Lab 10: Jolly-Seber Analysis and the Robust Design

In this lab we examine the use of open-population capture-recapture data to estimate parameters in addition to survival rates, specifically recruitment, abundance, and population growth rate. See the lecture notes (JS, robust models) and Chapters 18 and 19 for more details. We consider 2 basic kinds of data structures:

• Releases and recaptures of marked animals over "primary" sampling periods, between which the population is assumed to be open to birth, death/ permanent emigration. This type of data can be modeled with several procedures, including:
• Cormack-Jolly-Seber conditional models, providing estimates of survival
• Jolly-Seber models, providing estimates of survival, numbers of recruits, and abundance
• Pradel recruitment & survival models, providing estimates of survival and per-capita recruitment rates (from which can be computed growth rates)
• Releases and recaptures in "primary" periods, over which the population is assumed to be open to birth, death/ permanent emigration and (possibly) temporary emigration; and recaptures over "secondary" periods within primary periods, over which the population is assumed to be closed to birth, death, and movements. This design, known as the "Robust Design" provides estimates of abundance (based on closed population assumptions within primary period) and survival rates (based on recaptures between primary periods). Under certain conditions recruitment and other parameters, such as temporary emigration can also be estimated. The Robust Design

We will use throughout an example of male Microtus pennsylvanicus trapped in Maryland over 6 months, and daily over 5-day periods each month (cited in Chapters 17-19 of Williams et al.). The example will be re-formatted as necessary for input into various procedures in MARK and other programs.

Cormack-Jolly-Seber

First, we will use CJS analysis to estimate survival and recapture probabilities for these data. In this analysis, daily recaptures over the 5-day periods are ignored, except that if a mouse was captured once or more over the period it counts as a capture for that month. The data are formatted for program MARK (6 occasions, 1 group). Read them into MARK and perform model estimation and selection. When you have selected the "best" model, save the 'real parameter estimates' in a text file for later use.

Jolly-Seber analysis

The Jolly-Seber models are not conditional on releases at time i; that is, the unmarked animals captured at time i now become part of the likelihood, and the unknown number of marked and unmarked animals in the population is an (unknown) random variable. Exactly the same data are used for JS as CJS; it is only the modeling that is different (unconditional versus conditional) A JS parameterization exists in MARK; however, this procedure is highly unstable and convergence on estimates is problematic. Instead, I recommend using program JOLLY (download the extraction file; also available from the Patuxent Software Page) . Rather than run the model in class, I am here providing copies of the input and output files from a run of the microtus data in Jolly. Compare the survival estimates for the "best" (best fit, fewest parameters) JS model, to those for CJS; they should be similar (but will not be identical: these are different models!).

Pradel parameterization

There are a small number of JS models available in program JOLLY; in addition, the JS model is reparameterized in program MARK (see the input file), but as indicated above is not particularly stable. An alternative to JS that allows estimation of survival, recruitment, and growth rates, is the Pradel parameterization, based on combination of forward- and reverse-time capture histories. Read the data into MARK , using the "Pradel survival and recruitment" model (again, 6 occasions). Obtain estimates of survival [phi(i)], capture [p(i)], and recruitment [f(i)] under this model. Note that by definition of f(i) as # adults recruited to i+1 per adult at i, we have a simple demographic model of populations growth (for one age class):

N(i+1) = phi(i)*N(i) + f(i)*N(i)

or lambda(i)= N(i+1)/ N(i) = phi(i)+f(i)

In fact, the Pradel model has 2 equivalent parameterizations, one based on f(i) and one based on lambda(i) (a third parameterization only involves recruitment). The equivalence among these various models is provided in a pdf file supplied by White and colleagues. For the homework assignment you will want the second of these.

Robust Design

In the Robust Design, animals are potentially recaptured on multiple occasions (referred to as "secondary occasions") within each primary period. This scheme is illustrated schematically in the attached figure:

For instance, below are 6 primary periods (months), within each of which are 5 secondary occasions (days)

01101 01100 01011 11111 11101 11101

00010 11100 00000 10000 10100 10000

The population is assumed closed between secondary occasions, but open between primary occasions. For the JS and CJS analyses earlier, the secondary occasions were ignored; thus the capture histories above would have reduced to

111111

110111

Again, consider the Microtus data , which are now in MARK format; read this into MARK "Robust design" data type (30 occasions, 1 group). Specify 'Closed captures' in the window requesting 'closed capture data type'. The length of the time intervals (by default, all zero) determine which occasions constitute the 'primary' and 'secondary' occasions. For the Microtus data there are 6 months (primary occasions) and 5 days of sampling per month (secondary occasions). This is communicated to mark by setting the interval between occasions as 1 for occasions 5, 10, 15, 20, and 25, and leaving it as zero for all other occasions. The '1' will refer to the 1-month intervals, over which survival and other demographic parameters will be estimated.

The 'global' model will contain the following parameters (see the PIMs and PIM chart):

• Survival rates between each of the "sessions" (primary occasions)
• Temporary emigration rates (gamma") between each of the "sessions" (primary occasions)
• Probably of remaining outside the trapping area (gamma') given that the animal was outside at t-1
• Capture probabilities (p) for each of the sessions, different among days within sessions (secondary occasions)
• Recapture probabilities (c) for each of the sessions, different among days within sessions (secondary occasions)
• Abundance (N) for each session.

Although it is possible to run a number of pre-selected models using the run tool, I have found this tedious for the large number of parameter groups. Try the following:

• Pull up the PIM chart. Run the global model (all parameters time-specific as above)
• Run the following additional models
• gamma" and gamma' constant over time
• gamma" = gamma' and constant over time
• Both of the above with S constant over time

Hint: you can make parameters constant over time simply by right clicking on the parameter graphic in the PIM chart and selecting "constant". You can set 2 parameters equal by dragging the graphic for the one to line up over the other. Do not worry about gaps created in the PIM by this process; the program will automatically renumber the parameters when you run the job.

Assignment. Submit a brief (<4 pg) report via email covering the assignment. Be sure to attach any program input/ output needed to document your report (e.g., all MARK *.inp, *.dbf, and *.fpt files). Due next lab.

Last updated 08 December 2008