A closure test for time-specific capture-recapture data

The assumption of demographic closure in the analysis of capture-recapture data under closed-population models is of fundamental importance. Yet, little progress has been made in the development of omnibus tests of the closure assumption. We present a closure test for time-specific data that, in principle, tests the null hypothesis of closed-population model M_t against the open-population Jolly-Seber model as a specific alternative. This test is chi-square, and can be decomposed into informative components that can be interpreted to determine the nature of closure violations. The test is most sensitive to permanent emigration and least sensitive to temporary emigration, and is of intermediate sensitivity to permanent or temporary immigration. This test is a versatile tool for testing the assumption of demographic closure in the analysis of capture-recapture data.     

A hierarchical model for spatial capture-recapture data

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture-recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.     

Maximum likelihood inference for the band-read error model for capture-recapture data with misidentification

Environmental and Ecological Statistics - Misidentification of animals is a common problem for many capture-recapture experiments. Considerably misleading inference may be obtained when traditional...     

Combining multistate capture-recapture data with tag recoveries to estimate demographic parameters

Matrix population models that allow an animal to occupy more than one state over time are important tools for population and evolutionary ecologists. Definition of state can vary, including location for metapopulation models and breeding state for life history models. For populations whose members can be marked and subsequently reencountered, multistate mark-recapture models are available to estimate the survival and transition probabilities needed to construct population models. Multistate models have proved extremely useful in this context, but they often require a substantial amount of data and restrict estimation of transition probabilities to those areas or states subjected to formal sampling effort. At the same time, for many species, there are considerable tag recovery data provided by the public that could be modeled in order to increase precision and to extend inference to a greater number of areas or states. Here we present a statistical model for combining multistate capture-recapture data (e.g., from a breeding ground study) with multistate tag recovery data (e.g., from wintering grounds). We use this method to analyze data from a study of Canada Geese (Branta canadensis) in the Atlantic Flyway of North America. Our analysis produced marginal improvement in precision, due to relatively few recoveries, but we demonstrate how precision could be further improved with increases in the probability that a retrieved tag is reported.     

An EM algorithm for capture-recapture estimation

Analysis of capture—recapture data often involves maximizing a complex likelihood function with many unknown parameters. Statistical inference based on selection of a proper model depends on successful attainment of this maximum. An EM algorithm is developed for obtaining maximum likelihood estimates of capture and survival probabilities conditional on first capture from standard capture—recapture data. The algorithm does not require the use of numerical derivatives which may improve precision and stability relative to other estimation schemes. The asymptotic covariance matrix of the estimated parameters can be obtained using the supplemented EM algorithm. The EM algorithm is compared to a more traditional Newton-Raphson algorithm with both a simulated and a real dataset. The two algorithms result in the same parameter estimates, but Newton-Raphson variance estimates depend on a numerically estimated Hessian matrix that is sensitive to step size choice.     

Estimation of population density by spatially explicit capture-recapture analysis of data from area searches

The recent development of capture-recapture methods for estimating animal population density has focused on passive detection using devices such as traps or automatic cameras. Some species lend themselves more to active searching: a polygonal plot may be searched repeatedly and the locations of detected individuals recorded, or a plot may be searched just once and multiple cues (feces or other sign) identified as belonging to particular individuals. This report presents new likelihood-based spatially explicit capture-recapture (SECR) methods for such data. The methods are shown to be at least as robust in simulations as an equivalent Bayesian analysis, and to have negligible bias and near-nominal confidence interval coverage with parameter values from a lizard data set. It is recommended on the basis of simulation that plots for SECR should be at least as large as the home range of the target species. The R package "secr" may be used to fit the models. The likelihood-based implementation extends the spatially explicit analyses available for search data to include binary data (animal detected or not detected on each occasion) or count data (multiple detections per occasion) from multiple irregular polygons, with or without dependence among polygons. It is also shown how the method may be adapted for detections along a linear transect.     

A robust design capture-recapture model with multiple age classes augmented with population assignment data

The relative contribution of in situ reproduction versus immigration to the recruitment process is important to ecologists. Here we consider a robust design superpopulation capture-recapture model for a population with two age classes augmented with population assignment data. We first use age information to estimate the entry probabilities of new animals originating via in situ reproduction and immigration separately for all except the first period. Then we combine age and population assignment information with the capture-recapture model, which enables us to estimate the entry probability of in situ births and the entry probability of immigrants separately for all sampling periods. Further, this augmentation of age specific capture-recapture data with population assignment data greatly improves the estimators’ precision. We apply our new model to a capture-recapture data set with genetic information for banner-tailed kangaroo rats in Southern Arizona. We find that many more individuals are born in situ than are immigrants for all time periods. Young animals have lower survival probabilities than adults born in situ. Adult animals born in situ have higher survival probabilities than adults that were immigrants.     

