Evert Meelis

Statistical analysis of behavioural data : an approach based on time-structured models

Introduction Preliminary inspection of the observations Analysis of time-inhomogeneity Tests for exponentiality Tests of sequential dependency properties Simultaneous tests Analysis based on a (semi)-Markov description Examples of analyses based on continuous-time Markov chain modelling Appendices References Author index Subject index.

Metapopulation models for impact assessment of fragmentation

In Western Europe, fragmentation of natural habitat types is a considerable problem for nature conservation (Opdam et al., 1993, this volume). Guidelines for landscape design and management are badly needed. To develop these guidelines, we need a better understanding of the quantitative relation between landscape characteristics (such as size and configuration of natural elements) and the prospects for survival of plant and animal populations restricted to those elements. Moreover, we need to assess the effects of mitigating measures (e.g. restoring linear landscape elements) or measures that add to fragmentation (e.g. construction of roads and railways). Metapopulation models are an indispensable tool for understanding the dynamics of fragmented populations and for impact assessment of (de)fragmentation.

When did it really start or stop: the impact of censored observations on the analysis of duration

Behaviour is often described in terms of bout lengths. Because of censoring, some of these bout lengths may only be observed partially. For instance, when observation is finished after a fixed period the end moment of the last bout remains unknown. The only available information on such a bout length is that it exceeds a certain value. This value is the censored observed bout length. Censored data are quite common in ethology, but the problem is often not recognized. Therefore, the well established statistical methods that account for censoring are rarely used in ethology. We report on the consequences of using standard methods instead of methods adjusted to account for censoring. We demonstrate that the usual methods of dealing with censored observations, such as treating them as uncensored observations or omitting them altogether, leads more often to erroneous conclusions. When an unadjusted test is used for testing the equality of two censored samples of bout lengths, the probability of rejecting the null hypothesis when the samples are different is much lower than when an adjusted test is used. Moreover, especially when censoring patterns differ between samples, the probability of wrongly rejecting the null hypothesis may be increased.

Analysis of time-inhomogeneity in Markov chains applied to mother-infant interactions of rhesus monkeys

Abstract When studying the interaction between mother-infant pairs of rhesus monkeys, inhomogeneities appear to exist during the awake phase of the infant, even under externally constant circumstances. These inhomogeneities are obscured by the stochastic nature of the bout lengths as well as the transitions between the several behavioural acts. An accurate description of the interaction, with the changes in the behaviour during the awake phase included, is necessary in order to be able to quantify the influence of the mother on the social development of the infant and vice versa. A mathematical model is described belonging to the class of continuous time Markov chains. This model gives an adequate characterization of the behavioural processes in a restricted number of ethologically wellinterpretable parameters. New procedures for estimating these parameters are derived, as well as tests on hypotheses concerning the number and magnitude of abrupt behavioural changes of the pairs. The pervasive motivational changes prior to or after napping by infants could be described comprehensively by the parameters developed.

Time structure of self-grooming in the rat: self-facilitation and effects of hypothalamic stimulation and neuropeptides.

Specific brain manipulations, such as stimulation of the paraventricular nucleus of the hypothalamus (PVH) or injections of neuropeptides, increase self-grooming in the rat. Such manipulations also affect the different movements that constitute grooming. Using models to assess the time structure of these movements, the authors demonstrate that the rules that control the time structure within grooming are different from the ones that control its initiation. This study also showed that grooming is self-facilitating and that different brain manipulations in the same hypothalamic area induce structurally different kinds of grooming. The authors suggest that this part of the hypothalamus is not only involved in setting priorities to grooming, relative to other behaviors, but is also involved in the timing of different grooming components. These findings suggest that different neural mechanisms may be involved in the initiation and internal time structure of grooming.

A time-structured analysis of hypothalamically induced increases in self-grooming and activity in the rat.

