Sampling_Survey: Index of biomass and abundance

In IMPRESSPROJECT/ModelingPopulation: Modeling of an exploited population (structured by age)

Description

Returns the indices of abundance for each year, age and iteration, and indices of biomass for each year and iteration.

Usage

Sampling_Survey(Pop.Mod, type, par)

Arguments

Pop.Mod	A list containing the components returned by Population.Modeling function (main function).
type	indices type which can be "biomass" or "abundance".
par	list of the parameters required of computed the selected index. type="biomass": q_B which is the vector of annual catchability coefficients. gamma which is the density dependent parameter. CV which is the biomass coefficient of variation. Default value 0. type="abundance": q_A which is the matrix of annual and age specific catchability coefficients. gamma which is the density dependent parameter. CV which is the biomass coefficient of variation. Default value 0.

Details

The function returns the index of abundance for each year, age and iteration, and the index of biomass for each year and iteration. The biomass index for year t is

IB_t=q_B_t*BIO_t^{gamma}

where q_B_t is the catchability coefficient for year t and BIO_t is the biomass for year t when CV=0. If CV is different than 0 the biomass index for year t is

IB_t=q_B_t*BIO_t^{gamma}*epsilon_t

where q_B_t is the catchability coefficient, BIO_t is the biomass for year t, and epsilon_t is the residual generated from a log normal distribution center in zero and whose variability determined for the corresponding CV. The abundance index for year t and age i is

IA_it=q_A_it*N_it^{gamma}

where q_A_it is the catchability coefficient and N_it is the abundance for year t and age i when CV=0. If CV is different than 0 the abundance index for year t and age i is

IA_it=q_A_it*N_it^{gamma}*epsilon_it

where q_A_it is the catchability coefficient, N_it is the abundance for year t and age i, and epsilon_it is the residual generated from a log normal distribution center in zero and variability determined for the corresponding CV.

Value

An array containing the indices of abundance for each year, age, and iteration if "type=abundance" or the indices of biomass for each year and iteration if "type=biomass".

Author(s)

• Marta Cousido-Rocha

• Santiago Cerviño López

Examples

# First we introduce the basic parameters to define the population.
# Note that N0 is equal to 10000 individuals, and hence below we are
# consistent with this unit when we introduce the biological and
# stock-recruitment parameters.
ctrPop<-list(years=seq(1980,2020,by=1),niter=2,N0=10000,ages=0:15,minFage=4,
maxFage=7,ts=0,tc=0.5,tseed=NULL)

# Now, we introduce the biological parameters of the population.
# Note that L_inf is in cm, and a and b parameters allow us to relate
# the length in cm with the weight in Kg.
number_ages<-length(ctrPop$ages);number_years<-length(ctrPop$years)
M<-matrix(rep(0.4,number_ages*number_years),ncol = number_years)
colnames(M)<-ctrPop$years
rownames(M)<-ctrPop$ages
ctrBio<-list(M=M,CV_M=0.2, L_inf=124.5, t0=0, k=0.164, CV_L=0.2, CV_LC=0.2, a=4.5*10^(-6), b=3.1049,
           a50_Mat=3, ad_Mat=-0.5,CV_Mat=0.2)

# We continue introducing the fishing parameters.
# Below, we have different objects ctrSEL depending on which selectivity function is used.
# Constant selectivity
ctrSEL<-list(type="cte", par=list(cte=0.5),CV_SEL=0.2)

# Logistic selectivity
ctrSEL<-list(type="Logistic", par=list(a50_Sel=1.5, ad_Sel=-1),CV_SEL=0.2)

# Gamma selectivity
ctrSEL<-list(type="Gamma", par=list(gamma=10,alpha=15, beta=0.03),CV_SEL=0.05)

# Andersen selectivity
ctrSEL<-list(type="Andersen", par=list(p1=2,p3=0.2,p4=0.2,p5=40),CV_SEL=0.05)

f=rep(0.5,number_years)
ctrFish<-list(f=f,ctrSEL=ctrSEL)

# Finally, we show below the three possible stock recruitment relationship.
# The values of the parameters of Beverton-Holt Recruitment Model and Ricker
# Recruitment Model are ones suitables when the biomass is measured in Kg and
# the recruitment is measured as number of individuals.

a_BH=10000; b_BH=400; CV_REC_BH=0.2; a_RK=10; b_RK=0.0002; CV_REC_RK=0.2
# If the spawning stock recruiment relationship is constant:
SR<-list(type="cte",par=NULL)
# If the spawning stock recruitment relationship is Beverton-Holt Recruitment Model:
SR<-list(type="BH",par=c(a_BH,b_BH,CV_REC_BH))
# If the spawning stock recruitment relationship is Ricker Recruitment Model:
SR<-list(type="RK",par=c(a_RK,b_RK,CV_REC_RK))

# The following lines allow us to use the described function.
Pop.Mod<-Population.Modeling(ctrPop=ctrPop,ctrBio=ctrBio,ctrFish=ctrFish,SR=SR)

# Now,we can compute the index of abundance or biomass.
# For biomass index:
q_B<-rep(0.01,41);gamma<-1;CV<-0.2; par<-list(q_B,gamma,CV)
 #I<-Sampling_Survey(Pop.Mod,type="biomass",par=par)

# For abundance index:
q_A<-matrix(0.2,ncol=41,nrow=16);gamma<-1;CV<-0.2; par<-list(q_A,gamma,CV)
 #I<-Sampling_Survey(Pop.Mod,type="abundance",par=par)

IMPRESSPROJECT/ModelingPopulation documentation built on March 21, 2020, 12:14 a.m.