Disentangling the sources of variation in the survival of the European dipper

The population growth rate of the European dipper has been shown to decrease with winter temperature and population size. We examine here the demographic mechanism for this effect by analysing how these factors affect the survival rate. Using more than 20 years of capture-mark-recapture data (1974-1997) based on more than 4000 marked individuals, we perform analyses using open capture-mark-recapture models. This allowed us to estimate the annual apparent survival rates (probability of surviving and staying on the study site from one year to the next one) and the recapture probabilities. We partitioned the variance of the apparent survival rates into sampling variance and process variance using random effects models, and investigated which variables best accounted for temporal process variation. Adult males and females had similar apparent survival rates, with an average of 0.52 and a coefficient of variation of 40%. Chick apparent survival was lower, averaging 0.06 with a coefficient of variation of 42%. Eighty percent of the variance in apparent survival rates was explained by winter temperature and population size for adults and 48% by winter temperature for chicks. The process variance outweighed the sampling variance both for chick and adult survival rates, which explained that shrunk estimates obtained under random effects models were close to MLE estimates. A large proportion of the annual variation in the apparent survival rate of chicks appears to be explained by inter-year differences in dispersal rates.     

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.     

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.     

Discrepancy in regression estimates between log-normal and gamma: some case studies

In regression models with multiplicative error, estimation is often based on either the log-normal or the gamma model. It is well known that the gamma model with constant coefficient of variation and the log-normal model with constant variance give almost the same analysis. This article focuses on the discrepancies of the regression estimates between the two models based on real examples. It identifies that even though the variance or the coefficient of variation remains constant, but regression estimates may be different between the two models. It also identifies that for the same positive data set, the variance is constant under the log-normal model but non-constant under the gamma model. For this data set, the regression estimates are completely different between the two models. In the process, it explains the causes of discrepancies between the two models.     

Re-analysis of a banding study to test the effects of an experimental increase in bag limits of mourning doves

In 1966-1971, eastern US states with hunting seasons on mourning doves ( Zenaida macroura ) participated in a study designed to estimate the effects of bag limit increases on population survival rates. More than 400 000 adult and juvenile birds were banded and released during this period, and subsequent harvest and return of bands, together with total harvest estimates from mail and telephone surveys of hunters, provided the database for analysis. The original analysis used an ANOVA framework, and resulted in inferences of no effect of bag limit increase on population parameters (Hayne 1975). We used a logistic regression analysis to infer that the bag limit increase did not cause a biologically significant increase in harvest rate and thus the experiment could not provide any insight into the relationship between harvest and annual survival rates. Harvest rate estimates of breeding populations from geographical subregions were used as covariates in a Program MARK analysis and revealed an association between annual survival and harvest rates, although this relationship is potentially confounded by a latitudinal gradient in survival rates of dove populations. We discuss methodological problems encountered in the analysis of these data, and provide recommendations for future studies of the relationship between harvest and annual survival rates of mourning dove populations.     

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.     

Survival estimation and the effects of dependency among animals

Survival models assume that fates of individuals are independent, yet the robustness of this assumption has been poorly quantified. We examine how empirically derived estimates of the variance of survival rates are affected by dependency in survival probability among individuals. We used Monte Carlo simulations to generate known amounts of dependency among pairs of individuals and analyzed these data with Kaplan-Meier and Cormack-Jolly-Seber models. Dependency significantly increased these empirical variances as compared to theoretically derived estimates of variance from the same populations. Using resighting data from 168 pairs of black brant ( Branta bernicla nigricans ), we used a resampling procedure and program RELEASE to estimate empirical and mean theoretical variances. We estimated that the relationship between paired individuals caused the empirical variance of the survival rate to be 155% larger than the empirical variance for unpaired individuals. Monte Carlo simulations and use of this resampling strategy can provide investigators with information on how robust their data are to this common assumption of independent survival probabilities.     

