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.     

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.     

Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.     

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.     

Selection among open population capture-recapture models when capture probabilities are heterogeneous

Selection of a parsimonious model as a basis for statistical inference from capture-recapture data is critical, especially when using open models in the analysis of multiple, interrelated data sets (e.g. males and females, with two to three age classes, over three to five areas and 10-15 years). The global (i.e. most general) model for such data sets might contain hundreds of survival and recapture parameters. Here, we focus on a series of nested models of the Cormack-Jolly-Seber type wherein the likelihood arises from products of multinomial distributions whose cell probabilities are reparameterized in terms of survival ( phi ) and mean capture ( p ) probabilities. This paper presents numerical results on two information-theoretic methods for model selection when the capture probabilities are heterogeneous over individual animals: Akaike's Information Criterion (AIC) and a dimension-consistent criterion (CAIC), derived from a Bayesian viewpoint. Quality of model selection was evaluated based on the relative Euclidian distance between standardized theta and theta (parameter theta is vector-valued and contains the survival ( phi ) and mean capture ( p ) probabilities); this quantity (RSS = sigma{(theta i - theta i )/ theta i } 2 ) is a sum of squared bias and variance. Thus, the quality of inference (RSS) was judged by comparing the performance of the two information criteria and the use of the true model (used to generate the data), in relation to the model that provided the smallest RSS. We found that heterogeneity in the capture probabilities had a negligible effect on model selection using AIC or CAIC. Model size increased as sample size increased with both AIC- and CAIC-selected models.     

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.     

Evaluation of some random effects methodology applicable to bird ringing data

Existing models for ring recovery and recapture data analysis treat temporal variations in annual survival probability (S) as fixed effects. Often there is no explainable structure to the temporal variation in S 1 , … , S k ; random effects can then be a useful model: Si = E(S) + k i . Here, the temporal variation in survival probability is treated as random with average value E( k 2 ) = σ 2 . This random effects model can now be fit in program MARK. Resultant inferences include point and interval estimation for process variation, σ 2 , estimation of E(S) and var(Ê(S)) where the latter includes a component for σ 2 as well as the traditional component for v ar(S|S). Furthermore, the random effects model leads to shrinkage estimates, S i , as improved (in mean square error) estimators of Si compared to the MLE, S i , from the unrestricted time-effects model. Appropriate confidence intervals based on the S i are also provided. In addition, AIC has been generalized to random effects models. This paper presents results of a Monte Carlo evaluation of inference performance under the simple random effects model. Examined by simulation, under the simple one group Cormack-Jolly-Seber (CJS) model, are issues such as bias of σ 2 , confidence interval coverage on σ 2 , coverage and mean square error comparisons for inference about Si based on shrinkage versus maximum likelihood estimators, and performance of AIC model selection over three models: S i = S (no effects), Si = E(S) + k i (random effects), and S 1 , … , S k (fixed effects). For the cases simulated, the random effects methods performed well and were uniformly better than fixed effects MLE for the S i .     

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.     

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.     

Return rates in studies of life history evolution: Are biases large?

Studies of life history evolution in passerine birds often depend on examination of annual survival probability of adult birds. Most studies rely on return rates (proportion of marked individuals released in one year that are recaptured in the next year) to estimate annual survival probability. Yet, return rate includes both the probability of survival and the probability of recapturing or resighting the bird in the next time interval. We use numerical estimation to illustrate the increasing bias in return rate as an estimator of annual survival probability as recapture/resighting probability decreases. Recapture/resighting probability is normally assumed to be high and relatively invariant for recapture/resighting studies of color-banded territorial birds. We tested this assumption through examination of 11 color-banding studies of passerines. These studies showed that recapture/resighting probabilities vary strongly and cannot be generalized as high. In short, return rates generally are poor estimators of annual survival probabilities and use of return rates may strongly bias relationships explored in comparative studies or bias results of experiments to test survival costs of reproduction. Recapture/resighting probabilities should be estimated in all studies that attempt to estimate annual survival probabilities.     

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.     

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.     

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.     

Working life expectancies: the case of Finland 1980–2006

Summary.  Working life expectancy is the future time that a person is expected to spend in employment. The paper is concerned with its estimation jointly with the expected times spent in the related states of 'on disability pension' and 'other alive'. The method, which is novel in this field, first estimates year- and age-dependent probabilities of being in the states of interest by large sample multivariate logistic regression. Estimates of probabilities, and subsequently expectancies, are given for the case of Finnish women and men aged 16–64 years for selected years in the period 1980–2001, together with projections for 2006. Since 1996 the decline in the employment of males has largely been due to the increasing popularity of early retirement. It was not due to an increase in disability. There has been no such decline for women, and the working life expectancy for males has been predicted to decline to or to fall below the initially lower figure for females by 2006. Considering that the Finnish population is aging rapidly, these trends could entail serious social and economic consequences for society in the coming years because of a looming shortage in the labour force that could undermine the sustainability of a welfare state.     

