Insect population curves: modelling and application to butterfly transect data

Summary 1. Monitoring the abundance of insect populations is increasingly valuable to understand their population dynamics, plan management strategies and assess the attainment of conservation targets. As monitoring is often constrained in time and space, it is important to have a model of the temporal variation in numbers to enable limited field data to be fitted into a broader framework, and to estimate the total detectable population on a site. We use adult butterflies as a study system, because they are widely monitored, sensitive indicators of environmental change. 2. We derive a generic algebraic expression for the shape of the population curve that describes how the number of adult butterflies observed at a site varies through the flight period. This novel expression contains parameters corresponding to total detectable population, start-date and length of eclosion period, and mean life span. These can be optimised to fit observed series of counts (e.g. butterfly transect data, moth light-trap counts) for individual species, sites and years, using a reliable grid-refinement optimisation procedure. 3. Assumptions about survivorship and death rate are supported by field observations of the life span of two species tested. The modelled population curve (POPFIT) closely fits observed transect data for three further species. 4. We give two simplified methods of estimating the total transect population: from the Index of Abundance and from the peak population. We discuss extrapolation of transect results to estimate total site population, taking account of observed sampling efficiencies. 5. Our new method compares favourably with previous models for assessing patterns of population change at monitored sites and can assist with the planning of optimal monitoring strategies. As well as population estimates, it allows standardised phenological parameters to be derived from field data and provides a standard curve for theoretical studies. The method is applicable to all insect species whose adults have distinct, non-overwintering generations and to all other monitored organisms with similar demographies.