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

We modeled 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-yr-olds during this period, about three-quarters of the young that survived and returned as 3-yr-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 in 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-yr 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 due mainly to nocturnal disturbance and predation of chicks causing low productivity.

Connecticut

The use of resighting data to estimate the rate of population growth of the snail kite in Florida

The rate of population growth (lambda) is an important demographic parameter used to assess the viability of a population and to develop management and conservation agendas. We examined the use of resighting data to estimate lambda for the snail kite population in Florida from 1997-2000. The analyses consisted of (1) a robust design approach that derives an estimate of lambda from estimates of population size and (2) the Pradel (1996) temporal symmetry (TSM) approach that directly estimates lambda using an open-population capture-recapture model. Besides resighting data, both approaches required information on the number of unmarked individuals that were sighted during the sampling periods. The point estimates of lambda differed between the robust design and TSM approaches, but the 95% confidence intervals overlapped substantially. We believe the differences may be the result of sparse data and do not indicate the inappropriateness of either modelling technique. We focused on the results of the robust design because this approach provided estimates for all study years. Variation among these estimates was smaller than levels of variation among ad hoc estimates based on previously reported index statistics. We recommend that lambda of snail kites be estimated using capture-resighting methods rather than ad hoc counts.

Journal of Applied Statistics

Occam's shadow: levels of analysis in evolutionary ecology - where to next?

Evolutionary ecology is the study of evolutionary processes, and the ecological conditions that influence them. A fundamental paradigm underlying the study of evolution is natural selection. Although there are a variety of operational definitions for natural selection in the literature, perhaps the most general one is that which characterizes selection as the process whereby heritable variation in fitness associated with variation in one or more phenotypic traits leads to intergenerational change in the frequency distribution of those traits. The past 20 years have witnessed a marked increase in the precision and reliability of our ability to estimate one or more components of fitness and characterize natural selection in wild populations, owing particularly to significant advances in methods for analysis of data from marked individuals. In this paper, we focus on several issues that we believe are important considerations for the application and development of these methods in the context of addressing questions in evolutionary ecology. First, our traditional approach to estimation often rests upon analysis of aggregates of individuals, which in the wild may reflect increasingly non-random (selected) samples with respect to the trait(s) of interest. In some cases, analysis at the aggregate level, rather than the individual level, may obscure important patterns. While there are a growing number of analytical tools available to estimate parameters at the individual level, and which can cope (to varying degrees) with progressive selection of the sample, the advent of new methods does not reduce the need to consider carefully the appropriate level of analysis in the first place. Estimation should be motivated a priori by strong theoretical analysis. Doing so provides clear guidance, in terms of both (i) assisting in the identification of realistic and meaningful models to include in the candidate model set, and (ii) providing the appropriate context under which the results are interpreted. Second, while it is true that selection (as defined) operates at the level of the individual, the selection gradient is often (if not generally) conditional on the abundance of the population. As such, it may be important to consider estimating transition rates conditional on both the parameter values of the other individuals in the population (or at least their distribution), and population abundance. This will undoubtedly pose a considerable challenge, for both single- and multi-strata applications. It will also require renewed consideration of the estimation of abundance, especially for open populations. Thirdly, selection typically operates on dynamic, individually varying traits. Such estimation may require characterizing fitness in terms of individual plasticity in one or more state variables, constituting analysis of the norms of reaction of individuals to variable environments. This can be quite complex, especially for traits that are under facultative control. Recent work has indicated that the pattern of selection on such traits is conditional on the relative rates of movement among and frequency of spatially heterogeneous habitats, suggesting analyses of evolution of life histories in open populations can be misleading in some cases.

Journal of Applied Statistics

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.

Journal of Applied Statistics

Analysis of individual- and time-specific covariate effects on survival of Serinus serinus in north-eastern Spain

