1. In observational demographic data, the number of measured factors that could potentially drive demography (such as daily weather records between two censuses) can easily exceed the number of independent observations. Thus, identifying the important drivers requires alternatives to standard model selection and variable selection methods.2. Spline methods that estimate smooth functions over continuous domains (such as space or time) have the potential to resolve high-dimensional problems in ecological systems. We consider two examples that are important for many plant populations: competition with neighbours that vary in size and distance from the focal individual and climate variables during a window of time before a response (growth, survival, etc.) is measured. 3. For competition covariates, we use a simulation study based on empirical data to show that a monotone spline estimate of competition kernels via approximate AIC returns very accurate estimates. We then apply the method to long-term, mapped quadrat data on the four dominant species in an Idaho (US) sagebrush steppe community. 4. For climate predictors and their temporal lags, we use simulated data sets to compare functional smoothing methods with competing linear (LASSO) or machine learning (random forests) methods. Given sufficient data, functional smoothing methods outperformed the other two methods. 5. Functional smoothing methods can advance data-driven population modelling by providing alternatives to specifying competition kernels a priori and to arbitrarily aggregating continuous environmental covariates. However, there are important open questions related to modelling of nonlinear climate responses and size 9 climate interactions.

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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.

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