Incorporating the intraspecific occupancy-abundance relationship into zero-inflated models

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.

A pathway for multivariate analysis of ecological communities using copulas

We describe a new pathway for multivariate analysis of data consisting of counts of species abundances that includes two key components: copulas, to provide a flexible joint model of individual species, and dissimilarity-based methods, to integrate information across species and provide a holistic view of the community. Individual species are characterized using suitable (marginal) statistical distributions, with the mean, the degree of over-dispersion, and/or zero-inflation being allowed to vary among a priori groups of sampling units. Associations among species are then modeled using copulas, which allow any pair of disparate types of variables to be coupled through their cumulative distribution function, while maintaining entirely the separate individual marginal distributions appropriate for each species. A Gaussian copula smoothly captures changes in an index of association that excludes joint absences in the space of the original species variables. A permutation-based filter with exact family-wise error can optionally be used a priori to reduce the dimensionality of the copula estimation problem. We describe in detail a Monte Carlo expectation maximization algorithm for efficient estimation of the copula correlation matrix with discrete marginal distributions (counts). The resulting fully parameterized copula models can be used to simulate realistic ecological community data under fully specified null or alternative hypotheses. Distributions of community centroids derived from simulated data can then be visualized in ordinations of ecologically meaningful dissimilarity spaces. Multinomial mixtures of data drawn from copula models also yield smooth power curves in dissimilarity-based settings. Our proposed analysis pathway provides new opportunities to combine model-based approaches with dissimilarity-based methods to enhance understanding of ecological systems. We demonstrate implementation of the pathway through an ecological example, where associations among fish species were found to increase after the establishment of a marine reserve.

An integrated data model to estimate spatiotemporal occupancy, abundance, and colonization dynamics

Ecological invasions and colonizations occur dynamically through space and time. Estimating the distribution and abundance of colonizing species is critical for efficient management or conservation. We describe a statistical framework for simultaneously estimating spatiotemporal occupancy and abundance dynamics of a colonizing species. Our method accounts for several issues that are common when modeling spatiotemporal ecological data including multiple levels of detection probability, multiple data sources, and computational limitations that occur when making fine-scale inference over a large spatiotemporal domain. We apply the model to estimate the colonization dynamics of sea otters (Enhydra lutris) in Glacier Bay, in southeastern Alaska.

Expectations and Outcomes of Reserve Network Performance following Re-zoning of the Great Barrier Reef Marine Park

Networks of no-take marine reserves (NTMRs) are widely advocated for preserving exploited fish stocks and for conserving biodiversity. We used underwater visual surveys of coral reef fish and benthic communities to quantify the short- to medium-term (5 to 30 years) ecological effects of the establishment of NTMRs within the Great Barrier Reef Marine Park (GBRMP). The density, mean length, and biomass of principal fishery species, coral trout (Plectropomus spp., Variola spp.), were consistently greater in NTMRs than on fished reefs over both the short and medium term. However, there were no clear or consistent differences in the structure of fish or benthic assemblages, non-target fish density, fish species richness, or coral cover between NTMR and fished reefs. There was no indication that the displacement and concentration of fishing effort reduced coral trout populations on fished reefs. A severe tropical cyclone impacted many survey reefs during the study, causing similar declines in coral cover and fish density on both NTMR and fished reefs. However, coral trout biomass declined only on fished reefs after the cyclone. The GBRMP is performing as expected in terms of the protection of fished stocks and biodiversity for a developed country in which fishing is not excessive and targets a narrow range of species. NTMRs cannot protect coral reefs directly from acute regional-scale disturbance but, after a strong tropical cyclone, impacted NTMR reefs supported higher biomass of key fishery-targeted species and so should provide valuable sources of larvae to enhance population recovery and long-term persistence.

Estimating abundance while accounting for rarity, correlated behavior, and other sources of variation in counts

The class of N-mixture models allows abundance to be estimated from repeated, point count surveys while adjusting for imperfect detection of individuals. We developed an extension of N-mixture models to account for two commonly observed phenomena in point count surveys: rarity and lack of independence induced by unmeasurable sources of variation in the detectability of individuals. Rarity increases the number of locations with zero detections in excess of those expected under simple models of abundance (e.g., Poisson or negative binomial). Correlated behavior of individuals and other phenomena, though difficult to measure, increases the variation in detection probabilities among surveys. Our extension of N-mixture models includes a hurdle model of abundance and a beta-binomial model of detectability that accounts for additional (extra-binomial) sources of variation in detections among surveys. As an illustration, we fit this model to repeated point counts of the West Indian manatee, which was observed in a pilot study using aerial surveys. Our extension of N-mixture models provides increased flexibility. The effects of different sets of covariates may be estimated for the probability of occurrence of a species, for its mean abundance at occupied locations, and for its detectability.