, Volume 161, Issue 1–2, pp 155–164 | Cite as

Comparison of tree architecture using tree edit distances: application to 2-year-old apple hybrids

  • Vincent Segura
  • Aïda Ouangraoua
  • Pascal Ferraro
  • Evelyne Costes


In fruit trees, understanding genetic determinisms of architectural traits is considered as a promising manner to control vegetative development and yield regularity. In this context, our study aimed to classify 2-year-old apple hybrids on the basis of their architectural traits. From a fine phenotyping, trees were described as tree graphs, including topological and geometric information. To evaluate the similarity between trees, comparison methods based on edit operations (substitution, insertion and deletion) were carried out. Distance between two tree graphs was computed by minimising the sum of the costs of the edit operations applied to transform one tree into another. Two algorithms for the comparison of unordered and partially ordered tree graphs were applied to a sub-sample of the population, taking into account several geometric attributes. For each comparison, a dissimilarity matrix was computed, and subsequently trees were clustered. A local interpretation of the matched entities was proposed through schematic representations of the trees, and similarities between trees were analysed within and between clusters. The tree graphs, both unordered or partially ordered and whether the attributes were considered or not, were grouped, by clustering, according to the number of entities per tree. The robustness of the unordered comparison was demonstrated by its application to the whole population, since it provided results similar to those obtained on the sub-sample. Further developments towards a higher relative weight of geometric versus topological information are discussed in the perspective to define an architectural ideotype in apple.


Branching Clustering Geometry Malus x domestica Topology Tree graph 



This research was partly funded by a Ph.D. grant from ‘ACI Arborescences’ project, allocated to A. Ouangraoua, and a Ph.D. grant from INRA Genetic and Breeding Department and Languedoc-Roussillon Region, allocated to V. Segura. We are grateful to all the members of the ‘ACI Arborescences’ project for their fruitful discussions. We acknowledge G. Garcia and S. Feral for their contribution to field measurements and technical assistance in the orchard. We also acknowledge C. Smith for improving the English.


  1. Alméras T, Costes E, Salles JC (2004) Identification of biomechanical factors involved in stem shape variability between apricot tree varieties. Ann Bot 93:455–468PubMedCrossRefGoogle Scholar
  2. Beavis WD (1998) QTL analyses: power, precision, and accuracy. In: Paterson AH (ed) Molecular dissection of complex traits. CRC, New YorkGoogle Scholar
  3. Costes E, Guédon Y (2002) Modelling branching patterns in 1-year-old trunks of six apple cultivars. Ann Bot 89:513–524PubMedCrossRefGoogle Scholar
  4. De Wit I, Cook NC, Keulemans J (2004) Characterization of tree architecture in two-year-old apple seedling populations of different progenies with a common columnar gene parent. Acta Hortic 663:363–368Google Scholar
  5. Dickman DI, Gold MA, Flore JA (1994) The ideotype concept and the genetic improvement of tree crops. Plant Breed Rev 12:163–193Google Scholar
  6. Donald CM (1968) The breading of crop ideotypes. Euphytica 17:385–403CrossRefGoogle Scholar
  7. Edelin C (1991) Nouvelles données sur l’architecture des arbres sympodiaux: le concept de plan d’organisation. In: Edelin C (ed) L’Arbre, Biologie et développement. Naturalia Monspeliensia, MontpellierGoogle Scholar
  8. Ferraro P, Godin C (2000) A distance measure between plant architectures. Ann For Sci 57:445–461CrossRefGoogle Scholar
  9. Gallais A (1989) Théorie de la sélection en amélioration des plantes. Masson, ParisGoogle Scholar
  10. Godin C, Caraglio Y (1998) A multiscale model of plant topological structures. J Theor Biol 191:1–46PubMedCrossRefGoogle Scholar
  11. Godin C, Costes E, Sinoquet H (1999) A method for describing plant architecture which integrates topology and geometry. Ann Bot 84:343–357CrossRefGoogle Scholar
  12. Godin C, Guédon Y (2003) AMAPmod: exploring and modeling plant architecture. Version 2.1.16. CIRAD/INRA UMR Modélisation des plantes, MontpellierGoogle Scholar
  13. Godin C, Guédon Y, Costes E et al (1997) Measuring and analyzing plants with the AMAPmod software. In: Michalewicz M (ed) Advances in computational life science. CSIRO, AustraliaGoogle Scholar
  14. Guédon Y, Heuret P, Costes E (2003) Comparison methods for branching and axillary flowering sequences. J Theor Biol 225:301–325PubMedCrossRefGoogle Scholar
  15. Laurens F (1999) Review of the current apple breeding programmes in the world: objectives for scion cultivar improvement. Acta Hortic 484:163–170Google Scholar
  16. Laurens F, Audergon J, Claverie J et al (2000) Integration of architectural types in French programmes of ligneous fruit species genetic improvement. Fruits 55:141–152Google Scholar
  17. Lauri PE, Costes E (2004) Progress in whole tree architectural studies for apple cultivar characterization at INRA, France—contribution to the ideotype approach. Acta Hortic 663:357–362Google Scholar
  18. Lauri PE, Terouanne E, Lespinasse JM et al (1995) Genotypic differences in the axillary bud growth and fruiting pattern of apple fruiting branches over several years—an approach to regulation of fruit bearing. Sci Hortic 64:265–281CrossRefGoogle Scholar
  19. Lespinasse JM (1977) La conduite du pommier: types de fructification, incidence sur la conduite de l’arbre. INVUFLEC, ParisGoogle Scholar
  20. Lespinasse Y (1992) Le pommier. In: Gallais A, Bannerot H (eds) Amélioration des espèces végétales cultivées—objectifs et critères de sélection. INRA Editions, ParisGoogle Scholar
  21. Renton M, Guédon Y, Godin C et al (2006) Similarities and gradients in growth unit branching patterns during ontogeny in ‘Fuji’ apple trees: a stochastic approach. J Exp Bot 57:3131–3143PubMedCrossRefGoogle Scholar
  22. SAS Institute Inc (2000) SAS user’s guide: statistics. SAS Institute Inc., Cary, NC, USAGoogle Scholar
  23. Segura V, Cilas C, Laurens F et al (2006) Phenotyping progenies for complex architectural traits: a strategy for 1-year-old apple trees (Malus x domestica Borkh.). Tree Genet Genome 2:140–151CrossRefGoogle Scholar
  24. Segura V, Denancé C, Durel CE et al (2007) Wide range QTL analysis for complex architectural traits in a 1-year-old apple progeny. Genome 50:159–171PubMedCrossRefGoogle Scholar
  25. Ward JH (1963) Hierachical grouping to optimize an objective function. J Am Stat Assoc 58:236–244CrossRefGoogle Scholar
  26. Zhang K (1996) A constrained edit distance between unordered labeled trees. Algorithmica 15:205–222CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Vincent Segura
    • 1
  • Aïda Ouangraoua
    • 2
  • Pascal Ferraro
    • 2
  • Evelyne Costes
    • 1
  1. 1.INRA, UMR DAP, Equipe Architecture et Fonctionnement des Espèces FruitièresMontpellier CedexFrance
  2. 2.UMR LaBRI, Université de Bordeaux 1Talence CedexFrance

Personalised recommendations