# Using Data-Compressors for Classification Hunting Behavioral Sequences in Rodents as “Ethological Texts”

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## Abstract

**:**

## 1. Introduction

## 2. The Suggested Method

_{0}= {the behavioral sequences are generated by a single source} and the alternative hypotheses H

_{1}= {the behavioral sequences are generated by different sources}. We stored sequences of symbols (each corresponded to the performed behavioral element) into the text files (txt) (say, X, Y, Z). All species were compared with each other in pairs. Our task is to answer the question of how close these sources are to each other. To do this, first, we divide each source text file approximately in half. Suppose we are dealing with three sources. The first half we denote by X*, Y*, and Z*. We divide the second halves into fragments of the same size, for example, 120 bytes and designate them x

_{1}, x

_{2}… x

_{n}; y

_{1}, y

_{2}… y

_{n}and z

_{1}, z

_{2}… z

_{n}. In our example, let “n” be equal to 9, and thus, there will be 27 such sample files. Then we individually add each resulting fragment (x

_{i}, y

_{i}, z

_{i}) to the first halves (X*, Y* and Z*). We thus obtain 81 augmented text files (X*x

_{i}, X*y

_{i}, X*z

_{i}, Y*x

_{i}, Y*y

_{i}, Y*z

_{i}and etc). All files obtained, including the first halves of the source files X*, Y* and Z*, are separately archived. Then each pair (X, Y), (X, Z), and (Y, Z) is examined separately and the association coefficient is determined for each one. Let us consider the pair (X, Y) as an example. We then obtained the differences between the volumes of archives source files and the augmented files (let us denote this difference as Δ; Δ(X*y

_{i}) = ϕ(X*y

_{i}) − ϕ(X*)), the example: ϕ(X*y

_{1}) – ϕ(X*) = 59 b and ϕ(Y*y

_{1}) − ϕ(Y*) = 41 b; ϕ(X*y

_{2}) − ϕ(X*) = 69 b, and ϕ(Y*y

_{2}) − ϕ(Y*) = 46 b; ϕ(X*y

_{3}) − ϕ(X*) = 71 b, and ϕ(Y*y

_{3}) − ϕ(Y*) = 38 b and etc. (where ϕ is the archive). We thus detected the number of cases in which the difference between the volumes of the source files and the augmented files were the smallest. Suppose, we have in all nine cases Δ (X*y

_{i}) > Δ (Y*y

_{i}), in one from those Δ (X*x

_{i}) < Δ (Y*x

_{i}), and in the rest eight Δ (Y*x

_{i}) < Δ (X*x

_{i}). Put the number of these cases in the corresponding cells of the 2 × 2 table (see also Figure A1 in Appendix A). In the case of our example, to compare the sources “X” and “Y”, the matrix will have the following form (Table 1):

## 3. The Procedure

#### 3.1. Notions and Data Encoding

#### 3.2. Constructing Sequences for Hypothesis Testing

## 4. Results

## 5. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Animals and Housing

#### Experimental Scheme

Symbols | Behavioural Elements |
---|---|

Q | Running |

S | Walking |

W | Bite |

E | Capturing the prey by forepaws (only in rodents) |

R | Handling (only in rodents) |

H | Nibbling insects’ legs |

G | Carrying the prey in teeth |

D | Sniffing |

N | Pinning the prey down to the ground by one paw (only in shrew) |

M | The same, by two paws (only in shrew) |

C | Freezing |

V | Turning a body to 90° |

B | U-turn |

F | Turning a head |

Y | Rearing against the wall |

U | Backwards movement |

X | Self-grooming |

J | Jump |

I | Free-standing rearing |

**Figure A1.**Here is a procedure for processing data to obtain the 2 × 2 matrices. Step 1. We divide each source file approximately in half. Then we leave the first half unchanged and divide the second one into several fragments of the same volume. The program that we used to cut text files is in the public domain: https://github.com/m-novikov/sequence_cut. Step 2. To the first parts of the source files, we added individually the fragments containing behavioral sequences of the same species and thus obtained files: X*x

_{1}, Y*y

_{1}, etc. After that, to the first parts of the source files, we added individually the fragments containing sequences of another species and thus obtained files X*y

_{1}, Y*x

_{1}, etc. We thus obtained the augmented files and got a possibility to compare structural features of behavioral sequences of two species. Step 3. We now archive all files obtained individually. Step 4. For each pair of species, we calculate the difference between the archive containing the augmented file and the first half of the source file. Step 5. We detect cases in which the difference between the archive containing the augmented file and the first half of the source file was minimal and calculate the sum of numbers of these cases. Step 6. We place the obtained data into the cells of the 2 × 2 matrix.

