPB

! Flow(MPB,Macro)          *13C_MPB           - Flow(MPB,Macro)          *13C_Macro  +     &
! Flow(Meio,Macro)         *13C_Meio          - Flow(Meio,Macro)         *13C_Macro  +     &
! Flow(Detritus,Macro)     *13C_Detritus      - Flow(Detritus,Macro)     *13C_Macro  +     &
! Flow(Phytoplankton,Macro)*13C_Phytoplankton - Flow(Phytoplankton,Macro)*13C_Macro  >     &
! Flow(Micro,Macro)        *13C_Macro         - Flow(Micro,Macro)        *13C_Detritus
  




!!!!!!!!!!!!!!
!  Detritus  !
!!!!!!!!!!!!!!

! Flow(MPB,Detritus)*13C_MPB                - Flow(MPB,Detritus)*13C_Detritus             +  &
! Flow(Bacteria,Detritus)*13C_Bacteria      - Flow(Bacteria,Detritus)*13C_Detritus        +  &
! Flow(Meio,Detritus)*13C_Meio              - Flow(Meio,Detritus)*13C_Detritus            +  &
! Flow(Phytoplankton,Detritus)*13C_Phytoplankton - Flow(Phytoplankton,Detritus)*13C_Detritus +  &
! Flow(Refrac,Detritus)*13C_Refrac          - Flow(Refrac,Detritus)*13C_Detritus          +  &
! Flow(Macro,Detritus)*13C_Macro            - Flow(Macro,Detritus)*13C_Detritus           <  &
! Flow(Micro,Detritus)*13C_Detritus         - Flow(Micro,Detritus)*13C_MPB                


! Flow(MPB,Detritus)*13C_MPB                - Flow(MPB,Detritus)*13C_Detritus             +  &
! Flow(Bacteria,Detritus)*13C_Bacteria      - Flow(Bacteria,Detritus)*13C_Detritus        +  &
! Flow(Meio,Detritus)*13C_Meio              - Flow(Meio,Detritus)*13C_Detritus            +  &
! Flow(Phytoplankton,Detritus)*13C_Phytoplankton - Flow(Phytoplankton,Detritus)*13C_Detritus +  &
! Flow(Refrac,Detritus)*13C_Refrac          - Flow(Refrac,Detritus)*13C_Detritus          +  &
! Flow(Macro,Detritus)*13C_Macro            - Flow(Macro,Detritus)*13C_Detritus           > &
! 0

 

  
################################### END CONSTRAINT


