Full Open Population Capture–Recapture Models With Individual Covariates

Traditional analyses of capture–recapture data are based on likelihood functions that explicitly integrate out all missing data. We use a complete data likelihood (CDL) to show how a wide range of capture–recapture models can be easily fitted using readily available software JAGS/BUGS even when there are individual-specific time-varying covariates. The models we describe extend those that condition on first capture to include abundance parameters, or parameters related to abundance, such as population size, birth rates or lifetime. The use of a CDL means that any missing data, including uncertain individual covariates, can be included in models without the need for customized likelihood functions. This approach also facilitates modeling processes of demographic interest rather than the complexities caused by non-ignorable missing data. We illustrate using two examples, (i) open population modeling in the presence of a censored time-varying individual covariate in a full robust design, and (ii) full open population multi-state modeling in the presence of a partially observed categorical variable. Supplemental materials for this article are available online.     

Population Estimates From Aerial Photographic Surveys of Naturally and Variably Marked Bowhead Whales

Abundance, mortality, and population growth of bowhead whales (Balaena mysticetus) are estimated from captures of 4,894 putatively different individuals obtained from 10 years of systematic photographic surveys conducted during the spring migration when most of the Bering–Chukchi–Beaufort population of bowheads migrates past Point Barrow, Alaska. A stringent matching protocol designed to prevent false positive matches of the naturally, but variably marked individuals, led to 42 resightings between years. The flip side of this stringency is a presence of false negatives, i.e., some true recaptures are not recognized as such. The problem of false negatives is addressed by modeling the capture process and the matching process. The captures of an individual are assumed to follow a Poisson process with intensity depending stochastically on the individual whale and on the year. The probability of successfully matching a capture to a previous capture is estimated by logistic regression on the degree of marking and image quality. Individuals are recruited by the Pella–Tomlinson population model, and their mortality rate is assumed to be constant. The point estimate of yearly growth rate is 3.2%, and bowhead abundance in 2001 is estimated to be 8,250, similar to previous estimates.     

Mark-recapture with occasion and individual effects: Abundance estimation through Bayesian model selection in a fixed dimensional parameter space

We present a Bayesian mark-recapture method for explicitly communicating uncertainty about the size of a closed population where capture probabilities vary across both individuals and sampling occasions. Heterogeneity is modeled hierarchically using a continuous logistic-Normal model to specify the capture probabilities for both individuals that are captured on at least one occasion and individuals that are never captured and so remain undetected. Inference about how many undetected individuals to include in the model is accomplished through a Bayesian model selection procedure using MCMC, applied to a product space of possible models for different numbers of undetected individuals. Setting the estimation problem in a fixed dimensional parameter space enables the model selection procedure to be performed using the freely available WinBUGS software. The outcome of inference is a full “posterior” probability distribution for the population size parameter. We demonstrate this method through an example involving real mark-recapture data.     

Estimating Population Growth Rate From Capture–Recapture Data in Presence of Capture Heterogeneity

The direct estimation and modeling of population growth rate from capture–recapture data has now seen a number of applications. However, the original model cannot accommodate heterogeneous capture probabilities. While studying a population of small mammals Peromyscus maniculatus, we became concerned that the peak of population size may be estimated too late in the year because of heterogeneous catchability. Hence, we developed a variation of the original model with a finite number of catchability classes. The results obtained with the new model are more in agreement with the known biology of this population. A bibliographic appendix and computer code are available online.     

Analysis of an Extended Batch Marking Experiment Using Estimating Equations

Estimating equations give a flexible method of inference when the likelihood is either intractable or is not fully specified. Here we consider a batch marking experiment where the full likelihood is complex and without resorting to devices such as the computationally intensive expectation-maximization (EM) algorithm is intractable. However, a pseudo-likelihood that yields tractable estimating equations may be easily constructed and its effectiveness is demonstrated via simulation studies. The methodology was applied to study the abundance of Oriental weatherloach in a waterbody in South-Eastern Australia. The programs and data set used in this article are available in the online supplements.     

