Monitoring abundance and phenology in (multivoltine) butterfly species: A novel mixture model

Summary: Data from 'citizen science' surveys are increasingly valuable in identifying declines in widespread species, but require special attention in the case of invertebrates, with considerable variation in number, seasonal flight patterns and, potentially, voltinism. There is a need for reliable and more informative methods of inference in such cases. We focus on data consisting of sample counts of individuals that are not uniquely identifiable, collected at one or more sites. Arrival or emergence and departure or death of individuals take place during the study. We introduce a new modelling approach, which borrows ideas from the 'stopover' capture-recapture literature, that permits the estimation of parameters of interest, such as mean arrival times and relative abundance, or in some cases, absolute abundance, and the comparison of these between sites. The model is evaluated using an extensive simulation study which demonstrates that the estimates for the parameters of interest obtained by the model are reliable, even when the data sets are sparse, as is often the case in reality. When applied to data for the common blue butterfly Polyommatus icarus at a large number of sites, the results suggest that mean emergence times, as well as the relative sizes of the broods, are linked to site northing, and confirm field experience that the species is bivoltine in the south of the UK but practically univoltine in the north. Synthesis and applications. Our proposed 'stopover' model is parameterized with biologically informative constituents: times of emergence, survival rate and relative brood sizes. Estimates of absolute or relative abundance that can be obtained alongside these underlying variables are robust to the presence of missing observations and can be compared in a statistically rigorous framework. These estimates are direct indices of abundance, rather than 'sightings', implicitly adjusted for the possible presence of repeat sightings during a season. At the same time, they provide indices of change in demographic and phenological parameters that may be of use in identifying the factors underlying population change. The model is widely applicable and this will increase the utility of already valuable and influential long-standing surveys in monitoring the effects of environmental change on phenology or abundance.