Defining the limits to local density: alternative views of abundance–environment relationships

Abstract

Summary1. In many ecosystems, the local abundance of organisms is spatially heterogeneous. Ecologists often seek to explain this variation by modelling the central tendency of abundance as a function of a single dominant factor (central response, CR). An alternative approach is to model maximum and minimum abundance in relation to the dominant factor (limiting response, LR), thereby acknowledging that multiple factors may constrain abundance and create scatter in the relationship. In many ecosystems, including streams, abundance–environment relationships are traditionally expected to be CR models with a single dominant factor determining local abundance, but this hypothesis lacks rigorous test. This omission is of concern because CR modelled relationships form the foundations of many ecological tests, predictive and management tools that, consequently, may provide erroneous interpretations.2. In a survey designed to minimise variance in the data, we related densities of three taxa of stream invertebrates to near‐bed flow. Data were analysed using both ordinary least squares (OLS) regression and quantile regression, which have different characteristic results depending on whether the relationship is better described as a CR or LR model. For all three taxa, invertebrate responses to flow conformed most closely to LR models and were best described by quantile regression, although OLS regression revealed broadly similar general trends in this case.3. Based on the statistically modelled relationships, we were able to hypothesise which ecological mechanisms limited maximum abundance at this site, including dislodgement with high flow (Heptageniidae, Leuctridae), reduced oxygen uptake at low flow (Baetidae) and reduced provision of interstitial spaces at high flow (Leuctridae). Scatter in the relationships was attributable to multiple factors that may operate at different scales, including inter‐individual variation, alternative environmental gradients and biotic processes at the patch scale, and potential constraints of dispersal and settlement operating outside the patch.4. We illustrate how the choice of CR or LR model to describe abundance–environment relationships may affect tests of ecological theory and applied ecology. If our results are typical of other streams and other types of systems, greater use of LR models may transform the way many ecologists view ecosystems, thus having positive consequences for survey and experimental designs and highlighting weaknesses in existing management tools that are underpinned by CR models.