Carl J. Schwarz

A General Methodology for the Analysis of Capture-Recapture Experiments in Open Populations

We trace the development of a likelihood function representation for the open-population capture-recapture (Jolly-Seber) experiment. We find that the modelling of the birth process in the general model is not consistent with the reduced death-only model and that all formulations to date lead to difficulties in imposing constraints upon the parameters of the birth process. We propose a generalisation to the usual Jolly-Seber representation that models births using a multinomial distribution from a super-population. We show how this leads to simplifications in the numerical optimization of the likelihood and how constraints upon the parameters of the model can now be easily imposed. We show how covariate models using auxiliary variables such as sampling effort or weather conditions to explain capture or survival rates can also be easily added. We also show how this model can be generalised to more than one group of animals. Finally a numerical example is provided which fits a class of models where the capture probabilities, survival probabilities and birth probabilities can each vary over time or among groups or both. This permits sequential model fitting within a comprehensive model framework; an approach akin to that of Lebreton et al (Ecological Monographs, 62, 67-118).

Estimating Migration Rates Using Tag-Recovery Data

Tag-recovery data are used to estimate migration rates among a set of strata. The model formulation is a simple matrix extension of the formulation of a tag-recovery experiment discussed by Brownie et al. (1985, Statistical Inference from Band-Recovery Data-A Handbook, 2nd edition, Washington, D.C.: U.S. Department of the Interior). Estimation is more difficult because of the convolution of parameters between release and recovery and this convolution may cause estimates of the survival/ migration parameters to have low precision. Derived parameters of emigration, immigration, harvest derivation, and overall net survival are also estimated. The models are applied to estimate the migration of Pacific herring among spawning grounds off the west coast of Canada. If animals can be re-released after being recaptured, the model corresponds, in its migration/survival components, to that of Arnason (1972, Researches in Popiulation Ecology 13, 97-113). This correspondence is developed, leading to more efficient estimators of these parameters.

ESTIMATING TEMPORARY MIGRATION USING THE ROBUST DESIGN

One of the basic assumptions central to the analysis of capture-recapture experiments is that all marked animals remain in the population under study for the duration of the sampling, or if they migrate out of the population they do so permanently. Burnham (1993, in Marked Individuals in the Study of Bird Populations,199-213), Kendall and Nichols (1995, Applied Statistics 22, 751-762), and Kendall, Nichols, and Hines (in press) showed that completely random temporary emigration influences only estimates of the probability of capture, these now estimating the product of the temporary emigration rate and the conditional probability of capture given the animal remains in the population. Estimates of abundance or survival that refer to the entire population, including the temporary emigrants, remain unaffected. Kendall et al. (in press) further showed that Pollocks (1982, Journal of Wildlife Management 46, 757-760) robust design could be used to estimate the temporary emigration rate when the population was assumed closed during the secondary samples. We generalize this result to allow animals to enter and leave the population during the secondary samples. We apply the results to a study of Grey Seals and perform simulation experiments to assess the robustness of our estimator to errors in field identification of brands and other violations of our assumptions.

