Theoretical and Applied Genetics

, Volume 131, Issue 4, pp 775–786 | Cite as

Application of a partitioning procedure based on Rao quadratic entropy index to characterize the temporal evolution of in situ varietal and genetic diversity of bread wheat in France over the period 1981–2006

  • Rémi Perronne
  • Isabelle Goldringer
Original Article


Key message

We present and highlight a partitioning procedure based on the Rao quadratic entropy index to assess temporal in situ inter-annual varietal and genetic changes of crop diversity.


For decades, Western-European agroecosystems have undergone profound changes, among which a reduction of crop genetic diversity. These changes have been highlighted in numerous studies, but no unified partitioning procedure has been proposed to compute the inter-annual variability in both varietal and genetic diversity. To fill this gap, we tested, adjusted and applied a partitioning procedure based on the Rao quadratic entropy index that made possible to describe the different components of crop diversity as well as to account for the relative acreages of varieties. To emphasize the relevance of this procedure, we relied on a case study focusing on the temporal evolution of bread wheat diversity in France over the period 1981–2006 at both national and district scales. At the national scale, we highlighted a decrease of the weighted genetic replacement indicating that varieties sown in the most recent years were more genetically similar than older ones. At the district scale, we highlighted sudden changes in weighted genetic replacement in some agricultural regions that could be due to fast shifts of successive leading varieties over time. Other regions presented a relatively continuous increase of genetic similarity over time, potentially due to the coexistence of a larger number of co-leading varieties that got closer genetically. Based on the partitioning procedure, we argue that a tendency of in situ genetic homogenization could be compared to some of its potential causes, such as a decrease in the speed of replacement or an increase in between-variety genetic similarity over time.



This work was supported by a grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (LabEx BASC; ANR-11-LABX-0034). It has benefited from a previous project funded by the FRB that allowed in particular to collect and complete previous historical and genetic data and communicate the new indicator H T * to French stakeholders (Goffaux et al. 2011). We are grateful to the editor and two anonymous reviewers who helped improving the manuscript.

Author contribution statement

RP had the idea and performed the analyses. IG and RP discussed the approach and the results. IG and RP wrote the manuscript. IG and RP read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standard

The authors declare that the study comply with the current laws of France.

Supplementary material

122_2017_3034_MOESM1_ESM.pdf (1.3 mb)
Supplementary material 1 (PDF 1287 kb)
122_2017_3034_MOESM2_ESM.pdf (66 kb)
Supplementary material 2 (PDF 66 kb)
122_2017_3034_MOESM3_ESM.pdf (41 kb)
Supplementary material 3 (PDF 40 kb)
122_2017_3034_MOESM4_ESM.pdf (59 kb)
Supplementary material 4 (PDF 58 kb)
122_2017_3034_MOESM5_ESM.pdf (44 kb)
Supplementary material 5 (PDF 43 kb)
122_2017_3034_MOESM6_ESM.pdf (36 kb)
Supplementary material 6 (PDF 35 kb)
122_2017_3034_MOESM7_ESM.pdf (111 kb)
Supplementary material 7 (PDF 110 kb)
122_2017_3034_MOESM8_ESM.pdf (1.3 mb)
Supplementary material 8 (PDF 1357 kb)


