Uncertainty In Abundance Estimates Research Articles

Methods for Estimating Abundance and Associated Uncertainty from Passive Count Technologies

AbstractPassive count technologies (e.g., resistivity counters, infrared cameras, and sonar/hydroacoustic cameras) are increasingly being used to enumerate migratory fish populations, but methodologies for converting counts into abundance estimates with uncertainty are not available. Passive counters are typically paired with a secondary data collection method, such as video, images, or direct observation, to validate or correct the count data for false positives and false negatives. We developed a framework that incorporates measurement error into passive counter estimates based on a statistical comparison with validation data. We demonstrate this framework using resistivity counter and video validation data collected for Gates Creek Sockeye Salmon Oncorhynchus nerka as they migrated through a fish passage facility at the Seton Dam in British Columbia, Canada. We also conducted simulations to evaluate the trade‐offs between validation effort and accuracy and precision of abundance estimates, which can be used to plan passive counter postprocessing and validation. We found our method to be accurate and precise when abundance was high (i.e., >1,000), even when validation effort was low (i.e., 5% validation). There was a positive estimation bias when abundance was low (i.e., 100), and a minimum of 25% validation was required to achieve a CV of 15% and relative error less than 10%. When estimating abundance for small populations, higher validation effort is required to obtain sufficient precision in abundance estimates. Measurement error should not be overlooked in passive fish count technologies, and we provide a robust method for generating uncertainty in abundance estimates that increases their utility for population assessment and conservation.

Model-based localization of deep-diving cetaceans using towed line array acoustic data.

Passive acoustic monitoring using a towed line array of hydrophones is a standard method for localizing cetaceans during line-transect cetacean abundance surveys. Perpendicular distances estimated between localized whales and the trackline are essential for abundance estimation using acoustic data. Uncertainties in the acoustic data from hydrophone movement, sound propagation effects, errors in the time of arrival differences, and whale depth are not accounted for by most two-dimensional localization methods. Consequently, location and distance estimates for deep-diving cetaceans may be biased, creating uncertainty in abundance estimates. Here, a model-based localization approach is applied to towed line array acoustic data that incorporates sound propagation effects, accounts for sources of error, and localizes in three dimensions. The whale's true distance, ship trajectory, and whale movement greatly affected localization results in simulations. The localization method was applied to real acoustic data from two separate sperm whales, resulting in three-dimensional distance and depth estimates with position bounds for each whale. By incorporating sources of error, this three-dimensional model-based approach provides a method to address and integrate the inherent uncertainties in towed array acoustic data for more robust localization.

Understanding sea lamprey abundances in the Great Lakes prior to broad implementation of sea lamprey control

Control of invasive sea lamprey in the Great Lakes with a selective pesticide (lampricide) that targeted larval sea lamprey began in the late 1950's and continues to be one of the main methods for control. Although the Great Lakes Fishery Commission, which was formed with the mandate of controlling sea lamprey, often expresses the success of the sea lamprey control program in terms of percent reduction from lake-wide pre-lampricide control adult sea lamprey abundances, there remains a large amount of uncertainty surrounding these estimates. In this study, we gathered historical data on adult sea lamprey captures from trapping efforts from the mid-1950's through the late 1970's to better understand pre-control abundance. We used this information to estimate lake-wide population abundances of adult sea lamprey using a weighted linear regression that includes environmental and lampricide treatment predictor variables. We varied trapping efficiency for early trapping data to evaluate the uncertainty in abundance estimates. Pre-control adult sea lamprey abundances in all lakes were much greater than current population sizes, but estimates were quite sensitive to trapping efficiency. In Lake Superior, declines in abundance aligned with increases in control efforts, but in other lakes, declines were occurring prior to the onset of lampricide application, perhaps because of a loss of prey. We suggest that previous estimates of pre-control adult sea lamprey abundance may have been underestimated unless trapping efficiency was greater than what is currently achieved in the basin.

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture-recapture data.

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.

A new mark-recapture approach for abundance estimation of social species.

