A general framework for the aggregation model of coexistence


Stephen Hartley, School of Biological Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand. Tel: + 64 4 4635233, ext. 8135; Fax: + 64 4 4635331; E-mail: stephen.hartley@vuw.ac.nz


  • 1The aggregation model of coexistence has been used widely to explain the coexistence of competing species that utilize patchy and ephemeral resources. Over the years, it has been reformulated in many different ways, using different assumptions, indices and analyses, leading sometimes to contradictory conclusions. We present a general framework, from which many of the alternative approaches are derived as special cases.
  • 2A generalized distribution, composed of the distribution of visits across patches and the distribution of eggs per visit, is used to model changes in the mean individual-level experience of density that occur at different population-level densities.
  • 3New and more general criteria for coexistence are derived, based upon standard invasability analysis of Lotka–Volterra competition equations applied to a patchy system.
  • 4An important parameter in the new coexistence criteria is the mean per capita density of individuals in a single clutch ( inline image ). Until now this measure has been relatively ignored, experimentally and theoretically.
  • 5We confirm earlier findings that the random distribution of clutches may be a sufficient cause of aggregated egg distributions to allow coexistence between species of unequal competitive ability, but only if the product of competition coefficients is less than one.