Titi (sooty shearwaters) on Whero Island: Analysis of historic data using modern techniques

A reanalysis of titi (sooty shearwater, Puffinus griseus) banding data collected between 1940 and 1957 by Lance Richdale demonstrates that well-documented archival material can be usefully reanalyzed using newly developed statistical techniques. In this study, we compare the results obtained by Richdale using empirical techniques to those obtained using a multistate mark-recapture model. Although the two approaches produce similar estimates for some of the parameters, the multistate model additionally provides estimates of precision and can be used to answer biologically significant questions not raised by the original worker. Our analysis provides some evidence for two conclusions that Richdale put forward but could not justify rigorously: (a) nonbreeders have a lower survival rate than breeders, although the difference is not statistically significantly; and (b) nonbreeders are more difficult to capture than breeders. We argue that reanalysis should be carried out more frequently on historical data and lament the fact that it can be rare for such data to be made available for future scrutiny.     

A Capture–Recapture Model with Double-Marking,Live and Dead Encounters,and Heterogeneity of Reporting Due to Auxiliary Mark Loss

Capture–recapture (CR) models assume marked individuals remain at risk of capture, which may not be true if individuals lose their mark or emigrate definitively from the study area. Using a double-marking protocol, with a main and auxiliary mark, and both live encounters and dead recoveries at a large scale, partially frees CR models from this assumption. However, the auxiliary mark may fall off and its presence is often not mentioned when dead individuals are reported. We propose a new model to deal with heterogeneity of detection and uncertainty of the presence of an auxiliary mark in a multi-event framework. Our general model, based on a double-marking protocol, uses information from physical captures/recaptures, distant observations and main mark recoveries from dead animals. We applied our model to a 13-year data set of a harvested species, the Greater Snow Goose. We obtained seasonal survival estimates for adults of both sexes. Survival estimates differed between models where the presence of the auxiliary mark upon recovery was ignored versus those where the presence was accounted for. In the multi-event framework, seasonal survival estimates are no longer biased because the heterogeneity due to the presence of an auxiliary mark is accounted for in the estimation of recovery rates.     

Proportions of active ciliate taxa in soils

 Active and total soil ciliate populations were analyzed by a non-destructive method for 25 collections. Total numbers ranged from a few individuals in soils under stressed conditions to 750 g^–1 dry soil. Active ciliates were <15% (mainly r-selected colpodids) and 40–60% of the total ciliate population under stress conditions, respectively. About 55% (18–86%) of ciliates, both in active and total populations, were colpodids, and about half of these belonged to five taxa: Colpoda inflata, Colpoda steini, Cyrtolophosis elongata, Cyclidium mucicola, and Platyophyra vorax. Only about 5% of the 572 presently known soil ciliate species furnished most of the individuals. A hierarchical approach is suggested to explain the high diversity in the less abundant 95% species, and is extended to explain species distribution in stressed habitats. This study analyzed only mineral soils and found, in a comparison of agroecosystem soils and the adjacent woodlands they were derived from, that the former contained more active individuals and species of ciliates. Received: 15 June 2000     

Capture-Recapture Smooth Estimation of Age-Specific Survival Probabilities in Animal Populations

Yielding sound estimates of survival according to age in wild populations where senescence or other age-related variations may occur is very important to management decision makers, and remains challenging. This paper proposes to use penalized maximum likelihood to obtain smooth estimates of annual survival probabilities across age in populations of wild animals followed by capture–recapture. We propose to use two different types of smoothing penalties, and we use ν-fold cross-validation to select the best value of the tuning parameter for the intensity of smoothing. We then assess the accuracy of the method by a simulation study with two different shapes of the relationship between age and survival, and we conclude that a careful use of this method provides reliable noise-free estimates of age-specific annual survival. We apply this procedure to the motivating data from a population of roe deer known to exhibit a marked decrease of survival with age, and we compare our results with those previously published on this population.     

Tillage practice influences on the physical protection, bioavailability and composition of particulate organic matter

 This study was conducted to determine whether separation of particulate organic matter (POM) that is biologically labile from aggregate entrapped material improves the usefulness of POM as an index of soil C and N dynamics. The effects of conventional (CT) and no-tillage (NT) practices on POM were assessed using soils from three 10-year trials in Illinois. Loose and occluded POM in the 0–5 cm depth were separated from 1994 samples. Use of NT practices increased C and N contents at 0–5 cm relative to CT practices and those increases were most apparent in the occluded POM fraction. The correlation between total POM-N and potentially mineralizable N (PMN) was stronger than that between PMN and either the loose or occluded-POM fractions. In 1995, both the microbial biomass, estimated as chloroform-labile C (CFEC), and PMN were correlated with POM-C and N, but the relationship was weak when data (from different tillage and depth combinations) were not treated in aggregate. POM-C and CFEC were most strongly correlated in surface depths and in CT treatments. In NT 0–5 cm samples, PMN contents were similar (≈27 mg N kg^–1 soil) at all sites despite notable differences in POM-N concentrations; PMN was not related to POM-N in CT samples. There was no consistent relationship between PMN and POM-N contents in 5–30 cm samples. DRFTIR spectra indicated that carbohydrates were most abundant in POM at 0–5 cm. Relatively low PMN rates and enrichment of polysaccharides in POM in the sicl soil suggest that physical protection of labile organic substrates was more important at that site than at sites with lighter textured soils. Improved fractionation and incubation techniques and alleviation of laboratory artifacts will improve our ability to relate POM quantity, distribution and composition to biologically mediated C and N dynamics occurring in the field. Received: 2 December 1999     

