Pereyaslovets V., Erdakov L., Hidekel V. Dynamics and long-term cyclic changes in the number of some populations of forest subspecies of the reindeer // Principy èkologii. 2019. № 2. P. 88‒97. DOI: 10.15393/

Issue № 2

Original research


Dynamics and long-term cyclic changes in the number of some populations of forest subspecies of the reindeer

   Vladimir Mikhailovich
Ph.D., State Nature Reserve "Yuganskiy",
   Lev Nikolaevich
D.Sc., Institute of Systematics and Ecology of Animals, Siberian Branch of the Russian Academy of Sciences,
   Vladimir Veniaminovich
State Nature Reserve "Baikalskiy",
forest subspecies
population dynamics
long-term cycle
Summary: The population of the forest subspecies of the reindeer is declining rapidly; its range has divided into several isolated areas. For conservation purposes, a full study of its population characteristics is necessary, with an emphasis on population dynamics. To reveal the cyclical fluctuations in different populations, we used long-term data from the Yugansky, Sayano-Shushensky Baikalsky and Kuznetsky- Alatau nature reserves (zapoveniks) and from the Verkhne-Kondinsky sanctuary (zakaznik).The influence of the anthropogenic factor is excluded due to the strict protection rules in these territories. Besides, we estimated the influence of annual average air temperature and precipitation on the forest reindeer population dynamics in the Yugansky Nature Reserve. In calculations we used spectral analysis software. In all the studied territories except for the Baikalsky Nature Reserve, the populations are gradually and reliably declining. In the Baikalsky Nature Reserve a slight, statistically unreliable increase in the reindeer numbers is noted. In all the examined territories during a sufficient observation period of at least 20–30 years, the reindeer populations demonstrate power-dominant 15–20 year cyclic fluctuations. In the mid-frequency range, we revealed low-power 5- and 7-year cycles. In the high-frequency range (2–4 years), stable cycles are observed in all territories. In the Yugansky Nature Reserve, the correlation between the reindeer population dynamics cycling and precipitation and air temperatures was revealed. For each harmonic component of the population cycling, there are corresponding harmonics of these climatic parameters similar in period value. The most accurate adjustment is observed to the average annual precipitation values, which probably play a more significant role in the life of these ruminants compared to average annual temperatures.

© Petrozavodsk State University

Received on: 19 March 2019
Published on: 11 October 2019


Wild reindeer (Rangifer tarandus L., 1758) is one of the most important ungulate species that inhabits in the Northern regions of the Russian Federation. Quite prosperous in the past, this species is currently experiencing a huge anthropogenic load, which has a very negative impact on the state of its populations, some of them are on the verge of elimination. Forest subspecies of reindeer were particularly vulnerable. Currently, most of them are listed in the Red books of various levels. Reindeer are protected in the Republics of Karelia, Komi, Buryatia and Tyva, in the Khanty-Mansi, Nenets and Yamalo-Nenets Autonomous districts, in the Krasnoyarsk territory, in Omsk, Kemerovo, Irkutsk and other regions (Красная книга РФ, 2001). In recent years, some growth in its population was noted several regions, in particular on the territory of Khanty-Mansi Autonomous district (KHMAD) – Yugra in the area of the Yugan reserve. Reserves and wildlife refuges have made a significant contribution to the conservation process of this species due to the special regime. Reindeer that live on their territory are protected from human impact and can exist within the course of natural processes. Therefore, it is of great interest to determine the ecological and biological characteristics of such populations, among which the populational dynamics is one of the most significant.

We found it interesting to compare the cyclical dynamics of the number of reindeer in specially protected natural areas (SPNA) located in different parts of its range. Within the plain taiga the Verkhne-Kondinsky wildlife refug (241.6 thousand ha) and the Yugansk reserve (648.6 thousand ha) lies, in the mountain taiga zone the Sayano-Shushensky (390.4 thousand ha), Baikal (165.7 thousand ha) and Kuznetsky Alatau reserves (401.8 thousand ha) exists.

Verkhne-Kondinsky wildlife refug and Yugansk reserve are located on the territory of KHMAD-Yugra. The reindeer that lives on their territory belongs to a small subspecies – the forest reindeer (Rangifer tarandus fennicus Lonnberg, 1909) (KK KHMAD, 2013). The population of reindeer in KHMAD has experienced the strongest anthropogenic impact over the past 50 years. If in the second half of the 1960s its population was 15.5-16.5 thousand individuals, then by 2006 it had fallen to the critical level of 310 individuals (Новиков, 2011). The distribution of reindeer is focal. The rapid development of the oil and gas industry has caused large-scale destruction of its habitats. The influx of population has stimulated the rapid growth of poaching, which is the main limiting factor for this species. Because of the forests that were damaged by logging and fires, the food supply has significantly decreased. The Kondinsky forests were particularly affected – in the 1960s and 1970s, the area of cuttings in them was 81% of all cuttings in the KHMAD (Волков, Ларин, 2007). The territory of the Yugan reserve (before it became the reserve) was transformed to a much lesser extent. Due to environmental measures, the rate of decline in the number of reindeer has slowed down in the last decade (Переясловец, Стариков, 2016), and in some areas of Yugra, it has even registered a small increase.