## References

- Li, C.; Zhang, X.; Cao, Z. Triangular and Fibonacci number patterns driven by stress on core/shell microstructures. Science
**2005**, 309, 909–911. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lorenz, K.Z. The comparative method in studying innate behavior patterns. In Society for Experimental Biology, Physiological Mechanisms in Animal Behavior (Society’s Symposium IV); Cambridge University Press: Cambridge, UK, 1950; pp. 221–268. [Google Scholar]
- Blomberg, S.P.; Garland, T., Jr.; Ives, A.R. Testing for phylogenetic signal in comparative data: Behavioral traits are more labile. Evolution
**2003**, 57, 717–745. [Google Scholar] [CrossRef] - Malange, J.; Alberts, C.C.; Oliveira, E.S.; Japyassú, H.F. The evolution of behavioural systems: A study of grooming in rodents. Behaviour
**2013**, 150, 1295–1324. [Google Scholar] [CrossRef] - West-Eberhard, M.J. Developmental Plasticity and Evolution; Oxford University Press: New York, NY, USA, 2003. [Google Scholar]
- Li, M.; Chen, X.; Li, X.; Ma, B.; Vitányi, P.M. The similarity metric. IEEE Trans. Inf. Theory
**2004**, 50, 3250–3264. [Google Scholar] [CrossRef] - Cilibrasi, R.; Vitányi, P.M. Clustering by compression. IEEE Trans. Inf. Theory
**2005**, 51, 1523–1545. [Google Scholar] [CrossRef] [Green Version] - Xie, X.; Guan, J.; Zhou, S. Similarity evaluation of DNA sequences based on frequent patterns and entropy. BMC Genomics
**2015**, 16, S5. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huo, H.; Chen, X.; Guo, X.; Vitter, J.S. Efficient compression and indexing for highly repetitive DNA sequence collections. IEEE/ACM Trans. Comput. Biol. Bioinform.
**2020**, 14, 1–14. [Google Scholar] [CrossRef] - Forrester, G.S. A multidimensional approach to investigations of behaviour: Revealing structure in animal communication signals. Anim. Behav.
**2008**, 76, 1749–1760. [Google Scholar] [CrossRef] - Asher, L.; Collins, L.M.; Ortiz-Pelaez, A.; Drewe, J.A.; Nicol, C.J.; Pfeiffer, D.U. Recent advances in the analysis of behavioural organization and interpretation as indicators of animal welfare. J. R. Soc. Interface
**2009**, 6, 1103–1119. [Google Scholar] [CrossRef] [Green Version] - Gadbois, S.; Sievert, O.; Reeve, C.; Harrington, F.H.; Fentress, J.C. Revisiting the concept of behavior patterns in animal behavior with an example from food-caching sequences in Wolves (Canis lupus), Coyotes (Canis latrans), and Red Foxes (Vulpes vulpes). Behav. Process.
**2015**, 110, 3–14. [Google Scholar] [CrossRef] - Kershenbaum, A.; Blumstein, D.T.; Roch, M.A.; Akçay, Ç.; Backus, G.; Bee, M.A.; Coen, M.; Cao, Y.; Bohn, K.; Carter, G.; et al. Acoustic sequences in non-human animals: A tutorial review and prospectus. Biol. Rev.
**2016**, 91, 13–52. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Moore, T.Y.; Cooper, K.L.; Biewener, A.A.; Vasudevan, R. Unpredictability of escape trajectory explains predator evasion ability and microhabitat preference of desert rodents. Nat. Commun.
