Physica A 392 (2013) 710–721 Contents lists available at SciVerse ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Dynamics of three types of annual plants competing for water and light Andrzej Pe ¸ kalski * , Janusz Szwabiński Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-203 Wrocław, Poland article info Article history: Received 28 January 2012 Received in revised form 29 August 2012 Available online 2 November 2012 Keywords: Monte Carlo simulations Plant dynamics Annual plants Competition for light and water abstract We present and discuss a Monte Carlo model describing the dynamics of three types of annual plants which have different tolerances to shade and drought. External conditions (water and light) fluctuate around some values which are our control parameters and which decide how many resources the system receives. The plants compete with their nearest neighbours for the resources, however not in the same way. We show that for certain ranges of the control parameters a coexistence of the three species is observed. We discuss how the characteristics of the the plants — their number, germination, biomass or the number of nearest neighbours, depend on the two control parameters characterising external conditions. We show that elimination is done at the level of adult plants, not seedlings. We find also cooperative behaviour of plants in difficult conditions, as observed in field studies and we propose an explanation for this fact. Apart from plants tolerating shade but requiring more water and those tolerating drought but needing more light, which are common in nature, we introduce a third species with intermediary demands. We investigate under what conditions this new species could dominate and whether the total number of plants, regardless of their type, is larger with or without the intermediate plant. We show that in our model, like in nature, systems with two kinds of plants with opposite characteristics are, in general, as effective as a system with an additional third type of plants. We show that two contradictory hypotheses made by biologists, concerning the demands of plants in drought and shade, could be both true, however in different regimes. © 2012 Elsevier B.V. All rights reserved. 1. Introduction The interest of physicists in studying biological problems using methods developed in statistical physics has a long history [1–4]. Most of the studies are however devoted to animal populations. Only recently one of us published two papers [5,6] in which models of plant dynamics have been presented. In Ref. [5] the problem of annual plants competing for water has been studied, while in Ref. [6] the same kind of plants competed for sunlight. While in the first case the competition was symmetric, i.e. each competitor received the same amount of water, irrespective of its size, in the second paper possible asymmetry in the competition (larger plant takes more) has been accounted for. As follows from biological papers [7] the competition for water and light has indeed such a character. The dynamics of annual plants has been studied by biologists for a long time, both theoretically [8–10] and experimentally [11,12]. In theoretical works mostly the mean field type approach has been applied. Competition between different types of plants received less attention however. There are some rather old papers [13,14] in which a simple model of annual plants competing with perennials has been presented, again using a mean-field type philosophy. There are however very few biological papers [15,16] in which competition among annual plants having different tolerances to shade and drought, is studied. Unfortunately, the models presented there are not conclusive and no field data is presented. A paper by Goldberg and Fleetwood [17] gives some data, but without a definite * Corresponding author. Tel.: +48 71 3759354; fax: +48 71 3201409. E-mail addresses: apekal@ift.uni.wroc.pl (A. Pe ¸ kalski), szwabin@ift.uni.wroc.pl (J. Szwabiński). 0378-4371/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2012.09.029