  1. Abecassis J, Bergez J (2009) Les filières céréalières: organisation et nouveaux défis. Quae-FPH, ParisCrossRefGoogle Scholar
  2. Bonneuil C, Goffaux R, Bonnin I, Montalent P, Hamon C, Balfourier F, Goldringer I (2012) A new integrative indicator to assess crop genetic diversity. Ecol Indic 23:280–289CrossRefGoogle Scholar
  3. Bonnin I, Bonneuil C, Goffaux R, Montalent P, Goldringer I (2014) Explaining the decrease in the genetic diversity of wheat in France over the 20th century. Agric Ecosyst Environ 195:183–192CrossRefGoogle Scholar
  4. Botta-Dukát Z (2005) Rao’s quadratic entropy as a measure of functional diversity based on multiple traits. J Veg Sci 16:533–540CrossRefGoogle Scholar
  5. Brennan JP, Byerlee D (1991) The rate of crop varietal replacement on farms: measures and empirical results for wheat. Plant Var Seeds 4:99–106Google Scholar
  6. Calderini DF, Slafer GA (1998) Changes in yield and yield stability in wheat during the 20th century. Field Crop Res 57:335–347CrossRefGoogle Scholar
  7. Chiu C-H, Chao A (2014) Distance-based functional diversity measures and their decomposition: a framework based on Hill numbers. PLoS One 9(7):e100014CrossRefPubMedPubMedCentralGoogle Scholar
  8. Costanzo A, Bàrberi P (2014) Functional agrobiodiversity and agroecosystem services in sustainable wheat production. A review. Agron Sustain Dev 34:327–348CrossRefGoogle Scholar
  9. de Bello F, Lavergne S, Meynard C, Lepš J, Thuiller W (2010) The partitioning of diversity: showing Theseus a way out of the labyrinth. J Veg Sci 21:992–1000CrossRefGoogle Scholar
  10. Dixon J, Nalley L, Kosina P, La Rovere R, Hellin H, Aquino P (2006) Adoption and economic impact of improved wheat varieties in the developing world. J Agric Sci 144:489–502CrossRefGoogle Scholar
  11. Donini P, Law JR, Koebner RMD, Reeves JC, Cooke RJ (2000) Temporal trends in the diversity of UK wheat. Theor Appl Genet 100:912–917CrossRefGoogle Scholar
  12. Fu YB (2015) Understanding crop genetic diversity under modern plant breeding. Theor Appl Genet 128:2131–2142CrossRefPubMedPubMedCentralGoogle Scholar
  13. Goffaux R, Goldringer I, Bonneuil C, Montalent P, Bonnin I (2011) Quels indicateurs pour suivre la diversité des plantes cultivées. Le cas du blé tendre en France depuis un siècle. Fondation de Recherche pour la Biodiversité, ParisGoogle Scholar
  14. Gower JC (1971) A general coefficient of similarity and some of its properties. Biometrics 27:857–871CrossRefGoogle Scholar
  15. Hardy OJ, Charbonnel N, Fréville H, Heuertz M (2003) Microsatellite allele sizes: a simple test to assess their significance on genetic differentiation. Genetics 163:1467–1482PubMedPubMedCentralGoogle Scholar
  16. Hill MO (1973) Diversity and evenness: a unifying notation and its consequence. Ecology 54:427–432CrossRefGoogle Scholar
  17. Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6:65–70Google Scholar
  18. Hovmøller MS, Walter S, Bayles RA, Hubbard A, Flath K, Sommerfeldt N, Leconte M, Czembor P, Rodriguez-Algaba J, Thach T, Hansen JG, Lassen P, Justensen AF, Ali S, de Vallavieille-Pope C (2015) Replacement of the European wheat yellow rust population by new races from the centre of diversity in the near-Himalayan region. Plant Pathol 65:402–411CrossRefGoogle Scholar
  19. Huang X-Q, Wolf M, Ganal MW, Orford S, Koebner RMD, Röder MS (2007) Did modern plant breeding lead to genetic erosion in European winter wheat varieties? Crop Sci 47:343–349CrossRefGoogle Scholar
  20. Jost L (2006) Entropy and diversity. Oikos 113:363–375CrossRefGoogle Scholar
  21. Jost L (2007) Partitioning diversity into independent alpha and beta components. Ecology 88:2427–2439CrossRefPubMedGoogle Scholar
  22. Kimura M, Crow J (1964) The number of alleles that can be maintained in a finite population. Genetics 49:725–738PubMedPubMedCentralGoogle Scholar
  23. Krishna VV, Spielman DJ, Veettil PC (2016) Exploring the supply and demand factors of varietal turnover in Indian wheat. J Agric Sci 154:258–272CrossRefGoogle Scholar
  24. Legendre P (2014) Interpreting the replacement and richness difference components of beta diversity. Global Ecol Biogeogr 23:1324–1334CrossRefGoogle Scholar
  25. Lesk C, Rowhani P, Ramankutty N (2016) Influence of extreme weather disasters on global crop production. Nature 529:84–87CrossRefPubMedGoogle Scholar
  26. MacArthur RH (1965) Patterns of species diversity. Biol Rev 40:510–533CrossRefGoogle Scholar
  27. Marcon E, Scotti I, Hérault B, Rossi V, Lang G (2014) Generalization of the partitioning of shannon diversity. PLoS One 9(3):e90289CrossRefPubMedPubMedCentralGoogle Scholar
  28. Mignolet C, Schott C, Benoît M (2007) Spatial dynamics of farming practices in the Seine basin: methods for agronomic approaches on a regional scale. Sci Total Environ 375:13–32CrossRefPubMedGoogle Scholar
  29. Nei M (1973) Analysis of gene diversity in subdivided populations. Proc Natl Acad Sci USA 70:3321–3323CrossRefPubMedPubMedCentralGoogle Scholar
  30. Nei M, Li WH (1979) Mathematical model for studying genetic variation in terms of restriction endonucleases. Proc Natl Aca Sci USA 76:5269–5273CrossRefGoogle Scholar
  31. Ohta T, Kimura M (1973) A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet Res 22:201–204CrossRefPubMedGoogle Scholar
