James T. Thorson

Incorporating Time-Varying Catchability into Population Dynamic Stock Assessment Models

Catchability is an important parameter in many stock assessment models because it relates an index of abundance to stock size. We review the theory and evidence for time-varying catchability, its effects on stock assessment estimates, and methods to include time-varying catchability in stock assessments. Numerous studies provide strong evidence that time-varying catchability is common in most fisheries and many fishery-independent surveys and can be caused by anthropogenic, environmental, biological, and management processes. Trends in catchability over time can cause biased estimates of stock size and fishing mortality rates in stock assessment models that do not compensate for them. Methods that use descriptive and functional relationships have been developed to incorporate time-varying catchability in stock assessment models. We recommend that the default assumption for stock assessments should be that catchability varies over time and that multiple methods of including time-varying catchability should be applied. Additional studies are needed to determine relative performance of alternative methods and to develop methods for selecting among models.

Eco-Label Conveys Reliable Information on Fish Stock Health to Seafood Consumers

Concerns over fishing impacts on marine populations and ecosystems have intensified the need to improve ocean management. One increasingly popular market-based instrument for ecological stewardship is the use of certification and eco-labeling programs to highlight sustainable fisheries with low environmental impacts. The Marine Stewardship Council (MSC) is the most prominent of these programs. Despite widespread discussions about the rigor of the MSC standards, no comprehensive analysis of the performance of MSC-certified fish stocks has yet been conducted. We compared status and abundance trends of 45 certified stocks with those of 179 uncertified stocks, finding that 74% of certified fisheries were above biomass levels that would produce maximum sustainable yield, compared with only 44% of uncertified fisheries. On average, the biomass of certified stocks increased by 46% over the past 10 years, whereas uncertified fisheries increased by just 9%. As part of the MSC process, fisheries initially go through a confidential pre-assessment process. When certified fisheries are compared with those that decline to pursue full certification after pre-assessment, certified stocks had much lower mean exploitation rates (67% of the rate producing maximum sustainable yield vs. 92% for those declining to pursue certification), allowing for more sustainable harvesting and in many cases biomass rebuilding. From a consumer’s point of view this means that MSC-certified seafood is 3–5 times less likely to be subject to harmful fishing than uncertified seafood. Thus, MSC-certification accurately identifies healthy fish stocks and conveys reliable information on stock status to seafood consumers.

Modeling structured population dynamics using data from unmarked individuals

The study of population dynamics requires unbiased, precise estimates of abundance and vital rates that account for the demographic structure inherent in all wildlife and plant populations. Traditionally, these estimates have only been available through approaches that rely on intensive mark-recapture data. We extended recently developed N-mixture models to demonstrate how demographic parameters and abundance can be estimated for structured populations using only stage-structured count data. Our modeling framework can be used to make reliable inferences on abundance as well as recruitment, immigration, stage-specific survival, and detection rates during sampling. We present a range of simulations to illustrate the data requirements, including the number of years and locations necessary for accurate and precise parameter estimates. We apply our modeling framework to a population of northern dusky salamanders (Desmognathus fuscus) in the mid-Atlantic region (USA) and find that the population is unexpectedly declining. Our approach represents a valuable advance in the estimation of population dynamics using multistate data from unmarked individuals and should additionally be useful in the development of integrated models that combine data from intensive (e.g., mark-recapture) and extensive (e.g., counts) data sources.

Spatial factor analysis: a new tool for estimating joint species distributions and correlations in species range

Summary Predicting and explaining the distribution and density of species is one of the oldest concerns in ecology. Species distributions can be estimated using geostatistical methods, which estimate a latent spatial variable explaining observed variation in densities, but geostatistical methods may be imprecise for species with low densities or few observations. Additionally, simple geostatistical methods fail to account for correlations in distribution among species and generally estimate such cross-correlations as a post hoc exercise. We therefore present spatial factor analysis (SFA), a spatial model for estimating a low-rank approximation to multivariate data, and use it to jointly estimate the distribution of multiple species simultaneously. We also derive an analytic estimate of cross-correlations among species from SFA parameters. As a first example, we show that distributions for 10 bird species in the breeding bird survey in 2012 can be parsimoniously represented using only five spatial factors. As a second case study, we show that forward prediction of catches for 20 rockfishes (Sebastes spp.) off the U.S. West Coast is more accurate using SFA than analysing each species individually. Finally, we show that single-species models give a different picture of cross-correlations than joint estimation using SFA. Spatial factor analysis complements a growing list of tools for jointly modelling the distribution of multiple species and provides a parsimonious summary of cross-correlation without requiring explicit declaration of habitat variables. We conclude by proposing future research that would model species cross-correlations using dissimilarity of species’ traits, and the development of spatial dynamic factor analysis for a low-rank approximation to spatial time-series data.