The Siberian forest reindeer (Rangifer tarandus Valentinae Flerov, 1933) lives in the Altai-Sayan region (in the Kuznetsky Alatau and Sayano-Shushensky nature reserves). The history of its population almost coincides with the history of the forest reindeer population in KHMAD-Ugra. By the middle of the XX century, its range in this region was continuous, and its population reached high values (Соколов, 1975, 1983). In the future, the population declined sharply, and the range split into isolated areas. Today, the Altai-Sayan population of forest reindeer is included in the Red books of the Federal and regional levels. The situation has improved with the organization of several reserves, and there is a tendency to restore the population (Бондарь, 2015).

The purpose of this work is to study the cyclical nature of the long-term dynamics of the number of forest reindeer. The tasks were:

- to calculate the parameters of the spectra of the cycling number;

- to determine the parameters of the periodic components of long-term population dynamics;

- to find out possible external synchronizers that give stability to fluctuations in the number of forest reindeer.


The data of long-term (in most reserves) accounts of the number of reindeer were used as material. In the Yugan reserve and Verkhne-Kondinsky wildlife refug, the number of reindeers was determined basing on the results of winter route surveys (Приклонский, 1973; Кузякин, 1979), conducted annually in February and March. In the Yugan nature reserve, 6832.4 km was covered with counting routes records for 1988-2018. To assess the relationship between the climatic parameters of the habitat (average annual precipitation and average annual air temperature) and dynamics of the number of reindeer in the Yugansk nature reserve, the data from the “Ugut” weather station, located 25 km from its border, were used. In the Verkhne-Kondinsky wildlife refug during 1971-2010, 10,631 km were covered with records (Воробьев, 2015).

In the mountain reserves of the Altai-Sayan region, the method of visual recording of reindeer was used as the main method (Новиков, 1954; Насимович, 1963). The stock of the species in the protected area was calculated annually (Васильченко и др., 2008). The longest series of observations (1988-2008) was carried out in the Sayano-Shushensky reserve, in the Kuznetsky Alatau reserve, it is much smaller (2002-2008). Data on the number of reindeer in the Baikal reserve was collected by V. V. Hidekel, who personally conducted accounting work during 2012-2017.


To detect latent fluctuations in population numbers, a fast Fourier analysis was used. The empirically determined count parameters – the summation step, the length of the autocorrelation function, the shape and width of the correlation window. Calculations were performed using standard methods (Ердаков, 2011; Телепнев, Ердаков, 2014). The counting programs owned by Institute of Systematics and Ecology of Animals of the Siberian Branch of the RAS were used. The power spectral density was estimated using the Welch method (Марпл-мл., 1990).

For trends, we tested the hypothesis about the difference of the coefficients from zero and calculated the coefficient of determination R2. The obtained values were reflected in the text only if the null hypothesis about the equality of both regression coefficients to zero was discarded. Otherwise, linear regression was excluded from the process model. We used the WebPlotDigitizer program to digitize graphs. For statistical calculations, we used the Past software package.


Some statistical characteristics give a general idea of the state of forest reindeer populations in each area of the study (table. 1). It is difficult to measure the average numbers because of differences in accounting methods, but these geographical populations are quite comparable in terms of the range of variation. The comparison of the gradual change in their average number from year to year is also quite objective. The latter characterizes their polynomial trend.


Table 1. Statistical characteristics of parameters of long-term dynamics of the number of forest reindeer on the territory of various protected areas

SPNA n, years

Number M ± m, ind.


CV, %


Yugan reserve 31 184.3 ± 34.80 193.73 105.12 217.591 – 2.222 * t;

σ > 0.05

Verkhne-Kondinsky wildlife refug

40 152 ± 31.39 198.54 130.62 402.120 – 12.827 * t

R2 = 0.570; σ ≤ 0.01

Sayano-Shushensky reserve 21 47.62 ± 5.03 23.04 48.38 81.158 – 3.354 * t
R2 = 0.816; σ ≤ 0.01

Kuznetsky Alatau reserve

5 85.8 ± 18.13 40.53 44.24 84.400 – 16.00 * t;

σ > 0.05

Baikal reserve 6 23 ± 1.81 4.43 19.26 4.567 + 0.085 * t;

σ > 0.05

Note. n – is the number of years under consideration, M – mean, m – error of mean, σ – standard deviation, CV – coefficient of variation, R2 – coefficient of determination.


