A model of the ring-recovery reporting process for the Cape Griffon Gyps coprotheres

By their very nature, statistical models are constructed on the basis of a number of simplifying assumptions. It is usual to assume that all the individuals in a 'group' or 'cohort' have similar survival, recovery or reporting probabilities. From a number of earlier studies of the Cape Griffon Gyps coprotheres in southern Africa, it is clear that there have been many violations of these assumptions of homogeneity. To get a better understanding of the process whereby a dead ringed bird is found and reported, an analysis was undertaken of 575 recoveries from 7130 individuals ringed as nestlings. From a series of univariate generalized linear models, it was found that the proportion of ringed birds reported dead varied with the following factors: (1) ring prefix (representing different grades and thicknesses of aluminium): there was considerable variation in reporting rate between cohorts fitted with different ring prefix series used; (2) metal type: birds fitted with monel metal rings were reported at a rate twice that of those bearing aluminium rings; (3) colour rings: recoveries of birds with colour rings were much more likely to be reported than birds with only a metal ring; (4) epoch: the reporting rate has increased steadily from the 1950s through to the mid-1980s. All of these factors are confounded and so a number of multivariate generalized linear models were constructed. It was found that the variations in the cohort-specific reporting rate could be described well by a model including factors for metal-ring type and the presence or absence of colour rings. Using the tougher monel metal ring along with a set of colour rings more than doubles the reporting rate and their continued use is strongly recommended for future studies. The year-to-year variations could be accounted for by this model but the colony of ringing did not enter the model. The models used were based on two assumptions: (i) the reporting rate was constant for all individuals within a given cohort and (ii) the recoveries were complete. It is argued that the results are congruent with these assumptions. There is now a clearer model of the manner in which the ring-recovery reporting process proceeds and this has opened the way to building a more realistic statistical model to estimate survival in the Cape Griffon.     

Separation of hunting and natural mortality using ring-return models: an overview

Ring-recovery methodology has been widely used to estimate survival rates in multi-year ringing studies of wildlife and fish populations (Youngs & Robson, 1975; Brownie et al. , 1985). The Brownie et al. (1985) methodology is often used but its formulation does not account for the fact that rings may be returned in two ways. Sometimes hunters are solicited by a wildlife management officer or scientist and asked if they shot any ringed birds. Alternatively, a hunter may voluntarily report the ring to the Bird Banding Laboratory (US Fish and Wildlife Service, Laurel, MD, USA) as is requested on the ring. Because the Brownie et al. (1985) models only consider reported rings, Conroy (1985) and Conroy et al. (1989) generalized their models to permit solicited rings. Pollock et al. (1991) considered a very similar model for fish tagging models which might be combined with angler surveys. Pollock et al. (1994) showed how to apply their generalized formulation, with some modification to allow for crippling losses, to wildlife ringing studies. Provided an estimate of ring reporting rate is available, separation of hunting and natural mortality estimates is possible which provides important management information. Here we review this material and then discuss possible methods of estimating reporting rate which include: (1) reward ring studies; (2) use of planted rings; (3) hunter surveys; and (4) pre- and post-hunting season ringings. We compare and contrast the four methods in terms of their model assumptions and practicality. We also discuss the estimation of crippling loss using pre- and post-season ringing in combination with a reward ringing study to estimate reporting rate.     

Separation of hunting and natural mortality using ring-return models: An overview

