AOBPreview originally published online on May 23, 2005
Annals of Botany 2005 96(1):137-148; doi:10.1093/aob/mci159
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Maximum Likelihood Inference and Bootstrap Methods for Plant Organ Growth via Multi-phase Kinetic Models and their Application to Maize
1 INRA-INAPG UMR Environnement et Grandes Cultures, 78850 Thiverval-Grignon, France and 2 INRA-INAPG UMR d'Agronomie, INRA Bâtiment EGER, 78850 Thiverval-Grignon, France
* For correspondence. E-mail Bruno.Andrieu{at}grignon.inra.fr
Received: 9 December 2004 Returned for revision: 21 February 2005 Accepted: 25 March 2005 Published electronically: 23 May 2005
• Background and Aims Fitting the parameters of models of plant organ growth is a means to investigate how environmental conditions affect plant architecture. The aim of this article is to evaluate some non-linear methods for fitting the parameters of multi-phase models of the kinetics of extension of plant organs such as laminae, sheaths and internodes.
• Methods A set of computational procedures was developed allowing parameter-fitting of multi-phase models, using the maximum likelihood criterion, in which phases are identified with reference to ontogenic processes. Two bootstrap methods were compared to assess the precision of the estimates of fitted parameters, and of functions of these parameters such as the final leaf length, and the duration and rate of the rapid extension phase. Methods were applied to an experimental dataset, representing the kinetics of laminae, sheaths and internodes along the maize shoot, for two contrasting densities.
• Key Results A set of multi-phase models was proposed to describe the extension of laminae, sheaths and internodes along the shoot. The distinguishable phases differed between laminae, sheaths and internodes. For sheaths and laminae, but not for internodes, the same model could be fitted to all phytomers along the shoot. The variation of parameters along the shoot and between density treatments, as well as derived functions such as the durations of the phases of extension, are presented for laminae. It was the duration of the fast extension period, rather than its rate, which determined the difference in final length between treatments.
• Conclusions Such methods permit a large degree of objectivity and facilitate the analysis of such rather complicated but co-ordinated datasets. The work also illustrates some natural limitations of maximum likelihood methods, and viable ways of overcoming them by including a priori knowledge in the model fitting method are discussed.
Key words: Zea mays, maximum likelihood, bootstrap, architectural model, maize, multi-phase kinetic model, extension
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