MSSURVIV

Introduction

Program MSSURVIV (Multi-State-SURVIVal analysis) computes parameter estimates of survival/transition and capture probability under the multistate models described in "Capture‑recapture Studies for Multiple Strata including non‑Markovian Transition Probabilities" (Brownie et. al., 1993). Actually, MSSURVIV is a specially modified version of Dr. G. White's program SURVIV (White, 1983) which incorporates the multistate models. With this program and it's companion program, CNVMEMOV, users are able to get parameter estimates for these complex models from capture‑history data without having to specify the cell probabilities.

MSSURVIV is intended to be used in a situation where one is interested in not only survival and capture probabilities, but also transition probabilities (the probability of moving from one stratum to another). The strata may be defined as any discrete categories to which captured animals can be assigned at any given time. For example, strata may be based on such factors as capture location or individual variables such as breeding status or weight class. This situation may be thought of as a more general Jolly-Seber model where a matrix of survival/transition probabilities replaces a single survival rate and a vector of capture probabilities replaces a single capture probability.

Output from MSSURVIV includes survival/movement probability estimates, capture probability estimates, goodness-of-fit tests, and likelihood-ratio tests. Estimates may be computed under the "Markovian" models or the "Non-Markovian/memory" models. The Markovian models assume that survival/transition probabilities of an animal depend on the stratum in which the animal is located at the beginning of the interval. The parameters under these models would be a matrix of survival/transition probabilities and a vector of capture probabilities for each time-period. Optionally, MSSURVIV may be instructed to decompose the combined survival/transition probabilities into separate survival and transition probabilities. Non-Markovian models assume that survival/transition probabilities for the interval (i, i+1) depend not only on stratum at time i, but also on stratum at i-1. These models produce much larger matrices of parameter estimates than Markovian models.

By default, three models are generated for either of these two model-sets. The three models are analogous to Models "D", "B", and "A" produced by program JOLLY for standard Jolly-Seber analysis (Pollock et. al., 1990). Model "D" computes estimates under the assumption that survival/transition probabilities and capture probabilities are constant over time. Model "B" assumes survival/transition probabilities are constant over time, but capture probabilities are time-dependent. Model "A" assumes both survival/transition and capture probabilities are time-dependent. If necessary, users may examine these models to generate statements for their own models.

The experimental situation to which this program applies is one in which animals are initially marked with a unique tag, and released. This process is repeated for each of the sampling periods. Information used to assign the animal to the proper stratum (eg. sex, weight, age, capture location, ...) is recorded for each capture of each animal. Using these data, the capture-history of each animal is generated consisting of codes indicating the status of the animal at each capture period. For example, if an animal were captured in stratum A in time-period 1, not captured in periods 2 and 3, and captured in stratum B in time-period 4, the capture history would be: "A 0 0 B". If the variable of interest is a continuous variable, cutpoints must be defined to break it into discrete strata (eg., weight -> weight-class) before the capture-history records can be generated.

Input to MSSURVIV consists of statements which define the capture data and statements defining the selected model structure. The format of the input file is the same as for program SURVIV except that no cell probabilities need be given. The statements defining the data consist of the number of animals captured and released in each time-period and stratum, and the number next recaptured in each subsequent time-period and stratum. Statements which set parameters equal to other parameters define model structure.

Although MSSURVIV eliminates the need for specifying cell probabilities, the job of summarizing capture-history records and defining model structure can be very complicated and can lead to errors. Program CNVMEMOV was created to automate this process. CNVMEMOV reads as input the capture-history records and produces all of the statements necessary to run program MSSURVIV under the "Markovian" or "memory" model sets described above.

Using CNVMEMOV

To run CNVMEMOV, type CNVMEMOV at the DOS prompt and respond to the program prompts. When the program is run, the following should appear on the screen:

Program CNVMEMOV ‑ Converts "Capture‑history" data into

MSSURVIV input data

Date compiled: 1/23/98

Programmer: James E. Hines

Biological Research Div., USGS

11510 American Holly Dr. #201

Patuxent Wildlife Research Center

Laurel, MD. 20708‑4017

email: jim_hines%40usgs.gov

Version 2.0 ‑ added capability for >2 age‑classes

added capability for >1 group

** Note: The order of age‑classes in old version was

ADULT followed by YOUNG. In this version

the order must be from youngest to oldest.

** Also: The old version used "GROUP" as a synonym of

"STRATA". (That was stupid!) In this version

"STRATA" are the transitional states and

"GROUPS" are the separate classification

of animals to/from which animals cannot move.

Examples of STRATA might be location,

breeding‑status, weight‑class.

Examples of GROUP might be sex, species.

After this informatory text is printed, CNVMEMOV attempts to open an output file called CNVMEMOV.OUT. This is the file which will contain the summarized data to be input to program MSSURVIV. If this file already exists (from a previous run) the program will ask if it is OK to overwrite this file. If "y" or "Y" is typed, CNVMEMOV will proceed. Any other response will abort the program.

*** Output file (CNVMEMOV.OUT) exists!, overwrite(Y/N)? Y

The next prompt is for the name of the input file containing the capture-history records. Respond with any legal filename, including drive and subdirectory if not in the current directory.

Enter the name of the file containing the capture‑history records

FILE:C:\MSSRV\SAMPLE.DAT

If the input file does not exist, CNVMEMOV will print an error message and abort. If it does exist, the first five lines of the file will be displayed on the screen. This helps the user find the column numbers needed for later prompts.

FILE:C:\MSSRV\SAMPLE.DAT

1 2 3 4 5 6 7

....5....0....5....0....5....0....5....0....5....0....5....0....5....0

A000 491

A00A 15

A00B 12

A00C 11

A0A0 37

......................................................................

The next prompt is for the number of strata and time-periods. The program requires that you enter two numbers separated by a comma, e.g.,

Enter the number of strata, time‑periods, age-classes and groups:

STRATA,TIME‑PERIODS,AGE-CLASSES,GROUPS(eg 3,7,1,1):3,4,1,1

In this example, there are 4 capture periods, 3 strata (designated A, B, and C), 1 age-class and 1 group.

The next prompt is for the codes representing each stratum. These are the codes which represent each of the strata of capture in the capture-history records. Any character other than the ones in this list indicate that the animal was not captured in a time-period. Selected strata may be omitted from an analysis by not including them in the this list. Any single character may be used to represent each of the strata, e.g.,

Enter the codes representing each strata:

(If upper case in input file, type upper case here.)

STRATA CODES(no quotes or spaces‑ eg 123):ABC

CNVMEMOV will distinguish between lower and upper case characters for these codes, so it is imperative that these codes match the codes in the data file. If "abc" were entered instead of "ABC", none of the captures would be used.

The next prompt asks for the column numbers containing stratum codes for each time period. The first five lines of data have been listed previously to help locate the column numbers, e.g.,

If strata codes are in consecutive columns, enter the

column number of the first strata code,

Or enter 0 if they are not sequential

FIRST COLUMN OF STRATA CODES:1

The next prompt asks for the column number containing the fate on last capture. If the data set contains a field indicating whether animals were released or not released (e.g., dead in trap), the column number of this field would be entered here. If there is no such field in the data, enter 0 and it will be assumed that all animals were released on last capture. Any non-blank character in this column indicates that the animals were not released on last capture.

Enter column number containing fate on last capture, or

0 if all captured animals were always released.

Note: Any non‑blank character in this column is

interpreted as indicating that the animal was

not released

FATE COLUMN:0

If more than one group was specified in the earlier prompt, the next prompt would ask for the column number containing the group of the animals. If the data set contains a field indicating a group the animals belong to, (e.g. sex, size), the column number of this field would be entered here. As with the strata codes, upper/lower case is significant here.

