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 survival and movement rates in multi-state tag-return and capture-recapture models

There has been growing interest in the estimation of transition probabilities among stages (Hestbeck et al. , 1991; Brownie et al. , 1993; Schwarz et al. , 1993) in tag-return and capture-recapture models. This has been driven by the increasing interest in meta-population models in ecology and the need for parameter estimates to use in these models. These transition probabilities are composed of survival and movement rates, which can only be estimated separately when an additional assumption is made (Brownie et al. , 1993). Brownie et al. (1993) assumed that movement occurs at the end of the interval between time i and i + 1. We generalize this work to allow different movement patterns in the interval for multiple tag-recovery and capture-recapture experiments. The time of movement is a random variable with a known distribution. The model formulations can be viewed as matrix extensions to the model formulations of single open population capturerecapture and tag-recovery experiments (Jolly, 1965; Seber, 1965; Brownie et al. , 1985). We also present the results of a small simulation study for the tag-return model when movement time follows a beta distribution, and later another simulation study for the capture-recapture model when movement time follows a uniform distribution. The simulation studies use a modified program SURVIV (White, 1983). The Relative Standard Errors (RSEs) of estimates according to high and low movement rates are presented. We show there are strong correlations between movement and survival estimates in the case that the movement rate is high. We also show that estimators of movement rates to different areas and estimators of survival rates in different areas have substantial correlations.     

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.     

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.     

General class of estimators in multi-character surveys

In this paper, a general class of estimators for the estimation of a finite population total in multi-character surveys is proposed. It is shown that the estimators proposed by Arnab (2002), Amahiaet al. (1989) and Bansal and Singh (1985) are the special cases of the proposed class of estimators. The proposed class of estimators is always more efficient than the estimator proposed by Rao (1966).     

The use of a mixture model for estimating vaccine efficacy

In this note a mixture model is applied to examine the effects of vaccination. It can directly estimate the efficacy parameters and their standard errors for the two models suggested in Smith et al. (1994) and Haber et al.(1991a). Furthermore, it can be shown that the action of the vaccine for the two models are equivalent. We illustrate the procedure to an outbreak of mumps in a middle school in Ashtabula County, Ohio.     

Assessing the use of sample selection models in the estimation of fertility postponement effects

Several studies have shown that at the individual level there exists a negative relationship between age at first birth and completed fertility. Using twin data in order to control for unobserved heterogeneity as possible source of bias, Kohler et al. (2001) showed the significant presence of such "postponement effect" at the micro level. In this paper, we apply sample selection models, where selection is based on having or not having had a first birth at all, to estimate the impact of postponing first births on subsequent fertility for four European nations, three of which have now lowest-low fertility levels. We use data from a set of comparative surveys (Fertility and Family Surveys), and we apply sample selection models on the logarithm of total fertility and on the progression to the second birth. Our results show that postponement effects are only very slightly affected by sample selection biases, so that sample selection models do not improve significantly the results of standard regression techniques on selected samples. Our results confirm that the postponement effect is higher in countries with lowest-low fertility levels.     

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.     

Estimation of long-term trends and variation in avian survival probabilities using random effects models

We obtained banding and recovery data from the Bird Banding Laboratory (operated by the Biological Resources Division of the US Geological Survey) for adults from 129 avian species that had been continuously banded for > 24 years. Data were partitioned by gender, banding period (winter versus summer), and by states/provinces. Data sets were initially screened for adequacy based on specific criteria (e.g. minimum sample sizes). Fifty-nine data sets (11 waterfowl species, the Mourning Dove and Common Grackle) met our criteria of adequacy for further analysis. We estimated annual survival probabilities using the Brownie et al. recovery model {St, ft} in program MARK. Trends in annual survival and temporal process variation were estimated using random effects models based on shrinkage estimators. Waterfowl species had relatively little variation in annual survival probabilities (mean CV = 8.7% and 10% for males and females, respectively). The limited data for other species suggested similar low temporal variation for males, but higher temporal variation for females (CV = 40%). Evidence for long-term trends varied by species, banding period and sex, with no obvious spatial patterns for either positive or negative trends in survival probabilities. An exception was Mourning Doves banded in Illinois/Missouri and Arizona/New Mexico where both males (slope = -0.0122, se = 0.0019 and females (slope = -0.0109 to -0.0128, se = 0.0018 -0.0032) exhibited declining trends in survival probabilities. We believe our approach has application for large-scale monitoring. However, meaningful banding and recovery data for species other than waterfowl is very limited in North America.     

Model‐based Prediction In Ecological Surveys Including Those with Incomplete Detection

This paper explores and develops model‐based predictors for surveys of plants and wildlife including those with incomplete detection. The methodology allows for estimating a detection function to account for objects which were not detected at the time of the survey. The model‐based theory utilises generalized linear models (GLMs) and is either new or adapted from other areas of sampling. A simulation study is used to validate the estimators and comparisons are made with an integrated likelihood approach. An aerial survey of kangaroos in western New South Wales is used to illustrate the theory. The area within 50m of the aircraft is treated as a strip transect and mark‐recapture methods are used to estimate the detection function.     

Variance reduction for kernel estimators in clustered/longitudinal data analysis

We develop a variance reduction method for the seemingly unrelated (SUR) kernel estimator of Wang (2003). We show that the quadratic interpolation method introduced in Cheng et al. (2007) works for the SUR kernel estimator. For a given point of estimation, Cheng et al. (2007) define a variance reduced local linear estimate as a linear combination of classical estimates at three nearby points. We develop an analogous variance reduction method for SUR kernel estimators in clustered/longitudinal models and perform simulation studies which demonstrate the efficacy of our variance reduction method in finite sample settings.     