Accurate estimates of population abundance are a critical component of species conservation efforts in order to monitor the potential recovery of populations. Capture-mark-recapture (CMR) is a widely used approach to estimate population abundance, yet social species moving in groups violate the assumption of CMR approaches that all individuals in the population are detected independently. We developed a closed CMR model that addresses an important characteristic of group-living species–that individual-detection probability typically is conditional on group detection. Henceforth termed the Two-Step model, this approach first estimates group-detection probability and then–conditional on group detection–estimates individual-detection probability for individuals within detected groups. Overall abundance is estimated assuming that undetected groups have the same average group size as detected groups. We compared the performance of this Two-Step CMR model to a conventional (One-Step) closed CMR model that ignored group structure. We assessed model sensitivity to variation in both group- and individual-detection probability. Both models returned overall unbiased estimates of abundance, but the One-Step model returned deceptively narrow Bayesian confidence intervals (BCI) that failed to encompass the correct population abundance an average 52% of the time. Contrary, under the Two-Step model, CI coverage was on average 96%. Both models had similar root mean squared errors (RMSE), except for scenarios with low group detection probability, where the Two-Step model had much lower RMSE. For illustration with a real data set, we applied the Two-Step and regular model to non-invasive genetic capture-recapture data of mountain gorillas (Gorilla beringei beringei). As with simulations, abundance estimates under both models were similar, but the Two-Step model estimate had a wider confidence interval. Results support using the Two-Step model for species living in constant groups, particularly when group detection probability is low, to reduce risk of bias and adequately portray uncertainty in abundance estimates. Important sources of variation in detection need to be incorporated into the Two-Step model when applying it to field data.

Improvements in estimating an acoustic target strength–length relationship for hoki (Macruronus novaezeladiae)

Hoki (Macruronus novaezelandiae) is New Zealand's largest fishery. Acoustic surveys of spawning hoki provide abundance indices for informing management of the stocks. For estimating fish abundance using acoustic methods, relationships between the acoustic backscatter from a single fish, commonly known as the acoustic target strength (TS), and fish length are required. Here we present in situ data on TS from individual live hoki, collected using a trawl-mounted acoustic-optical system (AOS). Deriving TS–length relationships from measurements of individual fish is complicated because of the very large stochastic variability in TS from the same fish, and from individual fish of similar length. A new TS–total length relationship of TS=24.5log10(TL)−83.9 was derived based on a weighted non-linear least-squares fit to acoustic backscattering cross-section measurements from 62 New Zealand hoki between 35 and 93cm TL. It was necessary to use a weighted fitting method to appropriately account for variance, as not doing so can introduce a bias to the estimated mean TS. Using the new TS–TL relationship decreases absolute estimates of hoki abundance by 50–60% from those currently used in stock assessment, but has little impact on relative indices. Estimated 90% confidence intervals around the new TS–TL relationship based on bootstrapping suggested uncertainty in mean TS of ±1.5dB at typical New Zealand hoki lengths, with resulting uncertainty in abundance estimates of up to 50%. Further in situ measurements and modelling are required to reduce this uncertainty and to investigate potential differences in TS between AOS-measured and ‘undisturbed’ fish.

Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?

Density dependence in population growth rates is of immense importance to ecological theory and application, but is difficult to estimate. The Global Population Dynamics Database (GPDD), one of the largest collections of population time series available, has been extensively used to study cross-taxa patterns in density dependence. A major difficulty with assessing density dependence from time series is that uncertainty in population abundance estimates can cause strong bias in both tests and estimates of strength. We analyse 627 data sets in the GPDD using Gompertz population models and account for uncertainty via the Kalman filter. Results suggest that at least 45% of the time series display density dependence, but that it is weak and difficult to detect for a large fraction. When uncertainty is ignored, magnitude of and evidence for density dependence is strong, illustrating that uncertainty in abundance estimates qualitatively changes conclusions about density dependence drawn from the GPDD.

Uncertainty in hydroacoustic‐derived fisheries data: An analysis of simultaneous hydroacoustic‐trawl surveys.