Ring-recovery methodology has been widely used to estimate survival rates in multi-year ringing studies of wildlife and fish populations (Youngs & Robson, 1975; Brownie et al. , 1985). The Brownie et al. (1985) methodology is often used but its formulation does not account for the fact that rings may be returned in two ways. Sometimes hunters are solicited by a wildlife management officer or scientist and asked if they shot any ringed birds. Alternatively, a hunter may voluntarily report the ring to the Bird Banding Laboratory (US Fish and Wildlife Service, Laurel, MD, USA) as is requested on the ring. Because the Brownie et al. (1985) models only consider reported rings, Conroy (1985) and Conroy et al. (1989) generalized their models to permit solicited rings. Pollock et al. (1991) considered a very similar model for fish tagging models which might be combined with angler surveys. Pollock et al. (1994) showed how to apply their generalized formulation, with some modification to allow for crippling losses, to wildlife ringing studies. Provided an estimate of ring reporting rate is available, separation of hunting and natural mortality estimates is possible which provides important management information. Here we review this material and then discuss possible methods of estimating reporting rate which include: (1) reward ring studies; (2) use of planted rings; (3) hunter surveys; and (4) pre- and post-hunting season ringings. We compare and contrast the four methods in terms of their model assumptions and practicality. We also discuss the estimation of crippling loss using pre- and post-season ringing in combination with a reward ringing study to estimate reporting rate.     

Estimating age-specific survival rates of tawny owls--recaptures versus recoveries

We compared estimates of annual survival rates of tawny owls ( Strix aluco ) ringed in southern Finland from several different sampling methods: recoveries of birds ringed as young; recaptures of birds ringed as young; recoveries of birds ringed as adults as well as young; combined recoveries and recaptures of birds ringed as young, and combined recoveries and recaptures of birds ringed as adults and young. From 1979 to 1998, 18 040 young owls were ringed, of which 983 were recaptured as breeders in subsequent years during this period, and 1764 were recovered dead at various locations. In addition, 1751 owls were ringed as adults, of which 612 were later recaptured and 199 were recovered dead. First-year survival rates estimated using only recoveries of birds ringed as young averaged 48%, while apparent survival rates estimated using only recaptures from birds ringed as young averaged 10-13%. Use of combined recapture-recovery models, or supplementary information from recoveries of birds ringed as adults, produced survival estimates of 30-37%. Survival estimates from young-recoveries-only models were biased high, because of violation of the assumption of constant recovery rates with age: birds dying in their first-year were one-third less likely to be found and reported than older birds. In contrast, recaptures-only models confounded emigration with mortality. Despite these differences in mean values, annual fluctuations in estimated first-year survival rates were similar with all models. Estimates of adult survival rates were similar with all models, while those for second-year birds were similar for all models except recaptures-only. These results highlight the potential biases associated with analysing either recaptures or recoveries alone of birds ringed as young, and the benefits of using combined data.     

Estimating survival rates from recoveries of birds ringed as young: A case study

Models for analysis of survival rates from recoveries of birds ringed as young were evaluated for lesser snow geese ringed on the breeding grounds at La Perouse Bay, Manitoba from 1970 to 1992. Analyses of birds ringed as adults and young indicate recovery rates were lower for young than for older birds and varied independently in the two age classes. Adult survival increased over the study, while that of immatures decreased. Using only recoveries of birds ringed as young, models incorporating observed variation in recovery rates were not identifiable. Many sets of constraints could be selected to make the model identifiable, but there was no objective way to distinguish among them, and each could lead to different conclusions. The observed changes in survival rates could not be estimated. Previous analyses have shown that models for birds ringed as young can be used to test even complex variation in survival rates, provided that recovery rates do not vary with age. Unfortunately, as shown by the geese, this assumption may often be violated and can only be tested with additional data, preferably from birds recaptured or ringed as sub-adults or adults.     

Estimating survival rates from recoveries of birds ringed as young: a case study

Models for analysis of survival rates from recoveries of birds ringed as young were evaluated for lesser snow geese ringed on the breeding grounds at La Perouse Bay, Manitoba from 1970 to 1992. Analyses of birds ringed as adults and young indicate recovery rates were lower for young than for older birds and varied independently in the two age classes. Adult survival increased over the study, while that of immatures decreased. Using only recoveries of birds ringed as young, models incorporating observed variation in recovery rates were not identifiable. Many sets of constraints could be selected to make the model identifiable, but there was no objective way to distinguish among them, and each could lead to different conclusions. The observed changes in survival rates could not be estimated. Previous analyses have shown that models for birds ringed as young can be used to test even complex variation in survival rates, provided that recovery rates do not vary with age. Unfortunately, as shown by the geese, this assumption may often be violated and can only be tested with additional data, preferably from birds recaptured or ringed as sub-adults or adults.     

