Untitled-1 ALCES SUPPL. 2, 2002 BALCIASKAS - MODELING OF MOOSE HUNTING 23 MODELING OF MOOSE HUNTING: PROTECTION OF COWS WITH TWINS Linas P. Balciaskas Institute of Ecology, Lithuanian Academy of Sciences, 232021, Akademijos 2, Vilnius, Lithuania ABSTRACT: I developed a simulation model to evaluate moose hunting strategies. The model incorporated age and sex-specific schedules for natural (nonhunting) mortality and fecundity. I evaluated 2 strategies for harvesting cow moose. In the first, cow moose were harvested irrespective of whether they were accompanied by calves. In the second, hunters were not allowed to kill cows accompanied by twin calves. Simulation results indicated that 500 calves/1000 cows could be saved under the second harvest strategy. ALCES SUPPLEMENT 2: 23-26 (2002) Key words: hunting, moose, numerical simulation, twins Moose are one of the most important game species in the USSR. In the European portion of the USSR, the goal of most game managers is to increase moose numbers. Traditional hunters in these regions do not understand or accept the concept of a se- lective harvest. For this reason, simulation modeling was used to evaluate the effect of different harvest strategies. In the first strategy, cow moose were harvested re- gardless of whether they were accompa- nied by calves. In the second, hunters were not allowed to kill cows accompanied by twin calves. Based on a comparison of the number of calves and embryos in cow moose harvested in the Kostroma region (Baskin, unpublished data), I assumed that individual cows consistently produce either single calves or twins. In contrast, moose density is too high in all parts of the Lithuanian Republic. The model was used to help determine the best strategy to reduce moose density while retaining the sex and age structure of the population. In particular, a strategy was needed that would preserve bulls in the 5.5 – 8.5 year age classes for trophy hunting, maximize meat production, and shooting opportunities. These needs can be ad- dressed using an optimizing model (Lopatin and Rosolovsky 1990). METHODS Simulations were run on a DVK-3 mi- crocomputer with OS RT11SJ and the model code was written in PASCAL. The model tallied moose numbers after each of a se- quence of discrete events: natural mortality, hunting mortality, and calving. The post- calving population was then subjected to that sequence in the next iteration of the model. Through tabulations, we tracked the sex and age structure of the population, proportions of cows with 0, 1, and 2 calves, and carcass weights in each sex and age category. In modeling the harvest in Lithua- nia, a harvest quota was set, then the antlerless portion (including calves) was set, and finally, the age distribution in each category was identified. Simulations ig- nored the potential effects of weather and nutrition. Output from the simulations was displayed on the screen, printed out, or saved as a separate file. For evaluating the twin protection strat- egies discussed above, I modeled only the MODELING OF MOOSE HUNTING - BALCIASKAS ALCES SUPPL. 2, 2002 24 Table 1. Initial set of parameters for moose population model. Age Percent Percent Percent Percent Percent Carcass Class females in females not females with females mortality mass (kg) (years) population pregnant one calf with twins max min 0.5 20.0 100.0 0.0 0.0 25.0 72.0 65.8 1.5 13.0 75.0 25.0 0.0 10.0 128.8 120.6 2.5 10.0 70.0 25.0 5.0 5.0 153.7 143.0 3.5 10.0 40.0 50.0 10.0 3.0 168.7 158.6 4.5 8.0 20.0 50.0 30.0 3.0 187.6 166.3 5.5 7.0 15.0 50.0 35.0 3.0 204.3 167.5 6.5 6.0 20.0 40.0 40.0 3.0 210.6 170.0 7.5 4.0 20.0 45.0 35.0 3.0 211.9 172.0 8.5 3.0 30.0 40.0 30.0 3.0 218.7 177.0 9.5 3.0 35.0 45.0 20.0 3.0 220.0 178.0 10.5 3.5 40.0 40.0 20.0 3.0 220.0 182.0 11.5 3.0 42.0 30.0 28.0 3.0 224.7 185.0 12.5 3.0 45.0 35.0 20.0 3.0 228.0 192.0 13.5 3.0 50.0 35.0 20.0 3.0 230.0 206.0 14.5 2.5 60.0 30.0 10.0 10.0 220.0 200.0 15.5 1.0 85.0 10.0 5.0 100.0 210.0 195.0 female portion of the population. I assumed that natural mortality, pregnancy rates, and fecundity rates remained constant through- out the simulations. Furthermore, I as- sumed that hunting maintains a stable popu- lation of mature cows and only the propor- tion of cows with single or twin calves varies. The probability for a cow to have a single calf was set as P1 (the probability of twins for the same cow was P2 = 1-P1), and the probability that that cow would have a single calf again next year was P3 (thus, the probability that a cow would twin in con- secutive years was P4 = 1-P3). As indi- cated earlier, if P2 is increased, P4 should increase as well because it is assumed that the ability to bear twins is inherited and individual to each cow. BIOLOGICAL PARAMETERS OF THE MODEL No single source of data was available for all 16 age classes used in the model, and the initial set of population parameters used in the model were a composite from several areas and authors. Several sources of data were used: Baleisis (1973, 1977) and the Society of Hunters and Fisherman (Baleisis and Butautas 1987, 1988) [Lithuania]; Filinov (1983) and Kozlo (1983) [various regions of the USSR]; and Sylven et al. (1979) [Swe- den]. The starting population contained 1,000 moose divided among 16 age classes (Table 1). Natural mortality was set at 3%, harvest mortality at 20%, and I assumed that equal numbers of cows and bulls were harvested. The sex ratio of newborn calves was 108 male calves/100 female calves. ALCES SUPPL. 