The role of statistics in studying the diversity of the collection of plant genetic resources at VIR

Biostatistics began to develop synchronously with the formation of the first collections of plant genetic resources (PGR) in the late 19th and early 20th centuries. Since the foundation of the PGR collection at VIR, the entire available range of experimental methods was employed in the field and in the laboratory to evaluate its genetic diversity according to phenotypic and genotypic indicators and to select accessions with a given set of characteristics for specific breeding tasks. The key point is to choose a statistical research method that is adequate to the task. The purpose of this review was to summarize typical statistical problems that arise during phenotypic assessments of PGR collections and methods appropriate for their solution.
When analyzing PGR collections, the basic element is to determine qualitative and quantitative characteristics of their accessions. Descriptive statistics methods make it possible to estimate the mean values and stability of economically valuable plant characters on the basis of several years of studying in one or more locations. These indicators are compiled into databases, included into catalogues constantly published by VIR, and used in the selection of accessions promising for breeding tasks.
It is often necessary to compare groups of accessions belonging to different species and having different geographic origin, test results in different ecogeographic environments, viability under various storage conditions, etc. The hypothesis of differences among several plant features or variants of the experiment based on sample data is tested using Student’s t-test and the analysis of variance. Modern methods for assessing the genotype × environment interaction are being actively developed.
The correlation and regression analysis is employed to identify weather and climate factors affecting valuable agronomic characters of accessions, such as yield, grain weight, resistance to biotic and abiotic factors, and quality indicators, and to find interrelationships among such characters that should be taken into account while developing a cultivar according to a given model. The active warming of the climate, which started in the 1970s, aroused the interest of biologists in disclosing crop yield trends and using time series analysis methods in regression modeling.
Those who describe a large PGR collection, examine phylogenetic relationships, select a representative sample, and build up core-collections would face a task of structuring the collection and identifying groups of similar accessions. The classification problem is solved by classification methods either without learning, such as the cluster analysis, or with learning, such as the discriminant analysis.
Analyzing PGR accessions for a large number of indicators requires identification of the most informative indicators, i.e., reducing the dimensions of the character space, accomplished by the principal component analysis or factor analysis techniques with a shift from real measured variables to a small number of hypothetical values, called factors.
The study of PGR collections is increasingly expanding beyond the limits of classical field observations of yield, for which biostatistics methods, based on the assumption of a normal distribution, were developed in the early 20th century. In the middle of the 20th century, nonparametric analytical methods and resampling techniques of computer simulation appeared.
The development of computers made it possible to make integrated data platforms that accumulated huge arrays of diverse PGR characteristics, and extend complex multidimensional methods available only to mathematicians to a wider range of researchers in various disciplines. Biostatistics methods associated with phenotypic data continue to evolve, ensuring improved assessment of the potential of PGR collections and providing integral information support to the modern genomic analysis.

1. Afanasyev V.N., Yuzbashev M.M., Gulyaeva T.I. Econometrics (Ekonometrika). Moscow: Finansy i Statistika; 2006. [in Russian]

2. Anderson M.J. Permutational multivariate analysis of variance (PERMANOVA). In: N. Balakrishnan, T. Colton, B. Everitt, W. Piegorsch, F. Ruggeri, J.L. Teugels (eds). Wiley StatsRef: Statistics Reference Online. Hoboken, NJ: John Wiley & Sons, Ltd.; 2017. p.1-15. DOI: 10.1002/9781118445112.stat07841

3. Ayvazyan S.A., Bukhshtaber V.M., Enyukov I.S., Meshalkin L.D. Applied statistics: classification and dimensionality reduction (Prikladnaya statistika: klassificatsiya i snizheniye razmernosti). Moscow: Finansy i Statistika; 1989. [in Russian]

4. Ayvazyan S.A., Enyukov I.S., Meshalkin L.D. Applied statistics: a study of dependencies (Prikladnaya statistika: issledovaniye zavisimostey). Moscow: Finansy i Statistika; 1985. [in Russian]

5. Ayvazyan S.A., Mkhitaryan V.S. Applied statistics in tasks and exercises (Prikladnaya statistika v zadachakh i uprazhneniyakh). Moscow: Unity-Dana; 2001. [in Russian]

6. Borovikov V.P. A popular introduction to modern data analysis in the STATISTICA system (Populyarnoye vvedeniye v sovremenny analiz dannykh v sisteme STATISTICA). Moscow: Goryachaya Liniya – Telekom; 2013. [in Russian]

7. Borovikov V.P. STATISTICA. The art of data analysis on a computer: for professionals (STATISTICA. Iskusstvo analiza dannykh na kompyutere: dlya professionalov). 2nd ed. St. Petersburg: Piter; 2003. [in Russian]

8. Box G., Jenkins G. Time series analysis. Forecasting and control. Issue 1. Moscow: Mir; 1974. [in Russian]

9. Dospekhov B.A. Methodology of field trial (with fundamentals of statistical processing of research results) (Metodika polevogo opyta [s osnovami statisticheskoy obrabotki resultatov issledovaniy]). 5th ed. Moscow: Agropromizdat; 1985. [in Russian]

10. Dubrov A.M., Mkhitaryan V.S., Troshin L.I. Multidimensional statistical methods (Mnogomernye statisticheskiye metody. Moscow: Finansy i Statistika; 2003. [in Russian]

11. Eberhart S.A., Russell W.A. Stability parameters for comparing varieties. Crop Science. 1966;6(1):36-40. DOI: 10.2135/cropsci1966.0011183X000600010011x