ESTIMATING PROCESSES OF COUNTS FROM CROSS-SECTIONAL AGGREGATE DATA, WITH AN APPLICATION TO MULTISTATE LIFE TABLES AND HEALTH EXPECTANCIES

This paper discusses the estimation of time‐dependent probabilities of a finite state‐space discrete‐time process using aggregate cross‐sectional data. A large‐sample version of multistate logistic regression is described and shown to be useful for analysing multistate life tables. The technique is applied to the estimation of disability‐free, severely disabled and other disabled survival curves and health expectancies in Australia, based on data from national health surveys in 1988, 1993 and 1998. A conclusion is that there has been a general upward trend in the future time expected to be spent in a state of disability, the picture being more pessimistic for males than females. For example, during 1988‐1998 the estimated increase in male life expectancy at birth of 2.7 years is decomposed as a decrease of 1.2 years in disability‐free health (life) expectancy and increases of 1.3 and 2.6 years, respectively, in states of severe disability and other disability.     

Confidence intervals for coefficients of variation in two-parameter exponential distributions

This article examines confidence intervals for the single coefficient of variation and the difference of coefficients of variation in the two-parameter exponential distributions, using the method of variance of estimates recovery (MOVER), the generalized confidence interval (GCI), and the asymptotic confidence interval (ACI). In simulation, the results indicate that coverage probabilities of the GCI maintain the nominal level in general. The MOVER performs well in terms of coverage probability when data only consist of positive values, but it has wider expected length. The coverage probabilities of the ACI satisfy the target for large sample sizes. We also illustrate our confidence intervals using a real-world example in the area of medical science.     

Modelling spatial-temporal covariance structures in monocropping barley trials

In long-term trials, not only are individual plot errors correlated over time but there is also a consistent underlying spatial variability in field conditions. The current study sought the most appropriate covariance structure of errors correlated in three dimensions for evaluating the productivity and time-trends in the barley yield data from the monocropping system established in northern Syria. The best spatial-temporal model found reflected the contribution of autocorrelations in spatial and temporal dimensions with estimates varying with the yield variable and location. Compared with a control structure based on independent errors, this covariance structure improved the significance of the fertilizer effect and the interaction with year. Time-trends were estimated in two ways: by accounting the seasonal variable contribution in annual variability (Method 1), which is suitable for detecting significant trends in short data series; and by using the linear component of the orthogonal polynomial on time (year), which is appropriate for long series (Method 2). Method 1 strengthened time-trend detection compared with the method of Jones and Singh [J. Agri. Sci., Cambridge 135 (2000), pp. 251-259] which assumed independence of temporal errors. Most estimates of yield trends over time from fertilizer application were numerically greater than the corresponding linear trends estimated from orthogonal polynomials in time (Method 2), reflecting the effect of accounting for seasonal variables. Grain yield declined over time at the drier site in the absence of nitrogen or phosphorus application, but positive trends were observed fairly generally for straw yield and for grain yield under higher levels of fertilizer inputs. It is suggested that analyses of long-term trials on other crops and cropping systems in other agro-ecological zones could be improved by taking spatial and temporal variability into account in the data evaluation.     

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.     

Estimating rates of population change for a neotropical parrot with ratio,mark-recapture and matrix methods

Robust methods for estimating rates of population change ( u ) are necessary for applied and theoretical goals in conservation and evolutionary biology. Traditionally, u has been calculated from either ratios of population counts (observed u or u obs ), or population models based on projection matrices (asymptotic u or u asy ,). New mark-recapture methods permit calculation of u from mark-resighting information alone (realized u or u rea ), but empirical comparisons with other methods are rare. In this paper, rates of population change were calculated for a population of green-rumped parrotlets ( Forpus passerinus ) that have been studied for more than a decade in central Venezuela. First, a ratio method based on counts of detected birds was used to calculate u obs. Next, a temporal symmetry method based on mark-recapture data (i.e. the u -parameterization introduced by Pradel, 1996) was used to calculate u rea . Finally, a stage-structured matrix model based on state-specific estimates of fecundity, immigration, local survival, and transition rates was used to calculate u asy . Analyses were conducted separately for females and males. Overall values of u from the three methods were consistent and all indicated that the finite rate of population change was not significantly different from 1. Annual values of u from the three methods were also in general agreement for a majority of years. However, u rea from the temporal symmetry method had the greatest precision, and apparently better accuracy than u asy . Unrealistic annual values of u asy could have been due to poor estimates of the transitional probability of becoming a breeder ( é ) or to a mismatch between the actual and the asymptotic stable stage distribution. In this study, the trade-off between biological realism and accuracy was better met by the temporal symmetry than the matrix method. Our results suggest that the temporal symmetry models can be applied with confidence to populations where less information may be available.     

Mark-resighting analysis of a California gull population

California gulls ( Larus californicus ) of known age and sex were censused on their breeding colony in 1979, 1980 and 1984 through 1993. Ages of 235 males and 196 females ranged from 4 to 27 years. Age classes used in the analysis were limited to 17, 4 through 19, and 20 or more as a final age category because data on gulls over 20 were sparse. Survival declined with age in a way that was parsimoniously modelled with a quadratic function. Other factors, sex and time, did not explain any variation in survival. Resighting depended on age, sex and time. Younger adults skipped breeding more frequently than did older adults, and females skipped breeding more frequently than did males. There was also good evidence for time dependence in resighting probability, but its inclusion in the model occurred at the expense of interpretability and precision. In a data set such as this, resighting probability may assume more importance than a mere 'nuisance parameter'. In this study, resighting history measured attendance at the breeding ground. In turn, attendance rates may be a manifestation of reproductive strategy, which can also have consequences for survival. In this situation, there may be heterogeneity in both survival and resighting probability that is unexplained by the model. While such complexity may well be a nuisance to deal with, it can also point to important biological questions.