Enter the column number containing the GROUP code,

GROUP COLUMN:

Enter groupe‑codes

(eg. MF for male, female)

GROUP‑CODES:

The next prompt is for the starting column of a frequency variable. If the capture-histories are summarized, the data will contain a frequency variable for each capture-history and the starting column is entered here. If the data are not summarized (i.e., one record per animal), enter 0 for the starting column, e.g.,

Enter starting column of cap‑history frequency, or

0 if capture‑histories are not summarized.

STARTING COLUMN:6

If a number greater than zero is entered for the frequency starting column, CNVMEMOV will prompt for the ending column of the frequency variable.

The next prompt is for the selection of model sets to be run with MSSURVIV. One or both of the model sets may be chosen, e.g.,

Enter 1 for the "MEMORY‑MOVEMENT model set

2 for the "MOVEMENT‑ONLY model set

3 for both model sets

4 for the "MOVEMENT‑ONLY model set w/ S-M parameterization

MODEL SETS (1,2,3, or 4):4

In some cases, it is desirable to compute estimates in terms of separate survival rate and movement probabilities rather than with transition probabilities that include both survival and movement. If we assume survival from time i to i+1 does not depend on stratum in time-period i+1, then we can rewrite _i^rs as _i^rs = S_i^rΨ_i^rs, where Ψ_i^rs is the conditional probability that an animal in stratum r at time i is in stratum s at time i+1, given that the animal is alive at i+1. The sum of the survival/transition probabilities is equal to the survival rate (i.e., = S_i^r, where is the probability that an animal alive in stratum r at period i is alive and in stratum s at period i+1, and S_i^r is the probability that an animal in stratum r at time i is alive at period i+1.) In a k-stratum experiment, we can compute a survival rate and k movement probabilities for each stratum and time-interval from the k transition probabilities, _i^rs. This computation may be done from the output for the movement-only model set, however the computation of variances would be very difficult. MSSURVIV can be instructed to treat survival rate and movement probabilities as separate parameters instead of combined transition probabilities in order to produce the desired estimates and variances. I have called this the "S-M parameterization" for the estimation of separate survival and movement parameters.

If the "MOVEMENT-ONLY model set with S-M parameterization" is chosen, CNVMEMOV will prompt for a stratum number. This number controls which movement probability is replaced by the survival probability in the output parameters. For the S‑M parameterization, the kHk survival/movement estimates for each time‑period will be changed to N survival estimates and kH(k‑1) movement estimates. Since the sum of the movement probabilities for any cohort must equal 1.0, one of the movement parameters is not needed (i.e., it is obtained as 1 minus the sum of the others). Any of the k movement parameters may be omitted, however, the optimization routine in MSSURVIV works better if the parameters are not close to 0.0 or 1.0. For this reason, the best movement parameter to omit is the one closest to 0.0 or 1.0.

For the S‑M parameterization, one of the 3

movement parameters must be replaced by the survival

parameter. Choose 0 to replace the diagonal parameter

(probability of returning to a stratum), or the index

of one of the 3 strata.

Stratum (0 or 1‑3)?3

By choosing 3, CNVMEMOV will produce the statements to cause MSSURVIV to use the "S‑M parameterization" of the movement-only model set. Instead of a 3H3 matrix of survival/movement probability estimates, MSSURVIV will compute 3 survival rate estimates and 6 movement probabilities for each time period. The 9 parameters for time i are:

S_i^A: probability of surviving from i to i+1 for animals captured in stratum A in time i,

Ψ_i^AA: probability of remaining in stratum A at times i and i+1,

Ψ_i^AB: probability of moving from stratum A in time i to stratum B in time i+1,

S_i^B: probability of surviving from i to i+1 for animals captured in stratum B in time i,

Ψ_i^BA: probability of moving from stratum B at time i to stratum A at time i+1,

Ψ_i^BB: probability of remaining in stratum B at timed i and i+1,

S_i^C: probability of surviving from i to i+1 for animals captured in stratum C in time i ,

Ψ_i^CA: probability of moving from stratum C at time i to stratum A at time i+1,

Ψ_i^CB: probability of moving from stratum C at time i to stratum B at time i+1.

The probability of moving from any stratum, X, to stratum C must be computed by subtracting the sum of Ψ_i^XA and Ψ_i^XB from 1.0.

The next prompt is for a title to appear on the output. Any string of characters (not including quotes) is acceptable as long as the length is less than 256, e.g.,

Enter a title to appear on the MSSURVIV output

TITLE(no quotes):MSSURVIV SAMPLE DATA (SAMPLE.DAT)

CNVMEMOV will output the number of records read and the total number of transitions. The total number of transitions can be used to determine if some of the strata need to be combined to help with convergence problems (See section on sparse data).

Here is the file created by CNVMEMOV which can be input to MSSURVIV:

PROC TITLE 'expected value data w/ 2 groups';

PROC MODEL NPAR=0036 ADDCELL NAGE=1 NYRS=04 STRATA=2 NGROUPS=2

PHIMISS=2;

COHORT=1000;236:;102:;76:;79:;22:;42:;

COHORT=1001;0:;338:;0:;156:;0:;64:;

COHORT=1236;267:;114:;77:;80:;

COHORT=1440;0:;444:;0:;183:;

COHORT=1343;260:;111:;

COHORT=1793;0:;495:;

COHORT=1000;62:;41:;11:;18:;2:;7:;

COHORT=1001;0:;105:;0:;29:;0:;8:;

COHORT=1062;74:;50:;14:;23:;

COHORT=1146;0:;135:;0:;40:;

COHORT=1085;83:;56:;

COHORT=1232;0:;158:;

LABELS;

S(001)=MOV(01,A,M) AA ;

S(002)=SRV(01,A,M) A ;

S(003)=MOV(01,A,M) BA ;

S(004)=SRV(01,A,M) B ;

S(005)=MOV(02,A,M) AA ;

S(006)=SRV(02,A,M) A ;

S(007)=MOV(02,A,M) BA ;

S(008)=SRV(02,A,M) B ;

S(009)=MOV(03,A,M) AA ;

S(010)=SRV(03,A,M) A ;

S(011)=MOV(03,A,M) BA ;

S(012)=SRV(03,A,M) B ;

S(013)=p(02,A,M) A ;

S(014)=p(02,A,M) B ;

S(015)=p(03,A,M) A ;

S(016)=p(03,A,M) B ;

S(017)=p(04,A,M) A ;

S(018)=p(04,A,M) B ;

S(019)=MOV(01,A,F) AA ;

S(020)=SRV(01,A,F) A ;

S(021)=MOV(01,A,F) BA ;

S(022)=SRV(01,A,F) B ;

S(023)=MOV(02,A,F) AA ;

S(024)=SRV(02,A,F) A ;

S(025)=MOV(02,A,F) BA ;

S(026)=SRV(02,A,F) B ;

S(027)=MOV(03,A,F) AA ;

S(028)=SRV(03,A,F) A ;

S(029)=MOV(03,A,F) BA ;

S(030)=SRV(03,A,F) B ;

S(031)=p(02,A,F) A ;

S(032)=p(02,A,F) B ;

S(033)=p(03,A,F) A ;

S(034)=p(03,A,F) B ;

S(035)=p(04,A,F) A ;

S(036)=p(04,A,F) B ;

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_D;

INITIAL; ALL= 0.500;

CONSTRAINTS;

S(005)=S(001) /* MOV(02,A,M) AA=MOV(01,A,M) AA */;

S(006)=S(002) /* SRV(02,A,M) A =SRV(01,A,M) A */;

S(007)=S(003) /* MOV(02,A,M) BA=MOV(01,A,M) BA */;

S(008)=S(004) /* SRV(02,A,M) B =SRV(01,A,M) B */;

S(009)=S(001) /* MOV(03,A,M) AA=MOV(01,A,M) AA */;

