| mr.closed {FSA} | R Documentation |
This function takes the number of marked animals, number of captured animals from a second sample, and the number of marked animals in the second sample and uses one of four methods to estimate the initial population size with associated confidence interval. This function will accept these data for multiple groups of fish and produce an overall estimate of the population size. In addition, this function takes the number of captured animals, number of marked animals, and the number of unmarked animals that are marked and returned to the population on each of a series of samples and uses one of two methods (Schnabel (1938) or Schumacher-Eschmeyer (1943)) to estimate the initial population size with associated confidence interval. These methods assume that the population is closed.
mr.closed(M,n,m,R,
type=c("Petersen","Chapman","Ricker","Bailey","Schnabel","SchumacherEschmeyer"),
labels=NULL,chapman.mod=TRUE)
## S3 method for class 'MRC':
summary(object,numdigs=0,incl.SE=FALSE,incl.all=FALSE,incl.inputs=TRUE,...)
## S3 method for class 'MRC':
confint(object,parm=NULL,level=conf.level,conf.level=0.95,numdigs=0,
ci.type=c("suggested","binomial","hypergeom","normal","Poisson"),
bin.type=c("wilson","exact","asymptotic"),incl.inputs=TRUE,...)
## S3 method for class 'MRC2':
plot(x,pch=19,col.pt="black",xlab=expression(M[i]),ylab=expression(m[i]%/%n[i]),
loess=FALSE,lty=2,lwd=2,col.loess="red",f=2/3,iter=5,...)
M |
A numeric representing the number of marked fish from the first sample (single-census) or numeric vector of marked fish prior to ith samples (multiple-census). |
n |
A numeric representing the number of captured fish in the second sample (single-census) or numeric vector of captured fish in ith sample (multiple-census). |
m |
A numeric representing the number of recaptured (marked) fish in the second sample (single-census) or numeric vector of recaptured (marked) fish in ith sample (multiple-census). |
R |
A numeric vector representing the number of marked fish returned to the population (multiple-census). |
type |
a string that identifies the type of calculation method to use. See details. |
labels |
A character or character vector used to label the rows of the resulting output matrix when using a single census method separated by groups. Must be the same length as M, n, and m. Defaults to upper-case letters if no values are given. |
chapman.mod |
A logical that represents whether the Chapman modification method should be used (=TRUE, default) or not (=FALSE) when performing the Schnabel multiple census method. |
object |
An object saved from the mr.closed call (i.e., of class MRC). |
x |
An object saved from the mr.closed call when using type="Schnabel" or type="SchumacherEschmeyer" (i.e., of class MRC2). |
numdigs |
The number of decimal digits to round the population estimates to. If incl.SE=TRUE then SE will be rounded to one more decimal place then given in numdigs. |
incl.SE |
A logical indicating whether the results should include the SE calculation. See details. |
incl.all |
A logical indicating whether an overall population estimate should be computed when using a single census method that has been separated into sub-groups. See details. |
incl.inputs |
A logical indicating whether a reminder of the inputted values and what type of method was used should be printed with the summary and confidence interval results. |
parm |
a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered. |
level |
Same as conf.level but used for compatability with generic confint function. |
conf.level |
A numeric representing the level of confidence to use for constructing confidence intervals. |
ci.type |
A string that identifies the type of confidence interval to contstruct. See details. |
bin.type |
A string that identifies the method used to construct binomial confidence intervals (default is "wilson"). This is only used if citype="binomial". See details of bin.ci |
pch |
A numeric used to indicate the type of plotting character. |
col.pt |
a string used to indicate the color of the plotted points. |
xlab |
A label for the x-axis ("Age" is the default). |
ylab |
A label for the y-axis ("log(Catch)" is the default). |
loess |
A logical indicating if a loess smoother line is fit to and shown on plot. |
lty |
a numeric used to indicate the type of line used for the loess line. |
lwd |
a numeric used to indicate the line width of the loess line. |
col.loess |
a string used to indicate the color of the loess line. |
f |
a numeric for the loess smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness. |
iter |
a numeric for the number of “robustifying” iterations which should be performed. Using smaller values of iter will make lowess run faster. |
... |
Additional arguments for methods. |
The main functions computes estimates of the initial population size for four possible single census methods chosen with the type argument. These methods are as follows:
type="P" | naive Petersen. |
type="C" | Chapman(1951) modification of the Petersen. |
type="CR" | Ricker(1975) modification of the Chapman modification. |
type="B" | Bailey(1951,1952) modification of the Petersen. |
In addition, two possible multiple census methods can also be chosen with the type argument. These methods are
type="Schnabel" | Schnabel (1938) method. |
type="SchumacherEschmeyer" | Schumacher and Eschmeyer (1943) method. |
A standard error for the single census population estimate will be computed if incl.SE=TRUE is used in summary. This is used primarily for historical purposes. The SE for the Petersen method is from Ricker(1975). The SE for the Chapman method uses the formula on page 60 of Seber(1982). The SE for the Ricker method uses formula 3.8 on page 78 of Ricker(1975). The SE for the Bailey method uses the formula on page 61 of Seber(1982). It is advised to use confidence intervals for the population estimate as described below and implemented with confint.
