Denis Barabé

Symmetry in Plants

Foreword - the aims and scope of the book a glance at each chapter, D. Barabe and R.V. Jean prologues - by a botanist, R.O. Erickson, by a mathematician, I. Adler, by a crystallographer, A. Mackay, by a molecular geneticist, A. Lima-de-Faria part 1 - basic information gathering in phyllotaxis - data-experimentation part 2 - pattern recognition in phylotaxis - description part 3 pattern generation in phyllotaxis - modelling part 4 origins of phyllotaxis - homology-comparative morphology-exotic phyllotaxis, literature, appendices.

The correlation between development of atypical bisexual flowers and phylogeny in the Aroideae (Araceae)

Abstract.u2002In the intermediate zone of the inflorescence of genera of Aroideae one can find flowers with male and female characteristics. Until now, two types of developmental sequences of atypical bisexual flowers (ABFs) have been recognized: the Philodendron type and the Cercestis type. In the Philodendron type, bisexual flowers generally consist of functional carpels and staminodes inserted on the same whorl. In the Cercestis type, the gynoecium and stamens are inserted on two different whorls. These different ontogenetic patterns represent two different pathways in the evolution of unisexual flowers in this subfamily. A molecular phylogenetic analysis of 33 genera of Araceae, based on the chloroplast trnL intron and trnL–F intergenic spacer sequences was carried out. We use this phylogenetic analysis and those published by French et al. (1995) and Mayo et al. (1997) to examine the distribution of the two types of ABFs in selected genera. Our results suggest that the two developmental patterns of ABFs in Aroideae sensu Mayo et al. (1997) do not correspond to two separate evolutionary lineages but rather are more or less consistent within clades. Although this new molecular phylogeny does not include all aroid genera, it corroborates in general, at the subfamily level, the molecular analysis of French et al. (1995) based on chloroplast DNA restriction site data and the analysis of Mayo et al. (1997) based on morphological and anatomical data.

Intergeneric and infrafamilial phylogeny of subfamily Monsteroideae (Araceae) revealed by chloroplast trnL-F sequences

The chloroplast trnL-F region was used as an independent data set for phylogenetic analysis of 118 aroid taxa. We investigated the intergeneric relationships of subfamily Monsteroideae (Araceae) and used this as a basis for an interspecific phylogenetic study of Rhaphidophora Hassk., the largest genus of the Monsteroideae. Results of the molecular tree were useful for inferring subfamilial and tribal circumscription and evolution in Araceae. Our results show that family Araceae consists of five clades that correspond to the subfamilies traditionally recognized. Starting from the most basal clade, these correspond to subfamilies Gymnostachydoideae and Orontioideae (proto aroids), with Lemna sp. (Lemnaceae) embedded in the Araceae and sister to the true aroids consisting of Pothoideae sister to Monsteroideae, immediately sister to Lasioideae and Aroideae. There is less agreement with existing tribal classifications. Complex relationships exist between members of the Monsteroideae. Our results show that Rhaphidophora and Epipremnum are paraphyletic with species of Rhaphidophora sampled, forming three informal groups with other genera of the Monstereae. Phylogenetic results may be used to suggest taxonomic changes to the current systematics of the monsteroids.

Phyllotaxis — The Way Ahead, A View on Open Questions and Directions of Research

Suggestions are made for future research in the multidisciplinary subject of phyllotaxis, and various promising viewpoints for the study of the phenomenon are pointed out.

PHYLLOTAXIS: OPEN AND CLOSED SYSTEMS

The inflorescence of Symplocarpus foetidus constitutes good material to analyse the biological processes and physical constraints involved in the development of plants. During the development of the inflorescence, two morphogenetic periods can be distinguished (i) before and (ii) during and after the development of floral parts. In the first period, when the floral primordia appear, the phyllotactic system could be explained by global processes at the inflorescence level. In the second period, the development of floral parts produces patterns which can be explained by local processes at the floral level. In this analysis the author defines the concepts of open system and closed system in phyllotaxis. In a closed system (e.g. spadix) the elements are arranged on a continuous and closed surface. In an open system (e.g. shoot apex) the elements appear on a surface periodically renewed and are removed from each other by the intercalary growth.

On the allometric growth of tissues in fruits

This paper deals with the relative growth of three different fruit tissues. Their morphogenetic periods and the mathematical constraints involved are described, and more precisely, the paper shows an allometric relationship (Y=nX m ) between the widths (X, Y) of the main tissues in stone fruits such as cherries, peaches and prunes. The mathematical relationships between the growth of the mesocarp and of the endocarp of somePrunus fruits are described, and it is proved that before the formation of the embryo, growth is allometric, in agreement with conclusions drawn from some experimental data. However, according to another study, the growth of the mesocarp and of the endocarp are ruled by autocatalytic and monomolecular functions, before as well as after the formation of the embryo. In this case, it is proved that if allometry exits in stone fruits, it can only be anantiometry (m=−1). To solve the dilemma, two main alternatives are proposed and discussed. We conclude that, while allometry is established on reasonable grounds before the formation of the embryo, after the formation of the embryo the mesocarp and endocarp evolve independently since a center for the coordination of growth no longer exists, and each tissue can grow according to its own independent rules.

SIMULATIONS OF TRANSITIONS FROM REGULAR TO STOCHASTIC PHYLLOTACTIC PATTERNS

The paper deals with a statistical method to analyze irregular phyllotactic patterns. To characterize the degree of order in phyllotactic systems, we determine the variation of the angle of divergence of a given leaf with regard to the preceding one. By knowing the range of uncertainty of the angle of divergence, it is possible to determine from which leaves rank a system becomes completely disorganized. We show that there is a quantitative link between the degree of uncertainty of the angle of divergence, and the number of regularly and randomly distributed leaves. To quantify this relationship, we deduced a formula from numerical simulations involving different ranges of uncertainty that can be observed in the angle of divergence in three different phyllotactic patterns: distichous (two orthostichies), opposite-decussate (four orthostichies) and spiral (137°). A χ2 statistical test allows us to determine the threshold of transition between ordered and disordered phyllotactic patterns with a fixed level of confidence. By using the sho mutants described by Itoh et al.1 as a case study, we show that this formula is useful mainly for analyzing the degree of order in phyllotactic mutants from two complementary points of view: the number of regularly distributed leaves and the degree of uncertainty of the divergence angle.

THE USE OF THE ABOAV-WEAIRE LAW TO ESTIMATE A BIOLOGICAL CONSTRAINT

Developmental processes may impose limitations and directionality in the mode of development of a particular structure. The main problem is to determine the nature and the respective effects of physical and biological constraints in the development of organisms. The Aboav-Weaire law is a semi-empirical law developed to explain the topological structure of physical materials. In the present paper, we make a formal analysis of the quantitative relationships between physical and biological constraints in biological structures by using the inflorescence of the Araceae as a case study. The Aboav-Weaire law permits to obtain a quantitative estimate of the biological constraint acting on the inflorescences of this family. In the case of the Araceae, the empirical curve presents a constant deviation with respect to the Aboav-Weaire law. This deviation is due to the presence of a biological constraint as opposed to a physical constraint. The biological constraint tends to decrease the variance of the number of sides while it is the inverse situation for the physical constraint. The results obtained using the Araceae model can be used to study the interrelationships between biological and physical constraints in any organism or biological structure.