Mark N. Maunder

AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models

Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem. Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number of parameters. The benefits of using AD are computational efficiency and high numerical accuracy, both crucial in many practical problems. We describe the basic components and the underlying philosophy of ADMB, with an emphasis on functionality found in no other statistical software. One example of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages of ADMB are flexibility, speed, precision, stability and built-in methods to quantify uncertainty.

Biomass, Size, and Trophic Status of Top Predators in the Pacific Ocean

Fisheries have removed at least 50 million tons of tuna and other top-level predators from the Pacific Ocean pelagic ecosystem since 1950, leading to concerns about a catastrophic reduction in population biomass and the collapse of oceanic food chains. We analyzed all available data from Pacific tuna fisheries for 1950–2004 to provide comprehensive estimates of fishery impacts on population biomass and size structure. Current biomass ranges among species from 36 to 91% of the biomass predicted in the absence of fishing, a level consistent with or higher than standard fisheries management targets. Fish larger than 175 centimeters fork length have decreased from 5% to approximately 1% of the total population. The trophic level of the catch has decreased slightly, but there is no detectable decrease in the trophic level of the population. These results indicate substantial, though not catastrophic, impacts of fisheries on these top-level predators and minor impacts on the ecosystem in the Pacific Ocean.

Fisheries: Decline of Pacific tuna populations exaggerated?

industrial fisheries in the Pacific Ocean and elsewhere since the 1950s. In their analysis of Japanese longline-fishery catchper-unit-effort (CPUE) data, Myers and Worm conclude that the community (species-aggregated) biomass of large pelagic fish, mainly tunas, was reduced by 80% during the first 15 years of exploitation and is now at 10% of pre-industrial levels. We show here that an assumption critical to this conclusion — namely, that Japanese longline CPUE acts as an accurate index of community biomass — is invalid. Our results indicate that biomass decline and fishing impacts are much less severe than is claimed by Myers and Worm. Interpretation of the species-aggregated CPUE as an index of community biomass rests on the assumption that catchability (a coefficient specifying the proportionality between CPUE and abundance) is constant across species and over time. The former is unrealistic because, among other things, the species have different depth distributions and hence different vulnerability to longline gear. The evolution of tuna longline fisheries in all oceans has seen changes in fishing strategies (and hence catchability) as different species have been targeted. In the early 1960s, Japanese longliners changed from targeting albacore (Thunnus alalunga) and yellowfin (T. albacares) for the canned-tuna market to bigeye (T. obesus) and yellowfin tuna for the Japanese sashimi market. Japanese longline CPUE for albacore declined rapidly not because of declining albacore abundance, but because of this change in species targeting. By contrast, Taiwanese longliners have consistently targeted albacore in subequatorial waters of all oceans, and their CPUE provides a better index of albacore abundance. These results show that CPUE has declined by 50% over 40 years in the South Pacific, but they do not replicate the rapid and much larger decline in CPUE in the 1960s evident in the Japanese data (Fig.1a). The Myers and Worm analysis excludes data from the equatorial Pacific, where the highest catches are taken and which is the core habitat for tropical tunas. When these data are included, yellowfin-tuna CPUE in the western Pacific is seen to decline by 70% over 50 years, during which time annual catches by longline and other methods increase from insignificant levels in the early 1950s to more than 400,000 tonnes by the late 1990s (Fig. 1b). By contrast, the CPUE for bigeye tuna has been stable for over 40 years, despite continuously increasing catch (Fig. 1c). Changes in fishing strategies designed to target the deeper-swimming and higher-value bigeye tuna occurred during the 1970s (ref. 3), making it unlikely that CPUE accurately reflects changes in abundance for either species unless it is adjusted to account for the shift in targeting. Unadjusted Japanese longline CPUE tends to overestimate abundance decline for yellowfin tuna and underestimate abundance decline for bigeye tuna. Stock assessments rely on a range of data in addition to CPUE, including catch, size composition, tagging and biological data. When stock-assessment models 6 that consider all the available data are applied to Pacific tunas, fishery-induced declines in abundance during the 1950s and 1960s of the magnitude proposed by Myers and Worm are found to be extremely unlikely. Moreover, where declines do occur, they are not, as claimed by Myers and Worm, due exclusively to fishing. It is impossible, for example, under conventional populationdynamics theory to attribute the pre-1970 decline in yellowfin CPUE to fishing at a time when the total catches were less than one-tenth of today’s catches. In summary, the trends in catches and CPUE (Fig. 1) and the results of stock-assessment modelling show that the basic assumption of Myers and Worm that CPUE is proportional to brief communications arising

Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS

1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.

Exploitation Rate Reference Points for West Coast Rockfish: Are They Robust and Are There Better Alternatives?

Abstract We explore several aspects of the robustness of exploitation rate reference points as a management tool. The spawner−recruit curve is an important consideration when developing exploitation rate reference points. The spawner−recruit curves for West Coast rockfish Sebastes spp. suggest low productivity compared with other stocks, but our ability to produce reliable estimates of productivity is hindered by the scarcity of reliable, fishery-independent surveys, the short time span of the data, high aging error, and the low exploitation levels. Implementation of reference exploitation rates usually assumes that we can estimate the absolute stock size and the ratio of current to virgin stock size. We show that management by reference exploitation rates is not robust to overestimation of stock size; in such cases, overexploited stocks will continue to be overexploited. We also show that if F 55% exploitation rates (i.e., rates that reduce the spawning potential per recruit to 55% of its value in the un...

A Simulation-Based Method to Determine Model Misspecification: Examples Using Natural Mortality and Population Dynamics Models

Abstract Recent developments in the models used in wildlife and fisheries science have allowed the inclusion of a wider range of data than previously. However, the diagnostics of such complex models have not kept pace. We describe a new diagnostic technique based on simulation analysis. Model misspecification was identified through simulation methods that created a distribution of likely parameter values for a model that was correctly specified. If the actual estimate of that parameter is outside the bounds of the simulated distribution, then the model is probably misspecified. We tested the reliability of the new diagnostic by introducing known-model misspecification into complex fisheries stock assessment models. We then compared the results from this new diagnostic with those of a more tradition fisheries diagnostic, namely, retrospective analysis. The simulation-based diagnostic was shown to identify inisspecification affecting the estimated dynamics more reliably than retrospective analysis.

A spatially structured tagging model to estimate movement and fishing mortality rates for the blue shark (Prionace glauca) in the North Atlantic Ocean

Large numbers of blue sharks are caught as bycatch, and have even become the target species in pelagic longline fisheries in the North Atlantic Ocean. The status of the stock is ambiguous due to the limitations of the fishery-dependent data. This study presents a spatially structured tagging model to estimate blue shark movement and fishing mortality rates in the North Atlantic Ocean. The model uses the blue shark tag-recovery data collected by the United States National Marine Fisheries Service Cooperative Shark Tagging Program (1965–2004). Four major geographical regions (two on each side of the ocean) are assumed. The blue shark fishing mortality rates (F) were found to be heterogeneous across the four regions. While the estimates of F obtained for the western North Atlantic Ocean were historically lower than 0.1 year–1, the F estimates over the most recent decade (1990s) in the eastern side of the ocean are rapidly approaching 0.2 year–1. Because of the particular life-history of the blue shark, these results suggest careful monitoring of the fishery as the juvenile and pregnant female segments of the stock are highly vulnerable to exploitation in the eastern North Atlantic Ocean.

The Ecuadorian Artisanal Fishery for Large Pelagics: Species Composition and Spatio-Temporal Dynamics.