S(010)=S(002) /* SRV(03,A,M) A =SRV(01,A,M) A */;

S(011)=S(003) /* MOV(03,A,M) BA=MOV(01,A,M) BA */;

S(012)=S(004) /* SRV(03,A,M) B =SRV(01,A,M) B */;

S(015)=S(013) /* p(03,A,M) A =p(02,A,M) A */;

S(016)=S(014) /* p(03,A,M) B =p(02,A,M) B */;

S(017)=S(013) /* p(04,A,M) A =p(02,A,M) A */;

S(018)=S(014) /* p(04,A,M) B =p(02,A,M) B */;

S(023)=S(019) /* MOV(02,A,F) AA=MOV(01,A,F) AA */;

S(024)=S(020) /* SRV(02,A,F) A =SRV(01,A,F) A */;

S(025)=S(021) /* MOV(02,A,F) BA=MOV(01,A,F) BA */;

S(026)=S(022) /* SRV(02,A,F) B =SRV(01,A,F) B */;

S(027)=S(019) /* MOV(03,A,F) AA=MOV(01,A,F) AA */;

S(028)=S(020) /* SRV(03,A,F) A =SRV(01,A,F) A */;

S(029)=S(021) /* MOV(03,A,F) BA=MOV(01,A,F) BA */;

S(030)=S(022) /* SRV(03,A,F) B =SRV(01,A,F) B */;

S(033)=S(031) /* p(03,A,F) A =p(02,A,F) A */;

S(034)=S(032) /* p(03,A,F) B =p(02,A,F) B */;

S(035)=S(031) /* p(04,A,F) A =p(02,A,F) A */;

S(036)=S(032) /* p(04,A,F) B =p(02,A,F) B */;

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_B;

INITIAL; RETAIN=MODL_D; CONSTRAINTS;

S(005)=S(001) /* MOV(02,A,M) AA=MOV(01,A,M) AA */;

S(006)=S(002) /* SRV(02,A,M) A =SRV(01,A,M) A */;

S(007)=S(003) /* MOV(02,A,M) BA=MOV(01,A,M) BA */;

S(008)=S(004) /* SRV(02,A,M) B =SRV(01,A,M) B */;

S(009)=S(001) /* MOV(03,A,M) AA=MOV(01,A,M) AA */;

S(010)=S(002) /* SRV(03,A,M) A =SRV(01,A,M) A */;

S(011)=S(003) /* MOV(03,A,M) BA=MOV(01,A,M) BA */;

S(012)=S(004) /* SRV(03,A,M) B =SRV(01,A,M) B */;

S(023)=S(019) /* MOV(02,A,F) AA=MOV(01,A,F) AA */;

S(024)=S(020) /* SRV(02,A,F) A =SRV(01,A,F) A */;

S(025)=S(021) /* MOV(02,A,F) BA=MOV(01,A,F) BA */;

S(026)=S(022) /* SRV(02,A,F) B =SRV(01,A,F) B */;

S(027)=S(019) /* MOV(03,A,F) AA=MOV(01,A,F) AA */;

S(028)=S(020) /* SRV(03,A,F) A =SRV(01,A,F) A */;

S(029)=S(021) /* MOV(03,A,F) BA=MOV(01,A,F) BA */;

S(030)=S(022) /* SRV(03,A,F) B =SRV(01,A,F) B */;

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_A;

INITIAL; RETAIN=MODL_B; CONSTRAINTS;

S(017)=1.0 /* p(04,A,M) A */;

S(018)=1.0 /* p(04,A,M) B */;

S(035)=1.0 /* p(04,A,F) A */;

S(036)=1.0 /* p(04,A,F) B */;

PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=1GRP_A;

INITIAL; RETAIN=MODL_A; CONSTRAINTS;

S(019)=S(001) /* MOV(01,A,F) AA=MOV(01,A,M) AA */;

S(020)=S(002) /* SRV(01,A,F) A =SRV(01,A,M) A */;

S(021)=S(003) /* MOV(01,A,F) BA=MOV(01,A,M) BA */;

S(022)=S(004) /* SRV(01,A,F) B =SRV(01,A,M) B */;

S(023)=S(005) /* MOV(02,A,F) AA=MOV(02,A,M) AA */;

S(024)=S(006) /* SRV(02,A,F) A =SRV(02,A,M) A */;

S(025)=S(007) /* MOV(02,A,F) BA=MOV(02,A,M) BA */;

S(026)=S(008) /* SRV(02,A,F) B =SRV(02,A,M) B */;

S(027)=S(009) /* MOV(03,A,F) AA=MOV(03,A,M) AA */;

S(028)=S(010) /* SRV(03,A,F) A =SRV(03,A,M) A */;

S(029)=S(011) /* MOV(03,A,F) BA=MOV(03,A,M) BA */;

S(030)=S(012) /* SRV(03,A,F) B =SRV(03,A,M) B */;

S(031)=S(013) /* p(02,A,F) A =p(02,A,M) A */;

S(032)=S(014) /* p(02,A,F) B =p(02,A,M) B */;

S(033)=S(015) /* p(03,A,F) A =p(03,A,M) A */;

S(034)=S(016) /* p(03,A,F) B =p(03,A,M) B */;

S(017)=1.0 /* p(04,A,M) A */;

S(035)=1.0 /* p(04,A,F) A */;

S(018)=1.0 /* p(04,A,M) B */;

S(036)=1.0 /* p(04,A,F) B */;

PROC TEST; PROC STOP;

The output file, CNVMEMOV.OUT, contains a title statement, statements to define the input data, label definitions, statements to describe models, a test statement and a stop statement.

The title statement is used to identify the data used in the analysis.

The model definition statements start with "PROC MODEL NPAR=0036 ADDCELL NAGE=1 NYRS=04 STRATA=2 NGROUPS=2 PHIMISS=2;" and end with "COHORT=1232;0:;158:; ". The "NPAR=36" indicates the maximum number of parameters (estimated or fixed) in any of the following models. In this example there are 4 (2H2) transition probability parameters for each of the 3 intervals (4 sample periods), giving 12 parameters per group. There are 2 capture probabilities for each period (not including the first) giving 6 parameters per group. So, the total number of paramters is 12x2+6x2=36. The NAGE, NYRS, STRATA, and NGROUPS keywords indicate the respective values for each, and PHIMISS indicates which of the transitions is to be computed by subtraction. In this case, PHIMISS=2 indicates that transitions to the 2^nd strata are to be computed as 1 - the probability of moving to the first strata.

The rest of the model definition statements contains the summary data in a form which could be thought of as a generalized "Leslie Method-B Table" or "m-array" where each 2H2 matrix is treated as one element in the m-array. Each of the records starts with "COHORT=x" where x is the number of animals released in a stratum and year. The numbers that follow indicate the number of recaptures in succeeding periods and strata. Figure 1 shows the structure of the m-array for these data.

Figure 1.

From the output file, the numbers of animals released in time period 1 are: 1000 from stratum 1 and 1001 from stratum 2. The matrix of recaptures in time period 2 of animals captured in time period 1 is:

Of the 676 animals captured in time period 2 which were also captured in time period 1, 236 animal started in stratum 1 and stayed in stratum 1, 102 animals started in 1 and moved to 2. (Row indicates stratum of previous capture. Column indicates stratum of capture.) 0 animals moved from 2 to 1 and 338 moved from 2 to 2.

The next 2 columns of rows 1-2 in the data are the matrix of transitions of animals captured in time period 3 that were last captured in time period 1 (not captured in time period 2). The last 2 columns in the first 2 rows form the matrix of transitions of animals captured in time period 4 which were last captured in time period 1 (not captured in time periods 2 or 3).

