Abstract
Temporal activity patterns in animals emerge from complex interactions between choices made by organisms as responses to biotic interactions and challenges posed by external factors. Temporal activity pattern is an inherently continuous process, even being recorded as a time series. The discreteness of the data set is clearly due to data-acquisition limitations rather than a true underlying discrete nature of the phenomenon itself. Therefore, curves are a natural representation for high-frequency data. Here, we fully model temporal activity data as curves integrating wavelets and functional data analysis, allowing for testing hypotheses based on curves rather than on scalar and vector-valued data. Temporal activity data were obtained experimentally for males and females of a small-bodied marsupial and modelled as wavelets with independent and identically distributed errors and dependent errors. The null hypothesis of no difference in temporal activity pattern between male and female curves was tested with functional analysis of variance (FANOVA). The null hypothesis was rejected by FANOVA and we discussed the differences in temporal activity pattern curves between males and females in terms of ecological and life-history attributes of the reference species. We also performed numerical analysis that shed light on the regularity properties of the wavelet bases used and the thresholding parameters.
Highlights
Temporal activity of animals is the result of behavioral responses to external factors, such as availability of food resources and predation risk, and the internal states of individuals, such as nutritional condition, aversion to risk and reproductive drive [1] [2] [3] [4]
Animal housing and experimental procedures were approved by Comissão de Ética no Uso de Animais, Universidade Estadual de Campinas. Experimental settings such as those used in our study provide relevant information for the study of animal temporal activity pattern, and for several areas of ecology and behavior including for example the association between social and sexual preferences and genetic variation at microsattelite loci
We used wavelets to model activity data as curves and functional data analysis, in particular functional analysis of variance, to test the hypothesis that the mean activity curves differed between male and female of the small marsupial G. microtarsus
Summary
Temporal activity of animals is the result of behavioral responses to external (environmental) factors, such as availability of food resources and predation risk, and the internal states of individuals, such as nutritional condition, aversion to risk and reproductive drive [1] [2] [3] [4]. Temporal activity pattern is marked with punctuations in the movement (pauses and changes in speed), temporally autocorrelated, and localized in nature [3] [9] [10]. Ecological and behavioral inference on patterns and processes of animal temporal activity are based on data with inherent autocorrelation and localization properties [3] [11]. Wavelets are functions that are able to represent a signal in a time series in both time and large and small scale domains [18]. Such decomposition into time-scale space allows the identification of the dominant modes of variability and how these modes vary with time [19]. Whenever wavelets are used, their statistical analysis is based on statistical tests designed for scalar or vector random variables and not functional data [23]
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