Estimation of an indicator of the representativeness of survey response

Nonresponse is a major source of estimation error in sample surveys. The response rate is widely used to measure survey quality associated with nonresponse, but is inadequate as an indicator because of its limited relation with nonresponse bias. Schouten et al. (2009) proposed an alternative indicator, which they refer to as an indicator of representativeness or R-indicator. This indicator measures the variability of the probabilities of response for units in the population. This paper develops methods for the estimation of this R-indicator assuming that values of a set of auxiliary variables are observed for both respondents and nonrespondents. We propose bias adjustments to the point estimator proposed by Schouten et al. (2009) and demonstrate the effectiveness of this adjustment in a simulation study where it is shown that the method is valid, especially for smaller sample sizes. We also propose linearization variance estimators which avoid the need for computer-intensive replication methods and show good coverage in the simulation study even when models are not fully specified. The use of the proposed procedures is also illustrated in an application to two business surveys at Statistics Netherlands.     

A notion of coherent conditional prevision for arbitrary random quantities

In the paper we give a notion of coherent prevision for arbitrary random quantities which extends the notions given by Holzer (1985) for bounded conditional random quantities and by Crisma et al. (1997) for arbitrary but unconditional random quantities. We show that the main properties of the prevision are preserved, apart from the multiplicative one which may fail in the presence of non-finite previsions. This work was partially supported by the MURST grant “Statistical models: Probabilistic foundations and procedures for inference and decisions”.     

A functional law of the iterated logarithm for kernel-type estimators of the tail index

Under von Mises's condition, the kernel tail index estimators of Csörgő et al. (Ann. Statist. 13 (1985) 1050) have been generalized by Groeneboon et al. (Ann. Statist. 31 (2003) 1956) for all real tail indices. Weak consistency and asymptotic normality of their kernel estimators have been established. In this paper, we present a characterization of the almost sure behavior of these estimators and we show their strong consistency.     

The best subset of parameters in min-max linear regression

These Fortran-77 subroutines provide building blocks for Generalized Cross-Validation (GCV) (Craven and Wahba, 1979) calculations in data analysis and data smoothing including ridge regression (Golub, Heath, and Wahba, 1979), thin plate smoothing splines (Wahba and Wendelberger, 1980), deconvolution (Wahba, 1982d), smoothing of generalized linear models (O'sullivan, Yandell and Raynor 1986, Green 1984 and Green and Yandell 1985), and ill-posed problems (Nychka et al., 1984, O'sullivan and Wahba, 1985). We present some of the types of problems for which GCV is a useful method of choosing a smoothing or regularization parameter and we describe the structure of the subroutines.Ridge Regression: A familiar example of a smoothing parameter is the ridge parameter X in the ridge regression problem which we write.     

Some coverage error models for census data

"Alternative models are presented for representing coverage error in surveys and censuses of human populations. The models are related to the capture-recapture models used in wildlife applications and to the dual-system models employed in the vital events literature. Estimation methodologies are discussed for one of the coverage error models." After a discussion of the theory underlying the methodology, "distinctions are made between two kinds of error: (a) sampling error and (b) error associated with the model. An example involving data from the 1980 U.S. census is presented. The problem of adjusting census and survey data for coverage error is also discussed."     

Estimation of general semi-parametric quantile regression

Quantile regression introduced by Koenker and Bassett (1978) produces a comprehensive picture of a response variable on predictors. In this paper, we propose a general semi-parametric model of which part of predictors are presented with a single-index, to model the relationship of conditional quantiles of the response on predictors. Special cases are single-index models, partially linear single-index models and varying coefficient single-index models. We propose the qOPG, a quantile regression version of outer-product gradient estimation method (OPG, Xia et al., 2002) to estimate the single-index. Large-sample properties, simulation results and a real-data analysis are provided to examine the performance of the qOPG.     

On using non identical and independent Bernoulli trials in human surveys

Unlike the usual randomized response techniques, as a pioneering attempt, this article focuses on using non identical independent Bernoulli trials in sensitive surveys. For this purpose, a general class of randomized response techniques is considered. The usual randomized response techniques are based on a fixed probability of having a yes answer. Contrary to usual techniques, in the proposed technique every respondent has a different probability of reporting a yes answer. With this setting, in most of the situations, the proposed technique is observed performing better in terms of variability. To illustrate and support the superiority of the proposed technique it is compared with models such as Warner (1965), Greenberg et al. (1969), Mangat and Singh (1990), and Mangat (1994) using identical Bernoulli trials. Relative efficiency and privacy protection are studied in detail using Warner (1965) and Mangat (1994) models.     

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129–150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171–178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.     

Delineating bird populations using ring recoveries

We delineate bird populations using cluster analysis to group ringing sites based on pairwise comparisons of recoveries. Clustering provides a quantitative (but non-unique) grouping that can be used to examine the relationships of bird distributions at both local and regional geographic scales. Clustering is based on similarity matrices composed of pairwise comparisons of recovery distributions from ringing sites. We demonstrate the method using mallard ( Anas platyrhynchos ) ring recoveries to group ringing sites in south-central Canada, and discuss the possibilities for these analyses for non-hunted species with few recoveries.