Following the data are the labels for each of the parameters. Internally, the parameters are called "S(1), S(2), ... S(NPAR). The labels relate these internal parameters to meaningful labels for these models. If the "Movement-only" model was chosen, the transition probabilities are labeled "PHI" followed by the time period in parenthesis and the transition. So, "PHI(01) AB" is the probability of survival from time period one to time period two and moving from stratum "A" to stratum "B". If the "Memory-movement" models were chosen, there will be three strata following the time period for each "PHI" since transition in time period i depends on stratum of capture in time period i-1 as well as in time period i. If the S-M parameterization is chosen, the survival parameter (SRV) will be followed by time period, age, and group in parenthesis, followed the stratum of capture in time period i. The movement parameters (MOV) will be followed by the time period, age, and group in parenthesis, then stratum in time period i and stratum in period i+1.

In all models, capture-probability parameters are labeled "p" and are followed by time period of capture, age, and group in parentheses, and stratum of capture.

After the label definitions come the model definitions for each model. Each model starts with a "PROC ESTIMATE" statement. Options on the "PROC ESTIMATE" statement include "NOVAR" which inhibits printing of the variance-covariance matrix, the number of significant digits, "NSIG" (i.e., number of digits following the decimal point which do not change at the end of the iterative process), the maximum number of function evaluations, "MAXFN", and the name of the model. If the variance-covariance matrix of parameter estimates is desired, delete the string "NOVAR" using a text editor.

CNVMEMOV produces the model definitions from most restrictive (model "D") to most general (model "A"). The reason for this is that the most restrictive model has the fewest estimable parameters and converges more easily. Final estimates from this model can then be input as starting values to more general models. MSSURVIV requires starting values for all models and CNVMEMOV sets all parameters to 1/(# of strata) for the first model to ensure that the estimates of transition probability are less than or equal to 1.0. (INITIAL; ALL=0.333;).

The statements following the "CONSTRAINTS" statement describe each model in terms of the most general model. In model "D", the survival and movement probabilities are assumed to be constant across time, so the survival and movement probabilities for time period two and three are set equal to the survival and movement probabilities for time period one. The capture probabilities are also assumed constant over time, so the capture probabilities for time periods 3 and 4 are set equal to the capture probabilities for time period 2. These equalities must be specified in terms of parameter number which can be obtained from the labels section. In the example, the first constraint is "S(005)=S(001);". A comment appears immediately after the constraint which indicates which parameters are constrained.

The sequence of statements starting with "PROC ESTIMATE ... NAME=MODL_B" cause MSSURVIV to produce estimates under the model with time-specific capture probabilities and constant survival and movement probabilities. The initial values are set equal to the final values obtained for model "D" (INITIAL; RETAIN=MODL_D;), and the constraints on the survival and movement probability parameters are the same as for model "D". Since capture probabilities may vary with time, there are no constraints on the capture probability parameters.

Statements for model "A" follow model "B". Model "A" assumes time-specific survival and movement probabilities and time-specific capture probabilities. Since there is no information on animals after the last time period, the last survival and movement probabilities and last capture probabilities cannot be separately estimated under model "A". For this reason, the last capture probability parameters have to be constrained to a constant. This causes the last survival/movement probability estimates to be the product of survival and movement and capture-probability for this model.

If more than one group is to be analyzed, CNVMEMOV produces one other model which is equivalent to model A except that the parameters are constrained equal across groups.

The "PROC TEST;" statement causes MSSURVIV to print tables of statistics used for comparison of the models. "PROC STOP;" causes MSSURVIV to stop execution even if more statements follow.

MSSURVIV

MSSURVIV prompts for one line of input to specify the name of the input and output files and command line options. When the program is run, the following prompt appears:

Enter command line parameters [i=in_file] [l=out_file]

[lines=n] [compile run] [noecho]:

At this prompt, any or all of the items enclosed in brackets may be specified. If "i=in_file" is specified, the input will be read from the file "in_file". Usually, this is the file created by CNVMEMOV and is called CNVMEMOV.OUT unless it has been renamed. A full pathname may be used to indicate a different directory. If this item is omitted, MSSURVIV expects the input from the keyboard. (Cntl-Break will abort the program).

If "l=out_file" is specified, output from MSSURVIV will be directed to the file "out_file". The default output file is the CRT screen. To direct output directly to the printer, use "l=lpt1".

If "lines=n" is included, MSSURVIV will print a header and the title in the output file after every n lines. The default value for n is 9999.

The "noecho" option causes MSSURVIV to suppress printing of the input data. This option is useful when there are several runs of models on the same data and you would like to conserve paper, but at least one run should contain a listing of the data to check for "typos".

To run the sample data file with MSSURVIV, enter the following at the above prompt:

i=cnvmemov.out l=sample.out

The output produced by MSSURVIV contains a listing of the input data, estimates of the parameters under each model, a goodness-of-fit test for each model, an AIC statistic for each model, and between model tests. The following output was created using MSSURVIV on the sample data file listed previously:

SURVIV ‑ Survival Rate Estimation with User Specified Cell Probabilities

3‑May‑93 11:15:40 Version 1.5(PC/XMM) April, 199 Page 001

INPUT ‑‑‑ PROC TITLE 'MSSURVIV SAMPLE DATA (SAMPLE.DAT) ';

CPU time in seconds for last procedure was 0.00

INPUT ‑‑‑ PROC MODEL NPAR=037 ADDCELL;

INPUT ‑‑‑ COHORT=1006;

INPUT ‑‑‑ 211:;71:;71:;54:;35:;35:;15:;12:;11:;

INPUT ‑‑‑ COHORT=1006;

INPUT ‑‑‑ 71:;211:;71:;35:;54:;35:;12:;15:;11:;

INPUT ‑‑‑ COHORT=1010;

INPUT ‑‑‑ 71:;71:;213:;35:;35:;55:;12:;12:;13:;

INPUT ‑‑‑ COHORT=1353;

INPUT ‑‑‑ 284:;95:;95:;71:;44:;43:;

INPUT ‑‑‑ COHORT=1353;

INPUT ‑‑‑ 95:;284:;95:;44:;71:;43:;

INPUT ‑‑‑ COHORT=1355;

INPUT ‑‑‑ 95:;95:;285:;44:;44:;71:;

INPUT ‑‑‑ COHORT=1598;

INPUT ‑‑‑ 332:;108:;109:;

INPUT ‑‑‑ COHORT=1598;

INPUT ‑‑‑ 108:;332:;109:;

INPUT ‑‑‑ COHORT=1600;

INPUT ‑‑‑ 108:;108:;324:;

The next part of the output lists the parameter estimates and goodness-of-fit test statistics for model "D". The "Number of parameters in model" is the value in the "PROC MODEL NPAR=37" statement. Since survival, movement and capture probabilities are constant over time, the 12 parameters (3 survival probabilities, 6 movement probabilities and 3 capture probabilities) for time period 2 and 12 parameters for time period 3 were set equal to those for time period 1. The one fixed parameter controls which movement probability is replaced by survival in the parameters. This leaves 12 estimable parameters (3 survival probabilities, 6 movement probabilities and 3 capture probabilities).

INPUT ‑‑‑ PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_D;

Number of parameters in model = 37

Number of parameters set equal = 24

Number of parameters fixed = 1

Number of parameters estimated = 12

Before the estimates are printed, MSSURVIV prints the final value of the function determined by the optimization routine and error-code. If the error-code is not zero, an error or warning message is printed indicating a problem with the data. This may happen when the data are sparse and some parameters are inestimable.

