How emergence and death assumptions affect count-based estimates of butterfly abundance and lifespan

rGAI: An R package for fitting the generalized abundance index to seasonal count data

The generalized abundance index (GAI) provides a useful tool for estimating relative population sizes and trends of seasonal invertebrates from species' count data and offers potential for inferring which external factors may influence phenology and demography through parametric descriptions of seasonal variation. We provide an R package that extends previous software with the ability to include covariates when fitting parametric GAI models, where seasonal variation is described by either a mixture of Normal distributions or a stopover model which provides estimates of life span. The package also generalizes the models to allow any number of broods/generations in the target population within a defined season. The option to perform bootstrapping, either parametrically or nonparametrically, is also provided. The new package allows models to be far more flexible when describing seasonal variation, which may be dependent on site-specific environmental factors or consist of many broods/generations which may overlap, as demonstrated by two case studies. Our open-source software, available at https://github.com/calliste-fagard-jenkin/rGAI, makes these extensions widely and freely available, allowing the complexity of GAI models used by ecologists and applied statisticians to increase accordingly.

Agent-based models reveal limits of mark-release-recapture estimates for the rare butterfly, Bhutanitis thaidina (Lepidoptera: Papilionidae)

Insect diversity and abundance are in drastic decline worldwide, but quantifying insect populations to better conserve them is a difficult task. Mark-release-recapture (MRR) is widely used as an ecological indicator for insect populations, but the accuracy of MRR estimates can vary with factors such as spatial scale, sampling effort and models of inference. We conducted a 3-year MRR study of B. thaidina in Yanzigou valley, Mt. Gongga but failed to obtain sufficient data for a robust population estimate. This prompted us to integrate B. thaidina life history information to parameterize agent-based models and evaluate the conditions under which successful MRR studies could be conducted. We evaluated: (1) the performance of MRR models under different landscape types, and (2) the influence of experimental design on the accuracy and variance of MRR-based estimates. Our simulations revealed systematic underestimates of true population parameters by MRR models when sampling effort was insufficient. In a total of 2772 simulations, subjective decisions in sampling protocol (e.g., frequency, number of sampling locations, use of spatially explicit models, type of estimands) accounted for nearly half of the variation in estimates. We conclude that MRR-based estimates could be improved with the addition of more field-specific parameters.

A generalized abundance index for seasonal invertebrates

At a time of climate change and major loss of biodiversity, it is important to have efficient tools for monitoring populations. In this context, animal abundance indices play an important rôle. In producing indices for invertebrates, it is important to account for variation in counts within seasons. Two new methods for describing seasonal variation in invertebrate counts have recently been proposed; one is nonparametric, using generalized additive models, and the other is parametric, based on stopover models. We present a novel generalized abundance index which encompasses both parametric and nonparametric approaches. It is extremely efficient to compute this index due to the use of concentrated likelihood techniques. This has particular relevance for the analysis of data from long-term extensive monitoring schemes with records for many species and sites, for which existing modeling techniques can be prohibitively time consuming. Performance of the index is demonstrated by several applications to UK Butterfly Monitoring Scheme data. We demonstrate the potential for new insights into both phenology and spatial variation in seasonal patterns from parametric modeling and the incorporation of covariate dependence, which is relevant for both monitoring and conservation. Associated R code is available on the journal website.

Dynamic Models for Longitudinal Butterfly Data

We present models which provide succinct descriptions of longitudinal seasonal insect count data. This approach produces, for the first time, estimates of the key parameters of brood productivities. It may be applied to univoltine and bivoltine species. For the latter, the productivities of each brood are estimated separately, which results in new indices indicating the contributions from different generations. The models are based on discrete distributions, with expectations that reflect the underlying nature of seasonal data. Productivities are included in a deterministic, auto-regressive manner, making the data from each brood a function of those in the previous brood. A concentrated likelihood results in appreciable efficiency gains. Both phenomenological and mechanistic models are used, including weather and site-specific covariates. Illustrations are provided using data from the UK Butterfly Monitoring Scheme, however the approach is perfectly general. Consistent associations are found when estimates of productivity are regressed on northing and temperature. For instance, for univoltine species productivity is usually lower following milder winters, and mean emergence times of adults for all species have become earlier over time, due to climate change. The predictions of fitted dynamic models have the potential to improve the understanding of fundamental demographic processes. This is important for insects such as UK butterflies, many species of which are in decline. Supplementary materials for this article are available online.