Investigating the effects of hunting on the survival of British pigeons and doves by analysis of ringing recoveries

Recent changes in British hunting legislation have protected the stock dove Columba oenas since 1 October 1982, and removed protection from the collared dove Streptopelia decaocto after 1 April 1977; the woodpigeon Columba palumbus has remained legal quarry throughout. Ringing recoveries offer a means of comparing annual survival rates before and after the change in legislation. Care is needed in the construction of the recovery matrices to remove inhomogeneities in the data and ensure that each 'year' runs from the day of legislative change. Annual survival rates were estimated by maximum likelihood using multinomial models conditioned on the recoveries; there was no evidence of age- or time-related variation in reporting rates. The annual survival rate of the stock dove was constant, at 54 +/- 3%. For both the collared dove and the woodpigeon, estimates of survival rates in the first year after ringing were not consistent between birds ringed as young and those ringed as adults, but nevertheless averaged less before 1977 than after 1977; annual survival rates of birds that survived the first year after ringing did not differ between time periods, and were 64 +/- 2% for the collared dove and 61 +/- 2% for the woodpigeon. The proportion of recoveries reported shot or trapped was only 14% for the collared dove, compared with 79% for the woodpigeon, and remained constant before and after 1977 for both species; in the case of the stock dove, the proportion reported shot or trapped before and after 1982 fell from 70% to 34%. The change in quarry status had no effect on annual survivorship or population size of either the stock dove or the collared dove, while the woodpigeon has increased regularly in abundance despite heavy shooting.     

Estimating avian dispersal distances from data on ringed birds

Data from birds ringed as chicks and recaptured during subsequent breeding seasons provide information on avian natal dispersal distances. However, national patterns of ring reports are influenced by recapture rates as well as by dispersal rates. While an extensive methodology has been developed to study survival rates using models that correct for recapture rates, the same is not true for dispersal. Here, we present such a method, showing how corrections for spatial heterogeneity in recapture rate can be built into estimates of dispersal rates if detailed atlas data and ringing totals can be combined with extensive data on birds ringed as chicks and recaptured as breeding adults. We show how the method can be implemented in the software package SURVIV (White, 1992).     

Uses of ringing data for the conservation and management of bird populations: A ringing scheme perspective

This review considers current and potential uses of ring-recovery and mark-recapture methods for conservation-oriented research by European ringing schemes. These schemes are concerned mainly with large-scale studies of the demography and movements of widespread species, much of the data being gathered by volunteers. The data holdings and data-gathering potential of the 33 European ringing schemes are outlined. Over 110 million birds have been ringed in Europe giving rise to 1.8 million recoveries. Some 64% of these recoveries are held in the computerized EURING data bank. Passerines comprise 43% of all recoveries and only 15% are of waterfowl. Currently, about 4 million birds are ringed each year and 90 000 recoveries are reported. Ringing effort is much higher in northern and western Europe than in southern and eastern Europe. Most schemes have recorded the ringing and recovery details of birds that have been recovered in computer files but most ringing data are held only on paper. These ringing data must be computerized for rigorous analyses of survival or movements. Without such computerization, future widespread ringing will be of little value. Five key areas of conservation-oriented research using data from European ringing schemes are identified; monitoring, investigating the causes of population declines, impacts of hunting, flyway networks and seabird studies. Current work and future research opportunities in these areas are discussed, and conservation priorities are identified. Demographic studies for monitoring and identifying the causes of declines are developing well, and are likely to be enhanced further by more gathering of mark-recapture data from standardized projects (such as constant effort sites), by improved access to computerized ringing data and by the development of more flexible, user-friendly software for ring-recovery analysis. Interest in studies of movements is reviving, with quantitative methods starting to be applied to population turnover at migratory stop-over sites (Jolly-Seber models) and to movements between sites (multi-state models). Future planned ringing studies will be important for testing ideas about the dynamics of meta-populations. European ringing schemes have the opportunity to enhance greatly their contribution to conservation over the next decade. This will require better access to computerized data and the development of more planned, cooperative projects at European and national scales. The close collaboration of biologists and statisticians in the analysis of previously collected data should be extended to the review of existing sampling strategies and to the development of new projects.     