For the SPNA with the longest series of observations, we calculated chronograms of the reindeer population number dynamics (figure), which allow us to estimate approximately possible multi-year cycles, as well as to compare the synchronicity of changes in the number of reindeer in the general period of time (1988-2011). 



Chronogram of the population number (I) and spectra of its long-term fluctuations (II) in the reindeer (Rangifer tarandus): a – Yugansky Reserve, b – Verkhne-Kondinsky wildlife refug, c – Sayano-Shushensky Reserve (I – X-axis – Time, year; Y-axis – number, individuals; II – X-axis – Period, year; Y-axis – Power,


The chronogram data was transferred to the time scale (II) and thus the hidden periodic components of the reindeer population course were estimated, which allows us to compare visually the totality of long-term cycles in different populations. To clarify the spectral estimates of the dynamics of the number in reindeer on protected areas, their characteristics are summarized in the table 2. This allows to compare periodic components that are not only dominant in power, but also weakly displayed in graphic images.


Table 2. The ratio of the size and power of the periodic components of long-term population dynamics in different populations of forest reindeer 

SPNA Period, years








Baikal reserve - - - - - 3.0 0.507 - -
Kuznetsky Alatau reserve

- - - - - 3.2 43.51 - -
Verkhne-Kondinsky wildlife refug

20.9 74.89 - 7.4 18.28 - 4.7 20.09 3.5 12.32 2.8 8.66 2.3 5.15
Sayano-Shushensky reserve 17.4 6.43 - 7.6 2.40 5.5 1.60 4.2 1.29 3.4 0.84 2.8 0.87 -
Yugan reserve 28.4 51.67 - 7.0 25.23 5.2 44.35 4.1 51.99 2.9 43.72 2.4 44.82 2.2 23.31


15.3 31.39 - - 5.9 24.92 - 3.7 26.81 2.8 30.56 2.4 15.01

16.5 0.142 - 7.2 0.173 - 4.0 0.26 - 2.9 0.129 -

Note. Weather characteristics are given only for the Yugan reserve; in the lines, the upper digit is the period, years; the lower one is the power (amplitude).


In the Baikal reserve, a small but statistically unreliable positive population trend was noted. Perhaps the reindeer herd in this reserve is growing slowly. However, despite the special regime that excludes the influence of anthropogenic factors, the number of forest reindeer in most SPNA (during the observation period) gradually and reliably decreases. A similar pattern is observed in a large part of its range. So, in the Arkhangelsk region, the number of forest reindeers (primarily due to mass poaching using snowmobiles) began to decline rapidly from the late 1980s. By the beginning of the XXI century, the habitat of forest reindeer in this region again acquired a focal character (Мамонтов, Ефимов, 2011). In the last five years this species has almostly disappeared in the Eastern regions of Karelia (Панченко, Блюдник, 2009). The Yakut population of forest reindeer is in a similar state, which under the influence of anthropogenic influence (poaching, development of mineral deposits, forest fires and transformation of habitats of the species) has significantly reduced its number (Мордосов, Кривошапкин, 2008). For herbivorous mammals such as reindeer, changes in vegetation cover as a result of anthropogenic impacts or climate changes, accompanied by changes in the forage quality of vegetation, are always accompanied by fluctuations (pulsation) in the boundaries and number of the populations (Абатуров, 2005).

The average long-term number of reindeer in the SPNA under consideration differs significantly due to the low number of species in the reserves of the Altai-Sayan region (ASR). However, this does not prevent comparison of statistical parameters of different populations. In KHMAD-Yugra the number of reindeer has a significant range of variation, whereas in the ASR this indicator is relatively stable.  

Long-term population dynamics often represent on the chronogram (see figure, Ia) a complex sawtooth curve, and many cyclical fluctuations can be determined by the distances between maxima or minima. Such a chronogram can be like a smoothed trajectory, but even then it will show at least small local peaks (see figure, Ib, c). In order to establish them more accurately, it is necessary to present the accounting data not on the time scale, but on the frequency scale. Then the resulting spectrum of oscillations will show their value and the ratio of their powers (see figure, IIb).

Visually, on the spectrum of the dynamics of the number of reindeer in the Yugan reserve (see figure, IIA), ~2-3-year fluctuations are clearly visible, then (close to it) ~4 - and ~6-year fluctuations (see figure, IIA). Of the low-frequency oscillations, ~10-20-year and 30-year periodic components are shown on the spectrum. The range of fluctuations in the number of reindeer from the Verkhne-Kondinsky wildlife refug (see figure, IIb) has an absolutely dominant ~20-30-year fluctuation in power. Its peak with a very wide base seems to mask several low-frequency cycles. All other cycles, and they are also present on the spectrum, are insignificant in power, and many of them coincide with the period of fluctuations recorded in the Yugan reserve (see figure, IIA), which makes the dynamics of the number of reindeer in these areas quite comparable. The dynamics of the number of reindeer in the Sayano-Shushensky reserve almost repeats that of the Verkhne-Kondinsky wildlife refug (see figure, IIS). Here the low-frequency rhythm absolutely dominates in power too, but some peaks are also shown in the middle frequencies.