We developed models for the analysis of recapture data for 2678 serins (Serinus serinus) ringed in north-eastern Spain since 1985. We investigated several time- and individual-specific factors as potential predictors of overall mortality and dispersal patterns, and of gender and age differences in these patterns. Time-specific covariates included minimum daily temperature, days below freezing, and abundance of a strong competitor, siskins (Carduelis spinus) during winter, and maximum temperature and rainfall during summer. Individual covariates included body mass (i.e. body condition), and wing length (i.e. flying ability), and interactions between body mass and environmental factors. We found little support of a predictive relationship between environmental factors and survival, but good evidence of relationships between body mass and survival, especially for juveniles. Juvenile survival appears to vary in a curvilinear manner with increasing mass, suggesting that there may exist an optimal mass beyond which increases are detrimental. The mass-survival relationship does seem to be influenced by at least one environmental factor, namely the abundance of wintering siskins. When siskins are abundant, increases in body mass appear to relate strongly to increasing survival. When siskin numbers are average or low the relationship is largely reversed, suggesting that the presence of strong competition mitigates the otherwise largely negative aspects of greater body mass. Wing length in juveniles also appears to be related positively to survival, perhaps largely due to the influence of a few unusually large juveniles with adult-like survival. Further work is needed to test these relationships, ideally under experimentation.

Journal of Applied Statistics

Model-based estimation of individual fitness

Fitness is the currency of natural selection, a measure of the propagation rate of genotypes into future generations. Its various definitions have the common feature that they are functions of survival and fertility rates. At the individual level, the operative level for natural selection, these rates must be understood as latent features, genetically determined propensities existing at birth. This conception of rates requires that individual fitness be defined and estimated by consideration of the individual in a modelled relation to a group of similar individuals; the only alternative is to consider a sample of size one, unless a clone of identical individuals is available. We present hierarchical models describing individual heterogeneity in survival and fertility rates and allowing for associations between these rates at the individual level. We apply these models to an analysis of life histories of Kittiwakes ( Rissa tridactyla ) observed at several colonies on the Brittany coast of France. We compare Bayesian estimation of the population distribution of individual fitness with estimation based on treating individual life histories in isolation, as samples of size one (e.g. McGraw & Caswell, 1996).

Brittany Coast

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 S1,..., Sk; random effects can then be a useful model: Si = E(S) + ??i. Here, the temporal variation in survival probability is treated as random with average value E(??2) = ??2. This random effects model can now be fit in program MARK. Resultant inferences include point and interval estimation for process variation, ??2, estimation of E(S) and var (E??(S)) where the latter includes a component for ??2 as well as the traditional component for v??ar(S??\S??). Furthermore, the random effects model leads to shrinkage estimates, Si, 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 Si 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 ??s2, confidence interval coverage on ??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: Si ??? S (no effects), Si = E(S) + ??i (random effects), and S1,..., Sk (fixed effects). For the cases simulated, the random effects methods performed well and were uniformly better than fixed effects MLE for the Si.

Journal of Applied Statistics

Approaches for the direct estimation of lambda, and demographic contributions to lambda, using capture-recapture data

We first consider the estimation of the finite rate of population increase or population growth rate, u i , using capture-recapture data from open populations. We review estimation and modelling of u i under three main approaches to modelling openpopulation data: the classic approach of Jolly (1965) and Seber (1965), the superpopulation approach of Crosbie & Manly (1985) and Schwarz & Arnason (1996), and the temporal symmetry approach of Pradel (1996). Next, we consider the contributions of different demographic components to u i using a probabilistic approach based on the composition of the population at time i + 1 (Nichols et al., 2000b). The parameters of interest are identical to the seniority parameters, n i , of Pradel (1996). We review estimation of n i under the classic, superpopulation, and temporal symmetry approaches. We then compare these direct estimation approaches for u i and n i with analogues computed using projection matrix asymptotics. We also discuss various extensions of the estimation approaches to multistate applications and to joint likelihoods involving multiple data types.

Journal of Applied Statistics

Investigations of potential bias in the estimation of lambda using Pradel's (1996) model for capture-recapture data

Pradel's (1996) temporal symmetry model permitting direct estimation and modelling of population growth rate, u i , provides a potentially useful tool for the study of population dynamics using marked animals. Because of its recent publication date, the approach has not seen much use, and there have been virtually no investigations directed at robustness of the resulting estimators. Here we consider several potential sources of bias, all motivated by specific uses of this estimation approach. We consider sampling situations in which the study area expands with time and present an analytic expression for the bias in u i We next consider trap response in capture probabilities and heterogeneous capture probabilities and compute large-sample and simulation-based approximations of resulting bias in u i . These approximations indicate that trap response is an especially important assumption violation that can produce substantial bias. Finally, we consider losses on capture and emphasize the importance of selecting the estimator for u i that is appropriate to the question being addressed. For studies based on only sighting and resighting data, Pradel's (1996) u i ' is the appropriate estimator.

