Semiparametric regression in capture-recapture modeling

Capture-recapture models were developed to estimate survival using data arising from marking and monitoring wild animals over time. Variation in survival may be explained by incorporating relevant covariates. We propose nonparametric and semiparametric regression methods for estimating survival in capture-recapture models. A fully Bayesian approach using Markov chain Monte Carlo simulations was employed to estimate the model parameters. The work is illustrated by a study of Snow petrels, in which survival probabilities are expressed as nonlinear functions of a climate covariate, using data from a 40-year study on marked individuals, nesting at Petrels Island, Terre Adélie.     

Constant-parameter capture-recapture models

Jolly (1982, Biometrics 38, 301-321) presented modifications of the Jolly-Seber model for capture-recapture data, which assume constant survival and/or capture rates. Where appropriate, because of the reduced number of parameters, these models lead to more efficient estimators than the Jolly-Seber model. The tests to compare models given by Jolly do not make complete use of the data, and we present here the appropriate modifications, and also indicate how to carry out goodness-of-fit tests which utilize individual capture history information. We also describe analogous models for the case where young and adult animals are tagged. The availability of computer programs to perform the analysis is noted, and examples are given using output from these programs.     

On identifiability in capture-recapture models

We study the issue of identifiability of mixture models in the context of capture-recapture abundance estimation for closed populations. Such models are used to take account of individual heterogeneity in capture probabilities, but their validity was recently questioned by Link (2003, Biometrics 59, 1123-1130) on the basis of their nonidentifiability. We give a general criterion for identifiability of the mixing distribution, and apply it to establish identifiability within families of mixing distributions that are commonly used in this context, including finite and beta mixtures. Our analysis covers binomial and geometrically distributed outcomes. In an example we highlight the difference between the identifiability issue considered here and that in classical binomial mixture models.     

Augmenting superpopulation capture-recapture models with population assignment data

Summary Ecologists applying capture–recapture models to animal populations sometimes have access to additional information about individuals' populations of origin (e.g., information about genetics, stable isotopes, etc.). Tests that assign an individual's genotype to its most likely source population are increasingly used. Here we show how to augment a superpopulation capture–recapture model with such information. We consider a single superpopulation model without age structure, and split each entry probability into separate components due to births in situ and immigration. We show that it is possible to estimate these two probabilities separately. We first consider the case of perfect information about population of origin, where we can distinguish individuals born in situ from immigrants with certainty. Then we consider the more realistic case of imperfect information, where we use genetic or other information to assign probabilities to each individual's origin as in situ or outside the population. We use a resampling approach to impute the true population of origin from imperfect assignment information. The integration of data on population of origin with capture–recapture data allows us to determine the contributions of immigration and in situ reproduction to the growth of the population, an issue of importance to ecologists. We illustrate our new models with capture–recapture and genetic assignment data from a population of banner‐tailed kangaroo rats Dipodomys spectabilis in Arizona.     

Logistic regression for dependent binary observations

The likelihood of a set of binary dependent outcomes, with or without explanatory variables, is expressed as a product of conditional probabilities each of which is assumed to be logistic. The models are called regressive logistic models. They provide a simple but relatively unknown parametrization of the multivariate distribution. They have the theoretical and practical advantage that they can be analyzed and fitted as in logistic regression for independent outcomes, and with the same computer programs. The paper is largely expository and is intended to motivate the development and usage of the regressive logistic models. The discussion includes serially dependent outcomes, equally predictive outcomes, more specialized patterns of dependence, multidimensional tables, and three examples.     

Logistic回归模型及其在昆虫学中的应用

介绍了应用Logistic回归分析对二值反应的试验数据进行分析的方法 ,以及Logistic回归分析模型参数估计及其统计检验的方法 ,并结合 1个实际例子说明了Logistic回归模型的应用。     

Autoregressive models for capture-recapture data: a Bayesian approach

In this article, we incorporate an autoregressive time-series framework into models for animal survival using capture-recapture data. Researchers modeling animal survival probabilities as the realization of a random process have typically considered survival to be independent from one time period to the next. This may not be realistic for some populations. Using a Gibbs sampling approach, we can estimate covariate coefficients and autoregressive parameters for survival models. The procedure is illustrated with a waterfowl band recovery dataset for northern pintails (Anas acuta). The analysis shows that the second lag autoregressive coefficient is significantly less than 0, suggesting that there is a triennial relationship between survival probabilities and emphasizing that modeling survival rates as independent random variables may be unrealistic in some cases. Software to implement the methodology is available at no charge on the Internet.     