The artisanal fisheries of Ecuador operate within one of the most dynamic and productive marine ecosystems of the world. This study investigates the catch composition of the Ecuadorian artisanal fishery for large pelagic fishes, including aspects of its spatio-temporal dynamics. The analyses of this study are based on the most extensive dataset available to date for this fishery: a total of 106,963 trip-landing inspection records collected at its five principal ports during 2008 ‒ 2012. Ecuadorian artisanal fisheries remove a substantial amount of biomass from the upper trophic-level predatory fish community of the eastern tropical Pacific Ocean. It is estimated that at least 135 thousand metric tons (mt) (about 15.5 million fish) were landed in the five principal ports during the study period. The great novelty of Ecuadorian artisanal fisheries is the “oceanic-artisanal” fleet component, which consists of mother-ship (nodriza) boats with their towed fiber-glass skiffs (fibras) operating with pelagic longlines. This fleet has fully expanded into oceanic waters as far offshore as 100°W, west of the Galapagos Archipelago. It is estimated that nodriza operations produce as much as 80% of the total catches of the artisanal fishery. The remainder is produced by independent fibras operating in inshore waters with pelagic longlines and/or surface gillnets. A multivariate regression tree analysis was used to investigate spatio-environmental effects on the nodriza fleet (n = 6,821 trips). The catch species composition of the nodriza fleet is strongly influenced by the northwesterly circulation of the Humboldt Current along the coast of Peru and its associated cold waters masses. The target species and longline gear-type used by nodrizas change seasonally with the incursion of cool waters (< 25°C) from the south and offshore. During this season, dolphinfish (Coryphaena hippurus) dominates the catches. However, in warmer waters, the fishery changes to tuna-billfish-shark longline gear and the catch composition becomes much more diverse.

Comparison of Fixed Effect, Random Effect, and Hierarchical Bayes Estimators for Mark Recapture Data Using AD Model Builder

Mark-recapture studies are one of the most common methods used to obtain demographic parameters for wildlife populations. Time specific estimates of parameters representing population processes contain both temporal variability in the process (process error) and error in estimating the parameters (observation error). Therefore, to estimate the temporal variation in the population process, it is important to separate these two errors. Traditional random effect models can be used to separate the two errors. However, it is difficult to implement the required simultaneous maximization and integration for dynamic nonlinear non-Gaussian models. An alternative hierarchical Bayesian approach using MCMC integration is easier to apply, but requires priors for all model parameters.

Data reconstruction can improve abundance index estimation: An example using Taiwanese longline data for Pacific bluefin tuna

Catch-per-unit-effort (CPUE) is often the main piece of information used in fisheries stock assessment; however, the catch and effort data that are traditionally compiled from commercial logbooks can be incomplete or unreliable due to many reasons. Pacific bluefin tuna (PBF) is a seasonal target species in the Taiwanese longline fishery. Since 2010, detailed catch information for each PBF has been made available through a catch documentation scheme. However, previously, only market landing data with a low coverage of logbooks were available. Therefore, several nontraditional procedures were performed to reconstruct catch and effort data from many alternative data sources not directly obtained from fishers for 2001–2015: (1) Estimating the catch number from the landing weight for 2001–2003, for which the catch number information was incomplete, based on Monte Carlo simulation; (2) deriving fishing days for 2007–2009 from voyage data recorder data, based on a newly developed algorithm; and (3) deriving fishing days for 2001–2006 from vessel trip information, based on linear relationships between fishing and at-sea days. Subsequently, generalized linear mixed models were developed with the delta-lognormal assumption for standardizing the CPUE calculated from the reconstructed data, and three-stage model evaluation was performed using (1) Akaike and Bayesian information criteria to determine the most favorable variable composition of standardization models, (2) overall R2 via cross-validation to compare fitting performance between area-separated and area-combined standardizations, and (3) system-based testing to explore the consistency of the standardized CPUEs with auxiliary data in the PBF stock assessment model. The last stage of evaluation revealed high consistency among the data, thus demonstrating improvements in data reconstruction for estimating the abundance index, and consequently the stock assessment.