The interaction between spread of a plant species and its population growth rate is discussed. Three parameters, population growth rate at an infection site, fractional loss by dispersal and the distance this fraction can move were used to build a simple model of spread. The effect of changes in these parameters on rates of spread, patterns of spread and total population growth rate were examined using simulation. There was no simple arithmetic relationship between the parameters, spread and total population growth rate because of spatial limitations on the spreading population. Rates of total population growth tended to be exponential and rates of spread linear.
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Auld et al. (1980) studied this question.