**2017**, 8, 1–9. [Google Scholar] [CrossRef] [Green Version] - Whishaw, I.Q.; Faraji, J.; Kuntz, J.R.; Agha, B.M.; Metz, G.A.; Mohajerani, M.H. The syntactic organization of pasta-eating and the structure of reach movements in the head-fixed mouse. Sci. Rep.
**2017**, 7, 10987. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Casarrubea, M.; Aiello, S.; Di Giovanni, G.; Santangelo, A.; Palacino, M.; Crescimanno, G. Combining quantitative and qualitative data in the study of feeding behavior in male Wistar rats. Front. Psychol.
**2019**, 10, 881. [Google Scholar] [CrossRef] [PubMed] - McCowan, B.; Doyle, L.R.; Hanser, S.F. Using information theory to assess the diversity, complexity, and development of communicative repertoires. J. Comp. Psychol.
**2002**, 116, 166–172. [Google Scholar] [CrossRef] [PubMed] - Kadota, M.; White, E.J.; Torisawa, S.; Komeyama, K.; Takagi, T. Employing relative entropy techniques for assessing modifications in animal behavior. PLoS ONE
**2011**, 6, e28241. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Peng, Z.; Genewein, T.; Braun, D.A. Assessing randomness and complexity in human motion trajectories through analysis of symbolic sequences. Front. Hum. Neurosci.
**2014**, 8, 168. [Google Scholar] [CrossRef] [Green Version] - Gauvrit, N.; Singmann, H.; Soler-Toscano, F.; Zenil, H. Algorithmic complexity for psychology: A user-friendly implementation of the coding theorem method. Behav. Res. Methods
**2016**, 48, 314–329. [Google Scholar] [CrossRef] [Green Version] - Fisher, R.A. Statistical Methods, Experimental Design, and Scientific Inference; Oliver & Boyd: Edinburgh, UK, 1956. [Google Scholar]
- Reznikova, Z.; Levenets, J.; Panteleeva, S.; Ryabko, B. Studying hunting behaviour in the striped field mouse using data compression. Acta Ethol.
**2017**, 20, 165–173. [Google Scholar] [CrossRef] - Ryabko, B.; Reznikova, Z.; Druzyaka, A.; Panteleeva, S. Using ideas of Kolmogorov complexity for studying biological texts. Theory Comput. Syst.
**2013**, 52, 133–147. [Google Scholar] [CrossRef] [Green Version] - Reznikova, Z.; Levenets, J.; Panteleeva, S.; Novikovskaya, A.; Ryabko, B.; Feoktistova, N.; Gureeva, A.; Surov, A. Using the data-compression method for studying hunting behavior in small mammals. Entropy
**2019**, 21, 368. [Google Scholar] [CrossRef] [Green Version] - Levenets, J.V.; Panteleeva, S.N.; Reznikova, Z.I.; Gureeva, A.V.; Feoktistova, N.Y.; Surov, A.V. Experimental Comparative Analysis of Hunting Behavior in Four Species of Cricetinae Hamsters. Biol. Bull.
**2019**, 46, 1182–1191. [Google Scholar] [CrossRef] - Ryabko, B.; Guskov, A.; Selivanova, I. Using data-compressors for statistical analysis of problems on homogeneity testing and classification. In Proceedings of the 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 25–30 June 2017; IEEE: Piscataway, NJ, USA, 2017; pp. 121–125. [Google Scholar] [CrossRef] [Green Version]
- Fisher, R.A. On the interpretation of χ2 from contingency tables, and the calculation of P. J. R. Stat. Soc.
**1922**, 85, 87–94. [Google Scholar] [CrossRef] - Fisher, R.A. Statistical Methods for Research Workers; Oliver and Boyd: New York, NY, USA, 1950. [Google Scholar]

