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Discrete Dynamic Model of Community of Species Sus Scrofa L Cubs In The Aviary





Introduction

Global warming, along with other problems, raises the issue of evolving changes in the habitation of animals. Consequently, there are changes in structural relations between communities. Thus, the investigation requires a systematic approach, along with an appropriate method of mathematical modeling. Currently, there are a wide range of such developed methods, specifically a method which describes the relations between the structure and the stability of biological systems [1]. These are special case of similar relations in multi-agent systems of different nature. Stating, agents and agent systems are particular sets of objects of arbitrary nature.
The Method of Discrete Modeling of Dynamic Systems with Feedback (DMDS), developed at the V.N. Karazin Kharkiv National University [2] permits the findings of the most probable structure between-agent and intra-agent relations in multi-agent systems of different nature. Stating, all possible, in principle, types between-agent relations: "plus-plus", "minus-minus", "minus-plus", "minus-zero", "plus-zero", and "zero-zero". The intra-agent relations are of three types: "plus-plus", "minus-minus", and "zero-zero".
DMDS has lead to the creation of sufficiently effective models of various biological objects, such as a system of antioxidant protection of organisms [2] and the population dynamics for various Crimean population of mollusks Rapana sp. [3]. The systemic aspects of territorial behavior of animals are significantly informative in the analysis of nature in relation to their communities [5, 6]. For this analysis, there exist a wide range of methods for investigation of territorial behavior of animals. However, the extreme climate changes may require an expansion of this range and new methods developed, stating how quickly less labor-intensive methods focus on modern informational and other knowledge-intensive, e.g. aerospace technology. In our paper, the use of DMDS for development of relatively simple quick methods for investigation of spatial animal behavior is proposed.
The first step in a model of relations in reference to stabilized animal community was built by DMDS. As a reference community, we used a community of Sus scrofa L. cubs (non-pedigreed pigs) in the aviary at the Kharkiv Zoo. In this case, the agents are the numbers of animal groups, localized on different parts of the aviary; the parts differ by localization of sources of the stimulus (in our study, food). For example, relation "plus-minus" indicates that a large size of one group leads to decreasing size of the other one and vice versa, a small size of one group would cause an increasing size of the other. During the investigation, the structure of the relation in this community was revealed.

Structure Identification

The localization of animals was investigated with the assistance of digital imaging, made at one minute intervals during a thirty two minute span. Animals were divided into three groups as follows:
- Animals, which eat food from a trough (Gr. I).
- Animals near a trough, which are ready to begin eating as soon as free space appears (Gr. II).
- Animals, not included in the first and the second group. Animals situated at a greater distance from a trough than animals of the first and second group (Gr. III).
Using Pearsonfs correlation coefficient between the sizes of groups, we identified the structure of relations between these groups by DMDS. Negative feedbacks were revealed from this structure, and specifically these feedbacks are responsible for the homeostasis of the systems according to known concepts [7].

Results

DMDS modeling revealed three most probable variants of the structure relations between the three groups. In all three variants, there are intra-agent relations of type "minus-minus" (in all variants for Gr. I and III, in two variants for Gr. II). According to these relations, the sizes of groups cannot take a critical high or low value. The nature of between-agent relations in all three variants are consistent with the absence of mutual avoidance of animals, observed in the aviary for a long period of time and with the antagonistic relationship between them. All negative relations between-agent affects are consistent with the pattern of animal movement: hungry pigs move to a trough and after eating away from a trough.

Result review

The variation of relations, obtained by DMDS for the community of species Sus scrofa L. cubs (chosen as a reference), which have a stable, lasting relationship, which are consistent with the biological and ethological sense of observed state in the aviary. An important role of intra-agent relations of type "minus-minus" under the absence of between-agent relations of this type is consistent with the known proposition [1] concerning the prevalence of intra specific competition in stable biological systems, as well as the results of numerical experiments, presenting great stability of systems in which the intra-agent competition is more difficult than between-agent one, compared with the systems for which the strength of both these types of competition is high enough [8]. The methods used for material gathering made it somewhat difficult to observe data and did not take into account several important ethological aspects. Subsequently, this approach for building models of territorial animal behavior by DMDS modeling allows for decreased requirements to data precision and therefore, can be used in combination with effective modern methods of gathering actual zoological and environmental data ( e.g., aerospace). We can make the following tentative conclusion.

Conclusion

1. The discrete modeling of dynamic system of relations between animal group sizes, situated in different positions during feeding, allows identifying a number of systemic factors that determine the nature of territorial animal behavior. 2. The systemic factor identified by DMDS, which determine stable territorial animal behavior, is prevalent of intra-group relations of type "minus-minus" and relatively weak between-group negative relations.
3. The use of DMDS for identifying systemic factors can decrease requirements to data precision of zoological and environmental materials. As a result, this opens the prospect for new applications for aerospace remote sensing methods for environmental information gathering.

References

[1] Kokkoris G. D., Jansen V. A. A., Loreau M., Troumbis A. Y. Variability in interaction strength and implications for biodiversity. Journal of Animal Ecology (2002), 71. - P. 362-371.
[2] Bespalov Yu. G, Derecha L. N, Zholtkevych G. N, Nosov K.V. Discrete model of the system with negative feedback // Review of V. N. Karazin Kharkiv National University, Ser. Matematical Modeling. Infirmation technologies. automatic control system. # 833, 2008. - P. 27-38.
[3] Bespalov Yu. G, Zholtkevych G. N, Nosov K.V., Marchenko V. S., Marchenko G. P., Utevsky A. Yu. Geolibiology effects investigation with the help of discrete model of dynamic systems with feedback. VIII International Gamow Summer Astronomic School "Astronomy on the joint of sciences: astrophysics, cosmology, radioastronomy, astrobiology". - Reports. - Odessa (Ukraine), August 18-23 2008. - P. 12 - 13.
[4] Hardin G. The cybernetics of competition: a biologist's view of society, Persp. Biol. Med. (1963), 7. - P. 58-84.
[5] Goodenough, J., McGuire, B., & Wallace, R.A. (1993). Perspectives on animal behavior. N.Y.: John Wiley & Sons.
[6] Slater, P.J.B. (1990). An introduction to ethology. Cambridge: Cambridge University Press.
[7] Homeostasis: Origins of the Concept. Langley, National Library of Medicine (1973). Langley, L. L. (Ed.). Stroudsburg, PA: Dowden Hutchinson, and Ross Inc.
[8] Laboratory of adaptive mechanisms modeling, School of Biology, V. N. Karazin Kharkiv National University. http://www-mam.univer.kharkov.ua/eng.
About Author Zholtkevych G. N., Nosov K. V., Bespalov Yu. G., Grigoryev A.Yu., Bondarenko I.V. :

Zholtkevych G. N., Ph.D. in Mathematics, D.Sc. in Engineering, professor*
Nosov K. V., Ph.D. in Mathematics, research scientist*
Bespalov Yu. G., MS in Biology, senior research scientist*
Grigoryev A. Yu., Ph. D. in Veterinary Medicine, professor, Director of Kharkiv Zoo**
Bondarenko I. V., MS in Veterinary, Department Head of Kharkiv Zoo**

* V. N. Karazin Kharkiv National University (Kharkiv, Ukraine)
** Kharkiv Zoo (Kharkiv, Ukraine)


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