Journal of Applied Statistics

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.

Wyoming

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, 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.

Journal of Applied Statistics

Evaluation of alternative model selection criteria in the analysis of unimodal response curves using CART

We investigated CART performance with a unimodal response curve for one continuous response and four continuous explanatory variables, where two variables were important (i.e. directly related to the response) and the other two were not. We explored performance under three relationship strengths and two explanatory variable conditions: equal importance and one variable four times as important as the other. We compared CART variable selection performance using three tree-selection rules ('minimum risk', 'minimum risk complexity', 'one standard error') to stepwise polynomial ordinary least squares (OLS) under four sample size conditions. The one-standard-error and minimum risk-complexity methods performed about as well as stepwise OLS with large sample sizes when the relationship was strong. With weaker relationships, equally important explanatory variables and larger sample sizes, the one-standard-error and minimum-risk-complexity rules performed better than stepwise OLS. With weaker relationships and explanatory variables of unequal importance, tree-structured methods did not perform as well as stepwise OLS. Comparing performance within tree-structured methods, with a strong relationship and equally important explanatory variables, the one-standard-error rule was more likely to choose the correct model than were the other tree-selection rules. The minimum-risk-complexity rule was more likely to choose the correct model than were the other tree-selection rules (1) with weaker relationships and equally important explanatory variables; and (2) under all relationship strengths when explanatory variables were of unequal importance and sample sizes were lower.

Journal of Applied Statistics

Digital-map grids of mean-annual precipitation for 1961-90, and generalized skew coefficients of annual maximum streamflow for Oklahoma

This digital report contains two digital-map grids of data that were used to develop peak-flow regression equations in Tortorelli, 1997, 'Techniques for estimating peak-streamflow frequency for unregulated streams and streams regulated by small floodwater retarding structures in Oklahoma,' U.S. Geological Survey Water-Resources Investigations Report 97-4202. One data set is a grid of mean annual precipitation, in inches, based on the period 1961-90, for Oklahoma. The data set was derived from the PRISM (Parameter-elevation Regressions on Independent Slopes Model) mean annual precipitation grid for the United States, developed by Daly, Neilson, and Phillips (1994, 'A statistical-topographic model for mapping climatological precipitation over mountainous terrain:' Journal of Applied Meteorology, v. 33, no. 2, p. 140-158). The second data set is a grid of generalized skew coefficients of logarithms of annual maximum streamflow for Oklahoma streams less than or equal to 2,510 square miles in drainage area. This grid of skew coefficients is taken from figure 11 of Tortorelli and Bergman, 1985, 'Techniques for estimating flood peak discharges for unregulated streams and streams regulated by small floodwater retarding structures in Oklahoma,' U.S. Geological Survey Water-Resources Investigations Report 84-4358. To save disk space, the skew coefficient values have been multiplied by 100 and rounded to integers with two significant digits. The data sets are provided in an ASCII grid format.

Oklahoma

Controlling for varying effort in count surveys: An analysis of Christmas Bird Count data

The Christmas Bird Count (CBC) is a valuable source of information about midwinter populations of birds in the continental U.S. and Canada. Analysis of CBC data is complicated by substantial variation among sites and years in effort expended in counting; this feature of the CBC is common to many other wildlife surveys. Specification of a method for adjusting counts for effort is a matter of some controversy. Here, we present models for longitudinal count surveys with varying effort; these describe the effect of effort as proportional to exp(B effortp), where B and p are parameters. For any fixed p, our models are loglinear in the transformed explanatory variable (effort)p and other covariables. Hence, we fit a collection of loglinear models corresponding to a range of values of p and select the best effort adjustment from among these on the basis of fit statistics. We apply this procedure to data for six bird species in five regions, for the period 1959-1988.