Modelling age variation in survival and reporting rates for recovery models

In this paper, we focus on models for recovery data from birds ringed as young. In some cases, it is important to be able to include in these models a degree of age variation in the reporting probability. For certain models this has been found, empirically, to result in completely flat likelihood surfaces, due to parameter redundancy. These models cannot then be fitted to the data, to produce unique parameter estimates. However, empirical evidence also exists that other models with such age variation can be fitted to data by maximum likelihood. Using the approach of Catchpole and Morgan (1996b), we can now identify which models in this area are parameter-redundant, and which are not. Models which are not parameter-redundant may still perform poorly in practice, and this is investigated through examples, involving both real and simulated data. The Akaike Information Criterion is found to select inappropriate models in a number of instances. The paper ends with guidelines for fitting models to data from birds ringed as young, when age dependence is expected in the reporting probability.     

Modelling age variation in survival and reporting rates for recovery models

In this paper, we focus on models for recovery data from birds ringed as young. In some cases, it is important to be able to include in these models a degree of age variation in the reporting probability. For certain models this has been found, empirically, to result in completely flat likelihood surfaces, due to parameter redundancy. These models cannot then be fitted to the data, to produce unique parameter estimates. However, empirical evidence also exists that other models with such age variation can be fitted to data by maximum likelihood. Using the approach of Catchpole and Morgan (1996b), we can now identify which models in this area are parameter-redundant, and which are not. Models which are not parameter-redundant may still perform poorly in practice, and this is investigated through examples, involving both real and simulated data. The Akaike Information Criterion is found to select inappropriate models in a number of instances. The paper ends with guidelines for fitting models to data from birds ringed as young, when age dependence is expected in the reporting probability.     

Transient animals in a resident population of snow geese: Local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

Transient animals in a resident population of snow geese: local emigration or heterogeneity?

The estimation of survival rates from analysis of recapture of individually marked animals assumes that all individuals are equally likely to be re-encountered. This assumption is frequently violated in natural populations due to movements to and from the sampling area. We evaluated potential sources of heterogeneity using data from recaptures of 36000 individually marked female lesser snow geese, Anser c. caerulescens , from an expanding population in northern Manitoba, Canada. By stratifying individuals according to marking age and origin (hatched at the colony or not), we assessed the degree to which variation in apparent survival reflected permanent or temporary differences in emigration and effects of handling. In general, for birds ringed as adults, estimated apparent survival rates were significantly lower during the first year after ringing than in subsequent years. By comparing birds ringed as adults (classified by origin) with those ringed as goslings, we were able to demonstrate that these differences are not due to permanent emigration from the colony by transient individuals or heterogeneity of individual capture probability, but more likely reflect differences among individuals in their response to initial marking. Approximately 25% of birds permanently emigrate from the sampling area following marking.     