Final function value 15221.852 (Error Return = 0)

Number of significant digits 6

Number of function evaluations 499

95% Confidence Interval

I Parameter S(I) Standard Error Lower Upper

‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑

1 1 MOV(01) AA 0.602077 0.187276E‑01 0.565371 0.638784

2 2 MOV(01) AB 0.199345 0.142051E‑01 0.171503 0.227187

3 3 SRV(01) A 0.689183 0.141482E‑01 0.661453 0.716914

4 4 MOV(01) BA 0.199345 0.142051E‑01 0.171503 0.227187

5 5 MOV(01) BB 0.602077 0.187276E‑01 0.565371 0.638784

6 6 SRV(01) B 0.689183 0.141482E‑01 0.661453 0.716914

7 7 MOV(01) CA 0.200379 0.142887E‑01 0.172373 0.228385

8 8 MOV(01) CB 0.200379 0.142887E‑01 0.172373 0.228385

9 9 SRV(01) C 0.686058 0.141657E‑01 0.658293 0.713823

10 1 MOV(02) AA 0.602077 0.187276E‑01 0.565371 0.638784

11 2 MOV(02) AB 0.199345 0.142051E‑01 0.171503 0.227187

12 3 SRV(02) A 0.689183 0.141482E‑01 0.661453 0.716914

13 4 MOV(02) BA 0.199345 0.142051E‑01 0.171503 0.227187

14 5 MOV(02) BB 0.602077 0.187276E‑01 0.565371 0.638784

15 6 SRV(02) B 0.689183 0.141482E‑01 0.661453 0.716914

16 7 MOV(02) CA 0.200379 0.142887E‑01 0.172373 0.228385

17 8 MOV(02) CB 0.200379 0.142887E‑01 0.172373 0.228385

18 9 SRV(02) C 0.686058 0.141657E‑01 0.658293 0.713823

19 1 MOV(03) AA 0.602077 0.187276E‑01 0.565371 0.638784

20 2 MOV(03) AB 0.199345 0.142051E‑01 0.171503 0.227187

21 3 SRV(03) A 0.689183 0.141482E‑01 0.661453 0.716914

22 4 MOV(03) BA 0.199345 0.142051E‑01 0.171503 0.227187

23 5 MOV(03) BB 0.602077 0.187276E‑01 0.565371 0.638784

24 6 SRV(03) B 0.689183 0.141482E‑01 0.661453 0.716914

25 7 MOV(03) CA 0.200379 0.142887E‑01 0.172373 0.228385

26 8 MOV(03) CB 0.200379 0.142887E‑01 0.172373 0.228385

27 9 SRV(03) C 0.686058 0.141657E‑01 0.658293 0.713823

28 10 p(02) A 0.504711 0.261849E‑01 0.453389 0.556034

29 11 p(02) B 0.504711 0.261849E‑01 0.453389 0.556034

30 12 p(02) C 0.506079 0.264600E‑01 0.454217 0.557940

31 10 p(03) A 0.504711 0.261849E‑01 0.453389 0.556034

32 11 p(03) B 0.504711 0.261849E‑01 0.453389 0.556034

33 12 p(03) C 0.506079 0.264600E‑01 0.454217 0.557940

34 10 p(04) A 0.504711 0.261849E‑01 0.453389 0.556034

35 11 p(04) B 0.504711 0.261849E‑01 0.453389 0.556034

36 12 p(04) C 0.506079 0.264600E‑01 0.454217 0.557940

37 ‑37 PARAMETER 37 3.00000 0.000000 3.00000 3.00000

Cohort Cell Observed Expected Chi‑square Note

‑‑‑‑‑‑ ‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑

1 1 211 210.682 0.000 0 < P < 1

1 2 71 69.756 0.022 0 < P < 1

1 3 71 69.676 0.025 0 < P < 1

1 4 54 52.763 0.029 0 < P < 1

1 5 35 33.390 0.078 0 < P < 1

1 6 35 33.209 0.097 0 < P < 1

1 7 15 15.365 0.009 0 < P < 1

1 8 12 12.701 0.039 0 < P < 1

1 9 11 12.599 0.203 0 < P < 1

1 10 491 495.859 0.048 0 < P < 1

1 Cohort df= 9 0.549 P = 1.0000

2 1 71 69.756 0.022 0 < P < 1

2 2 211 210.682 0.000 0 < P < 1

2 3 71 69.676 0.025 0 < P < 1

2 4 35 33.390 0.078 0 < P < 1

2 5 54 52.763 0.029 0 < P < 1

2 6 35 33.209 0.097 0 < P < 1

2 7 12 12.701 0.039 0 < P < 1

2 8 15 15.365 0.009 0 < P < 1

2 9 11 12.599 0.203 0 < P < 1

2 10 491 495.859 0.048 0 < P < 1

2 Cohort df= 9 0.549 P = 1.0000

3 1 71 70.077 0.012 0 < P < 1

3 2 71 70.077 0.012 0 < P < 1

3 3 213 210.137 0.039 0 < P < 1

3 4 35 33.400 0.077 0 < P < 1

3 5 35 33.400 0.077 0 < P < 1

3 6 55 52.196 0.151 0 < P < 1

3 7 12 12.672 0.036 0 < P < 1

3 8 12 12.672 0.036 0 < P < 1

3 9 13 15.139 0.302 0 < P < 1

3 10 493 500.230 0.105 0 < P < 1

3 Cohort df= 9 0.845 P = 0.9997

4 1 284 283.353 0.001 0 < P < 1

4 2 95 93.817 0.015 0 < P < 1

4 3 95 93.709 0.018 0 < P < 1

4 4 71 70.963 0.000 0 < P < 1

4 5 44 44.907 0.018 0 < P < 1

4 6 43 44.663 0.062 0 < P < 1

4 7 721 721.587 0.000 0 < P < 1

4 Cohort df= 6 0.115 P = 1.0000

5 1 95 93.817 0.015 0 < P < 1

5 2 284 283.353 0.001 0 < P < 1

5 3 95 93.709 0.018 0 < P < 1

5 4 44 44.907 0.018 0 < P < 1

5 5 71 70.963 0.000 0 < P < 1

5 6 43 44.663 0.062 0 < P < 1

5 7 721 721.587 0.000 0 < P < 1

5 Cohort df= 6 0.115 P = 1.0000

6 1 95 94.015 0.010 0 < P < 1

6 2 95 94.015 0.010 0 < P < 1

6 3 285 281.916 0.034 0 < P < 1

6 4 44 44.809 0.015 0 < P < 1

6 5 44 44.809 0.015 0 < P < 1

6 6 71 70.025 0.014 0 < P < 1

6 7 721 725.411 0.027 0 < P < 1

6 Cohort df= 6 0.124 P = 1.0000

7 1 332 334.662 0.021 0 < P < 1

7 2 108 110.805 0.071 0 < P < 1

7 3 109 110.678 0.025 0 < P < 1

7 4 1049 1041.855 0.049 0 < P < 1

7 Cohort df= 3 0.167 P = 0.9828

8 1 108 110.805 0.071 0 < P < 1

8 2 332 334.662 0.021 0 < P < 1

8 3 109 110.678 0.025 0 < P < 1

8 4 1049 1041.855 0.049 0 < P < 1

8 Cohort df= 3 0.167 P = 0.9828

9 1 108 111.013 0.082 0 < P < 1

9 2 108 111.013 0.082 0 < P < 1

9 3 324 332.890 0.237 0 < P < 1

9 4 1060 1045.083 0.213 0 < P < 1

9 Cohort df= 3 0.614 P = 0.8932

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

G Total (Degrees of freedom = 42) 3.275

Pr(Larger Chi‑square) = 1.0000

With pooling, Degrees of freedom = 42 Pearson Chi‑square = 3.244

Pr(Larger Chi‑square) = 1.0000

Log‑likelihood = ‑160.17616 Akaike Information Criterion = 344.35231

CPU time in seconds for last procedure was 2.00

INPUT ‑‑‑ PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_B;