Journal of Agricultural, Biological, and Environme

Reanalysis indicates little evidence of reduction in eagle mortality rate by automated curtailment of wind turbines

Unintended consequences of renewable energy development include collision-caused deaths of birds and bats. Energy companies may risk prosecution if protected species are among the casualties. Shutting down turbines during high collision-risk conditions could reduce mortality rates, and several companies are developing systems to identify such conditions. A recent peer-reviewed article published in the Journal of Applied Ecology reported a remarkable ‘82% (75%–89%) reduction in the fatality rate’ of eagles at a wind energy facility due to a device marketed as Identiflight®—remarkable because of the impressive effect size and the extremely high level of precision. We show that reported results stem from four major errors, which, when corrected, give an unremarkable estimate of 50% (−159%, 89%) reduction (or possible increase) in the fatality rate. The errors include the following: (i) Ignoring annual variation . They compare the average number of eagle fatalities over 4 years before activation of Identiflight® to the number in a single year after, ignoring annual variation in fatalities. (ii) Unfounded causal inference . Lack of replication (one treatment year at one site) is ignored, leading to unwarranted causal inference. (iii) Inflated effect size . Effect size is inflated by assuming (without providing evidence) that the difference in fatality relative to the mean at a neighbouring site would be exactly repeated at the treatment site. Furthermore, the observed difference in fatalities at the control site depends strongly on the arbitrarily chosen date distinguishing the ‘Before’ and ‘After’ periods, yielding unreliable results. (iv) Inconsistency of data . It is unclear why 7 of 42 reported eagle fatalities were not included in the data analyzed, potentially further inflating the estimated effect size. Synthesis and applications . The recent claim, published in the Journal of Applied Ecology, that ‘Eagle fatalities are reduced by automated curtailment of wind turbines’ is not supported by the data but stems from errors that led to strongly overstated effect size and precision, and unfounded inference. In theory, automated curtailment has obvious potential for reducing eagle fatalities, but several more years of data at several locations and appropriate statistical analyses will be required to evaluate its effectiveness and to inform management prescriptions involving this technology.

Journal of Applied Ecology

Mapping rice areas of South Asia using MODIS multitemporal data

Our goal is to map the rice areas of six South Asian countries using moderate-resolution imaging spectroradiometer (MODIS) time-series data for the time period 2000 to 2001. South Asia accounts for almost 40% of the world's harvested rice area and is also home to 74% of the population that lives on less than $2.00 a day. The population of the region is growing faster than its ability to produce rice. Thus, accurate and timely assessment of where and how rice is cultivated is important to craft food security and poverty alleviation strategies. We used a time series of eight-day, 500-m spatial resolution composite images from the MODIS sensor to produce rice maps and rice characteristics (e.g., intensity of cropping, cropping calendar) taking data for the years 2000 to 2001 and by adopting a suite of methods that include spectral matching techniques, decision trees, and ideal temporal profile data banks to rapidly identify and classify rice areas over large spatial extents. These methods are used in conjunction with ancillary spatial data sets (e.g., elevation, precipitation), national statistics, and maps, and a large volume of field-plot data. The resulting rice maps and statistics are compared against a subset of independent field-plot points and the best available subnational statistics on rice areas for the main crop growing season (kharif season). A fuzzy classification accuracy assessment for the 2000 to 2001 rice-map product, based on field-plot data, demonstrated accuracies from 67% to 100% for individual rice classes, with an overall accuracy of 80% for all classes. Most of the mixing was within rice classes. The derived physical rice area was highly correlated with the subnational statistics with R 2 values of 97% at the district level and 99% at the state level for 2000 to 2001. These results suggest that the methods, approaches, algorithms, and data sets we used are ideal for rapid, accurate, and large-scale mapping of paddy rice as well as for generating their statistics over large areas.

South Asia

N-mixture models for estimating population size from spatially replicated counts

Spatial replication is a common theme in count surveys of animals. Such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability. In this article, I describe a class of models (n-mixture models) which allow for estimation of population size from such data. The key idea is to view site-specific population sizes, n, as independent random variables distributed according to some mixing distribution (e.g., Poisson). Prior parameters are estimated from the marginal likelihood of the data, having integrated over the prior distribution for n. Carroll and Lombard (1985, Journal of American Statistical Association 80, 423-426) proposed a class of estimators based on mixing over a prior distribution for detection probability. Their estimator can be applied in limited settings, but is sensitive to prior parameter values that are fixed a priori. Spatial replication provides additional information regarding the parameters of the prior distribution on n that is exploited by the n-mixture models and which leads to reasonable estimates of abundance from sparse data. A simulation study demonstrates superior operating characteristics (bias, confidence interval coverage) of the n-mixture estimator compared to the Caroll and Lombard estimator. Both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence.

Biometrics