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###### FUNCIONES IM(), EDAD(), GRUPO_EDAD() y ab() #######
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# Libraries
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library(egg)
library(gdata)
library(dplyr)
library(tidyr)
library(FSA)
library(utils)
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# PREAMBULO
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# Delete all objets of workspace
rm(list=ls(all=TRUE))
options(digits = 9, scipen=999)
set.seed(1234)
##########################################################As a rule, if the marginal increment is translucent it is not counted because it is not fully formed. in the for cycle above, we calculate the proportion of the traslucent increment i in relation of the inncrement i-1.
IM <- function(x){
im <- rep(NA, length(auxAge2$RADIO_TOTAL))
rt <- auxAge2$RADIO_TOTAL
df <- auxAge2
for(i in 1:dim(df)[1]){
RT <- numeric(); RT = rt[i]
temp <- numeric(); temp = df[i,c(9:32)]
if(all(is.na(as.numeric(temp))))
im[i] <- 0.249
else
X1 = numeric(); X1 = temp[which(is.na(as.numeric(temp)))[1]-2]
X2 = numeric(); X2 = temp[which(is.na(as.numeric(temp)))[1]-1]
if(length(X1) > 0 & length(X2) > 0)
if(as.numeric(X1) > 0 & as.numeric(X2) > 0)
im[i] <- (RT-as.numeric(X2))/(as.numeric(X2)-as.numeric(X1))
else
im[i] <- 0.249
else
im[i] <- 0.249
}
im[which(im > 1)] <- 0.249
im[which(im <= 0)] <- 0.249
return(im)
} To estimate the biological age, the number of radii recorded and the nature of the otolith edge are considered. If the otolith edge is hyaline (values 3 or 4 of the variable BORDE), one is added to the number of radii counted.
EDAD <- function(x,y){
z <- numeric(length = length(x))
for(i in 1:length(x)){
if(y[i] > 2)
z[i] <- x[i] + 1
else
z[i] <- x[i]
}
return(z)
}The age group is the number of calendar years after the date of capture, for this purpose each fish will be assigned depends on the year in wich it was spawned and on the date of capture, simplifying the identification of annual class per fish.
This estimate is calculated with the number of rings observed in the otolith, the type of edge of the otolith and an arbitrary date of birth. In Chile, the first date of birth is taken as a convention on January 1.
GRUPO_EDAD <- function(x){
m <- as.numeric(Age$MES)
b <- as.numeric(Age$BORDE)
im <- as.numeric(Age$Im)
ge <- rep(NA, length(Age$Age))
for(i in 1:length(x)){
if(m[i] <= 5 & b[i] <= 2)
ge[i] <- x[i] + 1
else if(m[i] == 6 & b[i] == 1 & im[i] >= 0.250)
ge[i] <- x[i] + 1
else if(m[i] == 6 & b[i] == 2)
ge[i] <- x[i] + 1
else if(m[i] == 7 & b[i] == 1 & im[i] >= 0.350)
ge[i] <- x[i] + 1
else if(m[i] == 7 & b[i] == 2)
ge[i] <- x[i] + 1
else if(m[i] == 8 & b[i] %in% c(1,2) & im[i] >= 0.500)
ge[i] <- x[i] + 1
else if(m[i] == 9 & b[i] == 2 & im[i] >= 0.700)
ge[i] <- x[i] + 1
else
ge[i] = x[i]
}
return(ge)
}The length-weight relationship is widely used in fisheries to estimate weight from the length of an individual and also to estimate condition indices. The most frequently used expression for this relationship corresponds to the allometric equation where the weight is expressed as a function of length, and its parameters are estimated by linear regression of log-transformed data. Since variability in weight usually increases with length, this transformation has the advantage that it tends to stabilize the weight variance, but introduces a bias factor in back-transformed predictions which requires correction.
The weight/length model is:
\[W_i = a*L_i^b\] We can derive a simple linear regression model applying a logarithmic transformation:
\[ln(W_i) = ln(a)+b*ln(L_i)\]
where Wi represents the weight and Li the length of the i-th fish; a and b correspond to the intercept and slope, respectively.
AB <- function(x){
ab <- x %>%
filter(!is.na(LONGITUD_ESPECIMEN),
!is.na(PESO_ESPECIMEN)) %>%
group_by(ANO,MACROZONA,TRIMESTRE) %>%
mutate(L_LH = log(LONGITUD_ESPECIMEN),
L_W = log(PESO_ESPECIMEN)) %>%
summarise(Slope = lm(L_W ~ L_LH)$coefficients[2],
Intercept = exp(lm(L_W ~ L_LH)$coefficients[1]),
Correlation = cor(L_W,L_LH),
N = n()) %>%
mutate(bmax = round(Slope,1)) %>%
left_join(PR,by = c("bmax")) %>%
rename(tempbmax1 = bmax,
tempA = temp1,
tempC = temp2 ) %>%
mutate(bmax= round(round(Slope,1) - 0.1,1)) %>%
left_join(PR,by = c("bmax")) %>%
rename(tempbmax2 = bmax,
tempB = temp1,
tempD = temp2) %>%
mutate(a1 = as.numeric(tempA - ((tempbmax1 - Slope) * (tempA - tempB)) / (tempbmax1 - tempbmax2)),
a2 = as.numeric(tempC - ((tempbmax1 - Slope) * (tempC - tempD)) / (tempbmax1 - tempbmax2))) %>%
dplyr::select(-starts_with('temp'))
return(ab)
}Once a key is available, samples of fish that were only measured for length can be distributed to age groups accordingly.
