POPULATION VARIANCE AND DETERMINISTIC STABILITY ANALYSIS

1. Prompted by the simulation studies of Morrison & Barbosa (1987) and of Taylor (1992), an examination was made of the relationship between population variance and the magnitude of the dominant eigenvalue from stability analyses of linearized stable systems. Explicit expressions were derived for continuous and discrete-time systems and hence it fo llows that. for determination of local variance, simulations are not r equired. 2. Drawing on earlier studies it is shown that population var iance can increase or decrease as the eigenvalue increases; the latter could be associated with the tracking of 'environmental noise'. Accur ate modelling of the process noise is important in this respect. 3. Th e above suggest that the magnitude of the eigenvalue of the linearized deterministic system will not, in general, allow inference as to the character of population variance or the higher order distributions suc h as extinction time. As yet, no general rules have been developed tha t allow identification of whether or not the stability eigenvalue conv eys more information than that relating to the existence of an attract ive equilibrium and the oscillatory or otherwise approach to the equil ibrium.