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Suburban Deer Population Model

Model development: This model is the result of an adaptive management approach to estimating deer population densities in suburban Chicago, Illinois. Empirical data was combined in Stella 5.0 software (HPS 1997) to produce deer population estimates in semi-isolated suburban landscape. Empirical data was collected from a 1,500 km2 study area encompassing Cook and DuPage Counties in northeastern Illinois from winter 1992 through summer 1998. This data includes survival and movement information from 147 radio-collared white-tailed deer (129 females, 18 males) and sex ratio and recruitment information collected from 2,599 lethally removed deer (1,573 females, 1,026 males). Capture and culling techniques were reviewed and approved by the University of Illinois' Lab Animal Care Committee.

What makes this model unique is that it was constructed from an extensive radio-telemetry data set for suburban deer life histories used in combination with reproductive data collected from continuous intensive annual deer culling programs (1992 through 1997). This allowed us to build important density-dependent factors directly into the model. Furthermore, this model provides a tool for managers attempting to estimate variable populations of suburban deer and provides credibility founded in scientific research to highly scrutinized suburban deer management programs. We thank the Forest Preserve Districts of Cook and DuPage Counties, Cook County Animal Control and Chicago Wilderness for funding this project.

Minimum system requirements:

Model input: The model is preset to run on an annual increment beginning April 1 (time t) and ending April 1 the following year (time t +1). The model requires only an initial population size and size of the area to be managed (in km2). However, the user must keep in mind that this is an accounting model designed for an adaptive management approach and the more empirical data provided by the user the better the predicted model output. Likewise, the initial population estimate is crucial for accurately depicting population estimates at time t + 1. We recommend the best available data for this input. deer modelInitial population estimates might be derived from adjusted aerial or spotlight counts (Beringer et al. 1998, Farfarman and DeYoung 1986) or if marked deer are available a capture-recapture model design could be used (Pollock et al. 1990). The adult deer sex ratio is also an important input, which can be provided by the user. The proportion of females in the population at time t has a significant influence within the density-dependent recruitment function of the model and controlled management programs tend to target mature females resulting in sexually skewed populations. Previous harvest information or sex ratios collected during deer counts could be applicable for sex ratio input. We will discuss later how to incorporate the previous years sex ratio harvest information into the model. Manual removals (e.g., translocation or lethal removals) also are input provided by the user. These are the removals required to achieve a certain population size and can be entered as a range of numbers using the sensitivity analysis function in Stella 5.0. We encourage additional data input from managers including survival information, immigration/emigration rates or recruitment curves using the skeletal structure of this model.

Model output: The model will provide an estimate of deer population size (number of deer) or density (deer per km2) at both monthly and annual increments. The sensitivity-analysis function in Stella 5.0 software allows the user to predict annual population shifts in response to harvest of females and males. Some examples of questions the model was designed to answer include, 1) given a known suburban deer population size at time t what would be the population size at time t +1 under different management strategies (e.g., no harvest, harvest of variable numbers deer, etc.), 2) given a population at a selected deer density at time t what will be the predicted outcome of a set harvest at time t +1, t + 2, etc.

Running the model: To run the model you first need to enter the size of the area you intend to manage and the initial population size. Double click on the AREA symbol located in the bottom left corner of the model. Enter the area (Km2) and click OK. Now double click the INT POP box and type in a beginning population number at time t (model preset at April 1) and click OK. To run the model click RUN from the RUN drop down menu. To review output double click on TABLE 1 (upper left hand corner of model). The output displays a final population size and deer density at time t +1 (April 1 of the following year). To review output for a different month, let's assume December 1, the model must be adjusted. There are numerous ways to achieve this, but the simplest is to stop the FINAL POP and DEER DENSITY accounting functions at November 30. Remember that the model is preset to run from time t (April 1, month 1) to time t + 1 (April 1, month 13), so in this time schedule December is month number 9. Therefore, all additions and subtractions from the population must be included through November 30th, but must cease after this time. To achieve this first click the X in the upper right corner of the screen to return to the model and then double click on FINAL POP (bottom center of model). Within the IF TIME statement change the month (TIME) from 13 to 9 and select OK. Re-run the model and view the output in TABLE 1 for FINAL POP and DEER DENSITY. Observe how these numbers have changed and appear next to month 8 accounting for all additions and subtractions through November 30th. These results are the December 1 (month 9) population estimate. Now exit from the table and repeat this process changing the month back to 13 in FINAL POP.

