Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Estimating equations for parameters in stochastic growth models from tag-recapture data

James (1991, Biometrics 47, 1519-1530) constructed unbiased estimating functions for estimating the two parameters in the von Bertalanffy growth curve from tag-recapture data. This paper provides unbiased estimating functions for a class of growth models that incorporate stochastic components and explanatory variables. a simulation study using seasonal growth models indicates that the proposed method works well while the least-squares methods that are commonly used in the literature may produce substantially biased estimates. The proposed model and method are also applied to real data from tagged rack lobsters to assess the possible seasonal effect on growth.

Investigation of movement and factors influencing post-release survival of line-caught coral reef fish using recreational tag-recapture data

Six species of line-caught coral reef fish (Plectropomus spp., Lethrinus miniatus, Lethrinus laticaudis, Lutjanus sebae, Lutjanus malabaricus and Lutjanus erythropterus) were tagged by members of the Australian National Sportsfishing Association (ANSA) in Queensland between 1986 and 2003. Of the 14,757 fish tagged, 1607 were recaptured and we analysed these data to describe movement and determine factors likely to impact release survival. All species were classified as residents since over 80% of recaptures for each species occurred within 1 km of the release site. Few individuals (range 0.8-5%) were recaptured more than 20 km from their release point. L. sebae had a higher recapture rate (19.9%) than the other species studied (range 2.1-11.7%). Venting swimbladder gases, regardless of whether or not fish appeared to be suffering from barotrauma, significantly enhanced (P < 0.05) the survival of L. sebae and L. malabaricus but had no significant effect (P > 0.05) on L. erythropterus. The condition of fish on release, subjectively assessed by anglers, was only a significant effect on recapture rate for L. sebae where fish in "fair" condition had less than half the recapture rate of those assessed as in "excellent" or "good" condition. The recapture rate of L. sebae and L. laticaudis was significantly (P < 0.05) affected by depth with recapture rate declining in depths exceeding 30 m. Overall, the results showed that depth of capture, release condition and treatment for barotrauma influenced recapture rate for some species but these effects were not consistent across all species studied. Recommendations were made to the ANSA tagging clubs to record additional information such as injury, hooking location and hook type to enable a more comprehensive future assessment of the factors influencing release survival.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

NMFS Cooperative SharkTagging Program, 1962-93: An Atlas of SharkTag and Recapture Data

The National Marine Fisheries Service (NMFS) Cooperative Shark Tagging Program (CSTP) is part of continuing research directed to the study of the biology of large Atlantic sharks. The CSTP was initiated in 1962 at the Sandy Hook Laboratory in New Jersey under the Department of Interior's U.S. Fish and Wildlife Service (USFWS). During the late 1950's and early 1960's, sharks were considered a liability to the economy of resort communities, of little or no commercial value, and a detriment to fishermen in areas where sharks might damage expensive fishing gear or reduce catches of more commercially valuable species.

Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .

A maximum likelihood approach for estimating growth from tag–recapture data

The Fabens method is commonly used to estimate growth parameters k and l infinity in the von Bertalanffy model from tag-recapture data. However, the Fabens method of estimation has an inherent bias when individual growth is variable. This paper presents an asymptotically unbiassed method using a maximum likelihood approach that takes account of individual variability in both maximum length and age-at-tagging. It is assumed that each individual's growth follows a von Bertalanffy curve with its own maximum length and age-at-tagging. The parameter k is assumed to be a constant to ensure that the mean growth follows a von Bertalanffy curve and to avoid overparameterization. Our method also makes more efficient use nf thp measurements at tno and recapture and includes diagnostic techniques for checking distributional assumptions. The method is reasonably robust and performs better than the Fabens method when individual growth differs from the von Bertalanffy relationship. When measurement error is negligible, the estimation involves maximizing the profile likelihood of one parameter only. The method is applied to tag-recapture data for the grooved tiger prawn (Penaeus semisulcatus) from the Gulf of Carpentaria, Australia.

Bomb radiocarbon and tag-recapture dating of sandbar shark (Carcharhinus plumbeus)

The sandbar shark (Carcharhinus plumbeus) was the cornerstone species of western North Atlantic and Gulf of Mexico large coastal shark fisheries until 2008 when they were allocated to a research-only fishery. Despite decades of fishing on this species, important life history parameters, such as age and growth, have not been well known. Some validated age and growth information exists for sandbar shark, but more comprehensive life history information is needed. The complementary application of bomb radiocarbon and tag-recapture dating was used in this study to determine valid age-estimation criteria and longevity estimates for this species. These two methods indicated that current age interpretations based on counts of growth bands in vertebrae are accurate to 10 or 12 years. Beyond these years, we could not determine with certainty when such an underestimation of age begins; however, bomb radiocarbon and tag-recapture data indicated that large adult sharks were considerably older than the estimates derived from counts of growth bands. Three adult sandbar sharks were 20 to 26 years old based on bomb radiocarbon results and were a 5- to 11-year increase over the previous age estimates for these sharks. In support of these findings, the tag-recapture data provided results that were consistent with bomb radiocarbon dating and further supported a longevity that exceeds 30 years for this species.