STATUS AND TRENDS IN DEMOGRAPHY OF NORTHERN SPOTTED OWLS, 1985-2003

Abstract We analyzed demographic data from northern spotted owls (Strix occidentalis caurina) from 14 study areas in Washington, Oregon, and California for 1985–2003. The purpose of our analyses was to provide an assessment of the status and trends of northern spotted owl populations throughout most of their geographic range. The 14 study areas made up approximately 12% of the range of the subspecies and included federal, tribal, private, and mixed federal and private lands. The study areas also included all the major forest types that the subspecies inhabits. The analyses followed rigorous protocols that were developed a priori and were the result of extensive discussions and consensus among the authors. Our primary objectives were to estimate fecundity, apparent survival (φ), and annual rate of population change (λ) and to determine if there were any temporal trends in these population parameters. In addition to analyses of data from individual study areas, we conducted 2 meta-analyses on each demographic parameter. One meta-analysis was conducted on all 14 areas, and the other was restricted to the 8 areas that constituted the Effectiveness Monitoring Plan for northern spotted owls under the Northwest Forest Plan. The average number of years of reproductive data per study area was 14 (range = 5–19), and the average number of recapture occasions per study area was 13 (range = 4–18). Only 1 study area had <12 years of data. Our results were based on 32,054 captures and resightings of 11,432 banded individuals for estimation of survival and 10,902 instances in which we documented the number of young produced by territorial females. The number of young fledged (NYF) per territorial female was analyzed by testing a suite of a priori models that included (1) effects of age, (2) linear or quadratic time trends, (3) presence of barred owls (Strix varia) in spotted owl territories, and (4) an even-odd year effect. The NYF varied among years on most study areas with a biennial cycle of high reproduction in even-numbered years and low reproduction in odd-numbered years. These cyclic fluctuations did not occur on all study areas, and the even–odd year effect waned during the last 5 years of the study. Fecundity was highest for adults (x̄ = 0.372, SE = 0.029), lower for 2-year-olds (x̄ = 0.208, SE = 0.032), and very low for 1-year-olds (x̄ = 0.074, SE = 0.029). Fecundity was stable over time for 6 areas (Rainier, Olympic, Warm Springs, H. J. Andrews, Klamath, and Marin), declining for 6 areas (Wenatchee, Cle Elum, Oregon Coast Range, Southern Oregon Cascades, Northwest California, and Simpson), and slightly increasing for 2 areas (Tyee, Hoopa). We found little association between NYF and the proportion of northern spotted owl territories where barred owls were detected, although results were suggestive of a negative effect of barred owls on the Wenatchee and Olympic study areas. The meta-analysis on fecundity indicated substantial annual variability with no increasing or decreasing trends. Fecundity was highest in the mixed-conifer region of eastern Washington (x̄ = 0.560, SE = 0.041) and lowest in the Douglas-fir (Pseudotsuga menziesii) region of the Oregon coast (x̄ = 0.306, SE = 0.039). We used Cormack–Jolly–Seber open population models and Program MARK to estimate apparent survival rates of owls >1 year old. We found no differences in apparent survival rates between sexes except for 1 area (Marin), which had only 6 years of data. Estimates of apparent survival from individual study areas indicated that there were differences among age classes with adults generally having higher survival than 1- and 2-year-olds. Apparent survival rates ranged from 0.750 (SE = 0.026) to 0.886 (SE = 0.010) for adults, 0.626 (SE = 0.073) to 0.886 (SE = 0.010) for 2-year-olds, and 0.415 (SE = 0.111) to 0.860 (SE = 0.017) for 1-year-olds. These estimates were comparable to survival rates from previous studies on the subspecies. We found evidence for negative time trends in survival rates on 5 study areas (Wenatchee, Cle Elum, Rainier, Olympic, and Northwest California) and no trends in survival on the remaining areas. There was evidence for negative effects of barred owls on apparent survival on 3 study areas (Wenatchee, Cle Elum, and Olympic). Survival rates of adult owls on the 8 Monitoring Areas generally were high, ranging from 0.85 (SE = 0.009) to 0.89 (SE = 0.010), but were declining on the Cle Elum, Olympic, and Northwestern California study areas. The meta-analysis of apparent survival indicated differences among regions and changes over time with a downward trend in the mixed-conifer and Douglas-fir regions of Washington. The meta-analysis of apparent survival also indicated that there was a negative association between fecundity and survival the following year, suggesting a cost of reproduction on survival. This effect was limited to the Douglas-fir and mixed-conifer regions of Washington and the Douglas-fir region of the Oregon Cascade Mountains. We used the reparameterized Jolly–Seber method (λRJS) to estimate annual rate of population change of territorial owls in the study areas. This estimate answers the question, Are these territorial owls being replaced in this geographically open population? Point estimates of λRJS were <1.0 for 12 of 13 study areas. The analyses provided strong evidence that populations on the Wenatchee, Cle Elum, Rainier, Olympic, Warm Springs, H. J. Andrews, Oregon Coast Ranges, and Simpson study areas were declining during the study. The mean λ̂RJS for the 13 study areas was 0.963 (SE = 0.009), suggesting that populations over all the areas were declining about 3.7% per year during the study. The mean λ̂RJS for the 8 monitoring areas for the Northwest Forest Plan was 0.976 (SE = 0.007) compared to a mean of 0.942 (SE = 0.016) for the other study areas, a 2.4-versus-5.8% decline per year. This suggested that owl populations on federal lands had higher demographic rates than elsewhere; thus, the Northwest Forest Plan appeared to have a positive effect on demography of northern spotted owls. Populations were doing poorest in Washington, where apparent survival rates and populations were declining on all 4 study areas. Our estimates of λRJS were generally lower than those reported in a previous analysis (λ̂RJS = 0.997, SE = 0.003) for many of the same areas at an earlier date. The possible causes of population declines include but are not limited to habitat loss from timber harvest and fires, competition with barred owls, and weather patterns.