We discussed earlier the importance of adult deer sex ratio in calculating the number of recruits into the population. Sex ratio information is difficult to collect in the field, but if deer are harvested in an unbiased manner, it is acceptable to use the previous years harvest ratio in an adaptive management approach. The present sex ratio is set at 60:40 females to males, but this can be changed if a different ratio is desired. This is easily done by first double clicking on MALE RATE located under INT POP in the center of the model. Then simply enter the new rate and select OK. Repeat this process for the FEMALE RATE so that the two combined equal one-hundred percent. Also, a function built into the model will automatically calculate the new sex ratio after deer have been harvested from the population. To calculate this first double click on FEMALES REMOVED located in the upper right hand corner of the model. Then enter the number of females harvested or estimated to be harvested and select OK. Now do the same for MALES REMOVED. Now double click on TABLE 1 and then double click on the table again to reveal a selection menu. Then, under the ALLOWABLE menu scroll down and select NEW FEMALE RATIO by clicking to highlight and then clicking the >> sign to the right and selecting OK. Now run the model to review the output under NEW FEMALE RATIO. This new ratio can then be inserted into FEMALE RATE as described above. Also, be sure to edit MALE RATE so that the two combined equal one-hundred percent. Now when the model is run this new sex ratio will be used in all calculations.

The strength of this model for management decisions lies within the Sensitivity Analysis function of Stella 5.0, which allows for input of multiple simultaneous deer removal scenarios. Exit from the table and select SENSI-SPECS under the Run menu. Then click in the box under # OF RUNS. Within the box enter the number of different removal strategies you are proposing (e.g. 5 runs). Then, under the ALLOWABLE menu scroll down and select first FEMALES REMOVED and then MALES REMOVED by highlighting each and then clicking the >> sign to the right. Then click on FEMLAES REMOVED under SELECTED (VALUE) so that it is highlighted. Now click on AD HOC under VARIATION TYPE and in the box to the right of the AD HOC VALUES type the first number of female deer you are predicting to remove from the population (e.g., 0), and click set. This selected value will appear in the box to the right under RUN #1. Now type in the next value (e.g. 10) and select SET. Continue to enter numbers until all RUNS #s have a corresponding VALUE. Now click on MALES REMOVED from the SELECTED (VALUE) menu and repeat the process. Once you have set your runs for females and males click OK to return to the model. Move the hand to TABLE 1 and double click. Double click again on the table to get a selection screen. Select COMPARATIVE under TABLE TYPE. Now select only one (1) of the fields (usually FINAL POP or DEER DENSITY) within the ALLOWABLE box by double clicking. This setup will produce a comparison of the multiple model runs for the selected variable. Make sure the ORIENTATION (Vertical) and REPORT INTERVAL (Every DT) are checked. Also, check ENDING BALANCES and INSTANTANEOUS under REPORT and REPORT FLOW VALUES. When this is complete click OK. Now select RUN from the drop down menu and click S-RUN. TABLE 1 now displays the results of various runs. Compare the runs and select a few which produced desired population estimates or densities. Then go back to SENSI-SPECS from the RUN drop down menu and click FEMALES REMOVED. Scroll down the RUN # VALUE box to see which numbers corresponded to the runs you selected as good. Now do the same for MALES REMOVED. To refine these numbers re-run SENSI-SPECS using values within the range of good values chosen. To exit from S-RUN and return the model to a standard RUN mode, double click on the table and uncheck COMPARATIVE under TABLE TYPE. Then reselect the variables you wish to view in the table. Also, go back to SENSI-SPECS under the RUN drop down menu and remove MALES and FEMALES REMOVED from the SELECTED VALUE.

Most other model variables such as natural removal rates (mortality rates) and the density-dependent recruitment can be adjusted within their respective control variables (see Stella 5.0 Technical Documentation).

Model verification: We recommend using an independent variable for verifying model predictions whenever possible. These variables might include deer-vehicle collisions, count data collected independent of model input data or harvest information. Verifying model predictions will provide support for population estimates and help direct possible input data adjustments.

Download the model (6 KB 'zip' archive)

Literature cited:
Beringer, J., L.P. Hansen and O. Sexton. 1998. Detection rates of white-tailed deer with a helicopter over snow. Wild. Soc. Bull. 26:24-28.

Farfarman, K.R. and C.A. DeYoung. 1986. Evaluation of spotlight counts of deer in South Texas. Wildl. Soc. Bull. 14:180-185.

High Performance Systems, Inc. 1997. STELLA Research software. Hanover, NH.

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

Starfield, A.M. 197. A pragmatic aproach to modeling for wildlife management. J. Wildl. Manage. 61:261-270.


Questions or comments are welcome and should be directed to the models authors:

    Dwayne R. Etter, Timothy R. Van Deelen
    Illinois Natural History Survey
    607 East Peabody Drive
    Champaign, IL 61820
    Phone: (217) 333-6855
    Fax: (217) 265-0374
    E-mail:detter@uiuc.edu
Copyright ©2004 Illinois Natural History Survey. All rights Reserved.