Estimation in capture-recapture models when covariates are subject to measurement errors

We consider estimation problems in capture-recapture models when the covariates or the auxiliary variables are measured with errors. The naive approach, which ignores measurement errors, is found to be unacceptable in the estimation of both regression parameters and population size: it yields estimators with biases increasing with the magnitude of errors, and flawed confidence intervals. To account for measurement errors, we derive a regression parameter estimator using a regression calibration method. We develop modified estimators of the population size accordingly. A simulation study shows that the resulting estimators are more satisfactory than those from either the naive approach or the simulation extrapolation (SIMEX) method. Data from a bird species Prinia flaviventris in Hong Kong are analyzed with and without the assumption of measurement errors, to demonstrate the effects of errors on estimations.     

The performance of mixture models in heterogeneous closed population capture-recapture.

Dorazio and Royle (2003, Biometrics 59, 351-364) investigated the behavior of three mixture models for closed population capture-recapture analysis in the presence of individual heterogeneity of capture probability. Their simulations were from the beta-binomial distribution, with analyses from the beta-binomial, the logit-normal, and the finite mixture (latent class) models. In this response, simulations from many different distributions give a broader picture of the relative value of the beta-binomial and the finite mixture models, and provide some preliminary insights into the situations in which these models are useful.     

The minimum capture proportion for reliable estimation in capture-recapture models.

We derive estimates of the minimum capture proportion required to obtain a reliable estimate of the population size for several continuous and discrete-time capture-recapture models. The models considered are M(0), M(t), M(b), M(h), M(ht), and M(tb) in the notation of Otis et al., (1978, Wildlife Monograph62, 1-135). Numerical results with simulation studies are given, and two real examples for the model M(h) are also considered. Potential applications of these results are suggested.     

基于标记-重捕模型开展野生动物红外相机种群监测的方法及案例

红外相机技术的广泛应用推动了动物种群生态学研究方法的发展和革新, 特别是基于标记-重捕模型框架通过非损伤取样方式对物种数量和密度等种群参数的可靠估计, 为保护濒危物种和评估保护成效提供了有力的科学依据。对于身体上具有独特天然标记的动物(如多数猫科动物), 可依据红外相机拍摄身体上的独特斑点或条纹鉴别个体, 再运用标记-重捕模型, 估计动物种群数量、密度等参数。本文概述了标记-重捕模型的基本原理、特点以及国内外的应用, 特别是近年来发展出的空间标记-重捕模型。总结了从相机布设到数据分析的具体流程、操作原则, 并以青城山家猫为实例, 展示了应用红外相机数据通过空间标记-重捕模型估计种群密度和数量的基本步骤。最后展望了该模型在种群动态、景观廊道设计、资源选择等方面的应用和发展趋势。     

Open capture-recapture models with heterogeneity: I. Cormack-Jolly-Seber model

In open population capture-recapture studies, it is usually assumed that similar animals (e.g., of the same sex and age group) have similar survival rates and capture probabilities. These assumptions are generally perceived to be an oversimplification, and they can lead to incorrect model selection and biased parameter estimates. Allowing for individual variability in survival and capture probabilities among apparently similar animals is now becoming possible, due to advances in closed population models and improved computing power. This article presents a flexible framework of likelihood-based models which allow for individual heterogeneity in survival and capture rates. Heterogeneity is modeled using finite mixtures, which have enough flexibility of distribution shape to accommodate a wide variety of different patterns of individual variation. The models condition on the first capture of each animal, and include as a special case the Cormack-Jolly-Seber model. Model selection is done either using Akaike's information criterion or by likelihood ratio tests, making available checks of different influences on survival rates. Bias in parameter estimates is reduced by including individual heterogeneity. Model selection and bias reduction are important in population studies and for making informed management decisions.     

Unified maximum likelihood estimates for closed capture-recapture models using mixtures

Agresti (1994, Biometrics 50, 494-500) and Norris and Pollock (1996a, Biometrics 52, 639-649) suggested using methods of finite mixtures to partition the animals in a closed capture-recapture experiment into two or more groups with relatively homogeneous capture probabilities. This enabled them to fit the models Mh, Mbh (Norris and Pollock), and Mth (Agresti) of Otis et al. (1978, Wildlife Monographs 62, 1-135). In this article, finite mixture partitions of animals and/or samples are used to give a unified linear-logistic framework for fitting all eight models of Otis et al. by maximum likelihood. Likelihood ratio tests are available for model comparisons. For many data sets, a simple dichotomy of animals is enough to substantially correct for heterogeneity-induced bias in the estimation of population size, although there is the option of fitting more than two groups if the data warrant it.