Minimum area requirements for an at-risk butterfly based on movement and demography

Determining the minimum area required to sustain populations has a long history in theoretical and conservation biology. Correlative approaches are often used to estimate minimum area requirements (MARs) based on relationships between area and the population size required for persistence or between species' traits and distribution patterns across landscapes. Mechanistic approaches to estimating MAR facilitate prediction across space and time but are few. We used a mechanistic MAR model to determine the critical minimum patch size (CMP) for the Baltimore checkerspot butterfly (Euphydryas phaeton), a locally abundant species in decline along its southern range, and sister to several federally listed species. Our CMP is based on principles of diffusion, where individuals in smaller patches encounter edges and leave with higher probability than those in larger patches, potentially before reproducing. We estimated a CMP for the Baltimore checkerspot of 0.7-1.5 ha, in accordance with trait-based MAR estimates. The diffusion rate on which we based this CMP was broadly similar when estimated at the landscape scale (comparing flight path vs. capture-mark-recapture data), and the estimated population growth rate was consistent with observed site trends. Our mechanistic approach to estimating MAR is appropriate for species whose movement follows a correlated random walk and may be useful where landscape-scale distributions are difficult to assess, but demographic and movement data are obtainable from a single site or the literature. Just as simple estimates of lambda are often used to assess population viability, the principles of diffusion and CMP could provide a starting place for estimating MAR for conservation.