Applying additive modelling and gradient boosting to assess the effects of watershed and reach characteristics on riverine assemblages

Abstract

Summary 1.Issues with ecological data (e.g. non-normality of errors, nonlinear relationships and autocorrelation of variables) and modelling (e.g. overfitting, variable selection and prediction) complicate regression analyses in ecology. Flexible models, such as generalized additive models (GAMs), can address data issues, and machine learning techniques (e.g. gradient boosting) can help resolve modelling issues. Gradient boosted GAMs do both. Here, we illustrate the advantages of this technique using data on benthic macroinvertebrates and fish from 1573 small streams in Maryland, USA. 2. We assembled a predictor matrix of 15 watershed attributes (e.g. ecoregion and land use), 15 stream attributes (e.g. width and habitat quality) and location (latitude and longitude). We built boosted and conventionally estimated GAMs for macroinvertebrate richness and for the relative abundances of macroinvertebrates in the Orders Ephemeroptera, Plecoptera and Trichoptera (%EPT); individuals that cling to substrate (%Clingers); and individuals in the collector ⁄ gatherer functional feeding group (%Collectors). For fish, models were constructed for taxonomic richness, benthic species richness, biomass and the relative abundance of tolerant individuals (%Tolerant Fish). 3. For several of the responses, boosted GAMs had lower pseudo R 2 s than conventional GAMs for in-sample data but larger pseudo R 2 s for out-of-bootstrap data, suggesting boosted GAMs do not overfit the data and have higher prediction accuracy than conventional GAMs. The models explained most variation in fish richness (pseudo R 2 = 0AE97), least variation in %Clingers (pseudo R 2 = 0AE28) and intermediate amounts of variation in the other responses (pseudo R 2 s between 0AE41 and 0AE60). Many relationships of macroinvertebrate responses to anthropogenic measures and natural watershed attributes were nonlinear. Fish responses were related to system size and local habitat quality. 4. For impervious surface, models predicted below model-average macroinvertebrate richness at levels above c. 3AE0%, lower %EPT above c. 1AE5%, and lower %Clingers for levels above c. 2AE0%. Impervious surface did not affect %Collectors or any fish response. Prediction functions for %EPT and fish richness increased linearly with log 10 (watershed area), %Tolerant Fish decreased with log 10 (watershed area), and benthic fish richness and biomass both increased nonlinearly with log 10 (watershed area). 5. Gradient boosting optimizes the predictive accuracy of GAMs while preserving the structure of conventional GAMs, so that predictor-response relationships are more interpretable than with other machine learning methods. Boosting also avoids overfitting the data (by shrinking effect estimates towards zero and by performing variable selection), thus avoiding spurious predictor effects

Using ensemble models to identify and apportion heavy metal pollution sources in agricultural soils on a local scale

“…Boosting incorporates the important advantages of treebased methods, such as handling different types of predictor variables and accommodating missing data and outliers, without requiring strong model assumptions (De'ath, 2007;Lawrence et al, 2004;Maloney et al, 2012). Fitting multiple boosted regression trees overcomes the biggest drawback of single tree models e their relatively poor predictive performance (Moisen et al, 2006).…”

Boosted Beta Regression

“…Although the confidence bands in Figure 6 encompass the zero line (and can therefore not be considered “statistically significant”), the negative pattern associated with the amount of developed land in a basin was observed for the majority of the 100 bootstrap samples. Such sensitivity to developed land (i.e., urbanization) has been shown for benthic macroinvertebrates in streams (e.g., [44]) with recent thresholds reported as low as 1.5% to 3.0% [16]. Thus, Ephemeroptera in lakes appear to be as sensitive to urban development as analogous taxa in streams.…”

“…In many applications, predictor-response relationships are nonlinear in nature [15], [16]. This means that the linear predictor of the classical beta regression model needs to be replaced by a more flexible function that allows for an appropriate quantification of nonlinear predictor effects.…”

A review of macroinvertebrate‐ and fish‐based stream health modelling techniques

“…To ensure that the smoothing functions are identifiable, they are restricted to have zero mean (Maloney, Schmid, & Weller, 2012).…”