Stressors and different manipulations of the paraventricular nucleus of the hypothalamus (PVH) increase self-grooming in the rat. To assess the effect of these PVH manipulations on the timing of grooming in relation to other ongoing behavior, the authors describe these behavioral responses by a time-structured model. The authors show the following: (a) Behavior in each treatment group can be described by a semi-Markov model. Effects of treatments can be described as changes in the parameters of this model, which reflect the tendencies to start and stop grooming and other activities. (b) The PVH manipulations increase self-grooming by increasing the tendencies to start grooming or by extending the period during which grooming occurs. (c) Grooming responses are accompanied by an increase in activity. (d) Different PVH manipulations change the temporal structure of behavior differentially, suggesting that distinct mechanisms within the PVH are involved in the precise timing of grooming in relation to other activities.

Testing for the number of change points in a sequence of exponential random variables

The literature on change point problems concerns almost exclusively situations with at most one change. Howeverm, in practice it is often not sure that this is so, especially in long observation periods. There is an urgent need for methods to deal with such observations. We give a procedure to determine the number of change points in a sequence of independent exponentially distributed variables, when there is no prior information concerning the (distribution of the) number, location or magnitude of the changes. The procedure is based on partitioning of the likelihood according to a hierarchy of sub–hypotheses. It consists of a sequence of likehood ratio tests of nested hypotheses corresponding to a decreasing number of change points. Here, we consider a maximum of two change points but it is easily generalized for a higher maximum. Since the distribution of the test statistics can, as yet, not be derived analytically, the properties of the procedure were analyzed by Monte Carlo methods. Under the hypothes...

Markov models for social interactions: analysis of electrical stimulation in the hypothalamic aggression area of rats

Abstract The analysis of experimental effects on social interactions is extremely difficult since animals usually react to one anothers behaviour as well as to the experimental treatment. Methods are described to analyse both treatment effects and social influence, based on a description by a continuous time Markov chain model, where the states represent combinations of acts of the interacting individuals. These methods were applied to agonistic interactions of rats under the influence of subthreshold electrical stimulation at a specific site in the hypothalamus. Above the threshold intensity such stimulation induced attacks in a situation where there is normally no violent behaviour. Subthreshold experiments at different intensities were performed to study the relation between the activated neural mechanism and agonistic interactions without fighting. There were two behaviourally different periods during each observation period. The opponents behaviour as well as current intensity significantly affected the experimental animals behaviour in both periods, although the effects were different in the two periods. Both effects were most profound in the second period. In this period increased current intensity made experimental animals more self-directed and yet more reactive to the opponents behaviour. Furthermore, opponents reduced the amount of contact behaviour shown by the experimental animals. Indeed it appears that their behaviour is aimed at reducing contact.

Interspecific interference between Apoanagyrus lopezi and A. diversicornis, parasitoids of the cassava mealybug Phenacoccus manihoti

The parasitoids Apoanagyrus lopezi De Santis and A. diversicornis (Howard) (Hymenoptera: Encyrtidae) have been introduced into Africa for the biological control of the cassava mealybug Phenacoccus manihoti Matile‐Ferrero (Homoptera: Pseudococcidae). We have studied competition between these species to investigate if they can coexist. Here we report on the influence of the simultaneous presence of non‐conspecific adult females on searching efficiency on patches. Wasps of either species foraged on discs of cassava leaf with mealybugs, while at the same time different numbers of non‐conspecifics were also depleting the patch. Patch area per parasitoid and number of hosts available to each parasitoid were equal in all treatments.

Non-parametric testing for the number of change points in a sequence of independent random variables

A non-parametric procedure is derived for testing for the number of change points in a sequence of independent continuously distributed variables when there is no prior information available. The procedure is based on the Kruskal–Wallis test, which is maximized as a function of all possible places of the change points. The procedure consists of a sequence of non-parametric tests of nested hypotheses corresponding to a decreasing number of change points. The properties of this procedure are analyzed by Monte Carlo methods and compared to a parametric procedure for the case that the variables are exponentially distributed. The critical values are given for sample sizes up to 200.