Significant shifts in latitudinal optima of North American birds.

Changes in climate can alter environmental conditions faster than most species can adapt. A prediction under a warming climate is that species will shift their distributions poleward through time. While many studies focus on range shifts, latitudinal shifts in species' optima can occur without detectable changes in their range. We quantified shifts in latitudinal optima for 209 North American bird species over the last 55 y. The latitudinal optimum (m) for each species in each year was estimated using a bespoke flexible non-linear zero-inflated model of abundance vs. latitude, and the annual shift in m through time was quantified. One-third (70) of the bird species showed a significant shift in their optimum. Overall, mean peak abundances of North American birds have shifted northward, on average, at a rate of 1.5 km per year (±0.58 SE), corresponding to a total distance moved of 82.5 km (±31.9 SE) over the last 55 y. Stronger poleward shifts at the continental scale were linked to key species' traits, including thermal optimum, habitat specialization, and territoriality. Shifts in the western region were larger and less variable than in the eastern region, and they were linked to species' thermal optimum, habitat density preference, and habitat specialization. Individual species' latitudinal shifts were most strongly linked to their estimated thermal optimum, clearly indicating a climate-driven response. Displacement of species from their historically optimal realized niches can have dramatic ecological consequences. Effective conservation must consider within-range abundance shifts. Areas currently deemed "optimal" are unlikely to remain so.

Non-linear models of species' responses to environmental and spatial gradients.

Species' responses to broad-scale environmental or spatial gradients are typically unimodal. Current models of species' responses along gradients tend to be overly simplistic (e.g., linear, quadratic or Gaussian GLMs), or are suitably flexible (e.g., splines, GAMs) but lack direct ecologically interpretable parameters. We describe a parametric framework for species-environment non-linear modelling ('senlm'). The framework has two components: (i) a non-linear parametric mathematical function to model the mean species response along a gradient that allows asymmetry, flattening/peakedness or bimodality; and (ii) a statistical error distribution tailored for ecological data types, allowing intrinsic mean-variance relationships and zero-inflation. We demonstrate the utility of this model framework, highlighting the flexibility of a range of possible mean functions and a broad range of potential error distributions, in analyses of fish species' abundances along a depth gradient, and how they change over time and at different latitudes.