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Modeling Elk Population by Reconstruction

Introduction

The debate over the number of elk in Arizona in the past two decades has hindered effective management. Consumptive users (i.e. hunters) have argued that the elk population should have priority over domestic livestock while ranchers argue that the population is too large and is detrimental to their operations. Unfortunately, empirical data from which to make informed decisions are limited.

The Arizona Game and Fish Department (AGFD) has surveyed the population and uses their results in developing management plans. Unfortunately, the validation of any single method is impossible in free-ranging ungulate populations (Bender and Spencer 1999). As a result, any estimate should be viewed as trend data from which informed decisions can be made. The objective of this element of the project was to explore another technique that has been used to estimate elk population size (i.e. reconstruction from harvest data and herd ratios; Bender and Spencer 1999) within several game management units in Arizona. We hypothesized that the reconstruction technique would yield results similar to the elk population estimates made by the AGFD.

Methods

The AGFD manages wildlife in more than 75 game management units. To simplify unit classifications and analyses, we queried the AGFD survey and harvest databases from 1988 to 1999 and determined elk were surveyed or hunted in 32 game management units (GMU). Data for elk on Indian lands were not available. Units were pooled where a population crossed unit boundaries, survey and harvest data could be combined, and where the AGFD pooled data for their model (e.g., 5A, 5B, 6A; 6B, 8, Camp Navajo). We did not subdivide units by direction (i.e. north, south, east, and west). We identified 5 GMUs or combinations of units that had adequate data (i.e. congruous hunt and survey data for > 5 consecutive years between 1988 and 1999) to compare the population estimates (i.e. 5A, 5B, 6A; 6B, 8, Camp Navajo; and 7; 9; and 22) (See Figures 5-9).

We compared the elk population between the AGFD estimates with values generated from reconstruction of harvest and herd ratios (obtained from the AGFD). Allen (1942) first described reconstructed population size from sex ratios, harvest number, and harvest percentage. Bender and Spencer (1999) recently used the technique to estimate elk populations in Michigan and Washington. However, one limitation of reconstruction is the need for estimates of annual male mortality. We calculated bull mortality from the percentage of yearling males in AGFD surveys, corrected for population trends using the formula:

MT = 1-[(1-YB)*l] (Bender and Spencer 1999).

 

To calculate l, we used the percent population change of bulls estimated by AGFD models as the instantaneous rate of increase (r). We estimated total numbers of elk (Nt) by:

 

NT = (K/MB)*(1+RC/B+RC/B*RC/C), numbers of bulls (NB ) by:
NB = K/MH, numbers of cows (NC ) by:
NC = NB *RC/B, and numbers of juveniles (NJ ) by:
NJ = NC *RC/C

where K = the number of bulls harvested, MB = the mean annual total bull mortality rate, RC/B = the ratio of cows to bulls in pre-hunt surveys, and RC/C = the ratio of calves to cows in pre-hunt surveys (Bender and Spencer 1999). We could not calculate confidence intervals because measures of variance were unavailable for some values. Bull harvest rates for a staggered-entry Kaplan-Meier estimator were not available, and harvest-per-unit-effort did not have a linear relationship with elk numbers, precluding the use of alternative methods for calculating mortality rates used by Bender and Spencer (1999).

We obtained AGFD estimates from Elk Management Summaries (AGFD, unpublished data). Unit 22 was modeled using GIS density estimates generated in 1991. The Holland and Fink (1997) model was used to model elk after the 1998-1999 elk season (5A, 5B, 6A) and the 1999-2000 elk season (6B, 8, Camp Navajo; 7; 9). Different models were used by the AGFD because as better models were developed their techniques were modified to take advantage of new information. For example, in response to research indicating that one population of elk uses units 5A, 5B, and 6A (Brown 1997), the AGFD started pooling data from these units for modeling in 1994.

Results

We calculated estimates of elk populations in 5 GMUs for comparison with AGFD estimates (Figures 5-9). In some years both estimates were similar (e.g., 1989-1992 in units 5A, 5B, 6A; Fig. 5) but in others reconstruction yielded higher estimates (e.g., 1977-1999 in unit 22; Fig. 9). Overall, in the 50 game-unit-year comparison (1 game unit year = 1 comparison for 1 year) estimates were similar (i.e. within 10% of each other) 24% of the time (n = 12). The reconstruction model produced higher estimates 50% of the time (n = 25) and lower estimates than the AGFD 26% of the time (n = 13). The reconstruction model indicates greater annual fluctuations in elk numbers than the AGFD models.

Discussion

A weakness of the models, particularly the reconstruction model, is their dependency on unbiased pre-hunt survey data. Most AGFD surveys occur in August, when elk are still sexually segregated. Bulls are underestimated, reducing the accuracy of the AGFD model (J. Goodwin, AGFD, personal communication). This inflates the percentage of yearling males in the population, a component of the bull mortality rate, and affects bull:cow ratios. Although the AGFD survey database includes numbers of yearling males, this age class was not consistently reported (J. Goodwin, AGFD, personal communication).

Bender and Spencer (1999) attributed all bull mortality in their reconstruction of the population of elk in Washington to harvesting. However, a significant number of bulls die of other causes in Arizona (e.g., wound loss, vehicle collisions, disease) (J. Goodwin, AGFD, personal communication). According to Goodwin, a bull mortality rate of approximately 12-15% fits best with the AGFD model. Because we did not have data to calculate the proportion of MB due to harvesting (PH), we divided the numerators of the equations for total numbers of elk and numbers of bulls by MB rather than MB *PH.

Cows and calves were harvested in most of the units. The reconstruction model ties the bull:cow and cow:calf ratios to bull harvest, and should be robust to any level of cow harvest assuming pre-hunt survey data is good and unbiased (L. Bender, Washington Department of Fish and Wildlife, personal communication). Because these assumptions were violated, the cow/calf harvest may have affected the model. Other data (e.g., accurate estimates of male mortality) would also make the reconstruction model more useful.

This portion of the study did not yield consistent results between the techniques used by AGFD and the Bender and Spencer (1999) model but it was instrumental in identifying weaknesses that could be corrected. Both techniques would benefit from acquiring field data when elk are not segregated, and the Bender and Spencer (1999) model would be enhanced by using empirical data of male mortality. Furthermore both modeling techniques allowed the identification of patterns in some GMUs (i.e. 9 and 22). These patterns can led to hypothesis testing using remote sensing data related to critical issues on the use of habitat by elk and livestock.