Studying dispersal at the landscape scale: efficient combination of population surveys and capture-recapture data

Researchers often rely on capture-mark-recapture (CMR) data to study animal dispersal in the wild. Yet their spatial coverage often does not encompass the entire dispersal range of the study individuals, sometimes producing misleading results. Information contained in population surveys and variation in population spatial structure can be used to overcome this issue. We build an integrated model in a multisite context in which CMR data are only collected at a subset of sites, but numbers of breeding pairs are counted at all sites. In a Black-headed Gull Chroicocephalus ridibundus population, the integrated-modeling approach induces an increase in precision for the demographic parameters of interest (variances, on average, were decreased by 20%) and provides a more precise extrapolation of results from the CMR data to the whole population. Patterns of condition-dependent dispersal are therefore made easier to detect, and we obtain evidence for colony-size dependence in recruitment, dispersal, and breeding success. These results suggest that first-time breeders disperse to small colonies in order to recruit earlier. The exchange of experienced breeders between colonies appears as a main determinant of the observed variation in colony sizes.     

Regression models for exceedance data via the full likelihood

Many situations in practice require appropriate specification of operating characteristics under extreme conditions. Typical examples include environmental sciences where studies include extreme temperature, rainfall and river flow to name a few. In these cases, the effect of geographic and climatological inputs are likely to play a relevant role. This paper is concerned with the study of extreme data in the presence of relevant auxiliary information. The underlying model involves a mixture distribution: a generalized Pareto distribution is assumed for the exceedances beyond a high threshold and a non-parametric approach is assumed for the data below the threshold. Thus, the full likelihood including data below and above the threshold is considered in the estimation. The main novelty is the introduction of a regression structure to explain the variation of the exceedances through all tail parameters. Estimation is performed under the Bayesian paradigm and includes model choice. This allows for determination of higher quantiles under each covariate configuration and upper bounds for the data, where appropriate. Simulation results show that the models are appropriate and identifiable. The models are applied to the study of two temperature datasets: maxima in the U.S.A. and minima in Brazil, and compared to other related models.     

Heteroscedastic semiparametric models for domestic water consumption aggregated data

Heteroscedastic additive and multiplicative models are proposed to disaggregate household data on water consumption from Athens and provide individual consumption estimates. The models adjust for heteroscedasticity assuming that variances relate to covariates. Household characteristics that can influence consumption are also included into models in order to allow for a clearer measurement of individual characteristics effects. Estimation is accomplished through a penalized least squares approach. The method is applied to a sample of real data related to domestic water consumption in Athens. The results show a greater consumption of water for males while the single-female households are these that use the lowest quantities of water. The consumption curves by age and gender are constructed presenting differences between the two sexes.

Analysing sperm competition data: simple models for predicting mechanisms

Summary Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P ₂), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between raffles (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a fertilization set immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time. Offprint requests to: G.A. Parker     

Confronting two-sex demographic models with data

Most population dynamics models explicitly track the density of a single sex. When the operational sex ratio can vary, two-sex models may be needed to understand and predict population trajectories. Various functions have been proposed to describe the relative contributions of females and males to recruitment, and these functions can differ qualitatively in the patterns that they generate. Which mating function best describes the dynamics of real populations is not known, since alternative two-sex models have not been confronted with experimental data. We conducted the first such comparison, using laboratory populations of the bean beetle Callosobruchus maculatus. Manipulations of the operational sex ratio and total density provided strong support for a demographic model in which the birth rate was proportional to the harmonic mean of female and male densities, and females, males, and their offspring made unique contributions to density dependence. We offer guidelines for transferring this approach to other, less tractable systems in which possibilities for sex ratio manipulations are more limited. We show that informative experimental designs require strong perturbations of the operational sex ratio. The functional form of density dependence (saturating vs. over-compensatory) and the relative contributions of each sex to density dependence can both determine in which direction and at which population densities such perturbations would be most informative. Our experimental results and guidelines for design strategies promote synthesis of two-sex population dynamics theory with empirical data.     

Modified Weibull multi-state models for the analysis of animal carcinogenicity data

The Peto test is the standard method of analysis used in carcinogenicity studies to compare tumor incidence in groups of animals. It assumes that tumors are either instantly fatal or have no effect on mortality and requires a judgement of the lethality of each tumor. To avoid this requirement, parametric multi-state models have been proposed. In addition these allow estimation of tumor onset and mortality rates. This paper considers two such models and presents a modification. It is shown that the modified models provide a better fit to carcinogenicity data and simulated data are used to show that the modified models provide a modest increase in test power relative to the Peto test.     

Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.     

Assessing tiger population dynamics using photographic capture-recapture sampling

Although wide-ranging, elusive, large carnivore species, such as the tiger, are of scientific and conservation interest, rigorous inferences about their population dynamics are scarce because of methodological problems of sampling populations at the required spatial and temporal scales. We report the application of a rigorous, noninvasive method for assessing tiger population dynamics to test model-based predictions about population viability. We obtained photographic capture histories for 74 individual tigers during a nine-year study involving 5725 trap-nights of effort. These data were modeled under a likelihood-based, "robust design" capture-recapture analytic framework. We explicitly modeled and estimated ecological parameters such as time-specific abundance, density, survival, recruitment, temporary emigration, and transience, using models that incorporated effects of factors such as individual heterogeneity, trap-response, and time on probabilities of photo-capturing tigers. The model estimated a random temporary emigration parameter of gamma" = gamma' = 0.10 +/- 0.069 (values are estimated mean +/- SE). When scaled to an annual basis, tiger survival rates were estimated at S = 0.77 +/- 0.051, and the estimated probability that a newly caught animal was a transient was tau = 0.18 +/- 0.11. During the period when the sampled area was of constant size, the estimated population size N(t) varied from 17 +/- 1.7 to 31 +/- 2.1 tigers, with a geometric mean rate of annual population change estimated as lambda = 1.03 +/- 0.020, representing a 3% annual increase. The estimated recruitment of new animals, B(t), varied from 0 +/- 3.0 to 14 +/- 2.9 tigers. Population density estimates, D, ranged from 7.33 +/- 0.8 tigers/100 km2 to 21.73 +/- 1.7 tigers/100 km2 during the study. Thus, despite substantial annual losses and temporal variation in recruitment, the tiger density remained at relatively high levels in Nagarahole. Our results are consistent with the hypothesis that protected wild tiger populations can remain healthy despite heavy mortalities because of their inherently high reproductive potential. The ability to model the entire photographic capture history data set and incorporate reduced-parameter models led to estimates of mean annual population change that were sufficiently precise to be useful. This efficient, noninvasive sampling approach can be used to rigorously investigate the population dynamics of tigers and other elusive, rare, wide-ranging animal species in which individuals can be identified from photographs or other means.     

Habitat selection models to account for seasonal persistence in radio telemetry data

Models for the analysis of habitat selection data incorporate covariates in an independent multinomial selections model (McCracken et al. 1998) Ramsey and Usner 2003 and an extension of that model to include a persistence parameter (2003). In both cases, all parameters are assumed to be fixed through time. Radio telemetry data collected for habitat selection studies typically consist of animal relocations through time, suggesting the need for an extension to these models. We use a Bayesian approach that allows for the habitat selection probabilities, persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to differ seasonally and/or when availabilities of habitats change throughout the study period due to weather or migration. We implement and compare the models using radio telemetry data for westslope cutthroat trout in two streams in eastern Oregon.     

A capture-recapture model with heterogeneity and behavioural response

We develop the non-parametric maximum likelihood estimator (MLE) of the full M_bh capture-recapture model which utilizes both initial capture and recapture data and permits both heterogeneity (h) between animals and behavioural (b) response to capture. Our MLE procedure utilizes non-parametric maximum likelihood estimation of mixture distributions (Lindsay, 1983; Lindsay and Roeder, 1992) and the EM algorithm (Dempsteret al., 1977). Our MLE estimate provides the first non-parametric estimate of the bivariate capture-recapture distribution.Since non-parametric maximum likelihood estimation exists for submodels M_h (allowing heterogeneity only), Mb (allowing behavioural response only) and M₀ (allowing no changes), we develop maximum likelihood-based model selection, specifically the Akaike information criterion (AIC) (Akaike, 1973). The AIC procedure does well in detecting behavioural response but has difficulty in detecting heterogeneity.     

Zero-inflated models with application to spatial count data

Count data arises in many contexts. Here our concern is with spatial count data which exhibit an excessive number of zeros. Using the class of zero-inflated count models provides a flexible way to address this problem. Available covariate information suggests formulation of such modeling within a regression framework. We employ zero-inflated Poisson regression models. Spatial association is introduced through suitable random effects yielding a hierarchical model. We propose fitting this model within a Bayesian framework considering issues of posterior propriety, informative prior specification and well-behaved simulation based model fitting. Finally, we illustrate the model fitting with a data set involving counts of isopod nest burrows for 1649 pixels over a portion of the Negev desert in Israel.