If incl.all=TRUE in the summary function and population estimates have been constructed for multiple sub-groups then an overall population estimate will be included by summing the population estimates for the multiple sub-grops. In this case, if incl.SE=TRUE, then an overall SE will be computed by taking the square root of the summed VARIANCES for the multiple sub-groups.
Confidence intervals for the initial population size estimated with the single census methods can be constructed using four different distributions as chosen with the ci.type argument. The hypergeometric method should be exact (with sampling without replacement) but is experimental at this point. The other three types of confidence intervals are constructed according to Seber (1982) but using computer algorithms to estimate the distributions rather than tables and graphs as in Seber (1982). If citype="suggested" then the type of confidence interval suggested by the rules in Seber (1982) is used.
If M contains an object from the caphist.sum function and the Schnabel or Schumacher-Eschmeyer methods has been chosen then n, m and R can be left missing or will be ignored. In this case, the function will extract the needed data from the schnabel.sum portion of the CapHist class object.
Confidence intervals for the initial population size using multiple census methods can be constructed using two different distributions (normal, Poisson) for the Schnabel method or the normal distribution for the Shumacher-Eschmeyer method as chosen with the ci.type argument. The confidence intervals are constructed according to Seber (1982) but using computer algorithms to estimate the distributions rather than tables and graphs as in Seber (1982). If citype="suggested" then the type of confidence interval suggested by the rules in Seber (1982) is used.
A list with the following items
M |
The number of marked fish from the first sample that was provided. |
n |
The number of captured fish in the second sample that was provided. |
m |
The number of recaptured (marked) fish in the second sample that was provided. |
M1 |
The adjusted (depending on type) number of marked fish from the first sample. |
n1 |
The adjusted (depending on type) number of captured fish in the second sample. |
m1 |
The adjusted (depending on type) number of recaptured (marked) fish in the second sample. |
cf |
A correction factor for the population estimate that depends on type. |
type |
The type of method used (provided by the user). |
meth |
A label for the type of method used. |
N |
The estimated initial population size. |
labels |
Labels for the rows of summary matrix. |
Derek H. Ogle, dogle@northland.edu
Krebs, C.J. 1999. Ecological Methodology. Addison-Welsey Educational Publishing, second edition.
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.
Seber, G.A.F. 1982. The Estimation of Animal Abundance. Edward Arnold, second edition.
Schnabel, Z.E. 1938. The estimation of the total fish population of a lake. American Mathematician Monthly, 45:348-352.
Schumacher, F.X. and R.W. Eschmeyer. 1943. The estimation of fish populations in lakes and ponds. Journal of the Tennessee Academy of Sciences, 18:228-249.
mr.open, poi.ci in NCStats, bin.ci in NCStats, hyper.ci in NCStats, binconf in Hmisc, lowess in stats
## Single census with no sub-groups
# Petersen estimate -- the default
mr1 <- mr.closed(346,184,49)
summary(mr1)
confint(mr1)
confint(mr1,ci.type="hypergeom")
# Chapman modificant of the Petersen estimate
mr2 <- mr.closed(346,184,49,type="Chapman")
confint(mr2)
# Chapman estimate showing the SE
summary(mr2,incl.SE=TRUE)
summary(mr2,incl.SE=TRUE,numdigs=1,labels="Second Example")
## Single census with sub-groups
marked <- c(93,35,72,16,46,20)
captured <- c(103,30,73,17,39,18)
recaps <- c(20,23,52,15,35,16)
lbls <- c("YOY","Juvenile","Stock","Quality","Preferred","Memorable")
mr3 <- mr.closed(marked,captured,recaps,type="Ricker",labels=lbls)
summary(mr3)
summary(mr3,incl.SE=TRUE)
summary(mr3,incl.SE=TRUE,incl.all=TRUE)
summary(mr3,incl.SE=TRUE,incl.all=TRUE,incl.inputs=FALSE)
confint(mr3)
## Multiple Census
#Data in summarized form
data(PikeNY)
attach(PikeNY)
# Schnabel method
mr4 <- mr.closed(n=n,m=m,R=R,type="Schnabel")
plot(mr4)
summary(mr4)
confint(mr4)
# Schumacher-Eschmeyer method
mr5 <- mr.closed(n=n,m=m,R=R,type="Schumacher")
summary(mr5)
confint(mr5)
detach(PikeNY)
## Capture history data summarized by caphist.sum()
data(PikeNYPartial1)
ch1 <- caphist.sum(PikeNYPartial1,-1) # ignore first column
# Schnabel method
mr6 <- mr.closed(ch1,type="Schnabel")
summary(mr6)
confint(mr6)
plot(mr6,loess=TRUE)