Quantifying Migration Behaviour Using Net Squared Displacement Approach: Clarifications and Caveats

Estimating migration parameters of individuals and populations is vital for their conservation and management. Studies on animal movements and migration often depend upon location data from tracked animals and it is important that such data are appropriately analyzed for reliable estimates of migration and effective management of moving animals. The Net Squared Displacement (NSD) approach for modelling animal movement is being increasingly used as it can objectively quantify migration characteristics and separate different types of movements from migration. However, the ability of NSD to properly classify the movement patterns of individuals has been criticized and issues related to study design arise with respect to starting locations of the data/animals, data sampling regime and extent of movement of species. We address the issues raised over NSD using tracking data from 319 moose (Alces alces) in Sweden. Moose is an ideal species to test this approach, as it can be sedentary, nomadic, dispersing or migratory and individuals vary in their extent, timing and duration of migration. We propose a two-step process of using the NSD approach by first classifying movement modes using mean squared displacement (MSD) instead of NSD and then estimating the extent, duration and timing of migration using NSD. We show that the NSD approach is robust to the choice of starting dates except when the start date occurs during the migratory phase. We also show that the starting location of the animal has a marginal influence on the correct quantification of migration characteristics. The number of locations per day (1–48) did not significantly affect the performance of non-linear mixed effects models, which correctly distinguished migration from other movement types, however, high-resolution data had a significant negative influence on estimates for the timing of migrations. The extent of movement, however, had an effect on the classification of movements, and individuals undertaking short- distance migrations can be misclassified as other movements such as sedentary or nomadic. Our study raises important considerations for designing, analysing and interpreting movement ecology studies, and how these should be determined by the biology of the species and the ecological and conservation questions in focus.     

A Genealogical Interpretation of Principal Components Analysis

Principal components analysis, PCA, is a statistical method commonly used in population genetics to identify structure in the distribution of genetic variation across geographical location and ethnic background. However, while the method is often used to inform about historical demographic processes, little is known about the relationship between fundamental demographic parameters and the projection of samples onto the primary axes. Here I show that for SNP data the projection of samples onto the principal components can be obtained directly from considering the average coalescent times between pairs of haploid genomes. The result provides a framework for interpreting PCA projections in terms of underlying processes, including migration, geographical isolation, and admixture. I also demonstrate a link between PCA and Wright''s f_st and show that SNP ascertainment has a largely simple and predictable effect on the projection of samples. Using examples from human genetics, I discuss the application of these results to empirical data and the implications for inference.     

A generalized standardization procedure in ecological ordination: Tests with Principal Components Analysis

Abstract. Standardization by norms of sample position vectors as well as by sample totals has been used frequently in vegetation ecology. Both standardizations are only special cases of the Generalized Standardization Procedure (GSP) described in this paper. The general procedure allows a wide choice of data transformations simply by varying values of a single standardization parameter. Principal Components Analysis (PCA) often involutes opposite ends of a coenospace, producing results that may be difficult to interpret. Experiments with simulated as well as field data sets revealed that involuted gradients can be unfolded if GSP is applied prior to PCA. Compared to Correspondence Analysis, GSP-PCA was superior in recovering the structure of analysed coenoclines.     

Hidden Markov Models and Animal Behaviour

This paper proposes the use of hidden Markov time series models for the analysis of the behaviour sequences of one or more animals under observation. These models have advantages over the Markov chain models commonly used for behaviour sequences, as they can allow for time-trend or expansion to several subjects without sacrificing parsimony. Furthermore, they provide an alternative to higher-order Markov chain models if a first-order Markov chain is unsatisfactory as a model. To illustrate the use of such models, we fit multivariate and univariate hidden Markov models allowing for time-trend to data from an experiment investigating the effects of feeding on the locomotory behaviour of locusts (Locusta migratoria).