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An Individual-Based Model of the Population Dynamics of the Arctic Fox (Vulpes lagopus semenovi) on Mednyi Island, Commander Islands, North Pacific

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Abstract

We have developed a spatially explicit individual-based model that imitates the population dynamics of the Arctic fox on Mednyi Island. In the Red Data Book of the Russian Federation, the Mednyi Arctic fox is listed as an endangered species. The model developed is based on data collected over 19 years of fieldwork. Annual marking of cubs in the study area allowed us to identify up to 80% of animals individually and to collect their life-history data. As a result, we identified the mortality rates of males and females of all age groups, the probabilities of breeding, litter sizes, the sex ratios of animals in different age groups, social structures, dispersion distances, and the patterns of making decisions in the selection of social partners and habitat patches. The model is spatially explicit, i.e., the heterogeneity of the habitat patches is defined in explicit form. The model works with a time step of one year. In simulations, demographic parameters such as population dynamics, population age structure, sex ratio in different age groups, and the structure and size of families conformed to the empirical data. An analysis of the model sensitivity to variations in mortality rates in different age groups showed that the sensitivity to shifts in cub mortality is much higher compared to adults of all age groups. Through increasing the cub mortality rate to 95% over a period of one to five years, we simulated the effect of the otodectic mange epizootic, which was observed in a real population of the Mednyi Arctic fox. The population recovery time after the end of the impact in the simulation was significantly longer compared to field data. We suggest that, in reality, with a low population size, the productivity of the population increases. This feedback that accelerates population recovery has not yet been introduced into the model. In conclusion, we discuss advantages of the individual-based modeling based on long-term field studies.

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Notes

  1. Most of the individual-based models of animal populations developed in recent decades are spatially explicit (spatially explicit models, Carter et al., 2015; Stenglein et al., 2015; Watkins et al., 2015). This is natural since modern data recording and processing technologies allow us to model the use of spaces and take into account biological processes that depend on space, for example, the landscape distribution of resources. Read more about the features of these models, for example, DeAngelis and Yurek, 2017).

  2. AnyLogic 7.0.2. The AnyLogic Company (former XJ Technologies). For more details: http://www.anylogic.com.

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ACKNOWLEDGMENTS

The authors are grateful to all the staff and students of Moscow State University who participated in the collection of field data: N.A. Bocharova, E.L. Dzhikiya, O.A. Filatova, E.S. Gerke, D.M. Glazov, A.M. Goltsman, O.A. Khoroshutina, Yu.I. Mikhnevich, O.G. Nanova, A.I. Ploshnitsa, A.A. Raspopova, L.V. Sagatelova-Pokrovskaya, S.N. Sergeev, A.N. Shienok, I.A. Volodin, E.S. Vorob’eva, and A.V. Zimenko. During editing of the manuscript, the remarks of N.A. Formozov and the anonymous reviewer proved to be very useful.

Funding

The data collection underlying the model was funded in different years by the Faculty of Biology, Moscow State University, the Abolits Fund of Actual Biology, INTAS, the MacArthur Foundation, Fauna and Flora Preservation Society, the Peoples’ Trust for Endangered Species and Task Force (UK), the Russian Foundation for Basic Research, and the Commander Islands State Nature Biosphere Reserve.

Author information

Authors and Affiliations

  1. Faculty of Biology, Moscow State University, 119234, Moscow, Russia

    M. E. Goltsman, L. Doronina & E. P. Kruchenkova

  2. Laboratory of Computer Modeling of Socio-Economical Processes, Central Economics and Mathematics Institute, Russian Academy of Sciences, 117418, Moscow, Russia

    E. D. Sushko

  3. Institute of Experimental Pathology, ZMBE, University of Münster, 48149, Münster, Germany

    L. Doronina

Authors
  1. M. E. Goltsman
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  2. E. D. Sushko
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  3. L. Doronina
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  4. E. P. Kruchenkova
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Corresponding authors

Correspondence to M. E. Goltsman, E. D. Sushko, L. Doronina or E. P. Kruchenkova.

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The authors declare that they have no conflict of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.

