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).

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).

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.

Estimating the emigration rate of fish stocks from marine sanctuaries using tag-recovery data

A critical process in assessing the impact of marine sanctuaries on fish stocks is the movement of fish out into surrounding fished areas. A method is presented for estimating the yearly rate of emigration of animals from a protected (“no-take”) zone. Movement rates for exploited populations are usually inferred from tag-recovery studies, where tagged individuals are released into the sea at known locations and their location of recapture is reported by fishermen. There are three drawbacks, however, with this method of estimating movement rates: 1) if animals are tagged and released into both protected and fished areas, movement rates will be overestimated if the prohibition on recapturing tagged fish later from within the protected area is not made explicit; 2) the times of recapture are random; and 3) an unknown proportion of tagged animals are recaptured but not reported back to researchers. An estimation method is proposed which addresses these three drawbacks of tag-recovery data. An analytic formula and an associated double-hypergeometric likelihood method were derived. These two estimators of emigration rate were applied to tag recoveries from southern rock lobsters (Jasus edwardsii) released into a sanctuary and into its surrounding fished area in South Australia.

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.

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.

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.

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.

The effect of timing of tagging on streamer-tag recapture rates for American lobster (Homarus americanus)

Streamer tags are commonly used to study the ecology and population biology of the American lobster (Homarus americanus). Aquarium observations suggest that streamer tag loss, either through tag-induced mortality or tag shedding, is related to the molt stage of the lobster at the time of tagging, and the molting event itself. Tag-induced mortality, where lobsters did not molt, occurred within eleven and sixteen days following tagging for lobsters tagged in postmolt (4%) and late premolt (10%) stages, respectively; whereas no lobsters tagged in early premolt or intermolt stages died. Taginduced mortality at time of molting was observed for lobsters tagged in late premolt stage (11%), and tag shedding was observed for lobsters tagged both in early (25%) and late premolt (11%) stages, but was significantly higher (P=0.014) for lobsters tagged in early premolt stages. Autopsies revealed that lobsters died mainly of organ perforations (hepato-pancreas and pericardial sac) following the tagging process, and rupture of the dorsal thoraco-abdominal membrane during the molting process. The total tag loss was estimated at 4% for lobsters tagged after molting, and 27% and 31% for lobsters tagged in early and late premolt stages, respectively. There was no tag loss for lobsters tagged in the intermolt stage during four months of laboratory observations (July−October). To minimize streamer tag loss, lobsters should be tagged during the intermolt or postmolt stage. Based on field studies, recapture rates for lobsters tagged in premolt stage are always lower than those of lobsters tagged in postmolt stage. Furthermore, recapture rates during the second year, for lobsters that molt in the year following tagging, were drastically reduced, and no lobster was recaptured after four years at large. Finally, to account for tag loss during the first year at large, a minimal adjustment of 24.9% (SD 2.9%) and 4.4% (SD 1.6%) for the recapture rate of lobsters tagged immediately before and after the molting season, respectively, is recommended. Adjustments beyond one year at large are not recommended for the American lobster at this time.