Mortality estimates from the descending limb of a catch curve.

Fits a linear model to the user-defined descending limb of a catch curve. Method functions extract estimates of the instantaneous (Z) and total annual (A) mortality rates with associated standard errors and confidence intervals. A plot method highlights the descending limb, shows the linear model on the descending limb, and, optionally, prints the estimated Z and A.

Usage

catchCurve(x, ...)

# S3 method for default
catchCurve(
  x,
  catch,
  ages2use = age,
  weighted = FALSE,
  negWeightReplace = 0,
  ...
)

# S3 method for formula
catchCurve(
  x,
  data,
  ages2use = age,
  weighted = FALSE,
  negWeightReplace = 0,
  ...
)

# S3 method for catchCurve
summary(object, parm = c("both", "all", "Z", "A", "lm"), ...)

# S3 method for catchCurve
coef(object, parm = c("all", "both", "Z", "A", "lm"), ...)

# S3 method for catchCurve
anova(object, ...)

# S3 method for catchCurve
confint(
  object,
  parm = c("all", "both", "Z", "A", "lm"),
  level = conf.level,
  conf.level = 0.95,
  ...
)

# S3 method for catchCurve
rSquared(object, digits = getOption("digits"), percent = FALSE, ...)

# S3 method for catchCurve
plot(
  x,
  pos.est = "topright",
  cex.est = 0.95,
  round.est = c(3, 1),
  ylab = "log(Catch)",
  xlab = "Age",
  ylim = NULL,
  col.pt = "gray30",
  col.mdl = "black",
  lwd = 2,
  lty = 1,
  ...
)

Arguments

x: A numerical vector of assigned ages in the catch curve or a formula of the form catch~age when used in catchCurve. An object saved from catchCurve (i.e., of class catchCurve) when used in the methods.
...: Additional arguments for methods.
catch: A numerical vector of catches or CPUEs for the ages in the catch curve. Not used if x is a formula.
ages2use: A numerical vector of ages that define the descending limb of the catch curve.
weighted: A logical that indicates whether a weighted regression should be used. See details.
negWeightReplace: A single non-negative numeric that will replace negative weights (defaults to 0). Only used when weighted=TRUE. See details.
data: A data.frame from which the variables in the x formula can be found. Not used if x is not a formula.
object: An object saved from the catchCurve call (i.e., of class catchCurve).
parm: A numeric or string (of parameter names) vector that specifies which parameters are to be given confidence intervals. If parm="lm" then confidence intervals for the underlying linear model are returned.
level: Same as conf.level. Used for compatibility with the generic confint function.
conf.level: A number representing the level of confidence to use for constructing confidence intervals.
digits: The number of digits to round the rSquared result to.
percent: A logical that indicates if the rSquared result should be returned as a percentage (=TRUE) or as a proportion (=FALSE; default).
pos.est: A string to identify where to place the estimated mortality rates on the plot. Can be set to one of "bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right" or "center" for positioning the estimated mortality rates on the plot. Typically "bottomleft" (DEFAULT) and "topright" will be “out-of-the-way” placements. Set pos.est to NULL to remove the estimated mortality rates from the plot.
cex.est: A single numeric character expansion value for the estimated mortality rates on the plot.
round.est: A numeric that indicates the number of decimal place to which Z (first value) and A (second value) should be rounded. If only one value then it will be used for both Z and A.
ylab: A label for the y-axis ("log(Catch)" is the default).
xlab: A label for the x-axis ("Age" is the default).
ylim: A numeric for the limits of the y-axis. If NULL then will default to a minimum of 0 or the lowest negative log catch and a maximum of the maximum log catch. If a single value then it will be the maximum of the y-axis. If two values then these will the minimum and maximum values of the y-axis.
col.pt: A string that indicates the color of the plotted points.
col.mdl: A string that indicates the color of the fitted line.
lwd: A numeric that indicates the line width of the fitted line.
lty: A numeric that indicates the type of line used for the fitted line.

Value

A list that contains the following items:

age The original vector of assigned ages.
catch The original vector of observed catches or CPUEs.
age.e A vector of assigned ages for which the catch curve was fit.
log.catch.e A vector of log catches or CPUEs for which the catch curve was fit.
W A vector of weights used in the catch curve fit. Will be NULL unless weighted=TRUE.
lm An lm object from the fit to the ages and log catches or CPUEs on the descending limb (i.e., in age.e and log.catch.e).

Details

The default is to use all ages in the age vector. This is appropriate only when the age and catch vectors contain only the ages and catches on the descending limb of the catch curve. Use ages2use to isolate only the catch and ages on the descending limb.

If weighted=TRUE then a weighted regression is used where the weights are the log(number) at each age predicted from the unweighted regression of log(number) on age (as proposed by Maceina and Bettoli (1998)). If a negative weight is computed it will be changed to the value in negWeightReplace and a warning will be issued.