Number of parameters in model = 37

Number of parameters set equal = 18

Number of parameters fixed = 1

Number of parameters estimated = 18

Final function value 15220.863 (Error Return = 0)

Number of significant digits 6

Number of function evaluations 636

95% Confidence Interval

I Parameter S(I) Standard Error Lower Upper

1 1 MOV(01) AA 0.601166 0.195100E‑01 0.562926 0.639405

2 2 MOV(01) AB 0.199036 0.146797E‑01 0.170264 0.227808

3 3 SRV(01) A 0.693013 0.149620E‑01 0.663688 0.722339

4 4 MOV(01) BA 0.199036 0.146797E‑01 0.170264 0.227808

5 5 MOV(01) BB 0.601166 0.195100E‑01 0.562926 0.639405

6 6 SRV(01) B 0.693013 0.149620E‑01 0.663688 0.722339

7 7 MOV(01) CA 0.199464 0.147250E‑01 0.170603 0.228325

8 8 MOV(01) CB 0.199464 0.147250E‑01 0.170603 0.228325

9 9 SRV(01) C 0.691332 0.149967E‑01 0.661939 0.720725

10 1 MOV(02) AA 0.601166 0.195100E‑01 0.562926 0.639405

11 2 MOV(02) AB 0.199036 0.146797E‑01 0.170264 0.227808

12 3 SRV(02) A 0.693013 0.149620E‑01 0.663688 0.722339

13 4 MOV(02) BA 0.199036 0.146797E‑01 0.170264 0.227808

14 5 MOV(02) BB 0.601166 0.195100E‑01 0.562926 0.639405

15 6 SRV(02) B 0.693013 0.149620E‑01 0.663688 0.722339

16 7 MOV(02) CA 0.199464 0.147250E‑01 0.170603 0.228325

17 8 MOV(02) CB 0.199464 0.147250E‑01 0.170603 0.228325

18 9 SRV(02) C 0.691332 0.149967E‑01 0.661939 0.720725

19 1 MOV(03) AA 0.601166 0.195100E‑01 0.562926 0.639405

20 2 MOV(03) AB 0.199036 0.146797E‑01 0.170264 0.227808

21 3 SRV(03) A 0.693013 0.149620E‑01 0.663688 0.722339

22 4 MOV(03) BA 0.199036 0.146797E‑01 0.170264 0.227808

23 5 MOV(03) BB 0.601166 0.195100E‑01 0.562926 0.639405

24 6 SRV(03) B 0.693013 0.149620E‑01 0.663688 0.722339

25 7 MOV(03) CA 0.199464 0.147250E‑01 0.170603 0.228325

26 8 MOV(03) CB 0.199464 0.147250E‑01 0.170603 0.228325

27 9 SRV(03) C 0.691332 0.149967E‑01 0.661939 0.720725

28 10 p(02) A 0.505482 0.303177E‑01 0.446059 0.564904

29 11 p(02) B 0.505482 0.303177E‑01 0.446059 0.564904

30 12 p(02) C 0.508702 0.305065E‑01 0.448909 0.568494

31 13 p(03) A 0.508786 0.302223E‑01 0.449551 0.568022

32 14 p(03) B 0.508786 0.302223E‑01 0.449551 0.568022

33 15 p(03) C 0.510598 0.304568E‑01 0.450903 0.570293

34 16 p(04) A 0.495451 0.328615E‑01 0.431042 0.559859

35 17 p(04) B 0.495451 0.328615E‑01 0.431042 0.559859

36 18 p(04) C 0.486934 0.325270E‑01 0.423181 0.550687

37 ‑37 PARAMETER 37 3.00000 0.000000 3.00000 3.00000

Cohort Cell Observed Expected Chi‑square Note

‑‑‑‑‑‑ ‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑

1 1 211 211.855 0.003 0 < P < 1

1 2 71 70.142 0.011 0 < P < 1

1 3 71 70.859 0.000 0 < P < 1

1 4 54 53.550 0.004 0 < P < 1

1 5 35 33.892 0.036 0 < P < 1

1 6 35 34.025 0.028 0 < P < 1

1 7 15 15.136 0.001 0 < P < 1

1 8 12 12.515 0.021 0 < P < 1

1 9 11 12.282 0.134 0 < P < 1

1 10 491 491.745 0.001 0 < P < 1

1 Cohort df= 9 0.240 P = 1.0000

2 1 71 70.142 0.011 0 < P < 1

2 2 211 211.855 0.003 0 < P < 1

2 3 71 70.859 0.000 0 < P < 1

2 4 35 33.892 0.036 0 < P < 1

2 5 54 53.550 0.004 0 < P < 1

2 6 35 34.025 0.028 0 < P < 1

2 7 12 12.515 0.021 0 < P < 1

2 8 15 15.136 0.001 0 < P < 1

2 9 11 12.282 0.134 0 < P < 1

2 10 491 491.745 0.001 0 < P < 1

2 Cohort df= 9 0.240 P = 1.0000

3 1 71 70.401 0.005 0 < P < 1

3 2 71 70.401 0.005 0 < P < 1

3 3 213 213.500 0.001 0 < P < 1

3 4 35 33.899 0.036 0 < P < 1

3 5 35 33.899 0.036 0 < P < 1

3 6 55 53.488 0.043 0 < P < 1

3 7 12 12.504 0.020 0 < P < 1

3 8 12 12.504 0.020 0 < P < 1

3 9 13 14.787 0.216 0 < P < 1

3 10 493 494.617 0.005 0 < P < 1

3 Cohort df= 9 0.387 P = 1.0000

4 1 284 286.793 0.027 0 < P < 1

4 2 95 94.952 0.000 0 < P < 1

4 3 95 95.656 0.004 0 < P < 1

4 4 71 69.682 0.025 0 < P < 1

4 5 44 44.109 0.000 0 < P < 1

4 6 43 43.401 0.004 0 < P < 1

4 7 721 718.407 0.009 0 < P < 1

4 Cohort df= 6 0.070 P = 1.0000

5 1 95 94.952 0.000 0 < P < 1

5 2 284 286.793 0.027 0 < P < 1

5 3 95 95.656 0.004 0 < P < 1

5 4 44 44.109 0.000 0 < P < 1

5 5 71 69.682 0.025 0 < P < 1

5 6 43 43.401 0.004 0 < P < 1

5 7 721 718.407 0.009 0 < P < 1

5 Cohort df= 6 0.070 P = 1.0000

6 1 95 95.066 0.000 0 < P < 1

6 2 95 95.066 0.000 0 < P < 1

6 3 285 287.496 0.022 0 < P < 1

6 4 44 44.044 0.000 0 < P < 1

6 5 44 44.044 0.000 0 < P < 1

6 6 71 68.134 0.121 0 < P < 1

6 7 721 721.150 0.000 0 < P < 1

6 Cohort df= 6 0.142 P = 0.9999

7 1 332 329.847 0.014 0 < P < 1

7 2 108 109.207 0.013 0 < P < 1

7 3 109 107.741 0.015 0 < P < 1

7 4 1049 1051.205 0.005 0 < P < 1

7 Cohort df= 3 0.047 P = 0.9974

8 1 108 109.207 0.013 0 < P < 1

8 2 332 329.847 0.014 0 < P < 1

8 3 109 107.741 0.015 0 < P < 1

8 4 1049 1051.205 0.005 0 < P < 1

8 Cohort df= 3 0.047 P = 0.9974

9 1 108 109.313 0.016 0 < P < 1

9 2 108 109.313 0.016 0 < P < 1

9 3 324 323.745 0.000 0 < P < 1

9 4 1060 1057.629 0.005 0 < P < 1

9 Cohort df= 3 0.037 P = 0.9981

‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑

G Total (Degrees of freedom = 36) 1.295

Pr(Larger Chi‑square) = 1.0000

With pooling, Degrees of freedom = 36 Pearson Chi‑square = 1.279

Pr(Larger Chi‑square) = 1.0000

Log‑likelihood = ‑159.18640 Akaike Information Criterion = 354.37280

CPU time in seconds for last procedure was 2.03

INPUT ‑‑‑ PROC ESTIMATE NOVAR NSIG=6 MAXFN=64000 NAME=MODL_A;