To clarify the picture, some parameters of the detected oscillations were calculated (see table. 2). The dynamics of the number of reindeer in the Yugan reserve showed several periodic components. In the band of high (2-4-year) frequencies, 2.1, 3.6 and 4.1-year fluctuations are noted (in descending order of power). There are quite significant power cycles in the middle (5-6-year) frequencies. In the low (10-17-year) frequencies of the spectrum, the periodic components are insignificant in power, but then (in 20-30-year frequencies) this indicator increases significantly and becomes dominant.

In the Yugan nature reserve and Verkhne-Kondinsky wildlife refug located in the same region, the spectral characteristics of the cyclical dynamics of the reindeer population coincide in most frequency bands of the spectrum (see table. 2). The most accurate coincidence of rhythms is observed in the middle frequency band (7.4-year cycle), as well as in high frequencies (2-to 5-year cycles). The peculiarities of the dynamics of population number spectra for these territories are also shown. They are expressed both in mismatches of the same density fluctuations in power, and in the manifestation of some fluctuations. Thus, in the Yugan reserve there are ~10 - and 5.5-year rhythms that are not recorded for the wildlife refug (see table. 2).

The range of fluctuations in the number of reindeer in the Sayano-Shushensky reserve is close to that in the Verkhne-Kondinsky wildlife refug, both in terms of the set of harmonic components and the ratio of their power (see figure, IIb, c; table. 2). In both territories the low-frequency fluctuations, approximately 20-year, dominated, the next by power ~7-year cycle. In addition, the harmonic components in high frequencies are almost identical. And this is despite there is a noticeable difference in the territories both in latitude and lie of the ground.

In terms of population size and variability, the groups of reindeer in the Sayano-Shushensky and Kuznetsky Alatau reserves are similar. The insignificant duration of observations in the "Baikal" and "Kuznetsky Alatau" reserves allowed us to identify confidently only one cycle is a 3-year cycle (see table. 2).

Fluctuations in the number of reindeer can be influenced by weather factors. For example, for the Yugansk reserve, when analyzing data by using the non-parametric methods, significant correlation coefficients between the number of forest reindeer and the weather (precipitation and air temperature) were not detected. We found a weak positive relationship between the number of reindeer and the average annual air temperature (r = 0.30895; P0.05 = 0.388, P0.01 = 0.496) and a weak negative relationship between the number of reindeer and the amount of precipitation (r = -0.12888, P0.05 = 0.388, P0.01 = 0.496). However, the analysis of hidden harmonic components of fluctuations of these parameters showed that fluctuations in the number of reindeer can maintain their stability by synchronizing with similar weather rhythms. In the Yugansk reserve, such synchronization is in good agreement with the temperature rhythms in each frequency band. In addition, fluctuations in the number of reindeer are particularly successful in synchronizing with fluctuations in the average annual precipitation. Almost all precipitation rhythms have a corresponding close cycle with fluctuations in the number of species (see table. 2). This is not surprising, paying attention to that in this area most of the year precipitation falls in the form of snow. The depth of the snow cover in winter plays an important role in the life of the reindeer. Energy costs for the movement of these ungulates, and, in part, for the extraction of food by them, depend on it. Forage and weather conditions significantly affect the state of the population of wild reindeer (Колпащников, 2000). Severe and snowy winters, combined with a high anxiety factor, can cause death or severe exhaustion of animals, which negatively affects the breeding process.


The course of long-term populational dynamics in forest reindeer populations is described by an irregular curve. This picture of population dynamics is due to many periodic components that are present in it.

For long-term cycling of the number of reindeer in all the considered territories, with sufficient duration of observations (20 years or more), dominant 20-30-year cycles of the population number are characteristic. In the middle frequencies, low-powered 5-and 7-year fluctuations are shown. In addition, in all examined cases, stable cycles are recorded in the band of high (2-4-year) frequencies.

Fluctuations in the number of forest reindeer can be synchronized with the periodic components of the climate in the habitat region. In the Yugansk Reserve, for each harmonic component of the population cycle of the reindeer, there are corresponding, close in value of the period, harmonics of climatic parameters. The most accurate synchronization occurs with the cycle of average annual precipitation, which may have a greater significance in the life of this ungulate species, than the cycle of average annual temperatures.


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