Edward A. Catchpole

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.

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).

Modelling the survival of British Lapwings Vanellus vanellus using ring-recovery data and weather covariates

Two sets of data are considered. One describes recovery data from Lapwings ringed as young in Britain in 1963–¸92. The other provides several weather covariates for the same period, and our objective is to try to relate these two data sets. We use score tests, provided by the computer package Eagle, to build a simple model which describes the data well. We first establish a need for time variation in the three basic elements of the model: first-year annual survival probability, adult annual survival probability and reporting probability. We then investigate the direct incorporation of covariates, using score tests, to give a limited set of models to compare. The final choice between these models is based on the Akaike information criterion (Arc). We find that adult annual survival is negatively related to measures of winter weather severity. In contrast to previous work, we have found a pronounced decline of reporting rate with time. Our methods produce appreciably higher estimates of adult survival than ...

Convective heat transfer in fire spread through fine fuel beds

An extensive set of wind-tunnel fires was burned to investigate convective heat transfer ahead of a steadily progressing fire front moving across a porous fuel bed. The effects of fuel and environmental variables on the gas temperature profile and the ‘surface wind speed’ (gas velocity at the fuel bed surface) are reported. In non-zero winds, the temperature of the air near the fuel bed surface decays exponentially with distance from the fire front. In zero winds, the temperature decreases rapidly within a very short distance of the flame front, then decays slowly thereafter. The maximum air temperature decreases as the free stream wind speed, packing ratio and fuel moisture content increase. The characteristic distance of the exponential decay increases strongly with the free stream wind speed and decreases with the packing ratio and surface area-to-volume ratio of the fuel. The surface wind speed depends strongly on the free stream wind speed, and to a lesser extent on packing ratio, fuel bed depth and fuel moisture content. There are three general regimes for the surface flow: (1) a constant velocity flow of approximately half the free stream flow, far from the flame front; (2) an intermediate zone of minimum flow characterised by low or reversed flow; and (3) a region near the flame front where the velocity rises rapidly almost to the free stream velocity. The boundaries between the three regions move further from the flame front with increasing wind speed, in a way which is only slightly affected by fuel geometry.

Modelling age variation in survival and reporting rates for recovery models

In this paper, we focus on models for recovery data from birds ringed as young. In some cases, it is important to be able to include in these models a degree of age variation in the reporting probability. For certain models this has been found, empirically, to result in completely flat likelihood surfaces, due to parameter redundancy. These models cannot then be fitted to the data, to produce unique parameter estimates. However, empirical evidence also exists that other models with such age variation can be fitted to data by maximum likelihood. Using the approach of Catchpole and Morgan (1996b), we can now identify which models in this area are parameter-redundant, and which are not. Models which are not parameter-redundant may still perform poorly in practice, and this is investigated through examples, involving both real and simulated data. The Akaike Information Criterion is found to select inappropriate models in a number of instances. The paper ends with guidelines for fitting models to data from bir...

Solving problems in parameter redundancy using computer algebra

A model, involving a particular set of parameters, is said to be parameter redundant when the likelihood can be expressed in terms of a smaller set of parameters. In many important cases, the parameter redundancy of a model can be checked by evaluating the symbolic rank of a derivative matrix. We describe the main results, and show how to construct this matrix using the symbolic algebra package Maple. We apply the theory to examples from the mark-recapture field. General code is given which can be applied to other models.

Bayesian methods for analysing ringing data

A major recent development in statistics has been the use of fast computational methods of Markov chain Monte Carlo. These procedures allow Bayesian methods to be used in quite complex modelling situations. In this paper, we shall use a range of real data examples involving lapwings, shags, teal, dippers, and herring gulls, to illustrate the power and range of Bayesian techniques. The topics include: prior sensitivity; the use of reversible-jump MCMC for constructing model probabilities and comparing models, with particular reference to models with random effects; model-averaging; and the construction of Bayesian measures of goodness-of-fit. Throughout, there will be discussion of the practical aspects of the work - for instance explaining when and when not to use the BUGS package.

Model selection in ring-recovery models using score tests

A strategy is outlined for selecting models for ring-recovery data using score tests. The approach is particularly valuable in avoiding unnecessary fitting of complicated, multiparameter models to data that do not require models of such complexity. Difficulties of convergence of iterative methods and potential boundary-estimation problems are thereby reduced. Data analyzed in Freeman and Morgan (1992, Biometrics 48, 217-236) are reanalyzed using score tests. These tests are repeated using both numerical and symbolic differentiation and also using both observed and expected information. We recommend using the expected information, and find that numerical differentiation is as good as symbolic differentiation. Motivated by the need to-describe a wide range of models succinctly, we also provide a new general notation for ring-recovery models.