Are individual based models a suitable approach to estimate population vulnerability? - a case study

Abstract

European populations of the Large Blue Butterfly Maculinea arion have experienced severe declines in the last decades, especially in the northern part of the species range. This endangered lycaenid butterfly needs two resources for development: flower buds of specific plants (Thymus spp., Origanum vulgare), on which young caterpillars briefly feed, and red ants of the genus Myrmica, whose nests support caterpillars during a prolonged final instar. I present an analytically solvable deterministic model to estimate the vulnerability of populations of M. arion. Results obtained from the sensitivity analysis of this mathematical model (MM) are contrasted to the respective results that had been derived from a spatially explicit individual based model (IBM) for this butterfly. I demonstrate that details in landscape configuration which are neglected by the MM but are easily taken into consideration by the IBM result in a different degree of intraspecific competition of caterpillars on flower buds and within host ant nests. The resulting differences in mortalities of caterpillars lead to erroneous estimates of the extinction risk of a butterfly population living in habitat with low food plant coverage and low abundance in host ant nests. This observation favors the use of an individual based modeling approach over the deterministic approach at least for the management of this threatened butterfly.

Keywords

• individual based model
• mathematical model
• environmental heterogeneity
• competition
• Maculinea arion