Mathematical modelling of dose-response relationship (hormesis) in allelopathy and its application.

Allelopathy arises from the release of chemicals by one plant species that affect other species in its vicinity, usually to their detriment. It has been demonstrated, in plant communities, to be a factor of ecological significance by influencing plant succession, dominance, climax formation, species diversity, structure of plant communities and productivity (Whittaker and Feeney, 1971; Rice, 1984; Chou, 1989). In agroecosystems, allelopathic effects between living weeds and crops, crops in mixtures, plant straw residue and succeeding crops during decomposition of residue are also well documented (Putnam, 1978; Rice, 1984). This phenomenon has been observed for over 2000 years. Reports as early as 300 BC document that many crop plants (eg., chick pea, barley, bitter vetch) destroyed weeds and inhibited the growth of other crop plants. The soil sickness problem in agriculture was specifically related to exudates of crop plants (Rice, 1984). However, intensive scientific research on this phenomenon only started on 20th century. The term allelopathy was first introduced by a German scientist Molisch in 1937 to include both harmful and beneficial biochemical interactions between all types of plants including microorganisms. Rice (1984) reinforced this definition in the first monograph on allelopathy. Contemporary researchers have broadened the context of allelopathy to include interactions between plants and higher animals, and have suggested that allelopathy may be part of a whole network of chemical communication between plants, and between plants and other organisms, including bacteria, yeasts, insects and mammals, and that such communication may contribute to plant defence (Harborne, 1987; Lovett and Ryuntyu, 1992; Einhellig, 1995; Siemens et al., 2002). Chemicals that impose allelopathic influences are called allelochemicals or allelochemics (Putnam and Tang, 1986). They may be largely classified as secondary plant metabolites, which are generally considered to be those compounds (such as alkaloids, isoprenoids, phenolics, flavonoids, terpenoids, and glucosinolates etc.) which do not play a role in primary metabolic processes essential for a plant’s survival, and are produced as offshoots of primary metabolic pathways. In contrast to primary metabolism, which comprises several hundreds of low molecular weight compounds, tens of thousands of secondary substances are known today, but only a limited number have been implicated as allelochemicals (Rice, 1984). Allelochemics are present in virtually all plant tissues, including leaves, flowers, fruits, stems, roots, rhizomes, seeds and pollen. They may be released from plants into the environment by means of four ecological processes: volatilisation, leaching, root exudation, and decomposition of plant residues. Several chemicals can be released together and may exert toxicities in an additive or synergistic manner (Putnam and Tang, 1986). During the last two decades, the science of allelopathy has attracted a great number of scientists from the diverse fields world wide and is now viewed from a multifaceted approach (Rice, 1984, 1985; Putnam and Tang, 1986; Rizvi and Rizvi, 1992; Inderjit, et al., 1995, 1999; Narwal et al., 1998; Macias et al. 1999; Chou et al., 1999; Kohli et al., 2001). This diverse interest has been greatly driven by the prospects that allelopathy holds for meeting increased demands for sustainability in agriculture and quality food production for humans, on reducing environmental damage and health hazards from chemical inputs, minimizing soil erosion, reducing reliance on synthetic herbicides, and for finding alternatives to replace them (Einhellig, 1995; Dakshini et al., 1999; Singh et al., 2001). Of the disciplines involved in allelopathy research, mathematical modelling is making increasingly significant contributions. Such theoretical contributions range from separating allelopathy from competition (Weidenhamer et al., 1989; Nakamaru and Iwasa, 2000), characterizing allelopathy and its ecological roles (Cheng, 1995; Dubey and Hussain, 2000; Goslee et al., 2001; Sole et al., 2005), elucidating fundamentals of allelopathy (An et al., 1993; Liu et al., 2003), simulating specific cases, eg. plant residue allelopathy (An et al., 1996) and plankton allelopathy (Mukhopadhyay et al., 1998, 2003), to the modelling of effects by external factors, such as density of target plants (Weidenhamer et al., 1989; Sinkkonen, 2001). This article, largely based on our previous modelling work, is to specifically discuss some fundamental issues associated with the dose-response phenomenon in allelopathic research, to review the latest developments in this area, and to further illustrate the above-mentioned contributions that mathematical modelling can make to this discipline.