**Figure 1.**A dendrogram of similarity between hunting behaviors in the species studied based on the association coefficients from Table 6.

x | y | |
---|---|---|

X* | 1 | 0 |

Y* | 8 | 9 |

x | z | |
---|---|---|

X* | 9 | 0 |

Z* | 0 | 9 |

y | z | |
---|---|---|

Y* | 5 | 0 |

Z* | 4 | 9 |

Species | Sizes of a Source Text Files (Bytes) | Numbers of Sequences in Source Text Files | Sizes of the First Parts of the Source Text Files (Bytes) | Number of the Sample Files Obtained |
---|---|---|---|---|

Rattus norvegicus | 2572 | 108 | 1290 | 9 |

Apodemus agrarius | 3343 | 83 | 1672 | 9 |

Phodopus campbelli | 1715 | 43 | 801 | 4 |

P. sungorus | 1585 | 76 | 792 | 6 |

Allocricetulus eversmanni | 1463 | 60 | 731 | 5 |

Al. curtatus | 2814 | 115 | 1407 | 9 |

Lasiopodomys gregalis | 1086 | 34 | 543 | 3 |

Alticola tuvinicus | 1319 | 157 | 659 | 5 |

Sorex araneus | 1637 | 61 | 818 | 5 |

Species | A. agrarius | L. gregalis |
---|---|---|

A. agrarius | 6 | 0 |

L. gregalis | 3 | 3 |

Species | R. nor. | A. ag. | P. cam. | P. sun. | Al. ev. | Al. cur. | L. gr. | Alt. tuv. | S. ar. |
---|---|---|---|---|---|---|---|---|---|

R. norvegicus | 0 | 0.58 | 1 | 0.74 | 0.37 | 0.24 | 1 | 0.85 | 1 |

A. agrarius | 0.58 | 0 | 0.28 | 0.87 | 0.85 | 1 | 0.58 | 0.86 | 0.93 |

P. campbelli | 1 | 0.28 | 0 | 0.53 | 0 | 0.44 | 0.73 | 1 | 1 |

P. sungorus | 0.74 | 0.87 | 0.53 | 0 | 0.83 | 0.49 | 1 | 1 | 1 |

Al. eversmanni | 0.37 | 0.85 | 0 | 0.83 | 0 | 0.45 | 0.6 | 1 | 1 |

Al. curtatus | 0.24 | 1 | 0.44 | 0.49 | 0.45 | 0 | 0.82 | 1 | 1 |

L. gregalis | 1 | 0.58 | 0.73 | 1 | 0.6 | 0.82 | 0 | 1 | 1 |

Alt. tuvinicus | 0.85 | 0.86 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |

S. araneus | 1 | 0.93 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |

Species | R. nor. | A. ag. | P. cam. | P. sun. | Al. ev. | Al. cur. | L. gr. | Alt. tuv. | S. ar. |
---|---|---|---|---|---|---|---|---|---|

R. norvegicus | X | 0.029* | 0.001 ** | 0.011 * | 0.360 | 1.000 | 0.005 ** | 0.005 ** | 0.001 ** |

A. agrarius | X | 1.000 | 0.002 ** | 0.005 ** | 0.001 ** | 0.180 | 0.003 ** | 0.003 ** | |

P. campbelli | X | 0.200 | 1.000 | 0.230 | 0.140 | 0.008 ** | 0.009 ** | ||

P. sungorus | X | 0.015* | 0.100 | 0.020* | 0.002 ** | 0.002 ** | |||

Al. eversmanni | X | 0.150 | 0.190 | 0.008 ** | 0.008 ** | ||||

Al. curtatus | X | 0.020* | 0.001 ** | 0.001 ** | |||||

L. gregalis | X | 0.020 * | 0.020 * | ||||||

Alt. tuvinicus | X | 0.008 ** | |||||||

S. araneus | X |

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**MDPI and ACS Style**

Levenets, J.; Novikovskaya, A.; Panteleeva, S.; Reznikova, Z.; Ryabko, B.
Using Data-Compressors for Classification Hunting Behavioral Sequences in Rodents as “Ethological Texts”. *Mathematics* **2020**, *8*, 579.
https://doi.org/10.3390/math8040579

**AMA Style**

Levenets J, Novikovskaya A, Panteleeva S, Reznikova Z, Ryabko B.
Using Data-Compressors for Classification Hunting Behavioral Sequences in Rodents as “Ethological Texts”. *Mathematics*. 2020; 8(4):579.
https://doi.org/10.3390/math8040579

**Chicago/Turabian Style**

Levenets, Jan, Anna Novikovskaya, Sofia Panteleeva, Zhanna Reznikova, and Boris Ryabko.
2020. "Using Data-Compressors for Classification Hunting Behavioral Sequences in Rodents as “Ethological Texts”" *Mathematics* 8, no. 4: 579.
https://doi.org/10.3390/math8040579