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ALCES SUPPL. 2, 2002 LOPATIN AND ROSOLOVSKY –  LESLIE MATRIX ANALYSES

77

EVALUATION OF THE STATE AND PRODUCTIVITY OF MOOSE

POPULATIONS USING LESLIE MATRIX ANALYSES

V. N. Lopatin and S. V. Rosolovsky

Institute of Evolutionary Animal Morphology and Ecology, Russian Academy of Science, 117071,

Moscow, Russia

ABSTRACT: We examined the use of a Leslie Matrix analysis for estimating moose (Alces alces)
population parameters and allowable harvests from a moose population near Leningrad, Russia,

during 1959 – 1975.  Leslie Matrix analysis indicated that moose fecundity and mortality exhibited

cyclic fluctuations.

ALCES SUPPLEMENT 2: 77-80 (2002)

Key words: Alces, fecundity, harvests, Leningrad, Leslie Matrix, mortality, populations, produc-
tivity

Evaluation of population status is a tra-

ditional problem of modern ecology.  Closely

associated with it are the practical problems

of determining management strategy.  Many

population models have been used to mimic

populations, but the question remains if these

models are representative of nature.  Many

quantitative methods have been used, but

solution of many mathematical and ecologi-

cal problems necessitates expansion of the

traditional methods of examining ecological

problems (Watt 1971, Jeffers 1981).

One method of expressing population

dynamics is through the use of a Leslie

Matrix model (Leslie 1945), which consid-

ers age–specific birth and survival rates.

Rusakov (1979) used a Leslie Matrix model

to examine a moose population in north-

western Russia.  Also, Peterson (1977)

used a Leslie Matrix model to examine

moose populations on Isle Royale, Michi-

gan, USA.  Based on these and similar

analyses (Aivazyan 1968, Pesaran and Slater

1984), we refined these methods for this

study as provided by Lopatin and Rosolovsky

(1988).  These modifications result in rates

of fecundity and mortality of individuals

dependent on changes in density.  For ex-

ample, knowing the fecundity and death

rate, one can determine the relative change

in numbers over time and can estimate

death rate.  The purpose of this paper is to

examine the dynamics of a moose popula-

tion near Leningrad, Russia for the period

1959 – 1975.

METHODS

We used a Leslie Matrix analysis to

examine moose population fluctuations

within the Leningrad Region, Russia, during

1959 – 1975 (Rusakov 1979).  Under natu-

ral conditions, fecundity rate is often diffi-

cult to obtain under field conditions.  Often,

field managers use the average number of

calves per cow as an estimate of fecundity

rate.  These ratios can be represented as

number of calves per female (X axis) and

death rate (Fig. 1).  This indicates that

population numbers are more sensitive to

changes in death rate than fecundity.  If the

numbers of calves per female and total

number in the moose population are deter-

mined accurately, equations derived from

Fig. 1 can be helpful in managing the moose

population.







LESLIE MATRIX ANALYSES – LOPATIN AND ROSOLOVSKY ALCES SUPPL. 2, 2002

80

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PESARAN, M., and L. SLATER.  1984.  Dy-

namic regressions: theory and algo-

rithms.  Finances and statistics.  Mos-

cow, Russia.  (In Russian).

PETERSON, R. O.  1977.  Wolf ecology and

prey relationships on Isle Royale.  U.S.

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graph 11:1–200.

RUSAKOV, O. S.  1979.  Moose.  Pages 174–

271 in Ungulates in northwestern USSR.
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sian).

SMITH, D. M.  1975.  Models in Ecology.

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WATT, C. W.  1971.  Ecology and manage-

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