Number of parameters in model = 37

Number of parameters set equal = 0

Number of parameters fixed = 4

Number of parameters estimated = 33

Final function value 15220.725 (Error Return = 0)

Number of significant digits 6

Number of function evaluations 2047

95% Confidence Interval

I Parameter S(I) Standard Error Lower Upper

1 1 MOV(01) AA 0.599759 0.343511E‑01 0.532431 0.667087

2 2 MOV(01) AB 0.202125 0.266281E‑01 0.149934 0.254316

3 3 SRV(01) A 0.695968 0.256308E‑01 0.645731 0.746204

4 4 MOV(01) BA 0.202125 0.266281E‑01 0.149934 0.254316

5 5 MOV(01) BB 0.599759 0.343511E‑01 0.532431 0.667087

6 6 SRV(01) B 0.695968 0.256308E‑01 0.645731 0.746204

7 7 MOV(01) CA 0.202418 0.266292E‑01 0.150224 0.254611

8 8 MOV(01) CB 0.202418 0.266292E‑01 0.150224 0.254611

9 9 SRV(01) C 0.693621 0.254932E‑01 0.643654 0.743588

10 10 MOV(02) AA 0.599667 0.307611E‑01 0.539375 0.659959

11 11 MOV(02) AB 0.200358 0.234554E‑01 0.154385 0.246330

12 12 SRV(02) A 0.688886 0.240379E‑01 0.641772 0.736001

13 13 MOV(02) BA 0.200358 0.234554E‑01 0.154385 0.246330

14 14 MOV(02) BB 0.599667 0.307611E‑01 0.539375 0.659959

15 15 SRV(02) B 0.688886 0.240379E‑01 0.641772 0.736001

16 16 MOV(02) CA 0.199464 0.234561E‑01 0.153490 0.245438

17 17 MOV(02) CB 0.199464 0.234561E‑01 0.153490 0.245438

18 18 SRV(02) C 0.691060 0.242737E‑01 0.643484 0.738637

19 19 MOV(03) AA 0.606055 0.200134E‑01 0.566829 0.645282

20 20 MOV(03) AB 0.196693 0.163667E‑01 0.164615 0.228772

21 21 SRV(03) A 0.343612 0.118589E‑01 0.320369 0.366856

22 22 MOV(03) BA 0.196693 0.163667E‑01 0.164615 0.228772

23 23 MOV(03) BB 0.606055 0.200134E‑01 0.566829 0.645282

24 24 SRV(03) B 0.343612 0.118589E‑01 0.320369 0.366856

25 25 MOV(03) CA 0.200082 0.166152E‑01 0.167517 0.232648

26 26 MOV(03) CB 0.200082 0.166152E‑01 0.167517 0.232648

27 27 SRV(03) C 0.337384 0.117992E‑01 0.314257 0.360510

28 28 p(02) A 0.501977 0.392744E‑01 0.424999 0.578955

29 29 p(02) B 0.501977 0.392744E‑01 0.425000 0.578955

30 30 p(02) C 0.511229 0.400706E‑01 0.432690 0.589767

31 31 p(03) A 0.510140 0.359640E‑01 0.439650 0.580629

32 32 p(03) B 0.510140 0.359640E‑01 0.439650 0.580629

33 33 p(03) C 0.511453 0.364904E‑01 0.439931 0.582974

34 ‑34 p(04) A 1.00000 0.000000 1.00000 1.00000

35 ‑35 p(04) B 1.00000 0.000000 1.00000 1.00000

36 ‑36 p(04) C 1.00000 0.000000 1.00000 1.00000

37 ‑37 PARAMETER 37 3.00000 0.000000 3.00000 3.00000

Cohort Cell Observed Expected Chi‑square Note

‑‑‑‑‑‑ ‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑

1 1 211 210.789 0.000 0 < P < 1

1 2 71 71.038 0.000 0 < P < 1

1 3 71 70.913 0.000 0 < P < 1

1 4 54 53.802 0.001 0 < P < 1

1 5 35 34.345 0.012 0 < P < 1

1 6 35 34.104 0.024 0 < P < 1

1 7 15 15.189 0.002 0 < P < 1

1 8 12 12.561 0.025 0 < P < 1

1 9 11 12.227 0.123 0 < P < 1

1 10 491 491.034 0.000 0 < P < 1

1 Cohort df= 9 0.188 P = 1.0000

2 1 71 71.038 0.000 0 < P < 1

2 2 211 210.789 0.000 0 < P < 1

2 3 71 70.913 0.000 0 < P < 1

2 4 35 34.345 0.012 0 < P < 1

2 5 54 53.802 0.001 0 < P < 1

2 6 35 34.104 0.024 0 < P < 1

2 7 12 12.561 0.025 0 < P < 1

2 8 15 15.189 0.002 0 < P < 1

2 9 11 12.227 0.123 0 < P < 1

2 10 491 491.034 0.000 0 < P < 1

2 Cohort df= 9 0.188 P = 1.0000

3 1 71 71.183 0.000 0 < P < 1

3 2 71 71.183 0.000 0 < P < 1

3 3 213 213.155 0.000 0 < P < 1

3 4 35 34.186 0.019 0 < P < 1

3 5 35 34.186 0.019 0 < P < 1

3 6 55 53.246 0.058 0 < P < 1

3 7 12 12.594 0.028 0 < P < 1

3 8 12 12.594 0.028 0 < P < 1

3 9 13 14.742 0.206 0 < P < 1

3 10 493 492.931 0.000 0 < P < 1

3 Cohort df= 9 0.359 P = 1.0000

4 1 284 285.131 0.004 0 < P < 1

4 2 95 95.267 0.001 0 < P < 1

4 3 95 95.329 0.001 0 < P < 1

4 4 71 69.347 0.039 0 < P < 1

4 5 44 43.702 0.002 0 < P < 1

4 6 43 43.186 0.001 0 < P < 1

4 7 721 721.038 0.000 0 < P < 1

4 Cohort df= 6 0.049 P = 1.0000

5 1 95 95.267 0.001 0 < P < 1

5 2 284 285.131 0.004 0 < P < 1

5 3 95 95.330 0.001 0 < P < 1

5 4 44 43.702 0.002 0 < P < 1

5 5 71 69.347 0.039 0 < P < 1

5 6 43 43.186 0.001 0 < P < 1

5 7 721 721.038 0.000 0 < P < 1

5 Cohort df= 6 0.049 P = 1.0000

6 1 95 95.281 0.001 0 < P < 1

6 2 95 95.281 0.001 0 < P < 1

6 3 285 287.864 0.029 0 < P < 1

6 4 44 43.799 0.001 0 < P < 1

6 5 44 43.799 0.001 0 < P < 1

6 6 71 68.050 0.128 0 < P < 1

6 7 721 720.925 0.000 0 < P < 1

6 Cohort df= 6 0.160 P = 0.9999

7 1 332 332.780 0.002 0 < P < 1

7 2 108 108.003 0.000 0 < P < 1

7 3 109 108.309 0.004 0 < P < 1

7 4 1049 1048.908 0.000 0 < P < 1

7 Cohort df= 3 0.006 P = 0.9999

8 1 108 108.003 0.000 0 < P < 1

8 2 332 332.780 0.002 0 < P < 1

8 3 109 108.309 0.004 0 < P < 1

8 4 1049 1048.908 0.000 0 < P < 1

8 Cohort df= 3 0.006 P = 0.9999

INPUT ‑‑‑ PROC TEST;

Submodel Name Log‑likelihood NDF Akaike Inf. Criter. G‑O‑F

‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑

1 MODL_D ‑160.17616 42 344.35231 1.0000

2 MODL_B ‑159.18640 36 354.37280 1.0000

3 MODL_A ‑159.04842 21 384.09683 1.0000

Likelihood Ratio Tests Between Models

General Reduced Degrees Pr(Larger

Submodel Submodel Chi‑square Freedom Chi‑square)

‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑ ‑‑‑‑‑‑‑‑‑‑‑

MODL_B MODL_D 1.980 6 0.9216

MODL_A MODL_D 2.255 21 1.0000

MODL_A MODL_B 0.276 15 1.0000

* * WARNING * * Sequence of models reinitialized to zero.

