Towards the use of distance sampling to monitorize mountain ungulates numbers.

Many management actions involving mountain ungulates require unbiased and precise estimations of their numbers. Topography, among other factors, makes difficult the use of direct methods and to assess the effective area sampled. On the other hand, social behaviour of animals increases the risk to violate the assumption that observations must be independent events. This could be avoided using the group or cluster size as a covariate and estimating density of animals through the density of clusters. In this paper we revise the increasing potential of Distance Sampling methodology to estimate mountain ungulate populations. We address different problems which compromise some of the assumptions and discuss several topics concerning the importance of assessing effective area sampled, estimation of g(0), and model selection when attempting to adapt the use of Distance Sampling to a three-dimensional scenarios, like mountainous habitats and ungulate populations

A continuous time version and a generalization of a Markovrecapture model for trapping experiments

Wileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined. © 2008 Elsevier Inc. All rights reserved

On the distribution of proportions and ratios as indicators of ungulate body condition

In the wildlife literature various studies have shown that the amount of fat around the kidneys is often a good indicator of body condition and health of ungulate species ([1],[2]). Wildlife biologies often measure the weights of fat around the kidneys and the kidneys themselves (without fat), comparing these two quantities and transforming them into a ratio or a proportion as surrogates of body condition of dead animals. Later, they use these indices as response variables to model the e®ect of covariates or treatments, such as age group and season of the year, on body condition. The more commonly used models are ANOVA-type. Most debate has been concentrated on whether or not to use a simple ANOVA model of ratios or proportions with ¯xed e®ects, or an ANCOVA model using fat weight as response variable, and the kidneys weight as a covariate ([3]). Results have taken by surprise some biologists because using one or another model with both response variables could lead to very di®erent results for what it considered the most important e®ects. In this manuscript we attempt to highlight the main di®erences and the distributional properties of these response variables, ratio and proportion

Taking individual heterogeneity in mortality risks into account in demographic studies of wild animal populations: development and use of statistical models.

The Cormarck-Jolly-Seber model incorporating frailty implemented in WinBUGS, using the 9000 kittiwake’s dataset monitorized during 22 years, showed that the convergence is very low over computational view. We developed different kind of multistate model, considering independence/dependence between random effect of breeding and survival probability. The last part of the work was dedicated to model selection with Bayesian framework

Mark-recapture estimators for dual frame population size of prominent nesting structures: the effect of uncertain detection probability

The combined mark-recapture and line transect sampling methodology proposed by Alpizar- Jara and Pollock [Journal of Environmental and Ecological Statistics, 3(4), 311–327, 1996; In Marine Mammal Survey and Assessment Methods Symposium. G.W. Garner, S.C. Amstrup, J.L. Laake, B.F.J. Manly, L.L. McDonald, and D.C. Robertson (Eds.), A.A. Balkema, Rotterdam, Netherlands, pp. 99–114, 1999] is used to illustrate the estimation of population size for populations with prominent nesting structures (i.e., bald eagle nests). In the context of a bald eagle population, the number of nests in a list frame corresponds to a ‘‘pre-marked’’ sample of nests, and an area frame corresponds to a set of transect strips that could be regularly monitored. Unlike previous methods based on dual frame methodology using the screening estimator [Haines and Pollock (Journal of Environmental and Ecological Statistics, 5, 245–256, 1998a; Survey Methodology, 24(1), 79–88, 1998b)], we no longer need to assume that the area frame is complete (i.e., all the nests in the sampled sites do not need to be seen). One may use line transect sampling to estimate the probability of detection in a sampled area. Combining information from list and area frames provides more efficient estimators than those obtained by using data from only one frame. We derive an estimator for detection probability and generalize the screening estimator. A simulation study is carried out to compare the performance of the Chapman modification of the Lincoln–Petersen estimator to the screening estimator. Simulation results show that although the Chapman estimator is generally less precise than the screening estimator, the latter can be severely biased in presence of uncertain detection. The screening estimator outperforms the Chapman estimator in terms of mean squared error when detection probability is near 1 wheareas the Chapman estimator outperforms the screening estimator when detection probability is lower than a certain threshold value depending on particular scenarios

Sessão Temática: Modelação Estatística com Aplicações às Ciências da Vida

O principal objectivo desta sessão é dar a conhecer à Comunidade Estatística Portuguesa uma pequeníssima parte das potenciais aplicações da Estatística nas Ciências da Vida. Apresentam-se três artigos de carácter expositor e informativo com várias aplicações realizadas no âmbito das dissertações do Mestrado em Matemática Aplicada às Ciências Biológicas do Instituto Superior de Agronomia da Universidade Técnica de Lisboa (ISA-UTL); aplicações na área das Pescas realizadas no Instituto Nacional de Investigação das Pescas e do Mar (IPIMAR); e nalmente, algumas aplica ções da Estatística na Genética com a intervenção de colegas da Faculdade de Ciências da Universidade de Lisboa (FCUL)

O modelo logspline aplicado aos transectos lineares.

A teoria denominada logspline density estimation, permite estimar o logaritmo de uma função densidade de probabilidade utilizando-se splines cúbicos, estima ção por máxima verosimilhança, e adição e remoção de nós seleccionados pelas estatísticas de Rao e Wald, respectivamente. Faz-se uma adaptação desta teoria para estimar a probabilidade de detecção sobre a linha central de um transecto percorrido, e consequentemente, a densidade populacional de animais no contexto da amostragem por distâncias. Avalia-se a metodologia das logsplines aplicadas aos transectos lineares através de um conjunto alargado de simulações, e comparam-se os resultados com a metodologia mais utilizada actualmente, implementada no programa DISTANCE (http://www.ruwpa.st-and.ac.uk/distance). Os nossos resultados mostram que a estima ção por logsplines é uma alternativa competitiva com os métodos actualmente mais utilizados. Em particular, a técnica revelou ser superior quando se tem funções de detecção do tipo exponencial negativa. Analisa-se um exemplo prático com população conhecida para exempli car a aplicabilidade destas técnicas

Captura-recaptura: um estudo de simulação para avaliar a performance de estimadores do tipo Lincoln-Petersen

Os modelos de captura-recaptura têm sido amplamente utilizados para estimar a dimensão de populações naturais. A forma mais simples de um estudo de captura-recaptura consiste em tirar, primeiro, uma amostra de indivíduos de dimens ão n1. Estes indivíduos são marcados e identi cados de forma única e devolvidos à área de estudo para que se integrem novamente à população de interesse. Posteriormente, uma amostra aleatória de dimensão n2 é também tirada da população. Na segunda amostra encontramos que n11 dos n2 animais capturados foram previamente marcados. Uma simples relação entre as proporções dos indivíduos marcados na popula ção e os indivíduos marcados na segunda amostra gera um estimador do tamanho da população de interesse. O estimador resultante é conhecido como o estimador de Lincoln-Petersen. Vários modelos probabilísticos associados a este estimador formam as bases para a teoria de amostragem em populações animais conhecida como capturarecaptura. Neste trabalho, apresentam-se e comparam-se as performances de quatro estimadores do tipo de Lincoln-Petersen propostos na literatura