Panagiotis Besbeas

The efficient integration of abundance and demographic data

A drawback of a new method for integrating abundance and mark-recapture-recovery data is the need to combine likelihoods describing the different data sets. Often these likelihoods will be formed by using specialist computer programs, which is an obstacle to the joint analysis. This difficulty is easily circumvented by the use of a multivariate normal approximation. We show that it is only necessary to make the approximation for the parameters of interest in the joint analysis. The approximation is evaluated on data sets for two bird species and is shown to be efficient and accurate. Copyright 2003 Royal Statistical Society.

An empirical model for underdispersed count data

We present a novel distribution for modelling count data that are underdispersed relative to the Poisson distribution. The distribution is a form of weighted Poisson distribution and is shown to have advantages over other weighted Poisson distributions that have been proposed to model underdispersion. One key difference is that the weights in our distribution are centred on the mean of the underlying Poisson distribution. Several illustrative examples are presented that illustrate the consistently good performance of the distribution.

Empirical Bayes approach to block wavelet function estimation

Wavelet methods have demonstrated considerable success in function estimation through term-by-term thresholding of the empirical wavelet coefficients. However, it has been shown that grouping the empirical wavelet coefficients into blocks and making simultaneous threshold decisions about all the coefficients in each block has a number of advantages over term-by-term wavelet thresholding, including asymptotic optimality and better mean squared error performance in finite sample situations. An empirical Bayes approach to incorporating information on neighbouring empirical wavelet coefficients into function estimation that results in block wavelet shrinkage and block wavelet thresholding estimators is considered. Simulated examples are used to illustrate the performance of the resulting estimators, and to compare these estimators with several existing non-Bayesian block wavelet thresholding estimators. It is observed that the proposed empirical Bayes block wavelet shrinkage and block wavelet thresholding estimators outperform the non-Bayesian block wavelet thresholding estimators in finite sample situations. An application to a data set that was collected in an anaesthesiological study is also presented.

Estimating Population Size and Hidden Demographic Parameters with State‐Space Modeling

Recent research has shown how process variability and measurement error in ecological time series can be separated using state‐space modeling techniques to combine individual‐based data with population counts. We extend the current maximum likelihood approaches to allow the incorporation of sex‐ and age‐dependent counts and provide an application to data from a population of Soay sheep living on the St. Kilda archipelago. We then empirically evaluate the performance and potential of the method by sequentially omitting portions of the data available. We show that the use of multivariate time series extends the power of the state‐space modeling approach. The variance of measurement error was found to be smaller for males and the sex ratio of lambs to be skewed toward females and constant over time. Our results indicated that demographic parameters estimated using state‐space modeling without relevant individual‐based data were in close agreement with those obtained from mark‐recapture‐recovery analyses alone. Similarly, estimates of population size obtained when the corresponding count observations were unavailable were close to those from the entire data set. We conclude that the approach illustrated here has great potential for estimating hidden demographic parameters, planning studies on population monitoring, and estimating both historical and future population size.

POPULATION GROWTH IN SNOW GEESE: A MODELING APPROACH INTEGRATING DEMOGRAPHIC AND SURVEY INFORMATION

There are few analytic tools available to formally integrate information coming from population surveys and demographic studies. The Kalman filter is a procedure that facilitates such integration. Based on a state-space model, we can obtain a likelihood function for the survey data using a Kalman filter, which we may then combine with a likelihood for the demographic data. In this paper, we used this combined approach to analyze the population dynamics of a hunted species, the Greater Snow Goose (Chen caerulescens atlantica), and to examine the extent to which it can improve previous demographic population models. The state equation of the state-space model was a matrix population model with fecundity and regression parameters relating adult survival and harvest rate estimated in a previous capture-recapture study. The observation equation combined the output from this model with estimates from an annual spring photographic survey of the population. The maximum likelihood estimates of the regression parameters from the combined analysis differed little from the values of the original capture-recapture analysis, though their precision improved. The model output was found to be insensitive to a wide range of coefficient of variation (CV) in fecundity parameters. We found a close match between the surveyed and smoothed population size estimates generated by the Kalman filter over an 18-year period, and the estimated CV of the survey (0.078-0.150) was quite compatible with its assumed value (approximately 0.10). When we used the updated parameter values to predict future population size, the model underestimated the surveyed population size by 18% over a three-year period. However, this could be explained by a concurrent change in the survey method. We conclude that the Kalman filter is a promising approach to forecast population change because it incorporates survey information in a formal way compared with ad hoc approaches that either neglect this information or require some parameter or model tuning.

