Author(s)

Barbara Henning¹, Airton Kist², Alusio Pinheiro³, Rafael L. Camargo⁴, Thiago M. Batista⁴, Everardo M. Carneiro⁴, Sérgio F. dos Reis⁵

¹Programa de Pós-graduação em Ecologia, Universidade Estadual de Campinas, Campinas, São Paulo, Brazil.
²Departamento de Matemática e Estatstica, Universidade Estadual de Ponta Grossa, Ponta Grossa, Brazil.
³Departamento de Estatstica, Universidade Estadual de Campinas, Campinas, Brazil.
⁴Departamento de Biologia Estrutural e Funcional, Universidade Estadual de Campinas, Campinas, Brazil.
⁵Departamento de Biologia Animal, Universidade Estadual de Campinas, Campinas, Brazil.

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.

Functional Analysis of Variance, High-Frequency Data, Temporal Activity Pattern, Shrinkage, Wavelet Thresholding

Henning, B. , Kist, A. , Pinheiro, A. , Camargo, R. , Batista, T. , Carneiro, E. and dos Reis, S. (2017) Modelling Animal Activity as Curves: An Approach Using Wavelet-Based Functional Data Analysis. Open Journal of Statistics, 7, 203-215. doi: 10.4236/ojs.2017.72016.