This is possible because it assumes that the sample of aged fish and the sample of fish measured for length are simple random samples from the same population, thus the probability that a fish is of a particular age, given its length is the same in both samples follows.
The individuals present in each length interval (Nj) are assigned to different ages according to a size-age key.
The number of individuals belonging to each age group according to size interval is estimated as:
\[N_{ij} = q_{ij}/N_j\] where:
The abundance by age group is obtained by:
\[N_i = \sum_{i=1}^{n} N_{ij} \]
where:
the average length for each age group is expressed as
\[ \bar{p_{i}} = \frac{\sum_{i=1}^{n} l_{j}n_{ij}}{ni} \]
Donde:
The variance of the mean length is expressed as
\[ P_i = \sum_{j=1} p_jq_{ij} \]
\[\sigma_{p_j} = \sum_{j=1}^{L} (\frac{p_j^{2}q_{ij}(1-q_{ij})}{n_{j}-1}+ \frac{p_{j}(q_{ij}-P_{i})^{2}}{N}) \]
Donde:
Assuming that the length is a normal random variable the expected function value of \(W_L\), will be defined as:
\[E(W) = a(\bar{p_{i}}^b+a_{1}\bar{p_{i}}^{b-2}\sigma^2+a_{2}\bar{p_{i}}^{b-4}\sigma^4)\]
where:
CATCH_AGE <- function(x){
auxAge4 <- x
# LECTURAS DE EDAD CON TALLAS SIN ESTIMACION PARA CADA MACROZONA POR TRIMESTRE
CaptTallaEdad <- auxAge4 %>%
group_by(CRITERIO,ANO,MACROZONA,TRIMESTRE,LONGITUD_ESPECIMEN,GRUPO_EDAD) %>%
summarise(FREC = n()) %>%
mutate(PROP_GRUPO = FREC/sum(FREC)) %>%
left_join(Length, by = c("CRITERIO","ANO","MACROZONA","TRIMESTRE","LONGITUD_ESPECIMEN")) %>%
mutate(CAPT = PROP_GRUPO*CAPT) %>%
ungroup()
# CAPTURAS A LA EDAD Y TALLA POR CADA MACROZONA Y TRIMESTRE
auxCatchAge <- CaptTallaEdad %>%
dplyr::select(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD,CAPT) %>%
group_by(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD) %>%
summarise(CAPT = sum(CAPT,na.rm=T)) %>%
ungroup() %>%
group_by(CRITERIO,ANO,MACROZONA, TRIMESTRE) %>%
mutate(PORC = CAPT/sum(CAPT,na.rm=T) *100)
auxCatchAge1 <- CaptTallaEdad %>%
mutate(tmed = LONGITUD_ESPECIMEN * CAPT,
varl = (LONGITUD_ESPECIMEN^2) * CAPT) %>%
filter(CAPT != 0) %>%
group_by(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD) %>%
summarise(VARL = sum(varl, na.rm = T),
TMED = sum(tmed, na.rm = T))
auxCatchAge2 <- CaptTallaEdad %>%
filter(CAPT != 0) %>%
group_by(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD) %>%
summarise(L_PR = weighted.mean(LONGITUD_ESPECIMEN, CAPT))
# CAPTURAS A LA EDAD
CatchAge <- auxCatchAge %>%
left_join(auxCatchAge2, by = c("CRITERIO","ANO","MACROZONA","TRIMESTRE","GRUPO_EDAD"))%>%
left_join(ab, by = c("CRITERIO","ANO","MACROZONA","TRIMESTRE"))%>%
dplyr::select(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD,CAPT,PORC,L_PR,Intercept,
Slope, Correlation, N,a1,a2)%>%
left_join(auxCatchAge1,by = c("CRITERIO","ANO","MACROZONA","TRIMESTRE","GRUPO_EDAD"))%>%
ungroup()%>%
mutate(VAR = abs((VARL-(L_PR*TMED))/(CAPT-1)),
P_PR = (Intercept * ((L_PR^Slope) +
a1 * (L_PR^(Slope-2)) * VAR +
a2 * (L_PR^(Slope-4)) * VAR^2))/1000,
CAPT_TON = (CAPT* P_PR) / 1000) %>%
group_by(CRITERIO,ANO,MACROZONA,TRIMESTRE)%>%
mutate(PORC_TON = (CAPT_TON / sum(CAPT_TON)) * 100)%>%
ungroup()%>%
dplyr::select(CRITERIO,ANO,MACROZONA,TRIMESTRE,GRUPO_EDAD,
CAPT,PORC,L_PR,VAR,P_PR,CAPT_TON,
PORC_TON)%>%
ungroup() %>%
filter(CAPT != 0) %>%
mutate(GE = "GE")%>%
unite(GRUPO_EDAD, GE,GRUPO_EDAD) %>%
mutate(ANO = as.numeric(ANO)) %>%
separate(GRUPO_EDAD, into = c("G","GRUPO_EDAD"), sep ="_") %>%
mutate(GRUPO_EDAD = as.numeric(GRUPO_EDAD)) %>%
dplyr::select(-G)
return(list(CatchAge, CaptTallaEdad))
} Panfili, J., Morales-Nin, B. 2002. Manual of fish sclerochronology. IFREMER-IRD coedition, Brest. pp. 129-134.
Pienaar L. and W. Ricker, 1968. Estimating mean weight from length statistic. J. Fish. Res. Board of Can. 25: 2743 - 2747.
Ricker W., 1958. Handbook of computations for biological statistics of fish populations. Bull. Fish. Res. Bd. Can., Nº 119.