Suggestions for future directions for studies of marked migratory landbirds from the perspective of a practitioner in population management and conservation

Significant population declines in landbird species have been documented recently from many areas of the earth, including Europe and North America. Identification of the major causes of these declines and effective management actions to reverse them is difficult, especially for populations of long-distance migrants that winter in tropical areas. Key-factor and sensitivity analyses of critical population parameters in the context of integrated population models provide one promising approach to solving these problems. Key population factors may include breeding productivity, first-year survival, recruitment of young, adult survival and permanent emigration of adults; each of these can be indexed or estimated using data from cooperative ringing programmes, but the usefulness of the indices or estimates is limited by deficiencies in the available data and limitations of the available models. Future methodological directions for ringing studies should include efforts to: (1) develop and implement techniques to distinguish young from adult birds through the first breeding season of the young birds; (2) implement radio-tracking to determine characteristics of dispersal of young birds and transient adults; and (3) implement increased ringing, DNA fingerprinting and stable-isotope analysis to determine correspondence of breeding and winter ranges. Future programme-related directions should include efforts to: (1) integrate multiple methods at individual sites to compare and validate the indices and estimates produced by the different methods; (2) develop cooperative programmes of winter-season mist-netting to generate mark-recapture data to estimate the seasonal components of survival; and (3) develop mutually compatible banding programmes in tropical countries. Future theoretical and analytical directions should include efforts to continue to develop, refine and utilize: (1) key-factor and sensitivity analyses to determine the major causes of population changes; (2) models for dispersal of young birds and transient adults to improve the usefulness of indices of the number of hatch-year and second-year birds; (3) models to determine the proportions of transients in Cormack-Jolly-Seber (CJS) mark-recapture analyses and to eliminate their effects on estimates of survival rate, population size and recruitment of residents; (4) integrated models of population processes that utilize data from multiple methods to provide estimates of first-year survival, recruitment rate of young and permanent emigration rate of adults, parameters that are difficult to obtain from a single method; (5) models to estimate seasonal components of survival to provide insights into the timing and causes of mortality; (6) models incorporating environmental variables and species-specific characteristics as covariates in CJS mark-recapture and key-factor analyses; (7) models for pooling and weighting data obtained from multiple sites in cooperative ringing projects; (8) models for identifying long-term trends in demographic parameters; and (9) techniques for selection of appropriate models. Finally, assumptions implicit in the use of indices of various demographic parameters need to be tested and field techniques need to be improved to increase the numbers of individuals marked and recaptured in order to allow more precise parameter estimation; this will increase the ability to test competing hypotheses of population dynamics from data gathered in ringing programmes.     

Survival rates of breeding common gulls in Estonia

The aim of the present paper was to estimate the survival rates of breeding common gulls, using mark-recapture data, gathered in 1968-1983 (16 sampling periods) in Estonia. We analyzed effects of age (breeding experience), year and sex on survival. Every year we observed more than 90% of the breeders and ringed about 95% of the nestlings. Two samples of gulls were used in the analyses. The first sample (347 individuals) consisted of birds thought to be first-time breeders when first observed in colony. The second sample (1269 individuals) may contain birds which have nested earlier. In the first sample, we did not detect any influence of age and sex on survival, but time dependence was significant and can be explained by winter severity. In cold winters the survival was lower (0.865) than in normal (0.896) and warm (0.929) winters. We suspect that the age effect on survival rate remained undetected owing to sparse data. In the second sample, we detected age- and time-dependent survival for both sexes. We also found differences between the sexes in recapture probability (in both samples). This was probably caused by lower site tenacity of females.     

Modelling postfledging survival and age-specific breeding probabilities in species with delayed maturity: A case study of Roseate Terns at Falkner Island,Connecticut