The importance of spatial models for estimating the strength of density dependence

Identifying the existence and magnitude of density dependence is one of the oldest concerns in ecology. Ecologists have aimed to estimate density dependence in population and community data by fitting a simple autoregressive (Gompertz) model for density dependence to time series of abundance for an entire population. However, it is increasingly recognized that spatial heterogeneity in population densities has implications for population and community dynamics. We therefore adapt the Gompertz model to approximate, local densities over continuous space instead of population-wide abundance, and allow productivity to vary spatially using Gaussian random fields. We then show that the conventional (nonspatial) Gompertz model can result in biased estimates of density dependence (e.g., identifying oscillatory dynamics when not present) if densities vary spatially. By contrast, the spatial Gompertz model provides accurate and precise estimates of density dependence for a variety of simulation scenarios and data availabilities. These results are corroborated when comparing spatial and nonspatial models for data from 10 years and -100 sampling stations for three long-lived rockfishes (Sebastes spp.) off the California, USA coast. In this case, the nonspatial model estimates implausible oscillatory dynamics on an annual time scale, while the spatial model estimates strong autocorrelation and is supported by model selection tools. We conclude by discussing the importance of improved data archiving techniques, so that spatial models can be used to reexamine classic questions regarding the existence and magnitude of density. dependence in wild populations.

Spatial variation buffers temporal fluctuations in early juvenile survival for an endangered Pacific salmon.

Spatial, phenotypic and genetic diversity at relatively small scales can buffer species against large-scale processes such as climate change that tend to synchronize populations and increase temporal variability in overall abundance or production. This portfolio effect generally results in improved biological and economic outcomes for managed species. Previous evidence for the portfolio effect in salmonids has arisen from examinations of time series of adult abundance, but we lack evidence of spatial buffering of temporal variability in demographic rates such as survival of juveniles during their first year of life. We therefore use density-dependent population models with multiple random effects to represent synchronous (similar among populations) and asynchronous (different among populations) temporal variability as well as spatial variability in survival. These are fitted to 25 years of survey data for breeding adults and surviving juveniles from 15 demographically distinct populations of Chinook salmon (Oncorhynchus tshawytscha) within a single metapopulation in the Snake River in Idaho, USA. Model selection identifies the most support for the model that included both synchronous and asynchronous temporal variability, in addition to spatial variability. Asynchronous variability (log-SD = 0·55) is approximately equal in magnitude to synchronous temporal variability (log-SD = 0·67), but much lower than spatial variability (log-SD = 1·11). We also show that the pairwise correlation coefficient, a common measure of population synchrony, is approximated by the estimated ratio of shared and total variance, where both approaches yield a synchrony estimate of 0·59. We therefore find evidence for spatial buffering of temporal variability in early juvenile survival, although between-population variability that persists over time is also large. We conclude that spatial variation decreases interannual changes in overall juvenile production, which suggests that conservation and restoration of spatial diversity will improve population persistence for this metapopulation. However, the exact magnitude of spatial buffering depends upon demographic parameters such as adult survival that may vary among populations and is proposed as an area of future research using hierarchical life cycle models. We recommend that future sampling of this metapopulation employ a repeated-measure sampling design to improve estimation of early juvenile carrying capacity.

Faster estimation of Bayesian models in ecology using Hamiltonian Monte Carlo

Summary Bayesian inference is a powerful tool to better understand ecological processes across varied subfields in ecology, and is often implemented in generic and flexible software packages such as the widely used BUGS family (BUGS, WinBUGS, OpenBUGS and JAGS). However, some models have prohibitively long run times when implemented in BUGS. A relatively new software platform called Stan uses Hamiltonian Monte Carlo (HMC), a family of Markov chain Monte Carlo (MCMC) algorithms which promise improved efficiency and faster inference relative to those used by BUGS. Stan is gaining traction in many fields as an alternative to BUGS, but adoption has been slow in ecology, likely due in part to the complex nature of HMC. Here, we provide an intuitive illustration of the principles of HMC on a set of simple models. We then compared the relative efficiency of BUGS and Stan using population ecology models that vary in size and complexity. For hierarchical models, we also investigated the effect of an alternative parameterization of random effects, known as non-centering. For small, simple models there is little practical difference between the two platforms, but Stan outperforms BUGS as model size and complexity grows. Stan also performs well for hierarchical models, but is more sensitive to model parameterization than BUGS. Stan may also be more robust to biased inference caused by pathologies, because it produces diagnostic warnings where BUGS provides none. Disadvantages of Stan include an inability to use discrete parameters, more complex diagnostics and a greater requirement for hands-on tuning. Given these results, Stan is a valuable tool for many ecologists utilizing Bayesian inference, particularly for problems where BUGS is prohibitively slow. As such, Stan can extend the boundaries of feasible models for applied problems, leading to better understanding of ecological processes. Fields that would likely benefit include estimation of individual and population growth rates, meta-analyses and cross-system comparisons and spatiotemporal models.

