BioSystems 57 (2000) 129 – 138 Succession processes in a food web of a two autotroph – one herbivore system Dipak Kesh *, A.K. Sarkar, A.B. Roy Department of Mathematics, Diision of Biomathematics, Centre for Mathematical Biology and Ecology, Jadapur Uniersity, Calcutta 700 032, India Received 17 February 2000; accepted 19 May 2000 Abstract This paper deals with the succession process of a food web model consisting of one herbivore, two autotrophs and available nutrient in the environment in a closed nutrient flux. The model provides a way of describing successional changes in the form of species replacement with increasing nutrient levels. It is shown that distinct threshold (with upper and lower) values of nutrient are required for progression of succession process. © 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Succession; Nutrient flux; Saturated equilibria; Uniform persistence www.elsevier.com/locate/biosystems 1. Introduction Ecosystem changes may be caused by fluctua- tions in the internal population interactions or by fluctuations of the controlling factors. Such changes could be cyclical changes or directional changes from less complex to more complex com- munities, and can be considered as progression in succession. During progressive succession there is usually an increase in productivity of biomass, related to stability and diversity of species. Suc- cession is a typical example of an irreversible process in ecology in which co-operation between organisms replace one another in a given region. The succession of species population may be a result of one or a combination of general factors: (i) phenotypic characteristics of species (some en- tering a disturbed area sooner than others and growing faster); (ii) externally imposed changes in one or more environmental parameters that fa- vour some species over the others; (iii) changes in the environment caused by the populations them- selves (see DeAngelis, 1992; Smith, 1990). In this paper a possible succession process due to changes in the amount of nutrients will be analysed on the assumption that succession ends in the formation of a stable climateric biocenosis. Rosenzweig (1971) studied a series of predator- prey models with different prey productivities and predator functional response curves, and estab- lished the possibility of oscillatory instability un- * Corresponding author. Tel.: +91-33-4720717; fax: +91- 33-4720964. E-mail address: dkesh@hotmail.com (D. Kesh). 0303-2647/00/$ - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S0303-2647(00)00092-7