Predicting Life-History Traits for Female New Zealand Sea Lions, <Emphasis Type="Italic">Phocarctos hookeri</Emphasis>: Integrating Short-Term Mark-Recapture Data and Population Modeling

The trade-off between survival and reproduction by individuals is central to understanding life-history parameters of a species. Few mammal species have life-history information from long-term research. Instead, demographic models are commonly utilized to investigate an individual’s life-history strategy, species dynamics, and population trends. This research investigates age-related survival and reproductive performance of adult female New Zealand (NZ) sea lions (Phocarctos hookeri), using multi-state mark-recapture data from known-age branded individuals over five years. The mark-recapture analysis was integrated with a population model to predict the lifetime reproductive output of female NZ sea lions. The integration of an analysis of short-term datasets with population modeling allows for the prediction of life-history parameters of long lived animals when long-term information is not available. While such approaches involve some caveats, it provides a framework for investigating population dynamics and is preferential to unsubstantiated assumptions. This technique can lead to better design and implementation of conservation management for long lived species.     

Challenging conservation of migratory species: Sahelian rainfalls drive first-year survival of the vulnerable Lesser Kestrel Falco naumanni

In the context of attested global changes, accurate estimation of whether climatic fluctuations impact on population demographic parameters is needed for adequate management, especially for migratory species. We present a capture-recapture analysis linking survival rates of the vulnerable Lesser Kestrel (Falco naumanni) to annual rainfalls in the Sahel region, considered as a proxy of climatic conditions on wintering grounds. Recapture data were obtained from field observations of individuals ringed and sexed as juveniles over a 14-year monitoring period (1994-2007). We addressed a common but problematic situation in birds where: (i) sex is known with certainty for first-summer or older birds but only suspected for juveniles, and (ii) a large proportion of individuals never return to the study population (e.g. transient behavior). Transient behavior and unknown sexes were explicitly integrated considering a two age class in a multistate capture-recapture model. Survival was time-varying for juveniles (geometric mean: 0.499 ± 0.021) but constant - and higher - for adults (0.718 ± 0.013). Yearling survival probabilities were strongly correlated with rainfalls in the Sahel, suggesting a high dependence of juvenile upon the wintering conditions. While taking sex uncertainty into account, we detected no sex-dependence in survival. Incorporating the sensitivity of survival of wintering migratory birds to climatic variables such as precipitations in arid Sahelian ecosystem may allow to model conservation scenarios with a greater realism. Finally, we encourage the development of international management strategies for migratory species on wintering areas in addition to the existing conservation actions on summering Mediterranean grounds.     

Diagnostic Goodness-of-Fit Tests for Joint Recapture and Recovery Models

Diagnostic goodness-of-fit tests for capture–recapture models are routinely used prior to model fitting and analysis. However, when data include a mixture of live recaptures and dead recoveries, it is frequently standard practice for the information from recoveries not to be used, so that tests are applied to the recapture data alone. We present new diagnostic tests for joint recapture–recovery data, which make full use of all of the data, and evaluate their power through simulation. The importance of including all available data is clearly shown. We see in addition that current procedures may fail to identify the correct model. The work is generalised to the case of multi-site joint recapture–recovery data and is illustrated on a data set of great cormorants. This article has supplementary material online.     

