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#' Clam bioenergetic population model differential equations
#'
#' @param Param a vector containing model parameters
#' @param Tint the interpolated water temperature at time t
#' @param Phy the interpolated phytoplankton at time t
#' @param DT the interpolated detritus at time t
#' @param POCint the interpolated POC at time t
#' @param POMint the interpolated POM at time t
#' @param TSSint the interpolated TSS at time t
#' @param Wd the weight of the clam at time t
#'
#' @return a list containing the clam weights, temperature limitation functions and metabolic rates at time t
#'
#' @import matrixStats plotrix rstudioapi
#'
#' @import stats utils
#'
Clam_pop_equations <- function(Param, Tint, Phy, DT, POCint, POMint, TSSint, Wd){
# Parameters definition
epsB=Param[1] # [J/g] Tissue energy content
epsDT=Param[2] # [J/mgC] Detritus energy content
epsPhy=Param[3] # [J/mgC] Phytoplankton energy content
epsO2=Param[4] # [mlO2/h] Energy consumed by the respiration of 1g of oxygen
alpha=Param[5] # [-] Feeding catabolism
CRmax=Param[6] # [l/d gDM] Maximum filtration rate
AEmax=Param[7] # [-] Maximum adsorption efficiency
Rmax=Param[8] # [mgO2/d gDM] maximum respiration rate
Amax=Param[9] # [J/d g] Maximum ingestion rate for 1g o mussel
q=Param[10] # [-] Weight exponent for filtration
Ks=Param[11] # [-] Half-saturation constant for AE
betaa=Param[12] # [1/Celsius degree] Temperature exponent fot anabolism
betac=Param[13] # [1/Celsius degree] Temperature exponent for catabolism
Tma=Param[14] # [Celsius degree] Maximum temperature for the anabolic process
Toa=Param[15] # [Celsius degree] Optimum temperature for the anabolic process
Tmc=Param[16] # [Celsius degree] Maximum temperature for the catabolic process
Toc=Param[17] # [Celsius degree] Optimum temperature for the catabolic process
aF=Param[18] # [-] Dry weight - wet weight conversion coefficient
bF=Param[19] # [-] Dry weight - wet weight exponent
a=Param[20] # [-] Dry weight - length conversion coefficient
b=Param[21] # [-] Dry weight - length exponent
lambda=Param[22] # [g/mg] Chlorophyll a - Phytoplankton conversion factor
# CATABOLISM
# Optimum temperature dependence for catabolism [dimensionless]
if (Tint >= Tmc) {
fc=0.0
} else {
fc=((Tmc-Tint)/(Tmc-Toc))^(betac*(Tmc-Toc))*exp(betac*(Tint-Toc))
}
C=Rmax*epsO2*fc*Wd # Daily catabolism [J/day]
# ANABOLISM
# Optimum temperature dependence for anabolism [dimensionless]
if (Tint >= Tma){
fa=0.0
}else {
fa=((Tma-Tint)/(Tma-Toa))^(betaa*(Tma-Toa))*exp(betaa*(Tint-Toa))
}
I=(CRmax*fa*Wd^q)*(DT*epsDT+Phy*epsPhy) # Daily ingestion [J/day]
encont=(DT*epsDT+Phy*epsPhy) # Energy content of ingested food [J/l]
Q=((POMint/TSSint)) # POM/TSS ratio [-]
if (Q>=1){
Q=1
}
AE=(Q/(Q+Ks)) # Limitation on ingested energy [-]
E=I*AE # Total ingested energy [J/d]
Aing=(1-alpha)*E # Daily anabolism [J/d]
# Daily anabolism limitation
if (Aing<Amax*Wd^q*fa){
A=Aing # Anabolic rate [J/d]
filt=CRmax*fa*Wd^q # [l/d]
A1=Amax*Wd^q*fa # Maximum anabolic rate [J/d]
}else{
A=Amax*Wd^q*fa # Anabolic rate [J/d]
filt=CRmax*fa*Wd^q # [l/d]
A1=Amax*Wd^q*fa # Maximum anabolic rate [J/d]
}
# Mass balance
dWd=((A)-C)/epsB # Weight increment [g/d]
tfun=cbind(fa, fc)
metab=cbind(A, C)
# Function outputs
output=list(dWd,tfun,metab)
return(output)
}
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