Optimal allocation of sample sizes between regular banding and radio-tagging for estimating annual survival and emigration rates

Many authors have shown that a combined analysis of data from two or more types of recapture survey brings advantages, such as the ability to provide more information about parameters of interest. For example, a combined analysis of annual resighting and monthly radio-telemetry data allows separate estimates of true survival and emigration rates, whereas only apparent survival can be estimated from the resighting data alone. For studies involving more than one type of survey, biologists should consider how to allocate the total budget to the surveys related to the different types of marks so that they will gain optimal information from the surveys. For example, since radio tags and subsequent monitoring are very costly, while leg bands are cheap, the biologists should try to balance costs with information obtained in deciding how many animals should receive radios. Given a total budget and specific costs, it is possible to determine the allocation of sample sizes to different types of marks in order to minimize the variance of parameters of interest, such as annual survival and emigration rates. In this paper, we propose a cost function for a study where all birds receive leg bands and a subset receives radio tags and all new releases occur at the start of the study. Using this cost function, we obtain the allocation of sample sizes to the two survey types that minimizes the standard error of survival rate estimates or, alternatively, the standard error of emigration rates. Given the proposed costs, we show that for high resighting probability, e.g. 0.6, tagging roughly 10-40% of birds with radios will give survival estimates with standard errors within the minimum range. Lower resighting rates will require a higher percentage of radioed birds. In addition, the proposed costs require tagging the maximum possible percentage of radioed birds to minimize the standard error of emigration estimates.     

Survival estimation and the effects of dependency among animals

Survival models assume that fates of individuals are independent, yet the robustness of this assumption has been poorly quantified. We examine how empirically derived estimates of the variance of survival rates are affected by dependency in survival probability among individuals. We used Monte Carlo simulations to generate known amounts of dependency among pairs of individuals and analyzed these data with Kaplan-Meier and Cormack-Jolly-Seber models. Dependency significantly increased these empirical variances as compared to theoretically derived estimates of variance from the same populations. Using resighting data from 168 pairs of black brant ( Branta bernicla nigricans ), we used a resampling procedure and program RELEASE to estimate empirical and mean theoretical variances. We estimated that the relationship between paired individuals caused the empirical variance of the survival rate to be 155% larger than the empirical variance for unpaired individuals. Monte Carlo simulations and use of this resampling strategy can provide investigators with information on how robust their data are to this common assumption of independent survival probabilities.     

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).     

Inference on the ratio of two coefficients of variation of two lognormal distributions

The coefficient of variation (CV) can be used as an index of reliability of measurement. The lognormal distribution has been applied to fit data in many fields. We developed approximate interval estimation of the ratio of two coefficients of variation (CsV) for lognormal distributions by using the Wald-type, Fieller-type, log methods, and method of variance estimates recovery (MOVER). The simulation studies show that empirical coverage rates of the methods are satisfactorily close to a nominal coverage rate for medium sample sizes.     

Asymptotic efficiency of a competing risks model: A two-sample case

A generalized Cox regression model is studied for the covariance analysis of competing risks data subject to independent random censoring. The information of the maximum partial likelihood estimates is compared with that of maximum likelihood estimates assuming a log linear hazard function.The method of generalized variance is used to define the efficiency of estimation between the two models. This is then applied to two-sample problems with two exponentially censoring rates. Numerical results are summarized ane presented graphically.The detailed results indicate that the semi-parametric model wrks well for a higher rate of censoring. A method of generalizing the result to type 1 censoring and the efficiency of estimating the coefficient of the covariate are discussecd. A brief account of using the results to help design experiments is also given.     

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.     