Completing the ecological jigsaw

A challenge for integrated population methods is to examine the extent to which different surveys that measure different demographic features for a given species are compatible. Do the different pieces of the jigsaw fit together? One convenient way of proceeding is to generate a likelihood for census data using the Kalman filter, which is then suitably combined with other likelihoods that might arise from independent studies of mortality, fecundity, and so forth. The combined likelihood may then be used for inference. Typically the underlying model for the census data is a state-space model, and capture–recapture methods of various kinds are used to construct the additional likelihoods. In this paper we provide a brief review of the approach; we present a new way to start the Kalman filter, designed specifically for ecological processes; we investigate the effect of break-down of the independence assumption; we show how the Kalman filter may be used to incorporate density-dependence, and we consider the effect of introducing heterogeneity in the state-space model.

METHODS FOR JOINT INFERENCE FROM PANEL SURVEY AND DEMOGRAPHIC DATA

A number of methods for joint inference from animal abundance and demographic data have been proposed in recent years, each with its own advantages. A new approach to analyzing panel survey and demographic data simultaneously is described. The approach fits population-dynamics models to the survey data, rather than to a single index of abundance derived from them and thus avoids disadvantages inherent in analyzing such an index. The methodology is developed and illustrated with British Lapwing data, and the results are compared with those obtained from existing approaches. The estimates of demographic parameters and population indices are similar for all methods. The results of a simulation study show that the new method performs well in terms of mean squared error.

Using uncertainty estimates in analyses of population time series

Recording and monitoring wildlife is crucial for the conservation of wild species and the protection of their environment. The most common type of information reported from a monitoring scheme is a time series of population abundance estimates, but the potential of such data for analyzing population dynamics is limited due to lack of information on sampling error. Recent work has shown that replicating the sampling process and analyzing replicates jointly in a dynamical model can considerably increase estimation efficiency compared to analyzing population estimates alone. This method requires that independent replicates are available, and model fitting can be complex in general. Often, however, population estimates are accompanied by standard errors, or standard errors may be estimated from raw data using a sampling model. We evaluate a method where standard errors are used in combination with population estimates to account for sampling variability in state-space models of population dynamics. The method is simple and lends itself readily to data derived from many sampling procedures but ignores uncertainty in the standard errors themselves. We simulate data from a Gaussian state-space model where several observations, which may come from different sites, are available for the population at each time. Fitting the simulated data, we show that the method yields similar or even better results than a method utilizing all observations, even when there are few observations at each time. This holds under a range of simulation settings involving heteroscedastic observation error, site effects, and correlation among observations. We illustrate the approach on real data from the North American Breeding Bird Survey and show that it performs well in comparison to a more difficult maximum-likelihood analysis of the full data under non-Gaussian sampling error.

Integrated squared error estimation of normal mixtures

Based on the empirical characteristic function, the integrated squared error criterion for normal mixtures is shown to have a simple form for a particular weight function. When the parameter of that function is chosen as the smoothed cross-validation selector in kernel density estimation, the estimator which minimises the criterion is shown to perform well in a simulation study. In comparison with maximum likelihood and a new recently proposed method there are better bias and standard deviation results for the method of this paper. Furthermore, the new estimator is less likely to fail and is appreciably more robust.

Integrated squared error estimation of Cauchy parameters

We show that integrated squared error estimation of the parameters of a Cauchy distribution, based on the empirical characteristic function, is simple, robust and efficient. The k-L estimator of Koutrouvelis (Biometrika 69 (1982) 205) is more difficult to use, less robust and at best only marginally more efficient.