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#' Clam bioenergetic individual model differential equations (alternative version)
#'
#' @param Param a vector containing model parameters
#' @param Tint the interpolated water temperature at time t
#' @param Chlint the interpolated chlorophyll at time t
#' @param Ww clam wet weight at time t
#'
#' @return a list containing the clam weights, temperature limitation functions and metabolic rates at time t
#'
#' @import matrixStats plotrix rstudioapi
#'
ClamF_ind_equations <- function(Param, Tint, Chlint, Ww){
# Parameters definition
Gdmax=Param[1] # [gDW^0.265 d^-1] Max growth rate on a dry weight base
Gwmax=Param[2] # [gDW^0.333 d^-1] Max growth rate on a wet weight base
Rdmax=Param[3] # [d^-1] Max respiration rate on a dry weight base
Rwmax=Param[4] # [d^-1] Max respiration rate on a wet weight base
p=Param[5] # [-] Dry weight - wet weight conversion exponent
k=Param[6] # [-] Wet weight - length conversion exponent
q=Param[7] # [-] Coefficient for allometric filter velocity
a=Param[8] # [cm] Wet weight - length conversion coefficient
b=Param[9] # [gWW] Dry weight - wet weight conversion coefficient
m=Param[10] # [-] Weight exponent for catabolism
n=Param[11] # [-] Weight exponent for anabolism
vf=Param[12] # [J/d g] Maximum ingestion rate for 1g o mussel
epsT=Param[13] # [-] Weight exponent for filtration
epsF=Param[14] # [-] Half-saturation constant for AE
TmaxG=Param[15] # [1/Celsius degree] Temperature exponent fot anabolism
ToptG=Param[16] # [1/Celsius degree] Temperature exponent for catabolism
TmaxR=Param[17] # [Celsius degree] Maximum temperature for the anabolic process
ToptR=Param[18] # [Celsius degree] Optimum temperature for the anabolic process
TmaxV=Param[19] # [Celsius degree] Maximum temperature for the catabolic process
ToptV=Param[20] # [Celsius degree] Optimum temperature for the catabolic process
betaG=Param[21] # [-] Dry weight - wet weight conversion coefficient
betaV=Param[22] # [-] Dry weight - wet weight exponent
betaR=Param[23] # [-] Dry weight - length conversion coefficient
niT=Param[24] # [-] Ratio of energetic demand satisfied by non planktonic material
kap=Param[25] # [mgChla/gC] Chlorophyll/Phytoplankton ratio
Tanab=min(Tint,TmaxG) # Temperature for anabolism < Max temperature for anabolism
Tcatab=min(Tint,TmaxR) # Temperature for catabolism < Max temperature for catabolism
Tfood=min(Tint,TmaxV) # Temperature for filtration < Max temperature for filtration
# Temperature limitation functions
FgT=(((TmaxG-Tanab)/(TmaxG-ToptG))^(betaG*(TmaxG-ToptG)))*exp(betaG*(Tanab-ToptG)) # Growth limitation [-]
FrT=(((TmaxR-Tcatab)/(TmaxR-ToptR))^(betaR*(TmaxR-ToptR)))*exp(betaR*(Tcatab-ToptR)) # Respiration limitation [-]
FvT=(((TmaxV-Tfood)/(TmaxV-ToptV))^(betaV*(TmaxV-ToptV)))*exp(betaV*(Tfood-ToptV)) # Filtration limitation [-]
# Maximum food ingestion
Wd=b*Ww^p # Dry weight value [g]
Fstar=Gdmax*FgT*(Wd^(1-0.3333*p))*epsT/(vf*FvT*(Wd^q)*epsF)
Ff=min(1, Chlint/Fstar+niT)
# ENERGETIC BALANCE
# Anabolism [gWW/d]
if (Chlint>Fstar) {
A=Gwmax*FgT*Ww^m
}else{
A=Ff*Gwmax*FgT*Ww^m
}
# Catabolism [gWW/d]
C=Rwmax*FrT*Ww^n
# Balance [gWW/d]
dWw=A-C
tfun=cbind(FgT, FrT, FvT)
metab=cbind(A, C)
# Function outputs
output=list(dWw,tfun,metab)
return(output) # ClamF_ind_equations output
}
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