Byron J. T. Morgan

Optimization using simulated annealing

Much work has been published on the theoretical aspects of simulated annealing. This paper provides a brief overview of this theory and provides an introduction to the practical aspects of function optimization using this approach. Different implementations of the general simulated annealing algorithm are discussed, and two examples are used to illustrate the behaviour of the algorithm in low dimensions. A third example illustrates a hybrid approach, combining simulated annealing with traditional techniques.

Factors influencing Soay sheep survival

We present a survival analysis of Soay sheep mark recapture and recovery data. Unlike previous conditional analyses, it is not necessary to assume equality of recovery and recapture probabilities; instead these are estimated by maximum likelihood. Male and female sheep are treated separately, with the higher numbers and survival probabilities of the females resulting in a more complex model than that used for the males. In both cases, however, age and time aspects need to be included and there is a strong indication of a reduction in survival for sheep aged 7 years or more. Time variation in survival is related to the size of the population and selected weather variables, by using logistic regression. The size of the population significantly affects the survival probabilities of male and female lambs, and of female sheep aged 7 or more years. March rainfall and a measure of the North Atlantic oscillation are found to influence survival significantly for all age groups considered, for both males and females. Either of these weather variables can be used in a model. Several phenotypic and genotypic individual covariates are also fitted. The only covariate which is found to influence survival significantly is the type of horn of first-year female sheep. There is a substantial variation in the recovery probabilities over time, reflecting in part the increased effort when a population crash was expected. The goodness of fit of the model is checked by using graphical procedures.

INTEGRATED RECOVERY/RECAPTURE DATA ANALYSIS

The integration of recovery and recapture data, providing information on the same individuals, is important for the stable fitting of a wide range of stochastic models, resulting in more realistic estimates of survival probabilities of wild animals than when either the recovery or recapture data are used separately. Previous integrated analyses have either concentrated on time-dependent parameters only or, in the age-dependent case, have not provided a flexible framework for model refinement and selection. We derive the likelihood for a general integrated model, allowing both age-and time-dependent parameters. The work of this paper was motivated by a set of recapture histories on shags (Phalacrocorax aristotelis), for which biological knowledge and previous data analysis suggest age dependence in both survival and recapture probabilities. We use these data to illustrate the general method. All model fitting is done by the method of maximum likelihood and the programming is done in MATLAB. For the shags, we found an annual survival probability of 0.87 (standard error 0.01) for birds of breeding age and 0.70 (0.02) for birds in their second and third years. First-year survival varied widely with time about an average of 0.46.

Sexual dimorphism, survival and dispersal in red deer

A detailed and extensive mark-recapture-recovery study of red deer on the island of Rum forms the basis of the modeling of this article. We analyze male and female deer separately, and report results for both in this article, but use the female data to demonstrate our modeling approach. We provide a model-selection procedure that allows us to describe the survival by a combination of age-classes, with common survival within each class, and senility, which is modeled continuously as a parametric function of age. Dispersal out of the study area is modeled separately. Survival and dispersal probabilities are examined for the possible influence of both environmental and individual covariates, including a range of alternative measures of population density. The resulting model is succinct and biologically realistic. We compare and contrast survival rates of male and female deer of different ages and compare the factors that affect their survival. We demonstrate large differences in the rate of senescence between males and females even though their senescence begins at the same age. The differences between the sexes suggest that, in population modeling of sexually size-dimorphic species, it is important to identify sex-specific survival functions.

Modelling Heron Survival Using Weather Data

There is a definite needfor methodology which will produce ageand time-specific survival probabilities from bird ringing studies in which only nestlings are ringed, and one possible approach to this problem is presented in this paper. Models are developed in which the survival rates for first-year birds are weather-dependent (and therefore time-speeific) and the rate for second-year birds is a constant, difterent from the constant annual survival rate assumed for all older birds, to describe the numbers of recoveries of rings from dead Grey Herons, A rdea cinerea, ringed as nestlings in Britain between 1955 and 1975. The models provide a good fit to the data and a useful and concise description of Heron survival. Comparison is made with the predictions of a modelfor heronry census data.

Non-uniqueness and inversions in cluster analysis

Care must be exercised when hierarchical methods of cluster analysis are used. Dendrograms may not be unique, and certain methods are prone to producing inversions. The nature and extent of these features are examined through two case-studies, and by applying seven methods to 20 data sets. Insufficient emphasis on the problems of non-uniqueness and of inversion is made in many text-books and also in computer packages and their manuals.

A Modelling Strategy for Recovery Data from Birds Ringed as Nestlings

In this paper we propose a strategy for analysing recovery data from birds ringed as nestlings. The approach advocated starts with a global model, involving calendar year dependence of both reporting and first-year survival rates, and age-dependence of survival rates for older birds. Likelihood ratio tests are then used to choose between a range of submodels. The strategy is illustrated through application to three data sets, on mallards, herring gulls, and blue-winged teal. The effect of age-dependence operating also on reporting rates is examined through matched simulations, since a model with age-dependent reporting rates cannot be fitted directly. This reveals an underestimation of the first-year survival rates, when the probability of recovery for first-year birds is greater than that for older birds. It is argued that this bias may not be serious and indeed may be allowed for in practice. For mallards and teal, comparisons are drawn with the results from other models that additionally analyse recoveries of birds ringed as adults; the same general conclusions are reached.

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.

WinBUGS for population ecologists: Bayesian modeling using Markov Chain Monte Carlo methods.

The computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Wurttemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.

The Analysis of Ring-Recovery Data Using Random Effects

We show how random terms, describing both yearly variation and overdispersion, can easily be incorporated into models for mark-recovery data, through the use of Bayesian methods. For recovery data on lapwings, we show that the incorporation of the random terms greatly improves the goodness of fit. Omitting the random terms can lead to overestimation of the significance of weather on survival, and overoptimistic prediction intervals in simulations of future population behavior. Random effects models provide a natural way of modeling overdispersion-which is more satisfactory than the standard classical approach of scaling up all standard errors by a uniform inflation factor. We compare models by means of Bayesian p-values and the deviance information criterion (DIC).