We modelled postfledging survival and age-specific breeding probabilities in endangered Roseate Terns ( Sterna dougallii ) at Falkner Island, Connecticut, USA using capture-recapture data from 1988-1998 of birds ringed as chicks and as adults. While no individuals bred as 2-year-olds during this period, about three-quarters of the young that survived and returned as 3-year-olds nested, and virtually all surviving birds had begun breeding by the time they reached 5 years of age. We found no evidence of temporal variation age of first breeding of birds from different cohorts. There was significant temporal variation in the annual survival of adults and the survival over the typical 3-year maturation period of prebreeding birds, with extremely low values for both groups from the 1991 breeding season. The estimated overwinter survival rate (0.62) for adults from 1991-1992 was about three-quarters the usual rate of about 0.83, but the low survival of fledglings from 1991 resulted in less than 25% of the otherwise expected number of young from that cohort returning as breeding birds; this suggests that fledglings suffered a greater proportional decrease in survival than did adults. The survival estimates of young from 1989 and 1990 show that these cohorts were not negatively influenced by the events that decimated the young from 1991, and the young from 1992 and 1993 had above-average survival estimates. The apparent decrease since 1996 in development of fidelity of new recruits to this site is suspected to be due mainly to nocturnal disturbance and predation of chicks causing low productivity.     

How useful are recoveries of North American passerines for survival analyses?

Of 17 000 000 passerines ringed in North America from 1955 to 1984, only 0.4% were ever recovered. Only 62 species had more than 100 recoveries, of which only 26 had more than 500 recoveries. Preliminary analyses using stochastic recovery models for four of the species with more than 500 recoveries suggest estimates of mean annual adult survival can be fairly precise (CV < 4%), but estimates of immature survival are much less precise (CV > 8%). Comparable estimates may be possible for other species with more than 100 recoveries, depending on the temporal and geographic distribution of ringings and recoveries. Further analyses are required to determine whether these estimates may be biased by heterogeneity in survival or recovery rates.     

Effects of neckbands on survival and fidelity of white-fronted and Canada geese captured as non-breeding adults

We conducted an experiment to examine the effect of neckbands, controlling for differences in sex, species and year of study (1991-1997), on probabilities of capture, survival, reporting, and fidelity in non-breeding small Canada ( Branta canadensis hutchinsi ) and white-fronted ( Anser albifrons frontalis ) geese. In Canada's central arctic, we systematically double-marked about half of the individuals from each species with neckbands and legbands, and we marked the other half only with legbands. We considered 48 a priori models that included combinations of sex, species, year, and neckband effects on the four population parameters produced by Burnham's (1993) model, using AIC for model selection. The four best approximating models each included a negative effect of neckbands on survival, and effect size varied among years. True survival probability of neckbanded birds annually ranged from 0.006 to 0.23 and 0.039 to 0.22 (Canada and white-fronted geese, respectively) lower than for conspecifics without neckbands. Changes in estimates of survival probability in neckbanded birds appeared to attenuate more recently, particularly in Canada Geese, a result that we suspect was related to lower retention rates of neckbands. We urge extreme caution in use of neckbands for estimation of certain population parameters, and discourage their use for estimation of unbiased survival probability in these two species.     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

Mixed-effects Models with Skewed Distributions for Time-varying Decay Rate in HIV Dynamics

After initiation of treatment, HIV viral load has multiphasic changes, which indicates that the viral decay rate is a time-varying process. Mixed-effects models with different time-varying decay rate functions have been proposed in literature. However, there are two unresolved critical issues: (i) it is not clear which model is more appropriate for practical use, and (ii) the model random errors are commonly assumed to follow a normal distribution, which may be unrealistic and can obscure important features of within- and among-subject variations. Because asymmetry of HIV viral load data is still noticeable even after transformation, it is important to use a more general distribution family that enables the unrealistic normal assumption to be relaxed. We developed skew-elliptical (SE) Bayesian mixed-effects models by considering the model random errors to have an SE distribution. We compared the performance among five SE models that have different time-varying decay rate functions. For each model, we also contrasted the performance under different model random error assumptions such as normal, Student-t, skew-normal, or skew-t distribution. Two AIDS clinical trial datasets were used to illustrate the proposed models and methods. The results indicate that the model with a time-varying viral decay rate that has two exponential components is preferred. Among the four distribution assumptions, the skew-t and skew-normal models provided better fitting to the data than normal or Student-t model, suggesting that it is important to assume a model with a skewed distribution in order to achieve reasonable results when the data exhibit skewness.