Chains of opportunity: A Markov model for acquisition of reusable resources

Abstract

A vacancy chain is a unique type of resource acquisition process composed of an interconnected series of events in which the gaining of a particular resource unit by one individual depends directly on prior acquisition events by other individuals. Taken from the sociological literature, vacancy chains may also describe the distribution of many types of animal resources such as burrows, dwellings and shelters. Using data on hermit crabs, we present a Markov model simulating a vacancy chain process, and test the model against field data. Our results show that a simple Markov model adequately describes shell acquisition in hermit crabs, and that models combining shell size and crude estimates of quality fit the data extremely well. We illustrate in detail how to generate vacancy chain models from ecological data, how to determine the number and size of organisms gaining new resource units from resource introductions of specific sizes, and how to statistically evaluate the accuracy of Markov models. Not recognizing the presence of a vacancy chain system may lead to serious errors in estimating resource dynamics and therefore in demographic and competition models based on these dynamics. Finally, we suggest some ways in which vacancy chain models can aid studies of competition, population dynamics, life histories, and conservation in species using this type of resource acquisition process.