12. Efimov V.M., Kovaleva V.Yu. Multidimensional analysis of biological data: a training manual (Mnogomerny analiz biologicheskikh dannykh: uchebnoye posobiye). 2nd ed. St. Petersburg: VIZR; 2008. [in Russian]

13. Efimova M.R., Petrova E.V., Rumyantsev V.N. General theory of statistics: a manual (Obshchaya teoriya statistiki: uchebnik). 2nd ed. Moscow: INFRA-M; 2007. [in Russian]

14. Eliseeva I.I., Isotov A.V., Kapralova E.B., Flud N.A., Shchirina A.N. Statistics (Statistika). I.I. Eliseeva (ed.). Moscow: KNORUS; 2006. [in Russian]

15. Eliseeva I.I., Kurysheva S.V., Kosteeva T.V., Pantina I.V., Mikhailov B.A., Neradovskaya Yu.V., Strohe H.G., Bartels K., Rybkina L.R. Econometrics (Ekonometrika). Moscow: Finansy i Statistika; 2007. [in Russian]

16. Enslein K., Ralston A., Wilf H.S. (eds). Statistical methods for digital computers. Moscow: Nauka; 1986. [in Russian]

17. Glotov N.V., Zhivotovsky L.A., Khovanov N.V., Khromov-Borisov N.N. Biometrics (Biometriya). Leningrad: Leningrad State University; 1982. [in Russian]

18. Iler A.M., Inouye D.W., Schmidt N.M., Høye T.T. Detrending phenological time series improves climate–phenology analyses and reveals evidence of plasticity. Ecology. 2017;98(3):647-655. DOI: 10.1002/ecy.1690

19. Khalafyan A.A. Statistica 6. Statistical data analysis (Statistica 6. Statisticheskiy analiz dannykh). Moscow: Binom; 2010. [in Russian]

20. Khizhnyak S.V., Puchkova E.P. Mathematical methods in agroecology and biology: a training manual (Matematicheskiye metody v agroekologii i biologii: uchebnoye posobiye) Krasnoyarsk: Krasnoyarsk State Agrarian University; 2019. [in Russian]

21. Kilchevsky A.V., Khotyleva L.V. Genotype and environment in plant breeding (Genotip i sreda v selektsii rasteniy). Minsk: Nauka i Tekhnika; 1989. [in Russian]

22. Malinovsky L.G. Classification of objects by means of discriminant analysis (Klassifikatsiya obyektov sredstvami diskriminantnogo analiza). Moscow: Nauka; 1979. [in Russian]

23. Novikova L.Yu. Methods for statistical processing of phenotypic data in plant genetic resources collections. St. Petersburg: VIR; 2024. [in Russian]

24. Pakudin V.Z. Parameters of environmental plasticity assessment in cultivars and hybrids (Parametry otsenki ekologicheskoy plastichnosti sortov i gibridov). In: L.V. Khotyleva (ed.). Theory of Selection in Plant Populations (Teoriya otbora v populyatsiyakh rasteniy). Novosibirsk: Nauka; 1976. p.178-189. [in Russian]

25. Reznik A.D. A book for those who do not like statistics, but are forced to use it. Nonparametric statistics in examples, exercises, and drawings (Kniga dlya tekh, kto ne lyubit statistiku, no vynuzhden yeyu polzovatsya. Neparametricheskaya statistika v primerakh, uprazhneniyakh i risunkakh). St. Petersburg: Rech; 2008. [in Russian]

26. Scheffé H. The analysis of variance. Moscow: State Publishing House of Physico-Mathematical Literature; 1963. [in Russian]

27. Simchera V.M. Methods of the multidimensional analysis of statistical data (Metody mnogomernogo analiza statisticheskikh dannykh). Moscow: Finansy i Statistika; 2008. [in Russian]

28. Sirotenko O.D. Fundamentals of agricultural meteorology. Vol. II. Methods of calculations and forecasts in agrometeorology. Book 1. Mathematical models in agrometeorology (Osnovy selskokhozyaystvennoy meteorologii. T. II. Metody raschetov i prognozov v agrometeorologii. Kniga 1. Matematicheskiye modeli v agrometeorologii: uchebnoye posobiye). Obninsk: VNIIGMI-MTsD; 2012. [in Russian]

29. Vuchkov I., Boyadjieva L., Solakov E. Applied linear regression analysis Prikladnoy lineyny regressionny analiz). Moscow: Finansy i Statistika; 1987. [in Russian]

30. Vukolov E.A. Fundamentals of statistical analysis: a workshop on statistical methods and operations research using the STATISTICA and EXCEL packages (Osnovy statisticheskogo analiza: praktikum po statisticheskim metodam i issledovaniyu operatsiy s ispolzovaniyem paketov STATISTICA i EXCEL). Moscow: FORUM; 2004. [in Russian]

31. Yan W., Hunt L.A., Sheng Q., Szlavnics Z. Cultivar evaluation and megaenvironment investigation based on GGE biplot. Crop Science. 2000;40(3):596-605. DOI: 10.2135/cropsci2000.403597x

32. Zaitsev G.N. Methodology of biometric calculations. Mathematical statistics in experimental botany (Metodika biometricheskikh raschetov. Matematicheskaya statistika v eksperimentalnoy botanike). Мoscow: Nauka; 1973. [in Russian]

33. Zobel R.W., Wright A.J., Gauch Jr. H.G. Statistical analysis of a yield trial. Agronomy Journal. 1988;80(3):388-393. DOI: 10.2134/agronj1988.00021962008000030002x