Better Catch Curves: Incorporating Age-Specific Natural Mortality and Logistic Selectivity

Abstract Catch-curve analysis is one of the simplest methods for stock assessment and is widely applied in data-poor fisheries. Conventional catch-curve methods rely on the strong assumptions of constant fishing and natural mortality rates above some fully selected age that is usually estimated by visually inspecting a plot of catch at age. Here, we evaluate the performance of three catch-curve methods that relax or modify these assumptions by (1) estimating logistic selectivity parameters, (2) assuming Lorenzen-form natural mortality (natural mortality that decreases with weight), and (3) using both methods simultaneously. We used simulation modeling and decision tables to compare estimates of fishing mortality from four catch-curve methods, including the conventional method, across a variety of observable and unobservable data characteristics. We then applied the methods to catch-at-age data for Atlantic menhaden Brevoortia tyrannus from the U.S. South Atlantic fishery management region and compared the...

Model‐based inference for estimating shifts in species distribution, area occupied and centre of gravity

Summary Changing climate is already impacting the spatial distribution of many taxa, including bees, plants, birds, butterflies and fishes. A common goal is to detect range shifts in response to climate change, including changes in the centre of the populations distribution (the centre of gravity, COG), population boundaries and area occupied. Conventional estimators, such as the abundance-weighted average (AWA) estimator for COG, confound range shifts with changes in the spatial distribution of available survey data and may be biased when the distribution of survey data shifts over time. AWA also does not estimate the standard error of COG in individual years and cannot incorporate data from multiple survey designs. To explicitly account for changes in the spatial distribution of survey effort, we propose an alternative species distribution function (SDF) estimator. The SDF approach involves calculating distribution metrics, including COG, population boundary and area occupied, directly from the predicted species distribution or density function. We illustrate the SDF approach using a spatiotemporal model that is available as an r package. Using simulated data, we confirm that the SDF substantially decreases bias in COG estimates relative to the AWA estimator. We then illustrate the method by analysing data from two data sets spanning 1977–2013 for 18 marine fishes along the U.S. West Coast. In our case study, the SDF estimator shows significant northward shifts for six of 18 species (with southward shifts for only 2), where two species (darkblotched and greenstriped rockfishes) have both a northward shift and a decreased area occupied. Pelagic species (e.g. Pacific hake and spiny dogfish) have more variable distribution than bottom-associated species. We also find substantial differences between AWA and SDF estimates of COG that are likely caused by shifts in sampling distribution (which affect the AWA but not the SDF estimator). We caution that common estimators for range shift can yield inappropriate inference whenever sampling designs have shifted over time. We conclude by suggesting further improvements in model-based approaches to analysing climate impacts, including methods addressing the impact of local and regional temperature changes on species distribution.

Using spatiotemporal species distribution models to identify temporally evolving hotspots of species co‐occurrence

Identifying spatiotemporal hotspots is important for understanding basic ecological processes, but is particularly important for species at risk. A number of terrestrial and aquatic species are indirectly affected by anthropogenic impacts, simply because they tend to be associated with species that are targeted for removals. Using newly developed statistical models that allow for the inclusion of time-varying spatial effects, we examine how the co-occurrence of a targeted and nontargeted species can be modeled as a function of environmental covariates (temperature, depth) and interannual variability. The nontarget species in our case study (eulachon) is listed under the U.S. Endangered Species Act, and is encountered by fisheries off the U.S. West Coast that target pink shrimp. Results from our spatiotemporal model indicated that eulachon bycatch risk decreases with depth and has a convex relationship with sea surface temperature. Additionally, we found that over the 2007-2012 period, there was support for an increase in eulachon density from both a fishery data set (+40%) and a fishery-independent data set (+55%). Eulachon bycatch has increased in recent years, but the agreement between these two data sets implies that increases in bycatch are not due to an increase in incidental targeting of eulachon by fishing vessels, but because of an increasing population size of eulachon. Based on our results, the application of spatiotemporal models to species that are of conservation concern appears promising in identifying the spatial distribution of environmental and anthropogenic risks to the population.