CPU time in seconds for last procedure was 0.00

INPUT ‑‑‑ PROC STOP;

CPU time in minutes for this job was 0.19

E X E C U T I O N S U C C E S S F U L

Hardware Considerations

Two versions of MSSURVIV are available for PC's. A small version which will work on older PC's running DOS without Extended memory or a math coprocessor is set up to handle up to 25 cohorts, 20 classes and 50 parameters. See appendix A to determine the possible combinations of strata and sample periods for these limits.

A larger version, compiled with a "DOS extender", requires a 386/387 or 486 PC, 640Kb RAM, and at least 10Mb of free hard disk space (although MSSURVIV will run faster with more RAM). The maximum number of cohorts, classes and parameters for this version are: 64, 64, and 250, respectively.

The source code for MSSURVIV has been successfully compiled and run on a Prime minicomputer running PrimeOS, and two different unix workstations.

The program has also been compiled for Windows and OS/2. The limitations for the Windows version are the same as the DOS extender version.

Software Installation

To install MSSURVIV on a PC simply make a sub-directory to contain the programs and copy the files from the floppy disk. The disk contains the executable program file, so no compilation is necessary unless you wish to alter the dimensions. Here are the commands to install the MSSURVIV programs onto the hard disk of a PC:

c:> mkdir mssrv

c:> cd mssrv

c:> xcopy a:*.* /s

To install MSSURVIV on other computers, a FORTRAN compiler will be required. The files must first be transferred to disk on the computer, then compiled and linked into an executable program file. A "make" file is included which will create the executable program file from the source files if the target computer has the make utility (as most Unix systems do). If the target computer doesn't have a make utility, a "batch" file is included to compile all of the routines. Most likely, the make file or batch file will have to be edited to reflect the names of the compiler and linker on the target system.

Literature Cited

Brownie, C., J.E. Hines, J.D. Nichols, K.H. Pollock, and J.B. Hestbeck. 1993. Capture-recapture studies for multiple strata including non-Markovian transition probabilities. Biometrics 49:1173-1187.

Pollock, K.H., J.D. Nichols, C. Brownie, and J.E. Hines. 1990. Statistical inference for capture-recapture experiments. Wildlife Monographs 107. 97pp.

White, G.C. 1983. Numerical estimation of survival rates from band-recovery and biotelemetry data. The Journal of Wildlife Management 47:716-728.

Appendix A: Maximum number of cohorts/classes/parameters for "Movement‑only" and "Memory-Movement" models.

"Movement-only" models

SAMPLE STRATA

PERIODS 1 2 3 4 5 6

3 2/ 2/ 4 4/ 4/ 12 6/ 6/ 24 8/ 8/ 40 10/10/ 60 12/ 12/ 84

4 3/ 3/ 6 6/ 6/ 18 9/ 9/ 36 12/12/ 60 15/15/ 90 18/ 18/126

5 4/ 4/ 8 8/ 8/ 24 12/12/ 48 16/16/ 80 20/20/120 24/ 24/168

6 5/ 5/10 10/10/ 30 15/15/ 60 20/20/100 25/25/150 30/ 30/210

7 6/ 6/12 12/12/ 36 18/18/ 72 24/24/120 30/30/180 36/ 36/252

8 7/ 7/14 14/14/ 42 21/21/ 84 28/28/140 35/35/210 42/ 42/294

9 8/ 8/16 16/16/ 48 24/24/ 96 32/32/160 40/40/240 48/ 48/336

10 9/ 9/18 18/18/ 54 27/27/108 36/36/180 45/45/270 54/ 54/378

11 10/10/20 20/20/ 60 30/30/120 40/40/200 50/50/300 60/ 60/420

12 11/11/22 22/22/ 66 33/33/132 44/44/220 55/55/330 66/ 66/462

13 12/12/24 24/24/ 72 36/36/144 48/48/240 60/60/360 72/ 72/504

14 13/13/26 26/26/ 78 39/39/156 52/52/260 65/65/390 78/ 78/546

15 14/14/28 28/28/ 84 42/42/168 56/56/280 70/70/420 84/ 84/588

16 15/15/30 30/30/ 90 45/45/180 60/60/300 75/75/450 90/ 90/630

17 16/16/32 32/32/ 96 48/48/192 64/64/320 80/80/480 96/ 96/672

18 17/17/34 34/34/102 51/51/204 68/68/340 85/85/510 102/102/714

19 18/18/36 36/36/108 54/54/216 72/72/360 90/90/540 108/108/756

20 19/19/38 38/38/114 57/57/228 76/76/380 95/95/570 114/114/798

"Memory‑Movement" models

SAMPLE STRATA

PERIODS 1 2 3 4 5 6

3 1/ 1/ 2 4/ 2/ 10 9/ 3/ 30 16/ 4/ 68 25/ 5/ 130 36/ 6/ 222

4 2/ 2/ 4 8/ 4/ 20 18/ 6/ 60 32/ 8/ 136 50/10/ 260 72/ 12/ 444

5 3/ 3/ 6 12/ 6/ 30 27/ 9/ 90 48/12/ 204 75/15/ 390 108/ 18/ 666

6 4/ 4/ 8 16/ 8/ 40 36/12/120 64/16/ 272 100/20/ 520 144/ 24/ 888

7 5/ 5/10 20/10/ 50 45/15/150 80/20/ 340 125/25/ 650 180/ 30/1,110

8 6/ 6/12 24/12/ 60 54/18/180 96/24/ 408 150/30/ 780 216/ 36/1,332

9 7/ 7/14 28/14/ 70 63/21/210 112/28/ 476 175/35/ 910 252/ 42/1,554

10 8/ 8/16 32/16/ 80 72/24/240 128/32/ 544 200/40/1,040 288/ 48/1,776

11 9/ 9/18 36/18/ 90 81/27/270 144/36/ 612 225/45/1,170 324/ 54/1,998

12 10/10/20 40/20/100 90/30/300 160/40/ 680 250/50/1,300 360/ 60/2,220

13 11/11/22 44/22/110 99/33/330 176/44/ 748 275/55/1,430 396/ 66/2,442

14 12/12/24 48/24/120 108/36/360 192/48/ 816 300/60/1,560 432/ 72/2,664

15 13/13/26 52/26/130 117/39/390 208/52/ 884 325/65/1,690 468/ 78/2,886

16 14/14/28 56/28/140 126/42/420 224/56/ 952 350/70/1,820 504/ 84/3,108

17 15/15/30 60/30/150 135/45/450 240/60/1,020 375/75/1,950 540/ 90/3,330

18 16/16/32 64/32/160 144/48/480 256/64/1,088 400/80/2,080 576/ 96/3,552

19 17/17/34 68/34/170 153/51/510 272/68/1,156 425/85/2,210 612/102/3,774

20 18/18/36 72/36/180 162/54/540 288/72/1,224 450/90/2,340 648/108/3,996

[1]Formerly: U.S. Fish & Wildlife Service, and National Biological Survey