Estimating abundance and phenology from transect count data with GLMs

Abstract

Estimating population abundance is central to population ecology. With increasing concern over declining insect populations, estimating trends in abundance has become even more urgent. At the same time, there is an emerging interest in quantifying phenological patterns, in part because phenological shifts are one of the most conspicuous signs of climate change. Existing techniques to fit activity curves (and thus both abundance and phenology) to repeated transect counts of insects (a common form of data for these taxa) frequently fail for sparse data, and often require advanced knowledge of statistical computing. These limitations prevent us from understanding both population trends and phenological shifts, especially in the at‐risk species for which this understanding is most vital. Here we present a method to fit repeated transect count data with Gaussian curves using linear models and show how robust abundance and phenological metrics can be obtained using standard regression tools. We then apply this method to nine years of Baltimore checkerspot data using generalized linear models (GLMs). This case study illustrates the ability of our method to fit even years with only a few non‐zero survey counts, and identifies a significant negative relationship between population size and growing degree days (GDD) each year. We believe our new method provides a key tool to unlock previously‐unusable data sets, and may provide a useful middle ground between ad hoc metrics of abundance and phenology, and custom‐coded mechanistic models.

Predicting surface abundance of federally threatened Jollyville Plateau Salamanders (Eurycea tonkawae) to inform management activities at a highly modified urban spring

“…Central Texas Eurycea salamander surface abundance is known to increase throughout the spring, peak in the summer, and decrease in autumn and winter ( Bowles, Sanders & Hansen, 2006 ; Pierce et al, 2010 ; Bendik, 2017 ). To account for this phenology, we included the quadratic effect of day-of-year (day 2 ) as a predictor within each model ( Kéry & Royle, 2016 ; Edwards & Crone, 2021 ). We included the lower-order term of “day” to adhere to the rules of marginality ( McCullagh & Nelder, 1989 ; Kéry & Royle, 2016 ).…”

Do demographic processes change at extremely low population size in western monarch butterflies?

“…These data included monarch observations across western North America from the late 1800s through 2020, but required careful attention to address its ad-hoc and presence-only nature. We used quantile regression (Cade and Noon 2003) to fit distance from overwintering sites through time as a Gaussian curve (Edwards and Crone 2021) (Figure 2B). We used the 0.9 quantile, which represents the boundary between the 10% of monarchs that were most distant and the remaining 90%, as a measure of breeding season range size that is robust to outliers (we find similar patterns for other quantiles; see Figure S2).…”

“…3B). In (40) we show how Gaussian curves can be fit with linear models; we combine this approach with the rq() function from the quantreg package, which fits a linear model with quantile regression (41). We used the 0.9 quantile to represent the outer boundary of the monarch range; this captures the expansion of monarchs into their summer breeding range while still being robust to outliers (but the specific quantile chosen did not matter: see below).…”

Phenological research based on natural history collections: Practical guidelines and a lepidopteran case study

“…For univoltine species, we fit phenometrics for species-cell-year combinations that had at least five observations, four distinct days of collecting and three distinct collectors. Three days with observations have been demonstrated to produce useful phenoestimates of unimodal species using survey data (Edwards & Crone, 2021). However, multimodal species may have longer durations and more complex seasonal abundances, making their phenometrics harder to estimate (Belitz et al, 2020).…”