Using POPAN-5 to analyse banding data

We describe some recent developments in the POPAN system for the analysis of mark-recapture data from Jolly-Seber (IS) type experiments and how this system applies to the analysis of banding data. We discuss some of the extra data requirements of JS studies, which provide estimates of abundance and entry/birth rates, over survival (CJS) studies. We discuss how POPAN implements a unified likelihood approach using a constrained maximization and show how this differs from a design-matrix approach used in CJS software. We illustrate the application of constraints and covariate models across groups with some examples drawn from the banding literature, including an example zvith age-class groups and we describe some of the resources in POPAN for carrying out standard tests for goodness-of-fit.

Estimating closed population size and number of marked animals from sighting data

We describe a new estimator of population size that can be formed when independent sightings are made of marked and unmarked animals in a closed population where a subset of the population is individually marked. Each marked animal must bear a unique mark but the number of marked animals alive in the population is unknown. The estimate can be used when no recaptures or removals of animals are possible during the experiment. An example is estimating the number of immature bald eagles (Haliaeetus leucocephalus) on a lake some years after banding of nestlings. We derive the maximum likelihood estimates for population size and number of marks, and we show how to develop confidence intervals and perform goodness-of-fit tests. Criteria are developed for determining the number of sightings required to yield satisfactory estimates

The mixed-model ANOVA: the truth, the computer packages, the books. Part I: balanced data

Abstract In contrast to the analysis of variance of fully fixed or fully random component models, the analysis of variance of mixed models is fraught with potential pitfalls. It is fortunate that there are simple rules for the correct analysis of balanced data; in the case of unbalanced data there are no simple results. The potential pitfalls in the path of a correct analysis are well-known. Despite this, some computer packages still report incorrect results for the balanced model and some textbooks gloss over or ignore some of these pitfalls.

POPAN-4: Enhancements to a system for the analysis of mark-recapture data from open populations

We describe recent developments in the POPAN system for the analysis of mark-recapture data from Jolly-Seber type experiments. The previous versions (POPAN-3 for SUN/OS workstations and POPAN-PC for IBM-PC running DOS or Windows) included general statistics gathering and testing procedures, a wide range of analysis options for estimating population abundance, survival and birth parameters, and a general simulation capability. POPAN-4 adds a very general procedure for fitting constrained models based on a new unified theory for Jolly-Seber models. Users can impose constraints on capture, survival and birth rates over time and/or across attribute groups (e.g. sex or age groups) and can model these rates using covariate models involving auxiliary variables (e.g. sampling effort).

The Jolly-seber model: More than just abundance

The Jolly-Seber model provides estimates of abundance, survival, and capture rates from capture-recapture experiments. This article will describe recent extensions to the following cases: (a) multiple-cohort studies where recruitment rates are compared among cohorts, (b) age-specific breeding proportions, and (c) population growth rates. Finally, new areas of research needed for this model are proposed.

Estimating the nest-success rate and the number of nests initiated by radiomarked mallards

We developed a methodology for estimating the nest-success rate, the total number of nests initiated, and the average number of nests initiated per breeding pair by a group of radiomarked mallard (Anas platyrhynchos) females. Our methodology allows incomplete observation of all nests initiated and is related to current nest-success models. However, our method relaxes the assumption of equal daily survival rates made by the Mayfield method, and it incorporates the detection probabilities of newly encountered nests, which are ignored by the Mayfield method. Model selection and model averaging using Akaikes Information Criterion (AIC) are used so that estimates are no longer conditional upon the best-fitting model. Estimated daily nest-survival rates in our example were 0.94 (SE = 0.005), which gives an estimated nest-success rate over 25 days of 0.20 (SE = 0.03). We estimated that our sample of 124 resident females initiated 237 (SE = 15) nests for an estimated 1.91 (SE = 0.12) nests initiated per female. This was substantially larger than the observed (uncorrected) 1.41 nests per female, despite the high sampling effort and the fact that the nests were located at an average of 5 days of age. Our estimate of nests initiated was substantially more precise than similar estimates derived using the Mayfield method. We estimate an approximate 6-fold reduction in the sample size required by our method compared to the Mayfield method to obtain comparable precision for this parameter.