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ALCES SUPPL. 2, 2002  BALCIASKAS - MODELING OF MOOSE HUNTING

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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unpublished data), I assumed that individual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

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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

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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

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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