Assessment of the relative impact of different natural enemies on population dynamics of the grain aphid Sitobion avenae in the ®eld M. PLANTEGENEST, 1 J. S. PIERRE, 1 C. A. DEDRYVER 2 and P. KINDLMANN 3 1 Ecole Nationale Supe Ârieure Agronomique de Rennes, Laboratoire d'Ecologie et Sciences Phytosanitaires, Rennes, France, 2 Institut National de la Recherche Agronomique, Laboratoire de Zoologie, Le Rheu, France and 3 Faculty of Biological Sciences, University of South Bohemia, Ceske  Budejovice, Czech Republic Abstract. 1. A detailed population dynamics model was devised to provide a tool for integrated pest management against the cereal aphid Sitobion avenae on winter wheat. 2. This model allowed investigation of the relative impact of different natural enemies on aphid population dynamics. 3. The output of the model was compared with a set of data collected in the western part of France from 1976 to 1986. 4. Fungal diseases accounted for 75% of the reduction in peak aphid density and were the key factor acting on aphid dynamics in this region. 5. This study highlights the importance of detailed population dynamics modelling of keystone species, like aphids, for elucidation of the relations between the keystone species and other species associated in the ecosystem. Key words. Cereal aphids, entomophthorales, modelling, parasitoid Hymenoptera, Von Foerster's equations, winter wheat. Introduction Cereal aphids have become serious pests in western Europe since the 1970s (Carter et al., 1980) and occasionally cause signi®cant yield losses. The three commonest species are the grain aphid Sitobion avenae F., the rose grain aphid Metopolophium dirhodum Wlk., and the bird-cherry oat aphid Rhopalosiphum padi Wlk., with S. avenae being the most damaging pest. Outbreaks of these species are, however, too sporadic to justify prophylactic control. The low frequency of outbreaks is generally attributed to the effect of natural enemies or to density-independent factors such as weather. The main natural enemies of grain aphids in the ®eld are fungus diseases (Entomophthorales) and parasitoids (Hymenoptera), while predators like Coccinellidae, Chrysopidae, Syrphidae, ground beetles, and spiders are much less important (Dedryver, 1987; Dixon et al., 1995; Kindlmann & Dixon, 1999a,b). The size of the effect of the main natural enemies in reducing aphid population densities is not clear and may vary geographically with climate and cereal phenology. The work reported here was designed to develop a method for the assessment of the relative importance of the natural enemies. This was achieved in two steps: a detailed population dynamics model for aphids in the absence of natural enemies was developed, and differences between predicted and observed densities were related to the presence of natural enemies. The main characteristics of aphid population dynamics (overlapping generations, short generation time, large popula- tion size, continuous reproduction) are easily incorporated into a deterministic age-structured simulation model based on Von Foerster's (1959) partial differential equations, similar to that used by Rodolphe et al. (1977) to describe white¯y Trialeurodes vaporariorum population dynamics. This model, continuous both in age and time, is a generalisation of Lotka's (1925) continuous model and Leslie's (1945) age-structured discrete model. It allows differentiation between the relative in¯uence of density-independent factors such as temperature and host plant characteristics, the effects of which are fairly well known, and the relative in¯uence of density-dependent factors (morphogenesis, immigration, natural enemies), which are too numerous to be taken into account exhaustively in a model. Von Foerster's model incorporates each life-history Correspondence: Dr Pavel Kindlmann, Faculty of Biological Sciences, University of South Bohemia, Branis Ïovska  31, 370 05 Ceske  Budejovice, Czech Republic. E-mail: pavel@entu.cas.cz 404 # 2001 Blackwell Science Ltd Ecological Entomology (2001) 26, 404±410 Ecological Entomology (2001) 26, 404±410