Additional information

Translated by N. Smolina

Appendices

APPENDIX 1

Model parameters

Parameter category

Parameter

Parameter value

Remarks

Source

Time

Simulation time step

1 year

All processes and events occurring at time intervals of less than a year are reflected only in abrupt changes in the values of variables when transiting from one step to another

 

Individual

Identification number

Code

 

Year and place of birth

Birth year and natal den code

Calculated in the course of the work of the model. In the starting state, they are based on empirical data of a long-term field study on Mednyi

Database of long-term field studies on Mednyi Island, L. Doronina

Sex

Male/female

Same

Age

From 0 at birth, and growing 1 year with each step

Same

Kin relationships

Collection of relatives: parents, brothers, and sisters, partners in the group

Same

Sites

Location identification

Identification code

 

Resource value

Whole number from 0 to 3 points (minimum 0, maximum 3)

Abundance of food resources on the site estimated by the size of seabird colonies

Goltsman et al., 2005, 2010

Presence of a den

Parameter equaling 0 (absence of a den) or 1 (presence of a den)

 

Database of long-term field studies on Mednyi Island

Distances to other sites

km

Based on GIS data

Breeding dens

Location identification

Identification code

Den/shelter of an Arctic fox that had at least once been occupied by a breeding pair over the 20-year period

Inhabitants

Collection (list) of the den inhabitants at a given step

Calculated on the basis of prognosis data in the course of the work of the model. In the starting state, based on empirical data of a long-term field study on Mednyi Island

Database of long-term field studies on Mednyi Island, L. Doronina

Life-history parameters

Mortality of males

From 0 to 1

Probability of male death in this age group

0-year-old male cubs

0.593

1 year old

0.470

2 years old

0.320

3 years old

0.350

4 years old

0.780

5 years old

0.780

 

6 years old

0.780

  

7 years old

0.780

8 years old

1

Female mortality1

From 0 to 1

Probability of female death in this age group

0-year-old female cubs

0.640

1 year old

0.164

2 years old

0.243

3 years old

0.304

4 years old

0.400

5 years old

0.636

6 years old

0.750

7 years old

0.750

8 years old

1

Participation of males in breeding

From 0 to 1

Probability of male reproduction in this age group

1-year-old males

0.183

2 years old

0.611

3 years old

0.630

4 years old

0.636

5 years old

0.330

6 years old

0.330

7 years old

0.000

8 years old

0.000

Participation of females in breeding

 

Probability of female reproduction in this age group

0 years old

0.000

1 years old

0.070

2 years old

0.480

3 years old

0.580

4 years old

0.560

5 years old

0.530

6 years old

0.800

7 years old

0.000

8 years old

0.000

 

Litter size

Whole number ≥0

Number of cubs in a litter. For the starting year, it corresponds to empirical data. Further, calculated on the basis of empirical distribution of probabilities of different size litters

Goltsman et al., 2005b

Sex ratio

From 0 to 1, ratio of males to the total number of animals

Ratio of males to the total number of animals. For the starting year, it corresponds to empirical data. Further, calculated

Database of long-term field studies on Mednyi Island 

Sex ratio in the litter

From 0 to 1, ratio of males to the total number of cubs

Ratio of males in a litter. For the starting year, it corresponds to empirical data. Further, calculated on the basis of the basic sex ratio 1 : 1 with correction depending on the resource value of the sites

Movements of agents

Choice of the habitation site (home range) in this year

Code of the new site in case of changing it or switching to a nomadic way of life

Probability of home range change for the Arctic foxes of different age and sex is the result of the work of a separate subprogram, implementing the algorithm of selection of a home range from the available collection of vacancies by the Arctic fox. The algorithm (see Model work scheme, paragraphs 10 and 11) is based on empirical data

Goltsman et al., 2005a

  1. 11The mortality rates used for different age classes are derived from empirical data. However, if the calculation of mortality does not use corrections for migration processes, i.e., leaving the study area equates to death, the death rates will be overestimated. The values of the error will be different in different age and sex groups, depending on the mobility of the animals in this group. Therefore, the mortality rates, which in this work were considered as “basic,” were calculated from empirical data with the introduction of corrections. The calculation of the corrections was based on two assumptions: (1) the number of animals that left the island’s investigated area (southern half of the island) is equal to the number of arrivals. This assumption is justified by the fact that the number of Arctic foxes during the study period was stable. (2) The ratio of ages among animals that left the study area and then returned after a year’s absence is the same as among those who left and did not return. That is, the tendency to return does not depend on age. This last assumption may be wrong, but until we obtain more accurate data, we accept it. For the entire period of observations on the studied part of the island, there were 33 females (20 yearlings, 6 two-year-olds, 5 three-year-olds, and 2 four-year-olds) and 15 males (13 yearlings, 1 two-year-old, and 1 three-year-old). Proceeding from this, untagged females and males that came to the studied part of the island were distributed by age in the same ratio. This correction has no effect on the structure of the model and the decision-making algorithms.

APPENDIX 2

Model interface

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Goltsman, M.E., Sushko, E.D., Doronina, L. et al. An Individual-Based Model of the Population Dynamics of the Arctic Fox (Vulpes lagopus semenovi) on Mednyi Island, Commander Islands, North Pacific. Biol Bull Russ Acad Sci 46, 929–945 (2019). https://doi.org/10.1134/S106235901908003X

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