Transboundary Movement of Atlantic Istiophorid Billfishes Among International and U.S. Domestic Management Areas Inferred from Mark-Recapture Studies

Billfish movements relative to the International Commission for the Conservation of Atlantic Tunas management areas, as well as U.S. domestic data collection areas within the western North Atlantic basin, were investigated with mark-recapture data from 769 blue marlin, Makaira nigricans, 961 white marlin, Tetrapturus albidus, and 1,801 sailfish, Istiophorus platypterus. Linear displacement between release and recapture locations ranged from zero (all species) to 15,744 km (mean 575, median 119, SE 44) for blue marlin, 6,523 km (mean 719, median 216, SE 33) for white marlin, and 3,845 km (mean 294, median 98, SE 13) for sailfish. In total, 2,824 (80.0%) billfish were recaptured in the same management area of release. Days at liberty ranged from zero (all species) to 4,591 (mean 619, median 409, SE 24) for blue marlin, 5,488 (mean 692, median 448, SE 22) for white marlin, and 6,568 (mean 404, median 320, SE 11) for sailfish. The proportions (per species) of visits were highest in the Caribbean area for blue marlin and white marlin, and the Florida East Coast area for sailfish. Blue marlin and sailfish were nearly identical when comparing the percent of individuals vs. the number of areas visited. Overall, white marlin visited more areas than either blue marlin or sailfish. Seasonality was evident for all species, with overall results generally reflecting the efforts of the catch and release recreational fishing sector, particularly in the western North Atlantic. This information may be practical in reducing the uncertainties in billfish stock assessments and may offer valuable insight into management consideration of time-area closure regulations to reduce bycatch mortality of Atlantic billfishes.

Estimating long-term growth-rate changes of southern bluefin tuna (Thunnus maccoyii) from two periods of tag-return data

Southern bluefin tuna (SBT) (Thunnus maccoyii) growth rates are estimated from tag-return data associated with two time periods, the 1960s and 1980s. The traditional von Bertalanffy growth model (VBG) and a two-phase VBG model were fitted to the data by maximum likelihood. The traditional VBG model did not provide an adequate representation of growth in SBT, and the two-phase VBG yielded a significantly better fit. The results indicated that significant change occurs in the pattern of growth in relation to a VBG curve during the juvenile stages of the SBT life cycle, which may be related to the transition from a tightly schooling fish that spends substantial time in near and surface shore waters to one that is found primarily in more offshore and deeper waters. The results suggest that more complex growth models should be considered for other tunas and for other species that show a marked change in habitat use with age. The likelihood surface for the two-phase VBG model was found to be bimodal and some implications of this are investigated. Significant and substantial differences were found in the growth for fish spawned in the 1960s and in the 1980s, such that after age four there is a difference of about one year in the expected age of a fish of similar length which persists over the size range for which meaningful recapture data are available. This difference may be a density-dependent response as a consequence of the marked reduction in the SBT population. Given the key role that estimates of growth have in most stock assessments, the results indicate that there is a need both for the regular monitoring of growth rates and for provisions for changes in growth over time (possibly related to changes in abundance) in the stock assessment models used for SBT and other species.

Dynamics of bigeye (Thunnus obesus) and yellowfin (T. albacares) tuna in Hawaii’s pelagic fisheries: analysis of tagging data with a bulk transfer model incorporating size-specific attrition

Tag release and recapture data of bigeye (Thunnus obesus) and yellowfin tuna (T. albacares) from the Hawaii Tuna Tagging Project (HTTP) were analyzed with a bulk transfer model incorporating size-specific attrition to infer population dynamics and transfer rates between various fishery components. For both species, the transfer rate estimates from the offshore handline fishery areas to the longline fishery area were higher than the estimates of transfer from those same areas into the inshore fishery areas. Natural and fishing mortality rates were estimated over three size classes: yellowfin 20–45, 46–55, and ≥56 cm and bigeye 29–55, 56–70, and ≥71 cm. For both species, the estimates of natural mortality were highest in the smallest size class. For bigeye tuna, the estimates decreased with increasing size and for yellowfin tuna there was a slight increase in the largest size class. In the Cross Seamount fishery, the fishing mortality rate of bigeye tuna was similar for all three size classes and represented roughly 12% of the gross attrition rate (includes fishing and natural mortality and emigration rates). For yellowfin tuna, fishing mortality ranged between 7% and 30%, the highest being in the medium size class. For both species, the overall attrition rate from the entire fishery area was nearly the same. However, in the specific case of the Cross Seamount fishery, the attrition rate for yellowfin tuna was roughly twice that for bigeye. This result indicates that bigeye tuna are more resident at the Seamount than yellowfin tuna, and larger bigeye tunas tend to reside longer than smaller individuals. This may result in larger fish being more vulnerable to capture in the Seamount fishery. The relatively low level of exchange between the Sea-mount and the inshore and longline fisheries suggests that the fishing activity at the Seamount need not be of great management concern for either species. However, given that the current exploitation rates are considered moderate (10–30%), and that Seamount aggregations of yellowfin and bigeye tuna are highly vulnerable to low-cost gear types, it is recommended that further increases in fishing effort for these species be monitored at Cross Seamount.