Temporal Variation in the Carrying Capacity of a Perennial Grass Population

Abstract

Density dependence and, therefore, K (carrying capacity, equilibrium population size) are central to understanding and predicting changes in population size (N). Although resource levels certainly fluctuate, K has almost always been treated as constant in both theoretical and empirical studies. We quantified temporal variation in K by fitting extensions of standard population dynamic models to 16 annual censuses of a population of the perennial bunchgrass Bouteloua rigidiseta. Variable-K models provided substantially better fits to the data than did models that varied the potential rate of population increase. The distribution of estimated values of K was skewed, with a long right tail (i.e., a few "jackpot" years). The population did not track K closely. Relatively slow responses to changes in K combined with large, rapid changes in K sometimes caused N to be far from K. In 13%-20% of annual intervals, K was so much larger than N that the population's dynamics were best described by geometric growth and the population was, in effect, unregulated. Explicitly incorporating temporal variation in K substantially improved the realism of models with little increase in model complexity and provided novel information about this population's dynamics. Similar methods would be applicable to many other data sets.