R source code
#########################################################################
## Part A

> rm(list=ls())
> library(Rcapture) # Load the Rcapture library
> 
> # A matrix of capture histories and their frequencies
> (  red.back <- data.frame(w1=c(0,0,0,1,1,1,1), w2=c(0,1,1,0,0,1,1), w3=c(1,0,1,0,1,0,1), freq=c(33,32,5,15,4,7,9))  ) 
  w1 w2 w3 freq
1  0  0  1   33
2  0  1  0   32
3  0  1  1    5
4  1  0  0   15
5  1  0  1    4
6  1  1  0    7
7  1  1  1    9
> 
> # Run the closed-population model
> # dfreq=TRUE indicates that red.back is a matrix of capture histories and frequencies
> (  cp1 <- closedp(red.back, dfreq=TRUE)  )

Number of captured units: 105 

Abundance estimations and model fits:
               abundance  stderr  deviance  df     AIC
M0                 172.5    19.5    21.771   5  55.584
Mt                 170.2    19.0    15.833   3  53.646
Mh Chao (LB)       238.3    46.2     9.332   4  45.145
Mh Poisson2        492.3   231.9     9.332   4  45.145
Mh Darroch        1230.0   998.0     9.332   4  45.145
Mh Gamma3.5       3418.5  3938.3     9.332   4  45.145
Mth Chao (LB)      234.4    44.9     2.939   2  42.752
Mth Poisson2       489.1   230.0     2.939   2  42.752
Mth Darroch       1245.3  1011.8     2.939   2  42.752
Mth Gamma3.5      3538.8  4083.2     2.939   2  42.752
Mb                1278.1  5122.5    14.901   4  50.714
Mbh                377.2   640.1    14.730   3  52.542

#########################################################################
## Part B

> rm(list=ls()) # Clear workspace
> library(Rcapture) # Load the Rcapture library
> 
> # Read in the matrix of capture histories
> (  duck4 <- read.csv("duck4.csv")  )
   t1 t2 t3 t4 freq
1   1  1  1  1   40
2   1  1  1  0    9
3   1  1  0  1   36
4   1  1  0  0   56
5   1  0  1  1   42
6   1  0  1  0   13
7   1  0  0  1   44
8   1  0  0  0  405
9   0  1  1  1   12
10  0  1  1  0    3
11  0  1  0  1   28
12  0  1  0  0   27
13  0  0  1  1   24
14  0  0  1  0   16
15  0  0  0  1  141
> 
> # Run the open-population Jolly-Seber model
> # dfreq=TRUE indicates that duck4 is a matrix of capture histories and frequencies
> # m="up" allows unequal capture probabilities in the model
> # neg=TRUE does not bound the gamma parameters to prevent survival probabilities outside [0-1], not that that matters here
> (  op.duck4 <- openp(duck4, dfreq=TRUE, m="up", neg=TRUE)  )

Model fit:
              deviance      df        AIC
fitted model    12.478       6    108.894

Test for trap effect:
                                   deviance      df        AIC
model with homogenous trap effect    11.787       5    110.202

Capture probabilities:
          estimate  stderr
period 1        --      --
period 2    0.4635  0.0354
period 3    0.4499  0.0349
period 4        --      --

Survival probabilities:
               estimate  stderr
period 1 -> 2    0.4716  0.0289
period 2 -> 3    0.7069  0.0438
period 3 -> 4        --      --

Abundances:
          estimate  stderr
period 1        --      --
period 2     455.2    26.1
period 3     353.4    17.8
period 4        --      --

Number of new arrivals:
               estimate  stderr
period 1 -> 2        --      --
period 2 -> 3      31.6    18.4
period 3 -> 4        --      --

Total number of units who ever inhabited the survey area:
             estimate  stderr
all periods     932.4       9

Total number of captured units: 896