Fish biomass estimates from hydroacoustic surveys contain uncertainty that must be quantified before such estimates are of use. To better understand uncertainty associated with down‐looking hydroacoustics, analyzes were conducted on simultaneously collected trawl and hydroacoustic data from over 200 sampling events in Lake Champlain, a mesotrophic freshwater lake located between New York, Vermont, and Quebec (Canada). A model set, which used a number of factors to explore sources of variance, was analyzed. Factors explored were acoustic density estimation method, sampling time, sampling season, water temperature, light, invertebrate presence, fish size, fish species, and collection depth. Trawl avoidance was higher during the day, and varied with trawl type. Sources of variance in hydroacoustic estimates were the size and depth of analysis regions, presence of invertebrates, and fish shoaling behavior. All fish species could not be differentiated using acoustic target strength, thus necessitating trawl collections to estimate species‐specific abundance. Trawl collection showed vertical separation of adult pelagic species in Lake Champlain, and suggested that side‐ or up‐looking hydroacoustic and surface gillnet surveys may be necessary to reduce uncertainty in abundance estimates. Surveys using multiple sampling methods likely result in abundance estimates closest to reality.

Latitudinal and interannual distribution of the European anchovy (Engraulis encrasicolus) and sardine (Sardina pilchardus) in the western Mediterranean, and sampling uncertainty in abundance estimates

Abstract Tugores, M. P., Iglesias, M., Díaz, N., Oñate, D., Miquel, J., and Giráldez, A. 2010. Latitudinal and interannual distribution of the European anchovy (Engraulis encrasicolus) and sardine (Sardina pilchardus) in the western Mediterranean, and sampling uncertainty in abundance estimates. – ICES Journal of Marine Science, 67: 1574–1586. On the Spanish Mediterranean continental shelf, late-autumn echo-integration acoustic surveys have been performed annually since the 1990s. The surveys coincide with the recruitment season of anchovy (Engraulis encrasicolus) and the start of the spawning season of sardine (Sardina pilchardus), and they provide estimates of stock size for the main fisheries in the area. Latitudinal distribution of the abundance of the two species from 2003 till 2006 is evaluated, and transitive geostatistical techniques applied to estimate the sampling uncertainty of the overall abundance estimate. The anchovy stock was found mainly in areas influenced by river run-off, in well-known anchovy spawning areas, suggesting that anchovy remained on their spawning grounds until late autumn or that survival was higher in these regions of enhanced productivity. By the time of the surveys, sardine were already occupying their spawning grounds over the continental shelf. The precision of the abundance estimates was generally high. The few cases of low precision were re-examined and found to stem most probably from processing errors, so the re-examination has contributed to an improvement in the accuracy of the estimates. The greater precision obtained in the southern subarea suggested a greater homogeneity in the spatial distribution of both species.

Joint nesting in the acorn woodpecker

Control of invasive sea lamprey in the Great Lakes with a selective pesticide (lampricide) that targeted larval sea lamprey began in the late 1950's and continues to be one of the main methods for control. Although the Great Lakes Fishery Commission, which was formed with the mandate of controlling sea lamprey, often expresses the success of the sea lamprey control program in terms of percent reduction from lake-wide pre-lampricide control adult sea lamprey abundances, there remains a large amount of uncertainty surrounding these estimates. In this study, we gathered historical data on adult sea lamprey captures from trapping efforts from the mid-1950's through the late 1970's to better understand pre-control abundance. We used this information to estimate lake-wide population abundances of adult sea lamprey using a weighted linear regression that includes environmental and lampricide treatment predictor variables. We varied trapping efficiency for early trapping data to evaluate the uncertainty in abundance estimates. Pre-control adult sea lamprey abundances in all lakes were much greater than current population sizes, but estimates were quite sensitive to trapping efficiency. In Lake Superior, declines in abundance aligned with increases in control efforts, but in other lakes, declines were occurring prior to the onset of lampricide application, perhaps because of a loss of prey. We suggest that previous estimates of pre-control adult sea lamprey abundance may have been underestimated unless trapping efficiency was greater than what is currently achieved in the basin.