• annual weed control;
  • density dependence;
  • stochastic model;
  • temporal variability

1.  Population models that are used to predict weed population dynamics or the impact of control measures on weed abundance typically ignore temporal variability in life-history parameters and control measures, and utilize mean arithmetic population growth rates to predict population abundance.

2.  We demonstrate that the persistence of weeds in a stochastically varying environment depends on the geometric mean population growth rate being greater than zero, rather than the arithmetic mean population growth rate being greater than zero.

3.  In a stochastically varying environment we show that temporal variability in fecundity, germination and survivorship will tend to decrease population size, relative to predictions based on arithmetic means. Conversely, variability in competitive effects and weed control will tend to increase population size, relative to predictions based on arithmetic mean values. The distinction between these two sets of parameters is that increases in the former will increase population growth rate, whereas increases in the latter will decrease it.

4.  We argue that population models based on arithmetic mean population growth rates will tend to over-estimate population size. Numerical simulations indicate that this bias may be considerable.

5.  Since short-term studies cannot, in general, estimate the geometric mean growth rate of a population we suggest several approaches for estimating the degree of bias in the predictions of models owing to the effects of variability. Accounting for such variability is necessary since current models for the dynamics of weed populations are based on arithmetic mean measures of population growth and hence likely to be biased.