Bias in transition-specific survival and movement probabilities estimated using capture-recapture data

Transition probabilities can be estimated when capture-recapture data are available from each stratum on every capture occasion using a conditional likelihood approach with the Arnason-Schwarz model. To decompose the fundamental transition probabilities into derived parameters, all movement probabilities must sum to 1 and all individuals in stratum r at time i must have the same probability of survival regardless of which stratum the individual is in at time i + 1. If movement occurs among strata at the end of a sampling interval, survival rates of individuals from the same stratum are likely to be equal. However, if movement occurs between sampling periods and survival rates of individuals from the same stratum are not the same, estimates of stratum survival can be confounded with estimates of movement causing both estimates to be biased. Monte Carlo simulations were made of a three-sample model for a population with two strata using SURVIV. When differences were created in transition-specific survival rates for survival rates from the same stratum, relative bias was <2% in estimates of stratum survival and capture rates but relative bias in movement rates was much higher and varied. The magnitude of the relative bias in the movement estimate depended on the relative difference between the transition-specific survival rates and the corresponding stratum survival rate. The direction of the bias in movement rate estimates was opposite to the direction of this difference. Increases in relative bias due to increasing heterogeneity in probabilities of survival, movement and capture were small except when survival and capture probabilities were positively correlated within individuals.     

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.     

Test for age-specificity in survival of the common tern

Much effort in life-history theory has been addressed to the dependence of life-history traits on age, especially the phenomenon of senescence and its evolution. Although senescent declines in survival are well documented in humans and in domestic and laboratory animals, evidence for their occurrence and importance in wild animal species remains limited and equivocal. Several recent papers have suggested that methodological issues may contribute to this problem, and have encouraged investigators to improve sampling designs and to analyse their data using recently developed approaches to modelling of capture-mark-recapture data. Here we report on a three-year, two-site, mark-recapture study of known-aged common terns (Sterna hirundo) in the north-eastern USA. The study was nested within a long-term ecological study in which large numbers of chicks had been banded in each year for > 25 years. We used a range of models to test the hypothesis of an influence of age on survival probability. We also tested for a possible influence of sex on survival. The cross-sectional design of the study (one year's parameter estimates) avoided the possible confounding of effects of age and time. The study was conducted at a time when one of the study sites was being colonized and numbers were increasing rapidly. We detected two-way movements between the sites and estimated movement probabilities in the year for which they could be modelled. We also obtained limited data on emigration from our study area to more distant sites. We found no evidence that survival depended on either sex or age, except that survival was lower among the youngest birds (ages 2-3 years). Despite the large number of birds included in the study (1599 known-aged birds, 2367 total), confidence limits on estimates of survival probability were wide, especially for the oldest age-classes, so that a slight decline in survival late in life could not have been detected. In addition, the cross-sectional design of this study meant that a decline in survival probability within individuals (actuarial senescence) could have been masked by heterogeneity in survival probability among individuals (mortality selection). This emphasizes the need for the development of modelling tools permitting separation of these two phenomena, valid under field conditions in which the recapture probabilities are less than one.     

The demography of the decline in the British willow warbler population

Since 1989, there has been a major and unprecedented decline in the breeding population of willow warblers ( Phylloscopus trochilus ) in southern Britain. Between 1986 and 1993 the numbers of willow warbler territories counted on monitoring plots declined by 47% in southern Britain, compared to a decline of 7% in northern Britain. Breeding densities of willow warblers are generally higher in the north and west of Britain, than in the south. Data from nest record cards provided evidence of only minor regional differences in breeding performance with a small but significant increase in the loss rate of nests during the nestling stage in 1989-1992 in southern Britain, compared with 1974-1988. Mark-recapture data collected at 18 constant effort sites and from one intensive study were used to estimate apparent survival rates of adults during the period 1987-1993. Program SURGE4 was used to test for differences in survival rates and recapture probabilities between years, sexes, sites and regions. Recapture probabilities differed between sites and between the sexes but not between years. Survival rates differed significantly between years (in southern Britain) but not between sexes or sites. In southern Britain, adult survival declined from 45% during 1987-1988 to 24% during 1991-1992, while in northern Britain there was no evidence that survival changed during the same period. Although the pattern of annual variation in survival differed between northern and southern Britain, this was due mainly to a much lower survival rate in southern Britain during 1991-1992. Declining survival rates of adult willow warblers have probably been a major cause of the observed population decline.     

