• demographic analysis;
  • matrix population models;
  • piospheres;
  • rangelands;
  • spatial patterns


  • 1
    Population modelling and field measurements of births, growth and deaths were used to investigate the long-term change in abundance of Atriplex vesicaria (Chenopodiaceae), a long-lived, palatable, perennial shrub, under sheep grazing. Of particular interest was whether A. vesicaria is at risk of being eliminated throughout grazed paddocks when the recommended practice of continuous grazing at conservative stocking rates is employed.
  • 2
    Time-invariant matrix population models indicated that the A. vesicaria population was in decline over much of the study paddock, but the rate of decline was greatest nearer to the water point (population growth rate λ ≈ 0·8). Time-varying stochastic matrix models projected that the A. vesicaria population would become locally extinct at most sites up to approximately 2200 m from water, occurring first closer to water (within 12–29 years). The population was stable (i.e. λ ≥ 1) at sites greater than 2200 m from water over the projection period of 100 years.
  • 3
    Decreases in adult survival and recruitment made the largest contributions to reductions in the population growth rate. However, there were spatial patterns centred on the water point in the degree to which particular demographic processes contributed to these reductions, because of a grazing gradient and the differential sensitivity of demographic processes to grazing. Thus decreases in recruitment contributed to reductions in the population growth rate at greater distances. Such responses, together with the sensitivity of the population growth rate to these processes, determined the spatial pattern in population growth.
  • 4
    The results suggest that piospheres (i.e. the zone of impact) continue to expand over many years under set-stocking so that the area around the water point that is devoid of A. vesicaria becomes larger. The process of expansion appears to first involve the inhibition of recruitment, followed by eventual mortality of established shrubs.
  • 5
    The large contribution of adult survival to the population growth rate in A. vesicaria suggests that minimizing the mortality of established adults should be a priority for management. This is likely to involve resting from grazing at critical times such as during extended dry periods. This may also permit increased levels of recruitment during subsequent moister periods.