Response of the soil microbial biomass and nematode population to a wetting event in nitrogen-amended Negev desert plots

 Water and N availability are the major limiting factors of primary production in desert ecosystems, and the response of soil biota to these two factors is of great importance. We examined the immediate response of soil nematodes and the microbial biomass to a single pulse of water amendment in N-treated plots in the Israeli Negev desert. Plots were treated with 0, 50 and 100 kg NH₄NO₃ ha^–1 in December 1992, and at the end of the summer period (August 1993) the plots were exposed to a 15 mm water. Soil samples from the 0–10 cm layer were collected daily and analysed soil moisture, total soluble N, nematode populations and microbial biomass. Soil moisture increased to 8.5%, then gradually decreased to 2% during the 11 days of the study. Microbial biomass, soil respiration and metabolic quotient values did not exhibit any significant correlation with soil N levels. Free-living nematode population levels in the different plots were found to increase from a mean level of 45 500 to a mean level of 92 300 individuals m^–2. N treatment was found to affect the patterns of free-living nematode population dynamics. The results of this study demonstrated the importance of moisture availability levels and the ability to mobilize previous N inputs into available N which, occurring in pulses, can affect the microbial ecophysiological status, nematode population dynamics and the interrelationship between these two important components in the desert soil milieu. Received: 5 November 1998     

Designing a mark-recapture study to allow for local emigration

In using a population projection model to help manage the conservation of along-lived species, we usually need a reliable estimate of adult survival. Mark-recapture studies are often used to estimate survival, and typically require the assumption that there is no permanent emigration from the study area. We consider how such a study might be extended to allow for local emigration, that is, movement of individuals into an area peripheral to the study area. In particular, we focus on the question as to how much field effort is required in this peripheral area in order to obtain sufficiently precise estimates of both the survival probability and the probability of local emigration. We consider the use of multi-state, mark-recapture models as a means of providing these estimates and show how to assess the precision of a potential study design by calculating the expected confidence limits associated with the resulting estimates. We considera range of design scenarios for the situation that motivated this work, involving a population of Hector’s dolphins in New Zealand. For this case, it appears that there is little gain in precision once a capture probability of 0.4 is reached in the peripheral area.     

Climate Projections Using Bayesian Model Averaging and Space–Time Dependence

Projections of future climatic changes are a key input to the design of climate change mitigation and adaptation strategies. Current climate change projections are deeply uncertain. This uncertainty stems from several factors, including parametric and structural uncertainties. One common approach to characterize and, if possible, reduce these uncertainties is to confront (calibrate in a broad sense) the models with historical observations. Here, we analyze the problem of combining multiple climate models using Bayesian Model Averaging (BMA) to derive future projections and quantify uncertainty estimates of spatiotemporally resolved temperature hindcasts and projections. One advantage of the BMA approach is that it allows the assessment of the predictive skill of a model using the training data, which can help identify the better models and discard poor models. Previous BMA approaches have broken important new ground, but often neglected space–time dependencies and/or imposed prohibitive computational demands. Here we improve on the current state-of-the-art by incorporating space–time dependence while using historical data to estimate model weights. We achieve computational efficiency using a kernel mixing approach for representing a space–time process. One key advantage of our new approach is that it enables us to incorporate multiple sources of uncertainty and biases, while remaining computationally tractable for large data sets. We introduce and apply our approach using BMA to an ensemble of Global Circulation Model output from the Intergovernmental Panel on Climate Change Fourth Assessment Report of surface temperature on a grid of space–time locations.     

A Measurement Error Model for Heterogeneous Capture Probabilities in Mark-Recapture Experiments: An Estimating Equation Approach

Logistic models for capture probabilities that depend on covariates are effective if the covariates can be measured exactly. If there is measurement error so that a surrogate for the covariate is observed rather than the covariate itself, simple adjustments may be made if the parameters of joint distribution of the covariate and the surrogate are known. Here we consider the case when a surrogate is observed whenever an individual is captured and the parameters must also be estimated from the data. An estimating equation regression calibration approach is developed and it is illustrated on a real dataset where the surrogate is an individual bird’s wing-length, which varies from occasion to occasion.     

The effects of capturing and marking on subsequent activity in Boloria acrocnema (Lepidoptera: Nymphalidae), with a comparison of different numerical models that estimate population size

Capturing and marking disrupts flight activity in the alpine fritillary butterfly, Boloria acrocnema. This effect is limited to the date an individual receives its mark, and does not appear to increase mortality significantly. It nevertheless can generate large positive biases in population size estimates, especially in single-census mark-recapture models. The bias may overestimate by 2 to 4 times the actual population size. Similar marking effects in several other Lepidoptera are also analysed. Tests for the presence of marking effects are reviewed, with discussion of the general influence they have on population data.