  32. Østergård H, Finckh MR, Fontaine L, Goldringer I, Hoad SP, Kristensen K, van Bueren ETL, Mascher F, Munk L, Wolfe MS (2009) Time for a shift in crop production: embracing complexity through diversity at all levels. J Sci Food Agric 89:1439–1445CrossRefGoogle Scholar
  33. Perronne R, Hannachi M, Lemarié S, Fugeray-Scarbel A, Goldringer I (2016) La filière blé tendre en France entre 1980 et 2006: principales hypothèses de l’influence du contexte économique et des changements organisationnels et institutionnels sur l’évolution de la diversité cultivée. Notes et études socio-économiques 41:83–113Google Scholar
  34. Perronne R, Makowski D, Goffaux R, Montalent P, Goldringer I (2017a) Temporal evolution of varietal, spatial and genetic diversity of bread wheat between 1980 and 2006 strongly depends upon agricultural regions in France. Agric Ecosyst Environ 236:12–20CrossRefGoogle Scholar
  35. Perronne R, Diguet S, de Vallavieille-Pope Claude, Leconte M, Enjalbert J (2017b) A framework to characterize the commercial life cycle of crop varieties: application to the case study of the influence of yellow rust epidemics on French bread wheat varieties. Field Crops Res 209:159–167CrossRefGoogle Scholar
  36. R Development Core Team (2015) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  37. Rangnekar D (2002) R&D appropriability and planned obsolescence: empirical evidence from wheat breeding in the UK (1960–1995). Ind Corp Change 11:1011–1029CrossRefGoogle Scholar
  38. Rao CR (1982) Diversity and dissimilarity coefficients—a unified approach. Theor Popul Biol 21:24–43CrossRefGoogle Scholar
  39. Rauf S, Teixeira da Silva JA, Khan AA, Naveed A (2010) Consequences of plant breeding on genetic diversity. Int J Plant Breed 4:1–21CrossRefGoogle Scholar
  40. Ricotta C (2005) Additive partitioning of Rao’s quadratic diversity: a hierarchical approach. Ecol Mod 183:365–371CrossRefGoogle Scholar
  41. Ricotta C, Szeidl L (2009) Diversity partitioning of Rao’s quadratic entropy. Theor Popul Biol 76:299–302CrossRefPubMedGoogle Scholar
  42. Roussel V, Koenig J, Beckert M, Balfourier F (2004) Molecular diversity in French bread wheat accessions related to temporal trends and breeding programmes. Theor Appl Genet 108:920–930CrossRefPubMedGoogle Scholar
  43. Silhol P (2010) Indicateurs de biodiversité: flux variétal, segmentation et concentration du marché pour huit espèces de grandes cultures de 1985 à 2007.Synthèse des principales études relatives à l’évaluation du progrès génétique. GNIS, Economie et Statistiques, ParisGoogle Scholar
  44. Simpson EH (1949) Measurement of diversity. Nature 163:688CrossRefGoogle Scholar
  45. Singh RP, Hodson DP, Jin Y, Huerta-Espino J, Kinyua MG, Wanyera R, Njau P, Ward RW (2006) Current status, likely migration and strategies to mitigate the threat to wheat production from race Ug99 (TTKS) of stem rust pathogen. CAB Rev Perspect Agric Vet Sci Nutr Nat Resour 1:1–13Google Scholar
  46. Smale M (1998) Indicators of varietal diversity in bread wheat grown in developing countries. In: Evenson RE, Gollin D, Santaniello V (eds) Agricultural values of plant genetic resources. CABI Publishing, Wallingford, pp 85–95Google Scholar
  47. Smale M, Singh J, di Falco S, Zambrano P (2008) Wheat breeding, productivity and slow variety change: evidence from the Punjab of India after the Green Revolution. Aust J Agric Resour Econ 52:419–432CrossRefGoogle Scholar
  48. Srinivasan CS, Thirtle C, Palladino P (2003) Winter wheat in England and Wales, 1923–1995: what do indices of genetic diversity reveal? Plant Genet Resour 1:43–57CrossRefGoogle Scholar
  49. Trnka M, Rötter RP, Ruiz-Ramos M, Kersebaum KC, Olesen JE, Žalud Z, Semenov MA (2014) Adverse weather conditions for European wheat production will become more frequent with climate change. Nat Clim Change 4:637–643CrossRefGoogle Scholar
  50. Ullstrup AJ (1972) The impacts of the southern corn leaf blight epidemics of 1970–1971. Annu Rev Phytopathol 10:37–50CrossRefGoogle Scholar
  51. van de Wouw M, Kik C, van Hintum T, van Treuren R, Visser B (2009) Genetic erosion in crops: concept, research results and challenges. Plant Genet Resour Charact Util 8:1–15CrossRefGoogle Scholar
  52. van de Wouw M, van Hintum T, Kik C, van Treuren R, Visser B (2010) Genetic diversity trends in the twentieth century crop cultivars: a meta analysis. Theor Appl Genet 120:1241–1252CrossRefPubMedPubMedCentralGoogle Scholar
  53. Witcombe J, Packwood A, Raj A, Virk D (1998) The extent and rate of adoption of modern cultivars in India. In: Witcombe J, Virk D, Farrington J (eds) Seeds of choice. Making the most of new varieties for small famers. Oxford and IBH, New Delhi, pp 53–68CrossRefGoogle Scholar
  54. Xiao Y, Mignolet C, Mari J-F, Benoît M (2014) Modeling the spatial distribution of crop sequences at a large regional scale using land-cover survey data: a case from France. Comput Electron Agric 102:51–63CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.GQE – Le Moulon, INRA, Univ. Paris-Sud, CNRS, AgroParisTechUniversité Paris-SaclayGif-Sur-YvetteFrance
  2. 2.INRA, VetAgro Sup, UMR Ecosystème PrairialClermont-FerrandFrance

Personalised recommendations