Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance and Williams' formula which enables the implementation of the algorithm in a recursive way.Comment: Free Software for Agglomerative Hierarchical Clustering using Multidendrograms available at http://deim.urv.cat/~sgomez/multidendrograms.ph

Aspects of the design and analysis of signal-detection experiments

Presents guidelines for users of the simple Yes/No signal detection experiment who want to design their experiments to ensure a given precision for estimators of d. Additionally, simulations of small-scale Yes/No and rating-method experiments are employed to investigate when the use of asymptotic results is justified. The way in which the pay-off matrix for the Yes/No experiment may be manipulated to optimize precision is demonstrated. Large experiments may be needed to provide precise unbiased estimation of d, with sampling distributions that are not appreciably skewed

Selecting age structure in integrated population models

Integrated population modelling is widely used in ecology when data at the individual level are combined with independent time series measuring population abundance. However there is no formal assessment of how to select the best integrated model. Here we focus on the important case of determining the age-structure for annual survival probabilities of wild animals, involving comparing state–space models with different numbers of states. The work is motivated by real data sets, and evaluated by simulation. We reject the naïve use of AIC, and advocate the use of likelihood-ratio tests, based on combined data. We demonstrate using simulation that typical asymptotic chi-square distributions of likelihood-ratio test statistics to compare integrated models apply when the corresponding state–space models have the same state variables. In addition, for linear state–space models with matching initial conditions the correct chi-square distributions may also hold when models apparently have different state–spaces. The results for comparing integrated models also have relevance for state–space modelling alone. A senescence case study is provided which incorporates a step-up approach and illustrates the use of the recommendations of the paper in practice

Diagnostic Goodness-of-Fit Tests for Joint Recapture and Recovery Models

Diagnostic goodness-of-fit tests for capture–recapture models are routinely used prior to model fitting and analysis. However, when data include a mixture of live recaptures and dead recoveries, it is frequently standard practice for the information from recoveries not to be used, so that tests are applied to the recapture data alone. We present new diagnostic tests for joint recapture–recovery data, which make full use of all of the data, and evaluate their power through simulation. The importance of including all available data is clearly shown. We see in addition that current procedures may fail to identify the correct model. The work is generalised to the case of multi-site joint recapture–recovery data and is illustrated on a data set of great cormorants. This article has supplementary material online

Methods for exact perturbation analysis

1. The dominant eigenvalue of the population projection matrix provides the asymptotic growth rate of a population. Perturbation analysis examines how changes in vital rates affect this rate. The standard approach to evaluating the effect of a perturbation uses sensitivities and elasticities to provide a linear approximation, which is often inappropriate. 2. A transfer function approach provides the exact relationship between growth rate and perturbation. An alternative approach derives the exact solution using symbolic algebra by calculating the matrix characteristic equation in terms of the perturbation parameters and the symptotic growth rate. 3. This provides integrated sensitivities and plots of the exact relationship. The same method may be used for any perturbation structure, however complicated. 4. The simplicity of the new method is illustrated through two examples - the killer whale and the lizard orchid

Modelling survival at multi-population scales using mark-recapture data

The demography of vertebrate populations is governed in part by processes operating at large spatial scales that have synchronizing effects on demographic parameters over large geographic areas, and in part, by local processes that generate fluctuations that are independent across populations. We describe a statistical model for the analysis of individual monitoring data at the multi-population scale that allows us to (1) split up temporal variation in survival into two components that account for these two types of processes and (2) evaluate the role of environmental factors in generating these two components. We derive from this model an index of synchrony among populations in the pattern of temporal variation in survival, and we evaluate the extent to which environmental factors contribute to synchronize or desynchronize survival variation among populations. When applied to individual monitoring data from four colonies of the Atlantic Puffin (Fratercula arctica), 67% of between-year variance in adult survival was accounted for by a global spatial-scale component, indicating substantial synchrony among colonies. Local sea surface temperature (SST) accounted for 40% of the global spatial-scale component but also for an equally large fraction of the local-scale component. SST thus acted at the same time as both a synchronizing and a desynchronizing agent. Between-year variation in adult survival not explained by the effect of local SST was as synchronized as total between-year variation, suggesting that other unknown environmental factors acted as synchronizing agents. Our approach, which focuses on demographic mechanisms at the multi-population scale, ideally should be combined with investigations of population size time series in order to characterize thoroughly the processes that underlie patterns of multi-population dynamics and, ultimately, range dynamics