| mr.open {FSA} | R Documentation |
This function takes the two parts of a Method B table and uses the Jolly-Seber method to estimate the population size at each possible sample period and the survival rate and number of additional individuals added to the population between possible sample periods. This method assumes that the population is open.
mr.open(mb.top,mb.bot,ci.type=c("Jolly","Manly"),conf.level=0.95,
phi.type=c("SD","SE"))
## S3 method for class 'MRO':
summary(object,type=c("all","observables","estimates"),...)
## S3 method for class 'MRO':
confint(object,parm=c("all","N","phi","B"),level=NULL,conf.level=NULL,...)
mb.top |
A matrix that contains the “top” of the Method B table (i.e., a contingency table of capture sample (columns) and last seen sample (rows)) or an object of class CapHist from the caphist.sum function. See details. |
mb.bot |
A data frame that contains the “bottom” of the Method B table (i.e., the number of marked fish in the sample (m), the number of unmarked fish in the sample (u), the total number of fish in the sample (n), and the number of marked fish returned to the population following the sample (R)). |
ci.type |
A text value that indicates whether the large sample method of Jolly (ci.type="Jolly") or the “arbitrary” method of Manly (ci.type="Manly") should be used to construct confidence intervals. |
conf.level |
a number indicating the level of confidence to use for constructing confidence intervals (default is 0.95). See details. |
phi.type |
a text value that indicates whether the standard error for phi should include only sampling variability (phi.type="SE") or sampling and individual variability (phi.type="SD",default). |
object |
An object saved from the mr.open call (i.e., of class MRO). |
type |
The type of summary to return. See details. |
parm |
a specification of which parameters are to be given confidence intervals. If missing, all parameters are considered. |
level |
Same as conf.level but used for compatability with generic confint function. |
... |
Additional arguments for methods. |
If mb.top contains an object from the caphist.sum function then mb.bot can be left missing or will be ignored. In this case, the function will extract the needed data from the methodB.top and methodB.bot portions of the CapHist class object.
Manly (1984) did not provide details for computing a confidence interval for the B parameter. Thus, confidence intervals for this parameter are not included in the output when ci.type="Manly" is used. Also, Manly's method does not compute standard errors; therefore, no standard errors are returned when ci.type="Manly" is used.
If type="observables" in the summary function then only items that can be observed from the data will be returned – n, m, R, r, and z. If type="estimates" in the summary function then only items that are estimated from observables will be returned – M, N, phi, B, and their associated standard errors.
The level of confidence is not set in the confint function, in contrast to most confint functions. Rather the confidence level is set in the main mr.open function.
A list with the following items
df |
A data frame that contains observable summaries from the data and estimates of the number of extant marked fish, population size for each possible sample period, survival rate between each possible pair of sample periods, and the number of additional individuals added to the population between each possible pair of sample periods. In addition to the estimates, values of the standard errors and the lower and upper confidence interval bounds for each parameter are provided (however, see the details above). |
ci.type |
The provided type of confidence intervals that was used. |
phi.type |
The provided type of standard error for phi that was used. |
conf.level |
The provided level of confidence that was used. |
Derek H. Ogle, dogle@northland.edu
Jolly, G.M. 1965. Explicit estimates from capture-recapture data with both death and immigration – stochastic model. Biometrika, 52:225-247.
Seber, G.A.F. 1965. A note on the multiple recapture census. Biometrika, 52:249-259.
Seber, G.A.F. 1982. The Estimation of Animal Abundance. Edward Arnold, second edition.
Leslie, P.H. and D. Chitty. 1951. The estimation of population parameters from data obtained by means of the capture-recapture method. I. The maximum likelihood equations for estimating the death-rate. Biometrika, 38:269-292.
Manly, B.F.J. Obtaining confidence limits on parameters of the Jolly-Seber model for capture-recapture data. Biometrics, 40:749-758.
Pollock, K.H., J.D. Nichols, C. Brownie, and J.E. Hines. 1991. Statistical inference for capture-recapture experiments. Wildlife Monographs, 107:1-97.
## First example -- capture histories summarized with caphist.sum() data(CutthroatAL) ch1 <- caphist.sum(CutthroatAL,-1) # ignore first column of fish ID ex1 <- mr.open(ch1) summary(ex1) summary(ex1) ## Second example - Jolly's data -- summarized data entered "by hand" s1 <- rep(NA,13) s2 <- c(10,rep(NA,12)) s3 <- c(3,34,rep(NA,11)) s4 <- c(5,18,33,rep(NA,10)) s5 <- c(2,8,13,30,rep(NA,9)) s6 <- c(2,4,8,20,43,rep(NA,8)) s7 <- c(1,6,5,10,34,56,rep(NA,7)) s8 <- c(0,4,0,3,14,19,46,rep(NA,6)) s9 <- c(0,2,4,2,11,12,28,51,rep(NA,5)) s10 <- c(0,0,1,2,3,5,17,22,34,rep(NA,4)) s11 <- c(1,2,3,1,0,4,8,12,16,30,rep(NA,3)) s12 <- c(0,1,3,1,1,2,7,4,11,16,26,NA,NA) s13 <- c(0,1,0,2,3,3,2,10,9,12,18,35,NA) jolly.top <- cbind(s1,s2,s3,s4,s5,s6,s7,s8,s9,s10,s11,s12,s13) n <- c(54,146,169,209,220,209,250,176,172,127,123,120,142) R <- c(54,143,164,202,214,207,243,175,169,126,120,120,0) m <- c(0,10,37,56,53,77,112,86,110,84,77,72,95) u <- n-m jolly.bot <- rbind(m,u,n,R) ex2 <- mr.open(jolly.top,jolly.bot) summary(ex2) confint(ex2) ex3 <- mr.open(jolly.top,jolly.bot,ci.type="Manly") summary(ex3) confint(ex3)