Fitting Variance Components Model and Fixed Effects Model for One-Way Analysis of Variance to Complex Survey Data

Under complex survey sampling, in particular when selection probabilities depend on the response variable (informative sampling), the sample and population distributions are different, possibly resulting in selection bias. This article is concerned with this problem by fitting two statistical models, namely: the variance components model (a two-stage model) and the fixed effects model (a single-stage model) for one-way analysis of variance, under complex survey design, for example, two-stage sampling, stratification, and unequal probability of selection, etc. Classical theory underlying the use of the two-stage model involves simple random sampling for each of the two stages. In such cases the model in the sample, after sample selection, is the same as model for the population; before sample selection. When the selection probabilities are related to the values of the response variable, standard estimates of the population model parameters may be severely biased, leading possibly to false inference. The idea behind the approach is to extract the model holding for the sample data as a function of the model in the population and of the first order inclusion probabilities. And then fit the sample model, using analysis of variance, maximum likelihood, and pseudo maximum likelihood methods of estimation. The main feature of the proposed techniques is related to their behavior in terms of the informativeness parameter. We also show that the use of the population model that ignores the informative sampling design, yields biased model fitting.     

Quasi-likelihood estimation for GLM with random scales

This paper uses random scales similar to random effects used in the generalized linear mixed models to describe “inter-location” population variation in variance components for modeling complicated data obtained from applications such as antenna manufacturing. Our distribution studies lead to a complicated integrated extended quasi-likelihood (IEQL) for parameter estimations and large sample inference derivations. Laplace's expansion and several approximation methods are employed to simplify the IEQL estimation procedures. Asymptotic properties of the approximate IEQL estimates are derived for general structures of the covariance matrix of random scales. Focusing on a few special covariance structures in simpler forms, the authors further simplify IEQL estimates such that typically used software tools such as weighted regression can compute the estimates easily. Moreover, these special cases allow us to derive interesting asymptotic results in much more compact expressions. Finally, numerical simulation results show that IEQL estimates perform very well in several special cases studied.     

Productivity indices and survival rate estimates from MAPS,a continent-wide programme of constant-effort mist-netting in North America

The Monitoring Avian Productivity and Survivorship (MAPS) programme is a cooperative effort to provide annual regional indices of adult population size and post-fledging productivity and estimates of adult survival rates from data pooled from a network of constant-effort mist-netting stations across North America. This paper provides an overview of the field and analytical methods currently employed by MAPS, a discussion of the assumptions underlying the use of these techniques, and a discussion of the validity of some of these assumptions based on data gathered during the first 5 years (1989-1993) of the programme, during which time it grew from 17 to 227 stations. Ageand species-specific differences in dispersal characteristics are important factors affecting the usefulness of the indices of adult population size and productivity derived from MAPS data. The presence of transients, heterogeneous capture probabilities among stations, and the large sample sizes required by models to deal effectively with these two considerations are important factors affecting the accuracy and precision of survival rate estimates derived from MAPS data. Important results from the first 5 years of MAPS are: (1) indices of adult population size derived from MAPS mist-netting data correlated well with analogous indices derived from point-count data collected at MAPS stations; (2) annual changes in productivity indices generated by MAPS were similar to analogous changes documented by direct nest monitoring and were generally as expected when compared to annual changes in weather during the breeding season; and (3) a model using between-year recaptures in Cormack-Jolly-Seber (CJS) mark-recapture analyses to estimate the proportion of residents among unmarked birds was found, for most tropical-wintering species sampled, to provide a better fit with the available data and more realistic and precise estimates of annual survival rates of resident birds than did standard CJS mark-recapture analyses. A detailed review of the statistical characteristics of MAPS data and a thorough evaluation of the field and analytical methods used in the MAPS programme are currently under way.