Chapter 1 Gene Regulatory Models for Plant Development and Evolution E.R. Alvarez-Buylla, M. Benı ´tez, M. Aldana, G.J. Escalera-Santos, A ´ . Chaos, P. Padilla-Longoria, and R. Verduzco-Va ´zquez 1.1 Introduction: the Need for Mathematical Models to Understand Plant Development During development, complex interactions amongst genetic and non-genetic ele- ments give rise to robust spatiotemporal patterns. Moreover, an important feature of biological systems is the nontrivial flow of information at several scales. When we consider the scale determined by the cell, we observe that it integrates information coming from gene regulatory networks (GRNs), biochemical pathways, and other microscopic processes. If we consider larger scales, then intercellular communica- tion, mechanical and geometric effects (such as growth, shape, and size), and environmental influences have to be taken into account. This is why understanding how patterns arise during development requires the use of formal dynamical models able to follow the concerted action of so many elements at different spatiotemporal scales. E.R. Alvarez-Buylla, M. Benı ´tez, M. Aldana, G.J. Escalera-Santos, A ´ . Chaos, P. Padilla-Longoria, and R. Verduzco-Va ´zquez C3, Centro de Ciencias de la Complejidad, Cd. Universitaria, UNAM, Me ´xico, D. F., Me ´xico E.R. Alvarez-Buylla, M. Benı ´tez, G.J. Escalera-Santos, and A ´ . Chaos Departamento de Ecologı ´a Funcional, Instituto de Ecologı ´a, Universidad Nacional Auto ´noma de Me ´xico, 3er Circuito Exterior Junto a Jardı ´n Bota ´nico, 04510 Distrito Federal, Coyoaca ´n, CU, Mexico e-mail: eabuylla@gmail.com, ealvarez@ecologia.unam.mx M. Aldana Instituto de Ciencias Fı ´sicas, Universidad Nacional Auto ´noma de Me ´xico, Campus Cuernavaca, Morelos, 62210, Mexico P. Padilla-Longoria Instituto de Investigaciones en Matema ´ticas Aplicadas y en Sistemas, Universidad Nacional Auto ´noma de Me ´xico, 04510, Distrito Federal, Mexico R. Verduzco-Va ´zquez Facultad de Ciencias, Universidad Auto ´noma del Estado de Morelos, Cuernavaca, Morelos, 62210, Mexico E.C. Pua and M.R. Davey (eds.), Plant Developmental Biology – Biotechnological Perspectives: Volume 1, DOI 10.1007/978-3-642-02301-9_1, # Springer-Verlag Berlin Heidelberg 2010 3