Testing

Tested the results of catch curve, both unweighted and weighted, against the results in Miranda and Bettoli (2007). Results for Z and the SE of Z matched perfectly. Tested the unweighted results against the results from agesurv in fishmethods using the rockbass data.frame in fishmethods. Results for Z and the SE of Z matched perfectly.

IFAR Chapter

11-Mortality.

References

Ogle, D.H. 2016. Introductory Fisheries Analyses with R. Chapman & Hall/CRC, Boca Raton, FL.

Maceina, M.J., and P.W. Bettoli. 1998. Variation in Largemouth Bass recruitment in four mainstream impoundments on the Tennessee River. North American Journal of Fisheries Management 18:998-1003.

Ricker, W.E. 1975. Computation and interpretation of biological statistics of fish populations. Technical Report Bulletin 191, Bulletin of the Fisheries Research Board of Canada. [Was (is?) from http://www.dfo-mpo.gc.ca/Library/1485.pdf.]

Author

Derek H. Ogle, DerekOgle51@gmail.com

Examples

plot(catch~age,data=BrookTroutTH,pch=19)


## demonstration of formula notation
cc1 <- catchCurve(catch~age,data=BrookTroutTH,ages2use=2:6)
summary(cc1)
#>    Estimate Std. Error  t value   Pr(>|t|)
#> Z  0.659987   0.136741 4.826549 0.01695159
#> A 48.314197         NA       NA         NA
cbind(Est=coef(cc1),confint(cc1))
#>         Est    95% LCI   95% UCI
#> Z  0.659987  0.2248162  1.095158
#> A 48.314197 20.1337012 66.551321
rSquared(cc1)
#> [1] 0.8859124
plot(cc1)
summary(cc1,parm="Z")
#>   Estimate Std. Error  t value   Pr(>|t|)
#> Z 0.659987   0.136741 4.826549 0.01695159
cbind(Est=coef(cc1,parm="Z"),confint(cc1,parm="Z"))
#>        Est   95% LCI  95% UCI
#> Z 0.659987 0.2248162 1.095158

## demonstration of excluding ages2use
cc2 <- catchCurve(catch~age,data=BrookTroutTH,ages2use=-c(0,1))
summary(cc2)
#>    Estimate Std. Error  t value   Pr(>|t|)
#> Z  0.659987   0.136741 4.826549 0.01695159
#> A 48.314197         NA       NA         NA
plot(cc2)


## demonstration of using weights
cc3 <- catchCurve(catch~age,data=BrookTroutTH,ages2use=2:6,weighted=TRUE)
summary(cc3)
#>     Estimate Std. Error t value   Pr(>|t|)
#> Z  0.6430183  0.1417433  4.5365 0.02004993
#> A 47.4296703         NA      NA         NA
plot(cc3)


## demonstration of returning the linear model results
summary(cc3,parm="lm")
#> 
#> Call:
#> stats::lm(formula = log.catch.e ~ age.e, weights = W, na.action = stats::na.exclude)
#> 
#> Weighted Residuals:
#>         1         2         3         4         5 
#> -0.008845 -0.551857  1.155519 -0.513606 -0.103196 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)   6.0086     0.5475  10.974  0.00162 **
#> age.e        -0.6430     0.1417  -4.536  0.02005 * 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 0.7988 on 3 degrees of freedom
#> Multiple R-squared:  0.8728,	Adjusted R-squared:  0.8304 
#> F-statistic: 20.58 on 1 and 3 DF,  p-value: 0.02005
#> 
cbind(Est=coef(cc3,parm="lm"),confint(cc3,parm="lm"))
#>                    Est   95% LCI   95% UCI
#> (Intercept)  6.0085938  4.266116  7.751072
#> age.e       -0.6430183 -1.094109 -0.191928

## demonstration of ability to work with missing age classes
df <- data.frame(age=c(  2, 3, 4, 5, 7, 9,12),
                 ct= c(100,92,83,71,56,35, 1))
cc4 <- catchCurve(ct~age,data=df,ages2use=4:12)
#> Warning: Some 'ages2use' not in observed ages.
summary(cc4)
#>     Estimate Std. Error  t value   Pr(>|t|)
#> Z  0.5139824  0.1495532 3.436786 0.04133277
#> A 40.1891060         NA       NA         NA
plot(cc4)


## demonstration of ability to work with missing age classes
## evein if catches are recorded as NAs
df <- data.frame(age=c(  2, 3, 4, 5, 6, 7, 8, 9,10,11,12),
                 ct= c(100,92,83,71,NA,56,NA,35,NA,NA, 1))
cc5 <- catchCurve(ct~age,data=df,ages2use=4:12)
summary(cc5)
#>     Estimate Std. Error  t value   Pr(>|t|)
#> Z  0.5139824  0.1495532 3.436786 0.04133277
#> A 40.1891060         NA       NA         NA
plot(cc5)