2, 2002 BALCIASKAS - MODELING OF MOOSE HUNTING 25 The probability P1 was modeled as varying from 0.4 to 0.8 and P3 varied from 0.3 to 0.7. Precise values are unknown. Based on data from the Kostroma region, we can assume the probability of twins recurring is 1.7, so P1 equals 0.3. However, more data must be analyzed to determine a precise probability level of twins recurring. We modeled female harvest ratios of 5%, 10%, 15%, and 20%. RESULTS AND MANAGEMENT IMPLICATIONS The value of protecting cows with twins was determined by comparing the number of calves born during 10 years of the first and second harvest strategies. This differ- ence was expressed as a percentage of (A) the number of calves born under the first strategy and (B) as a percentage of the initial number of cows (Table 2). When the harvest rate ranged from 10 to 15% of the mature cows, the protection of twins resulted in 3-5% more calves, compared to a strategy of no protection. Over a 10-year period, this could result in an increase of 300-500 individuals. With higher harvest rates, even more calves are recruited; however, the population may be- come saturated with twin-bearing cows. The harvest was limited to yearling cows, the only age class that would produce a single calf. Simulations with the 1987 harvest data from Lithuania (Table 3) indicate that moose density would remain stable for the first 5 years and that there would be a constant output of meat (Table 4). Overharvest of cows in the 6.5 age-class, however, results in a female-biased harvest in the sixth year. Moose numbers will decrease insignificantly but provide a higher yield of meat. Simulations with the 1988 harvest data indi- cate that moose numbers will decline 4% in the first 5 years and provide 25 tons of meat annually/1,000 moose. Overharvest of the population will occur later. The harvest quota can be increased up Table 2. Results of protecting cows with twins. Percent of Cows Harvested 5 10 15 20 P1 P3 A B A B A B A B 0.8 0.7 0.33 3.6 0.666 7.2 0.98 10.8 1.32 14.4 0.6 0.65 7.2 1.29 14.4 1.94 21.6 2.58 28.8 0.5 0.95 10.8 1.91 21.6 2.86 32.4 3.81 43.2 0.4 1.25 14.4 2.50 28.8 3.75 43.2 5.00 57.6 0.3 1.54 18.0 3.08 36.0 4.62 54.0 6.15 72.0 0.7 0.6 0.45 5.4 0.90 10.8 1.35 16.2 1.81 21.6 0.5 0.88 10.8 1.77 21.6 2.65 32.4 3.53 43.2 0.4 1.30 16.2 2.59 32.4 3.89 48.6 5.18 64.8 0.3 1.69 21.6 3.38 43.2 5.07 64.8 6.76 86.4 0.6 0.5 0.56 7.2 1.11 14.4 1.67 21.6 2.22 28.8 0.4 1.08 14.4 2.16 28.8 3.24 43.2 4.32 57.6 0.3 1.58 21.6 3.16 43.2 4.74 64.8 6.32 86.4 0.5 0.4 0.64 9.0 1.29 18.0 1.94 27.0 2.58 36.0 0.3 1.25 18.0 2.50 36.0 3.75 54.0 5.00 72.0 MODELING OF MOOSE HUNTING - BALCIASKAS ALCES SUPPL. 2, 2002 26 Table 4. Results of moose population modeling according to the harvest data from Lithuania. According to 1987 data According to 1988 data Year Number Number Harvest Meat Number Number Harvest Meat Alive Born Yield1 Alive Born Yield1 max min max min max min max min 1 517 506 135 121 192 25.3 513 508 131 120 192 25.7 2 519 506 129 117 195 25.5 513 502 126 114 194 25.8 3 517 503 126 116 195 25.5 509 498 123 114 193 25.8 4 511 492 119 110 194 25.4 502 488 117 109 191 25.6 5 502 477 114 103 191 25.2 485 472 105 100 188 25.2 1x 1000 kg. to 10% or more with an increased harvest of yearlings and a reduced harvest of cows. It should be stressed that for successful moose population management using the numeri- cal simulation models, precise knowledge of the sex and age structure of the population is needed. Gathering these data is a high priority for Lithuanian game managers. REFERENCES BALEISIS, P. R., and V. BUTAUTAS. 1987. Ungulate harvest during the 1986–1987 hunting season, data from antler inspec- tions. The Society of Hunters and Fish- ermen, Vilnius, Lithuania. , and . 1988. Ungulate harvest during the 1987–1988 hunting season, data from antler inspections. The Society of Hunters and Fishermen, Vilnius, Lithuania. BALEISIS, R. 1973. Biology and forestation: significance of moose in Lithuania. Dissertation paper No. 29. (In Rus- sian). . 1977. Moose. Moskslas, Vilnius, Lithuania. FILONOV, K.P. 1983. Moose and forest industry. Moscow, Russia. (In Rus- sian). KOZLO, P.G. 1983. Ecological/morphologi- cal analysis of moose population. Sci- ence and Technology. Minsk, Belarus. (In Russian). LOPATIN, V., and S. ROSOLOVSKY. 1990. Mathematical analysis of the efficient exploitation of moose populations. 5th Congress VTO:105–106. (In Russian). SYLVEN, S., M. ASPERS, J.-Å. ERIKSSON, and M. WILHELMSON. 1979. Regulated har- vesting of the moose population — a simulation study. Report 33. Swedish University of Agricultural Sciences, Uppsala, Sweden. Table 3. Moose harvest data from Lithuania (% of quota). Year Age Class 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 1987 32.7 11.5 14.4 13.4 6.8 8.7 4.0 2.1 2.4 1.2 1.7 0.5 0.4 0.1 0.1 – 1988 36.7 11.5 10.3 10.4 6.7 7.8 4.5 3.8 2.9 2.2 2.0 0.5 0.6 0.2 0.2 0.1